A method, device and equipment for determining flow field parameters of gas flow in a whole basin, and a storage medium

Abstract

The application discloses a flow field parameter determination method, device and equipment for full-basin gas flow and a storage medium, relates to the technical field of full-basin axisymmetric flow calculation, and comprises the following steps: establishing and decoupling Boltzmann model equations to obtain each sub-equation, i.e., a nonlinear source term sub-equation, a convection motion sub-equation and an axisymmetric source term sub-equation; analytically solving the nonlinear source term sub-equation to obtain a molecular velocity distribution function value; taking the value as an initial value, solving the convection motion sub-equation by using a finite volume method to obtain a first distribution function value; taking the value as an initial value, solving the axisymmetric source term sub-equation by using the finite volume method to obtain a second distribution function value, integrating the second distribution function value to obtain a current flow field macroscopic parameter, and judging whether convergence is achieved; if convergence is not achieved, the nonlinear source term sub-equation is updated, and the above steps are repeated until convergence is achieved, so that the target flow field macroscopic parameter is obtained, and the efficiency of determining the full-basin axisymmetric flow field parameter is improved.

Description

Technical Field

[0001] This invention relates to the field of axisymmetric flow technology across the entire flow domain, and particularly to a method, apparatus, equipment, and storage medium for determining flow field parameters of gas flow across the entire flow domain. Background Technology

[0002] Currently, kinetic methods for solving axisymmetric Boltzmann model equations belong to the field of rarefied gas dynamics. Axisymmetric flows are widespread in nature and have strong engineering applications in both orbital spacecraft and micro / nano devices. Numerical simulations of axisymmetric flow Boltzmann model equations, especially when using full three-dimensional simulations, face the challenges of enormous computational load and memory requirements. Compared to solving the three-dimensional equations, solving the simplified quasi-two-dimensional Boltzmann model equations for axisymmetric flows reduces computational and memory requirements by one dimension, significantly lowering the computational cost.

[0003] In recent decades, algorithms for simulating axisymmetric flows based on quasi-two-dimensional equations have developed rapidly. Some of these algorithms are derived from the quasi-two-dimensional axisymmetric Navier-Stokes (NS) equations. The most commonly used method for rarefied flow calculation is the direct simulation Monte Carlo (DSMC) method. DSMC obtains macroscopic physical quantities of the gas, such as density, velocity, energy, and heat flux, by tracking the free motion and collisions of a large number of molecules and performing statistical averaging, which is equivalent to directly solving the Boltzmann equations. Another method is the gas kinetics approach based on the Boltzmann model equations. This method constructs the time evolution solution of the axisymmetric source term in cylindrical coordinates based on the original Cartesian coordinate time evolution solution, and proposes a unified gas kinetics scheme for axisymmetric flows across the entire flow domain based on the finite volume method.

[0004] It is worth mentioning that, since the Navier-Stokes equations are based on the assumption of a continuous medium, their governing equations themselves have at least a quantitative difference from the actual situation in the rarefied flow region. Therefore, this type of algorithm cannot complete the simulation of axisymmetric flow across the entire flow domain.

[0005] Furthermore, since the DSMC method involves a statistical averaging process, statistical errors cause statistical fluctuations in low-speed flows. On the other hand, the physical space grid step size of the DSMC method is limited by the molecular mean free path, and the time step is limited by the molecular mean collision time. When simulating axisymmetric flows in continuous flow regions, this results in low computational efficiency and extremely large memory requirements, leading to computational difficulties. Therefore, simulating axisymmetric flows across the entire flow domain based on DSMC is not a suitable option.

[0006] As can be seen from the above, improving the efficiency of determining the flow field parameters of gas flow across the entire flow domain is an urgent problem to be solved. Summary of the Invention

[0007] In view of this, the purpose of this invention is to provide a method, apparatus, device, and storage medium for determining flow field parameters of gas flow across an entire flow domain, which can improve the efficiency of determining the flow field parameters of gas flow across an entire flow domain. The specific solution is as follows: Firstly, this application provides a method for determining flow field parameters of gas flow across an entire flow domain, including: The Boltzmann model equations describing the axisymmetric flow across the entire watershed are determined, and the Boltzmann model equations are decoupled and split to obtain sub-equations. The sub-equations include the current nonlinear source term sub-equations describing the collision relaxation process, the current convection motion sub-equations describing the location space convection motion process, and the current axisymmetric source term sub-equations describing the axisymmetric characteristics. The molecular velocity distribution function value is obtained by solving the current nonlinear source term equation using an analytical method. The molecular velocity distribution function value is set as the first initial value, and then the finite volume method is used to solve the current convection kinematic equation based on the first initial value to obtain the first distribution function value. The first distribution function value is set as the second initial value, and the finite volume method is used to solve the current axisymmetric source term equation based on the second initial value to obtain the second distribution function value; Integrating the second distribution function value in velocity space to obtain the current macroscopic parameters of the flow field, and determining whether the current macroscopic parameters of the flow field satisfy the flow field convergence condition. If yes, the calculation ends; if no, the current nonlinear source term equation is updated, and the process jumps back to the step of solving the current nonlinear source term equation analytically until the flow field convergence condition is met, and the target flow field macroscopic parameters are obtained.

[0008] Optionally, determining the Boltzmann model equations describing the axisymmetric flow across the entire watershed includes: The Boltzmann model equations describing axisymmetric flow across the entire flow domain are determined; the solution variables corresponding to the Boltzmann model equations are molecular velocity distribution functions; the molecular velocity distribution functions are functions determined based on time, position space, and velocity space; the Boltzmann model equations are used to describe the motion and collision processes of gas molecules in axisymmetric flow.

