Systems and methods for an improved heat engine

Abstract

Described herein are systems, methods, computer-readable media, and techniques for energy production systems (EPS), the EPS comprising: a Free Piston Stirling Engine (FPSE); and an encasement coupled the FPSE, the encasement further comprising an outer layer, the outer layer comprising a plurality of fins.

Description

SYSTEMS AND METHODS FOR AN IMPROVED HEAT ENGINECROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 571,972, filed March 29, 2024, and U.S. Provisional ApplicationNo. 63 / 660,172, filed June 14, 2024, each of which is incorporated herein by reference in its entirety.BACKGROUND

[0002] Data centers are confronted with a significant challenge in effectively managing the heat generated by servers. The use of traditional cooling methods results in elevated energy consumption, thus affecting operational expenditure and contributing to environmental concerns. Disclosed herein are innovative systems, methods, and techniques directed to reconfiguring data center cooling from a cost-incurring necessity into a strategic asset for reducing expenses and curtailing carbon emissions. These disclosures present data center cooling methodologies as a platform for cost efficiency and environmental conservation, rather than merely an obligatory operational taskSUMMARY

[0003] Recognized herein is a need for systems and methods that can effectively manage and utilize waste heat generated by data centers. The present disclosure provides systems and methods for converting low-grade waste heat from immersion-cooled data center equipment into usable electrical energy through an advanced heat engine technology. These systems and methods address inefficiencies in current processes by reconfiguring the perception of data center cooling from a cost-incurring necessity to a strategic asset with potential to significantly reduce operational expenses and curtail carbon emissions while maintaining optimal cooling performance.

[0004] In an aspect, a data center thermal management system comprises a plurality of computing devices immersed in a dielectric fluid such that operation of the computing devices transfers heat to the dielectric fluid to produce a heated dielectric fluid; a Free Piston Stirling Engine (FPSE) having a working fluid, a hot cylinder side, a cold cylinder side, and a regenerator positioned between the hot and cold cylinder sides; a topology -improved heat transfer apparatus in thermal communication with the hot cylinder side of the FPSE and comprising an organically- shaped structure with continuously curved, non-orthogonal geometries; a first fluid circuit configured to direct the heated dielectric fluid from the computing devices to the hot cylinderside of the FPSE; and a second fluid circuit configured to direct a cooling fluid to the cold cylinder side of the FPSE, the system being arranged to maintain a predetermined temperature differential across the FPSE by regulating flow in at least one of the fluid circuits, with the FPSE arranged to convert thermal energy from the heated dielectric fluid into electrical energy.

[0005] In some embodiments, the topology -improved heat transfer apparatus is produced by a computational optimization process that minimizes thermal resistance across the apparatus.

[0006] In some embodiments, the topology-improved heat transfer apparatus is configured with geometry defined by a topology optimization algorithm that utilizes one or more FPSE parameters — such as an internal diameter of the FPSE regenerator, an internal diameter of a pressure vessel, a mean charge pressure, a piston diameter, a piston amplitude, or a compression space volume — with the geometry sized to accommodate the predetermined temperature differential between the heated dielectric fluid and the cooling fluid.

[0007] In some embodiments, the system further comprises an additional heat exchanger positioned between the computing devices and the FPSE that transfers heat from the heated dielectric fluid to the working fluid contained in the FPSE.

[0008] In some embodiments, the system further comprises a chiller positioned within the second fluid circuit to cool the cooling fluid prior to its delivery to the cold cylinder side of the FPSE.

[0009] In some embodiments, the system further comprises a controller configured to monitor temperatures of the heated dielectric fluid and the cooling fluid via at least one temperature sensor in each fluid circuit and to control at least one adjustable flow control device to regulate flow rates in one or both fluid circuits so that the predetermined temperature differential across the FPSE is maintained.

[0010] In some embodiments, the topology-improved heat transfer apparatus is manufactured using an additive manufacturing process that forms the organically-shaped structure with continuously curved fluid passages and non-orthogonal geometries.

[0011] In some embodiments, the additive manufacturing process is a Direct Metal Laser Sintering process that fabricates the passages layer-by-layer with variable cross-sectional areas.

[0012] In some embodiments, the topology -improved heat transfer apparatus provides at least a 20% improvement in heat transfer efficiency compared to a conventional heat exchanger with linear channels and right-angled features.

[0013] In some embodiments, the system further comprises a renewable energy management module operatively connected to the first and second fluid circuits and to a renewable power source, the module being arranged to receive real-time data regarding renewable energy availability and grid load and to dynamically adjust operating parameters of the FPSE and flowrates in one or both fluid circuits to reduce reliance on non-renewable energy sources and lower the overall carbon footprint of the system.

[0014] In some embodiments, the system further comprises a water usage monitoring module configured to track water consumption in the second fluid circuit, with the controller programmed to adjust cooling parameters based on real-time water usage data to optimize water efficiency while maintaining the predetermined temperature differential across the FPSE.

[0015] In some embodiments, the computing devices comprise servers in a data center rack, with the dielectric fluid directly contacting the electronic components of the servers.

[0016] In some embodiments, the FPSE further comprises a reciprocally movable displacer and a power piston coupled to an electrical generator, with the first fluid circuit delivering the heated dielectric fluid to the hot cylinder side of the FPSE and the second fluid circuit delivering the cooling fluid to the cold cylinder side.

[0017] In some embodiments, the topology-improved heat transfer apparatus is positioned to provide thermal communication between the heated dielectric fluid directed to the hot cylinder side of the FPSE and the regenerator so that thermal energy from the heated dielectric fluid is more efficiently transferred into the FPSE for power generation, and the regenerator comprises a porous structure configured to enhance heat exchange and reduce thermal losses.

[0018] In some embodiments, the system further comprises an open-loop fluid circuit configured to deliver a cooling fluid from an external source selected from a municipal water supply, a natural body of water, a reclaimed water system, or a geothermal reservoir to the cold cylinder side of the FPSE and to discharge the warmed cooling fluid downstream, and a flow regulator configured to maintain a sufficient temperature differential across the FPSE for power generation, wherein waste heat from the dielectric fluid is transferred to the working gas of the FPSE and rejected to the open-loop cooling fluid prior to discharge.

[0019] In some embodiments, the system further comprises a temperature monitoring module configured to measure the temperature of the dielectric fluid and a controller configured to adjust the dielectric fluid’s flow rates based on real-time temperature data to optimize heat transfer into the FPSE, whereby the FPSE recovers thermal energy from the dielectric fluid and converts at least a portion thereof into electrical energy.

[0020] In some embodiments, the temperature monitoring module is configured to measure a first temperature range of the dielectric fluid as it exits the data center, a second temperature range as it exits a heat exchange region of the FPSE, and a third temperature range after it passes through a chiller.

[0021] In some embodiments, the system further comprises a secondary heat exchanger coupled to an ambient or industrial process selected from an HVAC system, a geothermal reservoir, an industrial fluid line, or an ambient-air cooling tower, a fluid circuit configured to direct partially cooled dielectric fluid from the FPSE to the secondary heat exchanger for additional heat transfer, and a return line configured to direct the dielectric fluid from the secondary heat exchanger back to the data center so that the dielectric fluid repeatedly circulates through the data center, the FPSE, and the secondary heat exchanger, thereby reducing overall cooling demand and recovering energy from the data center’s waste heat.

[0022] A method for capturing and converting waste heat to electricity from computing devices in a data center environment comprises providing an immersion cooling system in which at least one computing device is submerged in a dielectric fluid that absorbs waste heat, directing a heated dielectric fluid stream from the computing device(s) to a FPSE that includes a heat transfer apparatus configured to convert thermal energy into electrical energy, providing a cooling fluid stream to the cold side of the FPSE to facilitate a temperature differential between the heated dielectric fluid and the cooling fluid, and operating the FPSE under conditions sufficient to generate electrical power from the waste heat carried by the heated dielectric fluid.

[0023] In some embodiments, the method further comprises performing a computational optimization process to architecture a topology-improved heat transfer apparatus associated with the FPSE.

[0024] In some embodiments, the computational optimization process comprises performing one-dimensional Computational Fluid Dynamics (CFD) modeling of the FPSE, performing three- dimensional CFD modeling based on the one-dimensional results, and applying a topology optimization algorithm to generate an organically-shaped structure within the heat transfer apparatus.

[0025] In some embodiments, the method further comprises monitoring a temperature differential between the heated dielectric fluid stream and the cooling fluid stream and adjusting at least one of the flow rate of the heated dielectric fluid stream, the flow rate of the cooling fluid stream, or an operating parameter of the FPSE to maintain a temperature differential sufficient for efficient conversion of waste heat to electrical energy by the FPSE.

[0026] In some embodiments, the heated dielectric fluid stream has a temperature between 60 °C and about 90 °C while the cooling fluid stream has a temperature between 2 °C and about 25 °C.

[0027] In some embodiments, the method further comprises directing dielectric fluid exiting the topology-improved heat transfer apparatus to a chiller and returning cooled dielectric fluid from the chiller to the computing devices within the data center.

[0028] In some embodiments, operating the FPSE produces electrical energy that reduces the net power consumption of the data center by at least 5%.

[0029] In some embodiments, the method further comprises receiving real-time server utilization metrics from the computing devices, applying a machine learning algorithm trained on historical temperature and power data, and automatically adjusting at least one of the flow rate of the heated dielectric fluid stream or the flow rate of the cooling fluid stream in response to predicted changes in thermal load so as to maintain a predetermined temperature differential across the FPSE under varying data center workloads.

[0030] In some embodiments, the method further comprises implementing or retrofitting a waste heat recovery system in a data center to incorporate the FPSE by identifying connection points between an existing cooling tower and chiller system, performing a thermal audit of the data center to identify waste heat sources and quantities, mapping existing fluid circulation pathways in the cooling system, installing the FPSE in parallel with the existing cooling system — such that normal cooling operations are not disrupted by utilizing predetermined installation windows during scheduled maintenance periods, employing temporary cooling measures, and implementing the installation in phases — connecting a first fluid circuit from a heated dielectric fluid output of the data center to the hot side of the FPSE, connecting a second fluid circuit between the FPSE and the existing chiller system, integrating the FPSE’s control systems with an existing data center building management system to coordinate cooling and power generation operations, and commissioning the FPSE system by gradually increasing its thermal load while monitoring data center temperatures and performance metrics.

[0031] In some embodiments, the method further comprises monitoring the power usage effectiveness (PUE) of the data center, capturing waste heat from the computing devices using the immersion cooling system, directing the captured waste heat to the FPSE having the topology-improved heat transfer apparatus, generating electrical energy using the FPSE, feeding the generated electrical energy back into the data center power system, and calculating and documenting reductions in both energy consumption and associated carbon emissions attributable to FPSE operation such that the documented reductions qualify for carbon credit certification under applicable regulatory frameworks.

[0032] In some embodiments, the method further comprises documenting baseline energy consumption prior to FPSE installation, measuring actual energy generation and consumption reduction after implementation, calculating return on investment based on installation costs, energy savings, reduced cooling costs, and potential carbon credit value, and optimizing system parameters based on the measured performance to maximize financial returns.

[0033] In some embodiments, the method further comprises configuring a data center thermal management system to include a cooling tower, a chiller fluidically connected to the cooling tower, computing devices generating waste heat, and the FPSE arranged in parallel with the cooling tower and chiller such that a first fluid connection directs the heated dielectric fluid from the computing devices to the hot side of the FPSE before reaching the chiller and a second fluid connection directs a cooling fluid between the chiller and the cold side of the FPSE, with the FPSE extracting thermal energy without disrupting primary cooling functions.

[0034] In some embodiments, the method further comprises measuring incoming electrical power to the data center, measuring electrical power generated by the FPSE, measuring temperature differentials across the FPSE, calculating real-time cost savings based on current utility rates and FPSE power generation, projecting return on investment timelines based on operational data, adjusting FPSE operating parameters to maximize economic return, and generating reports documenting energy savings and carbon emission reductions.

[0035] In some embodiments, the method further comprises installing a modular FPSE system that comprises a standardized connection interface compatible with at least three different commercial data center cooling system configurations, quick-disconnect fluid couplings that allow servicing without disrupting data center operations, a topology -improved heat transfer apparatus configured to accommodate data-center-specific fluid temperature ranges, and a diagnostic system arranged to monitor system performance metrics, predict maintenance requirements based on operational patterns, schedule preventive maintenance during periods of low data center utilization, and detect potential failures before they impact data center operations.

[0036] In some embodiments, providing the standardized connection interface comprises ensuring the FPSE can be integrated with at least three different commercial data center cooling system designs without altering the core infrastructure.

[0037] In some embodiments, the method further comprises utilizing the quick-disconnect fluid couplings to perform routine FPSE maintenance while the data center remains operational, thereby minimizing downtime.

[0038] In some embodiments, the method further comprises monitoring system performance metrics in real-time using the diagnostic system and automatically initiating predictive maintenance alerts based on trending data.

[0039] In some embodiments, the method further comprises analyzing real-time data from temperature sensors, flow sensors, and power meters in both the heated dielectric fluid stream and the cooling fluid stream, and adjusting the FPSE operating frequency to optimize thermal-to- electric conversion efficiency.

[0040] In some embodiments, the method further comprises comparing current performance metrics against historical baseline data stored in a central management system, identifying any deviations or anomalies in FPSE performance, and initiating a troubleshooting procedure that includes fluid sampling, inspection of heat transfer surfaces, and firmware updates to the controller to proactively prevent major failures and maintain continuous data center operations.

[0041] Another aspect of the present disclosure provides a non-transitory computer readable medium comprising machine executable code that, upon execution by one or more computer processors, implements any of the methods above or elsewhere herein.

[0042] Another aspect of the present disclosure provides a system comprising one or more computer processors and computer memory coupled thereto. The computer memory comprises machine executable code that, upon execution by the one or more computer processors, implements any of the methods above or elsewhere herein.

[0043] Additional aspects and advantages of the present disclosure will become readily apparent to those skilled in this art from the following detailed description, wherein only illustrative embodiments of the present disclosure are shown and described. As will be realized, the present disclosure is capable of other and different embodiments, and its several details are capable of modifications in various obvious respects, all without departing from the disclosure.BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The novel features of the disclosure are set forth with particularity in the appended claims. A better understanding of the features and advantages of the present disclosure will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the disclosure are utilized, and the accompanying drawings of which:

[0045] FIG. 1 illustrates an example of a Free Piston Stirling Engine, in accordance with certain embodiments;

[0046] FIG. 2 illustrates an example of a Free Piston Stirling Engine, in accordance with certain embodiments;

[0047] FIG. 3 illustrates an example of a Free Piston Stirling Engine Heat Exchanger, in accordance with certain embodiments;

[0048] FIG. 4 illustrates an example of a Free Piston Stirling Engine Heat Exchanger, in accordance with certain embodiments;

[0049] FIG. 5 illustrates an example of a Free Piston Stirling Engine Heat Exchanger, in accordance with certain embodiments;

[0050] FIG. 6 illustrates an example of a Free Piston Stirling Engine Regenerator, in accordance with certain embodiments;

[0051] FIG. 7 illustrates an example of a Free Piston Stirling Engine Heat Exchanger, in accordance with certain embodiments;

[0052] FIG. 8 illustrates an example of a Free Piston Stirling Engine, in accordance with certain embodiments;

[0053] FIG. 9 illustrates an example of a Free Piston Stirling Engine, in accordance with certain embodiments;

[0054] FIG. 10 shows a computer system that is programmed or otherwise configured to implement methods disclosed herein;

[0055] FIG. 11 illustrates an example of FPSE schematic, in accordance with certain embodiments;

[0056] FIG. 12 presents a schematic of the one-dimensional (ID) engine model developed within the Software (e.g., SAGE software) in accordance with certain embodiments;

[0057] FIG. 13 presents a schematic of displacer subcomponents, in accordance with certain embodiments;

[0058] FIG. 14 illustrates an example of convergence history of optimization of engine thermal efficiency, in accordance with certain embodiments;

[0059] FIG. 15 illustrates an example of energy production of FPSE over time, in accordance with certain embodiments;

[0060] FIG. 16 illustrates an example of FPSE heat exchanger fins, in accordance with certain embodiments;

[0061] FIG. 17 illustrates an example of heat exchanger fins geometry for CFD simulation, in accordance with certain embodiments;

[0062] FIG. 18A illustrates an example of a cross-section of FPSE fine mesh top section, in accordance with certain embodiments;

[0063] FIG. 18B illustrates an example of a cross-section of FPSE fine mesh middle section, in accordance with certain embodiments;

[0064] FIG. 18C illustrates an example of a cross-section of FPSE fine mesh bottom section, in accordance with certain embodiments;

[0065] FIG. 19A illustrates an example of models used for air, in accordance with certain embodiments;

[0066] FIG. 19B illustrates an example of models used for solids, in accordance with certain embodiments;

[0067] FIG. 20 illustrates an example of boundary conditions specifications, in accordance with certain embodiments;

[0068] FIG. 21 illustrates an example of mesh sensitivity analysis results, in accordance with certain embodiments;

[0069] FIG. 22A illustrates a first example of a FPSE heat flux, in accordance with certain embodiments;

[0070] FIG. 22B illustrates a second example of a FPSE heat flux, in accordance with certain embodiments;

[0071] FIG. 23A illustrates a first example of the heat exchanger fins surface heat flux distribution from a top view perspective, in accordance with certain embodiments;

[0072] FIG. 23B illustrates a second example of the heat exchanger fins surface heat flux distribution from an angled perspective, in accordance with certain embodiments;

[0073] FIG. 24A illustrates an example of a FPSE air temperature contours at a side plane, in accordance with certain embodiments;

[0074] FIG. 24B illustrates an example of a FPSE air temperature contours at another side plane, in accordance with certain embodiments;

[0075] FIG. 24C illustrates an example of a FPSE air temperature velocity contours at a side plane, in accordance with certain embodiments;

[0076] FIG. 24D illustrates an example of a FPSE air pressure contours at a side plane, in accordance with certain embodiments;

[0077] FIG. 25 illustrates an example of a FPSE immersion fluid air temperature contours, in accordance with certain embodiments;

[0078] FIG. 26 illustrates an example of a FPSE heat transfer contract surfaces, in accordance with certain embodiments;

[0079] FIG. 27 illustrates an example of architecture space envelope around cylinder used for topology optimization, in accordance with certain embodiments;

[0080] FIG. 28 illustrates an example of conformal mesh obtained for the air domain and solid fin domains, in accordance with certain embodiments;

[0081] FIG. 29A illustrates an example of resulting geometry for topology optimization (TO), in accordance with certain embodiments;

[0082] FIG. 29B illustrates an example of input geometry for full simulation with boundary layers (BL), in accordance with certain embodiments;

[0083] FIG. 30A illustrates an example of a conventional finned heat exchanger, in accordance with certain embodiments;

[0084] FIG. 30B illustrates an example of a topology improved finned heat exchanger, in accordance with certain embodiments;

[0085] FIG. 31 illustrates an example of a conventional finned heat exchanger, in accordance with certain embodiments;

[0086] FIG. 32 illustrates an example of a topology -optimized finned heat exchanger, in accordance with certain embodiments;

[0087] FIG. 33 illustrates an example of a Heat recovery system, in accordance with certain embodiments;

[0088] FIG. 34 illustrates an example of a Heat recovery system for a closed loop cooling system, in accordance with certain embodiments;

[0089] FIG. 35 illustrates an example of a Heat recovery system for an open loop cooling system, in accordance with certain embodiments;

[0090] FIG. 36 illustrates an example of periodic boundary conditions, in accordance with certain embodiments;

[0091] FIG. 37 illustrates an example of generated mesh for TO simulation domain, in accordance with certain embodiments;

[0092] FIG. 38 illustrates an example of TO solver setup parameters, in accordance with certain embodiments;

[0093] FIG. 39 illustrates an example of TO solver convergence history, in accordance with certain embodiments;

[0094] FIG. 40 illustrates an example of Resulting geometry from TO(left) and Input geometry for full simulation with BL (right), in accordance with certain embodiments;

[0095] FIG. 41 illustrates an example of Solver Residuals (top) and Convergence of total heat transfer value (bottom) , in accordance with certain embodiments;

[0096] FIG. 42 illustrates an example of Fins solid temperature (top), in accordance with certain embodiments;

[0097] FIG. 43 illustrates an example of Fins surface heat flux, in accordance with certain embodiments;

[0098] FIG. 44 illustrates an example of Contours of temperature at (top) side plane, in accordance with certain embodiments;

[0099] FIG. 45 illustrates an example of (bottom) top plane, in accordance with certain embodiments;

[0100] FIG. 46 illustrates an example of Air gauge pressure contours at side plane, in accordance with certain embodiments;

[0101] FIG. 47 illustrates an example of Air velocity contours at side plane, in accordance with certain embodiments;

[0102] FIG. 48 illustrates an example Contours of temperature at the outlet of enclosure, in accordance with certain embodiments;

[0103] FIG. 49 illustrates an exemplary schematic of a free piston Stirling engine, showing a schematic representation (left) alongside an image of an actual engine embodiment (right), in accordance with certain embodiments;

[0104] FIG. 50 illustrates exemplary sample data points from experimental testing of a free piston Stirling engine, with power output data indicated on the left and displacer stroke data on the right, in accordance with certain embodiments;

[0105] FIG. 51 illustrates additional exemplary sample data points from experimental testing of a free piston Stirling engine, in accordance with certain embodiments;

[0106] FIG. 52 illustrates an exemplary variable data set list used for performance evaluation, in accordance with certain embodiments;

[0107] FIG. 53 illustrates an exemplary three-dimensional CAD geometry of a free piston Stirling engine, in accordance with certain embodiments;

[0108] FIG. 54 illustrates an exemplary convergence history of thermal efficiency optimization, in accordance with certain embodiments;

[0109] FIG. 55 illustrates an exemplary discretization of a free piston Stirling engine using polyhedral elements and an overset meshing technique, in accordance with certain embodiments;

[0110] FIG. 56 illustrates an exemplary conformal mesh obtained for the air domain (yellow) and the solid fins domain (blue), in accordance with certain embodiments;

[0111] FIG. 57 illustrates an exemplary first view of a topology-optimized fins cap, in accordance with certain embodiments;

[0112] FIG. 58 illustrates an exemplary second view of a topology-optimized fins cap, in accordance with certain embodiments; and

[0113] FIG. 59 illustrates an exemplary third view of a topology -optimized fins cap, in accordance with certain embodiments.DETAILED DESCRIPTION

[0114] Embodiments described herein are exemplary; variations, modifications, and equivalents are contemplated and fall within the scope of the appended claims. The descriptions, illustrations, specific examples, depictions, configurations, and relative proportions set forth herein are not limiting, as the invention is capable of other embodiments and variations.

[0115] As used herein, "comprise" and variations mean "including, but not limited to." Singular forms ("a," "an," "the") include plural referents and vice versa unless context dictates otherwise. "Or" is inclusive (A or B means A, B, or both A and B) unless otherwise stated.

[0116] Terms like "at least," "greater than," "no more than," or "less than" preceding a numerical series apply to each value in that series. Numerical ranges include endpoints and all intermediate values / sub -ranges as if explicitly written out. "About" or "approximately" indicates an acceptable error range (e.g., + / - 10% or + / - 5%, or within standard measurement limitations or recognized art practice) for a value. Where specific values are used without "about," an acceptable error range may still be assumed unless stated otherwise.

[0117] Relative terms (e.g., "on," "onto," "over," "connected," "coupled," "above," "below," "horizontal," "vertical") include director indirect relationships and different orientations unless specified otherwise (e.g., "directly on"). Terms like "first" and "second" distinguish elements and do not imply order unless context requires.

[0118] Claim terms are intended to have their plain and ordinary meaning unless explicitly defined otherwise in this specification. Specification statements, apart from explicit definitions or clear context, should not limit claim scope, even if a term is used consistently with a single meaning for clarity.

[0119] Operations may be performed concurrently or in different orders than illustrated. Functionality described as separate or single components may be implemented as combined or separate components, respectively. Plural instances may implement structures described as a single instance, and vice versa. These and other variations fall within the scope herein.

[0120] Certain techniques or operations may be implemented by hardware (e.g., dedicated circuitry like ASICs, FPGAs), software executed on processors, or a combination. References to "modules" encompass permanently or temporarily configured hardware or software units, which may be standalone or part of distributed systems. Hardware modules may be permanently configured (hardwired) or temporarily configuredby software (e.g., a general-purpose processor configured as different modules at different times). Modules may communicate via signals or stored information. Processors performing operations may reside in single or multiple locations.

[0121] As used herein, "artificial intelligence," "artificial intelligence techniques," "artificial intelligence operation," and "artificial intelligence algorithm" generally refer to any system or computational procedure that may take one or more actions that simulate human intelligence processes for enhancing or maximizing a chance of achieving a goal. The term “artificial intelligence” may include “generative modeling,” “machine learning” (ML), or “reinforcement learning” (RL). As used herein, the terms “machine learning,” “machine learning techniques,”“machine learning operation,” and “machine learning model” generally refer to any system or analytical or statistical procedure that may progressively improve computer performance of a task.

[0122] As used herein, the term "Continuously Curved" generally refers to any geometry or surface that transitions smoothly from one point to another without abrupt angles, edges, or breaks in curvature. In some instances, a geometry or surface is considered "continuously curved" if every interior corner or boundary maintains a minimum radius of curvature, such as at least about 1 mm, thereby avoiding any sharp or right-angled junctions. By way of example, a continuously curved fluid passage may consist of arcs, splines, or other curvilinear profiles that blend seamlessly, so that no portion of the passage includes an uninterrupted planar segment or a corner approximating 90° (or any other discontinuity). However, it may be understood that "continuously curved" is not strictly limited to circular or elliptical arcs and may include compound or irregular curves, provided that the flow path remains free of abrupt transitions that may create sharp edges or discrete corners.

[0123] As used herein, the term "Topology Optimization" generally refers to any computational or algorithmic process that iteratively modifies a given architecture space to optimize one or more performance objectives, such as minimizing thermal resistance, reducing weight, maximizing heat transfer, or optimizing fluid flow characteristics. In some embodiments, topology optimization involves systematically adding, removing, or reshaping material within a virtual 3D model based on input constraints (e.g., pressure drop limits, temperature gradients) and objective functions (e.g., maximizing heat dissipation, maintaining structural integrity). The method may incorporate gradient-based solvers, heuristic algorithms, genetic algorithms, or other numerical techniques to determine an “improved” geometry. By way of example, a topology optimization routine may begin with an initial block of material representing a heat exchanger and iteratively remove or reshape internal regions to achieve improved heat transfer performance, while respecting user-defined boundaries, physical constraints, or manufacturing limitations. However, as used herein, “topology optimization” is not limited to any particular solver, software, or algorithmic approach, provided that it involves modifying a structure’s geometry in an iterative and goal-driven manner.

[0124] As used herein, the term "Free Piston Stirling Engine (FPSE)" generally refers to a Stirling-cycle heat engine in which pistons (including a power piston and / or a displacer) move reciprocally without being mechanically linked to a crankshaft. Instead, pressure oscillations of a contained working gas (e.g., helium, hydrogen, air, or nitrogen) drive piston motion. The absence of direct mechanical linkages allows for self-adjusting stroke lengths, reduced friction, andsimpler sealing compared to traditional Stirling engines. A free piston Stirling engine typically comprises compression space, expansion space, and a regenerator, arrayed such that cyclical heating and cooling of the working gas produce reciprocating mechanical energy (which may be converted to electrical power via a linear alternator or other transducer).

[0125] As used herein, the term "Closed-Loop" generally refers to a fluid circuit in which the fluid (e.g., a dielectric or coolant fluid used in data centers) is continuously recirculated between components without intentional release to the environment. In a closed-loop system, the same fluid flows through, for example, a heat transfer apparatus, a chiller, and the computing devices (or waste heat source), returning in a cyclical manner. This contrasts with an open-loop system, which may draw in fluid from an external source and discharge at least a portion of that fluid to a reservoir or to the atmosphere, without recirculation.

[0126] As used herein, the term "Flow Passage Geometry" refers to the shape, dimensions, and spatial arrangement of any channel, conduit, or passage through which a fluid flows. A flow passage may be continuously curved, may include multi-level or nested channels, and may vary in cross-sectional area or radius of curvature. In some embodiments, the flow passage geometry is specifically topology-optimized to achieve improved heat transfer, lower pressure drop, or enhanced fluid distribution. The geometry may also encompass manifolds, branching pathways, and arrays of flow paths arrayed in parallel or series to suit desired thermal and fluidic performance in a data center’s immersion fluid management system.

[0127] As used herein, the term "Computational Fluid Dynamics (CFD)" generally refers to numerical simulation methods used to analyze and predict fluid flow, heat transfer, pressure distributions, and related phenomena in a defined physical domain. CFD may include onedimensional (ID) modeling, which simplifies flow into lumped or linear segments, and three- dimensional (3D) modeling, which resolves spatial variations of temperature, velocity, pressure, or other fluid properties. CFD tools typically employ methods such as the finite volume, finite element, or finite difference approaches, possibly coupled with turbulence models, heat transfer correlations, and phase-change models to capture complex physics. Results from ID and / or 3D CFD simulations may inform architecture constraints and objective functions in a topology optimization process.

[0128] As used herein, the term "Mean Charge Pressure" generally refers to the average or quasistatic gas pressure present within a sealed Stirling engine, particularly a free piston Stirling engine, when it is at rest or operating under stabilized conditions. In certain configurations, the mean charge pressure is regulated or preset by introducing or releasing the working gas (e.g., helium) into the engine’s pressure vessel. This parameter may modify the power output,operating frequency, piston amplitude, and efficiency of the engine. For example, a higher mean charge pressure often correlates with increased power density, albeit sometimes at the expense of greater stress on internal components.

[0129] As used herein, the term "Thermal Resistance" refers to a quantitative measure of the temperature difference (AT) required to induce a unit heat flow (q) across a specific material or system. It may be expressed in units such as m2K / W, indicating how a certain temperature gradient (in Kelvin or °C) translates into a given rate of heat transfer (in Watts) over a specified area. A lower thermal resistance indicates enhanced heat transfer or lower temperature gradients for a given heat flux. In the context of topology-optimized heat transfer apparatuses, reducing thermal resistance provides more efficient recovery of low-grade waste heat.

