OPTIMIZATION OF HEAT EXCHANGER TOPOLOGY

Abstract

Topology optimization, including the use of machine learning techniques, can be performed to improve one or more features of a heat exchanger design for production using additive manufacturing. The heat exchanger design can be optimized in terms of heat transfer efficiency, mass, mechanical requirements, and / or similar parameters. Design for additive manufacturing (DfAM) filters can be implemented to maintain the manufacturability of the heat exchanger design during topology optimization, and the topology optimization process can include heat transfer optimization, mechanical requirements optimization, and a support generation process.By applying DfAM filters, optimizing heat transfer and other heat exchanger characteristics, and optimizing mechanical requirements, the topology optimization process can generate an optimized heat exchanger that can be manufactured using additive manufacturing techniques.

Description

Title of the invention: Optimization of heat exchanger topology

[0001] GOVERNMENT LICENSE RIGHTS This invention was made with government support under Contract No. W912HZ22C0022, awarded and funded by the Engineers Research and Development Center of the U.S. Army Corps of Engineers. The government has certain rights to the invention.

[0002] REFERENCE TO A RELATED APPLICATION This application claims the benefit of U.S. Provisional Patent Application No. 63 / 733 827, filed on December 13, 2024. technical field

[0003] The present invention relates generally to the design of heat exchangers, and in particular to a topological optimization of heat exchangers to improve one or more characteristics. technological BACKGROUND

[0004] Heat exchangers can be used in various industries to transfer thermal energy between two media. Typically, a fluid-to-fluid heat exchanger (e.g., liquid-to-air, liquid-to-liquid) will include a working fluid that flows through the heat exchanger and transfers heat into or out of a region by conduction, convection, forced convection, and so on. The fluids can be gases, liquids, or phase-change substances such as refrigerants. The design of a fluid-to-fluid heat exchanger can affect its temperature handling capabilities, mass, required support structures, mechanical strength, and / or similar properties.However, traditional fluid-fluid heat exchangers have basic designs, such as tubes and fins, manufactured using conventional methods without considering the effects of the fluid-fluid heat exchanger design.

[0005] SUMMARY Certain aspects of the disclosure relate to a process comprising the steps of determining one or more operating conditions for a heat exchanger design, performing heat transfer optimization for the heat exchanger design based on the one or more operating conditions to generate a heat transfer-optimized heat exchanger design, and performing mechanical requirements optimization for the heat transfer-optimized heat exchanger design. in order to generate a heat exchanger design optimized in terms of heat transfer and mechanics, and to determine one or more supports for the heat exchanger design optimized in terms of heat transfer and mechanics in order to generate a final heat exchanger design.

[0006] In some embodiments, the performance of heat transfer optimization includes the step of performing a finite element method (FEM) analysis, the FEM analysis comprising the steps of solving a mass transfer problem and a heat transfer problem, determining a heat transfer rate using an objective function, determining a sensitivity of the objective function and adjusting the heat exchanger design on the basis of the FEM analysis, the heat transfer rate and the sensitivity.In some examples, the implementation of heat transfer optimization further includes the steps of evaluating whether the heat exchanger design is convergent for heat transfer; when the heat exchanger design is not convergent, repeating the FEM analysis, determining the heat transfer rate using the objective function, determining the sensitivity of the objective function, and adjusting the heat exchanger design based on the heat transfer rate and sensitivity; and when the heat exchanger design is convergent, generating the heat exchanger design optimized in terms of heat transfer.In some implementations, the process includes the step of implementing one or more DfAM filters for any of (i) heat transfer optimization, (ii) mechanical requirements optimization, or (iii) both (i) and (ii), the one or more DfAM filters including a thin feature minimum filter usable to minimize geometric features with a size less than a threshold size in the final heat exchanger design.

[0007] In certain implementations, the performance of the optimization of mechanical requirements includes the steps of performing a structural analysis for one or more mechanical requirements, determining an L1 standard of a difference between wall densities of the heat transfer optimized heat exchanger design and the heat transfer and mechanically optimized heat exchanger design using an objective function, determining a sensitivity of the objective function, and adjusting the heat transfer optimized heat exchanger design on the basis of the structural analysis, the L1 standard and the sensitivity.In some examples, the optimization of mechanical requirements further includes the steps of evaluating whether the heat exchanger design optimized in terms of heat transfer is convergent for one or more mechanical requirements, when the . If the heat exchanger design optimized in terms of heat transfer is not convergent, repeat the structural analysis, determine the L1 standard using the objective function, determine the sensitivity of the objective function, and adjust the heat exchanger design optimized in terms of heat transfer based on the L1 standard and sensitivity, and when the heat exchanger design optimized in terms of heat transfer is convergent, generate the heat exchanger design optimized in terms of heat transfer and mechanics.

[0008] In some implementations, performing the optimization of mechanical requirements includes the step of performing vibration fatigue load modeling. In some implementations, performing the heat transfer optimization for the heat exchanger design based on one or more operating conditions to generate the heat transfer-optimized heat exchanger design includes the step of generating a structure within the dimensions of a unit cell and arranging the structure repeatedly to generate a heat exchanger structure. In some implementations, the one or more operating conditions include a design envelope for the heat exchanger design.In some implementations, the process includes the step of implementing one or more DfAM filters for any of (i) heat transfer optimization, (ii) mechanical requirements optimization, or (iii) both (i) and (ii), the one or more DfAM filters including an operational support filter to minimize the support structures required in the final heat exchanger design. In some implementations, the process includes the step of implementing one or more DfAM filters for any of (i) heat transfer optimization, (ii) mechanical requirements optimization, or (iii) both (i) and (ii), the one or more DfAM filters including an operational projection filter to generate solid and void sections for heat exchanger design sections with fractional densities.

[0009] Certain aspects of the disclosure relate to a system comprising a memory storage; and a processing unit coupled to the memory storage, the processing unit being operational for: determining one or more operating conditions for a heat exchanger design, performing heat transfer optimization for the heat exchanger design based on the one or more operating conditions in order to generate a heat exchanger design optimized in terms of heat transfer, performing mechanical requirements optimization for the heat exchanger design optimized in terms of heat transfer in order to generate a heat exchanger design optimized in terms of both heat transfer and mechanics, and determining one or more supports for the design of a heat exchanger optimized in terms of heat transfer and mechanics in order to generate a final heat exchanger design.

[0010] In some implementations, heat transfer optimization consists of performing a FEM analysis, the FEM analysis comprising the steps of solving a mass transfer problem and a heat transfer problem, determining a heat transfer rate using an objective function, determining a sensitivity of the objective function and adjusting the heat exchanger design on the basis of the FEM analysis, the heat transfer rate and the sensitivity.In some examples, the implementation of heat transfer optimization further includes the steps of evaluating whether the heat exchanger design is convergent for heat transfer; when the heat exchanger design is not convergent, repeating the FEM analysis, determining the heat transfer rate using the objective function, determining the sensitivity of the objective function, and adjusting the heat exchanger design based on the heat transfer rate and sensitivity; and when the heat exchanger design is convergent, generating the heat exchanger design optimized in terms of heat transfer.In some implementations, the processing unit can further operate to implement one or more DfAM filters for any of (i) heat transfer optimization, (ii) mechanical requirements optimization, or (iii) both (i) and (ii), the one or more DfAM filters including a minimum thin feature filter operational to minimize geometric features with a size less than a threshold size in the final heat exchanger design.

[0011] In some implementations, the performance of the optimization of mechanical requirements includes the steps of performing a structural analysis for one or more mechanical requirements, determining an L1 standard of a difference between wall densities of the heat transfer optimized heat exchanger design and the heat transfer and mechanically optimized heat exchanger design using an objective function, determining a sensitivity of the objective function, and adjusting the heat transfer optimized heat exchanger design on the basis of the structural analysis, the L1 standard and the sensitivity.In some examples, performing the optimization of mechanical requirements also requires implementing one or more DfAM filters, the one or more DfAM filters comprising any of the following: (i) a minimum thin feature filter, (ii) a support filter, (iii) a projection filter, or (iv) any combination of (i)-(iii). In some examples, performing the optimization of mechanical requirements further includes the steps of... Evaluate whether the heat transfer optimized heat exchanger design is convergent for one or more mechanical requirements; when the heat transfer optimized heat exchanger design is not convergent, repeat the structural analysis, determine the L1 standard using the objective function, determine the sensitivity of the objective function, and adjust the heat transfer optimized heat exchanger design based on the L1 standard and sensitivity; and when the heat transfer optimized heat exchanger design is convergent, generate the heat transfer and mechanically optimized heat exchanger design.

[0012] In some implementations, performing the optimization of mechanical requirements includes the step of performing vibration fatigue load modeling. In some implementations, performing the heat transfer optimization for the heat exchanger design based on one or more operating conditions to generate the heat transfer-optimized heat exchanger design includes the step of generating a structure within the dimensions of a unit cell and arranging the structure repeatedly to generate a heat exchanger structure. In some implementations, the one or more operating conditions include a design envelope for the heat exchanger design.In some implementations, the processing unit is further operational for implementing one or more DfAM filters for any of (i) heat transfer optimization, (ii) mechanical requirements optimization, or (iii) both (i) and (ii), the one or more DfAM filters including an operational support filter to minimize the support structures required in the final heat exchanger design. In some implementations, the processing unit is further operational for the step of implementing one or more DfAM filters for any of (i) heat transfer optimization, (ii) mechanical requirements optimization, or (iii) both (i) and (ii), the one or more DfAM filters including an operational projection filter to generate solid and void sections for heat exchanger design sections with fractional densities.

[0013] A variety of additional inventive aspects will be set forth in the following description. The inventive aspects may relate to individual features and combinations of features. It should be understood that the preceding general description and the detailed description that follows are merely examples and explanations and are not exhaustive of the general inventive concepts on which the embodiments disclosed herein are based. Brief description of the drawings

[0014] The accompanying drawings, which are incorporated into and form part of the disclosure, illustrate several different embodiments of this disclosure. Regarding the drawings:

[0015] Fig. 1 is a functional diagram of an operating environment for optimizing heat exchangers in accordance with aspects of this disclosure.

