Stirling engine simulation method and system based on constant power heating and air cooling boundary

Abstract

The invention discloses a Stirling engine simulation method and system based on a constant power heating and air cooling boundary, and the method comprises the steps: S1, determining geometric parameters of components of a Stirling engine and fluid mechanics parameters and thermodynamic parameters of a selected working medium, and constructing an initial architecture of the Stirling engine; s2, performing preliminary design based on the initial architecture to obtain a design result; s3, comparing the design result with an actual value to obtain a comparison result; s4, when the comparison result is within a preset error range, completing the design; otherwise, updating iteration is carried out until a final design scheme is output, and the simulation design of the Stirling engine is completed. According to the method, various heat losses are considered, so that the Stirling engine simulation method has a more accurate simulation effect on parameters such as the heat exchange amount of a heater, the heat exchange amount of a cooler and the output power in the circulating process of the Stirling engine; and by adding constant-power heating and air cooling boundary conditions, simulation can be carried out under the condition that the heating power and the air cooling power are clear.

Description

Technical Field

[0001] The present invention relates to the field of Stirling engine design and simulation, and particularly to a Stirling engine simulation method and system for fixed-power heating and air-cooling boundary. Background Art

[0002] A Stirling engine nuclear reactor power supply that utilizes reactor fission energy and adopts a Stirling cycle as a dynamic thermoelectric conversion scheme has the advantages of high energy density, continuous output, stable operation, high thermal efficiency, etc. Compared with photovoltaic power supplies, chemical fuel power supplies, etc. that have limitations in application scenarios and service lives, the Stirling engine nuclear reactor power supply has non-negligible advantages in the fields of national defense and military, disaster relief, vehicle-mounted mobile nuclear power supplies, etc.

[0003] The design research of the Stirling engine nuclear reactor power supply starts from design and simulation, and the simulation calculation of the Stirling engine thermodynamic cycle should be realized through a simulation method with a certain reliable accuracy. The existing design method is to adjust the thermodynamic parameters and structural parameters of the Stirling engine to achieve the purpose that the heating power and cooling power meet the design requirements, and it cannot carry out the directional thermodynamic parameter design work with fixed thermal power heating and fixed-power air-cooling cooling as the design goals. At the same time, the accuracy of the Stirling engine simulation method also needs to be improved.

[0004] Based on this, a Stirling engine simulation method for fixed-power heating and air-cooling boundary is studied and developed, adding various heat losses to improve the accuracy of the simulation method; at the same time, adding fixed-power heating and air-cooling boundary conditions can complete the Stirling engine design and simulation work under the design requirements of a determined power. Summary of the Invention

[0005] To solve the technical problems in the above background, the present invention provides the following technical solutions:

[0006] A Stirling engine simulation method for fixed-power heating and air-cooling boundary, characterized in that the steps include:

[0007] S1. Determine the geometric parameters of the components of the Stirling engine and the hydrodynamic parameters and thermodynamic parameters of the selected working fluid, and construct the initial architecture of the Stirling engine;

[0008] S2. Based on the initial architecture, conduct a preliminary design to obtain a design result;

[0009] S3. Compare the design result with the actual value to obtain a comparison result;

[0010] S4. When the comparison result is within the preset error range, the design is completed; otherwise, update and iterate until the final design scheme is output to complete the simulation design of the Stirling engine.

[0011] Preferably, the geometric parameters include: the areas of the gas distribution piston and the power piston, the amplitude and frequency, the length, thickness, diameter and number of tubes of the heat exchange tubes of the heat exchanger, and the heat exchanger includes a cooler, a regenerator, and a heater; the thermodynamic parameters include: the specific heat ratio, the reference temperature, and the thermodynamic constant; the fluid mechanics parameters include: the dynamic viscosity at the reference temperature.

[0012] Preferably, the steps for performing the preliminary design include:

[0013] Based on the geometric parameters, calculate the wall temperature of the heat exchanger;

[0014] Based on the fluid mechanics parameters and the thermodynamic parameters, calculate the working medium temperature of the heat exchanger.