[0130] As used herein, the term "Low-Grade Waste Heat" generally refers to thermal energy at a temperature that is insufficient for many conventional high-temperature processes but may still be effectively utilized by systems configured to recover heat from lower temperature sources. In the context of data centers, low-grade waste heat may be present in immersion fluids or coolant streams that absorb heat from computing devices. In some instances, low-grade waste heat comprises fluids or gases below about 230°C, although other upper temperature thresholds (e.g., about 150°C or about 105°C) can be used depending on the application. For example, low-grade heat may include heat from immersion fluids in data centers. By way of illustration, a temperature range between about 70°C to about 105°C may be deemed “low-grade” in certain embodiments, where typical high-temperature recovery devices do not operate efficiently. However, it may be understood that “low-grade waste heat” is not restricted to any exact numerical cutoff and may encompass any temperature deemed insufficient for direct use in conventional high-temperature or high-pressure heat applications.

[0131] As used herein, the term "Waste Heat" generally refers to thermal energy that is not fully utilized in its originating process and may otherwise be discharged or dissipated to the environment without recovery. In various embodiments, waste heat may arise from industrial processes, commercial equipment, building operations, or electronic equipment — including data centers. Waste heat may be present in gaseous, liquid, or two-phase forms, including hot air, steam, exhaust gases, heated fluids (such as immersion or dielectric fluids), refrigerant fluids, or other thermally elevated by-products. In some instances, “waste heat” may be referred to as low- grade or medium-grade thermal energy, particularly where the temperature range is below about 230°C and would be inefficient for direct use in conventional high -temperature processes, yet still potentially recoverable for heat exchange, mechanical work, or electrical power generation.

[0132] As used herein, the term "conventional" generally refers to systems, methods, components, or designs that follow established, common, standard, or prior art practices, particularly those known prior to or not incorporating the specific topology optimization techniques, low-temperature differential configurations, or other improvements described in the present disclosure. For example, when referring to components such as heat exchangers or fins, 'conventional' typically indicates designs lacking the specific topology optimization resulting in continuously curved passages or amorphous structures as described herein. In broader contexts, 'conventional' may also refer to established technologies or approaches (e.g., conventional Stirling engines with kinematic linkages, conventional high-temperature processes) where the distinction from the systems and methods of the present disclosure is clear from the context.

[0133] As used herein, the term “data center” generally refers to any facility, installation, or building configured to house computer systems and associated components — including but not limited to servers, storage systems, networking equipment, and power supplies — for the purpose of processing, managing, and distributing digital information. In some embodiments, a data center includes specialized infrastructure for environmental control, such as cooling systems (e.g., immersion or dielectric fluid cooling), to manage the significant thermal energy generated by high-density computing operations. The term is intended to encompass a wide spectrum of facility types, including enterprise data centers, colocation data centers, hyperscale and cloud data centers, managed service data centers, telecom data centers, edge and micro data centers, containerized data centers, underwater data centers, and prospective hybrid architectures integrating specialized systems such as quantum computing processors. The disclosed systems and methods for improved waste heat recovery are particularly applicable to such diverse data center environments, where the effective capture and conversion of low-grade waste heat into usable energy can lead to enhanced energy efficiency, reduced operational costs, and lower environmental impact.

[0134] As used herein, the term “immersion fluid,” generally refers to any liquid, gas, or mixture thereof that is employed to directly cool electronic components or systems by submerging them in the fluid, while also providing electrical insulation. In some embodiments, the immersion fluid may be a dielectric fluid — such as a fluorocarbon-based fluid, silicone oil, or other non- conductive liquid — with high thermal conductivity and a low viscosity profile, suitable for efficient heat transfer. The immersion fluid is utilized in cooling systems for data centers, server farms, or similar high-density computing environments to manage and extract waste heat from the electronics. In embodiments where the immersion fluid serves as the heat source, it is configured to transfer low-grade thermal energy to a heat recovery device, such as a free pistonStirling engine, for conversion into mechanical or electrical energy. The term “immersion fluid” is intended to encompass all such fluids, regardless of their specific chemical composition or phase, that meet the criteria for effective thermal management and electrical insulation in electronic cooling applications.

[0135] As used herein, the term "Power Usage Effectiveness (PUE)" generally refers to any ratio or metric that compares the total energy consumption of a data center facility to the energy consumption of its IT equipment. The term is not limited to a specific calculation method or numerical threshold and is intended to broadly cover any measurement that assesses the energy efficiency of a data center.

[0136] As used herein, the term "Additive Manufacturing" generally refers to any fabrication process that constructs a three-dimensional object through successive deposition of material based on a digital model. Additive manufacturing is not limited to any specific technology and may include various techniques that build components with complex geometries and internal features unattainable by conventional subtractive methods.

[0137] As used herein, the term "Direct Metal Laser Sintering (DMLS)" generally refers to any additive manufacturing technique in which a laser is employed to selectively fuse fine metal powders layer-by-layer to form a solid part. DMLS is not limited to a single process or material system and is intended to cover any method that produces components with continuously curved internal channels and varying cross-sectional areas.

[0138] As used herein, the term "Renewable Energy Management Module" generally refers to any control system, device, or combination thereof that receives real-time data regarding renewable energy availability and grid load, and automatically adjusts system parameters to maximize the utilization of renewable energy sources. This term is intended to be broad and does not imply a specific architecture, algorithm, or hardware configuration.

[0139] As used herein, the term "Water Usage Monitoring Module" generally refers to any sensor system, control circuitry, or combination thereof configured to continuously track and record water consumption within a cooling system. The term is intended to cover any method or apparatus for monitoring water usage and does not require a specific technology or configuration.

[0140] As used herein, the term "Quick-Disconnect Fluid Couplings" generally refers to any connectors or fittings that provide rapid, secure, and tool-free attachment and detachment of fluid lines while minimizing fluid leakage. The term is intended to be broad and includes any architecture or configuration that facilitates efficient connection and disconnection in a fluid circuit without being limited to any particular mechanism or standard.Overview

[0141] In one aspect, disclosed herein are immersion fluid management systems for a data center, comprising: computing devices; an immersion fluid in thermal connection with the computing devices; a first conduit comprising a first stream, wherein the first stream comprises a first temperature; a second conduit comprising a second stream, wherein the second stream comprises a second temperature; a Free Piston Stirling Engine (FPSE) fluidically connected to the first conduit and the second conduit.

[0142] In one aspect disclosed herein are immersion fluid management system for a data center, comprising: computing devices; an immersion fluid in thermal connection with the computing devices; a first conduit comprising a first stream, wherein the first stream comprises a first temperature; a second conduit comprising a second stream, wherein the second stream comprises a second temperature; a Free Piston Stirling Engine (FPSE) fluidically connected to the first conduit and the second conduit.

[0143] In another aspect disclosed herein are immersion fluid management systems for a data center, comprising: computing devices, an immersion fluid in thermal connection with the computing devices, a first conduit comprising a first stream, wherein the first stream comprises a first temperature, a second conduit comprising a second stream, wherein the second stream comprises a second temperature, a Free Piston Stirling Engine (FPSE) fluidically connected to the first conduit and the second conduit.

[0144] In some embodiments, the system further comprises a Free Piston Stirling Engine (FPSE) fluidically connected to the second conduit. In some embodiments, the first stream comprises dielectric fluid. In some embodiments, the second stream comprises water. In some embodiments, a temperature of the first stream is equal to or greater than a temperature of the second stream. In some embodiments, the first stream comprises an output stream from the computing devices. In some embodiments, the second stream comprises an input stream to the computing devices. In some embodiments, the first conduit fluidically connects the computing devices to the FPSE. In some embodiments, the first stream enters the FPSE at a hot cylinder side. In some embodiments, the first stream transfers heat to the hot cylinder side. In some embodiments, the system further comprises a third conduit, wherein the third conduit comprises a third stream at a third temperature. In some embodiments, the third stream comprises a FPSE output stream. In some embodiments, the third conduit fluidically connects the FPSE to a heat exchanger. In some embodiments, the third stream comprises a temperature less than or equal to the first stream. In some embodiments, the system further comprises a fourth conduit, wherein the fourth conduit comprises a fourth stream at a fourth temperature. In some embodiments, thefourth conduit fluidically connects the heat exchanger to the FPSE. In some embodiments, the fourth temperature is equal to or less than the third temperature. In some embodiments, the fourth stream enters the FPSE at a cold cylinder side. In some embodiments, the system further comprises a fifth conduit, wherein the fifth conduit comprises a fifth stream at a fifth temperature. In some embodiments, the fifth temperature is equal to or greater than the fourth temperature. In some embodiments, the fifth conduit fluidically connects the heat exchanger to a chiller. In some embodiments, the second conduit fluidically connects the chiller to the computing devices. In some embodiments, the second stream comprises a temperature equal to or less than the fourth stream. In some embodiments, the FPSE is configured to convert thermal energy from the first stream into mechanical energy, and then into electrical power. In some embodiments, the fourth stream is configured to create a temperature differential between the hot cylinder side and the cold cylinder side. In some embodiments, the second conduit is configured to fluidically connect the chiller to the computing devices at a side opposite to that of the first conduit. In some embodiments, the first conduit is configured to fluidically connect the computing devices to the heat exchanger at a side opposite the fifth conduit. In some embodiments, the third conduit is configured to fluidically connect the FPSE to the heat exchanger at a side opposite the fourth conduit. In some embodiments, the fourth conduit is configured to fluidically connect the FPSE to the heat exchanger. In some embodiments, a temperature differential between the fourth stream and the first stream generates a temperature differential between the hot cylinder side and the cold cylinder side. In some embodiments, the immersion fluid comprises a dielectric fluid, wherein the dielectric fluid functions both to absorb heat from the electronics and facilitate the generation of additional electricity. In some embodiments, the computing devices comprises one or more of servers, storage systems, network devices, and power supplies. In some embodiments, the system comprises a closed loop system. In some embodiments, the system comprises an open loop system.

[0145] In yet another aspect described herein are organic FPSE, the organic FPSE comprising a housing having a first end and a second end, wherein the first end and the second end are positioned along a displacement axis of the housing, and wherein the first end and the second end are separated by a travel length, a displacer positioned within the housing, wherein the displacer is reciprocally movable within the housing along the displacement axis and over at least a portion of the travel length, a piston positioned configured to apply a force to the displacer in a proximal direction of the housing, a heating head configured to add thermal energy to a working fluid, and a regenerator configured to recover and store thermal energy from a heated working fluid andtransfer to a cooled working fluid, and at least one heat transfer apparatus having an organic topology.

[0146] In some embodiments, the organic topology of the at least one heat transfer apparatus was generated by a topology algorithm, wherein the topology algorithm is configured to receive one or more parameters of the FPSE and generate the organic topology for the heat transfer apparatus based at least in part on the one or more parameters of the FPSE. In some embodiments, the one or more parameters provided to the topology algorithm comprise engine architecture parameters. In some embodiments, the one or more parameters comprises one or more constraints, in some embodiments, the FPSE further comprises a pressure vessel, wherein one or more parameters comprises an internal diameter of the pressure vessel Dpwall, wherein the Dpwall comprises approximately 2.62 le-1 [m]. In some embodiments, the one or more parameters comprises an internal diameter of the regenerator Dregen, wherein Dregen comprises approximately 1 ,747e-l [m]. In some embodiments, the one or more parameters comprises the FPSE operates at a mean charge pressure Pcharge, wherein Pcharge comprises approximately 35 bar up to 70 bar. In some embodiments, the one or more parameters comprises a diameter of the piston Dpis, wherein Dpis comprises approximately 1.712e-l [m]. In some embodiments, the one or more parameters comprises an amplitude of the piston Xamp,pis, wherein Xamp,pis comprises approximately 7.953e-3 [m]. In some embodiments, the one or more parameters comprises a compression space volume Vcompression, wherein Vcompression comprises approximately 3.667e-4 [mA3], In some embodiments, the improved thermal efficiency (^thermal) of the FPSE comprises approximately 9.06%. In some embodiments, the improved net power output (Wnet) of the FPSE comprises approximately 2000W. In some embodiments, the improved heat input (Qin) of the FPSE comprises approximately 22060W. In some embodiments, the improved heat output (Qout) of the FPSE comprises approximately 20060W. In some embodiments, the organic topology of the at least one heat transfer apparatus is substantially devoid of right angles. In some embodiments, the organic topology of the at least one heat transfer apparatus is substantially devoid of straight lines. In some embodiments, the organic topology of the at least one heat transfer apparatus comprises an amorphous shape. In some embodiments, the at least part of the organic topology comprises a form configured to encase a pressure vessel and for a heat transfer rate of up to about 0.67x the max theoretical limit. In some embodiments, the FPSE improves a heat transfer rate (0.67 / 0.5 l)x that of a conventionally-finned FPSE.

[0147] In yet another aspect described herein are methods of designing a heat transfer apparatus for a FPSE, the method comprising providing one or more parameters of the FPSE into a topology algorithm, wherein the topology algorithm is configured to generate an organictopology for the heat transfer apparatus based at least in part on the one or more parameters of the FPSE. In some embodiments, topology algorithm is configured to generate the organic topology tailored to a specific application of the heat transfer apparatus. In some embodiments, specific application of the heat transfer apparatus is in a data center environment. In some embodiments, the method further comprises generating manufacturing instructions derived from the organic topology. In some embodiments, the method further comprises manufacturing the heat transfer apparatus based on the generated manufacturing instructions, wherein the architecture of the apparatus being guided by the organic topology.

[0148] In some embodiments, manufacturing the heat transfer apparatus, particularly components with organic topology derived from topology optimization, utilizes additive manufacturing processes. Additive manufacturing, as used herein, generally refers to fabrication processes that construct three-dimensional objects through successive deposition of material based on a digital model, enabling the creation of complex geometries, continuously varying cross-sectional profiles, and internal features often unattainable by conventional subtractive methods.

[0149] A specific technique, Direct Metal Laser Sintering (DMLS), may be employed, which uses a laser to selectively fuse fine metal powders layer-by-layer to form solid parts, including components with continuously curved internal channels and varying cross-sectional areas.

[0150] The use of additive manufacturing, such as DMLS, is particularly advantageous for producing the efficient and intricate heat exchangers resulting from topology optimization. Furthermore, the application of additive manufacturing can facilitate the integration of multiple components (e.g., heater, fins, and regenerator sections) into a unified structure. This integration can help minimize dead volume within the engine and associated thermodynamic losses, contributing to a more compact and efficient engine design overall. Manufacturing instructions derived from the organic topology generated by the topology algorithm can guide these additive manufacturing processes. While additive manufacturing is highlighted, subtractive manufacturing processes may also be used where appropriate for certain components or features.

[0151] In some embodiments, manufacturing comprises a subtractive manufacturing process. In some embodiments, the method further comprises discretizing a fluid domain into a plurality of components. In some embodiments, each component of the plurality of components comprises a control volume. In some embodiments, the method further comprises defining mass, temperature, and pressure for each control volume. In some embodiments, boundaries (e.g., nodes) between each control volume are used to represent and determine the mass flow rate between each control volume. In some embodiments, the method further comprises solving ofdifferential equations for conservation of mass, momentum, and energy within the discretized fluid domain. In some embodiments, system of differential equations is solved numerically. In some embodiments, solving the differential equations provides a detailed prediction of FPSE's performance under specified operating conditions. In some embodiments, solver, upon reaching a stabilized state, attains a maximum thermal efficiency of 9.06% for a heat source temperature of 80°C and a heatsink temperature of 5°C. In some embodiments, FPSE comprises a Carnot efficiency of about 42.5%. In some embodiments, topology algorithm iteratively adjusts the distribution of material within a predefined domain based on gradients, seeking the optimal structure to meet the defined objective, such as maximizing heat dissipation or minimizing pressure loss, with the aid of adjoint solver capabilities. In some embodiments, topology algorithm incorporates a one-dimensional, third-order modeling, simulation, and optimization of the FPSE. In some embodiments, the method further comprises discretizing an FPSE domain into a plurality of building blocks. In some embodiments, each building block represents elemental components of the FPSE such as heat exchangers, regenerators, and pistons. In some embodiments, each building block comprises a localized self-contained entity. In some embodiments, entire FPSE model comprises a summation of each component building blocks interconnected via mass flow rate, heat transfer, force, and pressure connectors. In some embodiments, power and displacer pistons are represented as rigid moving components that cause volume displacement in compression and expansion spaces. In some embodiments, all components of the FPSE including heat exchangers, pistons, and working spaces are incorporated in the model. In some embodiments, the method further comprises specifying an average operating pressure for the FPSE using a pressure source. In some embodiments, the method further comprises connecting the endpoints of the system to specified heat sources In some embodiments, configuration is used to estimate non-productive energy losses (e.g., parasitic losses). In some embodiments, a total of 75 input parameters for 9 components and their subcomponents are defined. In some embodiments, the method further comprises specifying the optimization variables. In some embodiments, optimization variables comprise one or more of an internal diameter of the pressure vessel, an internal diameter of the regenerator, an FPSE mean charge pressure, a piston diameter, a piston amplitude, a volume of compression space, a width, height, and length of cooling head channel, a width, height, and length of heating head channel, a regenerator length, a regenerator wrapped foil gap and thickness, an amplitude and spring stiffness of the displacer, and a volume of expansion space. In some embodiments, optimization variables are coupled with constraints. In some embodiments, constraints ensure geometric and thermodynamic viability of architecture and an objective function. In some embodiments,thermal efficiency, defined as the ratio of net work output to heat input (^ thermal = w_net / Q_in), is considered as the objective function. In some embodiments, the method further comprises ensuring a regenerator's diameter is larger than a diameter of the displacer rod. In some embodiments, the method further comprises ensuring a diameter of the pressure vessel is larger than the diameter of the regenerator. In some embodiments, the method further comprises ensuring that the form factor is maintained at a reasonable level, such that the flow distribution losses are minimal. In some embodiments, the method further comprises ensuring a diameter of the piston is larger than the diameter of the displacer rod. In some embodiments, the method further comprises ensuring a diameter of the piston has about a same diameter as the regenerator. In some embodiments, the method further comprises ensuring a sufficient volume in the dead space of the compression region to prevent any collision. In some embodiments, the method further comprises ensuring a sufficient volume in the dead space of the expansion region to prevent any collision. In some embodiments, the method further comprises ensuring a displacer operates freely by maintaining the components of a phasor force at zero. In some embodiments, the method further comprises ensuring a power output is obtained from the FPSE. In some embodiments, the method further comprises running the one-dimensional code to simulate the energy generation over a 48-hour period, resultingin a total energy production of 98kWh, under the assumption of fixed heat source and sink temperatures and availability of heat source for 24 hours per day. In some embodiments, discretization further comprises using polyhedral meshing to create conformal mesh interfaces between the parts In some embodiments, contacting faces between different parts share a same boundary face topology. In some embodiments, the method further comprises performing simulations using four different base cell sizes to ensure mesh size sensitivity and check for mesh convergence, resulting in more accurate and faster simulations due to the elimination of the need for face interpolation on contacting patches. In some embodiments, the method further comprises establishing five layers on interfacesbetween air and solid components to accurately capture thermal boundary layer. In some embodiments, the method further comprises identifying four distinct simulation domains in the CAD geometry, wherein the four distinct simulation domains comprises specifically the stainless steel enclosure, air, copper fins, and an Inconel half-cylinder. In some embodiments, the method further comprises assigning each region a specific simulation model based on the material. In some embodiments, boundary conditions are set such that the enclosure has adiabatic walls. In some embodiments, inner wall of a half cylinder has a convective heat transfer coefficient of 860 W / m2K at 300°C. In some embodiments, inlets for each pipe are set with parameters such as: Mass flow rate of 0.003184 kg / s, Temperature of 650°C, and Pressure of 101,325 Pa. In someembodiments, outlets are set as pressure outlets. In some embodiments, at least one enclosure surface comprises a roughness of about 0.05 mm. In some embodiments, average air temperature within the system is calculated to be about 502.3°C. In some embodiments, a maximum theoretical heat transfer value comprises about 3566W. In some embodiments, 1830W is extracted from the hot air to the fins. In some embodiments, topology algorithm utilizes gradient-based Topology (TO) for heat transfer and pressure optimization. In some embodiments, TO process begins by defining the architecture space envelope as well as the flow / thermal objective functions together with TO input parameters. In some embodiments, TO process utilizes conformal mesh to ensure conservation of heat transfer values. In some embodiments, surface mesh between all parts on the interface shares points at the interface to conserve heat transfer between parts. In some embodiments, smaller mesh cells result in finer fin surface. In some embodiments, smaller mesh cells result in larger fin surface area. In some embodiments, the method further comprises geometry preparation for full CFD simulation with Boundary Layers (BL). In some embodiments, geometry preparation comprises smoothing out initial derived part geometry, using a surface wrapper to create a watertight surface, importing the watertight surface of the improved geometry to the full case, subtracting the watertight surface from the air domain, imprinting it to the half cylinder geometry, and ensuring all interfaces are created properly. In some embodiments, jagged geometry obtained from TO is smoothed out and then re-imported back for CFD simulation for validation and verification purposes.

[0152] In yet another aspect described herein are methods of designing a heat transfer apparatus for a FPSE to be integrated into a waste heat production system, the method comprising providing one or more parameters of the FPSE into a one-dimensional (ID) Computational Fluid Dynamics (CFD) model, providing at least one output parameter of the ID CFD model into a three-dimensional (3D) Computational Fluid Dynamics (CFD) model, providing at least one output parameter of the 3D CFD model into a topology algorithm, and generating the heat transfer apparatus comprising an organic topology tailored for a waste heat production system.

[0153] In another aspect, disclosed herein are organic FPSE, the organic FPSE comprising a housing having a first end and a second end, wherein the first end and the second end are positioned along a displacement axis of the housing, and wherein the first end and the second end are separated by a travel length, a displacer positioned within the housing, wherein the displacer is reciprocally movable within the housing along the displacement axis and over at least a portion of the travel length, a piston positioned and configured to apply a force to the displacer in aproximal direction of the housing, a heating head configured to add thermal energy to a working fluid, and a regenerator configured to recover and store thermal energy from a heated working fluid and transfer to a cooled working fluid, and at least one heat transfer apparatus having an organic topology.

[0154] In some embodiments, the organic topology of the at least one heat transfer apparatus was generated by a topology algorithm, wherein the topology algorithm is configured to receive one or more parameters of the FPSE and generate the organic topology for the heat transfer apparatus based at least in part on the one or more parameters of the FPSE.

[0155] In some embodiments, the one or more parameters provided to the topology algorithm comprise engine architecture parameters.

[0156] In some embodiments, the one or more parameters comprises one or more constraints.

[0157] In some embodiments, the organic FPSE further comprising a pressure vessel, wherein one or more parameters comprises an internal diameter of the pressure vessel Dpwall, wherein the Dpwall comprises approximately 2.621e-l [m],

[0158] In some embodiments, the one or more parameters comprises an internal diameter of the regenerator Dregen, wherein Dregen comprises approximately 1.747e-l [m],

[0159] In some embodiments, the one or more parameters comprises the FPSE operates at a mean charge pressure Pcharge, wherein Pcharge comprises approximately 35 bar up to 70 bar.

[0160] In some embodiments, the one or more parameters comprises a diameter of the piston Dpis, wherein Dpis comprises approximately 1.712e-l [m],

[0161] In some embodiments, the one or more parameters comprises an amplitude of the piston Xamp,pis, wherein Xamp,pis comprises approximately 7.953e-3 [m],

[0162] In some embodiments, the one or more parameters comprises a compression space volume Vcompression, wherein Vcompression comprises approximately 3.667e-4 [mA3],

[0163] In some embodiments, the improved thermal efficiency (^thermal) of the FPSE comprises approximately 9.06%.

[0164] In some embodiments, the improved net power output (Wnet) of the FPSE comprises approximately 2000W.

[0165] In some embodiments, the improved heat input (Qin) of the FPSE comprises approximately 22060W.

[0166] In some embodiments, the improved heat output (Qout) of the FPSE comprises approximately 20060W.

[0167] In some embodiments, the organic topology of the at least one heat transfer apparatus is substantially devoid of right angles.

[0168] In some embodiments, the organic topology of the at least one heat transfer apparatus is substantially devoid of straight lines.

[0169] In some embodiments, the organic topology of the at least one heat transfer apparatus comprises an amorphous shape.

[0170] In some embodiments, the at least part of the organic topology comprises a form configured to encase a pressure vessel and for a heat transfer rate of up to about 0.67x the max theoretical limit.

[0171] In some embodiments, the FPSE improves a heat transfer rate (0.67 / 0.5 l)x (approximately 1.3 lx) that of a conventionally-finned FPSE.

[0172] In another aspect, disclosed herein are method of designing a heat transfer apparatus for a FPSE, the method comprising providing one or more parameters of the FPSE into a topology algorithm, wherein the topology algorithm is configured to generate an organic topology for the heat transfer apparatus based at least in part on the one or more parameters of the FPSE.

[0173] In some embodiments, the topology algorithm is configured to generate the organic topology tailored to a specific application of the heat transfer apparatus.

[0174] In some embodiments, the specific application of the heat transfer apparatus is in a data center environment.

[0175] In some embodiments, the method further comprises generating manufacturing instructions derived from the organic topology.

[0176] In some embodiments, the method further comprises manufacturing the heat transfer apparatus based on the generated manufacturing instructions, wherein the architecture of the apparatus being guided by the organic topology.

[0177] In some embodiments, the manufacturing comprises an additive manufacturing process.

[0178] In some embodiments, the additive manufacturing process comprises Direct Metal Laser Sintering (DMLS).

[0179] In some embodiments, the manufacturing comprises a subtractive manufacturing process.

[0180] In some embodiments, the method further comprises discretizing a fluid domain into a plurality of components.

[0181] In some embodiments, each component of the plurality of components comprises a control volume.

[0182] In some embodiments, the method further comprises defining mass, temperature, and pressure for each control volume.

[0183] In some embodiments, the boundaries (e.g., nodes) between each control volume are used to represent and determine the mass flow rate between each control volume.

[0184] In some embodiments, the method further comprises solving of differential equations for conservation of mass, momentum, and energy within the discretized fluid domain.

[0185] In some embodiments, the system of differential equations is solved numerically.

[0186] In some embodiments, solving the differential equations provides a detailed prediction of FPSE's performance under specified operating conditions.

[0187] In some embodiments, the solver, upon reaching a stabilized state, attains a maximum thermal efficiency of 9.06% for a heat source temperature of 80°C and a heatsink temperature of 5°C.

[0188] In some embodiments, the FPSE comprises a Carnot efficiency of about 42.5%.

[0189] In some embodiments, the topology algorithm iteratively adjusts the distribution of material within a predefined domain based on gradients, seeking the improved structure to meet the defined objective, such as maximizing heat dissipation or minimizing pressure loss, with the aid of adjoint solver capabilities.

[0190] In some embodiments, the topology algorithm incorporates a one-dimensional, third- order modeling, simulation, and optimization of the FPSE.

[0191] In some embodiments, the method further comprises discretizing an FPSE domain into a plurality of building blocks.

[0192] In some embodiments, each building block represents elemental components of the FPSE such as heat exchangers, regenerators, and pistons.

[0193] In some embodiments, each building block comprises a localized self-contained entity.

[0194] In some embodiments, the entire FPSE model comprises a summation of each component building blocks interconnected via mass flow rate, heat transfer, force, and pressure connectors.

[0195] In some embodiments, the power and displacer pistons are represented as rigid moving components that cause volume displacement in compression and expansion spaces.

[0196] In some embodiments, all components of the FPSE including heat exchangers, pistons, and working spaces are incorporated in the model.

[0197] In some embodiments, the method further comprises specifying an average operating pressure for the FPSE using a pressure source.

[0198] In some embodiments, the method further comprises connecting the endpoints of the system to specified heat sources In some embodiments, the configuration is used to estimate nonproductive energy losses (e.g., parasitic losses).

[0199] In some embodiments, a total of 75 input parameters for 9 components and their subcomponents are defined.

[0200] In some embodiments, the method further comprises specifying the optimization variables.

[0201] In some embodiments, the optimization variables comprise one or more of an internal diameter of the pressure vessel, an internal diameter of the regenerator, an FPSE mean charge pressure, a piston diameter, a piston amplitude, a volume of compression space, a width, height, and length of cooling head channel, a width, height, and length of heating head channel, a regenerator length, a regenerator wrapped foil gap and thickness, an amplitude and spring stiffness of the displacer, and a volume of expansion space.

[0202] In some embodiments, the optimization variables are coupled with constraints.

[0203] In some embodiments, the constraints ensure geometric and thermodynamic viability of architecture and an objective function.

[0204] In some embodiments, the thermal efficiency, defined as the ratio of net work output to heat input (^ thermal = w_net / Q_in), is considered as the objective function.

[0205] In some embodiments, the method further comprises ensuring a regenerator's diameter is larger than a diameter of the displacer rod.

[0206] In some embodiments, the method further comprises ensuring a diameter of the pressure vessel is larger than the diameter of the regenerator.

[0207] In some embodiments, the method further comprises ensuring that the form factor is maintained at a reasonable level, such that the flow distribution losses are minimal.

[0208] In some embodiments, the method further comprises ensuring a diameter of the piston is larger than the diameter of the displacer rod.

[0209] In some embodiments, the method further comprises ensuring a diameter of the piston has about a same diameter as the regenerator.

[0210] In some embodiments, the method further comprises ensuring a sufficient volume in the dead space of the compression region to prevent any collision.

[0211] In some embodiments, the method further comprises ensuring a sufficient volume in the dead space of the expansion region to prevent any collision.

[0212] In some embodiments, the method further comprises ensuring a displacer operates freely by maintaining the components of a phasor force at zero.

[0213] The method of any of the preceding claims, further ensuring a required power output is obtained from the FPSE.

[0214] In some embodiments, the method further comprises running the one-dimensional code to simulate the energy generation over a 48-hour period, resulting in a total energy production of98kWh, under the assumption of fixed heat source and sink temperatures and availability of heat source for 24 hours per day.

[0215] In some embodiments, the discretization further comprises using polyhedral meshing to create conformal mesh interfaces between the parts In some embodiments, the contacting faces between different parts share a same boundary face topology.

[0216] In some embodiments, the method further comprises performing simulations using four different base cell sizes to ensure mesh size sensitivity and check for mesh convergence, resulting in more accurate and faster simulations due to the elimination of the need for face interpolation on contacting patches.

