Improved method for a thermodynamic two-temperature model non-equilibrium energy system

Abstract

The application discloses an improved method of a thermodynamic two-temperature model non-equilibrium energy system, and mainly is used in the numerical simulation process of hypersonic thermochemical non-equilibrium flow. The method reconfigures the calculation form of each temperature energy mode representation and relaxation and transport process of the two-temperature model by referring to the calculation method of the one-temperature model equilibrium energy system, and re-models and calculates the equilibrium energy item represented by the vibration temperature by using a polynomial fitting method to replace the original complex and time-consuming exponential calculation mode. The method is good in adaptability to the existing thermodynamic two-temperature model solver framework, can improve the numerical stability of the thermochemical non-equilibrium flow simulation process and improve the calculation efficiency on the premise of ensuring the calculation precision.

Description

Technical Field

[0001] This invention belongs to the field of aerodynamics, specifically relating to a numerical calculation method for hypersonic thermochemical nonequilibrium flow. Background Technology

[0002] Using statistical thermodynamics, the total internal energy (e) of high-temperature gas molecules is generally decomposed into translational kinetic energy (ec). tr ), rotational energy (e rot ), vibrational energy (e) V ) and electron potential energy (e E Energy modes such as ) are respectively represented by translational temperature (T). tr ), rotational temperature (T) rot ), vibration temperature (T) V ) and electron temperature (T E Temperatures such as α, β, and γ are used as characterization temperatures for various energy modes. Based on assumptions such as whether the flow field temperature is sufficient to excite the corresponding energy modes and whether the energy modes can quickly reach equilibrium during the relaxation process, various thermodynamic temperature models have emerged, including one-temperature models, two-temperature models, three-temperature models, and multi-vibration temperature models.

[0003] The thermodynamic-temperature model (or single-temperature model) has two forms. The first neglects vibrational and electronic potential energy, considering only translational and rotational energy distributions. This method is suitable for lower temperatures where vibrational and electronic potential energy are not yet excited or are only partially excited, and their contribution to the total internal energy can be ignored. The second form uses a single temperature T to characterize all energy modes, i.e., T0. tr =T rot =T V =T E =T. This method assumes that all energy modes are in equilibrium and can be considered as a whole. In hypersonic nonequilibrium flow simulation methods, the thermodynamic-temperature model usually refers to the second case.

[0004] In the thermodynamic two-temperature model (or dual-temperature model), the vibrational energy modes of gas molecules are excited and cannot be ignored. It is assumed that the translational and rotational energy modes are in equilibrium, while the vibrational energy modes and the translational energy modes of free electrons are in another equilibrium state. Therefore, the distribution of the translational and rotational energy of the molecules is determined by the translational temperature (T). tr =T rot Characterized by vibrational temperature (T), its vibrational energy and electronic potential energy distributions are characterized separately. V =T E ) representation.

[0005] In the thermodynamic three-temperature model, gas molecules reach the level of ionization due to the increase in flow field temperature, and their electronic potential energy modes are further excited and cannot be ignored. At this point, it is assumed that the molecules possess three independent energy modes: the equilibrium translational and rotational energy modes, the vibrational energy mode, and the electronic potential energy mode, each represented by a translational temperature (T). tr =T rot ), vibration temperature (T) V ) and electron temperature (T E Characterization and computation.

[0006] The multi-vibrational-temperature model is a further refinement and extension of the two-temperature model. It isolates the vibrational modes of each polyatomic molecule and uses a corresponding vibrational temperature to characterize its vibrational energy distribution. Assuming a gas mixture consists of oxygen (O2), nitrogen (N2), and carbon dioxide (CO2), then the multi-vibrational-temperature model requires 3 to 5 vibrational temperatures to describe and calculate the vibrational energy distribution of each molecule. Because a carbon dioxide molecule has three vibrational energy modes, if all its vibrational modes were excited, then three vibrational temperatures would be needed for the carbon dioxide molecule alone.

