A method for predicting the performance of a stirling generator

Abstract

The application discloses a kind of stirling generator performance prediction method.This method is established by force balance equation and volume equation to the gas distribution piston, power piston, compression cavity and expansion cavity inside stirling generator respectively, combined with ideal gas equation, mass conservation equation and energy conservation equation, constructs the heat-dynamics coupling model of stirling generator including kinetic parameters and thermodynamic parameters;According to the input kinetic parameters, the running frequency, displacement amplitude of gas distribution piston and power piston and the phase difference of two pistons are calculated;Further solve the thermodynamic model, obtain the change of temperature, pressure, mass and mass flow of working medium;Then the results are substituted into motor model, obtain effective voltage, effective current and effective electric power;Through heat-dynamics coupling solution and combined with motor model, the whole process of heat-work-electricity conversion is solved and calculated, so as to realize the heat-dynamics-electricity parameter prediction of stirling generator, provide theoretical guidance for whole machine fault diagnosis and optimization design.

Description

Technical Field

[0001] The present invention belongs to the technical field of generators, relates to generator performance prediction, and particularly relates to a Stirling generator performance prediction method. Background Art

[0002] A Stirling generator is a device that converts thermal energy directly into electrical energy. Its operating principle is based on the Stirling cycle. Stirling generators have the advantages of high efficiency, simple structure, light weight, fast startup, low noise, and long life. Furthermore, when the temperature ratio between the high and low temperature ends is 2 to 3, they can achieve a thermoelectric conversion efficiency of up to 30%. Therefore, they have broad application prospects in space missions such as deep space exploration, lunar landings, and Mars landings. However, the experimental construction and research of Stirling generators require a lot of manpower and material resources. Inappropriate design parameters may cause the generator to malfunction and even cause dangers such as cylinder collisions. Therefore, it is of great significance to establish a high-fidelity numerical model that can accurately predict the performance of Stirling generators and provide theoretical support for their design. Existing Stirling generator performance prediction models can usually only predict thermodynamic or kinetic characteristics, and it is difficult to take both into account simultaneously. In fact, the Stirling generator is a system with a high degree of coupling between thermodynamics and kinetics. Only by organically combining the thermodynamic model with the kinetic model can its internal heat-power-electricity conversion mechanism be revealed, accurate performance prediction can be achieved, and the coupling influence of its internal multiple parameters on performance can be clarified. This will help researchers clarify the energy conversion process of the generator and provide guidance for the design of the thermal-dynamic-electrical parameters of the whole machine, thereby achieving the optimal design of the Stirling generator and further improving energy utilization efficiency. Summary of the Invention

[0003] In view of the shortcomings of the existing technology, the purpose of the present invention is to provide a Stirling generator performance prediction method, which realizes the calculation of the whole process of heat-power-electricity conversion through thermal-dynamic coupling solution and the addition of a motor model, thereby improving the accuracy of Stirling generator performance prediction.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] A method for predicting Stirling generator performance comprises the following steps:

[0006] S1. Inputting known structural parameters and operating parameters of the Stirling generator into the dynamic model;

[0007] S2. Set the initial heater wall temperature and numerically solve the dynamic model using the fourth-order Runge-Kutta method to obtain the time series of displacement and velocity of the valve piston and power piston;

[0008] Perform fast Fourier transform on the time series of the displacement of the valve piston and the power piston to calculate the operating frequency, displacement amplitude and phase difference between the valve piston and the power piston;

[0009] S3. Substitute the operating frequency, displacement amplitude, and phase difference between the two pistons into the thermodynamic model, numerically solve the thermodynamic model using the fourth-order Runge-Kutta method, and calculate the working fluid temperature, pressure change, mass change, and mass flow change in the heater and cooler;

[0010] Perform temperature convergence iteration on the sum of the temperature differences between the heater and cooler working fluids obtained by two consecutive calculations until the sum of the temperature differences between the heater and cooler working fluids obtained by two consecutive calculations is less than the set temperature convergence value;

[0011] S4. Calculate the system loss based on the calculation result of S3 to obtain the calculated value of input heat;

[0012] Perform heat convergence iteration between the calculated value of the input heat and the heating power in the operating parameters until the difference between the calculated value of the input heat and the heating power is less than the set convergence value;

[0013] After S5 and S4 converge, the working fluid temperature in the heater corrected by the iterative correction of S3 in S4 replaces the heater wall temperature initially set in S2. S2 is run to calculate the time series of the displacement and velocity of the power piston and the valve piston, which are then brought into the generator model to obtain the output voltage, output current, and output electric power.