[0016] Figure 2 is an illustration of a cell structure generation process unitary in accordance with aspects of this disclosure.

[0017] Fig. 3 is an illustration of a thin feature minimization filter visualization in accordance with aspects of this disclosure.

[0018] Figure 4 is an illustration of a support filter visualization according to aspects of this disclosure.

[0019] The [Fig.5] is a graph of a projection filter output in accordance with aspects of this disclosure.

[0020] Fig. 6 is an illustration of heat exchangers as an example in accordance with aspects of this disclosure.

[0021] Figure 7 is a flowchart of a process for optimizing a heat exchanger heat in accordance with aspects of this disclosure.

[0022] The [Fig.8] is a flowchart of a heat transfer optimization process in accordance with aspects of this disclosure.

[0023] Figure 9 is a flowchart of a process for optimizing mechanical requirements. in accordance with aspects of this disclosure.

[0024] The [Fig. 10] is a functional diagram of a computer device in accordance with aspects of this disclosure.

[0025] The [Fig. 11] is a functional diagram of a communication device in accordance with aspects of this disclosure. DETAILED DESCRIPTION

[0026] The preceding summary and the detailed description that follows are for illustrative purposes only and should not be considered as limiting the scope of the disclosure as described and claimed. Furthermore, features and / or variations may be provided in addition to those described. For example, embodiments of the disclosure may be directed toward various combinations and sub-combinations of features described in the example embodiments.

[0027] The detailed description that follows refers to the accompanying drawings. Wherever possible, the same numerical references are used in the drawings and the following description to designate identical or similar elements. Although While the disclosure embodiments can be described, modifications, adaptations, and other implementations are possible. For example, substitutions, additions, or modifications may be made to the elements illustrated in the drawings, and the processes described herein may be modified by substitution, rearrangement, or addition of steps to the disclosed processes. Accordingly, the detailed description that follows does not limit the disclosure. Instead, the appropriate scope of the disclosure is defined by the appended claims.

[0028] Heat exchangers can be used in various industries to transfer thermal energy between two media. Typically, a fluid-to-fluid heat exchanger (e.g., liquid-to-air, liquid-to-liquid) will include a working fluid that flows through the heat exchanger and transfers heat into or out of a region by conduction, convection, forced convection, and so on. The fluids can be gases, liquids, or phase-change substances such as refrigerants. The design of a fluid-to-fluid heat exchanger can affect its temperature handling capabilities, mass, required support structures, mechanical strength, and / or similar properties. However, traditional fluid-to-fluid heat exchangers may have basic designs (e.g., consisting of tubes and fins) and can be manufactured using conventional manufacturing techniques.Furthermore, traditional heat exchangers can be designed and manufactured without considering the effects of fluid-fluid heat exchanger design.

[0029] Additive manufacturing can be implemented for the production of heat exchangers so that the heat exchangers can be designed to meet specific requirements or desired characteristics. For example, additive manufacturing techniques allow heat exchangers to be designed in any shape to meet required or desired characteristics, rather than requiring the use of basic designs (e.g., tubes, fins). A topology optimization process, using, for example, machine learning techniques, can be used to optimize the characteristics of a heat exchanger under a given set of operating conditions, for example, by maximizing heat transfer capacity, minimizing mass, and / or the like.The use of machine learning techniques can enable the topology optimization process to perform extensive trial-and-error simulations and other operations to determine an optimized design within the timeframe required to manufacture new heat exchangers. The processing power and time required to generate optimized designs using conventional computers and / or humans may present computational costs and time constraints that are too high to reasonably consider. the optimized designs that can be created using the systems and processes described here.

[0030] In example implementations, the topology optimization process aims to generate topologically optimized models for a heat exchanger design with appropriate design constraints for additive manufacturing (DfAM). For example, a finite element (FE) model can be used to solve fluid flow and heat transfer problems to obtain the velocity and temperature field of the design domain, and filters can be applied to the design variable to enforce the DfAM constraints. Density-based topology optimization can also be applied to optimize the material distribution and maximize heat transfer between two fluids: an internal fluid flowing inside the heat exchanger structure and an external fluid flowing outside the heat exchanger structure.After determining a heat transfer-optimized design, a density-based topology optimization step can be performed to ensure the heat exchanger design meets the mechanical requirements of the given application, for example, through vibration fatigue load modeling (e.g., to meet aeronautical vibration load requirements). Furthermore, a support generation algorithm can be implemented to create support structures for the optimized design. By applying the DfAM constraints, optimizing heat transfer and other heat exchanger characteristics, and optimizing the mechanical requirements, the topology optimization process can generate an optimized heat exchanger that can be manufactured using additive manufacturing techniques.For example, the generated design is a heat exchanger that is free of unsupported structures, has managed cantilever angles, has maintained minimum feature sizes without compromising the structural integrity or performance of the design, and / or other features that allow the heat exchanger to be manufactured and used.

[0031] The generation of optimized heat exchanger designs as described herein can reduce development and production time for heat exchanger designs. For example, the generation of an optimized heat exchanger as described herein can be completed in three months or less in some embodiments. Initial model generation can take approximately seven days, first-round analysis can take approximately fourteen days, model refinement can take approximately seven days, final analysis can take approximately fourteen days, heat exchanger fabrication can take approximately fourteen days, and post-processing can take approximately twenty-one days in implementations in For example, the design and production of traditional heat exchangers can take ten months or more, including initial sizing calculations taking approximately seven days, supply chain scheduling taking about one month, and lead times of nine months or more in the example implementations. Furthermore, user input may not be required during the generation of optimized heat exchanger designs, as algorithms perform the heat exchanger development, thus saving resources.

[0032] Figure 1 is a functional diagram of an operating environment 100 for optimizing heat exchangers. The operating environment 100 includes a heat exchanger optimization system 102, one or more external systems 104, and one or more user devices 106. The heat exchanger optimization system 102 can communicate with one or more external systems 104 to exchange information, perform distributed processing steps, and / or the like. The external systems 104 can include storage systems (e.g., databases), computers, servers, sensors, and / or the like. By way of example, the external systems 104 can include a database for algorithms, a database for models, a database for heat exchanger characteristics, distributed computing systems, and so on.The heat exchanger optimization system 102 can also communicate with one or more user devices 106 to enable users to receive data and input data associated with heat exchanger design, such as input operating conditions, desired design characteristics, design constraints, and so on.

[0033] One or more motors (i.e., components, subsystems) of the heat exchanger optimization system 102 can activate services of the heat exchanger optimization system 102. In some embodiments, the heat exchanger optimization system 102 includes a DfAM filter motor 110, a heat transfer optimization motor 120, a mechanical requirements optimization motor 130, and a support generation motor 140. [Fig. 1] illustrates an embodiment of various motors for the heat exchanger optimization system 102 to perform operations, but the heat exchanger optimization system 102 and / or other systems can perform identical or similar functions with a different combination of systems, motors, and / or analogous components.The heat exchanger optimization system 102 will be primarily designated as performing the operations and processes described herein, but other systems may perform the operations and processes in additional embodiments.

[0034] The heat exchanger optimization system 102 may further include a storage system 150 and a communication system 160. The storage system 150 may store instructions for the operation of the heat exchanger optimization system 102, such as algorithms, models, heat exchanger operating conditions (e.g., design constraints, a design envelope, desired heat exchanger characteristics, etc.), and the like. The communication system 160 enables communication with local and / or remote devices, for example, via wired connections, wireless connections, a network, etc. Thus, the heat exchanger optimization system 102 can communicate with external systems 104 and user devices 106 using the communication system 160.The 160 communication system may include Wi-Fi capabilities, cellular capabilities, short-range communication capabilities, and / or analog capabilities.

[0035] The above-described elements of the operating environment 100 (for example, the heat exchanger optimization system 102, the components of the heat exchanger optimization system 102, the external systems 104, the user devices 106, etc.) can be implemented in hardware, in software (including firmware, resident software, microcode, etc.), in a combination of hardware and software, or in any other circuit or system. The elements of the operating environment 100 can be implemented in electrical circuits comprising discrete electronic elements, packaged or integrated electronic chips containing logic gates (for example, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), a system-on-a-chip (SoC), etc.).), a circuit using a microprocessor, or on a single chip containing electronic components or microprocessors. Furthermore, the elements of operating environment 100 can also be implemented using other technologies capable of performing logical operations such as, for example, AND, OR, and NOT, including, but not limited to, mechanical, optical, fluidic, and quantum technologies. As described in more detail below in relation to Figures 10 and 11, the elements of operating environment 100 can be implemented in a computing device 1000 and / or a communication device 1100.

[0036] In some embodiments, the heat exchanger optimization system 102 and / or other devices may use machine learning to optimize heat exchanger models given a set of operating conditions to satisfy heat exchanger characteristics as described herein. In general, machine learning is directed towards the design and the The development of techniques that take data (e.g., network statistics, performance indicators) as input and recognize complex patterns within the data. A common pattern among machine learning techniques is the use of an underlying model M, whose parameters are optimized to minimize the cost function associated with M, given the input data. For example, in the context of classification, the model M might be a straight line that separates the data into two classes (e.g., labels) such that M = a*x + b*y + c, and the cost function would be the number of misclassified points. The learning process then works by adjusting the parameters a, b, and c so that the number of misclassified points is minimized. After this optimization (or learning) phase, the model M can classify new data points.Often, M is a statistical model, and the cost function is inversely proportional to the probability of M, given the input data.

