A high-precision prediction method for boundary transition of supersonic aircraft

Abstract

The application discloses a high-precision prediction method for boundary layer transition of a supersonic aircraft, and belongs to the field of aerodynamics. In view of the technical problems of insufficient prediction precision of the existing transition and incapability of processing complex geometry and nonlinear effects, the application directly solves a nonlinear disturbance N-S equation, and combines a multi-block structured grid generation, basic flow steady-state calculation, disturbance flow parameter configuration and initialization, high-precision discrete operator precalculation, explicit time advancing solving and frequency domain transition extraction and other technical means, so that the limitation of traditional methods is broken through, and the cross-flow instability and transition saturation process can be accurately captured. The method can provide reliable prediction support for aerodynamic design and thermal protection of a hypersonic aircraft, significantly reduces experimental cost and improves research and development efficiency.

Description

Technical Field

[0001] This invention relates to the field of aerodynamics, and more specifically to a high-precision prediction method for the boundary transition of supersonic aircraft. Background Technology

[0002] Boundary layer transition significantly affects the mechanical properties of high Mach number vehicles, such as drag, lift, and torque, as well as their heat transfer characteristics, including surface heat flux and temperature, making it a critical factor in their design and safe operation. Although research on laminar-turbulent transition has been ongoing for over a century since Reynolds' pioneering work, accurately predicting the transition of high-speed boundary layers with complex geometries remains extremely difficult. Hypersonic boundary layer transition characteristics depend on the influence of multiple factors, such as the boundary layer outer edge Mach number, wall temperature, angle of attack, surface roughness, local pressure gradient, nose / leading edge bluntness, and the disturbed environment. These numerous influencing factors make it difficult to elucidate the transition laws, resulting in significant challenges in transition prediction. Furthermore, the strong coupling effect of these parameters makes determining the impact of individual parameters on stability and transition even more difficult. For example, changing the leading edge or nose bluntness can affect other parameters, potentially relating to multiple factors such as the boundary layer outer edge Mach number and temperature, the local Reynolds number, and the pressure gradient.

[0003] The main methods for transition research include flight experiments, wind tunnel experiments, and numerical simulation. Flight experiments can conduct transition studies in real flight environments, but they face serious challenges such as high cost, high risk, difficulty in precise measurement, and poor repeatability. Compared with flight experiments, wind tunnel experiments have the advantages of low cost and high efficiency, but they still have many difficulties and are expensive. The main difficulties lie in the Reynolds number limitation, wind tunnel noise level, short flow duration, and how to generate controllable environmental disturbances. With the development of computer technology and numerical simulation algorithms, numerical simulation has been widely used in transition research in recent years.

[0004] Among these methods, the Linear Stability Theory (LST) and Parabolized Stability Equations (PSE) methods cannot handle sensitivity problems or consider the effects of complex geometries; the BiGlobal / TriGlobal methods require solving large eigenvalue problems and cannot adapt to complex geometries. In contrast, the time-progression method based on linearized / nonlinear compressible perturbation NS equations (LCNS / NCNS) is a means that balances computational accuracy and efficiency, and is an efficient tool for stability analysis of complex geometries. The LCNS method, based on linearized compressible NS equations, does not require any assumptions about the geometry made by traditional stability analysis tools such as LST and PSE. It can be used to study most instability mechanisms in hypersonic boundary layer transitions, such as linear sensitivity, first and second mode instabilities, transient growth, transverse instabilities, and absolute / global instabilities. Although this method is linearized, it can still capture certain weak nonlinear effects, such as secondary instability, because it can use unsteady fundamental flows. Summary of the Invention

[0005] To address the problem of low accuracy in existing supersonic vehicle transition prediction technologies, this invention provides a...

[0006] A high-precision prediction method for the boundary transition of a supersonic vehicle includes:

[0007] S1. Basic flow field calculation: Based on the aircraft model, generate multiple structured meshes and boundary conditions, input the incoming flow parameters and call the laminar flow solver to perform steady-state calculations, and output the basic flow original variable information;

[0008] S2. Disturbance flow parameter configuration and initialization: Import the basic flow original variable information and disturbance solution control parameters, generate a zero disturbance initial field or read historical flow field data according to whether to continue calculation, and output the initial flow field for unsteady disturbance calculation;

[0009] S3. Pre-calculation of flow field variables and discrete operators: Based on the basic flow original variable information, calculate the sound velocity, enthalpy and transport coefficient matrix, calculate the uniform time step of the whole field in combination with CFL number constraints, and pre-calculate the grid template weight operator according to the selected high-precision format, and output the pre-calculated flow field attribute array and discrete operator library.