[0014] The present invention also has the following technical features:

[0015] Preferably, the structural parameters described in S1 include: the number, length and width of the channels of the heater, regenerator and cooler; the equilibrium volume of the compression chamber and the expansion chamber; the diameter, mass, stiffness and damping coefficient of the gas distribution piston, gas distribution piston rod and power piston; the linear damping coefficient and nonlinear damping coefficient of the load; the motor constant, inductance and resistance of the generator;

[0016] Operating parameters include: charging pressure, working fluid type, cooler temperature, and heating power.

[0017] Preferably, the kinetic model includes:

[0018] The force balance equation of the valve piston:

[0019]

[0020] The force balance equation of the power piston:

[0021]

[0022] The volume equation of the expansion chamber is:

[0023] V e =V e0 +A d x d

[0024] The volume equation of the compression chamber:

[0025] V c =V c0 -(A d -A R )x d +(A p -A R )x p

[0026] Where A, x, P, F, c, k, V, and m are piston cross-sectional area, displacement, pressure, load reaction force, damping coefficient, spring stiffness, volume, and mass, respectively; subscripts d, e, c, b, R, and load represent the valve piston, expansion chamber, compression chamber, back pressure chamber, valve piston rod, and load, respectively; For speed, is the acceleration; V eo Represents the initial volume of the expansion chamber; V co Indicates the initial volume of the compression chamber.

[0027] Working chamber pressure equation:

[0028]

[0029] Where S is the introduced pressure linearization parameter, and its expression is:

[0030]

[0031] Preferably, the thermodynamic model is as follows:

[0032] Mass of working fluid in compression chamber, cooler, regenerator, heater and expansion chamber:

[0033] m c =pV c / (RT c )

[0034] m k =pV k / (RT k )

[0035] m r =pV r / (RT r )

[0036] m h =pVh / (RT h )

[0037] m e =pV e / (RT e )

[0038] Changes in working fluid mass in the compression chamber, cooler, regenerator, heater and expansion chamber:

[0039] δm c =(pdV c +V c dp / γ) / (RT ck )

[0040] δm e =(pdV e +V e dp / γ) / (RT he )

[0041] δm k =m k dp / p

[0042] δm r =m r dp / p

[0043] δm h =m h dp / p

[0044] Where p, V, and T are pressure, volume, and temperature, respectively; subscripts c, k, r, h, and e represent the compression chamber, cooler, regenerator, heater, and expansion chamber, respectively; γ is the specific heat ratio of the working gas;

[0045] Compression chamber temperature change:

[0046]

[0047] Expansion chamber temperature change:

[0048]

[0049] Where V c is the volume of the compression chamber, V e is the volume of the expansion cavity, m c is the mass of the working medium in the compression chamber, m e is the mass of the working fluid in the expansion chamber.

[0050] Energy equation in the heater:

[0051]

[0052] Energy equation in the cooler:

[0053]

[0054] Energy equation in the regenerator:

[0055]

[0056] Where Q is the heat, subscripts h, k, and r represent heater, cooler, and regenerator, respectively; c v is the constant pressure specific heat capacity of the working gas, m ck =-δ mc , m kr =m ck -δm k , m he =δm e , m rh =m he -δm h , represents the mass flow from one component to another; T rh 、T he 、T ck 、T kr Indicates the temperature of the interface between components;

[0057] The expression of the circulating work in the compression chamber is:

[0058] δW c =pdV c

[0059] The expression of the circulation work in the expansion chamber is:

[0060] δW e =pdV e

[0061] Preferably, the sum of the temperature differences between the heater and cooler working fluids obtained by two consecutive calculations in S3, terror, is calculated by the following formula:

[0062] terror=|Th1-Th0|+|Tk1-Tk0|

[0063] Where T h is the working medium temperature in the heater; T k is the working fluid temperature in the cooler; subscript 0 represents the working fluid temperature obtained in the previous calculation; subscript 1 represents the working fluid temperature obtained in this calculation.