[0015] Preferably, the method for calculating the wall temperature of the heat exchanger includes: according to the heat exchange area of the heater pipeline and the thermal conductivity obtained from the heating pipe material, and then using the heat conduction formula to calculate the steady-state wall temperature of the heater:

[0016]

[0017] In the formula, T wh represents the wall temperature of the heater, unit: K; T whsource represents the heat source temperature, unit: K; Q hin represents the designed heat power, unit: W; l hthickness represents the wall thickness of the heater, unit: m; λ h represents the thermal conductivity of the heating pipe, unit: W / (m·K); A h represents the heat exchange area of the heating pipe, unit: m 2 ;

[0018] According to the pipe arrangement mode, arrangement layers and geometric parameters of the cooler, as well as the average flow velocity of the cooling air and the thermodynamic and fluid mechanics parameters at different temperatures, use the Zhukauskas formula to obtain the Nusselt number of the cooling air, so as to obtain the convective heat transfer coefficient and calculate the wall temperature of the cooler:

[0019]

[0020] In the formula, T wk is the surface temperature of the cooler, unit: K; T kgas is the temperature of the cooling air, unit: K; Q kin is the designed cooling power of the air-cooled machine, which is negative, unit: W; A k is the surface heat exchange area of the cooler pipeline, unit: m 2 .

[0021] Preferably, when the comparison result between the designed thermal power and the actual heat transfer amount of the heater and the comparison result between the designed cooling power and the actual heat transfer amount of the cooler are outside the operating error range, the heat source temperature is updated through the heat conduction formula, and the cooling air temperature is updated through the convective heat transfer formula, and recalculated until the difference between the designed power of the two heat exchangers and the actual heat transfer amount in the simulation is within the preset error range, which is regarded as the success of the iteration.

[0022] Preferably, when the comparison result of the working medium temperature of the heat exchanger is outside the operating error range, the initial working medium temperature of the heat exchanger is updated for iteration until the iteration is successful. The iteration method of the working medium temperature of the heat exchanger is as follows:

[0023]

[0024] In the formula, h represents the surface convective heat transfer coefficient of the heater or cooler, unit: W / (m2·K); λ represents the thermal conductivity of the heater or cooler, unit: W / (m·K); d represents the inner diameter of the tube of the heater or cooler, unit: m.

[0025] The present invention also provides a Stirling engine simulation system for the boundary of constant power heating and air cooling. The system is used to implement the above method and includes: a construction module, a design module, a comparison module, and an iteration module;

[0026] The construction module is used to determine the geometric parameters of the components of the Stirling engine and the hydrodynamic parameters and thermodynamic parameters of the selected working medium, and construct the initial architecture of the Stirling engine;

[0027] The design module is used to perform a preliminary design based on the initial architecture to obtain a design result;

[0028] The comparison module is used to compare the design result with the actual value to obtain a comparison result;

[0029] The iteration module is used to complete the design when the comparison result is within the preset error range; otherwise, update and iterate until the final design scheme is output to complete the simulation design of the Stirling engine.

[0030] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0031] The present invention takes into account various heat losses, so that the Stirling engine simulation method has a more accurate simulation effect on parameters such as the heat transfer amount of the heater, the heat transfer amount of the cooler, and the output power in the Stirling engine cycle process; also, by adding constant power heating and air cooling boundary conditions, it is possible to simulate the working cycle process of the Stirling engine under the condition of clear heating power and air cooling power, and obtain appropriate working conditions, such as the temperature and pressure of the working chamber, etc., which makes up for the defect that the Stirling engine working condition design cannot be carried out with a clear power as the boundary in the previous design method. Description of the Drawings

[0032] To more clearly illustrate the technical solution of the present invention, the accompanying drawings required for use in the embodiments will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.

[0033] Figure 1 It is a schematic flowchart of the method according to an embodiment of the present invention;

[0034] Figure 2 It is a schematic flowchart of the process framework according to an embodiment of the present invention. Detailed implementation manners

[0035] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0036] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0037] Embodiment 1

[0038] As Figure 1 shown, it is a schematic flowchart of the method of this embodiment, and the steps include:

[0039] S1. Determine the geometric parameters of the components of the Stirling engine and the hydrodynamic parameters and thermodynamic parameters of the selected working fluid, and construct the initial architecture of the Stirling engine.

[0040] Among them, the geometric parameters include: the areas, amplitudes, and frequencies of the distribution piston and the power piston, the lengths, thicknesses, diameters, and numbers of tubes of the heat exchange tubes of the heat exchanger, and the heat exchanger includes a cooler, a regenerator, and a heater; the thermodynamic parameters include: the specific heat ratio, the reference temperature, and the thermodynamic constant; the hydrodynamic parameters include: the dynamic viscosity at the reference temperature.

