Stirling generator performance prediction method

Abstract

The invention discloses a Stirling generator performance prediction method. According to the method, a stress balance equation and a volume equation are established for a gas distribution piston, a power piston, a compression cavity and an expansion cavity in the Stirling generator respectively, and an ideal gas equation, a mass conservation equation and an energy conservation equation are combined; constructing a thermal-dynamic coupling model of the Stirling generator, wherein the thermal-dynamic coupling model comprises kinetic parameters and thermodynamic parameters; according to the input kinetic parameters, the operation frequencies and displacement amplitudes of a gas distribution piston and a power piston and the phase difference of the two pistons are calculated; further solving the thermodynamic model to obtain the temperature, pressure, mass and mass flow change of the working medium; substituting the result into a motor model to obtain effective voltage, effective current and effective electric power; through thermal-dynamic coupling solution and in combination with a motor model, solution calculation of the whole thermal-power-electricity conversion process is realized, so that thermal-dynamic-electricity parameter prediction of the Stirling generator is realized, and theoretical guidance is provided for fault diagnosis and optimization design of the whole machine.

Description

Technical Field

[0001] The invention belongs to the technical field of generators, relates to generator performance prediction, and specifically 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, and its working principle is based on the Stirling cycle. Stirling generators have the advantages of high efficiency, simple structure, light weight, fast start-up, low noise and long life. Moreover, when the temperature ratio between the high and low temperature ends is 2 to 3, it can achieve a thermoelectric conversion efficiency of up to 30%. Therefore, it has shown broad application prospects in space missions such as deep space exploration, lunar landing and Mars landing. However, the experimental construction and research of Stirling generators require a lot of manpower and material resources. Improper design parameters may cause the generator to fail to work properly and even cause dangers such as cylinder collision. Therefore, it is of great significance to establish a high-fidelity numerical model that can accurately predict the performance of Stirling generators, which can 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 at the same time. In fact, the Stirling generator is a system with highly coupled 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 to 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 deficiencies in the prior art, the purpose of the present invention is to provide a method for predicting the performance of a Stirling generator, which realizes the calculation of the entire process of heat-power-electricity conversion by solving the thermal-dynamic coupling and adding a motor model, thereby improving the accuracy of the Stirling generator performance prediction.

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

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

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

[0007] S2, setting the initial heater wall temperature, numerically solving the dynamic model by the fourth-order Runge-Kutta method, and obtaining the time series of the displacement and velocity of the valve piston and the 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, substituting the operating frequency, displacement amplitude and phase difference between the two pistons into the thermodynamic model, numerically solving the thermodynamic model by the fourth-order Runge-Kutta method, and calculating 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 difference between the heater and the cooler obtained by two consecutive calculations, until the sum of the temperature difference between the heater and the cooler obtained by two consecutive calculations is less than the set temperature convergence value;

[0011] S4. Calculate the system loss according to 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 S3 in S4 replaces the heater wall temperature initially set in S2, and S2 is run to calculate the time series of the displacement and velocity of the power piston and the valve piston, which are 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, the regenerator and the cooler; the balanced volume of the compression chamber and the expansion chamber; the diameter, mass, stiffness and damping coefficient of the gas distribution piston, the gas distribution piston rod and the power piston; the linear damping coefficient and nonlinear damping coefficient of the load; the motor constant, inductance and resistance of the generator;

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

[0017] Preferably, the kinetic model comprises:

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

[0019]

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

[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] Wherein, A, x, P, F, c, k, V, 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 respectively represent valve piston, expansion chamber, compression chamber, back pressure chamber, valve piston rod, and load; 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 the expression is:

[0030]

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

[0032] The mass of working fluid in the 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 the mass of the working fluid 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, T are pressure, volume, and temperature respectively; subscripts c, k, r, h, and e represent 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 fluid 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 cycle 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 calculated twice in succession in S3, terror, is calculated by the following formula:

[0062] terror=|Th 1 -Th 0 |+|Tk 1 -Tk 0 |

[0063] Where T h is the working fluid temperature in the heater; T k is the working fluid temperature in the cooler; subscript 0 represents the working fluid temperature calculated last time; subscript 1 represents the working fluid temperature calculated this time.

[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] T 1 =Twh 0 -(Q cal -Q in ) / ξ

[0067] Where Twh 0 is the heater wall temperature used in this calculation; Twh 1 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 inductance of the stator, 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 a force balance equation and a volume equation for the internal valve piston, power piston, compression chamber and expansion chamber of the Stirling generator respectively, and combines the ideal gas equation, the mass conservation equation and the energy conservation equation to construct a Stirling generator thermal-dynamic coupling model including dynamic parameters and thermodynamic parameters; according to the input dynamic parameters, the operating frequency, displacement amplitude and phase difference of the valve piston and the power piston are calculated; the thermodynamic model is further solved to obtain the changes in the temperature, pressure, mass and mass flow rate of the working fluid; the calculation results of the dynamic model are used to make up for the limitation that the thermodynamic model cannot characterize the dynamic characteristics, and the calculation results of the thermodynamic model are used to correct the calculation of the dynamic model, so as to realize the coupled solution of thermodynamics and dynamics; the motor model is further added to realize the solution and calculation of the whole process of heat-work-electricity conversion, thereby realizing the prediction of the thermal-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 diagram of the electric power calculation results of the present invention and the experimental electric power results;

[0082] Figure 3 It 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 in conjunction with embodiments.

[0084] This embodiment provides a free-piston Stirling generator performance prediction method, taking the 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 not only related to the dynamic parameters, but also to the thermodynamic parameters.