[0064] Preferably, the heat convergence iteration between the calculated value of the input heat and the heating power in the operating parameters described in S4 is corrected in the following manner: if the difference between the calculated value of the input heat and the heating power is greater than the set heat convergence value, the heater wall temperature is updated, and S2, S3, and S4 are repeated until the difference between the calculated value of the input heat and the heating power is less than the set convergence value;

[0065] The heater wall temperature is updated as follows:

[0066] Twh1=Twh0-(Q cal -Q in ) / ξ

[0067] Where Twh0 is the heater wall temperature used in this calculation; Twh1 is the updated heater wall temperature, which will be used as the heater wall temperature in the next calculation; Q cal is the calculated value of input heat; Q in is the heating power; ξ is the temperature correction coefficient.

[0068] Preferably, the generator model described in S5 is as follows:

[0069] The formula for calculating the electromotive force of the generator is:

[0070]

[0071] in is the electromotive force of the motor, is the power piston speed, K e is the motor constant.

[0072] Voltage balance equation:

[0073]

[0074] Among them I alt is the output current value, R alt 、R load are the internal resistance of the generator and the resistance of the external load, L alt is the stator inductance, is the capacitance value of the tuning capacitor.

[0075] Voltage calculation formula:

[0076] U=I alt ×R Load

[0077] Furthermore, the voltage balance equation is numerically solved by the fourth-order Runge-Kutta method to obtain the output current of the Stirling generator.

[0078] Compared with the prior art, the present invention has the following technical effects:

[0079] The Stirling generator performance prediction method of the present invention establishes force balance equations and volume equations for the valve piston, power piston, compression chamber and expansion chamber inside the Stirling generator respectively, and combines the ideal gas equation, mass conservation equation and energy conservation equation to construct a thermo-dynamic coupling model of the Stirling generator including kinetic parameters and thermodynamic parameters; according to the input kinetic parameters, the operating frequency, displacement amplitude and phase difference of the valve piston and power piston are calculated; the thermodynamic model is further solved to obtain changes in the temperature, pressure, mass and mass flow rate of the working fluid; the calculation results of the kinetic model are used to make up for the limitation of the thermodynamic model that cannot characterize the kinetic characteristics, and the calculation results of the kinetic model are used to correct the calculation of the kinetic model, thereby realizing the coupled solution of thermodynamics and kinetics; further adding a motor model realizes the solution and calculation of the whole process of heat-power-electricity conversion, thereby realizing the prediction of the thermo-dynamic-electrical parameters of the Stirling generator, and providing theoretical guidance for the fault diagnosis and optimization design of the whole machine. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 is a flow chart of the present invention;

[0081] Figure 2 A comparison chart of the electric power calculation results and the experimental electric power results of the present invention;

[0082] Figure 3 The figure is a comparison chart of the thermoelectric efficiency calculation results and experimental results of the present invention. DETAILED DESCRIPTION

[0083] The specific contents of the present invention are further explained in detail below with reference to the embodiments.

[0084] This embodiment provides a performance prediction method for a free-piston Stirling generator, taking a free-piston Stirling engine as the main prediction object. By performing force analysis on the valve piston and the power piston, which is a typical multi-degree-of-freedom vibration system, the displacement amplitude and operating frequency of the valve piston and the power piston are related not only to the dynamic parameters, but also to the thermodynamic parameters.

[0085] By establishing the force balance equation and volume equation for the valve piston, power piston, compression chamber and expansion chamber inside the free piston Stirling generator, respectively, and combining the ideal gas equation, mass conservation equation and energy conservation equation, a free piston Stirling generator thermal-dynamic coupling model including dynamic parameters and thermodynamic parameters is established; according to the input structural parameters and operating parameters, the dynamic model calculates the operating frequency, displacement amplitude and phase difference between the valve piston and the power piston; further, the thermodynamic model is used to obtain the working fluid temperature change, pressure change, mass change and mass flow change; further, the motor model is used to obtain the effective voltage, effective current and effective electric power. The specific method is as follows: Figure 1 The specific implementation steps are as follows:

[0086] S1. Input the known structural parameters and operating parameters of the Stirling generator into the dynamic model;

[0087] Structural parameters include: the number, length and width of channels of the heater, regenerator and cooler; the equilibrium volume of the compression chamber and expansion chamber; the diameter, mass, stiffness and damping coefficient of the valve piston, valve piston rod and power piston; the linear damping coefficient and nonlinear damping coefficient of the load; the motor constant, inductance and resistance of the generator.

[0088] Operating parameters include: charging pressure, working fluid type, cooler temperature, and heating power.