[0010] S4. Time-progression solution of the perturbation flow: Starting from the initial flow field calculated by the unsteady perturbation, and combining the flow field attribute array and discrete operator library, the original perturbation variables are converted into conserved variables. The inviscid flux, viscous flux and excitation source term are solved in sequence. The flow field is updated using an explicit time-progression scheme. The conversion of conserved variables to original variables and boundary condition processing are completed. The perturbation flow field evolution data is output.

[0011] S5. Transition Feature Extraction and Verification: Extract the wall pulsation information from the disturbance flow field evolution data, use frequency domain analysis to obtain the evolution curve of pressure pulsation amplitude along the flow direction, determine the transition position by amplitude saturation feature points, and compare and verify with experimental data.

[0012] Furthermore, S1 specifically includes:

[0013] S1.1. Based on the aforementioned aircraft model, generate a multi-block structured mesh in Plot3D format and boundary conditions in Generic format;

[0014] S1.2. Input the preset incoming Mach number, unit Reynolds number, static temperature and wall thermal boundary conditions, and use the laminar flow NS equation solver to iteratively solve and obtain the basic flow original variable information.

[0015] Furthermore, S2 specifically includes:

[0016] S2.1. Input the mesh, boundary conditions, basic flow primitive variable information, and disturbance solution control parameter file;

[0017] S2.2. Generate the initial perturbation flow field. Depending on whether the perturbation flow field is a continuation calculation, choose to generate a zero-perturbation initial flow field or read in the perturbation flow field information that has been calculated previously.

[0018] S2.3. Based on the basic flow original variable information and the disturbance solution control parameter file, configure the disturbance flow excitation source term, the specific expression of which is:

[0019]

[0020] in, For fluid density, The component of the wall normal velocity. For flow direction coordinates, For the spanning coordinates, The location of the disturbance center. For time variables, To be perpendicular to - The normal coordinates of the wall of the plane. For the blowing and suction amplitude, For spatial scale parameters, For spanwise wavenumber, It is the angular frequency.

[0021] Furthermore, S3 specifically includes:

[0022] S3.1. Based on the basic flow's original variable information, calculate the basic flow's sound velocity, enthalpy, viscosity coefficient, and thermal conductivity coefficient, and store them in array form to construct the flow field attribute array, where the viscosity coefficient... and thermal conductivity The formula for calculation is:

[0023]

[0024] in, For the Mach number of the incoming flow, For unit Reynolds number, For temperature, This is Sutherland's constant. For the incoming flow to be at a constant temperature, For specific heat ratio, It is a Prandtl number;

[0025] S3.2. Based on the basic flow information and the Cronbach's alpha number (CFL) constraint, calculate the uniform time step Δt across the entire field and store it in the flow field attribute array. The calculation formula is:

[0026]

[0027] in, , , These are the spectral radii of the momentum equation, specifically expressed as:

[0028]

[0029]

[0030]

[0031] in, Let x be the inverter velocity in the x-direction. Let be the inverter velocity in the y-direction. Let be the inverter velocity in the z-direction. For the local speed of sound, , , For measurement coefficients;

[0032] S3.3. Based on the boundary conditions, assign values ​​to the physical quantities on the basic flow virtual mesh and update the flow field attribute array;

[0033] S3.4. Depending on whether the shock capture format WENO is used, complete the calculation of the grid point template weight operator and construct the pre-calculated discrete operator library;

[0034] S3.5. Based on the original variable information of the basic flow, calculate the total energy, viscosity coefficient and thermal conductivity coefficient of the disturbed flow, and add them to the flow field attribute array.

[0035] Furthermore, S4 specifically includes:

[0036] S4.1. Transform the original disturbance variables in the initial flow field into conserved variables. The expression is:

[0037]

[0038] in, For the perturbation flow density, velocity, and energy components, These are the basic flux density, velocity, and energy components.