[0037] In various implementations, the heat exchanger optimization system 102 and / or other devices may use one or more supervised, unsupervised, or semi-supervised machine learning models. Generally, supervised learning involves using a training dataset to train the model to apply labels to the input data. For example, the training data might include a telemetry sample that has been labeled as indicative of acceptable or unacceptable performance. Unsupervised techniques do not require a training label set. While a supervised learning model may search for previously seen patterns that have been labeled as such, an unsupervised model may instead search for sudden changes or patterns in the behavior of the metrics.Semi-supervised learning models are a mixed approach that uses a small set of labeled training data.

[0038] Example machine learning techniques that the heat exchanger optimization system 102 and / or other devices may use include nearest neighbor (NN) techniques (e.g., k-NN models, replicator NN models, etc.), statistical techniques (e.g., Bayesian networks, etc.), clustering techniques (e.g., k-means, mean shift, etc.), neural networks (e.g., reservoir networks, artificial neural networks, etc.), support vector machines (SVMs), generative adversarial networks (GANs), long-term memory (LSTM), logistic or other regression, Markov models or chains, principal component analysis (PCA) (e.g., for linear models), singular value decomposition (SVD), artificial neural networks (ANN) to multilayer perceptron (MLP) (e.g., for nonlinear models), reservoir network replication (e.g., for nonlinear models, typically for time series), random forest classification, and / or analog.

[0039] In other embodiments, the heat exchanger optimization system 102 and / or other devices may also use one or more generative artificial intelligence / machine learning models. While discriminative models can simply perform pattern matching for purposes such as anomaly detection, classification, or the like, generative approaches can generate new content or other data (e.g., audio, video / images, text, etc.) based on an existing body of training data. Examples of generative approaches may include, but are not limited to, GANs, large language models (LLMs), other transformer models, etc.

[0040] The heat exchanger optimization system 102 can determine operating conditions and other heat exchanger characteristics for the design and optimization of a heat exchanger. For example, the heat exchanger optimization system 102 can receive operating conditions from one or more external systems 104 and / or one or more user devices 106. The operating conditions can include an operating temperature, environmental fluid characteristics, a design envelope (i.e., available space for the heat exchanger or the otherwise expected dimensions of the heat exchanger), expected mechanical stresses (e.g., vibration, torsion, etc.), an indication of the desired heat transfer performance, mass requirements, fluid characteristics, and / or the like.The heat exchanger optimization system 102 can use design constraints to target desired heat transfer performance, mass requirements, and so on, or the heat exchanger optimization system 102 can target maximizing heat transfer performance, minimizing mass, and so on when generating an optimized heat exchanger.

[0041] Figure 2 is an illustration of a cell structure generation process unit cell 200. In some embodiments, the design constraint information includes, or the heat exchanger optimization system 102 otherwise receives, the dimensions for a unit cell 202. In other embodiments, the heat exchanger optimization system 102 uses predetermined dimensions for the unit cell 202. The unit cell 202 can be a fundamental building block for the heat exchanger, and the The heat exchanger optimization system 102 can generate a heat exchanger structure 204 within the dimensions of the unit cell 202 to optimize the heat exchanger characteristics. The structure 204 can include a channel for the internal fluid to flow through and the external fluid to flow around.

[0042] The heat exchanger optimization system 102 can then construct the heat exchanger structure 206 by arranging the structure 204 repeatedly. Thus, the heat exchanger optimization system 102 can generate a heat exchanger structure 206 that is repetitive since it is constructed from the arrangement of a plurality of structures 204. The heat exchanger structure 206 can be an arrangement of structures 204 linearly along a longitudinal axis, repeated in a planar network with periodicity in two directions (for example, as shown in [Fig. 2]), repeated in a volumetric network with periodicity in three orthogonal directions, or arranged in other forms (for example, to meet the operating requirements of the heat exchanger, for sizing and shaping for installation in a planned area).The use of the unit cell structure generation process 200 can reduce computational complexity, manufacturing complexity, maintenance complexity and / or similar while allowing the heat exchanger optimization system 102 to meet the desired heat exchanger characteristics.

[0043] Once the heat exchanger optimization system 102 determines the operating conditions and / or analogy, the heat exchanger optimization system 102 can perform a topology optimization to determine an optimized heat exchanger design (e.g., an optimized material distribution) within the heat exchanger design envelope. In some embodiments, the heat exchanger optimization system 102 uses an initial heat exchanger design and modifies the initial design based on the topology optimization. The initial heat exchanger can be a finned design in example implementations. The heat exchanger optimization system 102 can use an initial design, operating conditions, and / or analogy as initial input for the topology optimization.The heat exchanger optimization system 102 can define a design variable, designated in the equations of this document as x, with the initial design, operating conditions, and / or analogous parameters, and adjust the design variable to generate an optimized heat exchanger design. For example, the geometry of the design domain can be predefined to a fin structure to aid faster convergence of the optimized heat exchanger. In some embodiments, the design domain is... initialized to have partial polymer fillings that improve thermal conductivity in heat exchangers. DfAM Filters

[0044] The heat exchanger optimization system 102 can, for example via the DfAM filter engine 110, implement one or more filters with respect to the algorithms used in topology optimization to apply DfAM constraints and enable the generation of optimized heat exchangers that can be manufactured using additive manufacturing processes. By way of example, the filters can include thin feature minimization to eliminate features smaller than a threshold size, support filters to ensure structural integrity without requiring support structures that compromise the heat exchanger characteristics, a projection filter to determine void and solid sections of the heat exchanger design, and / or the like.Examples of DfAM constraints include a minimum wall thickness, the largest unsupported cantilever angle, the largest unsupported horizontal round hole and / or roof size, an arched roof radius requirement, a maximum cantilever value and a maximum slender feature value.

[0045] Figure 3 illustrates a visualization of a thin feature minimization filter. Thin features in additive manufacturing (e.g., powder bed fusion additively manufactured parts) pose potential challenges in terms of manufacturability and feature sensitivity to high degrees of thermal distortion. To avoid such manufacturability challenges, the heat exchanger optimization system implements the thin feature minimization filter during heat exchanger design via topology optimization.

[0046] The thin feature minimization filter minimizes the generation of geometric features smaller than a threshold size (e.g., a user-specified value). The heat exchanger optimization system 102 then designs the heat exchanger so that it does not contain any features smaller than the threshold during topology optimization. The heat exchanger optimization system 102 can convert the threshold for the converted minimum feature size into a grid dimension-scale parameter thin feature value R that gives more weight to all elements within the neighborhood region of the radius defined by the thin feature value R for an element 302. The thin feature minimization filter visualization 300 illustrates the neighborhood 304 of element 302 as governed by the thin characteristic value R.

[0047] The thin feature minimization filter can be applied to any element 302 of the heat exchanger, which can be defined in space at position (i, j, k). The heat exchanger optimization system 102 can generate a heat exchanger with multiple elements 302 as building blocks, and the heat exchanger optimization system 102 can apply the thin feature minimization filter to any element 302. The element 302 is shown as a cube in the thin feature minimization filter visualization 300, but the elements 302 can have other shapes in other embodiments.

[0048] Figure 4 illustrates a visualization of support filter 400. The heat exchanger optimization system 102 can implement the support filter so that the heat exchanger is designed with self-supporting structures to require fewer support structures. Minimizing the required support structures can improve heat exchanger performance, as supports can unnecessarily add mass to the heat exchanger, reducing heat transfer performance and / or the like. Thus, the support filter can include a self-supporting constraint implemented in the topology optimization so that the heat exchanger optimization system 102 generates self-supporting heat exchanger designs.A self-supporting structure, or a structure that requires fewer supports, can improve the additive manufacturability of the optimal heat exchanger design, by reducing the need for additional support structures and facilitating the support removal process in post-processing.

[0049] In some embodiments, the support filter with a self-supporting character constraint algorithm is based on the rule that the density of an element 302 must not exceed the maximum density of the support elements 404 beneath it. In the illustrated three-dimensional case, the support elements 404 are defined as the five elements directly beneath the element 302. Equation 1, shown below, numerically defines the rule that the density of an element 302 must not exceed the maximum density of the support elements 404 beneath the element 302: XiijM-Xirjrkmax ​where x^^ = max^jj^ Xt.^^, x^j^ x^j^ x^.^

[0050] In equation 1, xi,jX represents element 302, and and represent the five support elements 404. The constraints Self-supporting characteristics can be defined by the total violation of the self-supporting criteria. Numerically, this can be formulated as the sum of the self-supporting character violations of all elements as shown in equation 2: = XyA0-5- AyA

[0051] In equation 2, g(x) represents the self-supporting constraint. The The self-supporting constraint indicates an increased need for support among elements, such as element 302 and support elements 404, as the value of the self-supporting constraint increases. The value of the self-supporting constraint is derived from the sum of the differences between the density of each component (e.g., element 302) and the maximum density of its support elements (e.g., support elements 404), with each difference multiplied by the square root of xi,jX to minimize interruption of low-density elements. A is the step function specified as shown below in Equation 3: ij,k ~ (3) \0ifxiJrk-xiJxmax<0

[0052] The heat exchanger optimization system 102 can thus generate self-supporting heat exchanger designs and minimize the required support structures by implementing the support filter. In some embodiments, the heat exchanger optimization system 102 can take into account the construction direction (for example, the direction layers will be added during the additive manufacturing process) and / or the installation orientation during the heat exchanger design so that it is self-supporting or otherwise designed to reduce the number of supports required. For example, the construction direction can be perpendicular to the internal fluid flow direction.Within the heat exchanger structure, the 102 heat exchanger optimization system can incorporate a triangular arched roof into the heat exchanger design. This arched roof is formed inside the internal fluid channel based on the implementation of the support filter. The triangular arched roof makes the inner roof self-supporting and eliminates or reduces the need for additional support. Externally, the external fluid flow channel changes direction to match the construction direction. In this way, the heat exchanger channels can be self-supporting, significantly reducing the need for additional supports.

