Supersonic flow field simulation method and system, electronic device and readable storage medium

Abstract

The application relates to an ultrasonic speed flow field simulation method, system, electronic equipment and readable storage medium. The simulation method comprises the following steps: S1, a standard k-omega SST turbulent flow model is acquired; S2, a multi-physical mechanism turbulent flow model containing compressible physical mechanism and shock physical mechanism is constructed based on the standard k-omega SST turbulent flow model; and S3, initial conditions of a target flow field are acquired, and simulation calculation is carried out on the target flow field based on the multi-physical mechanism turbulent flow model. The application greatly expands the applicability of the standard k-omega SST turbulent flow model by adding the ability to capture the impact and compression effect, and improves the performance of the standard k-omega SST turbulent flow model in various working scenarios.

Description

Technical Field

[0001] This invention relates to the field of fluid technology, and in particular to a method, system, electronic device, and readable storage medium for simulating supersonic flow fields. Background Technology

[0002] As the core of hypersonic vehicles, the air-breathing supersonic propulsion system plays a crucial role in the entire vehicle's development. Extensive research indicates that the supersonic combustion ramjet engine is the most promising propulsion device. It typically consists of key components such as an inlet, isolation section, concave combustion chamber, and tail nozzle. It allows incoming flow to enter at supersonic speeds, and within this channel, flow characteristics such as supersonic boundary layers, shock waves, shock trains, flow separation, shear layers, and large-scale separation are distributed, and their interactions are numerous, posing a significant challenge to accurately assessing its intrinsic performance. Compared to traditional subsonic and transonic vehicles, the flow mechanisms of hypersonic vehicles are far more complex, making ground / flight testing riskier, more costly, and longer. In this context, computational fluid dynamics (CFD) technology stands out because it can provide quantitative flow field data with a certain degree of accuracy under extreme operating conditions and offer intuitive information about the fully simulated flow field. According to incomplete statistics, numerical simulation now accounts for 90% of the entire development process. In fact, the greatest advantage of numerical simulation is that it can identify many unfavorable factors and find avoidance strategies through a large number of simulation calculations in the early stage, thereby determining a better solution. This process is inseparable from the Reynolds-Averaged Navier-Stokes (RANS) method, and it will continue to play an important role in the coming decades.

[0003] The k-ω SST turbulence model is one of the most widely used RANS methods in engineering. It cleverly combines the classical k-ω and k-ε models, controlling the conversion between the two models through a "smart" mixing function F1; it introduces the influence of principal Reynolds stresses using the Bradshaw assumption, and ensures that this effect only applies to the near-wall turbulent boundary layer through function F2. In essence, the SST model comprehensively integrates the characteristics of free flow, boundary layer turbulent flow, and near-wall adverse pressure separation flow, thus constructing a well-rounded eddy viscosity model.

[0004] The SST model, with its straightforward and easy-to-understand modeling approach, has been widely adopted and promoted by researchers, achieving remarkable success in the aerospace field. However, inherent limitations of turbulence models restrict further applications, especially in the hypersonic domain, where even the excellent SST model has not been immune. It is understood that the most significant difference between air-breathing hypersonic propulsion systems and conventional flows is the compressibility of the flow and the interference of complex wave structures. The SST model lacks a systematic consideration of this difference, thus necessitating targeted corrections and the development of engineering turbulence models suitable for the complex flows of air-breathing hypersonic propulsion systems. Summary of the Invention

[0005] The purpose of this invention is to provide a method, system, electronic device, and readable storage medium for simulating supersonic flow fields.

[0006] To achieve the above-mentioned objectives, this invention provides a method for simulating supersonic flow fields, comprising the following steps:

[0007] S1. Obtain the standard k-ωSST turbulence model;

[0008] S2. Construct a multi-physics mechanism turbulence model based on the standard k-ωSST turbulence model, which includes compressible physical mechanisms and shock wave physical mechanisms; wherein, the multi-physics mechanism turbulence model is expressed as:

[0009]

[0010]

[0011]

[0012]

[0013]

[0014]

[0015] f c =F(M t )(2.2-2.2f s )

[0016]

[0017]

[0018]

[0019]

[0020] Where, ξ * =2.0, Mt0 =0.25, D() / Dt represents the mass derivative, ρ represents density, k represents turbulent kinetic energy, t represents time, τ ij Represents Reynolds stress, u i The velocity in the i-th direction of the Cartesian coordinate system is represented by x. j β represents the distance in the j-direction of the Cartesian coordinate system. * ω represents the constant of the turbulent kinetic energy dissipation term, μ represents the specific dissipation rate, and μ represents the molecular viscosity. t σ represents turbulent eddy viscosity. k γ represents the constant of the turbulent kinetic energy diffusion term, γ represents the constant of the specific dissipation rate generation term, and v t σ represents the turbulent eddy viscosity coefficient, β represents the specific dissipation rate dissipation term constant, and σ represents the turbulent eddy viscosity coefficient. ω F1 represents the diffusion term constant of the specific dissipation rate, and σ represents the mixing function. ω2 Let a1 represent the cross-diffusion term constant, and f represent the structural parameters. c Let f represent the shock-compressible function. s Represents the shock function, β i * M represents the constant of the turbulent kinetic energy dissipation term in the original standard SST model. t F(M) represents the turbulent Mach number. t F1 represents the turbulent Mach number function, F2 represents the boundary layer function, c represents the local sound speed, H represents the Heaviside step function, F3 represents the shock-turbulent boundary layer function, S represents the strain rate, and β represents the local sound speed. i S represents the specific dissipation rate dissipation term constant in the standard SST model. ii τ represents the volume expansion rate. s Δ represents the time scale, tanh represents the hyperbolic function, and Δ represents the representative mesh scale in a finite volume element.