[0039] S4.2. Solve for the inviscid flux of the perturbed flow, specifically the inviscid flux of the perturbed flow in the x, y, and z directions. , , The specific expression is:

[0040]

[0041]

[0042]

[0043] in, These are the pressures of the basic flow and the turbulent flow, respectively.

[0044] S4.3. Solve for the viscous flux of the disturbed flow, specifically the viscous flux of the disturbed flow in the x, y, and z directions. The specific expression is:

[0045]

[0046] in, and The viscosity coefficients of the basic flow and the disturbed flow are given. and These are the viscous stress terms for the basic flow and the disturbed flow, respectively. These are the linearized components of the viscous terms in the energy equation;

[0047] S4.4. Apply the disturbance flow excitation source term configured in S2;

[0048] S4.5. Update the conserved variables using an explicit time-progression format, combined with the time step;

[0049] S4.6. Based on the aforementioned boundary conditions, complete the boundary condition processing for the disturbed flow;

[0050] S4.7. Convert the updated conserved variables back to the original variables and output the perturbation flow field evolution data.

[0051] The beneficial effects of this invention are:

[0052] This invention overcomes the limitations of traditional stability analysis methods in handling complex geometric shapes and sensitivity problems by using the perturbation compressible Navier-Stokes equations in a general curvilinear coordinate system. It balances computational accuracy and efficiency, providing a reliable and high-precision prediction method for the aerodynamic design and thermal protection of hypersonic vehicles. Attached Figure Description

[0053] Figure 1 This is a flowchart of the present invention;

[0054] Figure 2 Schematic diagram of the coordinate system for calculating a straight swept wing;

[0055] Figure 3 Crossflow profiles of the basic flow at different stations;

[0056] Figure 4 wall and spanwise sections (y, z) Schematic diagram;

[0057] Figure 5 This is a graph showing the amplitude distribution of pressure pulsations on the wall. Detailed Implementation

[0058] The technical solution of the present invention will be further described below with reference to embodiments, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention. In the following embodiments, process equipment or devices not specifically specified are all conventional equipment or devices in the art. Unless specifically specified, the technical means used in the embodiments of the present invention are all conventional means well known to those skilled in the art.

[0059] Example 1, combined with Figure 1 This embodiment describes a high-precision prediction method for the boundary transition of a supersonic vehicle, comprising:

[0060] S1. Basic flow field calculation: Based on the aircraft model, generate multiple structured meshes and boundary conditions, input the incoming flow parameters and call the laminar flow solver to perform steady-state calculations, and output the basic flow original variable information;

[0061] S2. Disturbance flow parameter configuration and initialization: Import the basic flow original variable information and disturbance solution control parameters, generate a zero disturbance initial field or read historical flow field data according to whether to continue calculation, and output the initial flow field for unsteady disturbance calculation;

[0062] S3. Pre-calculation of flow field variables and discrete operators: Based on the basic flow original variable information, calculate the sound velocity, enthalpy and transport coefficient matrix, calculate the uniform time step of the whole field in combination with CFL number constraints, and pre-calculate the grid template weight operator according to the selected high-precision format, and output the pre-calculated flow field attribute array and discrete operator library.

[0063] S4. Time-progression solution of the perturbation flow: Starting from the initial flow field calculated by the unsteady perturbation, and combining the flow field attribute array and discrete operator library, the original perturbation variables are converted into conserved variables. The inviscid flux, viscous flux and excitation source term are solved in sequence. The flow field is updated using an explicit time-progression scheme. The conversion of conserved variables to original variables and boundary condition processing are completed. The perturbation flow field evolution data is output.

[0064] S5. Transition Feature Extraction and Verification: Extract the wall pulsation information from the disturbance flow field evolution data, use frequency domain analysis to obtain the evolution curve of pressure pulsation amplitude along the flow direction, determine the transition position by amplitude saturation feature points, and compare and verify with experimental data.

[0065] Furthermore, S1 specifically includes:

[0066] S1.1. Based on the aforementioned aircraft model, generate a multi-block structured mesh in Plot3D format and boundary conditions in Generic format;

[0067] S1.2. Input the preset incoming Mach number, unit Reynolds number, static temperature and wall thermal boundary conditions, and use the laminar flow NS equation solver to iteratively solve and obtain the basic flow original variable information.