[0053] Figure 5 is a graph of a projection filter output. The heat exchanger optimization system 102 can also implement a projection filter in certain embodiments to generate or otherwise determine void and solid sections of the heat exchanger design. Topology optimization may include generating heat exchanger sections with fractional densities, and the heat exchanger optimization system 102 can determine whether each section should be a void or a solid section, given that additive manufacturing processes will not include manufacturing sections with fractional densities. The heat exchanger optimization system 102 can use Equation 4 to apply the projection filter: _ tanh[j8 / ))+ tanh(^^-p)) (4) % tanh(^7j)+ tanh(^lz / ))

[0054] In equation 4, A is the final density of the associated element (e.g., zero when the element is a void, one when the element is a solid). is the filter sharpness parameter and is a fractional threshold. Both the filter sharpness parameter and the fractional threshold can be adjusted as desired to modify the fractional density values ​​that the heat exchanger optimization system 102 will determine to be a void or a solid. X is the fractional density of the associated element as indicated by the heat exchanger design generated before treatment by the projection filter.

[0055] Figure 500 illustrates the final density for each value of the fractional density with different filter sharpness parameters and the fractional threshold set at 0.5. As shown, the final density generally converges to a fractional density less than 0.5 exhibiting a final density of zero (i.e., a void) and a fractional density greater than 0.5 exhibiting a final density of one (i.e., a solid). The filter sharpness parameter and the fractional threshold can be adjusted to modify the relationship between the final density and the fractional density in example implementations. Heat transfer optimization

[0056] Once the DfAM filters are determined, the heat exchanger optimization system 102, for example via the heat transfer optimization engine 120, can perform heat transfer optimization to optimize the heat exchanger design for heat transfer and / or other heat exchanger characteristics. The purpose of heat transfer optimization is to optimize the given heat exchanger design space, subject to sets of loads, boundary conditions, and constraints (for example, based on the determined operating conditions and the DfAM filters), to maximize the heat transfer performance of the heat exchanger. minimize mass and / or similar. In example implementations, the heat exchanger optimization system 102 may prioritize heat transfer performance and attempt to meet secondary desired characteristics such as mass minimization without affecting heat transfer performance.

[0057] Optimizing the heat exchanger design may include a flow analysis (FEM). The FEM analysis may involve solving a mass transfer problem to determine the flow of the internal and external fluids for the optimized design and a heat transfer problem to maximize the heat transfer capacities between the internal and external fluids based on the determined flows (e.g., the transfer of thermal energy from the hot fluid to the cold fluid). The heat transfer performance may be represented as the heat recovered by the cold fluid and / or the heat dissipated by the hot fluid. The heat exchanger optimization system 102 may control the pressure drop on each fluid to regularize the geometry and impose restrictions on the pumping power, manifesting the pressure drop controlled in the algorithm as a constraint.The mass transfer problem can output the velocity and maximum pressure constraints for the fluids (e.g., velocity matrices and pressure matrices). The heat transfer problem can output the temperatures for the fluids (e.g., temperature matrices).

[0058] Once the heat exchanger optimization system 102 performs the FEM analysis (e.g., solves the mass transfer problem and the heat transfer problem), the heat exchanger optimization system 102 can input the solution (e.g., the temperatures for the fluids as output from the heat transfer problem) into an objective function to maximize the heat transfer between the two fluids, evaluate the sensitivity of the objective and constraint functions, and optimize the heat exchanger design. The heat exchanger optimization system 102 can use the objective function to determine a heat transfer rate between the first fluid and the second fluid (e.g., based on a value of an associated cost function of the heat transfer rate between the first fluid and the second fluid).The Heat Exchanger Optimization System 102 can use the Asymptote Displacement Method (ADM) to optimize heat exchanger design for heat transfer in example embodiments. The Heat Exchanger Optimization System 102 can perform heat exchanger optimization repeatedly, iteratively updating the heat exchanger design until the design converges. to satisfy the heat exchanger characteristics, resulting in a heat exchanger design optimized in terms of heat transfer.

[0059] As described above, the design variable x is used to model the design domains of the three physical phases—the internal fluid, the external fluid, and the solid structure of the heat exchanger. In example implementations, the Heaviside projection filter is applied to the design variable with low and high threshold values ​​defined as 0.05 and 0.95, respectively, creating intermediate variables A1 (the first fluid), x2 (the second fluid), and xs (the solid structure of the heat exchanger). The physical domains are defined with the resulting variables: first fluid domain: xi = 1, x2 = 0, and xs = 0; second fluid domain: xi = 0, x2 = 1, and xs = 0; and solid domain: xi = 0, x2 = 0, and xs = 1.In some embodiments, the heat exchanger optimization system 102 can apply an erosion-dilation based filter to the optimization model to generate the solid interface to separate the two fluid domains. The filter can also adjust the minimum wall thickness between the fluids.

[0060] The heat exchanger optimization system 102 can perform heat transfer optimization using one or more appropriate assumptions for the operating conditions in order to accurately model the physical processes of interest. For example, the heat exchanger optimization system 102 can assume that the fluids are in a steady state, being incompressible with constant properties in example implementations. This assumption applies to the decoupling of the energy equation from the mass and momentum conservation equations. Since only the fluid velocity impacts heat transfer and not the other way around, the heat exchanger optimization system 102 solves the two fluid systems independently, first for their velocity and pressure fields, and then for the conjugate heat transfer solution in order to determine the temperature field throughout the domain..

[0061] The mass transfer problem for the internal and external fluids can be solved separately using the FEM. The FEM can be governed by the Navier-Stokes equation under the assumption of steady-state, incompressible, low Reynolds number laminar flow. A Brinkman friction term can be used to penalize flow outside its domain. The solution can contain all three velocity and pressure components for each node. The heat exchanger optimization system 102 can operate under one or more simplified assumptions or features to simplify the mass transfer problem while maintaining sufficient accuracy to generate an optimized heat exchanger design. Assumptions can include non-slip wall boundary conditions and / or the assumption that a profile exists of fully developed velocity at the inlets and zero pressure at the outlets in example implementations. For example, the mass and momentum conservation equations for steady-state flow of the first incompressible fluid (e.g., the internal fluid) while ignoring body forces can be expressed as shown in equations 5 and 6: V • lï1=0 (5) p1(u1*7)u1 = ^1V2M1-Vp1-a(x1)u1 (6)

[0062] u is the velocity vector (e.g., the inlet velocity), q is the dynamic viscosity, p is the pressure, and p is the fluid density. The subscript 1 denotes the first fluid. The Brinkman friction term a(x)u is incorporated to penalize fluid flow outside its dedicated subdomain.

[0063] For certain operating conditions of interest, the Reynolds number of the second fluid (for example, the external fluid) is sufficiently high for the flow to be turbulent. The steady-state flow of the second fluid is thus modeled using a steady-state Reynolds-mean Navier-Stokes (RANS) turbulence model based on the incompressible apparent viscosity with equation 0, as shown in equations 7 and 8: 7 • u2 = 0 (7) P2(u2-7)h2 = (p2+^)V2u2-7p2-a(x2)u2 (s)

[0064] The subscript 2 denotes the second fluid. Pt is the apparent turbulent viscosity. It should be noted that is the molecular viscosity, determined by the fluid of interest, but that Pt is a flow characteristic that varies in space and therefore requires appropriate modeling, as will be described in more detail here. For both fluid dynamics problems, a(x) constitutes the inverse permeability of the porous media, as described in equation 9: [0,x€ ûfi (9) a(x.) = i . „ for i=l,2

[0065] When a = °°, the penalty component dominates the Navier-Stokes equation, inducing zero velocity for fluids external to the fluid subdomain (i.e., the domain becomes relatively impermeable to flow, and the flow will be directed around it). Conversely, with a = 0, the equation remains unpenalized, allowing the fluid to move without restriction (i.e., a flow without obstacles). No-slip velocity boundary conditions can be applied to all solid boundaries. The inlet velocity profile can be assumed to be fully developed, and the outlet can be defined at a pressure zero gauge while the heat exchanger optimization system 102 performs heat transfer optimization.

[0066] The Stokes equation in the matrix formulation using the FEM approach can to be written as indicated in equation 10: C(u)+K Glrn . g t Mao)

[0067] C(Ù) is the convection matrix, K is the viscosity matrix, G is the gradient matrix, Q? is the divergence matrix, M is the stabilization matrix, U and P are unknown nodal velocities and pressures, F and H are nodal forces.

[0068] The heat transfer problem can include obtaining the temperature field of the design domain by solving the convection-diffusion equation. The equation can be discretized and solved using the FEM with the same mesh structure as the mass transfer problem. A Streamline-Upwind Petrov-Galerkin (SUPG) stabilization can be applied to the problem to stabilize the convection-dominated equation. Furthermore, the heat transfer problem uses the global velocity field, which is the sum of the velocities from the two fluid problems: U = Mi + W². This assumes that the two fluid domains are well separated in the final design (e.g., the internal fluid contained by the heat exchanger structure and the external fluid held outside by the heat exchanger structure). The solution to the heat transfer problem includes the temperature of each node.

[0069] The heat exchanger optimization system 102 can operate under one or more simplified assumptions or features to simplify the heat transfer problem while maintaining sufficient accuracy to generate an optimized heat exchanger design. Assumptions may include a constant temperature at the respective fluid inlets, thermal insulation (zero heat flux) at the remaining boundaries, and / or an isotropic material for heat conduction (e.g., k is a constant) in example implementations.