[0007] In hypersonic thermochemical nonequilibrium flow simulation methods, one-temperature models and two-temperature models are commonly used, with other temperature models derived and extended from two-temperature models. One-temperature models often employ polynomial fitting methods to calculate molecular internal energy and related parameters, such as the Chemkin fitting method. Polynomial fitting methods offer advantages such as simple mathematical modeling, unified computational form, and easy partial derivative solutions; therefore, one-temperature models using polynomial fitting methods typically exhibit high computational efficiency and good stability. In publicly available literature, the vibrational energy and electronic potential energy related terms of two-temperature models are mainly calculated using molecular kinetic theory methods. These mathematical expressions contain numerous exponential calculations, resulting in time-consuming numerical computations and low efficiency. Furthermore, exponential calculations are susceptible to numerical fluctuations, leading to out-of-bounds phenomena such as "NAN" (non-linear numbers) and "INF" (extreme values), causing computational interruptions and divergences. Therefore, two-temperature models using molecular kinetic theory methods to calculate various energy modes typically suffer from problems such as high computational time, low efficiency, and poor stability.

[0008] In summary, it is necessary to draw on the thermodynamic one-temperature model for calculating equilibrium energy systems and to modify and develop a more efficient and stable thermodynamic two-temperature model for calculating energy systems. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of existing technologies and provide an improved method for non-equilibrium energy systems using a two-temperature thermodynamic model, for numerical simulation of hypersonic thermochemical non-equilibrium flows. This invention draws upon the calculation method for equilibrium energy systems using a one-temperature model, reconstructs the representation of energy modes at each temperature in the two-temperature model, and recalculates the relaxation and transport processes. It employs a polynomial fitting method to remodel and calculate the equilibrium energy term represented by the vibrational temperature, replacing the original complex and time-consuming exponential calculation method.

[0010] The objective of this invention is achieved through the following technical solution:

[0011] A method for improving a nonequilibrium energy system based on a thermodynamic two-temperature model, the method comprising:

[0012] S1: Based on the calculation method of equilibrium energy system of one temperature model, the energy mode characterization of each temperature model and the calculation form of relaxation and transport process of two temperature models are reconstructed to obtain the equilibrium energy term characterized by vibration temperature;

[0013] S2: Using the values ​​calculated by the molecular kinetic theory method as the reference template point, the equilibrium energy term characterized by vibrational temperature is remodeled using the approximation interpolation method, resulting in a polynomial fitting method for calculating the vibrational equilibrium energy;

[0014] S3: Based on the thermodynamic two-temperature model solver framework, the calculation modules related to molecular internal energy, enthalpy and specific heat parameters are modified by applying energy system calculation methods, resulting in a thermodynamic two-temperature model solver that applies the improved energy system calculation method.

[0015] According to a preferred embodiment, in step S1, the calculation forms of the temperature energy mode characterization and relaxation and transport processes of the two reconstructed temperature models are as follows:

[0016] e i (T,T V ) = e tr,i (T)+e rot,i (T)+e V,i (T V )+e E,i (T V ) = c v,i ·(TT V )+e i (T V )

[0017] Where the subscript i represents a gas molecule, and T, T V These are the translational temperature and the vibrational temperature, respectively, c v,i For the translational rotational isochoric specific heat of molecules, e tr,i (T), e rot,i(T) represent the translational energy and rotational energy calculated from the translational temperature, respectively, e V,i (T V e E,i (T V () represent the vibrational energy and electronic potential energy calculated from the vibrational temperature, respectively, e i (T V ) = e tr,i (T V )+e rot,i (T V )+e V,i (T V )+e E,i (T V ) is the equilibrium energy characterized by vibration temperature, derived from a temperature model.

[0018] According to a preferred embodiment, the equilibrium energy calculation form for vibration temperature characterization is as follows:

[0019]

[0020] Where the subscript i represents a gas molecule, T V Where is the vibrational temperature, M is the molecular weight, R = 8.314 J / mol is the universal gas constant, and e i (T V ) represents the equilibrium energy term characterized by vibrational temperature, h i (T V ) represents the enthalpy value under thermodynamic equilibrium conditions characterized by vibration temperature.