[0021] S3. Obtain the initial conditions of the target flow field, and perform simulation calculations on the target flow field based on the multiphysics turbulence model.

[0022] According to one aspect of the present invention, step S2, the step of constructing a multi-physics turbulence model including compressible physical mechanisms and shock wave physical mechanisms based on the standard k-ωSST turbulence model, includes:

[0023] S21. Obtain flow mechanism parameters characterizing the flow mechanism, and obtain flow field functions characterizing the influence of compressible physical mechanisms and shock wave physical mechanisms on the flow based on the flow mechanism parameters;

[0024] S22. Based on the flow field function, perform directional correction on some model parameters of the standard k-ωSST turbulence model to obtain adaptive parameter expressions applicable to compressible physical mechanisms and shock wave physical mechanisms;

[0025] S23. Replace the corresponding parameter expression in the standard k-ωSST turbulence model with the obtained adaptive parameter expression to obtain the multiphysics turbulence model.

[0026] To achieve the above-mentioned objectives, this invention provides a simulation system for the aforementioned supersonic flow field simulation method, comprising:

[0027] The flow field condition input module is used to input the initial condition parameters of the supersonic flow field;

[0028] The flow field simulation module is used to receive the initial condition parameters transmitted by the flow field condition input module and perform flow field simulation.

[0029] The flow field simulation module is loaded with a multi-physics turbulence model that includes compressible physical mechanisms and shock wave physical mechanisms; wherein, the multi-physics turbulence model is expressed as:

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] f c =F(M t )(2.2-2.2f s )

[0037]

[0038]

[0039]

[0040]

[0041] Where, ξ * =2.0, M t0 =0.25, D() / Dt represents the mass derivative, ρ represents density, k represents turbulent kinetic energy, t represents time, τ ij Represents Reynolds stress, u i The velocity in the i-th direction of the Cartesian coordinate system is represented by x. jβ represents the distance in the j-direction of the Cartesian coordinate system. * ω represents the constant of the turbulent kinetic energy dissipation term, μ represents the specific dissipation rate, and μ represents the molecular viscosity. t σ represents turbulent eddy viscosity. k γ represents the constant of the turbulent kinetic energy diffusion term, γ represents the constant of the specific dissipation rate generation term, and v t σ represents the turbulent eddy viscosity coefficient, β represents the specific dissipation rate dissipation term constant, and σ represents the turbulent eddy viscosity coefficient. ω F1 represents the diffusion term constant of the specific dissipation rate, and σ represents the mixing function. ω2 Let a1 represent the cross-diffusion term constant, and f represent the structural parameters. c Let f represent the shock-compressible function. s Represents the shock function, β i * M represents the constant of the turbulent kinetic energy dissipation term in the original standard SST model. t F(M) represents the turbulent Mach number. t F1 represents the turbulent Mach number function, F2 represents the boundary layer function, c represents the local sound speed, H represents the Heaviside step function, F3 represents the shock-turbulent boundary layer function, S represents the strain rate, and β represents the local sound speed. i S represents the specific dissipation rate dissipation term constant in the standard SST model. ii τ represents the volume expansion rate. s Δ represents the time scale, tanh represents the hyperbolic function, and Δ represents the representative mesh scale in a finite volume element.

[0042] To achieve the above-mentioned objectives, the present invention provides an electronic device, including at least one processor, at least one memory, and a data bus;

[0043] The processor and the memory communicate with each other via the data bus;

[0044] The memory stores program instructions that are executed by the processor;

[0045] The processor invokes the program instructions to execute the aforementioned supersonic flow field simulation method.

[0046] To achieve the above-mentioned objectives, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the aforementioned supersonic flow field simulation method.

[0047] According to one aspect of the present invention, by incorporating the ability to capture shock waves and compression effects into the standard k-ωSST turbulence model, the present invention greatly expands its applicability and improves its performance in various working scenarios.

[0048] According to one aspect of the present invention, the multi-physics turbulence model employs a shock wave / boundary layer interaction identification function and utilizes shock wave and turbulent boundary layer functions to adjust the turbulent eddy viscosity coefficient, thereby improving the prediction accuracy of turbulent boundary layer / shock wave interactions. Furthermore, by using turbulent Mach number and mixing functions to consider compression effects, the dissipation capacity of non-equilibrium flow or the shock wave region is further enhanced.

[0049] According to one embodiment of the present invention, compared with traditional turbulence models or single-physics turbulence models, the multi-physics turbulence model of the present invention not only effectively maintains the performance of single-physics turbulence models, but also exhibits good performance in flows with multiple significant flow mechanisms. The multi-physics turbulence model has high accuracy and strong versatility, which is beneficial for simulating complex supersonic flows.

[0050] According to one aspect of the present invention, the problem of the inability of different mechanisms to coexist is effectively solved. It cleverly couples the shock wave physical mechanism and the compressible physical mechanism, two diametrically opposed capabilities, into a single model, providing a new solution for incompatible mechanisms. Attached Figure Description

[0051] Figure 1 This is a schematic diagram illustrating the steps of a supersonic flow field simulation method according to an embodiment of the present invention;

[0052] Figure 2 This is a schematic comparison diagram of the Van Driest average velocity profile at a velocity thickness δ = 0.0077 m according to one embodiment of the present invention;

[0053] Figure 3 This is a schematic diagram showing the pressure and temperature profile at a velocity thickness δ = 0.0077 m according to one embodiment of the present invention;

[0054] Figure 4 This is a schematic diagram illustrating the structural grid of a 24° slope according to one embodiment of the present invention;

[0055] Figure 5 The diagram schematically represents the superimposed density gradient contour lines, turbulent energy profiles of Ma=1 and 24° slopes, and streamline diagrams according to an embodiment of the present invention, wherein (a) represents the standard k-ωSST turbulence model, (b) represents the single compressible effect SST model (SST-C), (c) represents the single shock wave effect SST model (SST-S), and (d) the multi-physics mechanism SST model (SST-MP).