[0009] Optionally, the decoupling and splitting of the Boltzmann model equations to obtain sub-equations includes: The Boltzmann model equations are decoupled and split using the unsteady time splitting method to obtain independent sub-equations; The sub-equations include a current nonlinear source term sub-equation describing the collision relaxation process, a current convection motion sub-equation describing the position space convection motion process, and a current axisymmetric source term sub-equation describing axisymmetric properties.

[0010] Optionally, the step of solving the current nonlinear source term sub-equation using an analytical method includes: Based on the laws of conservation of mass, momentum and energy in the collision-relaxation process, the evolutionary expressions for molecular number density, macroscopic velocity, macroscopic temperature and collision frequency are obtained. The first weighting factor is determined based on each molecular velocity component, and the second weighting factor is constructed based on each molecular velocity component, the molecular axial velocity component, and the molecular radial velocity component. Based on the first weighting factor and the current nonlinear source term sub-equation, the first result to be integrated is determined, and the moment is obtained by integrating the first result to be integrated over the full velocity space to obtain the stress tensor evolution differential equation and stress tensor evolution expression during the collision process. Based on the second weighting factor and the current nonlinear source term equation, the second result to be integrated is determined, and the moment is obtained by integrating the second result to be integrated over the full velocity space to obtain the differential equation of heat flow evolution during the collision process. The heat flow evolution expression is determined based on the evolution expression to be processed and the stress tensor evolution expression; Based on the evolution expression to be processed and the heat flow evolution expression, determine the explicit expression of the molecular velocity distribution function in the current nonlinear source term equation, and determine the value of the molecular velocity distribution function based on the explicit expression of the molecular velocity distribution function.

[0011] Optionally, setting the molecular velocity distribution function value as a first initial value, and then using the finite volume method and based on the first initial value to solve the current convection kinematic equations to obtain the first distribution function value includes: The molecular velocity distribution function value is set as the first initial value, and the spatial convection motion sub-equation at the current position is discretized using the finite volume method and the first initial value to obtain the discretized first governing equation. The flux at the control volume unit interface is decomposed into a first positive flux and a first negative flux using the Steger-Warming flux splitting scheme and the first governing equation. The first right-hand side term of the control equation is obtained by using the second-order MUSCL interpolation method and the Minmod limiter, and reconstructing the distribution function of the control volume unit interface based on the first positive flux and the first negative flux. The first right-hand term is solved by time-advancing using the second-order Runge-Kutta method to obtain the value of the first distribution function.

[0012] Optionally, setting the first distribution function value as a second initial value, and using the finite volume method and based on the second initial value to solve the current axisymmetric source term equation to obtain the second distribution function value includes: The first distribution function value is set as the second initial value, and the current axisymmetric source term equation is discretized using the finite volume method to obtain the discretized second governing equation. The flux at the interface of the control volume unit is decomposed into a second positive flux and a second negative flux using the Steger-Warming flux splitting scheme and the second governing equation. The distribution function of the control volume unit interface is reconstructed using the second-order MUSCL interpolation method and the Minmod limiter to obtain the second right-hand term of the second control equation; The second right-hand term is solved by time-advancing the second term using the second-order Runge-Kutta method to obtain the value of the second distribution function at the next time step.

[0013] Optionally, the step of integrating and taking moments of the second distribution function value in velocity space to obtain the current macroscopic parameters of the flow field, and determining whether the current macroscopic parameters of the flow field satisfy the flow field convergence condition, if yes, the calculation ends; if no, the current nonlinear source term equation is updated, and the process jumps back to the step of solving the current nonlinear source term equation analytically, until the flow field convergence condition is met, thus obtaining the target flow field macroscopic parameters, includes: Integrating the second distribution function value in velocity space yields the current macroscopic parameters of the flow field. It is then determined whether the current macroscopic parameters of the flow field satisfy the flow field convergence condition. If the current macroscopic parameters of the flow field satisfy the flow field convergence condition, the current calculation process ends. If the current macroscopic parameters of the flow field do not meet the flow field convergence condition, then the current right-hand side of the current nonlinear source term equation is updated, and then the process jumps back to solving the current nonlinear source term equation using the analytical method until the flow field convergence condition is met; the flow field convergence condition is that the current flow field parameter residual corresponding to the current macroscopic parameters is less than a preset residual threshold. Based on the molecular velocity distribution function at the next moment and the current macroscopic parameters of the flow field, determine the target macroscopic parameters of the axisymmetric flow field across the entire flow domain, including pressure distribution, temperature distribution, and axial velocity distribution.

[0014] Secondly, this application provides a device for determining flow field parameters of gas flow across an entire flow domain, comprising: The model equation splitting module is used to determine the Boltzmann model equations describing the axisymmetric flow across the entire watershed, and to decouple and split the Boltzmann model equations to obtain sub-equations. The sub-equations include the current nonlinear source term sub-equations describing the collision relaxation process, the current convection motion sub-equations describing the location space convection motion process, and the current axisymmetric source term sub-equations describing the axisymmetric characteristics. The current nonlinear source term equation solving module is used to solve the current nonlinear source term equation using analytical methods to obtain the molecular velocity distribution function value; The current convection kinematics sub-equation solving module is used to set the molecular velocity distribution function value as the first initial value, and then use the finite volume method to solve the current convection kinematics sub-equation based on the first initial value to obtain the first distribution function value; The current axisymmetric source term equation solving module is used to set the first distribution function value as the second initial value, and solve the current axisymmetric source term equation using the finite volume method and based on the second initial value to obtain the second distribution function value; The flow field parameter generation and judgment module is used to integrate and calculate the moments of the second distribution function value in the velocity space to obtain the current flow field macroscopic parameters, and to determine whether the current flow field macroscopic parameters satisfy the flow field convergence condition. If yes, the calculation ends; if no, the current nonlinear source term equation is updated, and the process jumps back to the step of solving the current nonlinear source term equation analytically until the flow field convergence judgment condition is met, and the target flow field macroscopic parameters are obtained.