[0021] According to a preferred embodiment, the enthalpy value under thermodynamic equilibrium conditions characterized by vibration temperature is calculated using a polynomial fitting method as follows:

[0022]

[0023] Where the subscript i represents a gas molecule, T V denoted as vibration temperature, M as molecular weight, R = 8.314 J / mol as universal gas constant, and a0 to a5 as coefficients of the fitting polynomial.

[0024] According to a preferred embodiment, the formulas for calculating translational energy, rotational energy, vibrational energy, and electronic potential energy in the thermodynamic two-temperature model solver are as follows:

[0025]

[0026]

[0027]

[0028]

[0029] In the formula, the subscript i represents a gas molecule, mon. represents the type of monatomic gas molecule, and T, T V These are translational temperature and vibrational temperature, respectively, e tr,i (T), e rot,i (T) represent the translational energy and rotational energy calculated from the translational temperature, respectively, e V,i (T V e E,i (T V ) represent the vibrational energy and electronic potential energy calculated from the vibrational temperature, respectively; c v,i The isochoric specific heat is the translational rotation of molecules and is independent of temperature; M is the molecular weight, R = 8.314 J / mol is the universal gas constant, and h 0,i Let a0 be the enthalpy of formation of the molecule (J / kg), and a0 to a5 be the coefficients of the fitted polynomial.

[0030] According to a preferred embodiment, c v,i The isochoric specific heat of molecular translational rotation is expressed as follows:

[0031]

[0032] In the formula, the subscript i represents a gas molecule, mon. represents the type of monatomic gas molecule, M is the molecular weight, and R = 8.314 J / mol is the universal gas constant.

[0033] The aforementioned main solution of the present invention and its various further alternative solutions can be freely combined to form multiple solutions, all of which are solutions that can be adopted and are claimed by the present invention. Those skilled in the art, after understanding the solution of the present invention, will realize that there are many combinations based on existing technology and common knowledge, all of which are technical solutions to be protected by the present invention, and will not be exhaustively listed here.

[0034] The beneficial effects of this invention are:

[0035] This invention reconstructs the computational forms of the temperature energy mode representation, relaxation, and transport processes of two temperature models. It uses a polynomial fitting method to calculate the nonlinear energy term represented by the vibrational temperature, replacing the original complex and time-consuming exponential calculation method. This significantly reduces the computational load of the temperature energy mode representation, relaxation, and transport processes of gas molecules, thus reducing the computational time of the thermochemical nonequilibrium flow simulation process and improving the numerical computation efficiency.

[0036] This invention employs a polynomial fitting method to replace the original exponential calculation method. During numerical calculations, it is less prone to out-of-bounds problems such as "NAN" non-zero values ​​and "INF" extreme values ​​caused by numerical fluctuations, which can lead to calculation interruptions and divergences. Therefore, it improves the robustness of thermochemical non-equilibrium flow simulation processes and enhances numerical stability.

[0037] The fitting polynomial proposed in this invention is obtained by interpolating the thermodynamic parameters calculated using the molecular kinetic theory method as the reference template point. The deviation from the reference parameter values ​​is small, thus ensuring the accuracy of the numerical calculation. Furthermore, the new method only requires changes to the calculation modules related to parameters such as internal energy, enthalpy, and specific heat, requiring minimal modifications to the existing thermodynamic two-temperature model solver framework and exhibiting good adaptability. Attached Figure Description

[0038] Figure 1 Comparison of wall heat flux distribution in the flow simulation of the HEG shock tunnel cylindrical model experiment in Example 1;

[0039] Figure 2 Comparison of residual convergence curves from flow simulation of the HEG shock tunnel cylindrical model experiment in Example 1;

[0040] Figure 3 Comparison of wall heat flux distribution in flow simulation of Arc-Jet wind tunnel ball head model experiment in Example 2;

[0041] Figure 4 Comparison of residual convergence curves from flow simulation experiments using the Arc-Jet wind tunnel ball head model in Example 2. Detailed Implementation

[0042] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0043] It should be noted that, in order to make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0044] This invention discloses an improved method for a non-equilibrium energy system based on a thermodynamic two-temperature model. The specific implementation process includes the following steps:

[0045] Step S1: Reconstruct the energy mode representations of each temperature in the two temperature models and the calculation forms of relaxation and transport processes to obtain the equilibrium energy term represented by the vibration temperature.