[0056] Figure 6This is a schematic diagram illustrating the wall pressure distribution of a 24° slope according to one embodiment of the present invention;

[0057] Figure 7 This is a schematic representation of a slice with y = 10 at the center of a 24° compression angle according to an embodiment of the present invention. -4 Comparison of eddy viscosity distribution at point m;

[0058] Figure 8 The diagram schematically represents streamlines and eddy viscosity contours of a 24° slope according to an embodiment of the present invention, wherein (a) represents the standard k-ω SST turbulence model, (b) represents the single compressible effect SST model (SST-C), (c) represents the single shock wave effect SST model (SST-S), and (d) the multi-physics mechanism SST model (SST-MP). Detailed Implementation

[0059] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The embodiments cannot be described in detail here, but the embodiments of the present invention are not limited to the following embodiments.

[0060] like Figure 1 As shown, according to one embodiment of the present invention, the present invention provides a method for simulating supersonic flow fields based on a multi-physics mechanism turbulence model, comprising the following steps:

[0061] S1. Obtain the standard k-ωSST turbulence model;

[0062] S2. A multi-physics mechanism turbulence model incorporating compressible and shock wave physical mechanisms is constructed based on the standard k-ωSST turbulence model; wherein, the multi-physics mechanism turbulence model is expressed as:

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] f c =F(M t )(2.2-2.2f s )

[0070]

[0071]

[0072]

[0073]

[0074] Where, ξ * =2.0, M t0 =0.25, D() / Dt represents the mass derivative, ρ represents density, k represents turbulent kinetic energy, t represents time, τ ij Represents Reynolds stress, u i The velocity in the i-th direction of the Cartesian coordinate system is represented by x. j β represents the distance in the j-direction of the Cartesian coordinate system. * ω represents the constant of the turbulent kinetic energy dissipation term, μ represents the specific dissipation rate, and μ represents the molecular viscosity. t σ represents turbulent eddy viscosity. k γ represents the constant of the turbulent kinetic energy diffusion term, γ represents the constant of the specific dissipation rate generation term, and v t σ represents the turbulent eddy viscosity coefficient, β represents the specific dissipation rate dissipation term constant, and σ represents the turbulent eddy viscosity coefficient. ω F1 represents the diffusion term constant of the specific dissipation rate, and σ represents the mixing function. ω2 Let a1 represent the cross-diffusion term constant, and f represent the structural parameters. c Let f represent the shock-compressible function. s Represents the shock function. M represents the constant of the turbulent kinetic energy dissipation term in the original standard SST model. t F(M) represents the turbulent Mach number. t F1 represents the turbulent Mach number function, F2 represents the boundary layer function, c represents the local sound speed, H represents the Heaviside step function, F3 represents the shock-turbulent boundary layer function, S represents the strain rate, and β represents the local sound speed. i S represents the specific dissipation rate dissipation term constant in the standard SST model. ii τ represents the volume expansion rate. s Δ represents the time scale, tanh represents the hyperbolic function, and Δ represents the representative mesh scale in a finite volume element.

[0075] S3. Obtain the initial conditions of the target flow field and perform simulation calculations on the target flow field based on the multiphysics turbulence model.

[0076] According to one embodiment of the present invention, in step S1, the standard k-ωSST turbulence model is expressed as follows:

[0077]

[0078]

[0079] Where D() / Dt represents the mass derivative, ρ represents density, k represents turbulent kinetic energy, t represents time, and τ represents... ij Represents Reynolds stress, u i The velocity in the i-th direction of the Cartesian coordinate system is represented by x. j β represents the distance in the j-direction of the Cartesian coordinate system. * ω represents the constant of the turbulent kinetic energy dissipation term, μ represents the specific dissipation rate, and μ represents the molecular viscosity. t σ represents turbulent eddy viscosity. k γ represents the constant of the turbulent kinetic energy diffusion term, γ represents the constant of the specific dissipation rate generation term, and v t σ represents the turbulent eddy viscosity coefficient, β represents the specific dissipation rate dissipation term constant, and σ represents the turbulent eddy viscosity coefficient. ω F1 represents the diffusion term constant of the specific dissipation rate, and σ represents the mixing function. ω2 This represents the cross-diffusion term constant. Wherein, the Reynolds stress τ... ij and turbulent eddy viscosity μ t It can be solved by the following formula:

[0080]

[0081] Among them, u k Let x represent the velocity in the k-direction of the Cartesian coordinate system. k δ represents the distance along the k-direction in the Cartesian coordinate system. ij Represents the Kronecker symbol;

[0082]

[0083] Where a1 represents the structural parameter, Ω represents the vorticity, and F2 represents the boundary layer function;

[0084] Furthermore, the strain rate tensor and vorticity tensor involved are set separately, and are expressed as follows:

[0085]

[0086] Furthermore, the model constants are calculated based on the mixing function F1, i.e., its mixing method is expressed as:

[0087] φ=F1φ1+(1-F1)φ2 (6)

[0088] Where φ1 is the model constant in the original k-ω model, φ2 is the model constant in the standard k-ω model, and φ is the model constant in the SST model. Mixing only occurs in the wake region of the boundary layer.