[0015] Thirdly, this application provides an electronic device, comprising: Memory, used to store computer programs; A processor is used to execute the computer program to implement the aforementioned method for determining flow field parameters of gas flow across the entire flow domain.

[0016] Fourthly, this application provides a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the aforementioned method for determining flow field parameters of full-domain gas flow.

[0017] As can be seen from the above, before determining the flow field parameters for the full-domain gas flow, this application needs to determine the Boltzmann model equations describing the axisymmetric flow across the entire domain, and decouple and split the Boltzmann model equations to obtain the sub-equations. These sub-equations include the current nonlinear source term sub-equation describing the collision relaxation process, the current convective motion sub-equation describing the position space convective motion process, and the current axisymmetric source term sub-equation describing the axisymmetric characteristics. The current nonlinear source term sub-equations are solved analytically to obtain the molecular velocity distribution function values. These molecular velocity distribution function values ​​are set as the first initial values, and then a finite... The finite volume method is used to solve the current convection kinematic equations based on the first initial value to obtain the first distribution function value. The first distribution function value is set as the second initial value, and the finite volume method is used to solve the current axisymmetric source term equations based on the second initial value to obtain the second distribution function value. The second distribution function value is integrated in velocity space to obtain the current flow field macroscopic parameters. It is then determined whether the current flow field macroscopic parameters satisfy the flow field convergence condition. If yes, the calculation ends; if not, the current nonlinear source term equations are updated, and the process jumps back to the analytical method to solve the current nonlinear source term equations until the flow field convergence condition is met, thus obtaining the target flow field macroscopic parameters.

[0018] Therefore, this application first needs to determine the Boltzmann model equations describing the axisymmetric flow across the entire flow domain, and then decouple and split the Boltzmann model equations to obtain the sub-equations. Secondly, it uses an analytical method to solve the current nonlinear source term sub-equations to obtain the molecular velocity distribution function values. Then, it sets the molecular velocity distribution function values ​​as the first initial value, and uses the finite volume method based on the first initial value to solve the current convective motion sub-equations to obtain the first distribution function value. Next, it sets the first distribution function value as the second initial value, and uses the finite volume method based on the second initial value to solve the current axisymmetric source term sub-equations to obtain the second distribution function value. Finally, it integrates the second distribution function value in velocity space to obtain the current macroscopic parameters of the flow field, and determines whether the current macroscopic parameters of the flow field satisfy the flow field convergence condition. If yes, the calculation ends; if not, the current nonlinear source term sub-equations are updated, and the process jumps back to the analytical method to solve the current nonlinear source term sub-equations until the flow field convergence condition is met, thus obtaining the target flow field macroscopic parameters. This improves the efficiency of determining the flow field parameters for gas flow across the entire flow domain, thereby enhancing the user experience. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0020] Figure 1 This application discloses a flowchart of a method for determining flow field parameters for gas flow across an entire watershed. Figure 2 This is a schematic diagram comparing the pressure determined in this application with the pressure determined using DSMC; Figure 3 This is a schematic diagram comparing a specific temperature determined in this application with a temperature determined using DSMC. Figure 4 This is a schematic diagram comparing the axial velocity axis distribution of a specific external flow field disclosed in this application with experimental data; Figure 5 This is a schematic diagram of the flow field parameter determination device for full-domain gas flow disclosed in this application; Figure 6 This is a structural diagram of an electronic device disclosed in this application. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Large-scale models are designed and trained to provide more powerful and accurate model performance to handle more complex and massive datasets or tasks. High-quality labeled data is essential for achieving this, and improving the accuracy of the labeled data provided for large-scale models is a pressing issue. To address this, this application provides a method for determining flow field parameters of gas flow across the entire watershed. This method improves the accuracy of labeled data based on two data labeling processes and the calculation of consistency rate, allowing large-scale models to be trained on more accurate labeled data, thereby improving the accuracy of the output results of the trained large-scale models.

[0023] See Figure 1 As shown in the figure, this invention discloses a method for determining flow field parameters of gas flow across the entire flow domain, including: Step S11: Determine the Boltzmann model equations describing the axisymmetric flow across the entire watershed, and decouple and split the Boltzmann model equations to obtain sub-equations; the sub-equations include the current nonlinear source term sub-equations for describing the collision relaxation process, the current convection motion sub-equations for describing the location space convection motion process, and the current axisymmetric source term sub-equations for describing the axisymmetric characteristics.

[0024] In this embodiment, the present application requires determining the Boltzmann model equations corresponding to the full-domain gas flow of an axisymmetric aircraft, as shown below: (1); in, It is the distribution function; The partial derivative over time; for x Molecular velocities in the direction of motion; For spatial location x The partial derivative; Molecular velocity; For angle; For spatial location r The partial derivative; r For spatial location, This is the local equilibrium distribution function; It is the distribution function; The collision frequency.

[0025] Subsequently, in this embodiment of the application, the equation (1) needs to be split into nonlinear source term equation (2), position space convection motion equation (3), and axisymmetric source term equation (4) using the nonsteady time splitting method: (2); (3); (4); in, This is the collision source term.

[0026] Furthermore, , physical space , Speed ​​space , , Their subscripts are j, k, l, m, s.

[0027] Specifically, determining the Boltzmann model equations describing axisymmetric flow across the entire flow domain can include: determining the Boltzmann model equations describing axisymmetric flow across the entire flow domain; the solution variables corresponding to the Boltzmann model equations are molecular velocity distribution functions; the molecular velocity distribution functions are functions determined based on time, position space, and velocity space; and the Boltzmann model equations are used to describe the motion and collision processes of gas molecules in axisymmetric flow.