[0070] The equation governing the heat transfer problem can be equation 11 or equation 12 as indicated below: Cp(u*VT)-V =0(11) (wVT)-V« (D(^)VT) = 0(12)

[0071] In equation 11 and equation 12, Cp is the heat capacity, T is the temperature field, u is the overall velocity vector as described above, k is the thermal conductivity, and D is the heat diffusion coefficient. Heat diffusion varies and is interpolated based on its position in three subdomains. distinct: the first fluid (for example, the internal fluid), the second fluid (by for example, the external fluid) and the solid structure of the heat exchanger. Heat diffusion can be mathematically represented by equation 13: D(x) = ************* f L2fl ____i_ v çz Pfpi p2Pr2 A L2f2 (13)

[0072] The subscript s represents the solid structure of the heat exchanger. P is the density, k is the thermal conductivity, cpi is the specific heat capacity, Pt is the turbulent apparent viscosity and Pr2 is the turbulent Prandtl number (for example, 0.9). The matrix formulation of the heat transfer problem can be equation 14 as shown: [D(u)+L+KSUpg][T] = [F +F supgr] (14)

[0073] D(u) is the advection matrix, L is the conduction matrix, KSUpg is the stabilization matrix, T is the unknown nodal temperature, F and F Supg are respectively the thermal force and its stabilization vector.

[0074] The sensitivity of the objective and constraint functions can be determined by the adjoint method. In the adjoint method, the mass transfer equations and heat transfer equations are written in the form of residual equations. Then, The mass transfer and heat transfer equations are combined with an objective function using the adjoint variable (for example, a Lagrange multiplier A), which creates the Lagrange function. The partial derivative of the physical and objective functions with respect to the explicit variables (ul, u2, T) creates the vector The derivative of the Lagrange function with respect to the design variable x is derived using the chain rule. The objective function can be expressed as indicated in equation 15: f Up u2, (15)

[0075] n is a vector normal to the surface, F and F2 are the inlet and outlet sections of the fluid, respectively, for the first and second fluids. The objective function focused on the heat transfer rate of the internal fluid acting as the hot fluid can be expressed as shown in equation 16: (16) f outlet, 1 pj 1-Tdr1

[0076] The sensitivity analysis to determine the sensitivity of the objective function and the constraint functions can be expressed by equation 17: df af I t ^F1 I 1 dRp2 IJ dRT dx ~ àx ' -“Fl Sx ' AF2 dx ' AT dx (17)

[0077] Rpy R-F2' -Ry are the residual equations of the two mass transfer problems and the heat transfer problem, respectively. The Lagrange multipliers Âpj, ^F2 are obtained by solving the following three adjoint problems, Equation 18, Equation 19 and Equation 20: _ / af 1^(18) ( T i ( JL 1T _i_ [ )T i 1 \ auj / afi~ J. 1 aiq / \ / -^t] (19) / 1 _ / df i dRT ) 1 \ du2 / -“Fl- " \dll2 / ' \ du2 / -“T (20)

[0078] Once the sensitivity is determined, the heat exchanger optimization system 102 can adjust the heat exchanger design to improve the heat exchanger characteristics. The heat exchanger optimization system 102 can then assess whether the heat exchanger design is convergent to determine whether the design should be finalized or whether the heat exchanger optimization should be repeated.

[0079] Preliminary heat exchanger designs can be generated assuming laminar flow for the external fluid. The heat exchanger designs can then be evaluated using a feasible two-equation k-e turbulence model. The heat exchanger optimization system 102 can use the feasible k-e model to determine the turbulent viscosity and employ a new transport equation for the dissipation rate e to transport the mean square vorticity function. The unclosed Reynolds stress term in the momentum equation of the two-equation k-e model is closed by solving a transport equation for the turbulent kinetic energy k and the turbulent dissipation rate to find the apparent turbulent viscosity. The equations describing the incompressible turbulent flow The average steady-state equations can be written as equation 21, equation 22, and equation 23: _ n (21) 5xt “ u dU.- - ôU; np p / _ _ r}\ P dt + P G j dXi âx" + âxÿ ( " pUjUjJ (22) ôtT , TT dT _ a / dT \ (23) dt ' jdXj dXj ( adXj ) dX j

[0080] The quantity -pu j' ui is called the Reynolds stress tensor (for i, j (= 1,2,3), a is the thermal diffusivity, and u j' T is the temperature fluctuation. Sp = S.. is the strain rate tensor given by equation 24: C_iW.V 24) 2 \ aX; ' dXj /

[0081] The turbulent stress and the fluctuating components can be expressed by equation 25 and equation 26: -pUjU^p^. <25) (26) Uj 1 pr fâ-,

[0082] The transport equations can be expressed as equation 27 and equation 28: at(pk) + ^ / (pkUj) =^.((^+^)^ +Gk+Gb-pe+Sk (27) ïï(Pe) +^(PeUj) -^[(p+^}^]+PCiSije-PC2f^f + CleTC3eGb+Se (28)

[0083] Gk represents the production of turbulent kinetic energy due to mean velocity gradients and is given by equation 29: ,dUj (29) Gk= -pUiUjdï' k

[0084] Gb represents the production of turbulent kinetic energy due to buoyancy and is given by equation 30: (30)

[0085] 9i is the component of the gravitational vector in the zth direction. Prt is the turbulent Prandtl number and fi is the coefficient of thermal expansion given by equation 31: P — _1(ËP} (31) P~ P\dT J

[0086] Se and Sk are user-defined source terms. Cle and C2 are constants and C1=max[0.43, where T]=Sjj^ .(Je and (J k are turbulent Prandtl numbers for e and k.

[0087] The apparent turbulent viscosity described above can be represented using equation 32, equation 33, equation 34, equation 35, equation 36, Equation 37, equation 38, equation 39, equation 40, equation 41 and equation 42: p t = pc„<< 32 ' c -___1___ (33) (<34) Q.ij = Qjj - 2€ijkO)k (35) Qjj = Qjj - jk^k HAS o = 4.O4 (37) As = \[6cos(l) (38) $ = jcos- 1 ^ iv) ( 39 ) _ SijSjkSki (40) ~ s3 -pUjU^i^Sij <41) 'T'_ ar (42) uj1 pPrt

[0088] The apparent turbulent viscosity values ​​Vf can be estimated using a Gaussian process (GP) machine learning model. For example, once the space-averaged turbulent viscosity is extracted from the k-e-based calculations for each of the preliminary designs, a GP model can be trained using the area density as the input parameter. The area density is defined as the ratio of the total external surface area of ​​the heat exchanger to the volume occupied by the heat exchanger. The input for the GP model is the area density, and the output is the turbulent viscosity. The Gaussian function is expressed as a probability function as shown in Equation 43: , । i / (y-pfV43) p(y\p,a2j=£=;ex^-^

[0089] In equation 43, P is the mean and (j2 is the variance.

[0090] In certain embodiments, such as for aerospace applications, heat exchanger designs often take into account the wet weight of the system, the combined weight of the solid heat exchanger structure and the internal fluid. Therefore, the optimization challenge is to maximize the power density of the heat exchanger. This measurement is derived from the heat transfer rate of the internal fluid, normalized by the wet weight. The objective function taking into account the wet weight of the system can be expressed by equation 44: f / \ (44) J nu^ c 1-T d^ Z- * outlet. 1 A / " x{pi+xjps

[0091] Xiet xssont are the design variables for the first fluid (i.e. the internal fluid) and the solid structure of the heat exchanger, and P^ and Ps are the vectors of the density value of the first fluid and the solid structure of the heat exchanger.

[0092] The two objective functions of equation 15 and equation 44 can be used to optimize the design of the heat exchanger. For example, the initial objective function of equation 15 can be applied during the preliminary iterations, particularly when the solid wall boundary is still nascent and fluids are mixing. As the design progresses and the two fluid flows are distinctly separated, the objective function can be transferred to that represented by equation 44. This change of objective functions can ensure that the overall weight of the design remains under control.

[0093] To obtain a more structured design, pressure drop constraints can be imposed on both fluids. As described above, the pressure drop can be controlled to regularize the geometry and impose restrictions on the pumping power, manifesting the controlled pressure drop in the algorithm as a constraint. The pressure drop constraint can be expressed by equation 45: fr p1 dA^P^op for 1=1, 2 1 inlet, i (45)

[0094] P drop is 'a Prctc of maximum permissible pressure on the fluid i.

[0095] The final optimization problem can be formulated as equation 46: Find x = |xi, x 2, •••,%„] T (45) Maximize f(x, uj, u2, T) Subject to Rt>i = 0 for i= 1.2 R t = 0 Jp. P1 dA< P drop 1 mlet, i ui = 0 on rwaU, i U i Uin jOn F iniet i Pi 0 Oïl F'outlet'l TT Oll T^in / eC 1 • U — 0 On T^wa / h ^aar / erri xe R": 0 < x < 1

[0096] In equation 45, Rr and RT are the residual form of the fluid flow and heat transfer equations. Optimization of mechanical requirements

[0097] Once the heat exchanger optimization system 102 determines a heat exchanger design using heat exchanger optimization, the heat exchanger optimization system 102, for example via the mechanical requirements optimization engine 130, can perform mechanical requirements optimization. Mechanical requirements optimization includes modifying the heat exchanger design to ensure that the heat exchanger can withstand mechanical requirements while maintaining the most efficient material distribution. In example implementations, the mechanical requirements include vibration load requirements for aerospace applications. The load requirements can be a combination of a cyclic load with a frequency that varies with time and / or a cyclic load with a frequency equal to the natural frequency of the design.The heat exchanger optimization system 102 can optimize the heat exchanger to withstand a load where the cyclic load frequency varies continuously with respect to time in example implementations.