[0046] In the thermodynamic two-temperature model, the total specific internal energy e of gas molecule i is... i (T,T V The calculation form characterized by each temperature energy mode is as follows:

[0047] e i (T,T V ) = e tr,i (T)+e rot,i (T)+e V,i (T V )+e E,i (T V (1)

[0048] In the formula, T, T V These are translational temperature and vibrational temperature, respectively, e tr,i (T), e rot,i (T) represent the translational energy and rotational energy calculated from the translational temperature, respectively, e V,i (T V e E,i (T V ) represent the vibrational energy and electronic potential energy calculated from the vibrational temperature, respectively.

[0049] Translational kinetic energy e tr,i (T) and rotational energy e rot,i The formulas for calculating (T) are as follows:

[0050]

[0051] Where mon. represents the type of monatomic gas molecule, M i The molecular weight is (kg / mol), R = 8.314 J / (mol·K) is the universal gas constant, and h is the molecular weight. 0,i The enthalpy of formation of the molecule is expressed in J / kg.

[0052] The corresponding translational kinetic energy and isochoric specific heat c v,tr,i and rotational energy and isochoric specific heat c v,rot,i They are respectively

[0053]

[0054] Using the molecular kinetic theory method, the vibrational energy e V,i (T V ) and electron potential energy e E,i (T V The calculation formulas are as follows:

[0055]

[0056] Where e represents a free electron. In the vibrational energy calculation formula, nm is the number of vibrational modes of a polyatomic molecule, and g... i,m Let θ be the degeneracy of the m-th vibrational mode of molecule i. V,i,m Let g be the characteristic vibrational temperature corresponding to the m-th vibrational mode of molecule i. In the formula for calculating electronic potential energy, g0,i and g 1,i θ represents the degeneracy corresponding to the ground state i and the first electronically excited state of the molecule, respectively. E,i Let be the electronic characteristic temperature of molecule i.

[0057] The corresponding vibrational energy isochoric specific heat c v,V,i Electron potential energy and isochoric specific heat c v,E,i They are respectively

[0058]

[0059] Since the mathematical expressions for vibrational energy and electronic potential energy and their corresponding isochoric specific heat contain complex and cumbersome exponential calculations, which will affect the computational efficiency and numerical stability of the solver, it is necessary to modify and simplify the calculation methods of these terms.

[0060] Drawing upon the calculation method for equilibrium energy systems using a one-temperature model, the expression (1) for a non-equilibrium energy system using a two-temperature model is reconstructed as follows:

[0061] e i (T,T V ) = e tr,i (T)+e rot,i (T)+e V,i (T V )+e E,i (T V )

[0062] =c v,tr,i ·T+h 0,i +c v,rot,i ·T+e V,i (T V )+e E,i (T V )

[0063] =(c v,tr,i +c v,rot,i )·(TT V )+c v,tr,i ·T V +h 0,i +c v,rot,i ·T V +e V,i (T V )+e E,i (T V )

[0064] =c v,i ·(TT V )+e tr,i (T V )+e rot,i (T V )+eV,i (T V )+e E,i (T V )

[0065] =c v,i ·(TT V )+e i (T V )

[0066] In the formula c v,i =The constant is the specific heat at constant volume during translation and rotation, e i (T V That is, the equilibrium energy term characterized by vibrational temperature derived by imitating a temperature model.

[0067] Through the above reconstruction process, the total specific internal energy e of gas molecule i i (T,T V Therefore, it is rewritten as a linear energy term c characterized by translational temperature T. v,i ·T and the vibration temperature T V The nonlinear energy term e is characterized i (T V )-c v,i ·T V sum.

[0068] Step S2: Remodel the equilibrium energy term characterized by vibration temperature using an approximation interpolation method to obtain a polynomial fitting method for calculating vibration equilibrium energy.