[0028] Furthermore, in this embodiment of the application, the Boltzmann model equations need to be decoupled and split to obtain individual sub-equations. Specifically, decoupling and splitting the Boltzmann model equations to obtain individual sub-equations may include: using an unsteady time splitting method to decouple and split the Boltzmann model equations to obtain independent sub-equations; wherein, the sub-equations include the current nonlinear source term sub-equation for describing the collision relaxation process, the current convection motion sub-equation for describing the position space convection motion process, and the current axisymmetric source term sub-equation for describing the axisymmetric characteristics.

[0029] Step S12: Solve the current nonlinear source term equation using an analytical method to obtain the molecular velocity distribution function value.

[0030] In this embodiment, the analytical method is required to solve equation (2). Subsequently, the theoretical solution for equation (2) is as follows: (5); in, For the first n The moment of step; For the first n The distribution function of the step; For the first n +1 step.

[0031] It is worth mentioning that, in order to obtain the explicit expression corresponding to the above theoretical solution, the embodiments of this application need to specify the collision frequency. and the local equilibrium distribution function The evolutionary expression during the collision relaxation process, and the local equilibrium distribution function. It is related to molecular number density, macroscopic velocity, macroscopic temperature, and heat flux.

[0032] Since mass, momentum, and energy are conserved during the collision relaxation process, we can obtain: (6); in, for t The number density of molecules at time t; for t Within a certain timen The number density of molecules in a step; for t Moment x Direction and macroscopic speed; for t Within a certain time n Step x Direction and macroscopic speed; for t Moment y Direction and macroscopic speed; for t Within a certain time n Step y Direction and macroscopic speed; for t Macroscopic temperature at any given moment; for t Within a certain time n The macroscopic temperature of the step.

[0033] This means the collision frequency Since this process remains unchanged, equation (5) can be simplified to: (7); in, For time step; For the first n +1 step Q N ; For the first n Step Q N .

[0034] It is worth mentioning that, due to the collision item Involving heat flow In this application embodiment, a weighting factor is introduced. ,in, For molecular velocity, The velocity is the molecular velocity. Then, the left and right sides of equation (2) are multiplied by weighting factors. Then, integrating over the entire velocity space, we obtain the following differential equation: (8); in, For stress.

[0035] Subsequently, the expression corresponding to the solution is: (9); in, for t Stress at any moment for t Within a certain time nStress of the step.

[0036] Furthermore, this application's embodiments introduce weighting factors. ,in, For molecular velocity, The molecular velocity is given, and the left and right sides of equation (2) are multiplied by weight factors. Then, integrating over the entire velocity space, we obtain the following differential equation: (10); in, Let Pr be the heat flux and Pr be the Prandtl number.

[0037] The expression corresponding to the obtained solution is: (11); in, for t The constant flow of heat, for t Within a certain time n The heat flow of the steps.

[0038] Specifically, solving the current nonlinear source term equation using analytical methods can include: obtaining the evolutionary expressions for molecular number density, macroscopic velocity, macroscopic temperature, and collision frequency based on the conservation laws of mass, momentum, and energy during the collision-relaxation process; determining a first weighting factor based on each molecular velocity component, and constructing a second weighting factor based on each molecular velocity component, the molecular axial velocity component, and the molecular radial velocity component; determining the first result to be integrated based on the first weighting factor and the current nonlinear source term equation, and integrating and calculating moments over the full velocity space of the first result to be integrated to obtain the stress tensor evolution differential equation and stress tensor evolution expression during the collision process; determining the second result to be integrated based on the second weighting factor and the current nonlinear source term equation, and integrating and calculating moments over the full velocity space of the second result to be integrated to obtain the heat flow evolution differential equation during the collision process; determining the heat flow evolution expression based on the evolutionary expression to be processed and the stress tensor evolution expression; determining the explicit expression of the molecular velocity distribution function in the current nonlinear source term equation based on the evolutionary expression to be processed and the heat flow evolution expression, and determining the value of the molecular velocity distribution function based on the explicit expression of the molecular velocity distribution function.

[0039] Subsequently, the embodiment of this application yields the following expression for the change of the equilibrium distribution function with time during the collision relaxation process: (12); in, for t The local equilibrium distribution function at time t. For specific parameters; Let be the equilibrium distribution function, and its corresponding expression is shown below: (13); in, For quality, For pressure; Boltzmann's constant; For temperature; For random molecular velocities; It is a heat flow.

[0040] Subsequently, in this embodiment of the application, equation (12) is substituted into equation (7) to obtain: (14); The above expression is the analytical solution to the nonlinear source term equation.

[0041] Step S13: Set the molecular velocity distribution function value as the first initial value, and then use the finite volume method to solve the current convection kinematic equation based on the first initial value to obtain the first distribution function value.

[0042] In this embodiment, the finite volume method is required to solve equation (3), and the corresponding discrete form is: (15); in, for j,k,l,m,s The distribution function under the state, For source terms.

[0043] ; ; (16).

[0044] in, for x Spatial step size in the direction; The radial spatial step size, for j Flux at +1 / 2 for j Flux at -1 / 2 for k Flux at +1 / 2 for k Flux at -1 / 2 The distribution function, for x Directional interface normal vector, for y Directional interface normal vector This refers to the length or area of ​​the interface.

[0045] Specifically, the molecular velocity distribution function value is set as the first initial value. Then, the finite volume method is used to solve the current convection kinematic equations based on the first initial value to obtain the first distribution function value. This can include: setting the molecular velocity distribution function value as the first initial value and discretizing the current spatial convection kinematic equations using the finite volume method and the first initial value to obtain the discretized first governing equation; using the Steger-Warming flux splitting scheme and the first governing equation to decompose the flux at the control volume unit interface into a first positive flux and a first negative flux; using the second-order MUSCL interpolation method and the Minmod limiter, and based on the first positive flux and the first negative flux, reconstructing the distribution function at the control volume unit interface to obtain the first right-hand side term of the governing equation; and using the second-order Runge-Kutta method to solve the first right-hand side term over time to obtain the first distribution function value.

