Dynamic modeling and simulation method for opposed-piston stirling generator system

Abstract

The application relates to the field of simulation aided design, and provides a dynamic modeling and simulation method for a opposed free-piston Stirling power generation system. The dynamic modeling and simulation method for the opposed free-piston Stirling power generation system comprises a physical model simulation module group, a single-machine physical model containing an expansion cavity, a compression cavity, a hot-end heat exchanger, a regenerator, a cold-end heat exchanger, an ejector and a power piston is constructed; the expansion cavity is provided with a gas port; the single-machine physical model is multiplexed to obtain two single-machine physical models; the gas port of the expansion cavity of one single-machine physical model is connected with the gas port of the expansion cavity of the other single-machine physical model to realize thermodynamic coupling modeling of the opposed free-piston Stirling power generation system of the common expansion cavity type. The dynamic modeling and simulation method for the opposed free-piston Stirling power generation system can realize efficient simulation of dynamic coupling of heat, flow, machine and electricity multi-physical domains, supports reuse, has expansibility and maintainability, and can be used for various application scenarios.

Description

Technical Field

[0001] This invention relates to the field of simulation-aided design, and provides a dynamic modeling and simulation method for a Stirling generator system with opposed free pistons. Background Technology

[0002] The statements herein are provided only as background information in connection with this application and do not necessarily constitute prior art.

[0003] The free-piston Stirling generator is a highly efficient thermoelectric conversion device. Its main feature is the use of the Stirling cycle principle to efficiently convert heat energy into electrical energy. The advantages of this generator include high efficiency, long lifespan, and wide applicability to various heat sources, making it suitable for solar power generation, combined heat and power (CHP), and deep space exploration. By eliminating the traditional crank-connecting rod mechanism and gas-coupled between the exhaust manifold and the power piston, the free-piston Stirling generator eliminates lateral forces, significantly reducing mechanical wear and improving system efficiency. However, because this design does not fix the stroke and phase difference between the exhaust manifold and the power piston, the system is more sensitive to operating conditions and external loads.

[0004] Previous modeling and simulation methods for free-piston Stirling generators have mostly relied on certain ideal assumptions, such as the Schmidt isotherm or adiabatic assumption. These assumptions simplify the calculation process but ignore many complex energy losses in the real system, failing to accurately reflect the system's operating characteristics. Currently, most models have limitations in handling these complex factors, especially in dealing with nonlinear factors such as pressure drop losses, gap sealing, and key dynamic phenomena such as piston drift, where they generally exhibit poor accuracy. Therefore, existing simplified models cannot accurately predict the actual performance and dynamic response characteristics of free-piston Stirling generators under different operating conditions, limiting their further research and application. While CFD (Computational Fluid Dynamics) methods can achieve high accuracy in simulating free-piston Stirling generators, they consume enormous computational resources and are slow in computation speed. Summary of the Invention

[0005] This invention provides a dynamic modeling and simulation method for a free-piston Stirling generator system, which addresses the shortcomings of existing models in related technologies that cannot accurately predict the actual performance and dynamic response characteristics of a free-piston Stirling generator under different operating conditions.

[0006] This invention provides a dynamic modeling and simulation method for a Stirling generator system with opposed free pistons, comprising: Based on the physical model simulation module group, a single-machine physical model is constructed, including an expansion chamber, a compression chamber, a hot-end heat exchanger, a regenerator, a cold-end heat exchanger, an exhaust device, and a power piston; the expansion chamber has a gas port; By reusing the single-machine physical model, two single-machine physical models are obtained; The gas port of the expansion cavity of one single-machine physical model is connected to the gas port of the expansion cavity of another single-machine physical model to achieve thermodynamic coupling modeling of a co-expansion cavity type opposed free piston Stirling power generation system.

[0007] According to one embodiment of the present invention, the construction of the single-machine physical model includes: A constant-volume cavity module is used to model the hot-end heat exchanger, the regenerator, and the cold-end heat exchanger. The constant-volume cavity module calculates the convective heat transfer and gas pressure drop based on empirical correlation formulas. The formula for calculating the convective heat transfer is as follows: ; Q conv For convective heat transfer, Nu For Nusselt numbers, k For the thermal conductivity of gases, d h The hydraulic diameter, S x For wet period, L For the length of the heat exchanger, T w The wall temperature, T The gas temperature; The formula for calculating gas pressure drop is as follows: ; Δ p For gas pressure drop, f D The flow resistance coefficient is... K This is the local drag loss coefficient. ρ For gas density, u The velocity is the gas flow rate.