[0068] Specifically, this step utilizes Pointwise to generate multiple structured meshes, outputs the multiple structured meshes in Plot3D format and boundary conditions in Generic format, and uses the ARI_Hyper solver to calculate the laminar flow field. Taking a Mach 3.0 supersonic swept airfoil as an example, the swept airfoil model is a double-circular-arc airfoil with a fixed radius of curvature, a chord length of 150 mm, and a maximum thickness of 30 mm. The incoming Mach number is 3, the sweep angle Λ = 30°, the unit Reynolds number is 30 × 10⁶ / m, the static temperature is 121.42 K, and the wall temperature is 300 K. Figure 2As shown, the basic flow and the disturbed flow are solved in the same coordinate system (x, y, z), where x is perpendicular to the leading edge, z is parallel to the leading edge, and y is perpendicular to the xz plane. Considering the wind tunnel experiment's transition point is 60 mm from the leading edge, linear stability analysis (LST) yields the most unstable transverse current wave with a spanwise wavelength of 1.5 mm. Therefore, the computational domain is x = -10 ~ 75.0 mm along the chord length and z = 0 ~ 1.5 mm along the spanwise direction. The mesh size is 1400 × 200 × 30 along the flow direction (x), the wall normal direction (y), and the spanwise direction (z).

[0069] Figure 3 Crossflow velocity profiles at stations with different flow directions (x=10, 20, 40 and 60 mm) show that the boundary layer thickness and crossflow intensity gradually increase downstream: at stations with x=10~60 mm, the boundary layer thickness increases from 0.2 mm to 0.75 mm, and the maximum crossflow velocity amplitude relative to the incoming flow increases from 1.5% to 7.5%, which can easily lead to crossflow instability.

[0070] Furthermore, S2 specifically includes:

[0071] S2.1. Input the mesh, boundary conditions, basic flow primitive variable information, and disturbance solution control parameter file;

[0072] S2.2. Generate the initial perturbation flow field. Depending on whether the perturbation flow field is a continuation calculation, choose to generate a zero-perturbation initial flow field or read in the perturbation flow field information that has been calculated previously.

[0073] S2.3. Based on the basic flow original variable information and the disturbance solution control parameter file, configure the disturbance flow excitation source term, the specific expression of which is:

[0074]

[0075] in, For fluid density, The component of the wall normal velocity. For flow direction coordinates, For the spanning coordinates, The location of the disturbance center. For time variables, To be perpendicular to - The normal coordinates of the wall of the plane. For the blowing and suction amplitude, For spatial scale parameters, For spanwise wavenumber, It is the angular frequency.

[0076] Specifically, in the simulation of the evolution of unsteady perturbation flow, a wall-blowing method was used to induce transverse flowing waves. The blowing frequency was set to 48 kHz and the spanwise wavelength to 1.5 mm. These parameters correspond perfectly to the most unstable traveling wave frequency and spanwise wavelength obtained from the linear stability theory (LST) analysis, ensuring the effective excitation of typical unstable modes. To systematically study the nonlinear saturation phenomenon of transverse flowing waves, three different blowing amplitudes (A=0.0001, A=0.001, and A=0.01) were used in the implementation for comparative simulations. The differences in the simulation results between two types of solvers, LCNS (linearized compressible perturbation Navier-Stokes equations) and NCNS (nonlinear compressible perturbation Navier-Stokes equations), were also compared.

[0077] Furthermore, S3 specifically includes:

[0078] S3.1. Based on the basic flow's original variable information, calculate the basic flow's sound velocity, enthalpy, viscosity coefficient, and thermal conductivity coefficient, and store them in array form to construct the flow field attribute array, where the viscosity coefficient... and thermal conductivity The formula for calculation is:

[0079]

[0080] in, For the Mach number of the incoming flow, For unit Reynolds number, For temperature, This is Sutherland's constant. For the incoming flow to be at a constant temperature, For specific heat ratio, It is a Prandtl number;

[0081] S3.2. Based on the basic flow information and the Cronbach's alpha number (CFL) constraint, calculate the uniform time step Δt across the entire field and store it in the flow field attribute array. The calculation formula is:

[0082]

[0083] in, , , These are the spectral radii of the momentum equation, specifically expressed as:

[0084]

[0085]

[0086]

[0087] in, Let x be the inverter velocity in the x-direction. Let be the inverter velocity in the y-direction. Let be the inverter velocity in the z-direction. For the local speed of sound, , , For measurement coefficients;

[0088] S3.3. Based on the boundary conditions, assign values ​​to the physical quantities on the basic flow virtual mesh and update the flow field attribute array;

[0089] S3.4. Depending on whether the shock capture format WENO is used, complete the calculation of the grid point template weight operator and construct the pre-calculated discrete operator library;

[0090] S3.5. Based on the original variable information of the basic flow, calculate the total energy, viscosity coefficient and thermal conductivity coefficient of the disturbed flow, and add them to the flow field attribute array.