[0089] Furthermore, some other relationships used in the standard SST turbulence model are further defined, as follows:

[0090]

[0091]

[0092]

[0093]

[0094]

[0095] Two sets of constants used in the modeling:

[0096] First set of constants (φ1, Wilcox):

[0097] σ k1 =0.85, σ ω1 =0.5, β1=0.075

[0098] β * =0.09, κ=0.41,

[0099] The second set of constants (φ2, standard k-ε):

[0100] σ k2 =1.0, σ ω2 =0.856, β2=0.0828

[0101] β * =0.09, κ=0.41,

[0102] According to one embodiment of the present invention, step S2, which involves constructing a multi-physics turbulence model including compressible physical mechanisms and shock wave physical mechanisms based on the standard k-ωSST turbulence model, includes:

[0103] S21. Obtain flow mechanism parameters characterizing the flow mechanism, and based on the flow mechanism parameters, obtain flow field functions characterizing the influence of compressible physical mechanisms and shock wave physical mechanisms on the flow; in this embodiment, based on the local sound velocity c and turbulent kinetic energy k obtained from the flow field calculation, obtain the turbulent Mach number M, a parameter characterizing the compressibility effect. t Through the Heaviside step function, mixing function, boundary layer function, and critical value M t0 Constructing the turbulent Mach number function F(M) t Finally, by combining the shock function, a shock-compressibility function f that can identify the compressible region is obtained. c Similarly, the impact of shock wave physics on flow is primarily determined by the local volumetric expansion rate S. ii and time scale τs Therefore, a function f can be constructed to determine the shock wave region. s Then, it is combined with the boundary layer function F2 to construct the shock-turbulent boundary layer function F3. For this purpose, the flow mechanism parameters used to characterize the flow mechanism include: c, k, M. t , F(M t M t0 F1, F2, F s S ii , τ s , tanh, Δ, ω; where, in the step of obtaining the flow field function characterizing the influence of compressible physical mechanism and shock wave physical mechanism on the flow based on flow mechanism parameters, the constructed flow field function is expressed as:

[0104] Shock wave physics mechanism:

[0105]

[0106]

[0107]

[0108] Compressible physical mechanism:

[0109] f c =F(M t )(2.2-2.2f s )

[0110]

[0111]

[0112] S22. Based on the flow field function, some model parameters of the standard k-ωSST turbulence model are directionally corrected to obtain adaptive parameter expressions suitable for both compressible and shock wave physical mechanisms; in this embodiment, step S21 yields the shock wave-compressible function f, which can locate the compressible region. c And the shock-turbulent boundary layer function F3, which can locate the shock wave region, is then adjusted according to the influence of compressible physics mechanisms on the original standard SST model, specifically the dissipation rate constant β and the turbulent kinetic energy dissipation constant β. * Based on the influence of shock wave physics mechanisms on the original standard SST model, the turbulent eddy viscosity μ is adjusted. t Furthermore, based on the flow field function, the β in the standard k-ωSST turbulence model is... * ,β and μ t The model parameters are adjusted in a targeted manner, where the model parameter β... * And β are processed using a compressible physical mechanism for directional correction of the transformation method, which is expressed as: and Turbulent eddy viscosity μ t The transformation method is processed using shock wave physics mechanisms for directional correction, which is expressed as follows:

[0113] S23. Replace the corresponding parameter expressions in the standard k-ωSST turbulence model with the obtained adaptive parameters to obtain a multi-physics turbulence model. Specifically, combine the above modifications with the original standard SST turbulence model to form a more complete SST turbulence model, i.e., a multi-physics turbulence model.

[0114] According to one embodiment of the present invention, the present invention provides a simulation system for the aforementioned supersonic flow field simulation method, comprising:

[0115] The flow field condition input module is used to input the initial condition parameters of the supersonic flow field;

[0116] The flow field simulation module is used to receive the initial condition parameters transmitted by the flow field condition input module and perform flow field simulation.

[0117] The flow field simulation module is loaded with a multi-physics turbulence model that includes compressible and shock wave physical mechanisms; the multi-physics turbulence model is expressed as follows:

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124] f c =F(M t )(2.2-2.2f s )

[0125]

[0126]

[0127]

[0128]

[0129] Where, ξ * =2.0, M t0=0.25, D() / Dt represents the mass derivative, ρ represents density, k represents turbulent kinetic energy, t represents time, τ ij Represents Reynolds stress, u i The velocity in the i-th direction of the Cartesian coordinate system is represented by x. j β represents the distance in the j-direction of the Cartesian coordinate system. * ω represents the constant of the turbulent kinetic energy dissipation term, μ represents the specific dissipation rate, and μ represents the molecular viscosity. t σ represents turbulent eddy viscosity. k γ represents the constant of the turbulent kinetic energy diffusion term, γ represents the constant of the specific dissipation rate generation term, and v t σ represents the turbulent eddy viscosity coefficient, β represents the specific dissipation rate dissipation term constant, and σ represents the turbulent eddy viscosity coefficient. ω F1 represents the diffusion term constant of the specific dissipation rate, and σ represents the mixing function. ω2 Let a1 represent the cross-diffusion term constant, and f represent the structural parameters. c Let f represent the shock-compressible function. s Represents the shock function, β i * M represents the constant of the turbulent kinetic energy dissipation term in the original standard SST model. t F(M) represents the turbulent Mach number. t F1 represents the turbulent Mach number function, F2 represents the boundary layer function, c represents the local sound speed, H represents the Heaviside step function, F3 represents the shock-turbulent boundary layer function, S represents the strain rate, and β represents the local sound speed. i S represents the specific dissipation rate dissipation term constant in the standard SST model. ii τ represents the volume expansion rate. s denoted by time scale, tanh represents a hyperbolic function, and Δ represents a representative mesh scale in a finite volume element.