[0217] In some embodiments, the method further comprises establishing five layers on interfaces between air and solid components to accurately capture thermal boundary layer.

[0218] In some embodiments, the method further comprises identifying four distinct simulation domains in the CAD geometry, wherein the four distinct simulation domains comprises specifically the stainless steel enclosure, air, copper fins, and an Inconel half-cylinder.

[0219] In some embodiments, the method further comprises assigning each region a specific simulation model based on the material.

[0220] In some embodiments, the boundary conditions are set such that the enclosure has adiabatic walls.

[0221] In some embodiments, the inner wall of a half cylinder has a convective heat transfer coefficient of 860 W / m2K at 300°C.

[0222] In some embodiments, the inlets for each pipe are set with parameters such as: Mass flow rate of 0.003184 kg / s, Temperature of 650°C, andPressure of 101,325 Pa. In some embodiments, the outlets are set as pressure outlets.

[0223] In some embodiments, the at least one enclosure surface comprises a roughness of about 0.05 mm.

[0224] In some embodiments, the average air temperature within the system is calculated to be about 502.3°C.

[0225] In some embodiments, a maximum theoretical heat transfer value comprises about 3566W.

[0226] In some embodiments, the 1830W is extracted from the hot air to the fins.

[0227] In some embodiments, the topology algorithm utilizes gradient-based Topology (TO) for heat transfer and pressure optimization.

[0228] In some embodiments, the TO process begins by defining the architecture space envelope as well as the flow / thermal objective functions together with TO input parameters.

[0229] In some embodiments, the TO process utilizes conformal mesh to ensure conservation of heat transfer values.

[0230] In some embodiments, the surface mesh between all parts on the interface shares points at the interface to conserve heat transfer between parts.

[0231] In some embodiments, the smaller mesh cells result in finer fin surface.

[0232] In some embodiments, the smaller mesh cells result in larger fin surface area.

[0233] In some embodiments, the method further comprises geometry preparation for full CFD simulation with Boundary Layers (BL).

[0234] In some embodiments, the geometry preparation comprises smoothing out initial derived part geometry, using a surface wrapper to create a watertight surface, importing the watertight surface of the improved geometry to the full case, subtracting the watertight surface from the air domain, imprinting it to the half cylinder geometry, and ensuring all required interfaces are created properly.

[0235] In some embodiments, the jagged geometry obtained from TO is smoothed out and then re-imported back for CFD simulation for validation and verification purposes.

[0236] In another aspect, disclosed herein are methods of designing a heat transfer apparatus for a FPSE to be integrated into a waste heat production system, the method comprising providing one or more parameters of the FPSE into a one-dimensional (ID) Computational Fluid Dynamics (CFD) model, providing at least one output parameter of the ID CFD model into a three- dimensional (3D) Computational Fluid Dynamics (CFD) model, providing at least one output parameter of the 3D CFD model into a topology algorithm, and generating the heat transfer apparatus comprising an organic topology tailored for a waste heat production system.

[0237] In another aspect, disclosed herein are organic FPSE for a data center environment, the organic FPSE comprising a housing having a first end and a second end, wherein the first end and the second end are positioned along a displacement axis of the housing, and wherein the first end and the second end are separated by a travel length, a displacer positioned within the housing, wherein the displacer is reciprocally movable within the housing along the displacement axis and over at least a portion of the travel length, a piston positioned configured to apply a force to the displacer in a proximal direction of the housing, a heating head configured to receive thermal energy from an immersion fluid and add thermal energy to a working fluid, and a regenerator configured to recover and store thermal energy from a heated working fluid and transfer to a cooled working fluid, and at least one heat transfer apparatus having an organic topology tailored for the data center environment.

[0238] In another aspect, disclosed herein are method of designing a heat transfer apparatus for a FPSE to be integrated into a data center, the method comprising providing one or more parameters of the FPSE into a topology algorithm, wherein the topology algorithm is configured to generate an organic topology for the heattransfer apparatus based at least in part on the one or more parameters of the FPSE, and generating the organic topology tailored for the data center. Heat Recovery System

[0239] Heat Recovery System

[0240] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, a heat recovery system (HRS) configured to provide various benefits, including generating electricity from low-grade heat sources (e.g., below 230°C), enhancing energy efficiency of pre-existing energy conversion systems (e.g., data centers, industrial), and reducing greenhouse gas emissions.

[0241] The HRS may comprise a HRS efficiency up to about 23%.

[0242] In some cases, the formula for calculating the HRS efficiency comprises equation 1 (below).

[0243] In some cases, the HRS efficiency comprises between about 0% to about 100%.

[0244] In some cases, the HRS efficiency comprises between about 0% to about 5%, about 0% to about 10%, about 0% to about 15%, about 0% to about 20%, about 0% to about 25%, about 0% to about 30%, about 0% to about 35%, about 0% to about 40%, about 0% to about 45%, about 0% to about 50%, about 0% to about 100%, about 5% to about 10%, about 5% to about 15%, about 5% to about 20%, about 5% to about 25%, about 5% to about 30%, about 5% to about 35%, about 5% to about 40%, about 5% to about 45%, about 5% to about 50%, about 5% to about 100%, about 10% to about 15%, about 10% to about 20%, about 10% to about 25%, about 10% to about 30%, about 10% to about 35%, about 10% to about 40%, about 10% to about 45%, about 10% to about 50%, about 10% to about 100%, about 15% to about 20%, about 15% to about 25%, about 15% to about 30%, about 15% to about 35%, about 15% to about 40%, about 15% to about 45%, about 15% to about 50%, about 15% to about 100%, about 20% to about 25%, about 20% to about 30%, about 20% to about 35%, about 20% to about 40%, about 20% to about 45%, about 20% to about 50%, about 20% to about 100%, about 25% to about 30%, about 25% to about 35%, about 25% to about 40%, about 25% to about 45%, about 25% to about 50%, about 25% to about 100%, about 30% to about 35%, about 30% to about 40%, about 30% to about 45%, about 30% to about 50%, about 30% to about 100%, about 35% to about 40%, about 35% to about 45%, about 35% to about 50%, about 35% to about 100%, about 40% to about45%, about 40% to about 50%, about 40% to about 100%, about 45% to about 50%, about 45% to about 100%, or about 50% to about 100%.

[0245] In some cases, the HRS efficiency comprises between about 0%, about 5%, about 10%, about 15%, about20%, about 25%, about 30%, about 35%, about 40%, about 45%, about 50%, or about 100%.

[0246] In some cases, the HRS efficiency comprises between at least about 0%, about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, about 45%, or about 50%.

[0247] In some cases, the HRS efficiency comprises between at most about 5%, about 10%, about 15%, about20%, about 25%, about 30%, about 35%, about 40%, about 45%, about 50%, or about 100%.

[0248] In some cases, the HRS efficiency comprises up to about 23% efficiency.

[0249] In some cases, the HRS efficiency comprises up to about 30% efficiency.

[0250] In some cases, the HRS efficiency comprises up to about 45% efficiency.

[0251] In some cases, the HRS efficiency comprises up to about 60% efficiency.

[0252] For example, the input energy may be from an immersion fluid (e.g., heated dielectric fluid).

[0253] In further examples, the immersion fluid comprises heated dielectric fluids, coolant streams, or other low-temperature heat streams from electronic equipment.

[0254] In even further examples, the HRS is configured to be heated by immersion fluid from a data center.

[0255] In some cases, the HRS efficiency is dependent on a feature of the immersion fluid stream.

[0256] In some instances, the HRS efficiency may be dependent on the immersion fluid stream temperature and flow rate.

[0257] In some instances, the HRS efficiency comprises up to about 23% wherein the immersion fluid stream comprises a temperature up to about 500°C.

[0258] In some instances, the HRS efficiency comprises up to about 40% wherein the immersion fluid stream comprises a temperature up to about 500°C.

[0259] In some instances, the HRS efficiency comprises between about 7.5% to about 10%, wherein a heat source temperature comprises about 80°C and a heat sink temperature comprises about 5°C.

[0260] For example, the HRS efficiency may comprise between about 7.5% and 10%, wherein the immersion fluid stream comprises a temperature of up to about 80°C and the environment comprises a temperature of up to about 5°C.

[0261] In some cases, the HRS efficiency is dependent on a temperature differential between the immersion fluid stream and an environment (or heat sink).

[0262] In some instances, the HRS efficiency comprises between about 1% to about 50%, wherein the immersion fluid stream comprises a temperature of up to about 500°C and the environment comprises a temperature of between about -90°C to about 60°C.

[0263] In some cases, the HRS efficiency is dependent on the heat exchanger efficiency.

[0264] In some instances, the HRS efficiency comprises between about 20% and 40%, wherein the heat exchanger efficiency comprises between about 50% and 90%.

[0265] In some cases, the HRS efficiency is dependent on the scale of the data center or heat source.

[0266] The HRS may comprise a HRS energy production capability of up to about 250 kilowatt hours / day (kWh / day).

[0267] In some cases, the HRS energy production capability comprises between about 10 - 40 kilowatt hours / day.

[0268] In some cases, the HRS energy production capability comprises an average of about 30 kWh / day.

[0269] In some cases, the HRS energy production capability comprises up to about 8 kWh / day, wherein the heat source is available for 8 hours / day and a FPSE produces up to about 1 kW of power.

[0270] In some cases, the HRS energy production capability comprises up to about 6000 kWh / day, wherein the heat source is available for 24 hours / day and a FPSE produces about 250 kW of power.

[0271] In some cases, the HRS energy production capability comprises between about 0 kWh / day to about 6,000 kWh / day.

[0272] In some cases, the HRS energy production capability comprises between about 0 kWh / day to about 4 kWh / day, about 0 kWh / day to about 8 kWh / day, about 0 kWh / day to about 10 kWh / day, about 0 kWh / day to about 20 kWh / day, about 0 kWh / day to about 30 kWh / day, about 0 kWh / day to about 60 kWh / day, about 0 kWh / day to about 100 kWh / day, about 0 kWh / day to about 1,000 kWh / day, about 0 kWh / day to about 2,600 kWh / day, about 0 kWh / day to about 4,200 kWh / day, about 0 kWh / day to about 6,000 kWh / day, about 4 kWh / day to about 8 kWh / day, about 4 kWh / day to about 10 kWh / day, about 4 kWh / day to about 20 kWh / day, about4 kWh / day to about 30 kWh / day, about 4 kWh / day to about 60 kWh / day, about 4 kWh / day to about 100 kWh / day, about 4 kWh / day to about 1,000 kWh / day, about 4 kWh / day to about 2,600 kWh / day, about 4 kWh / day to about 4,200 kWh / day, about 4 kWh / day to about 6,000 kWh / day, about 8 kWh / day to about 10 kWh / day, about 8 kWh / day to about 20 kWh / day, about 8 kWh / day to about 30 kWh / day, about 8 kWh / day to about 60 kWh / day, about 8 kWh / day to about 100 kWh / day, about 8 kWh / day to about 1,000 kWh / day, about 8 kWh / day to about 2,600 kWh / day, about 8 kWh / day to about 4,200 kWh / day, about 8 kWh / day to about 6,000 kWh / day, about 10 kWh / day to about 20 kWh / day, about 10 kWh / day to about 30 kWh / day, about 10 kWh / day to about 60 kWh / day, about 10 kWh / day to about 100 kWh / day, about 10 kWh / day to about 1,000 kWh / day, about 10 kWh / day to about 2,600 kWh / day, about 10 kWh / day to about 4,200 kWh / day, about 10 kWh / day to about 6,000 kWh / day, about 20 kWh / day to about 30 kWh / day, about 20 kWh / day to about 60 kWh / day, about 20 kWh / day to about 100 kWh / day, about 20 kWh / day to about 1,000 kWh / day, about 20 kWh / day to about 2,600 kWh / day, about 20 kWh / day to about 4,200 kWh / day, about 20 kWh / day to about 6,000 kWh / day, about 30 kWh / day to about 60 kWh / day, about 30 kWh / day to about 100 kWh / day, about 30 kWh / day to about 1,000 kWh / day, about 30 kWh / day to about 2,600 kWh / day, about 30 kWh / day to about 4,200 kWh / day, about 30 kWh / day to about 6,000 kWh / day, about 60 kWh / day to about 100 kWh / day, about 60 kWh / day to about 1,000 kWh / day, about 60 kWh / day to about 2,600 kWh / day, about 60 kWh / day to about 4,200 kWh / day, about 60 kWh / day to about 6,000 kWh / day, about 100 kWh / day to about 1,000 kWh / day, about 100 kWh / day to about 2,600 kWh / day, about 100 kWh / day to about 4,200 kWh / day, about 100 kWh / day to about 6,000 kWh / day, about 1,000 kWh / day to about 2,600 kWh / day, about 1,000 kWh / day to about 4,200 kWh / day, about 1,000 kWh / day to about 6,000 kWh / day, about 2,600 kWh / day to about 4,200 kWh / day, about 2,600 kWh / day to about 6,000 kWh / day, or about 4,200 kWh / day to about 6,000 kWh / day.

[0273] In some cases, the HRS energy production capability comprises between about 0 kWh / day, about 4 kWh / day, about 8 kWh / day, about 10 kWh / day, about 20 kWh / day, about 30 kWh / day, about 60 kWh / day, about 100 kWh / day, about 1,000 kWh / day, about 2,600 kWh / day, about 4,200 kWh / day, or about 6,000 kWh / day.

[0274] In some cases, the HRS energy production capability comprises between about at least about 0 kWh / day, about 4 kWh / day, about 8 kWh / day, about 10 kWh / day, about 20 kWh / day, about 30 kWh / day, about 60 kWh / day, about 100 kWh / day, about 1,000 kWh / day, about 2,600 kWh / day, or about 4,200 kWh / day.

[0275] In some cases, the HRS energy production capability comprises between about at most about 4 kWh / day, about 8 kWh / day, about 10 kWh / day, about 20 kWh / day, about 30 kWh / day, about 60 kWh / day, about 100 kWh / day, about 1,000 kWh / day, about 2,600 kWh / day, about 4,200 kWh / day, or about 6,000 kWh / day.

[0276] In some cases, the formula for calculating the HRS efficiency comprises equation 1 : (Equation 1)

[0277] In equation 1, “q” comprises HRS efficiency, “I” comprises Input Energy in Immersion fluid, and “O” comprises Output from Recovered Heat.

[0278] In some cases, the HRS efficiency comprises between about 0% to about 100%. In some cases, the HRS efficiency comprises between about 0% to about 5%, about 0% to about 10%, about 0% to about 15%, about 0% to about 20%, about 0% to about 25%, about 0% to about 30%, about 0% to about 35%, about 0% to about 40%, about 0% to about 45%, about 0% to about 50%, about 0% to about 100%, about 5% to about 10%, about 5% to about 15%, about 5% to about 20%, about 5% to about 25%, about 5% to about 30%, about 5% to about 35%, about 5% to about 40%, about 5% to about 45%, about 5% to about 50%, about 5% to about 100%, about 10% to about 15%, about 10% to about 20%, about 10% to about 25%, about 10% to about 30%, about 10% to about 35%, about 10% to about 40%, about 10% to about 45%, about 10% to about 50%, about 10% to about 100%, about 15% to about 20%, about 15% to about 25%, about 15% to about 30%, about 15% to about 35%, about 15% to about 40%, about 15% to about 45%, about 15% to about 50%, about 15% to about 100%, about 20% to about 25%, about 20% to about 30%, about 20% to about 35%, about 20% to about 40%, about 20% to about 45%, about 20% to about 50%, about 20% to about 100%, about 25% to about 30%, about 25% to about 35%, about 25% to about 40%, about 25% to about 45%, about 25% to about 50%, about 25% to about l00%, about 30%to about 35%, about 30% to about 40%, about 30% to about 45%, about 30% to about 50%, about 30% to about 100%, about 35% to about 40%, about 35% to about 45%, about 35% to about 50%, about 35% to about 100%, about 40% to about 45%, about 40% to about 50%, about 40% to about 100%, about45% to about 50%, about45% to about 100%, or about 50% to about 100%. In some cases, the HRS efficiency comprises between about 0%, about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, about 45%, about 50%, or about 100%. In some cases, the HRS efficiency comprises between at least about 0%, about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, about 45%, or about 50%. In some cases, the HRS efficiency comprises between at most about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, about 45%, about 50%, or about 100%.

[0279] In some cases, the HRS efficiency comprises approximately up to about 23% efficiency. In some cases, the HRS efficiency comprises approximately upto about 30% efficiency. In some cases, the HRS efficiency comprises approximately up to about 45% efficiency. In some cases, the HRS efficiency comprises approximately up to about 60% efficiency. For example, the input energy in immersion fluid may be from an immersion fluid. In further examples, the immersion fluid comprises immersion fluid gases, hot liquids, or other low-temperature heat streams. In even further examples, the HRS is configured to be heated by immersion fluid from a data center.

[0280] In some cases, the HRS efficiency is dependent on a feature of an immersion fluid stream. In some instances, the HRS efficiency may be dependent on an immersion fluid stream temperature and flow rate.

[0281] In some instances, the HRS efficiency comprises upto about 23% wherein the immersion fluid stream comprises a temperature up to about 500°C. In some instances, the HRS efficiency comprises up to about 40% wherein the immersion fluid stream comprises a temperature up to about 500°C. In some instances, the HRS efficiency comprises between about 7.5% to about 10%, wherein a heat source temperature comprises about 80°C and a heat sink temperature comprises about 5°C. For example, the HRS efficiency may comprises between about 7.5% and 10%, wherein the immersion fluid stream comprises a temperature of up to about 80°C and the environment comprises a temperature of up to about 5 °C.

[0282] In some cases, the HRS efficiency is dependent on a temperature differential between an immersion fluid stream and an environment. In some instances, the HRS efficiency comprises between about 1% to about 50%, wherein the immersion fluid stream comprises a temperature of up to about 500°C and the environment comprises a temperature of between about -90°C to about 60°C.

[0283] In some cases, the HRS efficiency is dependent on the heat exchanger efficiency. In some instances, the HRS efficiency comprises between about 20% and 40%, wherein the heat exchanger efficiency comprises between about 50% and 90%.

[0284] In some cases, the HRS efficiency is dependent on a size of an immersion fluid generator (e.g., building or structure that produces the immersion fluid). In some instances, the HRS efficiency comprises between about 1% to about 50% wherein the immersion fluid generator comprises an industrial building (e.g., up to about 5 million sq. ft.). For example, the HRS efficiency may comprise up to about 45% efficiency wherein the immersion fluid generator comprises an industrial building (e.g., up to about 5 million sq. ft.). In further examples, the HRS efficiency may comprise about 23% efficiency, wherein the immersion fluid generator comprises an industrial building.

[0285] In some instances, the HRS efficiency comprises between about 1% to about 50% wherein the HRS comprises a domestic or residential building (e.g., up to about 2 million sq. ft.). For example, the HRS efficiency may comprise up to about 45% efficiency wherein the immersion fluid generator comprises a domestic or residential building. In further examples, the HRS efficiency may comprise 23% efficiency, wherein the immersion fluid generator comprises a domestic or residential building.

[0286] The HRS may comprise a HRS energy production capability of up to about 250 kilowatt hours / day (kWh / day). In some cases, the HRS energy production capability comprises between about 10 - 40 kilowatt hours / day. In some cases, the HRS energy production capability comprises an average of approximately 30 kWh / day. In some cases, the HRS energy production capability comprises upto about 8 kWh / day, wherein the immersion fluid source is available for 8 hours / day and a FPSE produces up to about 1 kW of power. In some cases, the HRS energy production capability comprisesup to about 6000 kWh / day, wherein the immersion fluid source is available for 24 hours / day and a FPSE produces about 250 kW of power.

[0287] In some cases, the HRS energy production capability comprises between about 0 kWh / day to about 6,000 kWh / day. In some cases, the HRS energy production capability comprises between about 0 kWh / day to about 4 kWh / day, about 0 kWh / day to about 8 kWh / day, about 0 kWh / day to about 10 kWh / day, about 0 kWh / day to about 20 kWh / day, about 0 kWh / day to about 30 kWh / day, about 0 kWh / day to about 60 kWh / day, about 0 kWh / day to about 100 kWh / day, about 0 kWh / day to about 1,000 kWh / day, about 0 kWh / day to about 2,600 kWh / day, about 0 kWh / day to about 4,200 kWh / day, about 0 kWh / day to about 6,000 kWh / day, about 4 kWh / day to about 8 kWh / day, about 4 kWh / day to about 10 kWh / day, about 4 kWh / day to about 20 kWh / day, about 4 kWh / day to about 30 kWh / day, about 4 kWh / day to about 60 kWh / day, about 4 kWh / day to about 100 kWh / day, about 4 kWh / day to about 1,000 kWh / day, about 4 kWh / day to about 2,600 kWh / day, about 4 kWh / day to about 4,200 kWh / day, about 4 kWh / day to about 6,000 kWh / day, about 8 kWh / day to about 10 kWh / day, about 8 kWh / day to about 20 kWh / day, about 8 kWh / day to about 30 kWh / day, about 8 kWh / day to about 60 kWh / day, about 8 kWh / day to about 100 kWh / day, about 8 kWh / day to about 1,000 kWh / day, about 8 kWh / day to about 2,600 kWh / day, about 8 kWh / day to about 4,200 kWh / day, about 8 kWh / day to about 6,000 kWh / day, about 10 kWh / day to about 20 kWh / day, about 10 kWh / day to about 30 kWh / day, about 10 kWh / day to about 60 kWh / day, about 10 kWh / day to about 100 kWh / day, about 10 kWh / day to about 1,000 kWh / day, about 10 kWh / day to about 2,600 kWh / day, about 10 kWh / day to about 4,200 kWh / day, about 10 kWh / day to about 6,000 kWh / day, about 20 kWh / day to about 30 kWh / day, about 20 kWh / day to about 60 kWh / day, about 20 kWh / day toabout 100 kWh / day, about 20 kWh / day to about 1,000 kWh / day, about 20 kWh / day to about 2,600 kWh / day, about 20 kWh / day to about 4,200 kWh / day, about 20 kWh / day to about 6,000 kWh / day, about 30 kWh / day to about 60 kWh / day, about 30 kWh / day to about 100 kWh / day, about 30 kWh / day to about 1 ,000 kWh / day, about 30 kWh / day to about 2,600 kWh / day, about 30 kWh / day to about 4,200 kWh / day, about 30 kWh / day to about 6,000 kWh / day, about 60 kWh / day to about 100 kWh / day, about 60 kWh / day to about 1,000 kWh / day, about 60 kWh / day to about 2,600 kWh / day, about 60 kWh / day to about 4,200 kWh / day, about 60 kWh / day to about 6,000 kWh / day, about 100 kWh / day to about 1,000 kWh / day, about 100 kWh / day to about 2,600 kWh / day, about 100 kWh / day to about 4,200 kWh / day, about 100 kWh / day to about 6,000 kWh / day, about 1,000 kWh / day to about 2,600 kWh / day, about 1,000 kWh / day to about 4,200 kWh / day, about 1,000 kWh / day to about 6,000 kWh / day, about 2,600 kWh / day to about 4,200 kWh / day, about 2,600 kWh / day to about 6,000 kWh / day, or about 4,200 kWh / day to about 6,000 kWh / day. In some cases, the HRS energy production capability comprises between about 0 kWh / day, about 4 kWh / day, about 8 kWh / day, about 10 kWh / day, about 20 kWh / day, about 30 kWh / day, about 60 kWh / day, about 100 kWh / day, about 1,000 kWh / day, about 2,600 kWh / day, about 4,200 kWh / day, or about 6,000 kWh / day. In some cases, the HRS energy production capability comprises between about at least about 0 kWh / day, about 4 kWh / day, about 8 kWh / day, about 10 kWh / day, about 20 kWh / day, about 30 kWh / day, about 60 kWh / day, about 100 kWh / day, about 1,000 kWh / day, about 2,600 kWh / day, or about 4,200 kWh / day. In some cases, the HRS energy production capability comprises between about at most about 4 kWh / day, about 8 kWh / day, about 10 kWh / day, about 20 kWh / day, about 30 kWh / day, about 60 kWh / day, about 100 kWh / day, about 1,000 kWh / day, about 2,600 kWh / day, about 4,200 kWh / day, or about 6,000 kWh / day.

[0288] The systems disclosed herein may improve over systems in the art by providing, in some cases, a Free Piston Stirling Engine (FPSE) configured to provide various benefits, including integration into a system where heat is generated (like a data center using immersion cooling) and extraction of heat from various immersion fluid streams (e.g., heated dielectric fluids, hot liquids, or other low-temperature heat streams), high efficiency, low maintenance, low noise, small space occupation, ease of integration, high power, fuel flexibility, cost saving, durability, regulatory and incentive opportunities, and scalability.

[0289] In some cases, the FPSE may be specifically configured for heat recovery from low temperature heat sources (e.g., below 230°C).

[0290] In some cases, the FPSE is configured for heat recovery in applications like data centers.

[0291] FIG. 1 shows a Free Piston Stirling Engine (FPSE). In FIG. 1, an exemplary FPSE 101 is shown. The FPSE 101 may comprise an improved thermodynamic heat engine 101. In some cases, the FPSE 101 comprises a first heat exchanger 102 and a second heat exchanger 103.

[0292] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, a FPSE configured to provide various benefits, including advanced materials with a maximized thermal conductivity, and maximized durability.

[0293] In some cases, the advanced materials with a maximized thermal conductivity comprise nano-structured substances. In some instances, a surface treatment may comprise the nano- structed substance. In some instances, the nano-structured substance may comprise A12O3. In some cases, the nano-structured substance may be introduced at an inlet to an enclosure. In some instances, the inlet to the enclosure may comprise an immersion fluid stream at an entry to a hot cylinder. In some instances, the nano-structured substance may be configured to increase heat transfer with a topology improved heat exchanger. For example, a magnetic filter may separate that nanoparticle at the discharge of enclosure wherein the immersion fluid (e.g., dielectric fluid) exits the enclosure. In further examples, the nanofluid may be reused for a new cycle. In some instances, the nano-structures substances comprise a thermal conductivity between about 0.15 W / mK and about 400 W / mK at room temperature and room pressure. In some instances, the nano-structures substances comprise a thermal conductivity of greater than about 400 W / mK at room temperature and room pressure. In some cases, the advanced materials with a maximized thermal conductivity comprise composites. In some cases, the advanced materials with a high thermal conductivity comprise alloys. In some cases, the advanced materials comprise a thermal conductivity of up to about 400 W / mK.

[0294] FIG. 2 shows a Free Piston Stirling Engine (FPSE). In FIG. 2, an FPSE 200 is shown.The FPSE 200 may comprise an improved thermodynamic heat engine 200. The FPSE 200 may comprise a housing 209. In some cases, the housing 209 comprises a first end 207. In some cases, the housing 209 comprises a second end 208. In some cases, the first end 207 of the housing 209 comprises a location vertically adjacent the second end 208 of the housing 209. In some cases, the first end 207 of the housing 209 comprises a location parallel adjacent to the second end 208 of the housing 209. In some cases, the first end 207 of the housing 209 comprises a location horizontally adjacent to the second end 208 of the housing 209. The FPSE 200 may comprise a middle section of the housing 209. In some cases, the middle section of the housing 209 comprises a location positioned between the first end 207 of the housing 209 and the second end 208 of the housing. In some cases, the middle section of the housing 209 comprises a location vertically adjacent to both the first end 207 of the housing 209 and the second end 208 of thehousing. In some cases, the middle section of the housing 209 comprises a location parallel adjacent to both the first end 207 of the housing 209 and the second end 208 of the housing. In some cases, the middle section of the housing 209 comprises a location horizontally adjacent to both the first end 207 of the housing 209 and the second end 208 of the housing. The FPSE 200 may comprise a displacer 206 positioned within the housing 209. In some cases, the first end 207 of the housing 209 and the second end 208 of the housing 209 may be positioned along a displacement axis 210 of the housing 209. In some instances, the first end 207 and the second end 208 are separated by a travel length. In some cases, the displacer 206 is reciprocally movable within the housing 209 along the displacement axis 210 and over at least a portion of the travel length. In some instances, the displacement axis 210 may comprise a travel length of the displacer. In further examples, the first end 207 and the second end 208 are separated by the travel length of the displacer. The FPSE 200 may comprise a heating head 203 disposed within the housing 209. In some cases, the first end 207 of the housing 209 comprises the heating head 203. In some cases, the second end of the housing 209 comprises the heating head 203. In some cases, a middle section of the housing 209 comprises the heating head 203. The FPSE 200 may comprise a regenerator 202 disposed within the housing 209. In some cases, the middle section of the housing 209 comprisesthe regenerator 202. In some cases, the first end 207 of the housing 209 comprises the regenerator 202. In some cases, the second end 208 of the housing 209 comprises the regenerator 202. The FPSE 200 may comprise a power piston 211 disposed within the housing 209. In some cases, the power piston 211 is positioned to apply a force to the displacer 206 in a proximal direction of the housing 209. In some cases, the second end 208 of the housing 209 comprisesthe power piston 211. In some cases, the first end 207 of the housing 209 comprises the power piston 211. In some cases, the middle section of the housing 209 comprises the power piston 211. The FPSE 200 may comprise a cooling head 201 disposed within the housing 209. In some cases, the second end 208 of the housing 209 comprises the cooling head 201. In some cases, the first end 207 of the housing 209 comprises the cooling head 201. In some cases, the middle section of the housing 209 comprises the cooling head 201.

[0295] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, a Free Piston Stirling Engine (FPSE) configured to provide various benefits, including an ability to operate at low temperature differentials (e.g., less than about 30°C), utilize heat from low grade temperature streams (e.g., providing flexibility in heat stream selection), maximize efficiency at low temperature differentials (e.g., between heat source and heat sink), minimize thermal stress on engine components, and minimize operating costs.

[0296] The FPSE may be configured to operate under low-temperature differentials between a heat source and a heat sink. In some cases, the heat source comprises a heating head. In some instances, the heating head is configured to receive heat from an immersion fluid stream. For example, the immersion fluid stream may comprise a heated dielectric fluid (e.g., from a data center). In even further examples, the temperature of the heating head may comprise about the temperature of the immersion fluid stream (e.g., below about 80°C).

[0297] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, a FPSE configured to provide various benefits, including operating at low temperatures (e.g., below 230°C).