[0008] According to one embodiment of the present invention, the empirical correlation includes a correlation for calculating the flow resistance coefficient and a correlation for calculating the Nusselt number; The correlation formula for the flow resistance coefficient of the finned laminar flow in the hot-end heat exchanger and the cold-end heat exchanger is as follows: ; The correlation formulas for the flow resistance coefficients of finned heat exchangers at the hot and cold ends are as follows: ; The correlation for the Nusselt number of the finned laminar flow in the hot-end heat exchanger and the cold-end heat exchanger is as follows: ; The correlation for the Nusselt number of turbulent flow in the finned heat exchangers at the hot and cold ends is as follows: ; The correlation for the flow resistance coefficient of the wire mesh type regenerator is as follows: ; The correlation for the Nusselt number of the wire mesh type regenerator is as follows: ; in, Re Let Reynolds number be 1. Va For Valencia numbers, c These are the structural parameters of the heat exchanger. Pr For Prandtl numbers, ε The average height of the irregular surface. Pe For Berkeley numbers, β The porosity is the porosity of the regenerator.

[0009] According to one embodiment of the present invention, the construction of the single-machine physical model further includes: A translational mechanical converter module is used to model the expansion chamber, compression chamber, and back chamber to convert the gas pressure acting on the piston end face into mechanical force.

[0010] According to one embodiment of the present invention, a custom dual-motion port translational mechanical converter is used to model the simultaneous action of the working gas in the compression chamber and the back chamber on two working areas: the discharger and the power piston.

[0011] According to one embodiment of the present invention, the construction of the single-machine physical model further includes: A custom-designed gap sealing element is used to simulate gap leakage between the piston and cylinder, assuming that the working gas flows through the gap seal in a Poisson flow pattern.

[0012] According to one embodiment of the present invention, the single-machine physical model further includes a motor-side model and an electrical load model; The motor-side model uses a translational electromechanical converter module to simulate the back electromotive force of a linear generator.

[0013] According to one embodiment of the present invention, the electrical load model includes an H-bridge circuit composed of metal-oxide-semiconductor transistors, a filter capacitor, and a DC resistive load.

[0014] According to one embodiment of the present invention, the single-machine physical model further includes: The dynamic mass of the discharger and the power piston is described using a mass module; A damper module is used to simulate the damping force on the discharger and the power piston; A spring module is used to simulate the stiffness force of leaf springs and magnetic springs.

[0015] According to one embodiment of the present invention, the construction of the single-machine physical model further includes: The thermal mass module was used to simulate the thermal capacity characteristics of the solid wall of the heat exchanger and the metal wire mesh packing inside the regenerator. A heat conduction module is used to simulate the axial heat conduction loss of the regenerator wall.

[0016] The dynamic modeling and simulation method for a Stirling power generation system with opposed free pistons provided by embodiments of the present invention is based on real physical mechanisms and comprehensively covers the core physical processes of the Stirling power generation system in terms of heat, mechanics, and electricity. It achieves full-link dynamic simulation from gas pressure to mechanical motion and then to electrical energy output, accurately capturing the transient behavior of the system during startup, steady-state operation, and under varying operating conditions. It is particularly suitable for analyzing key influencing factors such as temperature fluctuations of cold and heat sources and load changes, significantly improving the realism and engineering usability of simulation results. The reuse mechanism enables highly efficient system modeling, avoids repetitive work, ensures the structural consistency and parameter uniformity of the two subsystems, lays the foundation for the subsequent construction of a symmetrical co-expansion cavity system, and facilitates comparative analysis, fault diagnosis, and multi-condition testing, significantly improving modeling efficiency and the scalability of the simulation platform. The connection method successfully constructed a thermodynamic coupling model of a co-expansion cavity type opposed free piston Stirling power generation system, enabling two independent single-unit systems to achieve dynamic coordination in a gas pressure field. This effectively reproduces the operating mechanism of two pistons sharing the same expansion space in the actual system, improving the simulation accuracy of the system. It is particularly suitable for studying system stability, power matching and control strategies, and provides reliable technical support for the design optimization of novel opposed free piston Stirling power generation systems. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 This is a schematic view of the physical model simulation module group of the free piston Stirling power generation system provided by the present invention.