[0130] According to one embodiment of the present invention, an electronic device is provided, including at least one processor, at least one memory, and a data bus. In this embodiment, the processor and the memory communicate with each other via the data bus; the memory stores program instructions to be executed by the processor; the processor invokes the program instructions to execute the aforementioned supersonic flow field simulation method.

[0131] In this embodiment, the memory may be, but is not limited to, Random Access Memory (RAM), Read Only Memory (ROM), Programmable Read-Only Memory (PROM), Erasable Programmable Read-Only Memory (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), etc.

[0132] In this embodiment, the processor can be an integrated circuit chip with signal processing capabilities. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0133] According to one embodiment of the present invention, the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program, when executed by a processor, implements the aforementioned supersonic flow field simulation method.

[0134] If the aforementioned functions are implemented as software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0135] To further illustrate the technical effectiveness of this scheme, numerical simulations were performed to verify it under different flow fields.

[0136] In this embodiment, the numerical simulation process is based on a pre-set GPU parallel program. The RANS equations and turbulence model equations are solved using the finite volume method. The convection term uses the second-order AUSM+UP scheme, the viscosity term uses the second-order central difference, and the time integration uses the four-step second-order Runge-Kutta method.

[0137] Example 1

[0138] In this embodiment, the simulation calculation of supersonic flat plate flow is performed based on the aforementioned settings. Specifically, supersonic flat plate flow is the most common flow state and is an indispensable process for forming simple or complex flows. It is often selected as a typical example for evaluating numerical simulation prediction of turbulent boundary layers and wall friction. This paper uses the DNS results of Ma2.5 flat plate (see the literature ZHANG C, DUAN L, CHOUDHARI M M. Direct numerical simulation database for supersonic and hypersonic turbulent boundary layers[J]. AIAA journal,2018,56(11):4297-311.) as a control. The simulation adopts the assumption of a completely gaseous state, uses Sutherland's law to calculate gas viscosity, and adopts isothermal no-slip conditions on the wall with a wall temperature of 568K. Some incoming flow conditions are shown in Table 1. The computational domain is a flat plate of 1 m × 0.2 m × 0.01 m. Based on the mesh independence verification work, the mesh scheme is selected as 500 × 250 × 5, where the height of the first mesh layer from the wall is 10. -6 m.

[0139] Table 1

[0140] 2.50 823.6 0.1 270 568

[0141] Velocity profiles are typically used to measure the predictive power of turbulence models for boundary layer development. The normal and flow velocity distribution along the wall at thicker boundary layers is shown below. Figure 2 As shown. The velocity is calculated using the Van Driest transform, i.e.:

[0142]

[0143] in, It is the frictional velocity, τ w It is wall shear stress. It refers to the density near the wall surface.

[0144] The turbulent boundary layer can be divided into four parts: the linear sublayer, the transition layer, the logarithmic layer, and the outer boundary layer. The first three parts are collectively referred to as the inner boundary layer. In the inner layer, the turbulence model presented in this paper shows consistent prediction accuracy with DNS and standard SST in the linear sublayer and logarithmic layer. However, in the transition layer (region "1" in the figure), the results differ from those of DNS. In the outer boundary layer region (region "2" in the figure), the calculated peak value also deviates from the DNS data. This difference is because the fluid inertial force gradually weakens while the fluid viscous drag gradually increases in this region, making it difficult for RANS to predict this change well.

[0145] The inner layer of the turbulent boundary layer reflects the overall effect of turbulent molecular viscosity and turbulent eddy viscosity. In the region very close to the wall, due to the constraint of the solid wall, turbulent eddy viscosity is small relative to molecular viscosity. Therefore, this region can be approximated as being determined only by the inherent properties of the material (i.e., molecular viscosity), and through simplification, the analytical relationship for this region can be obtained: a linear law. In the boundary layer region relatively far from the wall, due to the influence of free flow, the fluid in this region is highly pulsating, so turbulent eddy viscosity plays a dominant role, while molecular viscosity is approximately small. Through simplification, the analytical law for this region can also be obtained: a logarithmic law. However, in the region between these two, since molecular viscosity and eddy viscosity jointly control the flow field characteristics, it is difficult to determine the exact size of this region, and it is not possible to obtain the functional law of this region simply through order-of-magnitude analysis. The condition that molecular viscosity equals eddy viscosity is often used to obtain an approximate model of this region, thus inherently lacking the ability to accurately describe the transition layer. Therefore, the velocity profile of the boundary layer exhibits the above phenomenon. In summary, the model presented in this paper has the same predictive ability for wall velocity distribution as the standard SST model, and can accurately reflect the development of the zero-pressure gradient turbulent boundary layer.

[0146] In engineering, more attention is often paid to the ability to capture macroscopic physical quantities of flow such as density, velocity, temperature and pressure. These physical quantities are important components of the three conservation laws of fluid mass, momentum and energy. Figure 2 The ability to predict density and velocity has already been demonstrated. Here, we present the normalized pressure and temperature distribution at a boundary layer thickness δ = 0.0077 m, as shown below. Figure 3 As shown. For the pressure distribution curve (solid arrow on the left side of the figure), the predictions of the three models are consistent, essentially showing zero pressure gradient. For the temperature distribution (solid arrow on the right side of the figure), the predictions of the three models are basically consistent, but in the outer layer of the turbulent boundary layer, the improved model gives a slightly higher temperature than the standard SST model, and the temperature distributions of the two improved models are completely consistent. Due to the constraint of the isothermal wall condition, the temperature is higher closer to the wall.