[0298] FIG. 8 illustrates an example of a Free Piston Stirling Engine. In the example of FIG. 8, the FPSE 800 comprises a hot cylinder 807. The hot cylinder 807 may comprise a heated working fluid. In some cases, the working fluid may be heated by a heating head 801. In some instances, the working fluid in the hot cylinder 807 comprises a temperature of between about 75°C to about 80°C. In some instances, the working fluid in the hot cylinder 807 comprises a temperature of up to about 75°C. In some instances, the working fluid in the hot cylinder 807 comprises a temperature of greater than about 75°C. For example, the working fluid in the hot cylinder 807 comprises a temperature of up to about 230°C. In the example of FIG. 8, the FPSE 800 comprises a cold cylinder 806. The cold cylinder 806 may comprise a cooled working fluid. In some instances, the cooled working fluid may be cooled by a cooling head 802. In some instances, the working fluid in the cold cylinder 806 comprises a temperature of between about 5°C to about 12°C. In some instances, the working fluid in the cold cylinder 806 comprises a temperature of about 10°C. In some instances, the working fluid in the cold cylinder 806 comprises a temperature of up to about 10°C. In some instances, the working fluid in the cold cylinder 806 comprises a temperature of greater than about 10°C. In the example of FIG. 8, the FPSE 800 comprises a regenerator 803. The regenerator 803 maybe configured to release heat or remove heat from a working fluid. In some instances, the regenerator comprises a temperature of between about 40°C to about 60°C. In some instances, the regenerator comprises a temperature of up to about 60°C. In some instances, the regenerator comprises a temperature of greater than 60°C. In some cases, the heat sink comprises a cooling head. In some instances, the cooling head comprises a water jacket. In some instances, the cooling head is configured to release heat to an environment. In even further examples, the temperature of the cooling head may comprise a temperature up to about 15°C. In even further examples, the temperature of the cooling head may comprise a temperature of between about 5°C to about 7°C. In even further examples, thetemperature of the cooling head may comprise a temperature of between about 12°C to about 15°C.

[0299] In some cases, the FPSE is configured to operate under a temperature differential of less than about 500°C. In some cases, the FPSE is configured to operate under a temperature differential of less than about 60°C. In some cases, the FPSE is configured to operate under a temperature differential of less than about 30°C. In some cases, the FPSE is configured to operate under a temperature differential between about 0°C to about 500°C. In some cases, the FPSE is configured to operate under a temperature differential between about 0°C to about 10°C, about 0°C to about 20°C, about 0°C to about 30°C, about 0°C to about 40°C, about 0°C to about 50°C, about 0°C to about 60°C, about 0°C to about 70°C, about 0°C to about 80°C, about 0°C to about 100°C, about O°C to about 250°C, about 0°C to about 500°C, about 10°C to about 20°C, about 10°C to about 30°C, about 10°C to about 40°C, about 10°C to about 50°C, about 10°C to about 60°C, about 10°C to about 70°C, about 10°C to about 80°C, about 10°C to about 100°C, about 10°C to about 250°C, about 10°C to about 500°C, about 20°C to about 30°C, about 20°C to about 40°C, about 20°C to about 50°C, about 20°C to about 60°C, about 20°C to about 70°C, about 20°C to about 80°C, about 20°C to about 100°C, about 20°C to about 250°C, about 20°C to about 500°C, about 30°C to about 40°C, about 30°C to about 50°C, about 30°C to about 60°C, about 30°C to about 70°C, about 30°C to about 80°C, about 30°C to about 100°C, about 30°C to about 250°C, about 30°C to about 500°C, about 40°C to about 50°C, about 40°C to about 60°C, about 40°C to about 70°C, about 40°C to about 80°C, about 40°C to about 100°C, about 40°C to about 250°C, about 40°C to about 500°C, about 50°C to about 60°C, about 50°C to about 70°C, about 50°C to about 80°C, about 50°C to about 100°C, about 50°C to about 250°C, about 50°C to about 500°C, about 60°C to about 70°C, about 60°C to about 80°C, about 60°C to about 100°C, about 60°C to about 250°C, about 60°C to about 500°C, about 70°C to about 80°C, about 70°C to about 100°C, about 70°C to about 250°C, about 70°C to about 500°C, about 80°C to about 100°C, about 80°C to about 250°C, about 80°C to about 500°C, about 100°C to about 250°C, about 100°C to about 500°C, or about 250°C to about 500°C. In some cases, the FPSE is configured to operate under a temperature differential between about 0°C, about 10°C, about 20°C, about 30°C, about 40°C, about 50°C, about 60°C, about 70°C, about 80°C, about 100°C, about 250°C, or about 500°C. In some cases, the FPSE is configured to operate under a temperature differential between at least about 0°C, about 10°C, about 20°C, about 30°C, about 40°C, about 50°C, about 60°C, about 70°C, about 80°C, about 100°C, or about 250°C. In some cases, the FPSE is configured to operate under a temperature differential between at most about10°C, about 20°C, about 30°C, about 40°C, about 50°C, about 60°C, about 70°C, about 80°C, about 100°C, about 250°C, or about 500°C.

[0300] The FPSE may be configured to maintain up to about a 45% efficiency at low temperature differentials. In some cases, the FPSE is configured to maintain up to about 45% efficiency at temperature differentials between about 0°C to about 500°C. In some cases, the FPSE is configured to maintain up to about 45% efficiency at temperature differentials between about 0°C to about 10°C, about 0°C to about 20°C, about 0°C to about 30°C, about 0°C to about 40°C, about 0°C to about 50°C, about 0°C to about 60°C, about 0°C to about 70°C, about 0°C to about 80°C, about 0°C to about 100°C, about 0°C to about 250°C, about 0°C to about 500°C, about 10°C to about 20°C, about 10°C to about 30°C, about 10°C to about 40°C, about 10°C to about 50°C, about 10°C to about 60°C, about 10°C to about 70°C, about 10°C to about 80°C, about 10°C to about 100°C, about 10°C to about 250°C, about 10°C to about 500°C, about 20°C to about 30°C, about 20°C to about 40°C, about 20°C to about 50°C, about 20°C to about 60°C, about 20°C to about 70°C, about 20°C to about 80°C, about 20°C to about 100°C, about 20°C to about 250°C, about 20°C to about 500°C, about 30°C to about 40°C, about 30°C to about 50°C, about 30°C to about 60°C, about 30°C to about 70°C, about 30°C to about 80°C, about 30°C to about 100°C, about 30°C to about250°C, about30°C to about 500°C, about40°C to about 50°C, about 40°C to about 60°C, about 40°C to about 70°C, about 40°C to about 80°C, about 40°C to about 100°C, about 40°C to about 250°C, about 40°C to about 500°C, about 50°C to about 60°C, about 50°C to about 70°C, about 50°C to about 80°C, about 50°C to about 100°C, about 50°C to about 250°C, about 50°C to about 500°C, about 60°C to about 70°C, about 60°C to about 80°C, about 60°C to about 100°C, about 60°C to about 250°C, about 60°C to about 500°C, about 70°C to about 80°C, about 70°C to about 100°C, about 70°C to about 250°C, about 70°C to about 500°C, about 80°C to about 100°C, about 80°C to about 250°C, about 80°C to about 500°C, about 100°C to about 250°C, about 100°C to about 500°C, or about 250°C to about 500°C. In some cases, the FPSE is configured to maintain up to about a 60% efficiency at temperature differentials between about 0°C, about 10°C, about 20°C, about 30°C, about 40°C, about 50°C, about 60°C, about 70°C, about 80°C, about 100°C, about 250°C, or about 500°C. In some cases, the FPSE is configured to maintain up to about a 60% efficiency at temperature differentials between at least about 0°C, about 10°C, about 20°C, about30°C, about40°C, about 50°C, about 60°C, about 70°C, about 80°C, about 100°C, or about 250°C. In some cases, the FPSE is configured to maintain up to about a 60% efficiency at temperature differentials between at most about 10°C, about 20°C, about 30°C, about 40°C, about 50°C, about 60°C, about 70°C, about 80°C, about 100°C, about 250°C, or about 500°C.

[0301] In some cases, the FPSE efficiency comprisesbetween about 0% to about 100%. In some cases, the FPSE efficiency comprises between about 0% to about 5%, about 0% to about 10%, about 0% to about 15%, about 0% to about 20%, about 0% to about 25%, about 0% to about 30%, about 0% to about 35%, about 0% to about 40%, about 0% to about 45%, about 0% to about 50%, about 0% to about 100%, about 5% to about 10%, about 5% to about 15%, about 5% to about 20%, about 5% to about 25%, about 5% to about 30%, about 5% to about 35%, about 5% to about 40%, about 5% to about 45%, about 5% to about 50%, about 5% to about 100%, about 10% to about 15%, about 10% to about 20%, about 10% to about 25%, about 10% to about 30%, about 10% to about 35%, about 10% to about 40%, about 10% to about 45%, about 10% to about 50%, about 10% to about 100%, about 15% to about 20%, about 15% to about 25%, about 15% to about 30%, about 15% to about 35%, about 15% to about 40%, about 15% to about 45%, about 15% to about 50%, about 15% to about 100%, about 20% to about 25%, about 20% to ab out 30 % , ab out 20 % to ab out 35 %, ab out 20 % to ab out 40 % , ab out 20 % to ab out 45 % , ab out 20% to about 50%, about 20% to about 100%, about 25% to about 30%, about 25% to about 35 % , ab out 25 % to ab out 40 %, ab out 25 % to ab out 45 %, ab out 25 % to ab out 50% , ab out 25 % to about 100%, about 30% to about 35%, about 30% to about 40%, about 30% to about 45%, about 30% to about 50%, about 30% to about 100%, about 35% to about 40%, about 35% to about 45%, about 35% to about 50%, about 35% to about 100%, about 40% to about 45%, about 40% to about 50%, about40%to about 100%, about45%to about 50%, about45%to about 100%, or about 50% to about 100%. In some cases, the FPSE efficiency comprises between about 0%, about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, about 45%, about 50%, or about 100%. In some cases, the FPSE efficiency comprises between at least about 0%, about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, about 45%, or about 50%. In some cases, the FPSE efficiency comprises between at most about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, about 45%, about 50%, or about 100%.

[0302] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, a heat exchanger which may be configured based on generative topology optimization configured to provide various benefits, including uniform heat flux distribution across the hot and cold cylinders for a maximized efficiency heat transfer process with minimum pressure drop. In some cases, the heat exchangers comprise a architecture configured for improved efficiency of heat transfer process at low temperature differentials (e.g., below 30°C). In some cases, the FPSE comprises a heat exchanger. In some cases, the FPSE comprises a plurality of heat exchangers.

[0303] FIG. 2 illustrates an example of a Free Piston Stirling Engine. The FPSE 200 may comprise a first heat exchanger 205. In some cases, the first heat exchanger 205 may comprise a heating head 203 and a plurality of fins. In some cases, the first heat exchanger 205 may comprise at least of portion of displacer 206. In some cases, the at least a portion of displacer 206 may comprise a hot tip. In some cases, the heating head 203 is positioned at the second end 208 of the housing 209. In some cases, the heating head 203 is positioned adjacent to the displacer 206. For example, the heating head 203 may be positioned adjacent to a hot cylinder. In further examples, the heating head 203 may be positioned adjacent to a hot tip. The FPSE 200 may comprise a second heat exchanger 204. In some cases, the second heat exchanger 204 may comprise a cooling head 201 and a plurality of fins. In some cases, the second heat exchanger 205 may comprise at least of portion of displacer 206. In some cases, the at least a portion of displacer 206 may comprise a cold tip or cold cylinder. In some cases, the cooling head 201 is positioned at the first end 207 of the housing 209. In some cases, the cooling head 201 is positioned adjacent to the displacer 206. For example, the cooling head 201 may be positioned adjacentto a cold tip. In further examples, the coolinghead 201 may be positioned adjacent to a cold cylinder. The FPSE 200 may comprise a third heat exchanger 202. In some cases, the third heat exchanger 202 may comprise a regenerator 202 and a plurality of fins. In some cases, the third heat exchanger 202 may comprise at least of portion of displacer 206. In some cases, at least the portion of displacer 206 may comprise an intermediate displacer section. For example, the intermediate displacer section may comprise a position between the cold tip and the hot tip. In some cases, the regenerator 202 is positioned between a first end 207 of the housing 209 and a second end 208 of housing 209. In some cases, the regenerator 202 is positioned adjacent to the displacer 206. For example, the regenerator 202 may be positioned adjacent to the intermediate displacer section. In some cases, the regenerator 202 is positioned between the first heat exchanger 205 and the second heat exchanger 204. In some instances, the regenerator 202 is positioned between the heating head 203 and the cooling head 201 .

[0304] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, a heat transfer process configured to provide various benefits, including efficiently managing thermal gradients in the FPSE hot cylinder, cold cylinder, and regenerator. Thermal gradient may comprise a rate of change of temperature within a component of the FPSE. In some cases, thermal gradient may comprise a rate of change of temperature within the hot cylinder. In some cases, thermal gradient may comprise a rate of change of temperature within the cold cylinder. In some cases, thermal gradient may comprise a rate of change of temperature within the regenerator. In some instances, the hot cylindercomprises the area wherein the working fluid is heated. In some instances, the cold cylinder comprises the area wherein the working fluid is cooled. In some instances, the regenerator comprises the area wherein the working fluid travels from the hot cylinder to the cold cylinder (e.g., and vice-versa). The heat exchangers disclosed herein may be configured to minimize a pressure drop between the hot cylinder and the cold cylinder.

[0305] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, heat exchanger materials configured to provide various benefits, including maximized thermal conductivity for efficient heat transfer, corrosion resistance to withstand various types of fluids, maximized mechanical properties for durability and pressure tolerance, ease of manufacturing and maintenance for practicality, and costeffectiveness for economic feasibility. The heat exchangers disclosed herein may be constructed using additive manufacturing techniques and advanced materials with a maximized thermal conductivity and durability. In some cases, the advanced materials with a maximized thermal conductivity comprise nano-structured substances. In some instances, a surface treatment may comprise the nano-structed substance. In some instances, the nano-structured substance may comprise A12O3. In some cases, the nano-structured substance may be introduced at an inlet to an enclosure. In some instances, the inlet to the enclosure may comprise an immersion fluid stream at an entry to a hot cylinder. In some instances, the nano-structured substance may be configured to increase heat transfer with a topology improved heat exchanger. For example, a magnetic filter may separate a nanoparticle at the discharge of enclosure where the immersion fluid (e.g., dielectric fluid) exits the enclosure. In further examples, a nanofluid maybe reused for a new cycle. In some instances, the nano-structures substances comprise a thermal conductivity between about 0. 15 W / mK and about 400 W / mK at room temperature and room pressure. In some instances, the nano-structures substances comprise a thermal conductivity of greater than about 400 W / mK at room temperature and room pressure. In some cases, the advanced materials with a maximized thermal conductivity comprise composites. In some cases, the advanced materials with a high thermal conductivity comprise alloys. In some cases, the advanced materials comprise a thermal conductivity of up to about 400 W / mK.

[0306] The heat exchangers disclosed herein may comprise conventional, unconventional, or complex geometries. In some cases, the heat exchangers comprise complex geometries (e.g., shown in FIG. 3, FIG. 4, FIG. 5, and FIG. 7). In some cases, the heat exchanger architecture comprises an organic form heat exchanger. In some cases, the organic form heat exchanger comprises a topology improved heat exchanger. For example, the heat exchanger may be topology improved utilizing advanced computational fluid dynamics simulations and adjointmethodology. In some cases, the heat exchanger comprises a topology improved width. In some instances, the heat exchanger comprises a topology improved exterior width. In some instances, the heat exchanger comprises a topology improved interior width. In some cases, the heat exchanger comprises a topology improved length. In some instances, the heat exchanger comprises a topology improved exterior length. In some instances, the heat exchanger comprises a topology improved interior length. In some cases, the heat exchanger comprises a topology improved depth. In some instances, the heat exchanger comprises a topology improved exterior depth. In some instances, the heat exchanger comprises a topology improved interior depth. In some cases, the heat exchanger comprises a topology improved area. In some cases, the heat exchanger comprises an inner layer and an outer layer. In some instances, the inner layer comprises a cooling head, regenerator, heating head, power piston, displacer, and a working fluid. In some instances, the inner layer comprises a plurality of fins. In some instances, the heat exchanger inner layer comprises an organic shape. For example, the organic shape may comprise a shape configured to maximize heat transfer and minimize pressure loss. In some instances, the heat exchanger inner layer comprises topology improved dimensions. In some instances, the outer layer comprises an external housing and a plurality of fins. In some instances, the outer layer comprises a cooling head, regenerator, heating head, power piston, displacer, and a working fluid. In some instances, the heat exchanger outer layer comprises an organic shape. In some instances, the heat exchanger outer layer comprises topology improved dimensions.

[0307] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, heat exchanger surface treatments configured to provide various benefits, including maximized heat transfer, maximized resistance to corrosion, minimized fouling, and maximized fluid dynamics. The heat exchangers disclosed herein may comprise a surface treatment on the outer layer or inner layer. In some cases, the heat exchangers comprise surface morphology changes. In some instances, the surface treatment may comprise epoxy coating (e.g., for corrosion resistance), nickel plating (e.g., for durability), anodizing (e.g., for aluminum heat exchangers), ceramic coating for heat resistance, electroless nickel plating for hardness and longevity, and PTFE (e.g., Teflon®) coating (e.g., for high-temperature and chemical resistance applications). In some cases, the surface treatment may be configured to reduce fouling. In some instances, the surface treatment may be configured to prevent fouling. In some cases, the surface treatment may be configured to increase resistance to corrosion. In some instances, the surface treatment may be configured to prevent corrosion. In some cases, the surface treatment may be configured to maximize a heat transfer surface area. In some cases, thesurface treatment may be configured to increase a heat transfer rate. In some cases, the surface treatment may be configured to reduce pressure drop.

[0308] In some cases, the formula for calculating the heat exchanger effectiveness comprises equation 2:Eff = 'OUT.C ~ Tin.c) / (Tin,H- Tin,c) (Equation 2)

[0309] In equation 2, “Eff’ comprises heat exchanger effectiveness, “Tout,C” comprises the final temperature of the cold fluid, “Tin,C” comprises the initial temperature of the cold fluid, and “Tin,H” comprises the initial temperature of the hot fluid.

[0310] The heat exchangers disclosed herein may be configured to maximize efficiency under varying external heat stream conditions. The heat source may comprise the heating head. In some cases, the heating head comprises a temperature below about 80°C. In some instances, the heating head is configured to receive an immersion fluid stream. For example, the immersion fluid stream comprises a heated dielectric fluid. In further examples, the immersion fluid may comprise immersion fluid gases, hot liquids, or other low-temperature heat streams. In even further examples, the immersion fluid stream comprises a temperature below about 80°C. In even further examples, the immersion fluid stream comprises a temperature below about 230°C. In some cases, the formula for calculating the heat exchanger efficiency comprises equation 2 (e.g., previously defined). In some cases, Tin,H comprises an initial temperature of a hot fluid. In some cases, Tout,H = final temperature of the hot fluid. In some cases, Tin,C = initial temperature of the cold fluid. In some cases, the hot fluid comprises a temperature between about 75°C and about 80°C. In some cases, the cold fluid comprises a temperature between about 5°C and about 12°C. For example, the heat exchanger may comprise up to about 45% efficiency. In some cases, the heat exchanger efficiency comprises between about 0% to about 100%. In some cases, the heat exchanger efficiency comprises between about 0% to about 5%, about 0% to about 10%, about 0% to about 15%, about 0% to about 20%, about 0% to about 25%, about 0% to about 30%, about 0% to about 35%, about 0% to about 40%, about 0% to about 45%, about 0% to about 50%, about 0% to about 100%, about 5% to about 10%, about 5% to about 15%, about 5% to about 20%, about 5% to about 25%, about 5% to about 30%, about 5% to about 35%, about 5% to about 40%, about 5% to about 45%, about 5% to about 50%, about 5% to about 100%, about 10% to about 15%, about 10% to about 20%, about 10% to about 25%, about 10% to about 30%, about 10% to about 35%, about 10% to about 40%, about 10% to about 45%, about 10% toabout 50%, about 10% to about 100%, about 15% to about 20%, about 15% to about 25%, about 15% to about 30%, about 15% to about 35%, about 15% to about 40%, about 15% to about 45%, about 15% to about 50%, about 15% to about 100%, about 20% to about 25%, about 20% to ab out 30 % , ab out 20 % to ab out 35 %, ab out 20 % to ab out 40 % , ab out 20 % to ab out 45 % , ab out 20% to about 50%, about 20% to about 100%, about 25% to about 30%, about 25% to about 35 % , ab out 25 % to ab out 40 %, ab out 25 % to ab out 45 %, ab out 25 % to ab out 50% , ab out 25 % to about 100%, about 30% to about 35%, about 30% to about 40%, about 30% to about 45%, about 30% to about 50%, about 30% to about 100%, about 35% to about 40%, about 35% to about 45%, about 35% to about 50%, about 35% to about 100%, about 40% to about 45%, about 40% to about 50%, about40%to about 100%, about45%to about 50%, about45%to about 100%, or about 50% to about 100%. In some cases, the heat exchanger efficiency comprises between about 0%, about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, about 45%, about 50%, or about 100%. In some cases, the heat exchanger efficiency comprises between at least about 0%, about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, about 45%, or about 50%. In some cases, the heat exchanger efficiency comprises between at most about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, about 45%, about 50%, or about 100%.

[0311] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, a plurality of fins configured to provide various benefits, including an organic layout and structure to maximize heat dissipation and thermal efficiency. The heat exchangers disclosed herein may comprise fin-type heat exchangers. In some cases, the fin-type heat exchangers comprise a plurality of fins. In some cases, the plurality of fins comprises a plurality of organic fins a varying size, shape, and distribution. In some cases, the plurality of organic fins is configured to maximize the efficiency of thermal pathways. The heat exchangers disclosed herein may comprise an outer layer (e.g., external surface). In some cases, the outer layer of the heat exchanger may comprise the plurality of fins. In some instances, the plurality of fins is configured to contact an ambient environment. For example, a working fluid may transfer heat to the plurality of fins. In further examples, the plurality of fins may transfer heat to an ambient environment. In some instances, the plurality of fins is configured to contact a heat stream. For example, a heated immersion fluid may transfer heat to the plurality of fins. In further examples, the plurality of fins may transfer heat to a heating head. The plurality of fins disclosed herein may comprise a architecture from an iterative manner that mimics an evolutionlike processes. In some cases, the plurality of fins architecture stems from generative topology optimization. In some instances, the plurality of fins comprise a plurality of topology improvedorganic fins (e.g., topology improved fins). In some cases, the plurality of fins comprises an organic shape. In some instances, the organic shape comprises any shape configured to efficiently transfer heat from a heat source to a working fluid (e.g., on a hot side of the engine). In some instances, the organic shape comprises any shape configured to efficiently transfer heat from a working fluid to a cooling source (e.g., on a cold side of the engine). In some instances, the organic shape comprises any shape configured to maximize a contact surface area between the working fluid and the plurality of fins. In some instances, the plurality of fins comprise a shape or cross section comprising a circle, equilateral triangle, isosceles triangle, scalene triangle, right triangle, square, rectangle, pentagon, hexagon, heptagon, octagon, nonagon, decagon, parallelogram, rhombus, trapezoid, oval, star, heart, crescent, sphere, cube, cylinder, cone, square pyramid, triangular pyramid, rectangular prism, triangular prism, hexagonal prism, tetrahedron, octahedron, dodecahedron, icosahedron, torus, hemisphere, or ellipsoid.

[0312] FIG. 3 shows a Free Piston Stirling Engine Heat Exchanger. In the example of FIG. 3, a first encasement 301 from the first heat exchanger 102 from the FPSE 101 of FIG. 1 is shown. In FIG. 3, the first encasement 301 comprises a plurality of fins 302. In FIG. 3, the plurality of fins 302 comprises one or more organic fins. For example, the one or more organic fins 302 may comprise a cylindrical shape. In FIG. 3, the plurality of fins comprises a spacing between one fin to another fin. Furthermore, in the example of FIG. 3, the plurality of fins comprises layers of fins. For example, in FIG. 3, the first encasement 301 comprises about 9 layers of organic fins. Moreover, the first encasement 301 comprises an external cooling head.

[0313] FIG. 4 shows a Free Piston Stirling Engine Heat Exchanger. In the example of FIG. 4, a second encasement 401 from the second heat exchanger 103 from the FPSE 101 of FIG. 1 is shown. In FIG. 4, the second encasement 401 comprises a plurality of fins 402. In FIG. 4, the plurality of fins 402 comprises one or more organic fins. For example, the one or more organic fins 402 may comprise a rectangular shape. In FIG. 4, the plurality of fins comprises a spacing between one fin to another fin. For example, the spacing may comprise a plurality of recessed rectangles. Furthermore, in the example of FIG. 4, the plurality of fins comprises layers of fins. For example, in FIG. 4, the second encasement 401 comprises about 9 layers of organic fins. Moreover, the second encasement 401 comprises an external heating head.

[0314] The heat exchangers disclosed herein may comprise a plurality of fins organically distributed for effective heat storage. In some cases, the plurality of fins is configured to store heat from a heat stream and release heat to the heating head. In some instances, the organic distribution of the plurality of fins is configured to maximize a contact surface area between the immersion fluid stream and the plurality of fins. In some instances, the organic distribution of theplurality of fins is configured to maximize a contact surface areabetween the plurality of fins and the heating head. The plurality of fins may comprise a maximized thermal mass configured for efficient heat storage. The heat exchangers disclosed herein may comprise a plurality of fins organically distributed for effective heat release. In some cases, the plurality of fins is configured to receive heat from a cooling head and release heat to the environment. In some instances, the organic distribution of the plurality of fins is configured to maximize a contact surface area between the environment and the plurality of fins. In some instances, the organic distribution of the plurality of fins is configured to maximize a contact surface area between the plurality of fins and the cooling head. The plurality of fins may comprise a maximized fin surface area configured for efficient heat release. In some cases, the plurality of fins may comprise a maximized fin thickness configured for efficient heat release. In some cases, the plurality of fins may comprise a maximized fin length configured for efficient heat release. In some cases, the plurality of fins may comprise a maximized fin width configured for efficient heat release.

[0315] The plurality of fins disclosed herein may comprise a bounding envelope size configured to provide maximized heat storage or maximized heat release. In some cases, the bounding envelope size comprises the physical dimensions within which each fin of the plurality of fins must fit. In some instances, each fin of the plurality of fins comprises a topology improved bounding envelope size. The plurality of fins disclosed herein may comprise a hierarchical arrangement of fins of different spacings allowed to enhance heat dissipation or heat storage. In some cases, the spacing comprises a distance between two adjacent fins. In some instances, the spacing between fins throughout the heat exchanger is uniform. For example, each fin in the plurality of fins may comprise an equidistant spacing between each fin. In some instances, the spacing throughout the heat exchanger is variable. For example, each fin in the plurality of fins may comprise a different distance spacing between each fin as between some or all other fins.

[0316] The plurality of fins may be disposed within a heat exchanger. FIG. 7 shows a Free Piston Stirling Engine Heat Exchanger. In the example of FIG. 7, a second encasement 701 from the second heat exchanger 204 from the FPSE 200 of FIG. 2 is shown. In FIG. 7, the second encasement 701 comprises a plurality of fins 702. In FIG. 7, the plurality of fins 702 comprises one or more organic fins. For example, the one or more organic fins 702 may comprise a porous material. In further examples, the porous material may comprise wire mesh, foil (e.g., made from copper, steel, nickel, etc.). Moreover, the second encasement 701 comprises an internal heating head. In FIG. 7, the plurality of fins 702 may comprise a plurality of sizes. For example, one organic fin may comprise a diameter less than another organic fin. Furthermore, the plurality of fins may comprise a pattern. For example, an organic fin may comprise a diameter less or morethan an adjacent organic fin around a circumference of a heat exchanger. In further examples, the plurality of fins comprises a topology improved diameter.

[0317] The plurality of fins disclosed herein may comprise a hierarchical arrangement of fins of different sizes configured to maximize heat dissipation and maximize heat exchanger efficiency. In some cases, the hierarchical arrangement of fins comprises an organic distribution of fins. In some instances, the organic distribution comprises non-uniform or varied architecture patterns in the placement, distribution, or sizing of the fins (e.g., mimicking natural or “organic” systems).

[0318] FIG. 5 shows a Free Piston Stirling Engine Heat Exchanger. In the example of FIG. 5, a first encasement 501 from the first heat exchanger 205 from the FPSE 200 of FIG. 2 is shown. In FIG. 5, the first encasement 501 comprises a plurality of fins 502. In FIG. 5, the plurality of fins 502 comprises one or more organic fins. For example, the one or more organic fins 502 may comprise a length equivalent to a length of the first encasement 501 . Moreover, the first encasement 501 comprises an internal cooling head.

[0319] The plurality of fins may comprise a distribution configured for maximum heat flux. In some cases, the plurality of fins may comprise an organic distribution configured for uniform temperature distribution. In some cases, the organic distribution maximizes surface area. In some instances, the plurality of fins may comprise organic fins. For example, the organic fins may comprise a topology improved surface area.

[0320] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, fin materials configured to provide various benefits, including maximized thermal conductivity for efficient heat transfer, maximized corrosion resistance to withstand various types of fluids, maximized mechanical properties for durability and pressure tolerance, ease of manufacturing and maintenance for practicality, and costeffectiveness for economic feasibility. In some cases, the fin material comprises nano-structured substances, composites, or alloys. In some cases, the fin material comprises copper. In some cases, the fin material comprises aluminum. In some cases, the plurality of fins comprises any material comprising a thermal conductivity up to about 205 W / mK at room temperature and room pressure.

[0321] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, a Free Piston Stirling Engine (FPSE) configured to provide various benefits, includingthe topology optimize heating head (e.g., referred to as heating head or heat source) configured to transfer heat from a heat stream to a working fluid inside the FPSE. The FPSE 200 may comprise a heating head 203 configured to add thermal energy to a workingfluid. In some cases, the working fluid is in thermal contact with the heating head 203. In some cases, the heating head is configured to add an improved amount of heat to the working fluid.