[0069] Based on the reconstructed equation (4) in step S1, the vibration equilibrium energy term e is adjusted using the Chemkin fitting method. i (T V Remodeling, i.e.

[0070]

[0071] In the formula h i (T V ) indicates the vibration temperature T V The enthalpy values ​​described are under thermodynamic equilibrium conditions, where a0 to a5 are the coefficients of the fitting polynomial.

[0072] Since vibrational energy is not excited or is not fully excited in the low-temperature region, the value calculated using the molecular kinetic theory method is very small, and the interpolation method has a large error in this temperature range, which can easily lead to negative specific heat values, violating the laws of physics. Therefore, within the temperature range of 800K to 30000K, several discrete vibrational temperatures are selected, and e is calculated according to equations (2) and (3) in step S1. i (T VThe actual value of ) is used to form a series of interpolation template points. Finally, the approximation interpolation method is used to obtain the specific values ​​of the fitting polynomial coefficients a0 to a5.

[0073] Here, for the temperature range above 800K, an interpolation template point is taken every 100K. The interpolation coefficients obtained by fitting the 11-component air reaction system are shown in Table 1.

[0074] Table 1. Fitting coefficients of the enthalpy values ​​of each component in the 11-component air reaction system (800K~3000K)

[0075]

[0076]

[0077] In the temperature range below 800K, the vibrational equilibrium energy term e i (T V The expression for ) ignores the vibrational energy e V,i (T V ) and electron potential energy e E,i (T V Neither of the two items are counted, that is

[0078] e i (T V ) = e tr,i (T V )+e rot,i (T V ) = c v,i ·T V +h 0,i (8)

[0079] Substituting into equation (5), we obtain the interpolation coefficients for gas molecule i in the temperature range below 800K as follows:

[0080]

[0081] Therefore, for the temperature range below 800K, the interpolation coefficients of the 11-component air reaction system are shown in Table 2.

[0082] Table 2. Fitting coefficients of the enthalpy values ​​of each component in the 11-component air reaction system (0K~800K)

[0083]

[0084] To ensure a smooth transition in the calculated values ​​near 800K, a smoothing method can be employed. Here, a simple and easy-to-implement method is used to obtain the interpolation coefficients. When the vibration temperature T... V When <600K, interpolation coefficients are given in Table 2; when the vibration temperature T VFor values ​​>1000K, interpolation coefficients are given as shown in Table 1; otherwise, interpolation coefficients are calculated as follows.

[0085]

[0086] In the formula, the subscript i represents the index of the interpolation coefficient, and a f,i a represents the interpolation coefficients given in Table 2. b,i This represents the interpolation coefficients given in Table 1.

[0087] Step S3: Based on the thermodynamic two-temperature model solver framework, the calculation modules related to parameters such as internal energy, enthalpy, and specific heat are modified by applying a new energy system calculation method to obtain a new thermodynamic two-temperature model solver that applies the improved energy system calculation method.

[0088] To minimize modifications to the original program code, the translational and rotational energies in the two temperature models are still calculated according to equation (2). Substituting equation (2) into equation (4), we obtain...

[0089]

[0090] Based on the physical definition that monatomic molecules have no vibrational modes, the right-hand side of equation (11) is used to calculate the vibrational energy of polyatomic molecules and the electronic potential energy of monatomic molecules, respectively.

[0091]

[0092] Correspondingly, the modified vibration energy has a constant-volume specific heat c v,V,i Electron potential energy and isochoric specific heat c v,E,i They are respectively

[0093]

[0094] Finally, the enthalpy h of gas molecules under non-equilibrium conditions i (T,T V The calculation formula becomes

[0095]

[0096] In the formula h i (T V ) represents the enthalpy value under vibration equilibrium conditions, calculated using a fitted polynomial.

[0097] Therefore, based on the thermodynamic two-temperature model solver framework and according to the above-mentioned improved method for non-equilibrium energy systems, only the vibrational energy and its isochoric specific heat, electronic potential energy and its isochoric specific heat, as well as the calculation modules for gas parameters such as molecular internal energy and enthalpy need to be modified.