[0019] Figure 2 This is a schematic view of the engine side of the opposed free piston Stirling generator system provided by the present invention.

[0020] Figure 3This is a schematic view of the hot-end heat exchanger in the opposed free piston Stirling power generation system provided by the present invention.

[0021] Figure 4 This is a schematic view of the regenerator in the opposed free piston Stirling power generation system provided by the present invention.

[0022] Figure 5 This is a schematic view of the cold-end heat exchanger in the opposed free piston Stirling power generation system provided by the present invention.

[0023] Figure 6 This is a schematic view of the motor side in the opposed free piston Stirling generator system provided by the present invention.

[0024] Figure 7 This is a schematic view of the electrical load side of the opposed free piston Stirling generator system provided by the present invention.

[0025] Figure 8 This is a schematic view of the controller load in the opposed free piston Stirling generator system provided by the present invention.

[0026] Figure 9 This is a schematic view of the physical model simulation module group of the opposed free piston Stirling power generation system provided by the present invention.

[0027] Figure 10 This is a schematic flowchart of the dynamic modeling and simulation method for the opposed free piston Stirling power generation system provided by the present invention. Detailed Implementation

[0028] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0029] The specific terms used in this specification are for illustrative purposes only and are not intended to limit the illustrated embodiments. For example, expressions such as "same" and "identical" not only indicate a strictly identical state, but also indicate a state with tolerances or differences in the degree of functionality. For example, expressions indicating relative or absolute arrangement such as "in a certain direction," "along a certain direction," "side by side," "perpendicular," "centered on," "concentric," or "coaxial" not only strictly indicate such an arrangement, but also indicate a state of relative displacement by tolerances or angles or distances with the same degree of functionality.

[0030] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0031] Furthermore, features specified as "first" or "second" may explicitly or implicitly include one or more of those features. In the description of this invention, unless otherwise stated, "multiple" means two or more. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly specified. In the description of the embodiments of this application, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, B1 and / or B2 can represent: B1 existing alone, B1 and B2 existing simultaneously, and B2 existing alone. Additionally, the character " / " in this document generally indicates that the preceding and following related objects have an "or" relationship.

[0032] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0033] like Figures 1 to 10 As shown, this embodiment of the invention provides a dynamic modeling and simulation method for a Stirling power generation system with opposed free pistons, including: Step 10: Based on the physical model simulation module group, construct a single-machine physical model including an expansion chamber, a compression chamber, a hot-end heat exchanger, a regenerator, a cold-end heat exchanger, an exhaustor, and a power piston; the expansion chamber has a gas port; Step 20: Reuse the single-machine physics model to obtain two single-machine physics models; Step 30: Connect the gas port of the expansion chamber of one single-machine physical model to the gas port of the expansion chamber of another single-machine physical model to achieve thermodynamic coupling modeling of the co-expansion chamber type opposed free piston Stirling power generation system.

[0034] The dynamic modeling and simulation method for a Stirling power generation system with opposed free pistons provided by embodiments of the present invention is based on real physical mechanisms and comprehensively covers the core physical processes of the Stirling power generation system in terms of heat, mechanics, and electricity. It achieves full-link dynamic simulation from gas pressure to mechanical motion and then to electrical energy output, accurately capturing the transient behavior of the system during startup, steady-state operation, and under varying operating conditions. It is particularly suitable for analyzing key influencing factors such as temperature fluctuations of cold and heat sources and load changes, significantly improving the realism and engineering usability of simulation results. The reuse mechanism enables highly efficient system modeling, avoids repetitive work, ensures the structural consistency and parameter uniformity of the two subsystems, lays the foundation for the subsequent construction of a symmetrical co-expansion cavity system, and facilitates comparative analysis, fault diagnosis, and multi-condition testing, significantly improving modeling efficiency and the scalability of the simulation platform. The connection method successfully constructed a thermodynamic coupling model of a co-expansion cavity type opposed free piston Stirling power generation system, enabling two independent single-unit systems to achieve dynamic coordination in a gas pressure field. This effectively reproduces the operating mechanism of two pistons sharing the same expansion space in the actual system, improving the simulation accuracy of the system. It is particularly suitable for studying system stability, power matching and control strategies, and provides reliable technical support for the design optimization of novel opposed free piston Stirling power generation systems.