[0322] FIG. 9 shows a Free Piston Stirling Engine. In some cases, the FPSE 900 comprises a topology improved heating head 901 . In some cases, the topology improved heating head 901 is configured to add heat to a working fluid. In some cases, the topology improved heating head 901 may be configured to maintain isothermal conditions as a working fluid expands and pressure decreases. The heating heads disclosed herein may comprise a architecture from an iterative manner that mimics an evolution-like processes. In some cases, the heating head architecture stems from generative topology optimization. In some cases, the heating head comprises an organic shape. In some cases, the organic shape comprises any shape configured to efficiently transfer heat from a heat source to a working gas (e.g., on a hot side of the engine). In some cases, the organic shape comprises any shape configured to efficiently transfer heat from a plurality of fins to a working gas (e.g., on a hot side of the engine). In some cases, the organic shape comprises any shape configured to maximize a contact surface area between the working gas and the heating head. In some instances, the contact surface area between the working gas and the heating head comprises a topology improved contact surface area. In some cases, the organic shape comprises any shape configured to maximize a contact surface area between the heating head and a plurality of fins. In some instances, the contact surface area between the heating head and the plurality of fins comprises a topology improved contact surface area. In some cases, the heating head comprises a shape or cross section comprising a circle, equilateral triangle, isosceles triangle, scalene triangle, right triangle, square, rectangle, pentagon, hexagon, heptagon, octagon, nonagon, decagon, parallelogram, rhombus, trapezoid, oval, star, heart, crescent, sphere, cube, cylinder, cone, square pyramid, triangular pyramid, rectangular prism, triangular prism, hexagonal prism, tetrahedron, octahedron, dodecahedron, icosahedron, torus, hemisphere, or ellipsoid. In some cases, the topology improved heating head 901 comprises a architecture of complex structures that may enhance heat transfer within the topology improved heating head 901 . For example, the topology improved heating head 901 is configured to increase efficiency of heat from the external heat source to the working fluid. For example, the efficiency transfer of heat from the external heat stream to the working fluid may comprise greater than 10%. In some cases, the topology improved heating head 901 is configured to maximize thermal performance of the FPSE. In some instances, the topology improved heating head 901 may comprise an improved internal structure. In further examples, the improved internal structure may comprise improved heat distribution. In even further examples, the topology improved heating head may comprise uniform temperature profiles (e.g., this, in turn, enhances thermalperformance of the FPSE). In some cases, the topology improved heating head 901 may comprise topology improved fins. In some instances, the topology improved fins may comprise topology improved internal fins. For example, the topology improved internal fins may be more efficient than conventional fins. In some instances, the topology improved fins may comprise topology improved external fins. For example, the topology improved external fins may be more efficient than conventional fins.

[0323] The heat exchangers disclosed herein may be configured to maximize heat transfer. In some cases, the heat exchangers are configured to ensure uniform heat flux distribution from a heat stream to a working fluid. In some cases, the heat exchangers are configured to maximize a uniform heat flux distribution from the heating head to the hot cylinder. In some cases, the heat exchanger comprises a topology improved surface to volume ratio. The heating heads disclosed herein may be configured to maximize efficiency under varying external heat stream conditions. In some cases, the heating head comprises a topology improved heating head 901 configured to maximize efficiency by minimizing thermal losses. In some instances, the topology improved heating head 901 is configured to maximize efficiency by maximizing the utilization of the heat from the external stream (e.g., heated immersion fluid). In some cases, the formula for calculating the heating head efficiency comprises equation 2. In some cases, Tin,H comprises an initial temperature of an immersion fluid stream. In some cases, Tout,H = final temperature of the immersion fluid stream. In some cases, Tin,C = initial temperature of the cold fluid (e.g., working fluid). In some cases, the immersion fluid stream comprises a temperature between about 75°C and about 80°C. In some cases, the working fluid comprises a temperature between about 75°C and about 80°C. For example, the heating head may comprise up to about 100% efficiency. In some cases, the heating head efficiency comprises between about 0% to about 100%. In some cases, the heating head efficiency comprises between about 0% to about 5%, about 0% to about 10%, about 0% to about 15%, about 0% to about 20%, about 0% to about 25%, about 0% to about 30%, about 0% to about 35%, about 0% to about 40%, about 0% to about 45%, about 0% to about 50%, about 0% to about 100%, about 5% to about 10%, about 5% to about 15%, about 5% to about 20%, about 5% to about 25%, about 5% to about 30%, about 5% to about 35%, about 5% to about 40%, about 5% to about 45%, about 5% to about 50%, about 5% to about 100%, about 10% to about 15%, about 10% to about 20%, about 10% to about 25%, about 10% to about 30%, about 10% to about 35%, about 10% to about 40%, about 10% to about 45%, about 10% to about 50%, about 10% to about 100%, about 15% to about 20%, about 15% to about 25%, about 15% to about 30%, about 15% to about 35%, about 15% to about 40%, about 15% to about 45%, about 15% to about 50%, about 15% to about 100%, about 20% toabout 25%, about 20% to about 30%, about 20% to about 35%, about 20% to about 40%, about 20% to about 45%, about 20% to about 50%, about 20% to about 100%, about 25% to about 30%, about 25% to about 35%, about 25% to about 40%, about 25% to about 45%, about 25% to about 50%, about 25% to about 100%, about 30% to about 35%, about 30% to about 40%, about 30% to about 45%, about 30% to about 50%, about 30% to about 100%, about 35% to about 40%, about 35% to about 45%, about 35% to about 50%, about 35% to about 100%, about 40% to about 45%, about 40% to about 50%, about 40% to about 100%, about 45% to about 50%, about 45% to about 100%, or about 50% to about 100%. In some cases, the heating head efficiency comprises between about 0%, about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about40%, about45%, about 50%, or about 100%. In some cases, the heating head efficiency comprises between at least about 0%, about 5%, about 10%, about 15%, about 20%, about25%, about 30%, about 35%, about 40%, about 45%, or about 50%. In some cases, the heating head efficiency comprises between at most about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, about 45%, about 50%, or about 100%. In some cases, the heat exchangers are configured to maximize a uniform heat flux distribution from the heating head to the plurality of fins. In some cases, the heat exchangers comprise a topology improved surface to volume ratio between the heating head to the plurality of fins. The heating heads disclosed herein may comprise a compact architecture configured for applications in both industrial and non-industrial settings. In some cases, the topology improved heating head 901 is configured to minimize material usage. In some instances, the topology improved heating head 901 minimizes material addition and maintains structural integrity. In some instances, the topology improved heating head 901 comprises a minimized weight of the heating head (e.g., contributing to a more lightweight and potentially cost-effective architecture). For example, the topology improved heating head 901 may comprise dimensions no greater than a conventional heating head. In some cases, the topology improved heating head 901 may be configured for heat stream characteristics. In some instances, the heat stream may comprise a low grade heat stream (e.g., below 230°C). In some cases, the topology improved heating head 901 is configured to minimize thermal gradients. In some instances, the topology improved heating head 901 may comprise minimized thermal gradients within the topology improved heating head 901 . In further examples, the topology improved heating head 901 may comprise improved (e.g., smoother) temperature profiles contributing to more stable and predictable engine operation. In some cases, the topology improved heating head 901 is configured to integrate with system constraints. In some instances, the topology improved heating head 901 may be configured for various system constraints (e.g., accordingto available space or structural requirements ensuringthat topology improved heating head architecture 901 aligns with the overall system architecture and constraints). In some cases, the topology improved heating head 901 is configured to provide maximized reliability and durability. In some instances, the topology improved heating head 901 may be configured for minimize stress concentrations and maximized structural robustness of the topology improved heating head 901 (e.g., leading to enhanced reliability and durability over the operational life of the FPSE).

[0324] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, a heat exchanger configured to provide various benefits, including a cooling head (e.g., also referred to as cooling head or heat sink) that facilitates heat rejection to a lower-temperature medium (e.g., often ambient air or another cooling fluid such as water). The FPSE 200 may comprise a cooling head 201 configured to release thermal energy from the working fluid. In some cases, the working fluid is in thermal contact with the cooling head 201. In some instances, the cooling head 201 comprises a thermal conductivity of up to about 400 W / mK at room temperature and room pressure. In some instances, the cooling head 201 comprises a topology improved surface area. In some cases, the cooling head 201 comprises a heat sink. In some instances, the temperature differential between the heat sink and the working fluid comprises up to about 56°C. In some instances, the temperature differential between the heat sink and the working fluid comprises greater than about 56°C. In some cases, the cooling head 201 comprises a heat sink. In some instances, the heat sink 201 comprises a liquid-cooled heat sink. For example, the liquid-cooled heat sink 201 may comprise a water-cooled heat sink. In some instances, the heat sink comprises a gas-cooled heat sink. For example, the gas-cooled heat sink 201 may comprise an air-cooled heat sink. The cooling heads disclosed herein may comprises a architecture from an iterative manner that mimics an evolution-like processes. In some cases, the cooling head architecture stems from generative topology optimization. In some cases, the cooling head comprises an organic shape. In some cases, the organic shape comprises any shape configured to efficiently transfer heat from a working fluid to the cooling head (e.g., on the cold side of the engine). In some cases, the organic shape comprises any shape configured to efficiently transfer heat from the cooling head to the plurality of fins (e.g., on the cold side of the engine). In some cases, the organic shape comprises any shape configured to maximize a contact surface area between the working gas and the cooling head. In some instances, the contact surface area between the working gas and the cooling head comprises a topology improved contact surface area. In some cases, the organic shape comprises any shape configured to maximize a contact surface area between the cooling head and a plurality of fins. In some instances, the contact surface area between the cooling head and the plurality of fins comprises atopology improved surface area. In some cases, the cooling head comprises a shape or cross section comprising a circle, equilateral triangle, isosceles triangle, scalene triangle, right triangle, square, rectangle, pentagon, hexagon, heptagon, octagon, nonagon, decagon, parallelogram, rhombus, trapezoid, oval, star, heart, crescent, sphere, cube, cylinder, cone, square pyramid, triangular pyramid, rectangular prism, triangular prism, hexagonal prism, tetrahedron, octahedron, dodecahedron, icosahedron, torus, hemisphere, or ellipsoid. In some cases, the heat exchangers are configured to ensure uniform heat flux distribution from a working fluid to a heat sink. In some cases, the heat flux distribution forms the working fluid to the heat sink comprises a uniform heat flux distribution from the working fluid to the heat sink. In some cases, the heat exchangers are configured to maximize a uniform heat flux distribution from the water jacket to the cold cylinder. In some instances, the heat exchanger comprises a topology improved surface to volume ratio between the water jacket to the cold cylinder of FPSE. The cooling heads disclosed herein may be configured to maximize efficiency under varying external heat stream conditions. FIG. 9 shows a Free Piston Stirling Engine. In some cases, the FPSE 900 comprises a topology improved water cooling head 902. In some cases, the topology improved cooling head 902 is configured to remove heat from a working fluid. In some cases, the topology improved cooling head 902 may be configured to maintain isothermal conditions as a working fluid compresses and pressure increases. In some cases, the topology improved cooling head 902 is configured to provide maximized heat rejection to an ambient environment. In some instances, the topology improved cooling head 902 comprises an external heat sink. For example, the topology improved cooling head 902 may be configured to maximize the heat transfer between a working fluid and a plurality of fins (e.g., improving the efficiency of heat rejection to the environment). In some cases, the topology improved cooling head 902 is configured to provide maximized heat dissipation. In some instances, the topology improved cooling head 902 may be comprise of intricate internal structures configured to maximize heat dissipation and maximize the efficiency of the cooling process. For example, the internal structure may comprise a topology improved internal structure. In further examples, the internal structures may comprise improved surface morphology. In some cases, the topology improved cooling head 902 is configured to provide maximized thermal performance. In some instances, the topology improved cooling head 902 may be configured for a maximized efficiency heat exchange between the working fluid and the cooling head (e.g., resulting in maximized thermal performance and heat rejection). In some cases, the topology improved cooling head 902 is configured to provide increased cooling efficiency. In some instances, the optimization process is configured to optimize the internal configuration of the topology improved cooling head 902which increases heat transfer rates. For example, increased heat transfer rates may be configured for maximized cooling efficiency and maximized temperature control within the FPSE. In some cases, the topology improved cooling head 902 comprises a architecture of complex structures configured to maximize heat transfer from the working fluid to the plurality of fins (e.g., and to the environment). In some cases, the formula for calculating the heating head efficiency comprises equation 2. In some instances, Tin,H comprises an initial temperature of a working fluid. In some instances, Tout,H = final temperature of the working fluid. In some instances, Tin,C = initial temperature of the cooling head. In some cases, the working fluid comprises a temperature between about 5°C and about 12°C. In some cases, the cooling head comprises a temperature between about 10°C and about 17°C. For example, the cooling head may comprise up to 100% efficiency. In some cases, the cooling head efficiency comprises between about 0% to about 100%. In some cases, the cooling head efficiency comprises between about 0% to about 5%, about 0% to about 10%, about 0% to about 15%, about 0% to about 20%, about 0% to about 25%, about 0% to about 30%, about 0% to about 35%, about 0% to about 40%, about 0% to about 45%, about 0% to about 50%, about 0% to about 100%, about 5% to about 10%, about 5% to about 15%, about 5% to about 20%, about 5% to about 25%, about 5% to about 30%, about 5% to about 35%, about 5% to about 40%, about 5% to about 45%, about 5% to about 50%, about 5% to about 100%, about 10% to about 15%, about 10% to about 20%, about 10% to about 25%, about 10% to about 30%, about 10% to about 35%, about 10% to about 40%, about 10% to about 45%, about 10% to about 50%, about 10% to about 100%, about 15% to about 20%, about 15% to about 25%, about 15% to about 30%, about 15% to about 35%, about 15% to about 40%, about 15% to about 45%, about 15% to about 50%, about 15% to about 100%, about 20% to about 25%, about 20% to about 30%, about 20% to about 35%, about 20% to about 40%, about 20% to about 45%, about 20% to about 50%, about 20% to about 100%, about 25% to about 30%, about 25% to about 35%, about 25% to about 40%, about 25% to about 45%, about 25% to about 50%, about 25% to about 100%, about 30% to about 35%, about 30% to about 40%, about 30% to about 45%, about 30% to about 50%, about 30% to about 100%, about 35% to about 40%, about 35% to about 45%, about 35% to about 50%, about 35% to about 100%, about 40% to about 45%, about 40% to about 50%, about 40% to about 100%, about 45% to about 50%, about 45% to about 100%, or about 50% to about 100%. In some cases, the cooling head efficiency comprises between about 0%, about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about40%, about45%, about 50%, or about 100%. In some cases, the cooling head efficiency comprises between at least about 0%, about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, about 45%, or about 50%. Insome cases, the cooling head efficiency comprises between at most about 5%, about 10%, about 15%, about 20%, about 25%, about 30%, about 35%, about 40%, about 45%, about 50%, or about 100%. In some cases, the heat exchangers are configured to maximize a uniform heat flux distribution from the water jacket to the plurality of fins. In some cases, the heat exchangers comprise a topology improved surface to volume ratio between the water jacket to the plurality of fins. The cooling heads disclosed herein may comprise a compact architecture configured for applications in both industrial and non-industrial settings. In some cases, the topology improved cooling head 902 comprises a minimized weight and minimized material usage. In some instances, the optimization process minimizes material addition and maintains structural integrity. In some instances, the optimization process reduces the weight of the cooling head 902 (e.g., contributing to a more lightweight and potentially cost-effective architecture). For example, the topology improved cooling head 902 may comprise a weight no greater than a weight of a conventional cooling head of a same power capacity, or a dimension no greater than a conventional cooling head of the same power capacity. In some cases, the topology improved cooling head 902 may be configured for cooling source characteristics. In some instances, the cooling source may comprise a cooling liquid (e.g., water). In some instances, the cooling source may comprise a cooling gas (e.g., air). In some cases, the topology improved cooling head 902 is configured to minimize thermal gradients. In some instances, the topology improved cooling head 902 is configured to minimize thermal gradients within the topology improved cooling head 902. In further examples, the topology improved cooling head 902 may comprise smoother temperature profiles contributing to more stable and predictable engine operation. In some cases, the topology improved cooling head 902 is configured to integrate with system constraints. In some instances, the topology improved cooling head 902 may be configured for various system constraints (e.g., such as available space or structural requirements, ensuring that the topology improved cooling head 902 aligns with the overall system architecture and constraints). In some cases, the topology improved cooling head 902 is configured to provide enhanced reliability and durability. In some instances, the topology improved cooling head 902 may minimize stress concentrations and maximize structural robustness (e.g., leading to enhanced reliability and durability over the operational life of the FPSE).

[0325] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, a regenerator configured to provide various benefits, including storing and releasing heat as the working fluid cycles between a hot heat exchanger and cold heat exchanger, and a maximized overall efficiency of the FPSE (e.g., by reducing heat losses). The regenerator may comprise a architecture from an iterative manner that mimics anevolution-like processes. In some cases, the regenerator architecture stems from generative topology optimization. In some cases, the generative topology optimization is configured to produce a topology improved regenerator. In some cases, the regenerator comprises an organic shape. In some cases, the organic shape comprises any shape configured to efficiently transfer heat from a working fluid to the cooling head (e.g., on the cold side of the engine). In some cases, the organic shape comprises any shape configured to efficiently absorb heat from a working fluid. In some cases, the organic shape comprises any shape configured to efficiently release heat from a working fluid. In some cases, the organic shape comprises any shape configured to maximize a contact surface area between the working fluid and the regenerator. In some instances, the contact surface area between the working fluid and the regenerator comprises a topology improved contact surface area. In some cases, the topology improved regenerator 903 comprises variable geometry. In some instances, the variable geometry comprises a geometry similar to shape memory alloys. In some cases, the regenerator comprises a shape or cross section comprising a circle, equilateral triangle, isosceles triangle, scalene triangle, right triangle, square, rectangle, pentagon, hexagon, heptagon, octagon, nonagon, decagon, parallelogram, rhombus, trapezoid, oval, star, heart, crescent, sphere, cube, cylinder, cone, square pyramid, triangular pyramid, rectangular prism, triangular prism, hexagonal prism, tetrahedron, octahedron, dodecahedron, icosahedron, torus, hemisphere, or ellipsoid.

[0326] FIG. 9 shows a Free Piston Stirling Engine. In some cases, the FPSE 900 comprises a topology improved regenerator 903. In some cases, the topology improved regenerator 903 is configured to connect the topology improved heating head 901 to the topology improved cooling head 902. In some cases, the topology improved regenerator 903 is configured to connect the hot cylinder to the cold cylinder. In some cases, the topology improved regenerator 903 is configured to absorb and store heat from a working fluid. In some instances, the topology improved regenerator 903 is configured to receive a working fluid during a heating phase of a Stirling cycle. For example, the heating phase comprises a working fluid moved from a cold cylinder to a hot cylinder (e.g., the working fluid passes through the regenerator). In further examples, the topology improved regenerator 903 absorbs and stores an improved amount of heat from a hot working fluid. In some cases, the topology improved regenerator 903 is configured to release heat to a working fluid. In some instances, the topology improved regenerator 903 is configured to receive a working fluid during a cooling phase of the Stirling cycle. For example, the cooling phase comprises a working fluid moved from a hot cylinder to a cold cylinder (e.g., the working fluid passes through the regenerator). In further examples, the topology improved regenerator 903 releases an improved amount of heat to the cold working fluid. In some cases, theregenerator comprises a thermal conductivity of up to 400 W / mK at room temperature and room pressure. In some cases, the regenerator comprises a topology improved surface area. In some cases, the temperature differential between the regenerator and the working fluid comprises between about 0°C to about 80°C.

[0327] FIG. 6 illustrates an example of a Free Piston Stirling Engine Regenerator. In some cases, the regenerator comprises a plurality of fins. In FIG. 6, the regenerator 202 comprises a plurality of fins 602. In some instances, in FIG. 6, the plurality of fins 602 are organically distributed for effective heat storage and heat release (e.g., to maintain the engine’s operational efficiency). In some cases, the topology improved regenerator 903 is configured to provide maximized thermal performance. In some instances, the topology improved regenerator 903 is configured to provide a maximized effective transfer of heat between the hot and cold ends of the regenerator 903 (e.g., resulting in maximized thermal performance and maximized efficiency in the FPSE). In some cases, the topology improved regenerator 903 is configured to provide minimized thermal gradients. In some instances, the topology improved regenerator 903 is configured to provide a uniform heat exchange and prevent localized temperature variations. In some cases, the topology improved regenerator 903 is configured to maximize heat exchange. In some instances, the topology improved regenerator 903 may comprise intricate internal structures to maximize heat exchange efficiency during a cyclic compression and expansion processes. In some cases, the topology improved regenerator 903 is configured to provide maximized heat storage capacity. In some instances, the topology improved regenerator 903 structure maximizes heat storage capacity (e.g., allowing it to store more heat during the hot phase and release more heat during the cold phase of the FPSE cycle). For example, the topology improved regenerator 903 may comprise a maximized thermal mass (mCP). In further examples, the topology improved regenerator 903 may comprise a topology improved thermal mass (mCP). The topology improved regenerator 903 may comprise a porous matrix regenerator. In some cases, the porous matrix regenerators may comprise materials with interconnected pores in various geometric shapes. In some instances, the pores may comprise a topology improved shape. In further examples, the pores may comprise a topology improved diameter. In even further examples, the pores may comprise a topology improved length.

[0328] FIG. 6 shows a Free Piston Stirling Regenerator. In the example of FIG. 6, the heat exchanger 202 from the FPSE 200 of FIG. 2 is shown. In some cases, the heat exchanger 202 comprises a regenerator. In some cases, the regenerator 202 comprises optimum porosity. In some instances, the topology improved regenerator 903 may comprise a porosity configured to maximize heat transfer and minimize pressure drop (e.g., optimizing its overall performance). Insome cases, the regenerator is configured to minimize a pressure drop. In some instances, the regenerator comprises a pressure drop no greater than about 3 kPa. In some instances, the regenerator comprises a pressure drop no greater than about 10 kPa. In some instances, the regenerator comprises a pressure drop greater than about 10 kPa. In some cases, the porosity comprises a ratio of void volume to total volume in the regenerator material. In some instances, the ratio of void volume to total volume in the regenerator material may comprise a topology improved ratio of void volume to total volume. In some cases, the topology improved regenerator 903 comprises a mesh or screen regenerator. In some instances, the mesh or screen regenerator may comprise a cylindrical or annular mesh structure. In some cases, the topology improved regenerator 903 comprises a stacked disc regenerators. In some instances, the stacked disc regenerators may comprise thin discs stacked together in a cylindrical or annular arrangement. In some cases, the topology improved regenerator 903 comprises a honeycomb regenerator. In some instances, the honeycomb regenerator may feature a hexagonal cell structure for efficient heat exchange. In some cases, the topology improved regenerator 903 comprises a random fiber regenerator. For example, the random fiber regenerators may utilize randomly oriented fibers or filaments for enhanced heat transfer. In some cases, the topology improved regenerator 903 comprises a structured matrix regenerator. For example, the structured matrix regenerators may involve engineered matrices with specific geometric patterns to optimize heat transfer and fluid flow. In some cases, the topology improved regenerator 903 comprises a fixed-plate regenerator. For example, the fixed-plate regenerators may consist of stacked fixed plates or fins creating channels for working fluid flow. In some cases, the topology improved regenerator 903 comprises a vortex-flow regenerator. For example, the vortex -flow regenerators may induce vortex flow through helical or spiral channels to enhance heat transfer in Free Piston Stirling Engines. In some cases, the topology improved regenerator 903 is configured to provide maximized adaptability to various working fluids. In some instances, the topology improved regenerator 903 architecture may be adapted to work efficiently with different working fluids, allowing for flexibility in choosing the most suitable fluid for specific applications. In some cases, the topology improved regenerator 903 is configured to adjust its characteristics in response to the temperature and flow pattern of the heat flow. In some instances, the regenerator may comprise a material configured to increase pore size when receiving heat. In some instances, the regenerator may comprise a material configured to decrease pore size when storing heat. In some cases, the topology improved regenerator 903 is configured to adjust its characteristics in response to the hot phase of the Stirling engine cycle (e.g., where the working fluid undergoes expansion as it absorbs heat from the external heat stream). In some instances, the topologyimproved regenerator 903 is configured to adjust its characteristics to absorb heat from the working fluid. In some cases, the topology improved regenerator 903 is configured to adjust its characteristics in response to the transition phase of the Stirling engine cycle (e.g., where the working fluid remains approximately at constant volume after the hot phase). In some instances, the topology improved regenerator 903 is configured to adjust its characteristics to undergo a change in temperature. In some cases, the topology improved regenerator 903 is configured to adjust its characteristics in response to the cold phase of the Stirling engine cycle (e.g., where the working fluid undergoes compression as it releases heat to the external heat sink). In some instances, the topology improved regenerator 903 is configured to adjust its characteristics to supply heat to the working fluid, releasing the stored thermal energy to the working fluid as it passes through during compression. In some cases, the topology improved regenerator 903 is configured to adjust its characteristics in response to the transition phase of the Stirling engine cycle (e.g., where the working fluid remains approximately at constant volume after the cold phase). In some instances, the topology improved regenerator 903 is configured to adjust its characteristics to undergo a change in temperature.

[0329] The systems disclosed herein may improve over systems in the art by providing, in some cases, a working fluid configured to provide various benefits, including a gas mixture specially formulation to maximize thermodynamic performance at lower temperatures (e.g., below 230°C), and thermal conductivity (e.g., compared to conventional pure gases used in similar applications).

[0330] The working fluid may comprise a novel gas mixture. In some cases, the mixture may comprise a formulation improved for use in a FPSE. In some cases, the working fluid may comprise a formulation configured to maximize a power output in the Stirling cycle with an immersion fluid input. In some cases, the working fluid is configured to generate a higher power outputthan a conventional working fluid (e.g., helium) at a same heat input. In some instances, the working fluid comprises a higher thermal conductivity. In some instances, the working fluid comprises a lower viscosity.

[0331] In some cases, the working fluid comprises any gas. In some instances, the gas comprises helium, hydrogen, air, or a combination thereof. In some cases, the working fluid comprises a thermal conductivity of at least about 0.15 W / mK at room temperature and room pressure. In some cases, the working fluid comprises a thermal conductivity of less than 0.15 W / mK at room temperature and room pressure. In some cases, the working fluid comprises a specific heat capacity of at least about 5.193 J / g°C at constant pressure (Cp). In some cases, the working fluid comprises a specific heat capacity of less than about 5.193 J / g°C at constant pressure (Cp).

[0332] The systems disclosed herein may improve over systems in the art by providing, in some cases, a minimized dead volume to provide various benefits, including increased efficiency, improved power output, enhanced compression ratio, improved heat exchange, smoother operation, reduced mechanical stress, enhanced control and compact FPSE architecture. The FPSE may comprise an improved engine architecture. In some cases, the FPSE may comprise a minimized dead volume. In some cases, the dead volume comprises space within the engine's cylinders that is not effectively used during the compression and expansion phases of the working fluid (e.g., typically a gas). In some instances, the minimized dead volume may be, at least in part, a result of utilizing advanced manufacturing techniques (AM) that integrates multiple parts into one. For example, the heating head, heating head fins and regenerator may be integrated into one. In alternative examples, the cooling head, cooling head fins, and regenerator may be integrated into one. In some cases, the FPSE comprises a topology improved dead volume. In some cases, the FPSE comprises a topology improved swept volume.

[0333] The systems disclosed herein may improve over systems in the art by providing, in some cases, a displacer configured to provide various benefits, including enhanced efficiency, reduced weight, improved durability and lifespan, improved size, and compatibility with advanced manufacturing techniques (e.g., such as 3D printing).

[0334] FIG. 8 illustrates an example of a Free Piston Stirling Engine. In the example of FIG. 8, the FPSE 800 comprises a displacer 805. In some cases, the displacer 805 is configured to move the bulk of a working fluid located between displacer and cold tip (e.g., as the piston expands the gas). In some instances, the temperature of the working fluid decreases (e.g., based on ideal gas law). For example, as gas temperature decreases it absorbs or lifts heat through cold tip causing a cold tip temperature to also decrease. In some cases, the displacer 805 is configured to move the bulk of a working fluid located between the displacer and the piston (e.g., as the piston compresses the gas). In some instances, the temperature of the working fluid increases (e.g., based on ideal gas law). For example, as the gas temperature increases, it rejects heat through the heat exchanger to the environment. In some cases, the displacer 805 is configured to facilitate the continuous operation of the FPSE. In some instances, by moving the cool gas back to the hot end for heating and expansion, the displacer provides the cycle to repeat, continuously converting heat energy into mechanical work. In some cases, the displacer 805 is configured to move the heated gas from the hot end to the cold end of the engine. In some instances, the displacer 805 moving cools the working gas, preparing it for the next part of the Stirling cycle. In some cases, a displacer 805 material comprises stainless steel, graphite, ceramic, composite, or a combination thereof. In some cases, a displacer material comprises a low-conductivity, heat-resistant material(e.g., such as stainless steel, ceramic, or graphite), to minimize heat loss and withstand the high temperatures of the hot end of the engine. In some cases, a shape of the displacer is cylindrical, allowing it to comfortably fit within the cylindrical body of the engine, thereby promoting an effective back-and-forth movement of the working fluid. In some cases, a displacer structure is made hollow, which reduces its weight and, therefore, the amount of energy necessary for moving it. In some cases, a dimensions of the displacer are carefully selected to ensure it fits inside the engine cylinder while leaving adequate clearance for the passage of the working fluid around its edges. In some cases, the displacer might exhibit porosity or be dotted with small holes, facilitating the flow of the working fluid through the displacer, rather than merely around it. In some cases, the displacer 805 comprises a topology improved structure. In some cases, the displacer 805 comprises a topology improved volume. In some cases, the displacer 805 comprises a cold tip. In some cases, a cold tip temperature comprisesbetween about 5°C to about 12°C temperature. In some cases, the cold tip temperature comprises greater than about 5 °C. In some cases, the cold tip temperature comprises less than about 80°C. In some cases, the displacer 805 comprises a hot tip. In some cases, the hot tip temperature comprises between about 75°C to about 80°C temperature. In some cases, the hot tip temperature comprises greater than about 75°C. In some cases, the cold tip temperature comprises less than about 80°C.