[0041] The purpose of this step is to establish the basic architecture of the Stirling engine, and subsequent steps further refine the details such as the heater pipes on this architecture. The geometric parameters define the physical dimensions and layouts of the components of the Stirling engine, providing a basis for subsequent thermal calculations and hydrodynamic analyses. The working fluid parameters determine the thermodynamic behavior of the working fluid during heating and cooling, affecting the heat transfer efficiency and the flow characteristics of the working fluid, and are factors that must be considered when designing the heat source and cooling system.

[0042] S2. Based on the initial architecture, conduct a preliminary design to obtain the design results.

[0043] Based on the geometric parameters and working fluid parameters determined in S1, preliminarily assume the design thermal powers and temperatures of the cold and heat sources. The specific steps are as follows:

[0044] Determine the design thermal power Q of the heat source according to the design objective hin , and preliminarily and reasonably assume the heat source temperature T when the heat source transfers heat to the heater pipe through heat conduction whsource . Determine the design cooling power Q of the air cooler kin , and preliminarily assume the cooling air temperature T kgas ;

[0045] According to the heat transfer area A of the heater pipe h , the thermal conductivity λ of the heating pipe material h , and then use the heat conduction formula to calculate the steady-state heater pipe wall temperature T wh . The specific calculation method is as follows:

[0046]

[0047] In the formula, T wh represents the heater pipe wall temperature, unit: K; T whsource represents the heat source temperature, unit: K; Q hin represents the design thermal power, unit: W; l hthickness represents the heater pipe wall thickness, unit: m; λ h represents the heating pipe thermal conductivity, unit: W / (m·K); A h represents the heating pipe heat transfer area, unit: m 2 .

[0048] According to the cooler pipe arrangement (staggered or in-line), the number of arrangement layers and geometric parameters, as well as the average flow velocity v of the cooling air gas and the thermodynamic and fluid dynamic parameters at different temperatures, etc., use the Zhukauskas formula for heat transfer of fluid flowing across tube bundles to obtain the Nusselt number Nu of the cooling air f , so as to obtain the convective heat transfer coefficient h gas , and calculate the cooler pipe wall temperature T wk . The specific calculation method is as follows:

[0049]

[0050] In the formula, Re f represents the cooling air Reynolds number; ρ gas represents the cooling air density, unit: kg / m 3 ; v gasRepresents the average flow velocity of the cooling air, unit: m / s; d k Represents the diameter of the cooling pipe, unit: m; μ gas Represents the dynamic viscosity of the cold air, unit: Pa·s.

[0051]

[0052] In the formula, unit: Pr f Represents the Prandtl number of the cooling air; c p Represents the specific heat capacity at constant pressure of the cooling air, unit: J / (kg·K); λ gas Represents the heat conduction coefficient of the cooling air, unit: W / (m·K). The same Pr w Determined according to the average wall temperature of the tube bundle; s 1 Represents the center distance between two adjacent tubes perpendicular to the cooling air, unit: m; s 2 Represents the center distance between two adjacent tubes parallel to the cooling air, unit: m.

[0053] Calculate Re f , Pr f and Pr w After that, use Table 1 and Table 2 to calculate the Nusselt number Nu of the cooling air f , for the tube bundle with the number of rows less than 16, the average heat transfer coefficient on its surface should be according to the correction factor ε given in Table 3 n , multiply the value obtained from Nu f by the correction factor ε n .

[0054] Table 1

[0055]

[0056] Table 2

[0057]

[0058] Table 3

[0059]

[0060] The calculation formula for the convective heat transfer coefficient on the surface of the cooling air is as follows:

[0061]

[0062] In the formula, h gas Represents the convective heat transfer coefficient on the surface of the cooling air, unit: W / (m 2 ·K).

[0063]

[0064] In the formula, T wkRepresents the surface temperature of the cooler, unit: K; T kgas Represents the temperature of the cooling air, unit: K; Q kin Represents the designed cooling power of the air-cooled machine, shown as a negative value, unit: W; A k Represents the heat transfer area of the cooler pipe surface, unit: m 2 .