[0098] Mechanical requirements optimization can be performed using a fatigue-constrained topology optimization. The objective of the optimization scheme is the L1 norm of the difference between the wall densities of the optimized model generated by the mechanical requirements optimization and that of the heat exchanger design obtained from the heat transfer optimization described above, ensuring that the output from the mechanical requirements optimization will be similar to the heat exchanger design obtained from the heat transfer-based topology optimization. The L1 norm function used as the objective function of the optimization and its sensitivity can be represented as shown in Equations 46 and 47: fw = 2.1(^-¾)] (46) Sensitivity = -^ = ' j ll, if^x^xj n (47)

[0099] The constraint used in the optimization can be the fatigue damage or failure criterion that ensures the mechanical requirements are met (for example, the combined load for aerospace applications would not exceed a fatigue damage value of one). The fatigue damage criterion can be based on fatigue damage or failure criteria accessible to the heat exchanger optimization system 102, for example, such as those received from one or more external systems 104 and / or one or more user devices 106. The fatigue damage constraint can be represented as shown in equations 48 and 49: 'S dt+-l<0 <48) ^i=l J oN(t) N(f)=^(49)

[0100] load is the number of load cases, f(t) is the load frequency as a function of time, N is the number of cyclic loads that would cause failure. Wq is the first natural vibration frequency of the model, θ is the application time in the case of a load with the natural frequency, B and m are material properties. The fatigue damage stress indicated in equation 48 can be formulated such that when a repetitive load is applied to the structure, the heat exchanger does not fail. The stress can also consider a cyclic load with a frequency equal to the natural frequency of the structure.

[0101] In an exemplary embodiment, the mechanical requirements consist of frequency sweep cycling and residence at natural frequencies. The fatigue damage equation may differ for each of the loading phases. For example, the fatigue damage variable for frequency sweep cycling and its sensitivity are given in equations 50 and 51 shown below. Equations 52 and 53, shown below, contain the expression for fatigue damage and its sensitivity for the residence phase at natural frequencies. _ 2^0V_e2_ y 1— Bln2^JC^l maxUnit (50) _m2m60 y* eC2 ( r (Cpn+1) £• (C-^m+l)\ ni-1 dx — B ln2 C.m+l \2 " 1 .. dx J max Unit (51) — ^O^dwell (52) g2~ N(o>0) d®2 _ / tdweii \ da>0 (53) dx \n(c^~ d(^ ) dx

[0102] Equation 54 and equation 55 expand the terms dw0 and of the equation dx of the,, 53: dcu0 _ ! u^^)u (54) dx “ 2^ aTMu dN(^ _ -2mBamaxUnit dA (55) dœ0 f dw0 t ' u / maxUiuW

[0103] The heat exchanger optimization system 102 can use any equation to model the heat exchanger design and perform a structural analysis to satisfy mechanical requirements. The structural analysis can generate one or more solutions to be used as input to the objective function. The heat exchanger optimization system 102 can apply DfAM filters as described above to maintain the manufacturability of the heat exchanger design. The heat exchanger optimization system 102 can then perform a structural analysis (e.g., a burst pressure test, a vibration and fatigue load test, etc.), calculate the objective function and sensitivity, and optimize the heat exchanger design.In some embodiments, the heat exchanger optimization system 102 uses MMA to optimize the heat exchanger design for mechanical requirements. The heat exchanger optimization system 102 can repeatedly perform the optimization of mechanical requirements, iteratively updating the heat exchanger design until the design has converged to satisfy the mechanical requirements, resulting in a heat exchanger design optimized in terms of both heat transfer and mechanics.

[0104] In some embodiments, the heat exchanger optimization system 102 can perform optimization for heat transfer and other heat exchanger characteristics and optimization for mechanical requirements simultaneously, or alternatively, be integrated into a single optimization process. In other embodiments, the heat exchanger optimization system 102 can perform further optimization for heat transfer and other heat exchanger characteristics after performing optimization for mechanical requirements. Thus, the heat exchanger optimization system 102 can adjust the heat exchanger design to optimize heat transfer and other heat exchanger characteristics while meeting mechanical requirements. Support generation

[0105] Once both heat transfer optimization and mechanical requirements optimization are complete, the heat exchanger optimization system 102, for example via the support generation engine 140, can generate all the necessary supports for unsupported features of the heat exchanger design. For example, the heat exchanger optimization system 102 evaluates the heat exchanger design to identify all unsupported areas and generates supports to support the identified unsupported areas. Self-supporting areas (for example, regions that satisfy cantilever constraints and / or other self-supporting constraints) can be evaluated as supported.The heat exchanger optimization system 102 can aim to generate the smallest and / or fewest supports needed to support identified unsupported areas in order to minimize the mass of the final heat exchanger design, maintain heat transfer capabilities, and / or similar.

[0106] In some embodiments, the topology-optimized heat exchanger will be in a voxel format, so the heat exchanger optimization system 102 uses voxel-based support generation to generate supports for the geometry. The heat exchanger optimization system 102 can identify unsupported voxels by evaluating an area below and / or around each voxel constituting the heat exchanger (for example, a three-by-three voxel area, a five-by-five voxel area, etc.). If any of the voxels in the evaluated area contains a solid voxel, the heat exchanger optimization system 102 can determine that the evaluated voxel is supported. If no solid voxels are present in the search area, the heat exchanger optimization system 102 can determine that the evaluated voxel is unsupported.

[0107] Once the heat exchanger optimization system 102 identifies unsupported voxels, it generates supports for all unsupported voxels. The heat exchanger optimization system 102 can use existing voxels as part of the heat exchanger design and employ a support angle criterion to generate the smallest and / or fewest supports for the unsupported voxels. For all part voxels in this subset, the distance between the part voxel and the unsupported voxel is calculated, and the nearest part voxel is selected to create the support for the unsupported voxel.Once all voxels of the heat exchanger are supported, the 102 heat exchanger optimization system can finalize the heat exchanger design, resulting in a final heat exchanger design that is heat transfer. and / or other optimized heat exchanger features, optimized for mechanical requirements, and fully supported.

[0108] In some embodiments, the resolution of the generated support voxels is selected so that the resolution is greater than that of the heat exchanger voxels, for example, so that the supports are not eroded when the final geometry is smoothed using smoothing algorithms. The geometry of the supports is an elliptical cylinder in the example embodiments. The heat exchanger optimization system 102 can create each cylinder connecting the unsupported voxel and the solid voxel base to which the support will be connected. The heat exchanger optimization system 102 can select the width of each ellipse so that the cross-section of the supports is a circle with a diameter equal to the minimum feature size of the additive manufacturing process (for example, as defined by the thin feature minimization filter).Furthermore, to maintain the structural integrity of the overall design, the Heat Exchanger Optimization System 102 can iteratively increase the size of the support structures so that the maximum Von Mises stress of the part under self-loading conditions is less than the material's yield strength. This ensures that the generated supports will support the targeted voxels identified as unsupported while maintaining the smallest possible size. Once the Heat Exchanger Optimization System 102 generates the supports, it can evaluate whether any supports can be removed using machining operations for the six coordinate directions. Support voxels that are in the line of sight and not obstructed by solid voxels can be marked as accessible supports. Examples of heat exchangers

[0109] Figure 6 illustrates examples of optimized heat exchangers 600. The example optimized heat exchangers 600 include a first optimized heat exchanger 602 and a second optimized heat exchanger 604. The first optimized heat exchanger 602 and the second optimized heat exchanger 604 include an inlet 610, an outlet 612, and optimized structures 204 arranged in the respective heat exchanger structure. In some embodiments, the heat exchanger optimization system 102 determines the respective optimized structures 204 for the first optimized heat exchanger 602 and the second optimized heat exchanger 604 based on the operating conditions of the respective heat exchanger, resulting in distinctive designs and / or arrangements of the respective optimized structures 204. Processes

[0110] Figure 7 is a flowchart of a process 700 for optimizing a heat exchanger. The process 700 can begin at operation 702, and operating conditions are determined. For example, the heat exchanger optimization system 102 determines the operating conditions for a heat exchanger design. The heat exchanger optimization system 102 can receive the operating conditions from one or more external systems 104 and / or one or more user devices 106 in example implementations. The operating conditions can include a design envelope, desired heat exchanger characteristics, design constraints, unit cell information, an operating temperature, environmental fluid characteristics, expected mechanical constraints, and / or the like.

[0111] In operation 704, heat transfer optimization is performed. For example, the heat exchanger optimization system 102 performs the heat transfer optimization as described above. The heat exchanger optimization system 102 can perform heat transfer optimization for the heat exchanger design based on one or more operating conditions determined in operation 702 in order to generate a heat exchanger design optimized in terms of heat transfer. DfAM filters such as a thin feature minimum filter, a support filter, a projection filter, and / or the like can be implemented to maintain the manufacturability of the heat exchanger.Achieving heat transfer optimization may involve generating a structure within the dimensions of a unit cell (e.g., unit cell 202) and arranging the structure repeatedly to generate a heat exchanger structure.

[0112] In step 706, mechanical requirements optimization is performed. For example, the heat exchanger optimization system 102 performs the mechanical requirements optimization as described above. The heat exchanger optimization system 102 can perform mechanical requirements optimization for the heat exchanger design optimized in terms of heat transfer in order to generate a heat exchanger design optimized in terms of both heat transfer and mechanics. DfAM filters such as a minimum thin feature filter, a support filter, a projection filter, and / or the like can be implemented to maintain the manufacturability of the heat exchanger. The performance of the mechanical requirements optimization may include performing vibration fatigue load modeling. In step 708, supports are determined.For example, the heat exchanger optimization system. 102 determines one or more supports for the design of a heat exchanger optimized in terms of heat transfer and mechanics in order to generate a final heat exchanger design.

[0113] The heat exchanger optimization system 102 can implement one or more DfAM filters for heat transfer optimization and / or heat exchanger optimization. For example, the heat exchanger optimization system 102 can implement an operational thin feature minimum filter to minimize geometric features smaller than a threshold size in the final heat exchanger design, an operational support filter to minimize support structures required in the final heat exchanger design, and / or an operational projection filter to generate solid and void sections for heat exchanger design sections with fractional densities. The thin feature minimum filter, projection filter, and / or support filter can be implemented as described above.