[0089] S2. Set the initial heater wall temperature and numerically solve the dynamic model using the fourth-order Runge-Kutta method to obtain the time series of displacement and velocity of the valve piston and power piston;

[0090] The time series of the displacements of the distribution piston and the power piston are subjected to fast Fourier transform to calculate the operating frequency, displacement amplitude and phase difference between the distribution piston and the power piston.

[0091] The kinetic model is as follows:

[0092] The force balance equation of the valve piston:

[0093]

[0094] The force balance equation of the power piston:

[0095]

[0096] The volume equation of the expansion chamber is:

[0097] V e =V e0 +A d x d

[0098] The volume equation of the compression chamber:

[0099] V c =V c0 -(A d -A R )x d +(A p -A R )x p

[0100] Where A, x, P, F, c, k, V, and m are piston cross-sectional area, displacement, pressure, load reaction force, damping coefficient, spring stiffness, volume, and mass, respectively; subscripts d, e, c, b, R, and load represent the valve piston, expansion chamber, compression chamber, back pressure chamber, valve piston rod, and load, respectively; For speed, is the acceleration; V eo Represents the initial volume of the expansion chamber; V co Indicates the initial volume of the compression chamber.

[0101] Working chamber pressure equation:

[0102]

[0103] Where S is the introduced pressure linearization parameter, and its expression is:

[0104]

[0105] S3. Substitute the operating frequency, displacement amplitude, and phase difference between the two pistons into the thermodynamic model to obtain the working fluid temperature, pressure change, mass change, and mass flow change in the heater and cooler;

[0106] The thermodynamic model is as follows:

[0107] Mass of working fluid in compression chamber, cooler, regenerator, heater and expansion chamber:

[0108] m c =pV c / (RT c )

[0109] m k =pV k / (RT k )

[0110] m r =pV r / (RT r )

[0111] m h =pV h / (RT h )

[0112] m e =pV e / (RT e )

[0113] Changes in working fluid mass in the compression chamber, cooler, regenerator, heater and expansion chamber:

[0114] δm c =(pdV c +V c dp / γ) / (RT ck )

[0115] δm e =(pdV e +V e dp / γ) / (RT he )

[0116] δm k =m k dp / p

[0117] δm r =m r dp / p

[0118] δm h =m h dp / p

[0119] Where p, V, and T are pressure, volume, and temperature, respectively; subscripts c, k, r, h, and e represent the compression chamber, cooler, regenerator, heater, and expansion chamber, respectively; γ is the specific heat ratio of the working gas;

[0120] Compression chamber temperature change:

[0121]

[0122] Expansion chamber temperature change:

[0123]

[0124] Where V c is the volume of the compression chamber, V e is the volume of the expansion cavity, m c is the mass of the working medium in the compression chamber, m e is the mass of the working fluid in the expansion chamber.

[0125] Energy equation in the heater:

[0126]

[0127] Energy equation in the cooler:

[0128]

[0129] Energy equation in the regenerator:

[0130]

[0131] Where Q is the heat, subscripts h, k, and r represent heater, cooler, and regenerator, respectively; c v is the constant pressure specific heat capacity of the working gas, m ck =-δm c , m kr =m ck -δm k , m he =δm e , m rh =m he -δm h , represents the mass flow from one component to another; T rh 、T he 、T ck 、T kr Indicates the temperature of the interface between components;

[0132] The expression of the circulating work in the compression chamber is:

[0133] δW c =pdV c

[0134] The expression of the circulation work in the expansion chamber is:

[0135] δW e =pdV e

[0136] The thermodynamic model is also numerically solved using the fourth-order Runge-Kutta method to obtain the working fluid temperature, pressure change, mass change, and mass flow change in the heater and cooler. The calculation results of the kinetic model are used to make up for the limitation of the thermodynamic model that cannot solve the kinetic characteristics, and the calculation results of the thermodynamic model are used to correct the calculation results of the kinetic model.

[0137] S3.1. Temperature convergence judgment

[0138] If the sum of the temperature differences between the heater and cooler working fluids obtained by two consecutive calculations is greater than the set temperature convergence value, the calculated working fluid temperature in the heater replaces the heater wall temperature initially set in S2, and the kinetic and thermodynamic solutions of steps S2 and S3 are repeated for iterative calculations; the iteration ends until the sum of the temperature differences between the heater and cooler working fluids obtained by two consecutive calculations is less than the set temperature convergence value.