[0065] After that, based on the hydrodynamic parameters and thermodynamic parameters, the temperature of the working fluid in the heat exchanger is calculated. In this embodiment, the initial assumption is that the working fluid temperature is the temperature of the corresponding heat exchanger wall surface, i.e., T gh = T wh , T gk = T wk , and then the Stirling engine thermodynamic cycle simulation calculation is carried out using the main equations of the adiabatic model in Table 4, and the calculation of the thermal loss terms is carried out based on the data of the adiabatic model, including the regenerator efficiency loss Q rloss , the heat transfer loss Q w due to the temperature difference between the heater and the cooler, the working fluid flow resistance loss W fr , the shuttle loss Q shuttle of the distribution piston, the working fluid leakage loss W leak , the air flow lag loss W gp , and the environmental radiation heat transfer loss Q radiation , and finally the actual heat transfer amount Q h1 , Q k1 .

[0066] Table 4

[0067]

[0068] The specific calculation formulas are as follows:

[0069]

[0070] St = 0.46Re -0.4 Pr -1

[0071] In the formula, Q r represents the heat recovered by the regenerator, unit: J; ε represents the heat regeneration efficiency of the regenerator; St represents the Stanton number; A wg represents the wetted perimeter area inside the regenerator, unit: m 2 ; A represents the free flow area inside the regenerator, unit: m 2 .

[0072]

[0073] In the formula, C ref represents the Reynolds resistance coefficient; V represents the volume of each cavity, unit: m3 ; A represents the free flow area in each cavity, unit: m 2 .

[0074]

[0075] In the formula, k m represents the thermal conductivity of the material, unit: W / (m·K); A w represents the cross-sectional area, unit: m 2 ; l represents the length of the material in the heat conduction part, unit: m.

[0076]

[0077] In the formula, z represents the stroke of the gas distribution piston, unit: m; k g represents the thermal conductivity of the working medium gas, unit: W / (m·K); D d represents the diameter of the gas distribution piston, unit: m; J represents the gas gap thickness between the gas distribution piston and the cylinder, unit: m; L d represents the axial length of the gas distribution piston, unit: m; T e and T c are the temperatures of the expansion cavity and the compression cavity respectively, unit: K.

[0078]

[0079] In the formula, ω represents the operating angular velocity, unit: rad / s; γ = c p / c v ; T cmean represents the average temperature of the compression cavity, unit: K; p mean represents the average pressure, unit: Pa; k g represents the thermal conductivity of the gas, unit: W / (m·K); ΔV represents the volume amplitude of the compression cavity, unit: m 3 ; V cmean represents the average volume of the compression cavity, unit: m 3 ; A cw represents the flow-through area in the compression cavity, unit: m 2 .

[0080] W leak = q leak C p T leak

[0081]

[0082] In the formula, q leak is the mass flow rate of the leaked working medium, unit: kg / s; D c is the diameter of the power piston, unit: m; Δp is the maximum pressure difference in the compression cavity, unit: Pa; h0 is the roughness of the cylinder block; η is the cycle efficiency; L is the axial length of the power piston, unit: m; u p is the speed of the power piston, unit: m / s.

[0083] Q radiation = εσA v (T w 4 - T a 4 )

[0084] In the formula, ε is the surface emissivity, unit: W / (m 2 ·K); σ is the Stefan–Boltzmann constant, which is 1.380649×10 -23 J / K; A v is the heat transfer area where the working chamber contacts the environment, unit: m 2 ; T w is the temperature of the working chamber wall, unit: K; T a is the ambient temperature of the working chamber, unit: K; Q radiation_h represents the heat dissipation of the heater to the environment; Q radiation_k represents the heat absorption of the cooler from the environment. The actual heat transfer quantity Q h1 of the heater obtained by simulation calculation and the actual heat transfer quantity Q k1 of the cooler are as follows, where Q radiation_k is negative:

[0085] Q h1 = Q h0 + Q w + Q rloss + Q shuttle + Q radiation_h

[0086] Q k1 = Q k0 + Q w + Q rloss + Q shuttle + W fr + W gp + W leak + Q radiation_k

[0087] In the formula, Q h0 is the ideal heat transfer quantity of the heater in the adiabatic model, unit: W; Q k0 is the ideal heat transfer quantity of the cooler in the adiabatic model, unit: W.

[0088] S3. Compare the design result with the actual value to obtain the comparison result.

[0089] S301. Compare the design thermal power Q hinThe actual heat exchange quantity Q of the heater h1 , and the designed cooling power Q kin and the actual heat exchange quantity Q of the cooler k1 . If it is within the operating error range, it is regarded as successful iteration.