[0147] As assumed by a perfect gas state, temperature, pressure, and density are mutually deterministic. In this example, pressure remains essentially constant, with temperature and density primarily responding to each other. The improved strategy influences the calculation of macroscopic physical quantities by altering the expression of turbulent eddy viscosity, thereby significantly changing the predictive power for the logarithmic layer and the outer layer of the turbulent boundary layer. Overall, the improved model of this invention possesses predictive power for zero-pressure gradient turbulent boundary layers consistent with the standard SST model, laying the foundation for further research on this strategy.

[0148] Example 2

[0149] In this embodiment, the simulation calculation of supersonic compression ramp flow is performed based on the aforementioned settings. Specifically, shock waves are the most common flow field structure in supersonic flow and one of the main contributors to complex turbulence in engineering. Supersonic compression ramp flow is a commonly used example for studying shock wave-induced flow separation phenomena. This paper selects a compression ramp test with an incoming Mach number Ma = 2.9 and a ramp angle of 24° as one of the evaluation examples. The DNS data is given in the reference "WU M, MARTIN M P. Direct numerical simulation of supersonic turbulent boundary layer over a compression ramp[J]. AIAA journal,2007,45(4):879-89." The simulation adopts the assumption of a completely gaseous state, uses Sutherland's law to calculate the gas viscosity, and assumes an adiabatic, no-slip wall condition. The incoming flow conditions are shown in Table 2. Based on the plate calculation results, the required plate length is calculated to be 0.4165m when the boundary layer thickness is 0.0067m. Other dimensions of the computational domain are: slope length 0.120m, channel height 0.150m, and spanwise width 0.010m. Based on the mesh independence results, the number of mesh nodes is selected as 457×451×11, with a minimum scale of 10 along the wall normal. -6 m, with a minimum grid size of 5×10⁻⁶ for the flow direction. -5 m, and densified along the corner points, the mesh is as follows Figure 4 As shown.

[0150] The basic structure of the supersonic compression corner flow field is as follows Figure 5As shown, the supersonic inflow passes through the turbulent boundary layer, contracts due to the slope geometry, changes direction, and forms a shock wave. The shock wave interacts with the turbulent boundary layer and is induced by the slope, forming a separated flow at the corner. The figure shows the normalized turbulent kinetic energy contour map, overlaid with density gradient contour lines and streamlines characterizing the shock wave structure; Mach 1 contour lines are also indicated. The inflow impacts the slope, possessing the maximum turbulent kinetic energy in the impact region. The flow field structure mainly consists of a backflow region and three types of shock waves: separated shock waves, slope-induced shock waves, and reattached shock waves. However, different models give different prediction results. Using the standard SST model prediction results as a benchmark, the single compressible effect SST model (SST-C) gives little change in the calculated flow field structure. The single shock wave effect SST model (SST-S) and the multi-physics mechanism SST model (SST-MP) predict different flow field structures: the separated shock wave is closer to the corner, the angle between the separated shock wave and the reattached shock wave is smaller, and the separated flow region is smaller. In this example, a comparison is made... Figure 5 (a) and Figure 5 (b) and comparison Figure 5 (c) and Figure 5 (d) It can be seen that the compressibility physical mechanism has a relatively small impact; compared with Figure 5 (a) and Figure 5 (c) and comparison Figure 5 (b) and Figure 5 (d) It can be seen that the physical mechanism of the shock wave effect plays a major role in its effect.

[0151] Wall pressure distribution along the flow path is often used as one of the methods to evaluate the location of shock-induced flow separation in this case study. The wall pressure distribution results obtained from turbulence models, experiments, and DNS are compared below. Figure 6 As shown, the horizontal axis is dimensionless based on the boundary layer thickness δ = 0.0067 m, and the vertical axis is based on the incoming flow pressure P. ∞ Dimensionless. The DNS (Discrete Synthetic Flow) model shows good overall agreement with the experimental wall pressure distribution. The pressure rise location calculated by the standard SST turbulence model and the single compressible effect SST model (SST-C) is significantly earlier than the experimental data, with a distance from the inflection point approximately 1.625 times that of the experiment. The calculation results of the single shock wave effect SST model (SST-S) and the multi-physics mechanism SST model (SST-MP) of this invention show good overall agreement with the experiment, accurately predicting the pressure rise location and the pressure distribution on the slope, which is better than the DNS results. As shown in the figure, the single compressible effect SST model (SST-C) did not improve the predictive ability of shock wave induced flow separation, but it did not reduce the prediction accuracy of the original standard SST model. The improved SST model (SST-S) and the multi-physics mechanism SST model (SST-MP) significantly improved the prediction accuracy of shock wave induced flow separation.

[0152] Compared to supersonic flat-plate flow, the flow field in a compression corner configuration becomes further complex, mainly due to the introduction of new physical mechanisms by the shock wave structure and the characteristics of the separated flow field. Since the RANS method uses time-progression to solve the steady-state numerical solution, the main flow physical mechanisms described by the standard SST model can be simplified to four parts: convection, generation, dissipation, and diffusion, as well as the main turbulent shear stress proportional to turbulent kinetic energy introduced based on a more accurate simulation of the strong adverse pressure gradient flow near the wall. Therefore, the mechanisms of shock waves and their induced flow separation are not included, resulting in a lower calculated turbulent kinetic energy, which in turn leads to a lower eddy viscosity coefficient, lower Reynolds stress, and weaker resistance to back pressure under the same pressure gradient.