[0114] Figure 8 is a flowchart of a process 800 for heat transfer optimization. The process 800 can be implemented within the process 700, for example, to perform operations 702 and 704. The process 800 can begin at operation 802, and operating conditions are determined. For example, the heat exchanger optimization system 102 determines the operating conditions for a heat exchanger design. The heat exchanger optimization system 102 can receive the operating conditions from one or more external systems 104 and / or one or more user devices 106 in example implementations.Operating conditions may include a design envelope, desired heat exchanger characteristics, design constraints, unit cell information, operating temperature, environmental fluid characteristics, expected mechanical constraints, and / or similar.

[0115] In operation 804, DfAM filters are implemented. For example, the heat exchanger optimization system 102 implements one or more DfAM filters such as a minimum thin feature filter, a support filter, a projection filter and / or the like to maintain the manufacturability of the heat exchanger.

[0116] In operation 806, a FEM analysis is performed. For example, the heat exchanger optimization system 102 performs an FEM analysis as described above. The FEM analysis may include the mass transfer problem and the heat transfer problem as described above.

[0117] In operation 808, the objective function and sensitivity are determined. For example, the heat exchanger optimization system 102 determines a rate Heat transfer can be measured using an objective function that employs one or more solutions from the FEM analysis as described above. Sensitivity can be determined in the same manner as described above.

[0118] During operation 810, the heat exchanger design is optimized in terms of heat transfer. For example, the heat exchanger optimization system 102 optimizes the heat exchanger design for heat transfer and / or other heat exchanger characteristics based on the heat transfer rate and sensitivity.

[0119] In decision 812, the potential convergence of the heat exchanger design for heat transfer is determined. When the heat exchanger design is not convergent, process 800 can proceed to operation 814, and the heat exchanger optimization system 102 can update heat exchanger design variables as needed (e.g., the design variable-*-). The process can then return to operation 804 so that heat transfer optimization can be performed iteratively. When the heat exchanger design converges at decision 812, the heat transfer-optimized heat exchanger design can be generated.

[0120] Figure 9 is a flowchart of a process 900 for optimizing mechanical requirements. Process 900 can be implemented in process 700, for example to perform operation 706. Process 900 can start at operation 902, and the heat exchanger design optimized in terms of heat transfer can be obtained, for example after the heat transfer optimization has been performed.

[0121] In operation 904, DfAM filters are implemented. For example, the heat exchanger optimization system 102 implements one or more DfAM filters such as a minimum thin feature filter, a support filter, a projection filter and / or the like to maintain the manufacturability of the heat exchanger.

[0122] In operation 906, a structural analysis is performed. For example, the heat exchanger optimization system 102 performs a structural analysis for one or more mechanical requirements as described above. In operation 908, the objective function and sensitivity are determined. For example, the heat exchanger optimization system 102 determines an L1 standard for the difference between the wall densities of the heat exchanger design optimized in terms of heat transfer and the heat exchanger design optimized in terms of both heat transfer and mechanics, using an objective function that employs one or more solutions from the structural analysis as described above. The sensitivity can be determined in the same way as described above.

[0123] During operation 910, the heat exchanger design is optimized for mechanical requirements. For example, the heat exchanger optimization system 102 optimizes the heat exchanger design in terms of heat transfer for one or more mechanical requirements based on the L1 standard and sensitivity.

[0124] In decision 912, it is determined whether the heat exchanger design optimized for heat transfer is convergent with respect to mechanical requirements. When the heat exchanger design is not convergent, process 900 can proceed to operation 914, and the heat exchanger optimization system 102 can update heat exchanger design variables as needed (e.g., the design variable). The process can then return to operation 904 so that the optimization of mechanical requirements can be performed iteratively. When the heat exchanger design is convergent at decision 912, the heat exchanger design optimized in terms of both heat transfer and mechanics can be generated.The optimized heat exchanger design can then be used by one or more systems to manufacture one or more optimized heat exchangers, for example by additive manufacturing.

[0125] In certain embodiments, a method for manufacturing an optimized heat exchanger includes performing additive manufacturing based on a final heat exchanger design produced through the steps of: determining one or more operating conditions for a heat exchanger design, performing heat transfer optimization for the heat exchanger design based on the one or more operating conditions in order to generate a heat exchanger design optimized in terms of heat transfer, performing mechanical requirements optimization for the heat exchanger design optimized in terms of heat transfer in order to generate a heat exchanger design optimized in terms of both heat transfer and mechanics,and determine one or more supports for the heat exchanger design optimized in terms of heat transfer and mechanics in order to generate a final heat exchanger design. The final heat exchanger design can be generated using any combination of the processes and techniques described here. Manufacturing systems can use manufacturing techniques, including additive manufacturing techniques, to produce a heat exchanger based on the final heat exchanger design.

[0126] In some embodiments, a heat transfer process includes the use of a heat exchanger designed according to a final heat exchanger design produced through the steps of: determining a or Several operating conditions for a heat exchanger design are considered; heat transfer optimization is performed for the heat exchanger design based on one or more operating conditions to generate a heat transfer-optimized heat exchanger design; mechanical requirements optimization is performed for the heat transfer-optimized heat exchanger design to generate a heat transfer and mechanically optimized heat exchanger design; and one or more supports are determined for the heat transfer and mechanically optimized heat exchanger design to generate a final heat exchanger design. The final heat exchanger design can be generated using any combination of the processes and techniques described herein.Manufacturing systems can use manufacturing techniques, including additive manufacturing techniques, to produce a heat exchanger based on the final heat exchanger design. Systems

[0127] Figure 10 is a functional diagram of a computer device 1000. As shown in Figure 10, the computer device 1000 may include a processing unit 1010 and a memory unit 1015. The memory unit 1015 may include a software module 1020 and a database 1025. During execution on the processing unit 1010, the software module 1020 may execute, for example, processes to optimize heat exchangers with respect to Figures 1 to 9. The computer device 1000, for example, may provide an operating environment for the heat exchanger optimization system 102, external systems 104, user devices 106, and the like. The heat exchanger optimization system 102, external systems 104, user devices 106, and similar systems can operate in other environments and are not limited to the computer device 1000.

[0128] The Computing Device 1000 can be implemented using a Wi-Fi access point, a tablet device, a mobile device, a smartphone, a telephone, a personal computer, a network computer, a main computer, a router, a switch, a server group, a network storage device, a network relay device, or another similar microcomputer-based device. The Computing Device 1000 can include any computing operating environment, such as handheld devices, multiprocessor systems, microprocessor-based or programmable electronic sending devices, minicomputers, mainframes, and the like. The Computing Device 1000 can also be implemented in distributed computing environments where tasks are performed by remote processing devices. The systems and devices mentioned above are examples, and the computer system 1000 may include other systems or devices.

[0129] Figure 11 illustrates an implementation of a communication device 1100 that can implement one or more of the heat exchanger optimization system 102, external systems 104, user devices 106, etc., of Figures 1 to 9. In various implementations, the communication device 1100 may include a logic circuit. The logic circuit may include physical circuits for performing operations described for one or more of the heat exchanger optimization system 102, external systems 104, user devices 106, etc., of Figures 1 to 9, for example. As shown in Figure 11, the communication device 1100 may include one or more of, but not limited to, a radio interface 1110, a baseband circuit 1130, and / or the computer device 1000.

[0130] The communication device 1100 can implement some or all of the structures and / or operations for the heat exchanger optimization system 102, the external systems 104, the user devices 106, etc., of Figures 1 to 9, a storage medium, and a logic circuit in a single computing entity, for example, entirely in a single device. Alternatively, the communication device 1100 can distribute parts of the structure and / or operations using a distributed system architecture, such as a client-station server architecture, a peer-to-peer architecture, a master-slave architecture, etc.

[0131] A radio interface 1110, which may also include an analog front end (AFE), may include a component or combination of components adapted to transmit and / or receive single-carrier or multi-carrier modulated signals (for example, including a complementary code key (CCK), orthogonal frequency-division multiplexing (OFDM), and / or single-carrier frequency-division multiple access (SC-FDMA) symbols), although the configurations are not limited to any specific interface or modulation scheme. The radio interface 1110 may include, for example, a receiver 1115 and / or a transmitter 1120. The radio interface 1110 may include bias controls, a crystal oscillator, and / or one or more antennas 1125. In additional or alternative configurations, the radio interface 1110 may use oscillators and / or one or more filters, as required.

[0132] The baseband circuits 1130 can communicate with the radio interface 1110 to process, receive and / or transmit signals and can include, for example, an analog-to-digital converter (ADC) to down-convert received signals with a digital-to-analog converter (DAC) 1135 to up-convert the signal conversion for transmission. In addition, baseband circuits 1130 may include a baseband or physical (PHY) layer processing circuit for PHY link layer processing of the respective receive / transmit signals. Baseband circuits 1130 may include, for example, a media access control (MAC) processing circuit 1140 for MAC link layer / data processing. Baseband circuits 1130 may include a memory control device for communicating with the MAC processing circuit 1140 and / or a computing device 1000, for example, via one or more interfaces 1145.

[0133] In certain configurations, the PHY processing circuit may include a frame construction and / or detection module, in combination with additional circuitry such as a buffer, for constructing and / or deconstructing communication frames. Alternatively, or in addition, the MAC 1140 processing circuit may share the processing for some of these functions or perform these processes independently of the PHY processing circuit. In some configurations, the MAC and PHY processing functions may be integrated into a single circuit.

[0134] With general reference to the above process, it is noted that certain aspects may be performed in different orders. Embodiments of the present invention, for example, are described above with reference to functional diagrams and / or operational illustrations of computer program processes, systems, and products according to embodiments of the invention. The functions / actions noted in the blocks may occur in the order indicated in any flowchart. For example, two blocks presented successively may in fact be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order, depending on the functionality / actions involved.