[0046] Step S14: Set the first distribution function value as the second initial value, use the finite volume method and solve the current axisymmetric source term equation based on the second initial value to obtain the second distribution function value.

[0047] In this embodiment, the second-order MUSCL interpolation and Minmod limiter method are used to reconstruct the left and right distribution function values ​​of the interface, resulting in the following form: (18); (19); in, The distribution function of the left interface. The distribution function of the right interface. The distribution function, for j +1 / 2 x Direction coordinates for j place x Direction coordinates for j +1 x Direction coordinates for j -1 x Direction coordinates For limiters.

[0048] Specifically, the first distribution function value is set as the second initial value. The finite volume method is used to solve the current axisymmetric source term sub-equation based on the second initial value to obtain the second distribution function value. This can include: setting the first distribution function value as the second initial value and discretizing the current axisymmetric source term sub-equation using the finite volume method to obtain the discretized second governing equation; using the Steger-Warming flux splitting scheme and the second governing equation to decompose the flux at the control volume unit interface into a second positive flux and a second negative flux; using the second-order MUSCL interpolation method and the Minmod limiter to reconstruct the distribution function at the control volume unit interface to obtain the second right-hand side term of the second governing equation; and using the second-order Runge-Kutta method to solve the second right-hand side term over time to obtain the second distribution function value at the next time step.

[0049] Step S15: Integrate the second distribution function value in the velocity space to obtain the current macroscopic parameters of the flow field, and determine whether the current macroscopic parameters of the flow field satisfy the flow field convergence condition. If yes, end the calculation; otherwise, update the current nonlinear source term equation and jump back to the step of solving the current nonlinear source term equation analytically until the flow field convergence condition is met, and obtain the target flow field macroscopic parameters.

[0050] In this embodiment, the second-order Runge-Kutta method is required for time-progression solving: ; (20); in, The distribution function used for intermediate transitions. For the first n The distribution function of the step. For the first n +1 step distribution function.

[0051] The above expression is the numerical solution format for the position space convection motion equation.

[0052] Furthermore, in this embodiment, the axisymmetric source term equation (4) needs to be solved using the finite volume method, and its corresponding discrete form is: (twenty one); in, ; ; (twenty two); in, The angle step size.

[0053] Subsequently, this embodiment of the application requires the use of the Steger-Warming flux splitting format to decompose the flux at the control volume unit interface into positive and negative fluxes, with the positive flux passing through... Calculations show that negative flux passes through Calculated.

[0054] (twenty three); in, It is a positive volumetric flux; For the flux on the left interface; It is a negative volumetric flux; This refers to the flux on the right interface.

[0055] Subsequently, second-order MUSCL interpolation and the Minmod limiter method are used to reconstruct the left and right distribution function values ​​of the interface, resulting in the following form: (twenty four); (25); in, for s The angle at +1 / 2, for s At the angle, for s The angle at +1, for s The angle at -1.

[0056] Subsequently, the second-order Runge-Kutta method was used for time-advanced solution: ； (26); It is worth mentioning that the above expression is the numerical solution format for axisymmetric source term equations.

[0057] Subsequently, in this embodiment of the application, the flow field parameters need to be determined based on the distribution function value obtained from the axisymmetric source term equation, and the right-hand side of the nonlinear source term equation needs to be calculated. If the flow field parameters meet the convergence condition, the calculation ends; otherwise, the solution is iterated from the first step until convergence.

[0058] The expression for the right-hand side of the nonlinear source term sub-equation is as follows: (27); in, This is the equilibrium distribution function.

[0059] Specifically, the process involves integrating the second distribution function value in velocity space to obtain the current macroscopic parameters of the flow field. It then determines whether these macroscopic parameters satisfy the flow field convergence condition. If so, the calculation ends; otherwise, it returns to the analytical solution of the current nonlinear source term equations until the flow field convergence condition is met, thus obtaining the target flow field macroscopic parameters. This process can include: integrating the second distribution function value in velocity space to obtain the current macroscopic parameters of the flow field, and determining whether these macroscopic parameters satisfy the flow field convergence condition. If the current macroscopic parameters satisfy the flow field convergence condition... If the current flow field macroscopic parameters do not meet the flow field convergence condition, the current right-hand side of the current nonlinear source term equation is updated, and then the process jumps back to solving the current nonlinear source term equation analytically until the flow field convergence condition is met. The flow field convergence condition is that the residual of the current flow field parameters corresponding to the current flow field macroscopic parameters is less than the preset residual threshold. Based on the molecular velocity distribution function at the next moment and the current flow field macroscopic parameters, the target flow field macroscopic parameters, including pressure distribution, temperature distribution and axial velocity distribution, corresponding to the axisymmetric flow field of the entire flow domain are determined.

[0060] In one specific embodiment, the test results obtained in this application are as follows: Axisymmetric nozzle plume problem of a 10N thrust attitude control engine; simulation conditions: total pressure 1.5MPa, total temperature 773K, external environment is vacuum. That is, the numerical simulation results agree well with the DSMC method and wind tunnel test data. Among them, Figure 2 This diagram illustrates a comparison between the pressure determined in this application and the pressure determined using DSMC. Figure 3 This is a schematic diagram comparing the temperature determined in this application with the temperature determined using DSMC. Figure 4 This is a schematic diagram comparing the axial velocity distribution of the external flow field calculated in this application with experimental data.