[0335] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, a power piston configured to provide various benefits, including increased efficiency, weight reduction, improved durability and lifespan, size optimization, and compatibility with advanced manufacturing techniques such as 3D printing. In some cases, the power piston generates mechanical power. FIG. 8 illustrates an example of a Free Piston Stirling Engine. In the example of FIG. 8, the FPSE 800 comprises a power piston 804. In some cases, the power piston 804 is configured to reciprocate back and forth. In some instances, the power piston motion 804 may be transferred to a load via a spring-mass system or directly used to generate electricity. In some cases, the power piston 804 is configured to move as a response to the expansion of a working gas (e.g., such as hydrogen or helium) enclosed in a sealed space. In some instances, when the gas is heated by an external heat stream at the hot end, it expands, pushing the power piston 804. For example, this motion may be transferred to a load via a spring-mass system or directly used to generate electricity. In some cases, the power piston 804 is configured to move in response to the contraction of the cooling working gas. In some instances, the cooling of the gas creates a vacuum effect, pulling the power piston 804 back to its original position. In further examples, the motion of this piston, similar to the heating and expansion phase, may be used to perform work. In some cases, the power piston 804 comprises atopology improved material. In some instances, the topology improved material comprises one or more of steel (e.g., for its strength and heat resistance), aluminum (e.g., for its light weight and good heat transfer capability), cast iron (e.g., for its excellent wear resistance and lubrication qualities), ceramics or composite materials (e.g., for high temperature operations), and bronze (e.g., for its high resistance to wear and excellent sliding properties). In some cases, the power piston 804 comprises a topology improved structure. In some cases, the power piston 804 comprises a topology improved material. In some instances, the topology improved material comprises one or more of steel (e.g., for its strength and heat resistance), aluminum (e.g., for its light weight and good heat transfer capability), cast iron (e.g., for its excellent wear resistance and lubrication qualities), ceramics or composite materials (e.g., for high temperature operations), and bronze (e.g., for its high resistance to wear and excellent sliding properties). In some cases, the power piston 804 comprises a topology improved structure.

[0336] The systems disclosed herein may improve over systems in the art by providing, in some cases, an FPSE configured to repeat a cyclic process. In some cases, the FPSE continues to repeat the cyclic process indefinitely. In some cases, the cyclic process comprises cyclically compress and expand the working fluid, extracting heat from the immersion fluid stream and converting it into mechanical power indefinitely.Heat Source

[0337] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing a heat exchanger configured to provide various benefits, including utilize immersion fluid from low grade temperature streams (e.g., below 230°C) and maximizing efficiency.

[0338] In some cases, the heat stream comprises an immersion fluid stream. In some instances, the immersion fluid may comprise a dielectric fluid. For example, the dielectric fluid may comprise materials such as fluorocarbon-based fluids, hydrofluorocarbon-based fluids, or silicone oils. In further examples, the dielectric fluid may comprise any fluid comprising a high dielectric constant, low viscosity, and / or excellent heat transfer properties.

[0339] In even further examples, the immersion fluid may comprise immersion fluid from a plurality of computers, data centers, or other computing equipment. In further examples, the dielectric fluid may originate from different cooling systems such as liquid immersion cooling systems, mineral oil-based systems, or other proprietary cooling solutions that employ synthetic fluids or coolants specifically configured for electronic equipment.

[0340] In some cases, the heat stream comprises a temperature between about 75°C to about 85°C. In some instances, the heat stream comprises a temperature of about 80°C.

[0341] In some cases, the heat stream comprises a thermal conductivity up to about 0.2 W / mK at room temperature and room pressure.Product By Process

[0342] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some cases, a method of designing a heat transfer apparatus configured to provide numerous benefits such as enhanced efficiency and precision in heat transfer architecture through integration of one-dimensional and three-dimensional Computational Fluid Dynamics modeling and topology optimization, capable of accommodating specific engine architecture parameters and optimizing for use in specific locations like data centers.

[0343] In some embodiments, a method of designing a heat transfer apparatus for a FPSE is provided. In some cases, the heat transfer apparatus may be configured by one or more processes. In some instances, the one or more processes may comprise one-dimensional (ID) Computational Fluid Dynamics (CFD) modeling of a FPSE. In some instances, the one or more processes may comprise three-dimensional (3D) CFD modeling of a FPSE. In some instances, the one or more processes may comprise topology optimization (TO). In some instances, the one or more processes may comprise integrating two or more of one-dimensional (ID) CFD modeling, three-dimensional (3D) CFD modeling, and topology optimization (TO). In some instances, the one or more processes may comprise integrating three or more of one-dimensional (ID) CFD modeling, three-dimensional (3D) CFD modeling, and topology optimization (TO). In some instances, the one or more processes may comprise integrating one-dimensional (ID) CFD modeling, three-dimensional (3D) CFD modeling, and topology optimization (TO).

[0344] In some instances, the architecture method may follow an ordered approach, beginning with one-dimensional (ID) Computational Fluid Dynamics (CFD) modeling, proceeding to three-dimensional (3D) CFD modeling, and culminating in topology optimization (TO). However, the flexibility of the methods disclosed allows for alternatives to this sequence. For example, three-dimensional (3D) CFD modeling could be executed prior to one-dimensional (ID) CFD modeling depending on the specific requirements or characteristics of the FPSE. Similarly, topology optimization (TO) could be initiated at various stages in the architecture process, either after the completion of ID CFD modeling and prior to 3D CFD modeling, or after the execution of both ID and 3D CFD modeling. Furthermore, each of these processes may operate synergistically to handle at least one engine architecture parameter, contributing to an improved FPSE architecture tailored for its specific location, such as a data center.

[0345] In some instances, the one or more processes may be configured to receive at least one engine architecture parameter configured for a FPSE. In some instances, the one or moreprocesses may be configured to create a topology improved FPSE for use in a specific location. For example, the specific location may comprise a data center. In some instances, the one or more processes may comprise integrating three-dimensional (3D) modeling, three-dimensional (3D) Computational Fluid Dynamics (CFD), and topology optimization (TO).

[0346] In some instances, each process within the method, namely one-dimensional (ID) Computational Fluid Dynamics (CFD) modeling, three-dimensional (3D) CFD modeling, and topology optimization (TO), can serve as a dynamic input and output to each other, promoting an iterative and integrated approach to the architecture. For example, the results derived from the ID CFD modeling, for instance, may serve as valuable input for the 3D CFD modeling, helping to refine and add granularity to the latter process. In further examples, the outputs of the 3D CFD modeling could feed into the topology optimization, providing data that informs the optimization process, ultimately fine-tuning the architecture to best meet the parameters of the FPSE. In even further examples, the outcomes from the topology optimization could be looped back into the ID and 3D CFD modeling processes, influencing subsequent iterations and potentially highlighting areas for further refinement or improvement. In further examples, the interconnected mechanism allows for a more holistic and adaptive architecture approach, yielding a heat transfer apparatus that is attuned to the specific requirements and conditions of its intended application.ID Third Order Modeling

[0347] In some embodiments, the method comprises modeling, simulating, and optimizing a Free Piston Stirling Engine (FPSE) using third-order modeling (Nodal analysis). In some cases, the method comprises modeling, simulating, and optimizing a Free Piston Stirling Engine (FPSE) using one-dimensional (ID) third-order modeling (Nodal analysis).

[0348] In some cases, the method comprises defining control volumes. In some instances, control volumes are defined by dividing the engine's components into multiple segments. For example, Each segment contains a certain mass, with nodes serving as the boundaries of these volumes and set pressure and temperature.

[0349] In some cases, the method further comprises discretizing an FPSE domain into a plurality of building blocks. In some instances, each building block represents elemental components of the FPSE such as heat exchangers, regenerators, and pistons. In some instances, each building block comprises a localized self-contained entity. In some instances, the entire FPSE model comprises a summation of each component building blocks interconnected via mass flow rate, heat transfer, force, and pressure connectors. In some instances, the power and displacer pistons are represented as rigid moving components that cause volume displacement in compression andexpansion spaces. In some instances, all components of the FPSE including heat exchangers, pistons, and working spaces are incorporated in the model. In some instances, the method further comprises specifying an average operating pressure for the FPSE using a pressure source. In some instances, the method further comprising connecting the endpoints of the system to specified heat sources. In some instances, the method further comprises the configuration is used to estimate non-productive energy losses (e.g., parasitic losses). In some cases, the third-order modeling further comprises discretizing a fluid domain into a plurality of components. In some instances, the third-order modeling further comprises each component of the plurality of components comprises a control volume. For example, the third-order modeling further comprises defining mass, temperature, and pressure for each control volume. In some instances, the third-order modeling further comprises boundaries (e.g., nodes) between each control volume are used to represent and determine the mass flow rate between each control volume. In some cases, the method comprises each component of the engine, such as expansion and compression spaces, heat exchangers, and gaps, is divided into interconnected cells. In some instances, these cells interact to form a matrix for each variable within each component, considering both spatial and time discretization.

[0350] In some cases, the method comprises formulating governing equations. In some instances, the governing equations are formulated in accordance with the conservation principles of mass, momentum, and energy. For example, the governing equations may account for any non-idealities during the engine simulation.

[0351] In some cases, the method comprises simplifying differential equations into a onedimensional (ID) format. In some instances, the ID equations are then solved numerically with small incremental time steps and mathematical stabilization techniques.

[0352] In some cases, the method comprises calculating the precise distribution of pressure, temperature, and mass in the engine at each time step. In some instances, the method comprises further solving of differential equations for conservation of mass, momentum, and energy within the discretized fluid domain. In some instances, the third-order modeling further comprises solving the system of differential equations numerically. In some instances, the method further comprises solving the differential equations provides a detailed prediction of FPSE s performance under specified operating conditions.

[0353] In some cases, the method further comprises, upon reaching a stabilized state, attains a maximum thermal efficiency of between about 9.0% to about 10.0% for a heat source temperature of between about 70°C and about 85°C and a heatsink temperature of between about1°C and about 10°C. In some cases, the third-order modeling further FPSE comprises a Carnot efficiency of between about 40% to about 50%.

[0354] In some cases, the method comprises a conducting a simulation using software like SAGE. In this model, each component of the engine is portrayed as a building block to construct the complete engine model.Input Parameters

[0355] In some embodiments, the method comprises defining input parameters for a third order modeling of a FPSE.

[0356] In some embodiments, the method comprises defining about 1 parameter, about 2 parameters, about 3 parameters, about 4 parameters, about 5 parameters, about 10 parameters, about 15 parameters, about 20 parameters, about 25 parameters, about 30 parameters, about 35 parameters, about40 parameters, about 45 parameters, about 50 parameters, about 55 parameters, about 60 parameters, about 65 parameters, about 70 parameters, about 75 parameters, about 80 parameters, about 85 parameters, about 90 parameters, about 95 parameters, about 100 parameters, or any sub-range in-between. In some cases, the method comprises defining between about 75 different input parameters.

[0357] In some embodiments, the method comprises defining about 1 parameter to about 2,000 parameters. In some embodiments, the method comprises defining about 1 parameter to about 10 parameters, about 1 parameter to about 25 parameters, about 1 parameter to about 50 parameters, about 1 parameter to about 75 parameters, about 1 parameter to about 100 parameters, about 1 parameter to about 250 parameters, about 1 parameter to about 500 parameters, about 1 parameter to about 750 parameters, about 1 parameter to about 1,000 parameters, about 1 parameter to about 1,500 parameters, about 1 parameter to about 2,000 parameters, about 10 parameters to about 25 parameters, about 10 parameters to about 50 parameters, about 10 parameters to about 75 parameters, about 10 parameters to about 100 parameters, about 10 parameters to about 250 parameters, about 10 parameters to about 500 parameters, about 10 parameters to about 750 parameters, about 10 parameters to about 1,000 parameters, about 10 parameters to about 1,500 parameters, about 10 parameters to about 2,000 parameters, about 25 parameters to about 50 parameters, about 25 parameters to about 75 parameters, about 25 parameters to about 100 parameters, about 25 parameters to about 250 parameters, about 25 parameters to about 500 parameters, about 25 parameters to about 750 parameters, about 25 parameters to about 1,000 parameters, about 25 parameters to about 1,500 parameters, about 25 parameters to about 2,000 parameters, about 50 parameters to about 75 parameters, about 50 parameters to about 100 parameters, about 50 parameters to about 250parameters, about 50 parameters to about 500 parameters, about 50 parameters to about 750 parameters, about 50 parameters to about 1,000 parameters, about 50 parameters to about 1,500 parameters, about 50 parameters to about 2,000 parameters, about 75 parameters to about 100 parameters, about 75 parameters to about 250 parameters, about 75 parameters to about 500 parameters, about 75 parameters to about 750 parameters, about 75 parameters to about 1,000 parameters, about 75 parameters to about 1,500 parameters, about 75 parameters to about 2,000 parameters, about 100 parameters to about 250 parameters, about 100 parameters to about 500 parameters, about 100 parameters to about 750 parameters, about 100 parameters to about 1,000 parameters, about 100 parameters to about 1,500 parameters, about 100 parameters to about 2,000 parameters, about 250 parameters to about 500 parameters, about 250 parameters to about 750 parameters, about 250 parameters to about 1,000 parameters, about 250 parameters to about 1,500 parameters, about 250 parameters to about 2,000 parameters, about 500 parameters to about 750 parameters, about 500 parameters to about 1,000 parameters, about 500 parameters to about 1,500 parameters, about 500 parameters to about 2,000 parameters, about 750 parameters to about 1,000 parameters, about 750 parameters to about 1,500 parameters, about 750 parameters to about2,000 parameters, about 1,000 parameters to about 1,500 parameters, about 1,000 parameters to about 2,000 parameters, or about 1,500 parameters to about 2,000 parameters. In some embodiments, the method comprises defining about 1 parameter, about 10 parameters, about 25 parameters, about 50 parameters, about 75 parameters, about 100 parameters, about 250 parameters, about 500 parameters, about 750 parameters, about 1,000 parameters, about 1,500 parameters, or about 2,000 parameters. In some embodiments, the method comprises defining at least about 1 parameter, about 10 parameters, about 25 parameters, about 50 parameters, about 75 parameters, about 100 parameters, about 250 parameters, about 500 parameters, about 750 parameters, about 1,000 parameters, or about 1,500 parameters. In some embodiments, the method comprises defining at most about 10 parameters, about 25 parameters, about 50 parameters, about 75 parameters, about 100 parameters, about250 parameters, about 500 parameters, about 750 parameters, about 1,000 parameters, about 1,500 parameters, or about 2,000 parameters.

[0358] In some instances, the input parameters may comprise one or more of a mean average engine pressure, piston amplitude, phase angle, geometrical parameters, dynamic variables, the type of working gas, or a combination thereof. In some instances, the input parameters may comprise one or more of the internal diameter of the pressure vessel, the engine's mean charge pressure, piston diameter, piston amplitude, compression space volume, cooling head channel dimensions (e.g., width, height, and length), heating head channel dimensions, regeneratordimensions (length, wrapped foil gap, and thickness), displacer amplitude, displacer spring stiffness, and expansion space volume.

[0359] In some instances, the input parameters may comprise one or more of displacer rod diameter, power piston length, power piston angle, number of cooling head heat exchanger channels, number of heating head HE channels, cooling head and heating head fin thickness, surface roughness for heating head, cooling head, and regenerator, power piston mass, displacer piston mass, heat exchangers, walls, engine operating frequency, working gas, heat sink temperature, heat source temperature.

[0360] In some embodiments, the input parameters contributing to the FPSE's operation include operational and physical aspects. In some cases, the operational and physical input parameters may comprise one or more of the internal diameter of the pressure vessel, the engine's mean charge pressure, piston diameter, piston amplitude, compression space volume, cooling head channel dimensions (e.g., width, height, and length), heating head channel dimensions, regenerator dimensions (length, wrapped foil gap, and thickness), displacer amplitude, displacer spring stiffness, and expansion space volume.

[0361] In some cases, the method comprises defining between about 0 and about 100 input parameters input parameters for one or more components of the FPSE. In some cases, the method comprises defining between about 0 and about 100 input parameters for each component. In some instances, the method comprises defining between about 0 and about 100 input parameters for about 1 component, about 2 components, about 3 components, about 4 components, about 5 components, about 6 components, about 7 components, about 8 components, about 9 components, about 10 components, about 11 components, about 12 components, about 13 components, about 14 components, about 15 components, about 16 components, about 17 components, about 18 components, about 19 components, about 20 components, about 21 components, about 22 components, about 23 components, about 24 components, about 25 components, about 26 components, about 27 components, about 28 components, about 29 components, about 30 components, about 31 components, about 32 components, about 33 components, about 34 components, about 35 components, about 36 components, about 37 components, about 38 components, about 39 components, about 40 components, about 41 components, about 42 components, about 43 components, about 44 components, about 45 components, about 46 components, about 47 components, about 48 components, about 49 components, about 50 components, or more. For example, the one or more components of the FPSE may comprise a regenerator, heating head, cooling head, piston,pressure shell, fluid channels, working spaces, displacer, heat exchanger fins, or a combination thereof.

[0362] In some cases, the method comprises diving the fluid domain inside the engine is into multiple control volumes or nodes. For example, each node may comprise a unique mass, temperature, and pressure. In some instances, the method comprises, for each node, differential equations representing the conservation of mass, momentum, and energy are established based on the fundamental laws of physics governing the engine's operation. For example, the differential equations are solved numerically using specific software tools.SAGE

[0363] In some embodiments, the method comprises using software (e.g., SAGE software) to represent and calculate each individual component of the engine and their interactions. For example, the software may be configured to adjust the defined input parameters within certain ranges (e.g., aiming to maximize the engine's thermal efficiency).

[0364] In some cases, the software (e.g., SAGE software) is configured to define input parameters within specified ranges using Software (e.g., SAGE software), a steady-periodic Stirling cycle architecture, and simulation program. In some instances, the optimization process adjusts the input parameters to enhance the engine's thermal efficiency, a metric defined as the ratio of net work output to input heat.

[0365] In some embodiments, the method further comprises defining optimization variables (e.g, such as input parameters), constraints to ensure geometric and thermodynamic architecture viability, and an objective function. In some cases, the method further comprises defining optimization variables (e.g., such as input parameters), constraints to ensure geometric and thermodynamic architecture viability, an objective function, or a combination thereof within the software (e.g., SAGE software). In some instances, the objective function comprises thermal efficiency, defined as the ratio of net work output to heat input (^ thermal = w_net / Q_in).

[0366] In some embodiments, the method further comprises defining one or more constraints. In some cases, the one or more constraints may comprise one or more of ensuring that regenerator diameter is larger than displacer rod diameter, ensuring that pressure vessel diameter is larger than regenerator diameter, ensuring that form factor is reasonable with minimal flow distribution losses, ensuring that piston diameter is larger than displacer rod diameter, ensuring that piston diameter has almost the same diameter as regenerator, ensuring that there are enough volume in dead space of compression region to avoid collision, ensuring that there are enough volume in dead space of expansion region to avoid collision, ensuring that displacer runs freely by making components of phasor force zero, ensuring that power output is obtained.

[0367] In some instances, the Displacer rod diameter comprises between about 0.005 [m] and about 0.02 [m]. In some instances, the Power piston length may comprise between about 0.025 [m] and about 0.1 [m]. For example, the Power piston angle may comprise between about 0 [deg] and 0 [deg]. In some instances, the number of cooling head and heating head Heat Exchanger channels can each comprise between about 1000 and about 4000. For example, the Cooling head and heating head fin thickness may comprise between about 2.5e-4 [m] and le-3 [m]. In some instances, the Surface roughness for the heating head, cooling head, and regenerator can comprise between about 5e-4 [m] and 2e-3 [m]. In some instances, the Power piston mass comprises between about 0.5 [kg] and 2 [kg]. In some instances, the Displacer piston mass may comprise between about 0.125 [kg] and 0.5 [kg]. In some instances, the Engine operating frequency may comprise between about 15 [Hz] and 60 [Hz], In some instances, the Heat sink temperature may comprise between about 2.5 [C] and 10 [C], In some instances, the Heat source temperature may comprise between about 40 [C] and 160 [C],

[0368] In some embodiments, the method further comprises producing a plurality of output parameters. In some cases, the plurality of output parameters may comprise thermal efficiency, net power output (Wnet), input heat (Qin), heat out (Qout), or a combination thereof. In some instances, the output parameters are obtained from the software. For example, the output parameters may provide valuable insights into the performance of the engine under various operating conditions. In further examples, the output parameters may deliver a comprehensive framework for simulating and optimizing FPSE operation. In even further examples, the output parameters may promote efficient utilization of low-grade heat sources towards sustainable energy management and carbon footprint reduction.

[0369] In some cases, the organic FPSE further comprises a pressure vessel. In some instances, the one or more parameters comprises an internal diameter of the pressure vessel (Dpwall). For example, the Dpwall may comprise between about 2.000e-l [m] to about 3.000e-l [m]. In further examples, the Dpwall may comprise at least 2.000e-l [m]. In further examples, the Dpwall may comprise at most 3.000e-l [m]. In further examples, the Dpwall may comprise between about2.400e-l [m] and 2.800e-l [m]. In further examples, the Dpwall may comprise between about2.600e-l [m] and 2.700e-l [m]. In further examples, the Dpwall may comprise between about 2.620e-l [m] and 2.630e-l [m],

[0370] In further examples, the Dpwall increases with increase of power output. In even further examples, the Dpwall decreases with reduction of power output.

[0371] In some cases, one or more parameters comprisesan internal diameter of the regenerator Dregen. In some instances, the Dregen comprises between about 1.000e-l [m] and about 2.000e-1 [m]. In some instances, the Dregen comprises between about 1.500e-l [m] and about 1.800 e-1 [m]. In some instances, the Dregen comprises between about 1.700e-l [m] and about 1.800 e-1 [m]. In some instances, the Dregen comprises between about 1.740e-l [m] and about 1.750 e-1 [m].

[0372] In some instances, the Dregen comprises between about 9.5e-2 [m] to about 6e-l [m]. In some instances, the Dregen comprises at most 1.750e-l [m]. In some instances, the Dregen comprises at least 1.740e-l [m],

[0373] In some cases, one or more parameters comprises a mean charge pressure (Pcharge) for FPSE operation. In some instances, the Pcharge comprises between about 50 bar and 90 bar. In some instances, the Pcharge comprises between about 40bar to about 70 bar. In some instances, the Pcharge comprises at most about 40bar. In some instances, the Pcharge comprises at least about 40bar. In some instances, the Pcharge comprises about 0 bar, about 5 bar, about 10 bar, about 15 bar, about 20 bar, about 25 bar, about 30 bar, about 35 bar, about 40 bar, about 45 bar, about 50 bar, about 55 bar, about 60 bar, about 65 bar, about 70 bar, about 75 bar, about 80 bar, about 85 bar, about 90 bar, about 95 bar, or about 100 bar.

[0374] In some cases, one or more parameters comprises a diameter of the piston (Dpis).

[0375] In some instances, the Dpis comprises between about 1.000e-l [m] and about 2.000 e-1 [m]. In some instances, the Dpis comprises between about 1.500e-l [m] and about 1.800 e-1 [m]. In some instances, the Dpis comprises between about 1.700e-l [m] and about 1.800 e-1 [m]. In some instances, the Dregen comprises between about 1.710e-l [m] and about 1.720 e-1 [m]. In some instances, Dpis comprises between about 9.318e-2 [m] to about 5.88e-l [m]. In some instances, Dpis comprises at most about 1.720e-l [m]. In some instances, Dpis comprises at least about 1.710e-l [m],

[0376] In some cases, one or more parameters comprises an amplitude of the piston Xamp,pis. In some instances, the Xamp,pis comprises between about 7.000e-3 [m] and about 8.000e-3 [m].In some instances, the Xamp,pis comprises between about 7.500e-3 [m] and about 8.000e-3 [m].In some instances, the Xamp,pis comprises between about 7.700e-3 [m] and about 8.000e-3 [m].In some instances, the Xamp,pis comprises between about 7.900e-3 [m] and about 8.000e-3 [m].In some instances, the Xamp,pis comprises between about 7.950e-3 [m] and about 7.960e-3 [m],

[0377] In some instances, Xamp,pis comprises between about 2.586e-3 [m] to about 1.074e-2 [m]. In some instances, the Xamp,pis comprises at most about 7.960e-3 [m]. In some instances, the Xamp,pis comprises at least about 7.950e-3 [m],

[0378] In some cases, one or more parameters comprises a compression space volume Vcompression. In some instances, Vcompression comprises between about 3.000e-4 [mA3] andabout 4.000e-4 [mA3], In some instances, Vcompression comprises between about 3.500e-4[mA3] and about 3.800e-4 [mA3], In some instances, Vcompression comprises between about 3.600e-4 [mA3] andabout 3.700e-4 [mA3], In some instances, Vcompression comprises between about 3.660e-4 [mA3] and about 3.670e-4 [mA3], In some instances, Vcompression comprises between about 3.993E-5 [mA3] to about 2.02e-3 [mA3], In some instances, Vcompression comprises at least about 3.993E-5 [mA3], In some instances, Vcompression comprises at most about 3.993E-5 [mA3],

[0379] In some cases, the improved thermal efficiency (^thermal) of the FPSE comprises between about 5.00% to about 15.00 %. In some cases, the improved thermal efficiency(rjthermal) of the FPSE comprisesabout 5.00%, about 6.00%, about 7.00%, about 8.00%, about9.00%, about 10.00%, about 11.00%, about 12.00%, about 13.00%, about 14.00%, about15.00%, about 16.00%, about 17.00%, about 18.00%, about 19.00%, about 20.00%, or any subrange in-between. In some instances, the improved thermal efficiency (rjthermal) of the FPSE comprises between about 8.0% to about 14.0%. In some instances, the improved thermal efficiency (^thermal) of the FPSE comprises at least about 8.0%. In some instances, the improved thermal efficiency (rjthermal) of the FPSE comprises at most about 14.0%.

[0380] In some cases, the improved net power output (Wnet) of the FPSE comprises between about 0W to about 5000W. In some cases, the improved net power output (Wnet) of the FPSE comprises about 0W, about 100W, about 600W, about 1100W, about 1600W, about 2100W, about 2600W, about 3100 W, about 3600 W, about4100W, about 4600W, or about 5100 W, or any sub-range in-between. In some instances, the improved net power output (Wnet) of the FPSE comprises between about 1000W to about 3000W. In some instances, the improved net power output (Wnet) of the FPSE comprises at least about 1000W. In some instances, the improved net power output (Wnet) of the FPSE comprises at most about 3000W.

[0381] In some instances, the improved heat input (Qin) of the FPSE comprises about 0 kW, about 1 kW, about 2 kW, about 3 kW, about 4 kW, about 5 kW, about 6 kW, about 7 kW, about 8 kW, about 9 kW, about 10 kW, about 11 kW, about 12 kW, about 13 kW, about 14 kW, about 15 kW, about 16 kW, about 17 kW, about 18 kW, about 19 kW, about 20 kW, about 21 kW, about 22 kW, about 23 kW, about 24 kW, about 25 kW, about 26 kW, about 27 kW, about 28 kW, about 29 kW, about 30 kW, about 31 kW, about 32 kW, about 33 kW, about 34 kW, about 35 kW, about 36 kW, about 37 kW, about 38 kW, about 39 kW, about 40 kW, about 41 kW, about 42 kW, about 43 kW, about 44 kW, about 45 kW, about 46 kW, about 47 kW, about 48 kW, about 49 kW, to about 50 kW, or any sub-range in-between. In some cases, the improved heat input (Qin) of the FPSE comprises between about 22kW to about 23 kW. In some instances,the improved heatinput (Qin) of the FPSE comprises between about 7.0 kW to about 35.0 kW. In some instances, the improved heat input (Qin) of the FPSE comprises at least about 7.0 kW. In some instances, the improved heat input (Qin) of the FPSE comprises at most about 35.00 kW.

[0382] In some cases, the improved heat output (Qout) of the FPSE comprises between about 20.60 kW and about 21.00 kW. In some instances, the improved heat output (Qout) of the FPSE comprises between about 6.00kW to about 32.00kW. In some instances, the improved heat output (Qout) of the FPSE comprises about 0 kW, about 1 kW, about 2 kW, about 3 kW, about 4 kW, about 5 kW, about 6 kW, about 7 kW, about 8 kW, about 9 kW, about 10 kW, about 11 kW, about 12 kW, about 13 kW, about 14 kW, about 15 kW, about 16 kW, about 17 kW, about 18 kW, about 19 kW, about 20 kW, about 21 kW, about 22 kW, about 23 kW, about 24 kW, about 25 kW, about 26 kW, about 27 kW, about 28 kW, about 29 kW, about 30 kW, about 31 kW, about 32 kW, about 33 kW, about 34 kW, about 35 kW, about 36 kW, about 37 kW, about 38 kW, about 39 kW, about 40 kW, about 41 kW, about 42 kW, about 43 kW, about 44 kW, about 45 kW, about 46 kW, about 47 kW, about 48 kW, about 49 kW, to about 50 kW, or any subrange in-between.

[0383] In some embodiments, the method further comprises running the one-dimensional code to simulate the energy generation over a period ranging from 24 to 72 hours, resulting in a total energy production ranging from 49kWh to 147kWh, under the assumption of fixed heat source and sink temperatures and availability of heat source for a duration varying from 12 to 36 hours per day. In some instances, the FPSE product produced through this method offers enhanced efficiency in harnessing low-grade heat sources, serving as an essential tool for sustainable energy management and carbon footprint reduction.3D Third Order Modeling

[0384] In some embodiments, the method comprises modeling, simulating, and optimizing a Free Piston Stirling Engine (FPSE) using third-order modeling (Nodal analysis). In some cases, the method comprises modeling, simulating, and optimizing a Free Piston Stirling Engine (FPSE) using three-dimensional (3D) third-order modeling (Nodal analysis).

[0385] In some embodiments, the method comprises the initial preparation of a comprehensive 3D model architecture of the Free Piston Stirling Engine (FPSE). In some cases, the 3D model architecture is inclusive of all its internal and external components. In some instances, the method comprises computational fluid dynamics (CFD) analysis, which simulates the flow of fluid, heat transfer, and forces acting within the engine. In further embodiments, the method encompasses the preparation of the geometry of the model, including dimensions and details of components such as the heat exchanger fins and cylinders.