[0091] Specifically, boundary conditions are categorized into inflow, outflow, symmetric, and wall boundary conditions. For inflow and outflow boundary conditions, the basic flow physical quantities on the virtual mesh can be directly specified as values ​​on the boundary. Wall conditions are categorized into adiabatic and isothermal wall cases. It is worth noting that the values ​​of the basic flow virtual mesh physical quantities remain unchanged during the perturbation flow calculation and do not require updating. The specific expression for the adiabatic wall temperature boundary condition is as follows:

[0092]

[0093] Where T is the temperature and n is the wall normal;

[0094] S3.4 with Directional inviscid flux derivative For example, the fifth-order WENO format expression is as follows:

[0095]

[0096] in , For half-point flux, the solution is obtained using a spatial discretization scheme. It can be divided into positive flux. and negative flux Calculation:

[0097]

[0098] The method for calculating positive flux is as follows:

[0099]

[0100] in The flux of the interpolation template is calculated as follows:

[0101]

[0102] Template weights are calculated as follows:

[0103]

[0104] in, For ideal weights, To minimize the parameter and prevent the denominator from being 0, The smoothness indicator factor for the interpolation template is calculated as follows:

[0105]

[0106] in, For the inviscid flux of the basic flow.

[0107] As can be seen from the above steps, the calculation method of the smoothness indicator factor of the interpolation template in the WENO scheme differs from that of directly solving the Navier-Stokes equations when solving the inviscid flux using the perturbation equations. In solving the perturbation equations, the template weight operator... and the smoothing indicator factor of the interpolation template Calculated using the inviscid flux of the basic flow, therefore The calculations are completed and saved before the perturbation flow simulation. In contrast, when directly solving the inviscid flux derivative of the Navier-Stokes equations using the WENO scheme... and Real-time calculation and updates are required, and perturbation equations can effectively reduce the amount of computation.

[0108] In S3.5, the energy of the disturbance flow The expression is:

[0109]

[0110] in, Specific heat ratio.

[0111] The expressions for the viscosity and thermal conductivity of the disturbed flow are:

[0112]

[0113]

[0114] Furthermore, S4 specifically includes:

[0115] S4.1. Transform the original disturbance variables in the initial flow field into conserved variables. The expression for the conserved variables is as follows:

[0116]

[0117] in For the perturbation flow density, velocity, and energy components, These are the basic flux density, velocity, and energy components.

[0118] S4.2. Solve for the inviscid flux of the perturbed flow, specifically the inviscid flux of the perturbed flow in the x, y, and z directions. , , The specific expression is:

[0119]

[0120]

[0121]

[0122] in, These are the pressures of the basic flow and the turbulent flow, respectively.

[0123] S4.3. Solve for the viscous flux of the disturbed flow, the specific expression of which is:

[0124]

[0125] in, and The viscosity coefficients of the basic flow and the disturbed flow are given. and These are the viscous stress terms for the basic flow and the disturbed flow, respectively. The linearized component of the viscous term in the energy equation is specifically expressed as follows:

[0126]

[0127]

[0128]

[0129] S4.4. Apply the disturbance flow excitation source term configured in S2;

[0130] Specifically, the disturbance is usually reflected in the wall normal momentum equation, such as the y-direction momentum equation, in the following form.

[0131]

[0132] The momentum source term function includes magnitude, spatial, and time components as follows:

[0133]

[0134] in For amplitude, They are respectively The shape of the perturbation in the direction. It is a time signal.

[0135] In the flow direction, the sinusoidal perturbation shape function in a typical case is:

[0136]

[0137] in The location of the disturbance. The slot width is for the forced term.

[0138] In the wall normal direction, i.e., the y-direction, it takes the form of a Gaussian function:

[0139]

[0140] in The location of the disturbance is in the direction normal to the wall. This represents the width of the Bell curve.