[0139] The initial temperatures of the working fluid in the heater and cooler are set to the wall temperatures of the heater and cooler, respectively;

[0140] The sum of the temperature differences between the heater and cooler working fluids obtained from two consecutive calculations, terror, is calculated using the following formula:

[0141] terror=|Th1-Th0|+|Tk1-Tk0|

[0142] Where T h is the working medium temperature in the heater; T k is the working fluid temperature in the cooler; subscript 0 represents the working fluid temperature obtained in the previous calculation; subscript 1 represents the working fluid temperature obtained in this calculation.

[0143] The recommended temperature convergence value is 1°C.

[0144] The working fluid temperature is updated in the following way: the working fluid temperature obtained in this calculation is used as the working fluid temperature input in the next calculation.

[0145] S4. Calculate system losses, including heat loss and work loss, based on the calculation results of S3 to obtain a calculated value of input heat;

[0146] Heat loss includes incomplete heat recovery loss, power piston gap leakage loss, valve piston shuttle loss, valve piston radiation loss, and heat conduction loss;

[0147] The specific formula is as follows:

[0148] Incomplete heat recovery loss:

[0149]

[0150] Where: Q r Incomplete heat recovery loss, is the mass flow rate of the working fluid in the regenerator, ε r is the heat recovery efficiency, NTU is the minimum number of heat transfer units, St is the Stanton number, L r is the regenerator length, d hr is the hydraulic diameter, T is the gas temperature;

[0151] Power piston clearance leakage loss:

[0152]

[0153] Where: Q leak is the power piston clearance leakage loss, is the mass flow rate of the working medium in the gap, D is the average diameter of the power piston gap, u p is the power piston speed, L is the power piston gap length, R g is the gas constant, g is the power piston gap thickness, μ is the dynamic viscosity, and P is the pressure;

[0154] Valve piston shuttle loss:

[0155]

[0156] Where: Z dp is the displacement of the valve piston, k dp is the thermal conductivity of the valve piston, D dp is the valve piston diameter, g dp Is the gap width between the valve piston and the cylinder wall, L dp Valve piston length, T e is the expansion chamber temperature, T c is the compression chamber temperature;

[0157] Radiation loss of valve piston:

[0158]

[0159] Where: A d is the cross-sectional area of ​​the valve piston, C0 is the Stefan-Boltzmann constant, T e is the expansion chamber temperature, T c is the compression chamber temperature;

[0160] Heat conduction loss:

[0161]

[0162] Where: k is the thermal conductivity of the valve piston or cylinder wall, A is the corresponding cross-sectional area, L is the length of the valve piston or cylinder wall, and ΔT is the temperature difference between the hot and cold wall surfaces.

[0163] Work loss includes heat exchanger pressure drop loss, finite speed loss, and hysteresis loss.

[0164] The specific formula is as follows:

[0165] Heat exchanger pressure drop loss:

[0166]

[0167] Where: f is the Reynolds friction factor, μ is the dynamic viscosity, V is the volume of the heat exchanger, G is the mass flow rate, l is the effective length of the heat exchanger, m is the mass flow rate, d k is the hydraulic diameter;

[0168] Finite speed loss:

[0169]

[0170] W fin spe =Δp fin spe ×ΔV e，c

[0171] Where: p represents instantaneous pressure, u p is the piston velocity, c is the average molecular velocity a is a constant defined as a where γ is the specific heat ratio, r g is the gas constant, ΔV is the volume change;

[0172] Hysteresis loss:

[0173]

[0174] Where: k g is the conductivity of the working gas, V m is half the volume swept by the working piston, ω is the angular frequency, T w is the chamber wall temperature, p mean is the average pressure in the engine, A w is the wetted area, usually the cross section of the piston, and γ is the specific heat ratio.

[0175] S4.1. Heat Convergence Judgment

[0176] The calculated value of heat input is the sum of heat absorption by the heater and heat loss of each part.

[0177] Iterative correction is performed between the input heat and the calculated value of the input heat. If the difference between the calculated value of the input heat and the heating power is greater than the set heat convergence value, the heater wall temperature is updated, and steps S2, S3, and S4 are repeated to re-iterate the temperature; until the difference between the calculated value of the input heat and the heating power is less than the set convergence value, the iteration ends.

[0178] The recommended heat convergence value is 0.1kW.