[0061] As can be seen from the above, the embodiments of this application first need to determine the Boltzmann model equations describing the axisymmetric flow across the entire flow domain, and decouple and split the Boltzmann model equations to obtain each sub-equation; secondly, the current nonlinear source term sub-equation is solved analytically to obtain the molecular velocity distribution function value; then, the molecular velocity distribution function value is set as the first initial value, and the current convective motion sub-equation is solved using the finite volume method based on the first initial value to obtain the first distribution function value; furthermore, the first distribution function value is set as the second initial value, and the current axisymmetric source term sub-equation is solved using the finite volume method based on the second initial value to obtain the second distribution function value; finally, the second distribution function value is integrated and moments are obtained in velocity space to obtain the current macroscopic parameters of the flow field, and it is determined whether the current macroscopic parameters of the flow field satisfy the flow field convergence condition. If yes, the calculation ends; if not, the current nonlinear source term sub-equation is updated, and the process jumps back to the step of solving the current nonlinear source term sub-equation analytically until the flow field convergence condition is met, and the target flow field macroscopic parameters are obtained. This improves the efficiency of determining the flow field parameters for gas flow across the entire flow domain, thereby enhancing the user experience.

[0062] Accordingly, see Figure 5 As shown, this application also provides a device for determining flow field parameters of gas flow across the entire flow domain, comprising: Model equation splitting module 11 is used to determine the Boltzmann model equations describing the axisymmetric flow across the entire watershed, and to decouple and split the Boltzmann model equations to obtain sub-equations; the sub-equations include the current nonlinear source term sub-equations describing the collision relaxation process, the current convection motion sub-equations describing the location space convection motion process, and the current axisymmetric source term sub-equations describing the axisymmetric characteristics. The current nonlinear source term equation solving module 12 is used to solve the current nonlinear source term equation using an analytical method to obtain the molecular velocity distribution function value; The current convection kinematics sub-equation solving module 13 is used to set the molecular velocity distribution function value as the first initial value, and then use the finite volume method to solve the current convection kinematics sub-equation based on the first initial value to obtain the first distribution function value; The current axisymmetric source term equation solving module 14 is used to set the first distribution function value as the second initial value, and use the finite volume method and the second initial value to solve the current axisymmetric source term equation to obtain the second distribution function value; The flow field parameter generation and judgment module 15 is used to integrate and calculate the moments of the second distribution function value in the velocity space to obtain the current flow field macroscopic parameters, and to determine whether the current flow field macroscopic parameters satisfy the flow field convergence condition. If yes, the calculation ends; if no, the current nonlinear source term equation is updated, and the process jumps back to the step of solving the current nonlinear source term equation analytically until the flow field convergence judgment condition is met, and the target flow field macroscopic parameters are obtained.

[0063] In some specific embodiments, the model equation splitting module 11 may specifically include: The Boltzmann model equation determination unit is used to determine the Boltzmann model equations describing axisymmetric flow across the entire flow domain; the solution variable corresponding to the Boltzmann model equations is the molecular velocity distribution function; the molecular velocity distribution function is a function determined based on time, position space, and velocity space; the Boltzmann model equations are used to describe the motion and collision processes of gas molecules in axisymmetric flow.

[0064] In some specific embodiments, the model equation splitting module 11 may specifically include: The model equation splitting sub-unit is used to decouple and split the Boltzmann model equations using the unsteady time splitting method to obtain independent sub-equations; wherein, the sub-equations include the current nonlinear source term sub-equation for describing the collision relaxation process, the current convection motion sub-equation for describing the position space convection motion process, and the current axisymmetric source term sub-equation for describing the axisymmetric properties.

[0065] In some specific embodiments, the current nonlinear source term sub-equation solving module 12 may specifically include: The evolution expression determination unit is used to obtain the evolution expressions to be processed, such as molecular number density, macroscopic velocity, macroscopic temperature, and collision frequency, based on the laws of conservation of mass, momentum, and energy in the collision-relaxation process. The weighting factor determination unit is used to determine a first weighting factor based on each molecular velocity component, and to construct a second weighting factor based on each molecular velocity component, molecular axial velocity component and molecular radial velocity component. The stress tensor evolution differential equation determination unit is used to determine the first result to be integrated based on the first weighting factor and the current nonlinear source term sub-equation, and to perform moment integration on the full velocity space of the first result to be integrated to obtain the stress tensor evolution differential equation and stress tensor evolution expression during the collision process. The heat flow evolution differential equation determination unit is used to determine the second result to be integrated based on the second weighting factor and the current nonlinear source term sub-equation, and to perform integral and moment calculation on the full velocity space of the second result to be integrated to obtain the heat flow evolution differential equation during the collision process. The heat flux evolution expression determination unit is used to determine the heat flux evolution expression based on the evolution expression to be processed and the stress tensor evolution expression; The molecular velocity distribution function expression determination unit is used to determine the explicit expression of the molecular velocity distribution function in the current nonlinear source term equation based on the evolution expression to be processed and the heat flow evolution expression, so as to determine the value of the molecular velocity distribution function based on the explicit expression of the molecular velocity distribution function.

[0066] In some specific embodiments, the current convection motion sub-equation solving module 13 may specifically include: The first governing equation generation unit is used to set the molecular velocity distribution function value as a first initial value, and to discretize the spatial convection motion sub-equation at the current position using the finite volume method and the first initial value to obtain the discretized first governing equation. The first flux decomposition unit is used to decompose the flux at the interface of the control volume unit into a first positive flux and a first negative flux using the Steger-Warming flux splitting scheme and the first governing equation. The first right-hand term generation unit is used to reconstruct the distribution function of the control volume unit interface based on the first positive flux and the first negative flux using the second-order MUSCL interpolation method and the Minmod limiter, so as to obtain the first right-hand term of the control equation. The first distribution function value generation unit is used to solve the first right-hand term using the second-order Runge-Kutta method to obtain the first distribution function value.