[0035] Please continue reading Figures 1 to 10The physical model simulation module consists of multiple functionally independent and combinable modeling units. The fixed-volume cavity module models the hot-end heat exchanger, regenerator, and cold-end heat exchanger. This module calculates the convective heat transfer and gas pressure drop inside each heat exchanger based on empirical correlations. Its input parameters include the working gas state, wall temperature, structural geometry, and flow state. The translational mechanical converter module models the expansion chamber, compression chamber, and back chamber. It converts the gas pressure acting on the piston end face into mechanical force and achieves energy coupling between the gas domain and the mechanical translational domain. The mass module describes the dynamic mass of the discharger and the power piston, while the damper module simulates the forces acting on the piston during its motion. The damping force and spring module simulates the stiffness force of leaf springs and magnetic springs; the custom gap sealing element simulates the tiny gap between the piston and cylinder, assuming that the gas flows through this gap according to the Poiseuille flow law, and calculates its leakage flow rate and pressure drop; the thermal mass module simulates the thermal capacity characteristics of the solid wall of the heat exchanger and the metal wire mesh packing inside the regenerator, and the heat conduction module simulates the heat conduction loss of the regenerator wall along the axial direction; the motor side model uses a translational electromechanical converter module to simulate the back electromotive force generation process of a linear generator, and the electrical load model consists of an H-bridge circuit composed of metal-oxide-semiconductor transistors, a filter capacitor, and a DC resistive load, realizing a complete closed loop of power output and load regulation. All modules interact with each other through an interface protocol to form a complete single-machine physical model, in which the expansion chamber has a gas port for connecting to the external gas path. This port is located at the closed end of the expansion chamber and supports fluid connection with other chambers or external systems.

[0036] After completing the construction of the first single-machine physical model, it is copied as a template to generate a second identical single-machine physical model. The two models are consistent in structure, parameters, initial conditions, and connection relationships. The configurations of expansion chamber, compression chamber, hot-end heat exchanger, regenerator, cold-end heat exchanger, discharger, power piston, mechanical components, thermodynamic module, electromechanical conversion module, and electrical load module are all the same. The connection logic and signal transmission paths between all modules are completely copied to ensure that the two models have the same physical characteristics and dynamic response capabilities. The reuse process is achieved through the "cloning" or "instantiation" function in the software system, without the need for remodeling, effectively saving modeling time and resources.

[0037] The gas ports of the expansion chambers of the first and second single-machine physical models are connected through a common flow channel. This connection point is set as a shared gas node, where the gas pressures of the two expansion chambers reach equilibrium, forming a common pressure space. The pistons on both sides are synchronously subjected to gas pressure, achieving symmetrical reciprocating motion with opposite phases. This connection method enables the two single-machine physical models to form a coupling relationship at the thermodynamic level. The gas flows periodically between the two expansion chambers, and the pressure fluctuations affect each other, thus achieving the physical equivalence of the co-expansion chamber structure. The entire connection process is completed in the simulation software by establishing a fluid interface and setting mass conservation and energy conservation constraints.

[0038] According to one embodiment of the present invention, constructing a single-machine physical model includes: A constant-volume cavity module is used to model the hot-end heat exchanger, regenerator, and cold-end heat exchanger. The constant-volume cavity module calculates the convective heat transfer and gas pressure drop based on empirical correlations. The formula for calculating the convective heat transfer is as follows: ; Q conv For convective heat transfer, Nu For Nusselt numbers, k For the thermal conductivity of gases, d h The hydraulic diameter, S x For wet period, L For the length of the heat exchanger, T w The wall temperature, T The gas temperature; The formula for calculating gas pressure drop is as follows: ; Δ p For gas pressure drop, f D The flow resistance coefficient is... K This is the local drag loss coefficient. ρ For gas density, u The velocity is the gas flow rate.

[0039] In one embodiment of the present invention, the fixed-volume cavity module is a numerical calculation unit established based on physical principles and experimental data. It contains a virtual cavity with a fixed volume, which represents the geometric space of the actual heat exchanger. The module automatically calculates the convective heat transfer and gas pressure drop by inputting information such as heat exchanger structural parameters, working gas state, and wall temperature, using a preset empirical correlation formula. The calculation of convective heat transfer is based on the law of conservation of energy, combined with the relationship between Nusselt number and heat transfer coefficient, and is determined by gas thermal conductivity, hydraulic diameter, wetted perimeter, heat exchanger length, wall temperature, and gas temperature. The calculation of gas pressure drop is based on the principle of conservation of momentum, comprehensively considering the effects of flow resistance coefficient, local resistance loss coefficient, gas density, and flow velocity. All calculation processes are solved in real time in the form of a nonlinear differential equation system within the simulation software to ensure that the results dynamically respond to changes in the real system.