[0090] S302. Calculate the working medium temperature T of the heater through the internal heat convection formula of the heat exchanger tube gh and the working medium temperature T of the cooler gk , and compare with the initially assumed working medium temperature T of the heat exchanger gh = T wh , T gk = T wk . If it is within the error allowable range, it passes.

[0091] S4. When the comparison result is within the preset error range, the design is completed; otherwise, update and iterate until the final design scheme is output, and the simulation design of the Stirling engine is completed.

[0092] If the comparison result in S301 is outside the error range, update the heat source temperature T through the heat conduction formula whsource , update the cooling air temperature T through the convective heat transfer formula kgas , and then start the calculation again from step S2 until the difference between the designed power of the two heat exchangers and the actual heat exchange quantity in the simulation is within the set acceptable error range, which is regarded as successful iteration. The update equations are as follows:

[0093]

[0094] If the comparison result in S302 is outside the error range, update the initial working medium temperature of the heat exchanger for iteration until successful iteration. The iteration method of the working medium temperature of the heat exchanger is as follows:

[0095]

[0096] In the formula, h is the surface convective heat transfer coefficient of the heater or cooler, unit: W / (m2·K); λ is the thermal conductivity of the heater or cooler, unit: W / (m·K); d is the inner diameter of the tube of the heater or cooler, unit: m. Finally, parameters such as the simulation output power and efficiency can be calculated, as well as the operating parameters under the designed heat power and designed cooling power conditions required by the design. Among them, Nu = 0.023Re 0.8 Pr n (for heating: n = 0.4; for cooling: n = 0.3). The overall process framework of the present invention is as Figure 2 shown.

[0097] Embodiment 2

[0098] This embodiment also provides a Stirling engine simulation system for the boundary between constant-power heating and air cooling, including: a construction module, a design module, a comparison module, and an iteration module; the construction module is used to determine the geometric parameters of the components of the Stirling engine and the hydrodynamic and thermodynamic parameters of the selected working fluid, and construct the initial architecture of the Stirling engine; the design module is used to perform a preliminary design based on the initial architecture to obtain a design result; the comparison module is used to compare the design result with the actual value to obtain a comparison result; the iteration module is used to complete the design when the comparison result is within a preset error range; otherwise, update and iterate until the final design scheme is output to complete the simulation design of the Stirling engine.

[0099] Next, in combination with this embodiment, it will be detailed how the present invention solves technical problems in real life.

[0100] Use the construction module to determine the geometric parameters of the components of the Stirling engine and the hydrodynamic and thermodynamic parameters of the selected working fluid, and construct the initial architecture of the Stirling engine.

[0101] Among them, the geometric parameters include: the areas, amplitudes and frequencies of the gas distribution piston and the power piston, the lengths, thicknesses, diameters and numbers of the heat exchange tubes of the heat exchanger, and the heat exchanger includes a cooler, a regenerator, and a heater; the thermodynamic parameters include: the specific heat ratio, the reference temperature, and the thermodynamic constant; the hydrodynamic parameters include: the dynamic viscosity at the reference temperature.

[0102] The purpose of this process is to establish the basic architecture of the Stirling engine, and subsequent steps further refine the details such as the heater pipes on this architecture. The geometric parameters define the physical dimensions and layouts of the components of the Stirling engine, providing a basis for subsequent thermal calculations and hydrodynamic analyses. The working fluid parameters determine the thermodynamic behavior of the working fluid during heating and cooling, affecting the heat transfer efficiency and the flow characteristics of the working fluid, and are factors that must be considered when designing the heat source and the cooling system.

[0103] The design module performs a preliminary design based on the initial architecture to obtain a design result.

[0104] Based on the geometric parameters and working fluid parameters determined in the construction module, preliminarily assume the design thermal powers and the temperatures of the cold and heat sources of the cold and heat sources. The specific process is as follows:

[0105] Determine the design thermal power Q hin of the heat source according to the design objective, and preliminarily and reasonably assume the heat source temperature T whsource when the heat source transfers heat to the heater pipes in the form of heat conduction. Determine the design cooling power Q kin of the air cooler, and preliminarily assume the cooling air temperature T kgas ;

[0106] According to the heat transfer area A h, the heating tube material obtains the thermal conductivity λ h , and then the steady-state heater tube wall temperature T is calculated using the heat conduction formula wh . The specific calculation method is as follows:

[0107]

[0108] In the formula, T wh represents the heater tube wall temperature, unit: K; T whsource represents the heat source temperature, unit: K; Q hin represents the designed heat power, unit: W; l hthickness represents the heater tube wall thickness, unit: m; λ h represents the heating tube thermal conductivity, unit: W / (m·K); A h represents the heating tube heat transfer area, unit: m 2 .