[0067] In some specific embodiments, the current axisymmetric source term sub-equation solving module 14 may specifically include: The second governing equation generation unit is used to set the first distribution function value as the second initial value and to discretize the current axisymmetric source term sub-equation using the finite volume method to obtain the discretized second governing equation. The second flux decomposition unit is used to decompose the flux of the control volume unit interface into a second positive flux and a second negative flux using the Steger-Warming flux splitting scheme and the second governing equation. The second right-hand term generation unit is used to reconstruct the distribution function of the control volume unit interface using the second-order MUSCL interpolation method and the Minmod limiter to obtain the second right-hand term of the second control equation. The second distribution function value generation unit is used to solve the second right-hand term using the second-order Runge-Kutta method to obtain the second distribution function value at the next time step.

[0068] In some specific embodiments, the flow field parameter generation and judgment module 15 may specifically include: The current flow field macroscopic parameter judgment unit is used to integrate and calculate the moment of the second distribution function value in the velocity space to obtain the current flow field macroscopic parameters, and to determine whether the current flow field macroscopic parameters meet the flow field convergence condition. If the current flow field macroscopic parameters meet the flow field convergence condition, the current calculation process ends. The right-hand side update unit is used to update the current right-hand side of the current nonlinear source term equation if the current macroscopic flow field parameters do not meet the flow field convergence condition, and then jump back to the analytical method to solve the current nonlinear source term equation until the flow field convergence condition is met; the flow field convergence condition is that the current flow field parameter residual corresponding to the current macroscopic flow field parameters is less than a preset residual threshold. The target flow field macroscopic parameter generation unit is used to determine the target flow field macroscopic parameters, including pressure distribution, temperature distribution and axial velocity distribution, corresponding to the axisymmetric flow field of the whole flow domain, based on the molecular velocity distribution function at the next moment and the current flow field macroscopic parameters.

[0069] Furthermore, embodiments of this application also disclose an electronic device, Figure 6 This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content of the diagram should not be construed as limiting the scope of this application. Specifically, the electronic device 20 may include: at least one processor 21, at least one memory 22, a power supply 23, a communication interface 24, an input / output interface 25, and a communication bus 26. The memory 22 stores a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the method for determining flow field parameters of full-domain gas flow disclosed in any of the foregoing embodiments. Furthermore, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0070] In this embodiment, the power supply 23 is used to provide operating voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and external devices, and the communication protocol it follows can be any communication protocol applicable to the technical solution of this application, and is not specifically limited here; the input / output interface 25 is used to acquire external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.

[0071] In addition, the memory 22, as a carrier for resource storage, can be a read-only memory, random access memory, disk or optical disk, etc. The resources stored thereon can include operating system 221, computer program 222, etc., and the storage method can be temporary storage or permanent storage.

[0072] The operating system 221 is used to manage and control the various hardware devices on the electronic device 20 and the computer program 222, which may be Windows Server, Netware, Unix, Linux, etc. In addition to including a computer program capable of performing the method for determining flow field parameters of full-domain gas flow executed by the electronic device 20 as disclosed in any of the foregoing embodiments, the computer program 222 may further include computer programs capable of performing other specific tasks.

[0073] Furthermore, this application also discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned method for determining flow field parameters of full-domain gas flow. Specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.

[0074] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0075] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0076] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0077] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the term "comprising" or any other variation thereof is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0078] The technical solutions provided in this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for determining flow field parameters of gas flow across an entire flow domain, characterized in that, include: The Boltzmann model equations describing the axisymmetric flow across the entire watershed are determined, and the Boltzmann model equations are decoupled and split to obtain sub-equations. The sub-equations include the current nonlinear source term sub-equations describing the collision relaxation process, the current convection motion sub-equations describing the location space convection motion process, and the current axisymmetric source term sub-equations describing the axisymmetric characteristics. The molecular velocity distribution function value is obtained by solving the current nonlinear source term equation using an analytical method. The molecular velocity distribution function value is set as the first initial value, and then the finite volume method is used to solve the current convection kinematic equation based on the first initial value to obtain the first distribution function value. The first distribution function value is set as the second initial value, and the finite volume method is used to solve the current axisymmetric source term equation based on the second initial value to obtain the second distribution function value; Integrating the second distribution function value in velocity space to obtain the current macroscopic parameters of the flow field, and determining whether the current macroscopic parameters of the flow field satisfy the flow field convergence condition. If yes, the calculation ends; if no, the current nonlinear source term equation is updated, and the process jumps back to the step of solving the current nonlinear source term equation analytically until the flow field convergence condition is met, and the target flow field macroscopic parameters are obtained.

2. The method for determining flow field parameters of gas flow across the entire flow domain according to claim 1, characterized in that, The determination of the Boltzmann model equations describing axisymmetric flow across the entire flow domain includes: The Boltzmann model equations describing axisymmetric flow across the entire flow domain are determined; the solution variables corresponding to the Boltzmann model equations are molecular velocity distribution functions; the molecular velocity distribution functions are functions determined based on time, position space, and velocity space; the Boltzmann model equations are used to describe the motion and collision processes of gas molecules in axisymmetric flow.

3. The method for determining flow field parameters of gas flow across the entire flow domain according to claim 2, characterized in that, The decoupling and splitting of the Boltzmann model equations yields sub-equations, including: The Boltzmann model equations are decoupled and split using the unsteady time splitting method to obtain independent sub-equations; The sub-equations include a current nonlinear source term sub-equation describing the collision relaxation process, a current convection motion sub-equation describing the position space convection motion process, and a current axisymmetric source term sub-equation describing axisymmetric properties.