[0153] To further demonstrate this, the near-wall surface y = 10 was extracted. -4 Turbulent eddy viscosity μ along the flow direction at point m t The distribution characteristics were analyzed, and the results are as follows: Figure 7 As shown in the figure, Reynolds stress is the product of the Reynolds / Favre average of the transient momentum conservation equation, and is the statistical average of the product of velocity fluctuations. It originates from the convection term and is related to the flow field gradient. Turbulent eddy viscosity is one of the most important flow parameters in Reynolds stress under the Boussinesq molecular assumption, and is a measure of the strength of its correlation with strain rate. As shown in the figure, it mainly presents the variation of turbulent eddy viscosity along the flow direction (x-axis) near the separation region induced by shock wave. In the separated flow predicted by the standard SST turbulence model, the trend of turbulent eddy viscosity variation is gradual, ranging from dimensionless... The resulting slope is relatively small, indicating a weak correlation with the strain rate, and thus provides a smaller Reynolds stress in this example. At zero velocity, the theoretical pressure is maximum P0; at flow separation, the theoretical pressure is P. s Then, with a separation length of l s Within that region, the resulting pressure gradient is approximately... In other words, it is necessary to l s Within the length, the pressure will be reduced from P0 to P s According to the momentum conservation equation, the pressure difference is mainly counteracted by the passive molecular viscous stress and Reynolds stress. However, in the turbulent boundary layer, the molecular viscous stress is much smaller than the Reynolds stress, so the momentum equation can be approximately simplified, and the pressure difference will be balanced by the Reynolds stress gradient. However, the figure shows that the Reynolds stress along the x-direction, at a distance Δx... s The Reynolds stress change Δτ provided by internal energy ij The value is relatively small. Therefore, the relationship given by the standard SST model is used. Further, we can obtain The distance Δx given by the standard SST model is currently known. s The value is too large and does not match the experimental value. To obtain results consistent with the experiment, the distance Δx needs to be reduced. s Value, i.e., reverse pressure gradient The Reynolds stress gradient will increase, and correspondingly, a larger reverse pressure gradient is required to maintain this gradient. Therefore, increasing the turbulent eddy viscosity is feasible without altering the physical meaning. However, the improved SST model shows a significant change in turbulent eddy viscosity in the separation region, within the same Δx. Right now As can be seen from the above, the standard SST model predicts a smaller pressure gradient, which is closely related to its calculation of a smaller turbulent eddy viscosity. By using the shock wave discriminant function to improve the calculation of turbulent eddy viscosity, the prediction accuracy of shock wave induced separation flow can be significantly improved.

[0154] The flow field structure characteristics of the supersonic compression corner example are as follows: Figure 8 As shown in the figure, P is included. k / ρε and F(M t (Cloud map, and overlaid with f) s The F1 and F2 contour lines are used to simultaneously display two contour maps and show a better distribution, where F(M) t ) < 0.0001 and P k The part / ρε<3.9 is not displayed. P k / ρε represents the relative magnitude of the generation and dissipation terms of turbulent kinetic energy. In the compression corner example, the shock wave structure and its induced separated flow characteristics are most significant. In the shock wave region, due to the significant change in the velocity gradient, the generation of turbulent kinetic energy is much greater than the dissipation. Therefore, the region with a ratio greater than 4 is mainly shown. Due to the use of a limiter, this ratio does not exceed 20. Figure 8 (a)- Figure 8 (c) It can be seen that P k / ρε has a maximum value in the shock wave region, which is close to 20. However, the multi-physics mechanism SST model (SST-MP) gives a lower ratio in the corresponding region. But at the junction of the separating shock wave and the reattached shock wave, the ratios given by the four models are basically the same, that is, they all indicate non-equilibrium effects in these regions, and the multi-physics mechanism model can reduce this non-equilibrium to the greatest extent. F(M t The discriminant function for compressibility effects used in the multi-physics mechanism SST model (SST-MP) is shown in the figure. As can be seen, this function mainly expresses two characteristics: the region of compressibility effect and the intensity of the compressibility effect. The single compressibility effect SST model (SST-C) gives the same region and intensity of compressibility effect as the standard SST model. The single shock wave effect SST model (SST-S) and the multi-physics mechanism SST model (SST-MP) give smaller regions of effect. Relatively speaking, the multi-physics mechanism SST model (SST-MP) represents a smaller intensity of compressibility effect. Therefore, multiple physics mechanisms can not only change the region of compressibility effect but also affect its intensity. sThis is the shock wave discrimination function, which can characterize the region where the shock wave is located, and is also related to P. k The non-equilibrium regions represented by / ρε largely overlap, providing a basis for accurately locating the non-equilibrium or shock wave regions. F1 and F2 are mixed functions; in this example, F2 = (M t The distribution is mainly concentrated around the isoline of the mixing function F1 = 0.1, and within the region of F2 > 0.1. This indicates that the compressibility effect correction introduced by the multi-physics mechanism SST model (SST-MP) is mainly concentrated in the peripheral region of the mixing function F1. In summary, through the above analysis, the main flow characteristics in the flow field, such as the non-equilibrium region, compressible region, shock wave region, and turbulent boundary layer, can be well distinguished, and corresponding physical laws can be introduced. As shown in the pressure prediction figure above, applying corresponding laws to the corresponding flow field structure can significantly improve the prediction accuracy.

[0155] The above description is merely an example of a specific solution of the present invention. For any devices and structures not described in detail herein, it should be understood that they are implemented using common devices and methods already available in the art.