[0109] According to the cooler pipe arrangement (staggered or in-line), the number of arrangement layers and geometric parameters, as well as the average flow velocity v of the cooling air gas and the thermodynamic and fluid dynamic parameters at different temperatures, etc., the Nusselt number Nu of the cooling air is obtained using the Zhukauskas formula for heat transfer of fluid flowing across tube bundles f , thereby obtaining the convective heat transfer coefficient h gas , and calculating the cooler tube wall temperature T wk . The specific calculation method is as follows:

[0110]

[0111] In the formula, Re f represents the cooling air Reynolds number; ρ gas represents the cooling air density, unit: kg / m 3 ; v gas represents the average flow velocity of the cooling air, unit: m / s; d k represents the diameter of the cooling tube, unit: m; μ gas represents the dynamic viscosity of the cold air, unit: Pa·s.

[0112]

[0113] In the formula, unit: Pr f represents the cooling air Prandtl number; c p represents the specific heat capacity at constant pressure of the cooling air, unit: J / (kg·K); λ gas represents the thermal conductivity of the cooling air, unit: W / (m·K). The same Pr w is determined according to the average wall temperature of the tube bundle; s 1 represents the distance between the centers of two adjacent tubes perpendicular to the cooling air, unit: m; s2 Denotes the center distance between two adjacent tubes parallel to the cooling air, unit: m.

[0114] Calculate Re f and Pr f and Pr w After that, use Table 1 and Table 2 to calculate the Nusselt number Nu of the cooling air f For a tube bundle with the number of rows less than 16, the average heat transfer coefficient on its surface should be based on the correction factor ε given in Table 3 n , multiply the obtained value of Nu f by the correction factor ε n .

[0115] The calculation formula for the convective heat transfer coefficient on the surface of the cooling air is as follows:

[0116]

[0117] In the formula, h gas Denotes the convective heat transfer coefficient on the surface of the cooling air, unit: W / (m 2 ·K).

[0118]

[0119] In the formula, T wk Denotes the surface temperature of the cooler, unit: K; T kgas Denotes the temperature of the cooling air, unit: K; Q kin Denotes the designed cooling power of the air-cooled machine, expressed as a negative value, unit: W; A k Denotes the heat transfer area of the cooler pipe surface, unit: m 2 .

[0120] After that, based on the hydrodynamic parameters and thermodynamic parameters, calculate the temperature of the working fluid in the heat exchanger. In this embodiment, the initial assumption is that the temperature of the working fluid is the temperature of the corresponding heat exchanger wall surface, that is, T gh = T wh , T gk = T wk , then use the main equations of the adiabatic model in Table 4 to perform the Stirling engine thermodynamic cycle simulation calculation, and calculate the thermal loss terms based on the data of the adiabatic model, including the regenerator efficiency loss Q rloss , the heat transfer loss Q w due to the temperature difference between the heater and the cooler, the working fluid flow resistance loss W fr , the distribution piston shuttle loss Q shuttle , the working fluid leakage loss W leak , the gas flow lag loss W gp and the environmental radiation heat transfer loss Q radiation , and finally obtain the actual heat transfer amount Q h1 of the heater and the cooler during the simulation process, Qk1 。

[0121] The specific calculation formula is as follows:

[0122]

[0123] St = 0.46Re -0.4 Pr -1

[0124] In the formula, Q r represents the heat recovery amount of the regenerator, unit: J; ε represents the heat recovery efficiency of the regenerator; St represents the Stanton number; A wg represents the wetted perimeter area inside the regenerator, unit: m 2 ; A represents the free flow area inside the regenerator, unit: m 2 。

[0125]

[0126] In the formula, C ref represents the Reynolds resistance coefficient; V represents the volume of each cavity, unit: m 3 ; A represents the free flow area inside each cavity, unit: m 2 。

[0127]

[0128] In the formula, k m represents the thermal conductivity of the material, unit: W / (m·K); A w represents the cross-sectional area, unit: m 2 ; l represents the length of the heat-conducting part of the material, unit: m.