[0135] The description and illustration of one or more embodiments provided in this application are not intended to limit or restrict the scope of the invention as claimed in any way. The embodiments, examples, and details provided in this application are deemed sufficient to confer ownership and enable others to manufacture and use the best embodiment of the claimed invention. The claimed invention shall not be construed as being limited to any one embodiment, example, or detail provided in this application. Whether represented and described in combination or separately, the various features (both structural and methodological) are intended to be selectively included or omitted to produce an embodiment with a particular set of features.Having received the description and illustration of the present application, a person skilled in the art may consider variations, modifications and alternative embodiments falling within . the spirit of the broader aspects of the general inventive concept incorporated in the present application which do not fall outside the broader scope of the claimed invention.

[0136] The exemplary embodiments described herein can be implemented using hardware, software, or a combination thereof, and can be implemented in one or more computer systems or other processing systems. However, the manipulations performed by these exemplary embodiments have often been referred to in terms such as input, which are generally associated with mental operations performed by a human operator. No such human operator capability is required in any of the operations described herein. On the contrary, the operations can be implemented entirely with machine operations. Machines useful for performing the operation of the exemplary embodiments presented herein include general-purpose digital computers or similar devices.

[0137] Embodiments of the disclosure, for example, may be implemented as a computer process (method), computer system, or manufactured item, such as a computer program product or a computer-readable medium. The computer program product may be a computer storage medium readable by a computer system and encoding a computer program of instructions to execute a computer process. The computer program product may also be a signal propagated on a medium readable by a computer system and encoding a computer program of instructions to execute a computer process. Accordingly, this disclosure may be implemented in hardware and / or software (including firmware, resident software, microcode, etc.).In other words, embodiments of this disclosure may take the form of a computer program product on a usable or computer-readable storage medium containing usable or computer-readable program code embedded in the medium for use by or in connection with an instruction-executing system. A usable or computer-readable medium may be any medium that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction-executing system, apparatus, or device. The usable or computer-readable medium may be, for example, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor propagation system, apparatus, device, or medium.

[0138] For more specific examples of machine-readable media (a non-exhaustive list), machine-readable media may include the following: An electrical connection with one or more wires, a laptop diskette, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, and a portable compact disc read-only memory (CD-ROM). It should be noted that the usable or computer-readable medium could even be paper or another suitable medium on which the program is printed, since the program can be captured electronically, for example, by optical scanning of the paper or other medium, then compiled, interpreted, or otherwise processed appropriately, if necessary, and then stored in computer memory.Furthermore, embodiments of disclosure can be implemented in an electrical circuit comprising discrete electronic components, packaged or integrated electronic chips containing logic gates, a circuit using a microprocessor, or on a single chip containing electronic components or microprocessors. Disclosure embodiments can also be implemented using other technologies capable of performing logical operations such as, for example, AND, OR, and NOT, including, but not limited to, mechanical, optical, fluidic, and quantum technologies. In addition, disclosure embodiments can be implemented in a general-purpose computer or in any other circuit or system.

[0139] Embodiments of disclosure can be implemented via a system-on-chip (SoC) where each or more of the elements described herein (for example, the elements of the heat exchanger optimization system 102) can be integrated onto a single integrated circuit. Such an SoC device can include one or more processing units, graphics units, communication units, system virtualization units, and various application functionality, all of which can be integrated (or "burned") onto the chip substrate as a single integrated circuit. When operating via an SoC, the functionality described herein, with respect to embodiments of disclosure, can be performed via application-specific logic integrated into other components of the computing device 1000 on the single integrated circuit (chip).

[0140] From a hardware perspective, a central processing unit typically includes one or more components, such as one or more microprocessors, to perform the arithmetic and / or logical operations required for program execution, and storage media, such as one or more memory cards (e.g., flash memory) for program and data storage, and random access memory for temporary storage of data and program instructions. From a software perspective, a CPU generally includes software residing on a storage medium (e.g., a memory card), which, when executed, directs The CPU performs transmission and reception functions. CPU software can run on an operating system stored on the storage medium, such as Unix or Windows, iOS, Linux, and similar systems, and can adhere to various protocols such as Ethernet, ATM, TCP / IP, and / or other connection-oriented or connectionless protocols. As is well known in the field, CPUs can run different operating systems and can contain different types of software, each type dedicated to a different function, such as manipulating and managing data / information from a particular source or transforming data / information from one format to another.It should therefore be clear that the embodiments described herein should not be interpreted as being limited to use with a particular type of server computer, and that any other type of device suitable for facilitating the exchange and storage of information may be used instead.

[0141] A central processing unit (CPU) may be a single CPU, or it may include several separate CPUs, each dedicated to a separate application, such as, for example, a data application, a voice application, and a video application. Software embodiments of the example embodiments shown herein may be supplied as a computer program product, or software, which may include a manufacturing article on an accessible or non-transient computer-readable medium (i.e., also called a "computer-readable medium") containing instructions. The instructions on the accessible or machine-readable medium may be used to program a computer system or other electronic device.Machine-readable media may include, but are not limited to, optical discs, CD-ROMs, and magneto-optical discs, or any other type of suitable machine-readable media for storing or transmitting electronic instructions. The techniques described herein are not limited to any particular software configuration. They may be applicable in any computing or processing environment. The terms "machine-accessible media," "machine-readable media," and "computer-readable media" used herein should include any non-transient media capable of storing, encoding, or transmitting a sequence of instructions for execution by a machine (e.g., a CPU or other type of processing device) and that causes the machine to perform any of the processes described herein.Furthermore, it is common in engineering to speak of software, in one form or another (e.g., program, procedure, process, application, module, unit, logic, etc.), as taking an action or producing a result. Such expressions are simply a shorthand way of indicating that the execution of software by a processing system causes the processor to perform an action to produce a result.

[0142] Although various exemplary embodiments have been described above, it should be understood that they have been presented by way of example, and not by way of limitation. It will be apparent to those skilled in the art that various modifications of form and detail can be made to them. Thus, the present invention should not be limited by any of the exemplary embodiments described above, but should be defined solely in accordance with the following claims and their equivalents.

Claims

Demands

1. Method, comprising the steps of: determining one or more operating conditions for a heat exchanger design; perform heat transfer optimization for heat exchanger design based on one or more operating conditions to generate a heat exchanger design optimized in terms of heat transfer; the realization of heat transfer optimization including the steps of performing a finite element method (FEM) analysis, in which the FEM analysis includes solving a mass transfer problem and a heat transfer problem, determining a heat transfer rate using an objective function, determining a sensitivity of the objective function and adjusting the heat exchanger design based on the FEM analysis, the heat transfer rate and the sensitivity; performing a mechanical requirements optimization for the heat exchanger design optimized in terms of heat transfer in order to generate a heat exchanger design optimized in terms of heat transfer and mechanics;and determine one or more supports for the design of a heat exchanger optimized in terms of heat transfer and mechanics in order to generate a final heat exchanger design, and to manufacture a heat exchanger by additive manufacturing from the final heat exchanger design.

2. System comprising: a memory storage; and a processing unit coupled to the storage memory, in which the processing unit is operational for: determining one or more operating conditions for a heat exchanger design; perform heat transfer optimization for heat exchanger design based on one or more operating conditions in order to generate a heat exchanger design optimized in terms of heat transfer; the implementation of heat transfer optimization consisting of performing a finite element method (FEM) analysis, in which the FEM analysis includes solving a mass transfer problem and a heat transfer problem, determining a heat transfer rate using an objective function, determining a sensitivity of the objective function and adjusting the heat exchanger design based on the FEM analysis, the heat transfer rate and the sensitivity; performing a mechanical requirements optimization for the heat transfer optimized heat exchanger design in order to generate a heat transfer and mechanically optimized heat exchanger design; and determining one or more supports for the heat transfer and mechanically optimized heat exchanger design in order to generate a final heat exchanger design.

3. A system according to claim 3, wherein the performance of heat transfer optimization further comprises the steps of: evaluating whether the heat exchanger design is convergent for heat transfer; when the heat exchanger design is not convergent, repeating the performance of the FEM analysis, determining the heat transfer rate using the objective function, determining the sensitivity of the objective function and adjusting the heat exchanger design on the basis of the heat transfer rate and sensitivity; and when the heat exchanger design is convergent, generating the heat transfer-optimized heat exchanger design.

4. System according to any one of claims 2 to 4, wherein the processing unit is further operational for implementing one or more DfAM filters for any of (i) heat transfer optimization, (ii) mechanical requirements optimization, or (iii) both (i) and (ii), the one or more DfAM filters comprising a minimum thin feature filter operational for minimizing geometric features with a size less than a threshold size in the final heat exchanger design.

5. A system according to any one of claims 2 to 5, wherein the performance of the optimization of mechanical requirements comprises the steps of: performing a structural analysis for one or more mechanical requirements; determining an L1 standard of a difference between wall densities of the heat transfer-optimized heat exchanger design and the heat transfer- and mechanically optimized heat exchanger design using an objective function; determining a sensitivity of the objective function; and adjusting the heat transfer-optimized heat exchanger design based on the structural analysis, the L1 standard, and the sensitivity.

6. System according to any one of claims 2 to 6, wherein the realization of the optimization of mechanical requirements includes vibration fatigue load modeling.

7. A system according to any one of claims 2 to 7, wherein the achievement of heat transfer optimization for heat exchanger design based on one or more operating conditions to generate the heat transfer-optimized heat exchanger design comprises the steps of: generating a structure in the dimensions of a unit cell; and arranging the structure repeatedly to generate a heat exchanger structure.

8. System according to any one of claims 2 to 8, wherein the processing unit is further operational to implement one or more DfAM filters for any of (i) heat transfer optimization, (ii) mechanical requirements optimization, or (iii) both (i) and (ii), the one or more DfAM filters comprising an operational support filter to minimize the support structures required in the final heat exchanger design.

9. A system according to any one of claims 2 to 9, wherein the processing unit is further operational for the step of implementing one or more DfAM filters for any of (i) heat transfer optimization, (ii) the optimization of mechanical requirements, or (iii) both (i) and (ii), one or more DfAM filters including an operational projection filter to generate solid sections and void sections for heat exchanger design sections with fractional densities.

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