[0098] Example 1: Flow simulation of a cylindrical model experiment in a HEG shock tunnel. The computational model and experimental conditions are referenced in "Hannemann K., High Enthalpy Flows in the HEG Shock Tunnel: Experiment and Numerical Rebuilding, AIAA 2003-0978, 41st Aerospace Sciences Meeting and Exhibit 6-9 January 2003, Reno, Nevada, 2003: 1-18". The numerical simulation uses a thermodynamic two-temperature, five-component Dunn-Kang chemical model. The flow rate is selected using the Steger scheme and the Minmod limiter. The CFL number is 20. Two sets of wall conditions are used: isothermal non-catalyzed wall and isothermal fully catalyzed wall (wall temperature 300K). The single-core serial iteration step number is 5000 steps.

[0099] Example 2: Flow simulation in an Arc-Jet wind tunnel ball head model experiment. The calculation model and experimental conditions were referenced in "Gokcen T..Effects of Flowfield Nonequilibrium on Convective Heat Transfer to a Blunt Body[R]. AIAA96-0352:1-11.". The simulation conditions were: inflow velocity 5630 m / s, inflow pressure 96.12 Pa, inflow temperature 970 K, and vibration temperature 2800 K. The numerical simulation used a thermodynamic two-temperature, five-component Park chemical model. The convection flux was selected using the Steger scheme and the Minmod limiter. The CFL number was 50. Two sets of wall conditions were used: isothermal non-catalyzed wall and isothermal fully catalyzed wall (wall temperature 1000 K). The simulation was performed using a 6-core parallel iteration with 20,000 steps.

[0100] Example 1 presents a comparison of the flow field vibration temperature distribution calculated by the method of this invention and the general method. Here, the "general method" refers to the method that uses molecular kinetic theory to calculate energy-related terms. It can be seen that, under convergence conditions, the vibration temperature contour cloud obtained by the two methods is consistent, indicating that the improved method can guarantee calculation accuracy and possesses both correctness and reliability.

[0101] Figure 1 Example 1 presents a comparison of the wall heat flux distribution calculated by the method of this invention and the general method. Here, the "general method" refers to the method that uses molecular kinetic theory to calculate energy-related terms. It can be seen that, under the same calculation conditions, the wall heat flux value calculated by the improved method is consistent with the value calculated by the general method, indicating that the improved method can guarantee calculation accuracy and possesses both correctness and reliability.

[0102] Figure 2 Based on Example 1, a comparison of the residual convergence curves calculated by the method of this invention and the general method is presented. Here, the "general method" refers to the method that uses molecular kinetic theory to calculate energy-related terms. It can be seen that, under the same computational conditions, the residual values ​​calculated by the improved method are consistent with those of the general method, further proving the correctness and reliability of the improved method, which has the same computational accuracy as the general method. Furthermore, after calculating the iteration synchronization number, the computation time of the improved method is reduced by approximately 20%, indicating that the improved method has a significant effect on improving the computational efficiency of the thermodynamic two-temperature model solver.

[0103] Example 2 presents a comparison of the flow field vibration temperature distribution calculated by the method of this invention and the general method. Here, the "general method" refers to the method that uses molecular kinetic theory to calculate energy-related terms. Under convergence conditions, the vibration temperature contour cloud obtained by the two methods is consistent, indicating that the improved method can guarantee calculation accuracy and possesses both correctness and reliability.

[0104] Figure 3 Example 2 presents a comparison of the wall heat flux distribution calculated by the method of this invention and the general method. Here, the "general method" refers to the method that uses molecular kinetic theory to calculate energy-related terms. It can be seen that, under the same calculation conditions, the wall heat flux value calculated by the improved method is consistent with the value calculated by the general method, indicating that the improved method can guarantee calculation accuracy and possesses both correctness and reliability.