[0129]

[0130] In the formula, z represents the stroke of the gas distribution piston, unit: m; k g represents the thermal conductivity of the working fluid gas, unit: W / (m·K); D d represents the diameter of the gas distribution piston, unit: m; J represents the gas gap thickness between the gas distribution piston and the cylinder, unit: m; L d represents the axial length of the gas distribution piston, unit: m; T e and T c are the temperatures of the expansion chamber and the compression chamber respectively, unit: K.

[0131]

[0132] In the formula, ω represents the operating angular velocity, unit: rad / s; γ = c p / c v ; T cmeanRepresents the average temperature of the compression chamber, unit: K; p mean Represents the average pressure, unit: Pa; k g Represents the gas thermal conductivity, unit: W / (m·K); ΔV represents the volume amplitude of the compression chamber, unit: m 3 ; V cmean Represents the average volume of the compression chamber, unit: m 3 ; A cw Represents the flow-through area in the compression chamber, unit: m 2 .

[0133] W leak =q leak C p T leak

[0134]

[0135] In the formula, q leak Is the mass flow rate of the leaked working fluid, unit: kg / s; D c Is the diameter of the power piston, unit: m; Δp is the maximum pressure difference in the compression chamber, unit: Pa; h 0 Is the roughness of the cylinder block; η is the cycle efficiency; L is the axial length of the power piston, unit: m; u p Is the speed of the power piston, unit: m / s.

[0136] Q radiation =εσA v (T w 4 -T a 4 )

[0137] In the formula, ε is the surface emissivity, unit: W / (m 2 ·K); σ is the Stefan–Boltzmann constant, which is 1.380649×10 -23 J / K; A v Is the heat transfer area where the working chamber contacts the environment, unit: m 2 ; T w Is the wall temperature of the working chamber, unit: K; T a Is the environmental temperature of the working chamber, unit: K; Q radiation_h Represents the heat dissipation from the heater to the environment; Q radiation_k Represents the heat absorption from the cooler to the environment. The actual heat transfer amount Q h1 Of the heater obtained by simulation calculation and the actual heat transfer amount Q k1 Of the cooler are as follows, where Q radiation_k Is negative:

[0138] Q h1 =Q h0 +Qw +Q rloss +Q shuttle +Q radiation_h

[0139] Q k1 =Q k0 +Q w +Q rloss +Q shuttle +W fr +W gp +W leak +Q radiation_k

[0140] In the formula, Q h0 is the ideal heat transfer amount of the heater in the adiabatic model, unit: W; Q k0 is the ideal heat transfer amount of the cooler in the adiabatic model, unit: W.

[0141] The comparison module compares the design result with the actual value to obtain a comparison result. The process includes:

[0142] (1) Compare the designed thermal power Q hin with the actual heat transfer amount Q h1 of the heater, and the designed cooling power Q kin with the actual heat transfer amount Q k1 of the cooler. If it is within the operating error range, it is regarded as a successful iteration.

[0143] (2) Calculate the working medium temperature T gh of the heater and the working medium temperature T gk of the cooler through the internal heat convection formula of the heat exchanger, and compare with the initially assumed working medium temperature T gh =T wh , T gk =T wk . If it is within the error tolerance range, it passes.

[0144] When the comparison result is within the preset error range, the design is completed; otherwise, use the iteration module to update and iterate until the final design scheme is output, and the simulation design of the Stirling engine is completed.

[0145] When the comparison result of the designed thermal power and the actual heat transfer amount of the heater, and the comparison result of the designed cooling power and the actual heat transfer amount of the cooler are outside the operating error range, update the heat source temperature through the heat conduction formula, update the cooling air temperature through the convective heat transfer formula, and recalculate until the difference between the design power of the two heat exchangers and the actual heat transfer amount of the simulation is within the preset error range, which is regarded as a successful iteration. The update equations are as follows:

[0146]

[0147] When the comparison result of the heat exchanger working medium temperature is outside the operating error range, update the initial heat exchanger working medium temperature for iteration until the iteration is successful. The heat exchanger working medium temperature iteration method is as follows:

[0148]

[0149] In the formula, h represents the surface convective heat transfer coefficient of the heater or cooler, unit: W / (m2·K); λ represents the thermal conductivity of the heater or cooler, unit: W / (m·K); d represents the inner diameter of the tube of the heater or cooler, unit: m.