[0141] For continuous forcing forces, the following single-frequency harmonic form is adopted:

[0142]

[0143] in, It is the angular frequency. For time.

[0144] S4.5. Update the conserved variables using an explicit time-progression format, combined with the time step;

[0145] Specifically, the governing equations can be written in the following form:

[0146]

[0147] in, The right-hand side of the equation contains convection and viscous terms, and its specific expression is as follows:

[0148]

[0149] The specific expression for the Runge-Kutta time-progression scheme with the three-step, third-order TVD property is as follows:

[0150]

[0151] in, .

[0152] S4.6. Based on the aforementioned boundary conditions, complete the boundary condition processing for the disturbed flow;

[0153] Specifically, the perturbation flow supports various boundary conditions, such as inflow, outflow, symmetric, and wall boundary conditions. For inflow boundary conditions, various forms of perturbation waves can be specified, such as entropy waves, vortex waves, acoustic waves, and TS waves. For supersonic outflow boundary conditions, an extrapolation method is used, and a region near the outlet is treated as a buffer. The numerical dissipation generated by the sparse mesh of the buffer and the low-order upwind scheme suppresses the non-physical reflection of the perturbation at the outlet boundary. For inviscid flow, the wall is set as a symmetric boundary condition. For viscous flow, velocity perturbations on the wall... The pressure disturbance is 0. The normal gradient is 0:

[0154]

[0155] The calculation of density perturbation depends on the wall temperature boundary conditions. Similar to the basic flow, the temperature perturbation boundary conditions are divided into two cases: adiabatic walls and isothermal walls. Using the linearized perturbation state equation, it can be derived that for an adiabatic wall, the normal temperature gradient is zero, and the wall density perturbation... The expression is:

[0156]

[0157] in This represents the density perturbation at the first grid point near the wall. For an isothermal wall, the wall temperature perturbation is zero. The derived expression for the wall density perturbation is:

[0158]

[0159] in, The average flow wall temperature, This represents the pressure disturbance at the first grid point near the wall.

[0160] S4.7. Convert the updated conserved variables back to the original variables and output the perturbation flow field evolution data. The specific formula is as follows:

[0161]

[0162]

[0163] In S5, such as Figure 4 As shown, for the working condition A=0.001, the transient distribution contour map of the wall pressure pulsation and the cropping at different spanwise positions (x=40, 53, 64, 72mm) are presented. The cloud map shows that the pressure pulsation contour lines correspond to the vortex axis of the crossflow, and there is a certain angle between the directions of the co-current and the vortex. According to the NCNS simulation results, the crossflow vortex develops and saturates along the flow direction, resulting in a "semi-mushroom-shaped" counter-rotating crossflow vortex. However, the LCNS simulation failed to simulate the crossflow vortex saturation phenomenon, indicating that nonlinear effects play a crucial role in crossflow vortex saturation.

[0164] like Figure 5 The figure shows the distribution of wall pressure pulsation amplitude under different blowing and suction intensities. For the case A=0.001, when x<60mm, the pressure pulsation amplitude near the blowing and suction channel oscillates violently, then enters a linear growth stage. The LCNS, NCNS, and PSE simulation results are consistent. When x>60mm, the LCNS and PSE simulation results maintain linear growth, while the NCNS gradually saturates. This is mainly because the LCNS and PSE failed to consider the nonlinear factors that appear after the disturbance amplitude becomes large. It is worth noting that the wind tunnel experiment observed the transition starting position at x=60mm, which is consistent with the position where the LCNS and NCNS simulation results show differences. For the case A=0.0001, the amplitude of the induced disturbance flow is small, and the LCNS and NCNS simulation results are completely consistent. Moreover, the trend is the same as the LCNS simulation results under the case A=0.001, indicating that there is no nonlinear effect in the evolution of the disturbance flow under this case. For the case A=0.01, the nonlinear effect is very strong, and the saturation point of the pressure pulsation amplitude simulated by NCNS is significantly advanced (x=45mm), and the downstream experiences a long saturation stage. The numerical simulation results are highly consistent with the wind tunnel experimental data, indicating that this method can be applied to the efficient and accurate simulation of the evolution of unstable waves in high Mach number boundary layers.