4. The method for determining flow field parameters of gas flow across the entire flow domain according to claim 3, characterized in that, The analytical method for solving the current nonlinear source term sub-equation includes: Based on the laws of conservation of mass, momentum and energy in the collision-relaxation process, the evolutionary expressions for molecular number density, macroscopic velocity, macroscopic temperature and collision frequency are obtained. The first weighting factor is determined based on each molecular velocity component, and the second weighting factor is constructed based on each molecular velocity component, the molecular axial velocity component, and the molecular radial velocity component. Based on the first weighting factor and the current nonlinear source term sub-equation, the first result to be integrated is determined, and the moment is obtained by integrating the first result to be integrated over the full velocity space to obtain the stress tensor evolution differential equation and stress tensor evolution expression during the collision process. Based on the second weighting factor and the current nonlinear source term equation, the second result to be integrated is determined, and the moment is obtained by integrating the second result to be integrated over the full velocity space to obtain the differential equation of heat flow evolution during the collision process. The heat flow evolution expression is determined based on the evolution expression to be processed and the stress tensor evolution expression; Based on the evolution expression to be processed and the heat flow evolution expression, determine the explicit expression of the molecular velocity distribution function in the current nonlinear source term equation, and determine the value of the molecular velocity distribution function based on the explicit expression of the molecular velocity distribution function.

5. The method for determining flow field parameters of gas flow across the entire flow domain according to claim 4, characterized in that, The step of setting the molecular velocity distribution function value as a first initial value, and then using the finite volume method and based on the first initial value to solve the current convection kinematic sub-equation to obtain the first distribution function value includes: The molecular velocity distribution function value is set as the first initial value, and the spatial convection motion sub-equation at the current position is discretized using the finite volume method and the first initial value to obtain the discretized first governing equation. The flux at the control volume unit interface is decomposed into a first positive flux and a first negative flux using the Steger-Warming flux splitting scheme and the first governing equation. The first right-hand side term of the control equation is obtained by using the second-order MUSCL interpolation method and the Minmod limiter, and reconstructing the distribution function of the control volume unit interface based on the first positive flux and the first negative flux. The first right-hand term is solved by time-advancing using the second-order Runge-Kutta method to obtain the value of the first distribution function.

6. The method for determining flow field parameters of gas flow across the entire flow domain according to claim 5, characterized in that, The step of setting the first distribution function value as the second initial value, and using the finite volume method and based on the second initial value to solve the current axisymmetric source term equation to obtain the second distribution function value includes: The first distribution function value is set as the second initial value, and the current axisymmetric source term equation is discretized using the finite volume method to obtain the discretized second governing equation. The flux at the interface of the control volume unit is decomposed into a second positive flux and a second negative flux using the Steger-Warming flux splitting scheme and the second governing equation. The distribution function of the control volume unit interface is reconstructed using the second-order MUSCL interpolation method and the Minmod limiter to obtain the second right-hand term of the second control equation; The second right-hand term is solved by time-advancing the second term using the second-order Runge-Kutta method to obtain the value of the second distribution function at the next time step.

7. The method for determining flow field parameters of gas flow across the entire flow domain according to any one of claims 1 to 6, characterized in that, The process involves integrating the second distribution function value in the velocity space to obtain the current macroscopic parameters of the flow field. It then determines whether these parameters satisfy the flow field convergence condition. If yes, the calculation ends; otherwise, the current nonlinear source term equation is updated, and the process returns to the analytical solution of the current nonlinear source term equation until the flow field convergence condition is met, thus obtaining the target flow field macroscopic parameters, including: Integrating the second distribution function value in velocity space yields the current macroscopic parameters of the flow field. It is then determined whether the current macroscopic parameters of the flow field satisfy the flow field convergence condition. If the current macroscopic parameters of the flow field satisfy the flow field convergence condition, the current calculation process ends. If the current macroscopic parameters of the flow field do not meet the flow field convergence condition, then the current right-hand side of the current nonlinear source term equation is updated, and then the process jumps back to solving the current nonlinear source term equation using the analytical method until the flow field convergence condition is met; the flow field convergence condition is that the current flow field parameter residual corresponding to the current macroscopic parameters is less than a preset residual threshold. Based on the molecular velocity distribution function at the next moment and the current macroscopic parameters of the flow field, determine the target macroscopic parameters of the axisymmetric flow field across the entire flow domain, including pressure distribution, temperature distribution, and axial velocity distribution.

8. A device for determining flow field parameters of gas flow across an entire flow domain, characterized in that, include: The model equation splitting module is used to determine the Boltzmann model equations describing the axisymmetric flow across the entire watershed, and to decouple and split the Boltzmann model equations to obtain sub-equations. The sub-equations include the current nonlinear source term sub-equations describing the collision relaxation process, the current convection motion sub-equations describing the location space convection motion process, and the current axisymmetric source term sub-equations describing the axisymmetric characteristics. The current nonlinear source term equation solving module is used to solve the current nonlinear source term equation analytically to obtain the molecular velocity distribution function value; The current convection kinematics sub-equation solving module is used to set the molecular velocity distribution function value as the first initial value, and then use the finite volume method to solve the current convection kinematics sub-equation based on the first initial value to obtain the first distribution function value; The current axisymmetric source term equation solving module is used to set the first distribution function value as the second initial value, and solve the current axisymmetric source term equation using the finite volume method and based on the second initial value to obtain the second distribution function value; The flow field parameter generation and judgment module is used to integrate and calculate the moments of the second distribution function value in the velocity space to obtain the current flow field macroscopic parameters, and to determine whether the current flow field macroscopic parameters satisfy the flow field convergence condition. If yes, the calculation ends; if no, the current nonlinear source term equation is updated, and the process jumps back to the step of solving the current nonlinear source term equation analytically until the flow field convergence judgment condition is met, and the target flow field macroscopic parameters are obtained.

9. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the method for determining flow field parameters of gas flow across the entire flow domain as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the method for determining flow field parameters of full-domain gas flow as described in any one of claims 1 to 7.

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