[0386] In additional embodiments, the method includes discretization of the 3D model using a polyhedral meshing technique to ensure accurate simulations. In some embodiments, the method comprises the discretization further comprising using polyhedral meshing to create conformal mesh interfaces between the parts. In some embodiments, the method comprises the contacting faces between different parts share a same boundary face topology. In some embodiments, the method further comprises performing simulations using four different base cell sizes to ensure mesh size sensitivity and check for mesh convergence. In some cases, the method increases the speed and accuracy of simulations due to the elimination of the need for face interpolation on contacting patches. In some embodiments, the method further comprises establishing between about one and about ten layers on interfaces between air and solid components to accurately capture thermal boundary layer. In some embodiments, the method further comprises identifying between about one and about 10 distinct simulation domains in the CAD geometry. In some cases, the method further comprises identifying between about four distinct simulation domains in the CAD geometry. In some instances, the four distinct simulation domains comprises specifically the stainless steel enclosure, air, copper fins, and an Inconel half-cylinder. In some embodiments, the method further comprises assigning each region a specific simulation model based on the material. In some embodiments, the method comprises setting boundary conditions. In some cases, the boundary conditions are set such that the enclosure has adiabatic walls.

[0387] In some embodiments, the method comprises the inner wall of a half cylinder has a convective heat transfer coefficient of between about 800 W / m2K at 300°C to about 1000 W / m2K at 300°C. In some cases, the method comprises the inner wall of a half cylinder has a convective heattransfer coefficient of between about 800 W / m2K at 300°C to about 900 W / m2K at 300°C. In some instances, the method comprises the inner wall of a half cylinder has a convective heat transfer coefficient of between about 850 W / m2K at 300°C to about 875 W / m2K at 300°C. For example, the method comprises the inner wall of a half cylinder has a convective heat transfer coefficient of between about 855 W / m2K at 300°C to about 865 W / m2K at 300°C.

[0388] In some embodiments, the method comprises inlets for each pipe are set with parameters. In some cases, the inlet pipe parameters may comprise a mass flow rate between about 0.001592 kg / s and about 0.006368 kg / s, temperature between about 325°C and 1300°C, or pressure between about 50,662.5 Pa and 202,650 Pa. In some instances, the inlet pipe parameters may comprise a mass flow rate between about 0.002388 kg / s and about 0.004776 kg / s, temperature between about487.5°C and 975°C, or pressure between about 75,993.75 Pa and 151,987.5 Pa. For example, the method comprises inlets for each pipe are set with parameters. In some cases, the inlet pipe parameters may comprise a mass flow rate between about 0.002866 kg / s and about0.003502 kg / s, temperature between about 585°C and 715°C, or pressure between about 91,192.5 Pa and 111,457.5 Pa.

[0389] In some embodiments, the method comprises pre-processing where each simulation domain, based on the material involved, is assigned a specific simulation model. In some cases, the method assigns appropriate boundary conditions to different parts of the FPSE model. In yet other embodiments, the method utilizes CFD simulations to predict heat transfer, flow patterns, and other performance details of the FPSE. In some instances, the method comprises postprocessing activities such as conducting a mesh independence study to ensure the reliability of the simulation and analyzing results. In certain embodiments, the method involves visualization and analysis of the simulation results, including temperature distribution, heat flux, air velocity, and pressure contours. In other embodiments, the method comprises the use of a Topology Optimization (TO) algorithm to iteratively optimize the architecture for improved heat dissipation or pressure loss minimization.

[0390] In some embodiments, the method comprises efficient heat transfer from the hot air to the fins, with approximately 1830W of heat extracted, signifying a high level of efficiency. In other embodiments, the method involves effective temperature regulation, with the air temperature falling within a narrow band around 400°C after passing over the fins. In further embodiments, the method includes regulation of airflow within the engine, demonstrated by a steady mass flow rate, which helps maintain desired temperature levels and optimize engine performance. In some cases, the method ensures an even distribution of heat flux across the external and internal surfaces of the fins, preventing localized heat concentration and thereby enhancing overall engine efficiency. In subsequent embodiments, the method includes conducting a mesh independence study to validate the reliability of the simulation, ensuring that outcomes are duly influenced by variations in the mesh size. Finally, in some embodiments, the method involves the employment of topology optimization in enhancing the heat exchanger architecture, thereby boosting the overall performance of the Free Piston Stirling Engine (FPSE).Topology Algorithm

[0391] The systems, the methods, and the techniques disclosed herein may improve over systems in the art by providing, in some embodiments, the organic topology of the at least one heat transfer apparatus was generated by a topology algorithm. In some instances, the topology algorithm is configured to receive one or more parameters of the FPSE. For example, the topology algorithm may be configured to generate the organic topology for the heat transfer apparatus based at least in part on the one or more parameters of the FPSE.

[0392] In some embodiments, the method comprises preparation of the model. In some cases, the preparation of the model comprises the initial model preparation involves setting up predefined solver parameters within a simulation software (e.g., such as STAR-CCM+). In some cases, the method comprises defining the geometry and meshing, establishing boundary conditions, and initializing the material properties.

[0393] In some embodiments, the method comprises sensitivity analysis of TO parameters. In some cases, the method comprises, wherein the initial testing of the model results in suboptimal performance, a parametric study is initiated to assess the influence of various TO solver parameters on the objective function (total heat transfer rate in this case). In some instances, the analysis explores parameters such as topology holes and source strength, penalty value, intensity of the improved fin surface smoothing, and step size.

[0394] In some embodiments, the method comprises initialization of the TO process. In some cases, after the sensitivity analysis and parametric studies, the TO algorithm is initialized. In some instances, the algorithm iteratively adjusts the distribution of material within the component (like the fins) based on the objective function.

[0395] In some cases, the method comprises geometry optimization. In some instances, based on the TO results, the 3D geometry of the component is improved to improve heat dissipation or minimize pressure loss. For example, the resulting geometry usually has an organic shape that provides efficient heat transfer performance.

[0396] In some cases, the method comprises post-processing & CFD verification. In some instances, after obtaining the improved geometry, the topology improved heat transfer apparatus undergoes smoothing and is reintroduced into the simulation for validation and verification through Computational Fluid Dynamics (CFD) simulations. For example, the progression represents a significant step towards refining the engine's performance.

[0397] In some cases, the method comprises evaluation and Analysis. In some instances, the final step comprises evaluation and analysis of the results obtained from TO and CFD. For example, the effectiveness and efficiency of the topology -optimized components are then assessed, providing valuable insights into the performance enhancement they bring about.

[0398] In some cases, the organic topology of the at least one heat transfer apparatus is substantially devoid of right angles. In some cases, the organic topology of the at least one heat transfer apparatus is substantially devoid of straight lines. In some cases, the organic topology of the at least one heat transfer apparatus comprises an amorphous shape.

[0399] In some cases, at least part of the organic topology comprises a form configured to encase a pressure vessel. In some cases, at least part of the organic topology comprises a formconfigured to shield a high-pressure chamber, envelop a pressure container, surround a compressed gas cylinder, cover a high-pressure vessel, or envelop a hydraulic reservoir.

[0400] In some instances, at least part of the organic topology comprises a form configured for a heat transfer rate up to a maximum theoretical limit. In some instances, with the assumption of maximum theoretical heat transfer limit between two temperature differentials being 1, the heat transfer comprises about 0.50 to about 0.75 of the max limit. In some instances, with the assumption of maximum theoretical heat transfer limit between two temperature differentials being 1, the heat transfer comprises about O.10, about 0.20, about 0.30, about 0.40, about 0.50, about 0.60, about 0.70, about 0.80, about 0.90, to about 1.00 of the max limit, or any sub-range in between.

[0401] For example, the heat transfer may comprise at least about 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.60, 0.61, 0.62, 0.63, 0.64, 0.65, 0.66, 0.67, 0.68 , 0.69, 0.70, 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79, 0.80, 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87, 0.88, 0.89, 0.90, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, to 0.99 of the max theoretical limit.

[0402] In some embodiments, the method comprises modeling, simulating, and optimizing a Free Piston Stirling Engine (FPSE) using a topology optimization algorithm,

[0403] In some embodiments, the topology algorithm utilizes gradient-based Topology (TO) for heat transfer and pressure optimization. In some embodiments, the TO process begins by defining the architecture space envelope as well as the flow / thermal objective functions together with TO input parameters. In some embodiments, the TO process utilizes conformal mesh to ensure conservation of heat transfer values. In some embodiments, the surface mesh between all parts on the interface shares points at the interface to conserve heat transfer between parts. In some embodiments, the smaller mesh cells result in finer fin surface. In some embodiments, the smaller mesh cells result in larger fin surface area. In some embodiments, the method further comprises geometry preparation for full CFD simulation with Boundary Layers (BL). In some embodiments, the geometry preparation comprises smoothing out initial derived part geometry, using a surface wrapper to create a watertight surface, importing the watertight surface of the improved geometry to the full case, subtracting the watertight surface from the air domain, imprinting it to the half cylinder geometry, and ensuring all interfaces are created properly. In some embodiments, the jagged geometry obtained from TO is smoothed out and then re-imported back for CFD simulation for validation and verification purposes.

[0404] In some cases, the method comprises providing one or more parameters of the FPSE into a topology algorithm. In some instances the topology algorithm is configured to generate an organic topology for the heat transfer apparatus based at least in part on the one or moreparameters of the FPSE. In some cases, the topology algorithm is configured to generate the organic topology tailored to a specific application of the heat transfer apparatus. In some instances, the specific application may comprise for use in data centers.

[0405] In some instances, the topology algorithm iteratively adjusts the distribution of material within a predefined domain based on gradients, seeking the optimal structure to meet the defined objective, such as maximizing heat dissipation or minimizing pressure loss, with the aid of adjoint solver capabilities.

[0406] In some embodiments, the topology optimization (TO) algorithm is configured is to augment heat transfer from hot air to the engine's fins. In some instances, the TO algorithm is configured to enhance the heat transfer up to about 1830W (e.g., from a max from a theoretical value of about 3566W). This amplification of heat extraction capabilities highlights the FPSE's potential to capitalize on low-grade heat sources more efficiently.Product

[0407] FIG. 31 illustrates a cross section of an FPSE, labeled as 3100. In some cases, FIG. 31 provides an overview of a conventional engine with specific components earmarked for topology optimization.

[0408] In some embodiments, component 3101 of the FPSE may be subject to topology optimization, in some cases, component 3101 may comprise elements such as a regenerator, heating head, cooling head, or heat exchanger fins.

[0409] In some embodiments, component 3102 may be selected for topology optimization. In some cases, component 3102 may comprise components like a regenerator, heating head, cooling head, or heat exchanger fins.

[0410] In some cases, component 3103 may be selected for topology optimization. In some instances, component 3103 may comprise elements like a regenerator, heating head, cooling head, or heat exchanger fins.

[0411] In some embodiments, component 3104 may be subject to topology optimization. In some cases, component 3104 may incorporate components such as a regenerator, heating head, cooling head, or heat exchanger fins.

[0412] In some embodiments, component 3105 of the FPSE may be improved using topology optimization methods. In some cases, component 3105 might comprise elements like a regenerator, heating head, cooling head, or heat exchanger fins.

[0413] FIG. 32 illustrates a topology-optimized component of an FPSE 3200. In some cases, component 3200 is the result of implementing topology optimization techniques on one or more of the parts 3101-3105 as shown in FIG. 31 . For instance, the improved FPSE component 3200may comprise a topology -optimized version of part 3401 (e.g., which may comprise a regenerator, heating head, cooling head, or heat exchanger fins). In further examples, after topology optimization, component 3200 represents an improved architecture with enhanced performance characteristics.

[0414] In further examples, Similar optimization techniques may also be applied to other parts of the FPSE, such as parts 3102, 3103, 3104, and 3105. In even further examples, each of these parts may comprise components like a regenerator, heating head, cooling head, or heat exchanger fins, which may be subject to topology optimization (e.g., to achieve superior operational efficiency).

[0415] In some cases, the method further comprises generating manufacturing instructions derived from the organic topology. In some instances, the method further comprises manufacturing the heat transfer apparatus (e.g., such as component 3200) based on the generated manufacturing instructions. In some cases, the architecture of the apparatus is guided by the organic topology. In some instances, the manufacturing comprises an additive manufacturing process. For example, the additive manufacturing process may comprise Direct Metal Laser Sintering (DMLS).

[0416] FIG. 57 illustrates an example of a first view of topology improved heat exchanger. In some embodiments, the first view may comprise a top view the topology improved heat exchanger. In some cases, the first view may comprise a top view of an external surface of the topology improved heat exchanger. FIG. 58 illustrates an example of a second view of topology improved heat exchanger. In some embodiments, the second view may comprise a side view the topology improved heat exchanger. In some cases, the second view may comprise a side view of an external surface of the topology improved heat exchanger.

[0417] FIG. 59 illustrates an example of a third view of topology improved heat exchanger. In some embodiments, the third view may comprise a bottom view the topology improved heat exchanger. In some cases, the third view may comprise a bottom view of an external surface of the topology improved heat exchanger. In some cases, the third view may comprise a bottom view of an internal surface of the topology improved heat exchanger.

[0418] In some embodiments, the topology improved heat exchanger may comprise a symmetrical pattern of holes. In some cases, the symmetrical pattern of holes may correlate to natural heat, pressure, temperature, or other contours of an input heat stream. In some instances, the input heat stream may comprise a output from computing devices. For example, the building may comprise a data center.

[0419] In some cases, the topology improved heat exchanger may comprise a plurality of heat exchanger fins. In some instances, the plurality of heat exchanger fins may be configured to encase one or more of a heating head, cooling head, regenerator, pressure shell, or other engine components.

[0420] In some cases, the topology improved heat exchanger may comprise a plurality of organic shapes. In some cases, the topology improved heat exchanger may comprise a plurality of non- planar surfaces. In some cases, the topology improved heat exchanger may comprise a plurality of angles. In some cases, the topology improved heat exchanger may comprise a plurality of recessed surfaces. In some cases, the topology improved heat exchanger may comprise a plurality of protruding surfaces.

[0421] In some embodiments, the topology improved heat exchanger may comprise an organic topology of the at least one heat transfer apparatus is substantially devoid of right angles. In some embodiments, the topology improved heat exchanger may comprise an organic topology of the at least one heat transfer apparatus is substantially devoid of straight lines. In some embodiments, the topology improved heat exchanger may comprise organic topology of the at least one heat transfer apparatus comprises an amorphous shape. In some embodiments, the topology improved heat exchanger may comprise at least part of the organic topology comprises a form configured to encase a pressure vessel and for a heat transfer rate of up to about 0.67x the max theoretical limit. In some embodiments, the topology improved heat exchanger may comprise FPSE improves a heat transfer rate (0.67 / 0.51 )x that of a conventionally -finned FPSE. Use Case

[0422] Referring to FIG. 33, an example of a Heat recovery system (HRS) 3300 is presented, integrating an FPSE with the cooling process of data center equipment immersed in a dielectric fluid. This creates a cycle that not only dissipates heat from the electronics but also generates additional electricity using the heat absorbed by the cooling fluid from the data center equipment as a heat source.

[0423] In system 3300. electricity is transferred to the data center 3304 via an input electricity connection 3301 .

[0424] Further, the system comprises a connection 3307 between the data center 3304 and engine 3302. In some instances, via connection 3307 one or more immersion fluid flows to the engine 3302.

[0425] Further, the system comprises a connection 3303 between the engine and a heat exchanger 3305. In some cases, the heat exchanger 3305 may cool down the immersion fluid.

[0426] Further, the system comprises a connection 3308 between the engine 3302 and the heat exchanger 3305. In some cases, the immersion fluid (e.g., cooled immersion fluid) flows from the heat exchanger 3305 to the chiller 3309 via connection 3308.

[0427] Further the system comprises a connection 3310 between the chiller 3309 and the data center 3304. In some cases, the chiller 3309 outputs, for example, cooled immersion fluid to the data center 3304 via connection 3310. In some instances, the cooled immersion fluid picks up heat from the data center 3304 to produce heated immersion fluid. For example, the heated immersion fluid may flow to the engine 3302 via connection 3307.

[0428] In some cases, the heat exchanger 3305 may be configured to perform a heat exchange with an ambient environment. In some instances, the heat exchanger 3305 may be configured to perform a heat exchange with an adjacent system like a heating, ventilation, and air conditioning (HVAC) system, an industrial process that generates excess heat, a cooling fluid such as water or refrigerant, or a geothermal energy source underground.

[0429] In some cases, the engine may convert thermal energy carried by the fluid into mechanical energy. In some instances, the engine may convert the mechanical energy into electrical power. For example, the engine may enhance overall energy efficiency.

[0430] In some cases, a chilling fluid (e.g., water) is circulated through the cold side of the FPSE to create a temperature differential. In some instances, the chilling fluid cooling down the working gas. For example, the chilling fluid may cool down the working gas while the FPSE converts excess thermal energy into electricity.

[0431] In some cases, the HRS 3300 (as depicted in FIG. 33) comprises several advantages, such as reduced energy consumption by reusing immersion fluid for power generation. In some instances, the HRS 3300 may reduce energy consumption by up to about lOOkWh or more, under the assumption of fixed heat source and sink temperatures and availability of heat source for 24 hours per day.

[0432] FIG. 34 illustrates an example of a Heat recovery system (HRS) for a closed loop cooling system. In some embodiments, the HRS comprises a closed loop system 3400. In some cases, the closed loop system 3400 comprises a first recirculation loop 3406. In some instances, closed loop system 3400 comprises a chiller 3403. For example, the chiller 3403 may output cold fluid to engine 3401 via connection 3404.

[0433] In some cases, the engine 3401 comprises a cooling head 3405. In some instances, a cold fluid flows into the cooling head 3405 of the engine. For example, the cold fluid may cool the working gas inside the engine 3401.

[0434] In some instances, closed loop system 3400 comprises a chiller 3403. For example, a warm fluid may flow out of engine 3401 via connection 3402 to chiller 3403. In further examples, first recirculation loop 3406 recirculates continuously. In some cases, the closed loop system 3400 comprises a second recirculation loop 3412. In some instances, engine 3401 further comprises a heating head 3410. In some instances, a computing system 3407 is connected to heating head 3409 via connection 3408. For example, an immersion fluid may flow out of computing system 3407 into heating head 3409 via connection 3408. In further examples, the immersion fluid may transfer heat to the working gas inside engine 3401 .

[0435] In some instances, heating head 3409 is connected to a chiller 3411 via connection 3410. For example, the immersion fluid may flow out of heating head 3409 into chiller 3411 via connection 3410. In some instances, the immersion fluid may enter the heating head 3409 at a first temperature range. In some instances, the immersion fluid may exit the heating head 3409 at a second temperature range. For example, the second temperature may be less than or equal to the first. In further examples, the first temperature range may comprise between about 75°C to about 80 °C and the second temperature may comprise a maximum temperature of about 80°C.

[0436] In some instances, immersion fluid may enter the immersion chiller 3411 via connection 3410 at the second temperature range. For example, the immersion chiller 3411 may cool the immersion fluid such that immersion fluid exits the immersion chiller 3411 at a third temperature range. In further examples, the third temperature range may be less than or equal to the second temperature range.

[0437] In some instances, the immersion chiller 3411 may be connected to computing system 3407 via connection 3412. For example, the immersion fluid at the third temperature range may travel via fluid connection 3412 to the computing system 3407. In further examples, the second recirculation loop 3413 recirculates continuously.

[0438] In some embodiments, the computing system 3407 comprises a data center. In some cases, the immersion fluid comprises a dielectric fluid. In some instances, the first temperature range comprises between about 75°C and about 105°C. In some instances, the second temperature range comprises at most about 105°C . In some instances, the third temperature range comprises between about 15°C and about 50°C.

[0439] FIG. 35 illustrates an example of a heat recovery system for an open loop cooling system, in accordance with certain embodiments; In some embodiments, the HRS comprises an open loop cooling system 3500. In some cases, the open loop cooling system 3500 comprises an input fluidic connection 3503. In some instances, the fluidic connection 3503 may comprise a connection between an input stream source 3502 and engine 3501. For example, the engine 3501comprises a cooling head 3504. In further examples, the input stream source 3502 may comprise a cooling fluid source. For example, the cooling fluid source may comprise a water source. In further examples, the water source may comprise an underground water source, rainwater collection system, a municipal water supply, a well, a lake, a river, a reservoir, a desalination plant, a recycled or reclaimed water system, a snowmelt collection system, a natural spring, or a combination thereof.

[0440] In some instances, the cooling fluid flows into the cooling head 3504 of the engine 3501. For example, the cooling fluid may cool the working gas inside the engine 3501 .

[0441] In some cases, the open loop cooling system comprises an output fluidic connection 3505. In some instances, the fluidic connection 3505 may comprise a connection between the engine 3501 and an external unit 3506. For example, the cooling fluid may flow out of engine 3501 via connection 3502 to the external unit 3506. In further examples, the external unit 3506 may comprise an external cooling tower, additional heat exchanger (e.g., such as a fin to heat exchanger pushing ambient fan through it). In further examples, the external unit 3506 may comprise an underground water source, rainwater collection system, a municipal water supply, a well, a lake, a river, a reservoir, a desalination plant, a recycled or reclaimed water system, a snowmelt collection system, a natural spring, or a combination thereof.

[0442] In some instances, the cooling fluid may enter the cooling head 3504 at a first cooling fluid temperature range. In some instances, the cooling fluid may exit the cooling head 3504 at a second cooling fluid temperature range. For example, the second cooling fluid temperature range may be greater than or equal to the first cooling fluid temperature range. In further examples, the first cooling fluid temperature range may comprise a temperature of between about 10 °C and about 15°C. In further examples, the second cooling temperature range may comprise between about 20°C and 25°C.

[0443] In some cases, the open loop cooling system 3500 comprises a recirculation loop 3513. In some instances, engine 3501 further comprises a heating head 3509. In some instances, computing system 3507 is connected to heating head 3509 via connection 3508. For example, the immersion fluid may flow out of computing system 3507 into heating head 3509 via connection 3508. In further examples, the immersion fluid may transfer heat to the working gas inside engine 3501.

[0444] In some instances, heating head 3509 is connected to immersion fluid chiller 3511 via connection 3510. For example, the immersion fluid may flow out of heating head 3508 into dielectric chiller 3511 via connection 3510. In some instances, the immersion fluid may enter the heating head 3509 at a first immersion fluid temperature range. In some instances, theimmersion fluid may exit the heating head 3509 at a second immersion fluid temperature range. For example, the second immersion fluid temperature range may be less than or equal to the first immersion fluid temperature range. In further examples, the first immersion fluid temperature range may comprise between about 75°C - 80°C and the second immersion fluid temperature range may comprise a maximum temperature of about 80°C.

[0445] In some instances, the immersion fluid may enter the immersion chiller 3511 via connection 3510 at the second immersion fluid temperature range. For example, the immersion fluid chiller 3511 may cool the immersion fluid such that immersion fluid exits the immersion chiller 3511 at a third temperature range. In further examples, the third immersion fluid temperature range may be less than or equal to the second immersion fluid temperature range.

[0446] In some instances, the immersion fluid chiller 3511 may be connected to computing system 3507 via connection 3512. For example, the immersion fluid at the third immersion fluid temperature range may travel via fluid connection 3512 to the computing system 3507. In further examples, the second recirculation loop 3513 recirculates.

[0447] In some embodiments, the computing system 3507 comprises a data center. In some cases, the immersion fluid comprises a dielectric fluid. In some instances, the first temperature range comprises between about 75°C and about 105°C. In some instances, the second temperature range comprises at most about 105°C . In some instances, the third temperature range comprises between about 15°C and about 50°C.

[0448] In some embodiments, the cooling fluid may comprise any liquid, gas or solid configured to remove heat from a working gas. In some cases, the cooling fluid may comprise water. In some cases, the cooling fluid may comprise air, refrigerants like Freon, ethylene glycol, propylene glycol, dielectric liquids, mineral oil, synthetic oils, helium gas, or even a mixture of water and antifreeze.

[0449] In some embodiments, the immersion fluid may comprise any liquid, gas, or solid configured to remove heat from computer equipment. In some cases, the immersion fluid may comprise a dielectric fluid. In some instances, the immersion fluid may be a dielectric fluid — such as Fluorinert, Novec engineered fluids, mineral oil, or synthetic oils — or a gaseous coolant like helium or nitrogen; alternatively, it may include phase-change materials that absorb heat through melting and solidification.

[0450] I. n some embodiments, the heat engine employed in the systems and methods may comprise enhanced heat exchangers. Such enhancement may be achieved, in some cases, through advanced design methodologies like Topology Optimization (TO), used in conjunction with Additive Manufacturing (AM). The use of TO and AM, for example, may result in heatexchanger architectures exhibiting improved efficiency and uniformity in heat transfer rates. In some instances, this may also reduce losses associated with uneven flow distribution compared to conventional designs. Furthermore, in some embodiments, Additive Manufacturing (AM) may facilitate the integration of multiple engine components (such as elements of a heater, regenerator, or cooler) into a unified structure. This integration, in some cases, may minimize dead volume and associated thermodynamic losses, leading to a more compact and efficient engine architecture.

[0451] In some embodiments, engine performance may be improved through the selection and use of particular working gases. In some cases, a variety of pure gases or gas mixtures may be employed, including gases exhibiting high thermal conductivity or properties that offer improved heat transfer or fluid dynamic characteristics compared to traditional working mediums.

[0452] FIG. 11 presents a schematic of a typical FPSE (1100). For example, the primary working areas and components (1101-1113) include compression and expansion spaces, an internal heat exchanger (comprising a heating head, cooling head, and regenerator), displacer and power pistons, flexures, and electrical components (like a linear generator, mover laminations). In some embodiments, a layered approach may be developed to architecture and optimize the FPSE for immersion fluid heat recovery (IFHR). In some cases, the approach is applied for IFHR in data centers. In some instances, the approach incorporates both 1 -D modeling and 3 -D Computational Fluid Dynamics (CFD) simulations and optimization. In some embodiments, the 1-D modeling approach provides comprehensive parametric studies and optimization of input parameters and working gases. In some cases, this identifies input parameters and working gases with the highest impact on performance. In some instances, 1-D modeling provides rapid and efficient turnarounds. For example, this allows for the exploration of an extensive architecture space in a timely manner. As an example, by reducing the architecture space using 1 -D optimization, the most efficient configurations that meet the imposed constraints and boundary conditions are chosen for further investigation using 3-D CFD simulations. In some embodiments, 3-D Computational Fluid Dynamics (CFD) may be utilized. In some cases, CFD investigates inefficiencies in heat exchange and pressure losses in the regenerator, heating head, and cooling head. In some instances, CFD is used for topology optimization (TO) of heat exchangers and the regenerator. For example, TO is applied to candidates identified from 1-D modeling to optimize the heat transfer rate. Modeling of Heat Engine In some embodiments, a Free Piston Stirling Engine (FPSE) configuration does not utilize mechanical linkage among pistons, diverging from traditional Stirling engines. In some cases, all elements exhibiting reciprocating motion operate independently, facilitated by variations in engine pressure. In some instances, the incorporationof a suitably configured mass-spring resonance mechanism allows the pistons' oscillating movements to become autonomously adapted to the engine's operating parameters. For example, the engine's thermodynamic and gas dynamic properties are entwined with the spring-piston dynamics. As an example, this requires integrated consideration for accurate modeling of engine behavior, rendering separate modeling methods not feasible. In some embodiments, three distinct modeling strategies existforthe proposed engine, characterized by their precision and intricacy. In some cases, Primary modeling involves definitive solutions for specialized cases of sinusoidal volume fluctuations and isothermal hot and cold spaces, drawing upon Schmidt's investigation, but does not account for losses directly. In some instances, Intermediate modeling leverages an adiabatic examination that deducts losses induced by heat transfer and fluid dynamics, building on a tailored version of Schmidt's study and necessitating non-linear time integration of model equations. For example, Intermediate modeling postulates adiabatic expansion and compression regions. As an example, Advanced modeling (Nodal analysis) provides the most precise method among these strategies. In some instances, Advanced modeling utilizes control volumes or nodes to resolve one-dimensional governing equations directly, depicting concurrent energy and fluid shifts by solving conservation of mass, momentum, and energy, thereby including engine nonidealities during simulation. In some embodiments, Advanced modeling (Nodal analysis) is performed to attain accurate estimations of the engine's performance under imposed boundary conditions. In some cases, this modeling is performed in steps including: 1) Discretization of the fluid domain in different components into several control volumes which contain mass, temperature and pressure, 2) Setting up differential equations for conservation of mass, momentum and energy, and 3) Solving the system of equations numerically. In some instances, nodes are defined as boundaries between control volume cells and define the mass flow rate across each cell. In some embodiments, the aforementioned modeling methods operate on a onedimensional approach. In some cases, flow characteristics are modeled singularly along the longitudinal axis of each component. In some instances, differential equations are reduced to one dimension and numerically solved in minute incremental time steps. For example, mathematical stabilization techniques are employed to determine the pressure, temperature, and mass distribution in the engine after each respective time step. In some embodiments, a software tool configured for steady -periodic Stirling cycle architecture and simulation is utilized for the advanced (one-dimensional, third-order) modeling and optimization of the proposed engine. In some cases, this software represents each engine component as a building block, with the total model being an assembly of these interconnected component blocks via connectors for mass flow rate, heat transfer, force, and pressure. In some instances, each building block signifiesfundamental engine components, such as heat exchangers, regenerators, and pistons, operating as localized, self-contained entities. For example, both power and displacer pistons are rigid, moving parts that generate volume displacement in compression and expansion spaces. As an example, all working spaces (expansion and compression), alongside heat exchangers and gaps, are segmented into multiple interconnected cells through which components interact, and a matrix is subsequently generated for each variable in each component, alongside space and time discretization (see FIG. 12). In some instances, FIG. 12 provides a schematic (1200) of the developed one-dimensional engine model within the software environment, showing vital components including heat exchangers, pistons, and working spaces. For example, a pressure source is used to define the mean average engine pressure, while endpoints are linked to a point heat source and heat sink for estimating parasitic losses. In some embodiments, components in the model (see FIG. 12) have associated subcomponents, facilitating a thorough and accurate modeling of the heat engine's physics. In some cases, the displacer is composed of multiple subcomponents to simulate the engine's dynamic behavior as well as loss through gaps (see FIG. 13, 1300). In some embodiments, each primary and subcomponent requires the definition of particular input parameters for modeling and optimization. In some cases, these include boundary conditions, pressure value, engine operation frequency, piston amplitude, phase angle, geometric parameters, dynamic variables, working gas, and materials. In some instances, about 75 input parameters are specified across 9 components and their corresponding subcomponents. For example, given the substantial number of input parameters and the requirement for accurate timing coordination between power and displacer pistons to avoid collision, optimization is employed in lieu of manual input settings. In some embodiments, the optimization process mandates the specification of an objective function. In some cases, maximizing thermal efficiency is set as the objective function.