[0179] The heater wall temperature is updated as follows:

[0180] Twh1=Twh0-(Q cal -Q in ) / ξ

[0181] Where Twh0 is the heater wall temperature used in this calculation; Twh1 is the updated heater wall temperature, which will be used as the heater wall temperature in the next calculation; Q cal is the calculated value of input heat; Q in is the heating power. ξ is the temperature correction coefficient. A larger value will slow down the convergence speed, while a smaller value may cause no convergence. The recommended value is 400 to 800. In this example, ξ is 500.

[0182] S5. Generator Part Calculation

[0183] After step S4 converges, the working fluid temperature in the heater corrected by iterative correction in S3 in S4 replaces the heater wall temperature initially set in S2. The time series of displacement and velocity of the power piston and valve piston calculated by running S2 are substituted into the generator model to obtain the output voltage, output current and output electric power.

[0184] The generator model is as follows:

[0185] The formula for calculating the electromotive force of the generator is:

[0186]

[0187] in is the electromotive force of the motor, is the power piston speed, K e is the motor constant.

[0188] Voltage balance equation:

[0189]

[0190] Among them I alt is the output current value, R alt 、R load are the internal resistance of the generator and the resistance of the external load, L alt is the stator inductance, is the capacitance value of the tuning capacitor.

[0191] Voltage calculation formula:

[0192] U=I alt ×R Load

[0193] The voltage balance equation is numerically solved using a fourth-order Runge-Kutta method to obtain the output current of the Stirling generator. The output voltage of the generator is obtained from the load resistance and the output current, and thus the output power.

[0194] Verification results: The present invention was verified using experimental data from a certain institute’s Stirling generator. The results of electric power and efficiency are shown in the figure below. Figure 2 and Figure 3 shown.

[0195] Figure 2 The calculated electric power results shown in the figure are highly consistent with the experimental electric power results. This is because the dynamic method used in this model can effectively improve the prediction accuracy of the dynamic parameters of the Stirling generator. Therefore, the results obtained when the dynamic parameters are used to calculate the motor parameters are more reasonable.

[0196] Figure 3The comparison between the calculated results of thermoelectric efficiency and the experimental results is shown in the figure. The results show that both the trend and the results are in good agreement, indicating the rationality of the heat iteration convergence logic in this model. Since various heat and power losses are taken into account, a reasonable prediction of the input heat is achieved.

[0197] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for predicting Stirling generator performance, characterized in that: The following steps are involved: S1. Inputting known structural parameters and operating parameters of the Stirling generator into the dynamic model; S2. Set the initial heater wall temperature and numerically solve the dynamic model using the fourth-order Runge-Kutta method to obtain the time series of displacement and velocity of the valve piston and power piston; Perform fast Fourier transform on the time series of the displacement of the valve piston and the power piston to calculate the operating frequency, displacement amplitude and phase difference between the valve piston and the power piston; S3. Substitute the operating frequency, displacement amplitude, and phase difference between the two pistons into the thermodynamic model, numerically solve the thermodynamic model using the fourth-order Runge-Kutta method, and calculate the working fluid temperature, pressure change, mass change, and mass flow change in the heater and cooler; Perform temperature convergence iteration on the sum of the temperature differences between the heater and cooler working fluids obtained by two consecutive calculations until the sum of the temperature differences between the heater and cooler working fluids obtained by two consecutive calculations is less than the set temperature convergence value; S4. Calculate the system loss based on the calculation result of S3 to obtain the calculated value of input heat; Perform heat convergence iteration between the calculated value of the input heat and the heating power in the operating parameters until the difference between the calculated value of the input heat and the heating power is less than the set convergence value; After S5 and S4 converge, the working fluid temperature in the heater corrected by the iterative correction of S3 in S4 replaces the heater wall temperature initially set in S2. S2 is run to calculate the time series of the displacement and velocity of the power piston and the valve piston, which are then brought into the generator model to obtain the output voltage, output current, and output electric power.

2. The Stirling generator performance prediction method according to claim 1, wherein: The structural parameters described in S1 include: the number, length and width of the channels of the heater, regenerator and cooler; the equilibrium volume of the compression chamber and expansion chamber; the diameter, mass, stiffness and damping coefficient of the valve piston, valve piston rod and power piston; the linear damping coefficient and nonlinear damping coefficient of the load; the motor constant, inductance and resistance of the generator; Operating parameters include: charging pressure, working fluid type, cooler temperature, and heating power.