[0156] The above description is merely one embodiment of the present invention and is not intended to limit the invention. Those skilled in the art will recognize that the present invention can be modified and varied in various ways. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for simulating supersonic flow fields, characterized in that, Includes the following steps: S1. Obtain the standard k-ωSST turbulence model; S2. Construct a multi-physics mechanism turbulence model based on the standard k-ωSST turbulence model, which includes compressible physical mechanisms and shock wave physical mechanisms; wherein, the multi-physics mechanism turbulence model is expressed as: f c =F(M t )(2.2-2.2f s ) Where, ξ * =2.0, M t0 =0.25, D() / Dt represents the mass derivative, ρ represents density, k represents turbulent kinetic energy, t represents time, τ ij Represents Reynolds stress, u i The velocity in the i-th direction of the Cartesian coordinate system is represented by x. j β represents the distance in the j-direction of the Cartesian coordinate system. * ω represents the constant of the turbulent kinetic energy dissipation term, μ represents the specific dissipation rate, and μ represents the molecular viscosity. t σ represents turbulent eddy viscosity. k γ represents the constant of the turbulent kinetic energy diffusion term, γ represents the constant of the specific dissipation rate generation term, and v t σ represents the turbulent eddy viscosity coefficient, β represents the specific dissipation rate dissipation term constant, and σ represents the turbulent eddy viscosity coefficient. ω F1 represents the diffusion term constant of the specific dissipation rate, and σ represents the mixing function. ω2 Let a1 represent the cross-diffusion term constant, and f represent the structural parameters. c Let f represent the shock-compressible function. s Represents the shock function. M represents the constant of the turbulent kinetic energy dissipation term in the original standard SST model. t F(M) represents the turbulent Mach number. t F1 represents the turbulent Mach number function, F2 represents the boundary layer function, c represents the local sound speed, H represents the Heaviside step function, F3 represents the shock-turbulent boundary layer function, S represents the strain rate, and β represents the local sound speed. i S represents the specific dissipation rate dissipation term constant in the standard SST model. ii τ represents the volume expansion rate. s Δ represents the time scale, tanh represents the hyperbolic function, and Δ represents the representative mesh scale in a finite volume element. S3. Obtain the initial conditions of the target flow field, and perform simulation calculations on the target flow field based on the multiphysics turbulence model.

2. The supersonic flow field simulation method according to claim 1, characterized in that, Step S2, the step of constructing a multi-physics turbulence model including compressible physical mechanisms and shock wave physical mechanisms based on the standard k-ωSST turbulence model, includes: S21. Obtain flow mechanism parameters characterizing the flow mechanism, and obtain flow field functions characterizing the influence of compressible physical mechanisms and shock wave physical mechanisms on the flow based on the flow mechanism parameters; S22. Based on the flow field function, perform directional correction on some model parameters of the standard k-ωSST turbulence model to obtain adaptive parameters suitable for compressible physical mechanisms and shock wave physical mechanisms; S23. Replace the corresponding parameter expression in the standard k-ωSST turbulence model with the obtained adaptive parameter expression to obtain the multiphysics turbulence model.

3. A simulation system for the supersonic flow field simulation method according to any one of claims 1 to 2, characterized in that, include: The flow field condition input module is used to input the initial condition parameters of the supersonic flow field; The flow field simulation module is used to receive the initial condition parameters transmitted by the flow field condition input module and perform flow field simulation. The flow field simulation module loads a multi-physics turbulence model that includes compressible physical mechanisms and shock wave physical mechanisms; wherein, the multi-physics turbulence model is expressed as: f c =F(M t )(2.2-2.2f s ) Where, ξ * =2.0, M t0 =0.25, D() / Dt represents the mass derivative, ρ represents density, k represents turbulent kinetic energy, t represents time, τ ij Represents Reynolds stress, u i The velocity in the i-th direction of the Cartesian coordinate system is represented by x. j β represents the distance in the j-direction of the Cartesian coordinate system. * ω represents the constant of the turbulent kinetic energy dissipation term, μ represents the specific dissipation rate, and μ represents the molecular viscosity. t σ represents turbulent eddy viscosity. k γ represents the constant of the turbulent kinetic energy diffusion term, γ represents the constant of the specific dissipation rate generation term, and v t σ represents the turbulent eddy viscosity coefficient, β represents the specific dissipation rate dissipation term constant, and σ represents the turbulent eddy viscosity coefficient. ω F1 represents the diffusion term constant of the specific dissipation rate, and σ represents the mixing function. ω2 Let a1 represent the cross-diffusion term constant, and f represent the structural parameters. c Let f represent the shock-compressible function. s Represents the shock function. M represents the constant of the turbulent kinetic energy dissipation term in the original standard SST model. t F(M) represents the turbulent Mach number. t F1 represents the turbulent Mach number function, F2 represents the boundary layer function, c represents the local sound speed, H represents the Heaviside step function, F3 represents the shock-turbulent boundary layer function, S represents the strain rate, and β represents the local sound speed. i S represents the specific dissipation rate dissipation term constant in the standard SST model. ii τ represents the volume expansion rate. s denoted by time scale, tanh represents a hyperbolic function, and Δ represents a representative mesh scale in a finite volume element.

4. An electronic device, characterized in that, Includes at least one processor, at least one memory, and a data bus; The processor and the memory communicate with each other via the data bus; The memory stores program instructions that are executed by the processor; The processor invokes the program instructions to execute the supersonic flow field simulation method as described in any one of claims 1-2.

5. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the supersonic flow field simulation method as described in any one of claims 1-2.

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