[0150] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A Stirling machine simulation method for a constant power heating and air cooling boundary, characterized in that the steps include: S1. Determine the geometric parameters of the components of the Stirling engine and the fluid mechanics parameters and thermodynamic parameters of the selected working fluid, and construct the initial architecture of the Stirling engine; S2. Based on the initial architecture, perform preliminary design and obtain design results; S3. Compare the design result with the actual value to obtain a comparison result; S4. When the comparison result is within the preset error range, the design is completed; Otherwise, update and iterate until the final design solution is output to complete the simulation design of the Stirling machine.

2. The Stirling machine simulation method for constant power heating and air cooling boundary according to claim 1, characterized in that: The geometric parameters include: the area, amplitude and frequency of the valve piston and the power piston, the length, thickness, diameter and number of heat exchange tubes of the heat exchanger, and the heat exchanger includes a cooler, a regenerator and a heater; the thermodynamic parameters include: specific heat ratio, reference temperature, thermodynamic constants; the fluid mechanics parameters include: dynamic viscosity at the reference temperature.

3. The Stirling machine simulation method for constant power heating and air cooling boundary according to claim 2, characterized in that: The steps of carrying out the preliminary design include: Based on the geometric parameters, calculating the tube wall temperature of the heat exchanger; Based on the fluid mechanics parameters and the thermodynamic parameters, the working medium temperature of the heat exchanger is calculated.

4. The Stirling machine simulation method for constant power heating and air cooling boundary according to claim 3, characterized in that: The method for calculating the tube wall temperature of the heat exchanger includes: obtaining the thermal conductivity of the heating tube material according to the heat exchange area of ​​the heater tube, and then calculating the steady-state heater tube wall temperature using the heat conduction formula: Where, T wh Indicates the heater tube wall temperature, unit: K; T whsource Indicates the heat source temperature, unit: K; Q hin Indicates the design thermal power, unit: W; l hthickness Indicates the thickness of the heater tube wall, unit: m; λ h Indicates the thermal conductivity of the heating tube, unit: W / (m·K); A h Indicates the heat exchange area of ​​the heating tube, unit: m 2 ; According to the arrangement mode, number of layers and geometric parameters of the cooler pipes, the average flow rate of the cooling air and the thermodynamic and fluid dynamic parameters at different temperatures, the Nusselt number of the cooling air is obtained using the Zhukauskas formula, thereby obtaining the convective heat transfer coefficient and calculating the cooler pipe wall temperature: Where T wk is the surface temperature of the cooler, unit: K; T kgas is the cooling air temperature, unit: K; Q kin It is the designed cooling power of the air cooler, which is a negative value, unit: W; A k is the heat exchange area of ​​the cooler pipe surface, unit: m 2 .

5. The Stirling machine simulation method at the boundary of constant power heating and air cooling according to claim 1, characterized in that: When the comparison result between the designed thermal power and the actual heat exchange of the heater, and the comparison result between the designed cooling power and the actual heat exchange of the cooler are outside the operating error range, the heat source temperature is updated by the heat conduction formula, and the cooling air temperature is updated by the convection heat transfer formula. The iteration is considered successful when the difference between the designed power of the two heat exchangers and the actual simulated heat exchange is within the preset error range.

6. The Stirling machine simulation method at the boundary of constant power heating and air cooling according to claim 1, characterized in that: When the comparison result of the heat exchanger working fluid temperature is outside the operating error range, the initial heat exchanger working fluid temperature is updated and iterated until the iteration is successful. The heat exchanger working fluid temperature iteration method is as follows: Wherein, h represents the surface convection heat transfer coefficient of the heater or cooler, unit: W / (m2·K); λ represents the thermal conductivity coefficient of the heater or cooler, unit: W / (m·K); d represents the inner diameter of the heater or cooler tube, unit: m.

7. A Stirling machine simulation system with constant power heating and air cooling boundary, the system is used to implement the method according to any one of claims 1 to 6, characterized in that: include: Building module, design module, comparison module and iteration module; The construction module is used to determine the geometric parameters of the components of the Stirling machine and the fluid mechanics parameters and thermodynamic parameters of the selected working fluid, and to construct the initial architecture of the Stirling machine; The design module is used to perform a preliminary design based on the initial architecture to obtain a design result; The comparison module is used to compare the design result with the actual value to obtain a comparison result; The iteration module is used to complete the design when the comparison result is within a preset error range; Otherwise, update and iterate until the final design solution is output to complete the simulation design of the Stirling machine.

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