[0040] This modeling method can accurately characterize the convective heat transfer process between the working gas and the solid wall inside the heat exchanger, and accurately reflect the pressure drop loss caused by friction and local disturbances when the gas flows through the heat exchanger. It effectively overcomes the problem of ignoring actual energy loss under the traditional idealized assumptions, making the simulation model closer to the thermodynamic behavior of the real system, improving the accuracy of performance prediction of Stirling power generation system, and is especially suitable for analyzing the dynamic response characteristics of the system under high-precision design and complex operating conditions.

[0041] According to one embodiment of the present invention, the empirical correlation includes a correlation for calculating the flow resistance coefficient and a correlation for calculating the Nusselt number; The correlation formulas for the flow resistance coefficients of laminar flow with finned hot-end and cold-end heat exchangers are as follows: ; The correlation for the flow resistance coefficients of turbulent flow in finned hot-end and cold-end heat exchangers is as follows: ; The correlation for the Nusselt number in laminar flow with finned hot-end and cold-end heat exchangers is as follows: ; The correlation for the Nusselt number of turbulent flow in finned hot-end and cold-end heat exchangers is as follows: ; The correlation for the flow resistance coefficient of a wire mesh regenerator is as follows: ; The correlation for the Nusselt number of a wire mesh regenerator is as follows: ; in, Re Let Reynolds number be 1. Va For Valencia numbers,c These are the structural parameters of the heat exchanger. Pr For Prandtl numbers, ε The average height of the irregular surface. Pe For Berkeley numbers, β The porosity is the porosity of the regenerator.

[0042] In one embodiment of the present invention, empirical correlations are based on Sage, a general-purpose thermodynamic software in the field of Stirling engine and refrigeration engine research, and are applied to different heat exchanger types and flow states (laminar or turbulent). For finned hot-end and cold-end heat exchangers, the flow resistance coefficient in the laminar state is calculated using a function relationship based on the Reynolds number and the Wallenzi number, while in the turbulent state, the relative roughness and the Reynolds number are coupled for calculation. Correspondingly, the Nusselt number is calculated according to the flow regime, and its expression depends on the Reynolds number, Prandtl number, Wallenzi number, and heat exchanger structural parameters. For wire mesh regenerators, the flow resistance coefficient and Nusselt number are calculated based on parameters such as the Reynolds number, Bekele number, and porosity. All correlations are presented in dimensionless parameter form to ensure that the model has good versatility and cross-scale applicability. During the simulation, the system automatically determines the flow state based on the real-time calculated Reynolds number and calls the corresponding correlation for calculation.

[0043] This multi-state, multi-type empirical correlation system can comprehensively cover the actual operating conditions of the main heat exchangers in the Stirling power generation system, accurately capture the nonlinear change characteristics in the transition from laminar to turbulent flow, significantly improve the prediction accuracy of heat exchange efficiency and pressure drop loss, especially under non-steady-state conditions such as heat source fluctuations or load changes, it can effectively reflect the dynamic evolution of heat exchanger performance, provide a reliable basis for system control strategy optimization and design parameter adjustment, and avoid error accumulation caused by simplification assumptions.

[0044] According to one embodiment of the present invention, constructing a single-machine physical model further includes: A translational mechanical converter module is used to model the expansion chamber, compression chamber, and back chamber to convert the gas pressure acting on the piston end face into mechanical force.

[0045] In one embodiment of the present invention, the translational mechanical converter module is an interface element for connecting the gas domain and the mechanical translational domain. It contains a movable piston model located at the end of the expansion chamber, compression chamber, and back chamber. When gas pressure is applied to the piston end face, the module calculates the corresponding mechanical force according to Newton's second law and transmits it to the subsequent mechanical dynamics module. At the same time, the module also supports reverse function, that is, receiving displacement or velocity signals from the mechanical side and reversing to generate gas pressure changes, realizing bidirectional energy conversion. All calculations are based on the integral relationship between piston area and pressure distribution, and the module supports the simulation of nonlinear stiffness and damping effects.