[0085] By establishing force balance equations and volume equations 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. Specific methods include: Figure 1 As shown, the specific implementation steps are as follows:

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

[0087] The structural parameters include: the number, length and width of 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 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] The operating parameters include: charging pressure, working fluid type, cooler temperature, and heating power.

[0089] S2, setting the initial heater wall temperature, numerically solving the dynamic model by the fourth-order Runge-Kutta method, and obtaining the time series of the displacement and velocity of the valve piston and the power piston;

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

[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] Wherein, A, x, P, F, c, k, V, 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 respectively represent valve piston, expansion chamber, compression chamber, back pressure chamber, valve piston rod, and load; 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 the expression is:

[0104]

[0105] S3, substituting the operating frequency, displacement amplitude and phase difference between the two pistons into the thermodynamic model, and solving 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] The mass of working fluid in the 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 the mass of the working fluid 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, T are pressure, volume, and temperature respectively; subscripts c, k, r, h, and e represent 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 fluid 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 cycle 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 that the thermodynamic model 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 working fluids in the heater and the cooler 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; until the sum of the temperature differences between the working fluids in the heater and the cooler obtained by two consecutive calculations is less than the set temperature convergence value, the iteration ends.

[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 obtained from two consecutive calculations, terror, is calculated by the following formula:

[0141] terror=|Th 1 -Th 0 |+|Tk 1 -Tk 0 |

[0142] Where T h is the working fluid temperature in the heater; T k is the working fluid temperature in the cooler; subscript 0 represents the working fluid temperature calculated last time; subscript 1 represents the working fluid temperature calculated this time.

[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 by this calculation is used as the working fluid temperature input for the next calculation.

[0145] S4. Calculate system losses, including heat loss and work loss, based on the calculation results of S3, and 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 length of the regenerator, 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 fluid 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 gis 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] In the formula: 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, C 0 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 walls.

[0163] Work losses include 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] Wfin spe =Δp fin spe ×ΔV e，c

[0171] Where: p represents instantaneous pressure, u p is the piston speed, 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 input heat is the sum of the heat absorbed by the heater and the heat loss of each part.

[0177] Iterate and correct 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, update the heater wall temperature, repeat steps S2, S3, and S4, and 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 value for the set heat convergence value is 0.1kW.

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

[0180] T 1 =Twh 0 -(Q cal -Q in ) / ξ

[0181] Where Twh 0 is the heater wall temperature used in this calculation; Twh 1 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 inis 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 the iteration of 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 brought 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 inductance of the stator, is the capacitance value of the tuning capacitor.

[0191] Voltage calculation formula:

[0192] U=I alt ×R Load

[0193] The output current of the Stirling generator is obtained by numerically solving the voltage balance equation using the fourth-order Runge-Kutta method. The output voltage of the generator is obtained from the load resistance and the output current, and then the output power is obtained.

[0194] Results verification: The present invention was verified using experimental data of a Stirling generator from a certain institute. The results of electric power and efficiency are shown in Figure 2 and Figure 3 shown.

[0195] Figure 2The 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, when the dynamic parameters are used to calculate the motor parameters, the results obtained are more reasonable.

[0196] Figure 3 The 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 work losses are taken into account, a reasonable prediction of the input heat is achieved.

[0197] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A Stirling generator performance prediction method, 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, setting the initial heater wall temperature, numerically solving the dynamic model by the fourth-order Runge-Kutta method, and obtaining the time series of the displacement and velocity of the valve piston and the 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, substituting the operating frequency, displacement amplitude and phase difference between the two pistons into the thermodynamic model, numerically solving the thermodynamic model by the fourth-order Runge-Kutta method, and calculating 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 difference between the heater and the cooler obtained by two consecutive calculations, until the sum of the temperature difference between the heater and the cooler obtained by two consecutive calculations is less than the set temperature convergence value; S4. Calculate the system loss according to 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 S3 in S4 replaces the heater wall temperature initially set in S2, and S2 is run to calculate the time series of the displacement and velocity of the power piston and the valve piston, which are 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, characterized in that: The structural parameters described in S1 include: the number, length and width of the channels of the heater, regenerator and cooler; the balanced volume of the compression chamber and the 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; The operating parameters include: charging pressure, working fluid type, cooler temperature, and heating power.

3. The Stirling generator performance prediction method according to claim 1, characterized in that: The kinetic model includes: The force balance equation of the valve piston: The force balance equation of the power piston is: 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 Wherein, A, x, P, F, c, k, V, 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 respectively represent valve piston, expansion chamber, compression chamber, back pressure chamber, valve piston rod, and load; 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 the expression is:

4. The Stirling generator performance prediction method according to claim 1, characterized in that: The thermodynamic model is as follows: The mass of working fluid in the 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 the mass of the working fluid 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, T are pressure, volume, and temperature respectively; subscripts c, k, r, h, and e represent 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 fluid 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 cycle 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, characterized in that: The sum of the temperature differences between the heater and cooler obtained by two consecutive calculations described in S3, terror, is calculated by the following formula: terror=|Th1-Th0|+|Tk1-Tk0| Where T h is the working fluid temperature in the heater; T k is the working fluid temperature in the cooler; subscript 0 represents the working fluid temperature calculated last time; subscript 1 represents the working fluid temperature calculated this time.

6. The Stirling generator performance prediction method according to claim 1, characterized in that: 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; 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, characterized in that: 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 inductance of the stator, 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, characterized in that: 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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