[0453] In some embodiments, the optimization process includes optimization variables. In some cases, Table 1 illustrates non-limiting examples of optimization variables and their broad ranges. Table 1 : Example Variable Parameter Ranges for Modeling

[0454] In some embodiments, the optimization process includes constraints.

[0455] Table 2 presents non-limiting examples of constraints imposed on an optimizer to ensure a viable engine architecture geometrically and thermodynamically.Table 2 Example Modeling Constraints

[0456] Table 3 presents non-limiting examples of values or ranges for other input parameters for different components that are kept fixed or varied during optimization.Table 3. Example Fixed or Ranged Input Parameters for Modeling

[0457] In some embodiments, optimization is conducted to maximize FPSE thermal efficiency using inputs and constraints such as those described. In some cases, the convergence history for one optimization run (1400) is shown in FIG. 54 In some instances, as one non-limiting example result illustrated by FIG. 54, after about 50 iterations (1401) the solver reaches a stabilized status achieving a thermal efficiency (1402) of about 8.1%. For example, this specific 8.1% efficiency result corresponds to particular example conditions including a heat source temperature of 80°C (or between about 75°C and 85°C) and a heatsink temperature of 20°C (or between about 15°C and 25 °C). As an example, other optimization runs under different conditions, such as a heatsink temperature of 5°C (or between about 0°C and 10°C), yield different efficiencies, such as about 9.06%. In some embodiments, an optimization process yields a set of improved input variables and corresponding output parameters. In some cases, one particular set of improved input variables derived during such an optimization, along with the corresponding calculated output parameters for the specific, non-limiting example achieving 8.1 % efficiency, is listed in Table 4. In some embodiments, an optimization process yields a set of resulting input variables and corresponding output parameters.Table 4: Illustrative Set of Modeled Input and Output Parameters

[0458] In some embodiments, efficiency results are evaluated relative to theoretical limits. In some instances, the specific temperature differential shown in the non-limiting example of Table 4 (80°C source, 20°C sink) corresponds to a calculated Carnot efficiency of approximately 16.9%. In some cases, this indicates that, for this illustrative case, the developed FPSE exhibited about 52.01% of the theoretical Carnot efficiency. For example, this level of performance relative to the Carnot limit is higher than that of competitive technologies such as Organic Rankine Cycle (ORC) under certain low-temperature differential conditions. As an example, the FPSE's inherent thermodynamic characteristics provide Immersion fluid heat recovery even at very low temperatures (e.g., source temperatures below 100°C, or below 230°C) with high thermal efficiency. In some instances, based on the illustrative 1000W netpower output (Wnet) example from Table 4, assuming continuous 24 / 7 / 365 operation, the estimated annual energy production is calculated to be approximately 8760 kWh.3-D CFD Simulation of Heat Engine

[0459] The application of advanced (one-dimensional, third-order) modeling for the proposed engine provides swift assessments and initiates early architecture stages via comprehensive parametric analyses and optimization. However, this approach only caters to flow fluctuations alongthe axial direction, overlooking impacts of nonuniform flow distribution, conjugate heattransfer between the solid matrix and fluid, as well as the influence of dead zones and abrupt geometrical alterations within flow regions. In contrast, three-dimensional (3D) Computational Fluid Dynamics (CFD) effectively tackles these limitations, ensuring the architecture of all engine components meets the requisite criteria. This method, frequently dubbed as fourth-order modeling, stands as a trusted instrument for understanding and reducing losses within the engine. Conversely, primary, intermediate, and advanced one-dimensional modeling approaches necessitate empirical coefficients for heat transfer and flow friction, derived from particular engine calibrations. This constraint limits their suitability to engines with corresponding calibration data. However, CFD does not need tuning coefficients to align with experimental data, thus broadening its applicability and improving prediction precision. The 3D CFD tool was implemented for full engine simulation in the initial step, wherein simulation and optimization of individual components were conducted. This step ensures both internal and external heat exchangers, as well as the regenerator, demonstrate competitive performance when compared to the one-dimensional results and respective counterparts.TO Proof of Concept

[0460] To commence, 3-D CFD simulations were conducted on the external acceptor fins of a standard engine configuration to evaluate the efficacy of the topology-optimized (TO) heat exchanger and potential enhancements in heat transfer. Such fins are utilized to augment the heat transfer rate to the hot cylinder of the proposed engine. CFD was executed for a baseline case with conventional fins, followed by an improved case predicated on TO.

[0461] TO constitutes a computational method aimed at optimizing the arrangement of fluids and structures within a specified architecture space to amplify fluid flow properties, like minimizing pressure drop or maximizing flow uniformity and heat transfer, under defined boundary conditions and constraints. It employs variational principles and sensitivity analysis, often harnessing adjoint-based optimization techniques, to iteratively modify the fluid or structure distribution, thereby achieving designs that optimize fluid dynamic performance and energy efficiency . In essence, by repeatedly adjusting the distribution of material within the predefined domain based on these gradients, the algorithm seeks the ideal structure that fulfills the stated objective, such as maximizing heat dissipation or minimizing pressure loss . The benefits of using gradient-based TO for heat transfer and pressure optimization are multiple. It facilitates the automatic discovery of innovative architecture solutions that might not be intuitive, substantially enhancing performance while often diminishing material usage and weight. Furthermore, the method is more computationally efficient compared to manual optimizationtechniques, as it directly employs sensitivity information to steer the optimization process, thereby reducing the number of architecture iterations to reach an optimal solution .3-D Geometry - Baseline

[0462] FIG. 16 illustrates the three-dimensional schematic of a typical engine configuration along with an isolated view of the external acceptor fins. These conventional fins are uniformly distributed around the hot cylinder's periphery and constructed from copper.Computational Domain - Baseline

[0463] CFD simulations were conducted using STAR-CCM+ software for the upper section of the geometry demonstrated in FIG. 16. Generally, the top part of this engine type is frequently enclosed within a casing to facilitate heat exchange with a hot medium, which could either be combustion gases or hot air. Thus, the external acceptor fins were covered by an enclosure featuring four inlet and four outlet pipes (each with a diameter of 0.0349m) for hot air, as depicted in FIG. 17. Hot air enters the enclosure via side inlet pipes and, after exchanging heat with the exterior acceptor fins, is discharged from the top pipes.Discretization - Baseline

[0464] The employment of polyhedral meshing allowed for the attainment of conformal mesh interfaces among the components. This method ensures that interfaces between distinct parts share a consistent boundary face topology. Notable benefits of this technique include improved accuracy, expedited simulations, and the elimination of face interpolation on contact patches. Simulations were performed using four varied base cell sizes to assess mesh size sensitivity and convergence. Five layers were appended to the interfaces between air and solid components (fins, cylinder, enclosure) to capture the thermal boundary layer, as shown in FIG. 18.Pre-processing - Baseline

[0465] In the CAD geometry displayed in FIG. 18, four distinct simulation domains were discerned — namely, the enclosure (stainless steel), air, fins (copper), and the half-cylinder (Inconel). All other material properties were sourced from the STAR-CCM+ material library, except for Inconel, which was procured from . Each region was assigned a specific simulation model based on the designated material, as highlighted in FIG. 19.

[0466] Boundary conditions for the CFD simulation were established with reference to FIG. 20. The enclosure was assigned to be an adiabatic wall, and the inner wall of the half-cy Under was assigned a convective heat transfer coefficient with a value of 860 W / mA2-K at 300 °C (these values were determined based on known operating conditions of the engine and data from the manufacturer). The inlets (indicated by red arrows) were assigned a mass flow rate of 0.003184 kg / s per inlet, and temperature and pressure of 650°C and 101325Pa, respectively. For theoutlets (indicated by blue arrows), a pressure boundary condition was specified. It should be noted that the working fluid inside the enclosure was air at 101325 Pa and a surface roughness of 0.05 mm was assigned to all faces with a wall boundary condition.Results - Baseline

[0467] FIG. 21 illustrates the mesh independence study, where the quantity of mesh cells was increased, and the mean temperature of the inner shell convective surface was monitored.

[0468] FIG. 22 outlines the contours of surface temperature, while the heat flux is presented in FIG. 23, and contours of air temperature are presented in FIG. 24 A and 24B at various section planes.

[0469] Air velocity and pressure contours are showcased in FIGs. 24C and 24D, respectively. Meanwhile, the mean outlet air temperature from the enclosure is depicted in FIG. 25. The average air temperature was calculated to be 502.3 degrees Celsius.

[0470] The CFD results indicated that from the maximal theoretical heat transfer value of 3566W, about 1830W could be extracted from the hot air to the fins, as outlined in FIG. 26.Computational Domain - TO

[0471] Given that the conventional fins managed to transfer only approximately 50% of the maximum possible heat, a topology -optimized (TO) fin architecture was proposed, aiming to augment the heat extraction from the hot air stream within the enclosure. This was accomplished through the utilization of adjoint solver capabilities within STAR-CCM+, by defining flow / thermal objective functions together with input parameters, as shown in FIG. 27. All other boundary conditions and setup remain identical to those in the baseline case.

[0472] Considering the available computational resources, a periodic boundary condition was applied, and only one-eighth of the model domain was simulated, as displayed in FIG. 36.\

[0473] With the cell size of 0.5 mm in the optimization region, the TO domain was discretized with a total number of about 4,000,000 cells as illustrated in FIG. 37.Results - TO

[0474] Initially, the case was set up with pre-established solver parameters recommended by STAR-CCM+, but the initial test cases demonstrated poor optimization performance, marked by large fluctuations in heat transfer values followed by insignificant improvements, even with a large number of optimization iterations. Thus, a parametric study was conducted to examine the impact of various TO solver parameters on the objective function, which was defined as the total heat transfer rate from air to the exterior heat exchanger. This sensitivity analysis involved exploring the effects of topology holes and source strength, penalty value, intensity of reconstructed surface smoothing, and step size, with the last parameter exhibiting the mostsignificant impact on optimization results. It was observed that superior results were obtained with no hole formulation and simplified geometry processing, while penalty value and intensity of reconstructed surface smoothing had negligible impact on the results. Step size demonstrated a dominant, inverse correlation to mesh size, necessitating a doubling of step size when cell size was halved. However, excessive step sizes led to solver divergence, necessitating a balance in the selection of these two parameters. FIG. 38 depicts the solver setting parameters used for TO simulation based on preceding parametric studies.

[0475] The solver was operated, and the total heat transfer value to the half cylinder and solid volume ratio were monitored, as depicted in FIG. 39. As can be observed, the total heat transfer starts dropping after approximately 2900 iterations due to a high step size value. Although the step size can be further refined, it was deemed sufficient for the purpose of these simulations.TO Geometry Preparation (Smoothing)

[0476] Since the TO solver was not configured to accommodate Boundary Layers (BL) for simulation, it was to rerun the CFD for the improved heat exchanger using smoothed geometry that includes BL. FIG. 40 outlines the jagged and smoothed geometry of the TO-configured heat exchanger.Discretization - TO with BL

[0477] Owing to the intricate shape of the TO-based heat exchanger, conformal meshing was utilized, as illustrated in FIG. 56. As can be observed, surface mesh between all parts on the interface share points at the interface to ensure heat transfer conservation between parts. It is worth noting that the base mesh cell size significantly affects the optimization results. Specifically, smaller mesh cells yield a finer fin surface and a larger surface area.Pre-processing - TO with BL

[0478] The CFD setup remains consistent with the previous sections. The convergence history of heat transfer and residuals is depicted in FIG. 41.Results - TO with BL

[0479] FIG. 42 outlines the contours of surface temperature whilst the heat flux is presented in FIG. 43. Contours of temperature are presented in FIG. 44 and FIG. 45 at various section planes. As evident from FIG. 43 more uniform heat flux can be observed with the TO architecture heat exchanger.

[0480] Pressure contours and air velocity vectors are presented in FIG. 46 and FIG. 47 respectively whilst the average outlet air temperature from the enclosure was calculated to be 463.4 degC as shown in Figure 48.

[0481] The transition to 3-D CFD simulations represented a substantial improvement in performance, facilitating the refinement of internal and external heat exchangers. Through TO, the development of organically shaped HE was made possible. This led to an enhancement in heat transfer, with a value of 2258W, which is a 23% increase compared to conventional finned heat exchangers (1830W). There is possibility of further improvement by inclusion of additional constraints such as manufacturing limitation, surface area and weight. However, it was assumed that the obtained results are sufficient for the purpose of proof of concept.CFD Model Validation

[0482] Validation of the CFD model is a critical step to ensure the accuracy and dependability of the simulations. Comparing CFD outcomes with experimental data validates that the model accurately represents physical phenomena. This process establishes trust in the CFD predictions, enabling their confident application in architecture and decision-making processes. As such, before the complete engine CFD simulation was carried out, it was to develop a benchmark CFD model extensively validated against experimental data. While availability of thoroughly researched experimental data for this type of engine is limited, a comprehensive experimental investigation provided by NASA in the 1970s and 1980s offered valuable resources. The examined engine, referred to as RE-1000, is a Research Engine with a total power output of approximately IkW. It was tested under diverse operating conditions and hardware configurations, resulting in a total of 781 test points. RE-1000 is depicted in FIG. 49 with its components.

[0483] FIGs. 50 and 51 present a selection of experimental data points, including indicated power, thermal efficiency, displacer stroke, and pressure phase angle, along with temperature measurements and pressure values across different regions of RE-1000.

[0484] The decision was made to validate the CFD model against 17 distinct experimental data points from reference , as illustrated by the variable data sets shown in FIG. 52. As seen, various inputs were evaluated, including the heating head and cooling head temperatures, average working pressure, piston stroke length, and working fluid type.3-D Geometry

[0485] In .. n some embodiments, a CAD model of RE-1000 exists for CFD simulation (see FIG. 53), based on available geometrical data. In some cases, the CAD model includes all components such as the pressure vessel, power and displacer pistons, heating head tubes, and cooling head. In some instances, the model further incorporates the displacer rod, bounce space, all gaps, clearances, centering ports (which provide communication between the displacer gas spring and bounce space), and dead volumes.

[0486] In some embodiments, for discretization ofthe RE-1000, polyhedral meshes are utilized, known for their flexibility in fitting complex geometries and providing a balance between accuracy and computational efficiency. In some cases, within Simcenter STAR-CCM+, polyhedral meshes achieve high-quality simulations with fewer cells compared to purely tetrahedral meshes, leading to faster convergence and reduced computational cost. In some instances, to accommodate the movement of power and displacer pistons, an overset meshing technique is used, which is a numerical technique to handle complex moving geometries and multiple interacting objects within a flow field. For example, this method employs multiple overlapping grids, where each grid moves independently, allowing for flexibility in simulating dynamic and complex systems. As an example, an overset mesh consists of a main (background) grid and one or more overlapping (foreground) grids that overlap and exchange data at their boundaries through interpolation, allowing independent movement while maintaining simulation continuity and accuracy. FIG. 55 presents the generated overset mesh at various locations across the RE-1000.

[0487] In some embodiments, a benchmark model configuration exists. In some cases, the discretization employs the overset mesh technique, and all gaps and clearances are accounted for in the grid generation process. In some instances, pre-processing of the RE- 1000 model setup is established, wherein displacement equations for the power and displacer pistons are converted into velocities and assigned to relevant components to emulate the harmonic motion of these components. For example, evaluations are performed for alternative working fluids using 1-D and 3-D approaches to enhance heat transfer rates and reduce pressure drops. As an example, simulations for the entire engine are conducted, initially focusing on the original geometry incorporating results from prior analyses for conventional finned-style heating head, cooling head, and regenerator configurations. As another example, following the demonstrated effectiveness of TO in enhancing heat transfer processes, all mentioned heat exchangers are improved based on TO principles.

[0488] In some embodiments, building on the successes of CFD optimizations, various surface morphologies are investigated to augment the heat transfer process. In some cases, this initiative surpasses the limitations of conventional heat exchangers by introducing surfaces configured to maximize heat absorption and dissipation, thereby enhancing overall engine efficiency. In some embodiments, the working gas comprises any gas having high thermal conductivity and low viscosity (e.g., helium, hydrogen, air, nitrogen, or mixtures thereof. For example, these novel mixtures are evaluated for their thermal conductivity, viscosity, and overall compatibility withthe engine architecture. As an example, this evaluation identifies a working fluid to further enhance engine performance.

[0489] In some embodiments, the heat engine represents a advancement in waste heat source utilization, transforming a traditionally overlooked byproduct into a valuable energy source. In some cases, this innovation bolsters energy efficiency in various applications. In some instances, it contributes to environmental sustainability. For example, it reduces dependence on traditional fossil fuels. As an example, it decreases greenhouse gas emissions.

[0490] The systems disclosed herein may improve over systems in the art by providing, in some cases, a HRS configured to reduce a carbon dioxide emission. In some cases, the WSHR system is configured to utilize an waste heat source that comprises about 0.1% to about 15% greenhouse gases (e.g., Carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O), fluorinated gases, ozone (03), water vapor (H2O). In some instances, the waste heat source comprises more than 15% greenhouse gases. In some instances, the WSHR system is configured to utilize an waste heat source that comprises about 1.1 billion tons of CO2 / year. For example, the HRS may be configured to prevent 1 billion tons of CO2 / year for up to 100 years or more from atmospheric emission.

[0491] The systems disclosed herein may improve over systems in the art by providing, in some cases, a HRS configured to produce energy for storage.

[0492] In some cases, the HRS comprises an energy storage device. In some instances, the energy storage device comprises 1) batteries for storing electricity from the grid or renewable sources, 2) flywheels that store energy in a rotating mass, 3) thermal energy storage systems like ice storage or hot water storage tanks, 4) Superconducting Magnetic Energy Storage (SMES) systems that store energy in a magnetic field, 5) capacitors and super capacitors for storing energy in an electric field, 6) Pumped Hydroelectric Storage used for grid storage where energy is stored in the energy of water, 7) Compressed Air Energy Storage (CAES) which uses off-peak electricity to compress air for later use, or 8) Hydrogen Storage where electricity is used to split water into hydrogen and oxygen, wherein the hydrogen is stored for later use in a fuel cell.

[0493] In some cases, the HRS comprises a plurality of batteries configured for energy storage. In some instances, the plurality of batteries is attached to the HRS. In some instances, the HRS is configured to provide up to about 250 kilowatt hours / day to the plurality of batteries.

[0494] In some cases, the HRS comprises a plurality of solar panels configured for energy storage. In some instances, the plurality of solar panels is attached to the HRS. For example, the HRS is configured to provide up to about 250 kilowatt hours / day to the plurality of solar panels.

[0495] Artificial Intelligence

[0496] In some cases, the HRS comprises an artificial intelligence (Al) model.

[0497] In some cases, the Al model is configured to measure energy needs.

[0498] In some cases, the Al model is configured to collecting data from a plurality of HRS.

[0499] In some instances, the Al model is configured to via machine learning train on the data from the plurality of HRS.

[0500] In some instances, the Al model is configured to predict power output of HRS for different time horizons.

[0501] For example, the time horizon may comprise a short term, medium term, or long term.

[0502] In some cases, Al and ML may be used for predicting malfunction in the unit and scheduling in-advance maintenance and part replacement.

[0503] In some cases, machine learning (ML) may generally involve identifying and recognizing patterns in existing data in order to facilitate making predictions for subsequent data.

[0504] ML may include a ML model (which may include, for example, a ML algorithm).

[0505] Machine learning, whether analytical or statistical in nature, may provide deductive or abductive inference based on real or simulated data.

[0506] The ML model may be a trained model. ML techniques may comprise one or more supervised, semi-supervised, self-supervised, or unsupervised ML techniques.

[0507] For example, an ML model may be a trained model that is trained through supervised learning ( e.g., various parameters are determined as weights or scaling factors).

[0508] ML may comprise one or more of regression analysis, regularization, classification, dimensionality reduction, ensemble learning, meta learning, association rule learning, cluster analysis, anomaly detection, deep learning, or ultra-deep learning.

[0509] ML may comprise: k-means, k-means clustering, k-nearest neighbors, learning vector quantization, linear regression, non-linear regression, least squares regression, partial least squares regression, logistic regression, stepwise regression, multivariate adaptive regression splines, ridge regression, principal component regression, least absolute shrinkage and selection operation (LASSO), least angle regression, canonical correlation analysis, factor analysis, independent component analysis, linear discriminant analysis, multidimensional scaling, nonnegative matrix factorization, principal components analysis, principal coordinates analysis, projection pursuit, Sammon mapping, t-distributed stochastic neighbor embedding, AdaBoosting, boosting, gradient boosting, bootstrap aggregation, ensemble averaging, decision trees, conditional decision trees, boosted decision trees, gradient boosted decision trees, random forests, stacked generalization, Bayesian networks, Bayesian belief networks, naive Bayes,Gaussian naive Bayes, multinomial naive Bayes, hidden Markov models, hierarchical hidden Markov models, support vector machines, encoders, decoders, auto-encoders, stacked autoencoders, perceptrons, multi-layer perceptrons, artificial neural networks, feedforward neural networks, convolutional neural networks, recurrent neural networks, long short-term memory, deep belief networks, deep Boltzmann machines, deep convolutional neural networks, deep recurrent neural networks, large language models, vision transformers, or generative adversarial networks.

[0510] Training the ML model may include, in some cases, selecting one or more untrained data models to train using a training data set.

[0511] The selected untrained data models may include any type of untrained ML models for supervised, semi-supervised, self-supervised, or unsupervised machine learning.

[0512] The selected untrained data models may be specified based upon input ( e.g., user input) specifying relevant parameters to use as predicted variables or other variables to use as explanatory variables.

[0513] For example, the selected untrained data models may be specified to generate an output ( e.g., a prediction) based upon the input.

[0514] Conditions for training the ML model from the selected untrained data models may likewise be selected, such as limits on the ML model complexity or limits on the ML model refinement past a certain point.

[0515] The ML model may be trained ( e.g., via a computer system such as a server) using the training data set.

[0516] In some cases, a first subset of the training data set may be selected to train the ML model.

[0517] The selected untrained data models may then be trained on the first subset of training data set using appropriate ML techniques, based upon the type of ML model selected and any conditions specified for training the ML model.

[0518] In some cases, due to the processing power requirements of training the ML model, the selected untrained data models may be trained using additional computing resources ( e.g., cloud computing resources).

[0519] Such training may be performed iteratively to develop desired model characteristics.

[0520] In some cases, the performance of a trained ML model may be assessed, for instance, by applying the model to a subset of data to generate predictions.

[0521] The model's performance, based on these predictions, may inform further development or refinement.

[0522] For example, additional training may be performed to refine the ML model, which may comprise retraining using different data subsets or adjusting model parameters to align with operational requirements.

[0523] This iterative process of training and refinement may be employed to develop models with certain performance characteristics.

[0524] Once developed, the ML model may be stored for present or future use.

[0525] The ML model may be stored as sets of parameter values or weights configured for analysis of further input (e.g., further relevant parameters, explanatory variables, user interaction data, etc.).

[0526] This stored representation may also include analysis logic or performance indicators.

[0527] In some cases, a plurality of ML models may be stored, potentially configured for generating predictions under different sets of input data conditions.

[0528] The ML model(s) may be stored in a database (e.g., associated with a server).Computer systems

[0529] The present disclosure provides computer systems that are programmed to implement methods of the disclosure.

[0530] FIG. 10 shows a computer system 1001 that is programmed or otherwise configured to control, monitor, or regulate the HRS ( e.g., according to any of the systems, methods and techniques described herein).

[0531] The computer system 1001 may control various aspects of the HRS (e.g., according to any of the systems, methods and techniques described herein) of the present disclosure, such as, for example, regulating energy production, monitoring energy used by an energy user, collect data, predietpower output of HRS systems, predict malfunctions and schedule maintenance and part replacement.

[0532] The computer system 1001 may be an electronic device of a user or a computer system that is remotely located with respect to the electronic device.

[0533] The electronic device may be a mobile electronic device.

[0534] The computer system 1001 includes a central processing unit (CPU, also “processor” and “computer processor” herein) 1002, which may be a single core or multi core processor, or a plurality of processors for parallel processing.

[0535] The computer system 1001 also includes memory or memory location 1004 ( e.g., random-access memory, read-only memory, flash memory), electronic storage unit 1003 ( e.g., hard disk), communication interface 1005 ( e.g., network adapter) for communicating with one ormore other systems, and peripheral devices 1006, such as cache, other memory, data storage and / or electronic display adapters.

[0536] The memory 1004, storage unit 1003, interface 1005 and peripheral devices 1006 are in communication with the CPU 1002 through a communication bus (solid lines), such as a motherboard.

[0537] The storage unit 1003 may be a data storage unit (or data repository) for storing data.

[0538] The computer system 1001 may be operatively coupled to a computer network (“network”) 1007 with the aid of the communication interface 1005.

[0539] The network 1007 may be the Internet, an internet and / or extranet, or an intranet and / or extranet that is in communication with the Internet.

[0540] The network 1007 in some cases, is a telecommunication and / or data network.

[0541] The network 1007 may include one or more computer servers, which may provide distributed computing, such as cloud computing.

[0542] The network 1007, in some cases, with the aid of the computer system 1001, may implement a peer-to-peer network, which may provide devices coupled to the computer system 1001 to behave as a client or a server.

[0543] The CPU 1002 may execute a sequence of machine-readable instructions, which may be embodied in a program or software.

[0544] The instructions may be stored in a memory location, such as the memory 1004.

[0545] The instructions may be directed to the CPU 1002, which may subsequently program or otherwise configure the CPU 1002 to implement methods of the present disclosure.

[0546] Examples of operations performed by the CPU 1002 may include fetch, decode, execute, and writeback.

[0547] The CPU 1002 may be part of a circuit, such as an integrated circuit.

[0548] One or more other components of the system 1001 may be included in the circuit.

[0549] In some cases, the circuit is an application specific integrated circuit (ASIC).

[0550] The storage unit 1003 may store files, such as drivers, libraries, and saved programs.

[0551] The storage unit 1003 may store user data, e.g., user preferences and user programs.

[0552] The computer system 1001 in some cases, may include one or more additional data storage units that are external to the computer system 1001, such as located on a remote server that is in communication with the computer system 1001 through an intranet or the Internet.

[0553] The computer system 1001 may communicate with one or more remote computer systems through the network 1007.

[0554] For instance, the computer system 1001 may communicate with a remote computer system of a user ( e.g., control, monitor, or regulate the process for energy production ( e.g., according to any of the systems, methods and techniques described herein). Examples of remote computer systems include personal computers ( e.g., portable PC), slate or tablet PC’s ( e.g., Apple® iPad, Samsung® Galaxy Tab), telephones, Smart phones ( e.g., Apple® iPhone, Android-enabled device, Blackberry®), or personal digital assistants. The user may access the computer system 1001 via the network 1007.

[0555] Methods as described herein may be implemented by way of machine ( e.g., computer processor) executable code stored on an electronic storage location of the computer system 1001, such as, for example, on the memory 1004 or electronic storage unit 1003. The machine executable or machine readable code may be provided in the form of software. During use, the code may be executed by the processor 1002.

[0556] In some cases, the code may be retrieved from the storage unit 1003 and stored on the memory 1004 for ready access by the processor 1002.

[0557] In some situations, the electronic storage unit 1003 may be precluded, and machineexecutable instructions are stored on memory 1004.

[0558] The code may be pre-compiled and configured for use with a machine having a processer adapted to execute the code or may be compiled during runtime.

[0559] The code may be supplied in a programming language that may be selected to provide the code to execute in a pre-compiled or as-compiled fashion.

[0560] Aspects of the systems and methods disclosed herein, such as the computer system 1001, may be embodied in programming.

[0561] Various aspects of the technology may be thought of as “products” or “articles of manufacture” typically in the form of machine (or processor) executable code and / or associated data that is carried on or embodied in a type of machine readable medium.

[0562] Machine-executable code maybe stored on an electronic storage unit, such as memory ( e.g., read-only memory, random-access memory, flash memory) or a hard disk.

[0563] “Storage” type media may include any or all of the tangible memory of the computers, processors or the like, or associated modules thereof, such as various semiconductor memories, tape drives, disk drives and the like, which may provide non-transitory storage at any time for the software programming.

[0564] All or portions of the software may at times be communicated through the Internet or various other telecommunication networks.

[0565] Such communications, for example, may provide loading of the software from one computer or processor into another, for example, from a management server or host computer into the computer platform of an application server.

[0566] Thus, another type of media that may bear the software elements includes optical, electrical, and electromagnetic waves, such as used across physical interfaces between local devices, through wired and optical landline networks and over various air-links.

[0567] The physical elements that carry such waves, such as wired or wireless links, optical links, or the like, also may be considered as media bearing the software.

[0568] As used herein, unless restricted to non-transitory, tangible “storage” media, terms such as computer or machine “readable medium” refer to any medium that participates in providing instructions to a processor for execution.

[0569] Hence, a machine readable medium, such as computer-executable code, may take many forms, including a tangible storage medium, a carrier wave medium or physical transmission medium.

[0570] Non-volatile storage media include, for example, optical or magnetic disks, such as any of the storage devices in any computer(s) or the like, such as may be used to implement the databases, etc. shown in the drawings.

[0571] Volatile storage media include dynamic memory, such as main memory of such a computer platform.

[0572] Tangible transmission media include coaxial cables; copper wire and fiber optics, including the wires that comprise a bus within a computer system.

[0573] Carrier-wave transmission media may take the form of electric or electromagnetic signals, or acoustic or light waves such as those generated during radio frequency (RF) and infrared (IR) data communications.

[0574] Common forms of computer-readable media therefore include for example: a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD or DVD-ROM, any other optical medium, punch cards paper tape, any other physical storage medium with patterns of holes, a RAM, a ROM, a PROM and EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wave transporting data or instructions, cables or links transporting such a carrier wave, or any other medium from which a computer may read programming code and / or data.

[0575] Many of these forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to a processor for execution.

[0576] The computer system 1001 may include or be in communication with an electronic display 1008 that comprises a user interface (UI) 1009 for providing, for example, to control,...

Claims

CLAIMSWHAT IS CLAIMED IS:

1. An energy production system (EPS), the EPS comprising: a. computing devices; b. a Free Piston Stirling Engine (FPSE); and c. at least one topology improved heat transfer apparatus.

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