[0046] This module achieves a precise mapping between gas pressure and mechanical force, and is the core component for constructing a thermo-mechanical coupled system. It can realistically reproduce the motion behavior of a free piston driven by gas pressure, and is particularly suitable for analyzing the synergistic effect of piston inertia, mass and spring stiffness. It provides key support for studying the system's resonant frequency, phase difference and dynamic stability, and significantly improves the dynamic realism of the entire simulation model.

[0047] According to one embodiment of the present invention, a custom dual-motion port translational mechanical converter is used to model the simultaneous action of the working gas in the compression chamber and the back chamber on two working areas: the discharger and the power piston.

[0048] In one embodiment of the present invention, the custom dual-motion-port translational mechanical converter module is a specially designed mechanical interface with two independent motion ports corresponding to the motion directions of the discharger and the power piston, respectively. The module has two piston structures inside, each piston being connected to a cavity. The working gas in the compression cavity and the back cavity simultaneously acts on the end faces of the two pistons. By calculating the gas pressure on each piston separately and superimposing its contribution, the total mechanical force output is obtained. This module can handle the phase difference and asynchronous motion between the two moving parts, supports arbitrarily set area ratios, and can dynamically adjust the connection relationship of each port in the simulation to adapt to different system configurations.

[0049] This design accurately reflects the physical reality of the simultaneous action of the compression chamber and back chamber gas on two pistons in a co-expansion cavity type opposed free piston Stirling generator system. It solves the limitation of traditional single-port models in handling multi-area problems, making the simulation results more consistent with the stress state of the real system. It is especially significant in analyzing piston drift, phase locking and system detuning phenomena, and improves the reliability of the model under complex dynamic conditions.

[0050] According to one embodiment of the present invention, constructing a single-machine physical model further includes: A custom-designed gap sealing element is used to simulate gap leakage between the piston and cylinder. The gap sealing element assumes that the working gas flows through the gap seal in accordance with Poisson flow.

[0051] In one embodiment of the present invention, the customized gap sealing element is a dedicated module for simulating the minute gap between the piston and the cylinder. Its internal structure simulates a cylindrical gap channel in which gas flows axially. The flow pattern is assumed to be Poiseuille flow, i.e., a parabolic velocity distribution under laminar flow conditions. The module calculates the pressure drop and leakage flow rate based on the gas dynamic viscosity, gap height, piston diameter, and volumetric flow rate. The pressure drop expression is: ,in μ For gas dynamic viscosity, U For volumetric flow rate,L The gap length, D Given the piston diameter, all calculations are solved in the simulation software using differential equations to ensure dynamic response during the leakage process.

[0052] This modeling method can accurately reflect the leakage phenomenon between the piston and cylinder, and has a significant impact on the piston drift problem during long-term system operation. By introducing the Poiseuille flow assumption, it accurately captures the nonlinear leakage behavior of gas in tiny gaps, enabling the simulation model to predict piston drift caused by gap sealing, and providing a quantitative basis for optimizing drift suppression and return structure and improving system efficiency.

[0053] According to one embodiment of the present invention, the single-machine physical model further includes a motor-side model and an electrical load model; The motor-side model uses a translational electromechanical converter module to simulate the back electromotive force of a linear generator.

[0054] In one embodiment of the present invention, the motor-side model includes a translational electromechanical converter module connected to the motion path of the power piston to simulate the energy conversion process of a linear generator. When the piston reciprocates, the module calculates the induced electromotive force, i.e., the back electromotive force, based on its velocity and magnetic field strength. This back electromotive force is opposite to the direction of the current and constitutes an electromagnetic damping force. The motor-side model also includes components such as coil inductance and resistance, supporting the coupled calculation between voltage, current, and displacement. All electrical variables are dynamically updated over time, realizing closed-loop simulation of the entire thermo-mechanical-electrical process.

[0055] This model realistically reproduces the back electromotive force and electromagnetic damping effect generated by the linear generator during its motion. It is the foundation for realizing the system's power output and feedback control, and can accurately simulate the power output characteristics of the system under different loads. It provides key data support for controller design, efficiency evaluation and stability analysis, and is especially suitable for studying the dynamic response of the system during transient processes such as startup, shutdown and load change.

[0056] According to one embodiment of the present invention, the electrical load model includes an H-bridge circuit composed of metal-oxide-semiconductor transistors, a filter capacitor, and a DC resistive load.