[0105] Figure 4 Example 2 presents a comparison of the residual convergence curves calculated by the method of this invention and the general method. Here, the "general method" refers to the method using molecular kinetic theory to calculate energy-related terms. It can be seen that, under the same computational conditions, the residual values ​​calculated by the improved method are consistent with those of the general method, further demonstrating the correctness and reliability of the improved method, which possesses computational accuracy consistent with the general method. Furthermore, after calculating the iteration synchronization number, the computation time of the improved method is reduced by more than 10%, further proving that the improved method has a significant effect on improving the computational efficiency of the thermodynamic two-temperature model solver.

[0106] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An improved method for a non-equilibrium energy system based on a thermodynamic two-temperature model, characterized in that, The improvement method for the non-equilibrium energy system of the thermodynamic two-temperature model includes: S1: Based on the calculation method of equilibrium energy system of one temperature model, the energy mode characterization of each temperature model and the calculation form of relaxation and transport process of two temperature models are reconstructed to obtain the equilibrium energy term characterized by vibration temperature; S2: Using the values ​​calculated by the molecular kinetic theory method as the reference template point, the equilibrium energy term characterized by vibrational temperature is remodeled using the approximation interpolation method to obtain a polynomial fitting method for calculating vibrational equilibrium energy; S3: Based on the thermodynamic two-temperature model solver framework, the calculation modules related to molecular internal energy, enthalpy and specific heat parameters are modified by applying energy system calculation methods to obtain a thermodynamic two-temperature model solver that applies the improved energy system calculation methods; In step S1, the energy mode representation and calculation forms of relaxation and transport processes at each temperature in the reconstructed two temperature models are as follows: Subscript i Represents gas molecules, T , T V These are translational temperature and vibrational temperature, respectively. The specific heat at constant volume for the translational rotation of molecules. e tr,i ( T ), e rot,i ( T () represent the translational energy and rotational energy calculated from the translational temperature, respectively. e V,i ( T V ), e E,i ( T V ) represent the vibrational energy and electronic potential energy calculated from the vibrational temperature, respectively. This is the equilibrium energy characterized by vibrational temperature, derived from a temperature model. The equilibrium energy calculation form for vibration temperature characterization is as follows: Subscript i Represents gas molecules, T V For vibration temperature, M Molecular weight R =8.314 J / (mol) K) is the universal gas constant. The equilibrium energy term characterized by vibrational temperature. The enthalpy value under thermodynamic equilibrium conditions is used to characterize the vibrational temperature.

2. The improved method for a non-equilibrium energy system based on a thermodynamic two-temperature model as described in claim 1, characterized in that, The enthalpy under thermodynamic equilibrium conditions, characterized by vibrational temperature, is calculated using a polynomial fitting method. Subscript i Represents gas molecules, T V For vibration temperature, M Molecular weight R =8.314 J / (mol) K) is the universal gas constant. a 0~ a 5 represents the coefficients of the fitted polynomial.

3. The method for improving a non-equilibrium energy system using a thermodynamic two-temperature model as described in claim 2, characterized in that, The formulas for calculating translational energy, rotational energy, vibrational energy, and electronic potential energy in the thermodynamic two-temperature model solver are as follows: In the formula, the subscript i Represents gas molecules, mon . Represents a monatomic gas molecule type. T , T V These are translational temperature and vibrational temperature, respectively. e tr,i ( T ), e rot,i ( T () represent the translational energy and rotational energy calculated from the translational temperature, respectively. e V,i ( T V ), e E,i ( T V ) represent the vibrational energy and electronic potential energy calculated from the vibrational temperature, respectively; c v,i It is the isochoric specific heat of molecular translational rotation, which is independent of temperature; M Molecular weight R =8.314 J / (mol) K) is the universal gas constant. h 0,i The enthalpy of formation of the molecule is J / kg. a 0~ a 5 represents the coefficients of the fitted polynomial.

4. The method for improving a non-equilibrium energy system using a thermodynamic two-temperature model as described in claim 3, characterized in that, c v,i The isochoric specific heat of molecular translational rotation is expressed as follows: ， In the formula, the subscript i Represents gas molecules, mon . Represents a monatomic gas molecule type. M Molecular weight R =8.314 J / (mol) K) is the universal gas constant.

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