3. The Stirling generator performance prediction method according to claim 1, wherein: The kinetic model includes: The force balance equation of the valve piston: The force balance equation of the power piston: The volume equation of the expansion chamber is: In e =V e0 +A d x d The volume equation of the compression chamber: V c =V c0 -(A d -A R )x d +(A p -A R )x p Where A, x, P, F, c, k, V, and m are piston cross-sectional area, displacement, pressure, load reaction force, damping coefficient, spring stiffness, volume, and mass, respectively; subscripts d, e, c, b, R, and load represent the valve piston, expansion chamber, compression chamber, back pressure chamber, valve piston rod, and load, respectively; For speed, is the acceleration; V eo Represents the initial volume of the expansion chamber; V co represents the initial volume of the compression chamber; Working chamber pressure equation: Where S is the introduced pressure linearization parameter, and its expression is:

4. The Stirling generator performance prediction method according to claim 1, wherein: The thermodynamic model is as follows: Mass of working fluid in compression chamber, cooler, regenerator, heater and expansion chamber: m c =pV c / (RT c ) m k =pV k / (RT k ) m r =pV r / (RT r ) m h =pV h / (RT h ) m e =pV e / (RT e ) Changes in working fluid mass in the compression chamber, cooler, regenerator, heater and expansion chamber: δm c =(pdV c +V c dp / γ) / (RT ck ) δm e =(pdV e +V e dp / γ) / (RT he ) δm k =m k dp / p δm r =m r dp / p δm h =m h dp / p Where p, V, and T are pressure, volume, and temperature, respectively; subscripts c, k, r, h, and e represent the compression chamber, cooler, regenerator, heater, and expansion chamber, respectively; γ is the specific heat ratio of the working gas; Compression chamber temperature change: Expansion chamber temperature change: Where V c is the volume of the compression chamber, V e is the volume of the expansion cavity, m c is the mass of the working medium in the compression chamber, m e is the mass of the working fluid in the expansion chamber; Energy equation in the heater: Energy equation in the cooler: Energy equation in the regenerator: Where Q is the heat, subscripts h, k, and r represent heater, cooler, and regenerator, respectively; c v is the constant pressure specific heat capacity of the working gas, m ck =-δm c , m kr =m ck -δm k , m he =δm e , m rh =m he -δm h , represents the mass flow from one component to another; T rh 、T he 、T ck 、T kr Indicates the temperature of the interface between components; The expression of the circulating work in the compression chamber is: δW c =pdV c The expression of the circulation work in the expansion chamber is: δW e =pdV e 。 5. The Stirling generator performance prediction method according to claim 1, wherein: The sum of the temperature differences between the heater and cooler working fluids obtained by two consecutive calculations in S3, terror, is calculated by the following formula: terror=|Th1-Th0|+|Tk1-Tk0| Where T h is the working medium temperature in the heater; T k is the working fluid temperature in the cooler; subscript 0 represents the working fluid temperature obtained in the previous calculation; subscript 1 represents the working fluid temperature obtained in this calculation.

6. The Stirling generator performance prediction method according to claim 1, wherein: The heat convergence iteration described in S4 is performed between the calculated value of the input heat and the heating power in the operating parameters, and the correction method is: if the difference between the calculated value of the input heat and the heating power is greater than the set heat convergence value, the heater wall temperature is updated, and S2, S3, and S4 are repeated until the difference between the calculated value of the input heat and the heating power is less than the set convergence value; The heater wall temperature is updated as follows: Twh1=Twh0-(Q cal -Q in ) / ξ Where Twh0 is the heater wall temperature used in this calculation; Twh1 is the updated heater wall temperature, which will be used as the heater wall temperature in the next calculation; Q cal is the calculated value of input heat; Q in is the heating power; ξ is the temperature correction coefficient.

7. The Stirling generator performance prediction method according to claim 1, wherein: The generator model described in S5 is as follows: The formula for calculating the electromotive force of the generator is: in is the electromotive force of the motor, is the power piston speed, K e is the motor constant; Voltage balance equation: Among them I alt is the output current value, R alt 、R load are the internal resistance of the generator and the resistance of the external load, L alt is the stator inductance, is the capacitance value of the tuning capacitor; Voltage calculation formula: U=I alt ×R Load 。 8. The Stirling generator performance prediction method according to claim 7, wherein: The voltage balance equation is solved numerically by the fourth-order Runge-Kutta method to obtain the output current of the Stirling generator.

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