[0057] In one embodiment of the present invention, the electrical load model is composed of a full-bridge rectifier circuit, which includes four metal-oxide-semiconductor transistors connected in pairs to form an H-bridge topology. The four transistors control the conduction and cutoff of the current respectively to realize the rectification of AC to DC. At the same time, a filter capacitor is connected in parallel at the output terminal to smooth the output voltage fluctuation and reduce the harmonic content. The DC resistive load serves as the final energy consumption terminal, and its resistance value can be set according to requirements. The entire circuit regulates the output power through switching logic control and supports multiple operating modes such as pulse width modulation and phase control.

[0058] This electrical load model fully simulates common power electronic conversion devices in actual systems, and can realistically reflect the electrical behavior of the system when connected to an external power grid or energy storage device. It is especially suitable for analyzing the dynamic performance of the system in application scenarios such as active power factor correction and maximum power point tracking, improving the engineering practicality of simulation results, and providing a reliable test platform for system integration and control strategy verification.

[0059] According to one embodiment of the present invention, the single-machine physical model further includes: The dynamic mass of the discharger and the power piston is described using a mass module; A damper module is used to simulate the damping force on the discharger and the power piston; A spring module is used to simulate the stiffness force of leaf springs and magnetic springs.

[0060] In one embodiment of the present invention, the mass module is a lumped mass unit, the mass of which is equal to the mass of the discharger and the power piston, respectively. This module is connected to the mechanical motion path and is used to calculate the inertial force. The damper module is a linear or nonlinear damping element, the damping coefficient of which is set according to the actual operating environment of the system to simulate the energy dissipation of the piston during its movement due to factors such as mechanical friction and electromagnetic loss. The spring module is an elastic element with a specific stiffness, one end of which is connected to the piston and the other end is connected to the housing mass module to simulate the stiffness characteristics of leaf springs and magnetic springs.

[0061] This module combination fully constructs the mechanical dynamics foundation of the system, enabling the simulation model to accurately reflect the inertia, damping, and elastic characteristics of the piston. It plays an important role, especially in analyzing the system's resonant frequency, starting impact, and steady-state amplitude. It provides necessary tools for studying the system's dynamic stability, suppressing piston drift, and optimizing vibration control, and enhances the model's ability to reproduce real physical behavior.

[0062] In other words, the dynamic modeling and simulation method for opposed free piston Stirling generator systems provided in this embodiment of the invention can model single-unit free piston Stirling generators, considering the casing motion and suspension system. The casing is simulated using mass modules, and the suspension system consists of spring and damper modules, one end of which is connected to the casing and the other end to a fixed reference point. The exhaust manifold and power piston modules are connected to the casing, and their displacement relative to the casing is solved, which can be used to analyze the casing vibration of the generator system and to study vibration reduction.

[0063] According to one embodiment of the present invention, constructing a single-machine physical model further includes: The thermal mass module was used to simulate the thermal capacity characteristics of the solid wall of the heat exchanger and the metal wire mesh packing inside the regenerator. A heat conduction module is used to simulate the axial heat conduction loss of the regenerator wall.

[0064] In one embodiment of the present invention, the thermal mass module is a heat capacity unit, the heat capacity of which is equal to the heat capacity of the solid wall of the heat exchanger and the metal wire mesh packing inside the regenerator. This module reflects its temperature change by absorbing or releasing heat. Its calculation is based on the heat balance equation and supports the simulation of multi-node temperature distribution. The heat conduction module is a one-dimensional heat conduction path used to simulate the heat transfer along the axial direction of the regenerator wall. This module calculates the heat flux density based on the thermal conductivity, cross-sectional area and length of the wall material, thereby truly reflecting the temperature gradient inside the regenerator.

[0065] This modeling method can accurately capture the thermal inertia of heat exchangers and regenerators during the thermal response process. It is particularly important for the temperature field evolution of the system during the start-up phase and under varying operating conditions. This enables the simulation model to predict the decrease in heat exchange efficiency caused by heat conduction loss, providing a theoretical basis for optimizing heating / cooling rates and improving system response speed and efficiency.

[0066] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A dynamic modeling and simulation method for a Stirling generator system with opposed free pistons, characterized in that, include: Based on the physical model simulation module group, a single-machine physical model is constructed, including an expansion chamber, a compression chamber, a hot-end heat exchanger, a regenerator, a cold-end heat exchanger, an exhaust device, and a power piston; the expansion chamber has a gas port; By reusing the single-machine physical model, two single-machine physical models are obtained; The gas port of the expansion cavity of one single-machine physical model is connected to the gas port of the expansion cavity of another single-machine physical model to achieve thermodynamic coupling modeling of a co-expansion cavity type opposed free piston Stirling power generation system.

2. The dynamic modeling and simulation method for a Stirling power generation system with opposed free pistons according to claim 1, characterized in that, The construction of the single-machine physical model includes: A constant-volume cavity module is used to model the hot-end heat exchanger, the regenerator, and the cold-end heat exchanger. The constant-volume cavity module calculates the convective heat transfer and gas pressure drop based on empirical correlation formulas. The formula for calculating the convective heat transfer is as follows: ； Q conv For convective heat transfer, Nu For Nusselt numbers, k For the thermal conductivity of gases, d h The hydraulic diameter, S x For wet period, L For the length of the heat exchanger, T w The wall temperature, T The gas temperature; The formula for calculating gas pressure drop is as follows: ； Δ p For gas pressure drop, f D The flow resistance coefficient is... K This is the local drag loss coefficient. ρ For gas density, u The velocity is the gas flow rate.

3. The dynamic modeling and simulation method for a Stirling power generation system with opposed free pistons according to claim 2, characterized in that, The empirical correlations include correlations for calculating the flow resistance coefficient and correlations for calculating the Nusselt number; The correlation formula for the flow resistance coefficient of the finned laminar flow in the hot-end heat exchanger and the cold-end heat exchanger is as follows: ； The correlation formulas for the flow resistance coefficients of the finned type of the hot-end heat exchanger and the cold-end heat exchanger are as follows: ； The correlation for the Nusselt number of the finned laminar flow in the hot-end heat exchanger and the cold-end heat exchanger is as follows: ； The correlation for the Nusselt number of turbulent flow in the finned heat exchangers at the hot and cold ends is as follows: ； The correlation for the flow resistance coefficient of the wire mesh type regenerator is as follows: ； The correlation for the Nusselt number of the wire mesh type regenerator is as follows: ； in, Re Let Reynolds number be 1. Va For Valencia numbers, c These are the structural parameters of the heat exchanger. Pr For Prandtl numbers, ε The average height of the irregular surface. Pe For Berkeley numbers, β The porosity is the porosity of the regenerator.

4. The dynamic modeling and simulation method for a Stirling power generation system with opposed free pistons according to claim 1, characterized in that, The construction of the single-machine physical model also includes: A translational mechanical converter module is used to model the expansion chamber, compression chamber, and back chamber to convert the gas pressure acting on the piston end face into mechanical force.

5. The dynamic modeling and simulation method for a Stirling power generation system with opposed free pistons according to claim 4, characterized in that, For the working gas in the compression chamber and back chamber acting simultaneously on the two action areas of the exhauster and the power piston, a custom dual-motion port translational mechanical converter is used for modeling.

6. The dynamic modeling and simulation method for a Stirling power generation system with opposed free pistons according to claim 1, characterized in that, The construction of the single-machine physical model also includes: A custom-designed gap sealing element is used to simulate gap leakage between the piston and cylinder, assuming that the working gas flows through the gap seal in a Poisson flow pattern.

7. The dynamic modeling and simulation method for a Stirling power generation system with opposed free pistons according to claim 1, characterized in that, The single-machine physical model also includes a motor-side model and an electrical load model; The motor-side model uses a translational electromechanical converter module to simulate the back electromotive force of a linear generator.

8. The dynamic modeling and simulation method for a Stirling power generation system with opposed free pistons according to claim 7, characterized in that, The electrical load model includes an H-bridge circuit composed of metal-oxide-semiconductor transistors, a filter capacitor, and a DC resistive load.

9. The dynamic modeling and simulation method for a Stirling power generation system with opposed free pistons according to any one of claims 1 to 8, characterized in that, The single-machine physical model also includes: The dynamic mass of the discharger and the power piston is described using a mass module; A damper module is used to simulate the damping force on the discharger and the power piston; A spring module is used to simulate the stiffness force of leaf springs and magnetic springs.

10. The dynamic modeling and simulation method for a Stirling power generation system with opposed free pistons according to any one of claims 1 to 8, characterized in that, The construction of the single-machine physical model also includes: The thermal mass module was used to simulate the thermal capacity characteristics of the solid wall of the heat exchanger and the metal wire mesh packing inside the regenerator. A heat conduction module is used to simulate the axial heat conduction loss of the regenerator wall.

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