[0165] Although the invention has been described with reference to a limited number of embodiments, those skilled in the art will understand from the foregoing description that other embodiments are conceivable within the scope of the invention described herein. Furthermore, it should be noted that the language used in this specification has been chosen primarily for readability and instructional purposes, and not for the purpose of interpreting or limiting the subject matter of the invention. Therefore, many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the appended claims. The disclosure of the invention is illustrative and not restrictive, and the scope of the invention is defined by the appended claims.

Claims

1. A high-precision prediction method for boundary layer transition of a supersonic vehicle, characterized in that, include: S1. Basic flow field calculation: Based on the aircraft model, generate multiple structured meshes and boundary conditions, input the incoming flow parameters and call the laminar flow solver to perform steady-state calculations, and output the basic flow original variable information; S2. Disturbance flow parameter configuration and initialization: Import the basic flow original variable information and disturbance solution control parameters, generate a zero disturbance initial field or read historical flow field data according to whether to continue calculation, and output the initial flow field for unsteady disturbance calculation; S3. Pre-calculation of flow field variables and discrete operators: Based on the basic flow original variable information, calculate the sound velocity, enthalpy and transport coefficient matrix, calculate the uniform time step of the whole field in combination with CFL number constraints, and pre-calculate the grid template weight operator according to the selected high-precision format, and output the pre-calculated flow field attribute array and discrete operator library. S4. Time-progression solution of the perturbation flow: Starting from the initial flow field calculated by the unsteady perturbation, and combining the flow field attribute array and discrete operator library, the original perturbation variables are converted into conserved variables. The inviscid flux, viscous flux and excitation source term are solved in sequence. The flow field is updated using an explicit time-progression scheme. The conversion of conserved variables to original variables and boundary condition processing are completed. The perturbation flow field evolution data is output. S5. Transition Feature Extraction and Verification: Extract the wall pulsation information from the disturbance flow field evolution data, use frequency domain analysis to obtain the evolution curve of pressure pulsation amplitude along the flow direction, determine the transition position by amplitude saturation feature points, and compare and verify with experimental data.

2. The high-precision prediction method for the boundary transition of a supersonic vehicle according to claim 1, characterized in that, S1 specifically includes: S1.

1. Based on the aforementioned aircraft model, generate a multi-block structured mesh in Plot3D format and boundary conditions in Generic format; S1.

2. Input the preset incoming Mach number, unit Reynolds number, static temperature and wall thermal boundary conditions, and use the laminar flow NS equation solver to iteratively solve and obtain the basic flow original variable information.

3. The high-precision prediction method for the boundary transition of a supersonic vehicle according to claim 1, characterized in that, S2 specifically includes: S2.

1. Input the mesh, boundary conditions, basic flow primitive variable information, and disturbance solution control parameter file; S2.

2. Generate the initial perturbation flow field. Depending on whether the perturbation flow field is a continuation calculation, choose to generate a zero-perturbation initial flow field or read in the perturbation flow field information that has been calculated previously. S2.

3. Based on the basic flow original variable information and the disturbance solution control parameter file, configure the disturbance flow excitation source term, the specific expression of which is: in, For fluid density, The component of the wall normal velocity. For flow direction coordinates, For the spanning coordinates, The location of the disturbance center. For time variables, To be perpendicular to - The normal coordinates of the wall of the plane. For the blowing and suction amplitude, For spatial scale parameters, For spanwise wavenumber, It is the angular frequency.

4. The high-precision prediction method for the boundary transition of a supersonic vehicle according to claim 1, characterized in that, S3 specifically includes: S3.

1. Based on the basic flow's original variable information, calculate the basic flow's sound velocity, enthalpy, viscosity coefficient, and thermal conductivity coefficient, and store them in array form to construct the flow field attribute array, where the viscosity coefficient... and thermal conductivity The formula for calculation is: in, For the Mach number of the incoming flow, For unit Reynolds number, For temperature, This is Sutherland's constant. For the incoming flow to be at a constant temperature, For specific heat ratio, It is a Prandtl number; S3.

2. Based on the basic flow information and the Cronbach's alpha number (CFL) constraint, calculate the uniform time step Δt across the entire field and store it in the flow field attribute array. The calculation formula is: in, , , These are the spectral radii of the momentum equation, specifically expressed as: in, Let x be the inverter velocity in the x-direction. Let be the inverter velocity in the y-direction. Let be the inverter velocity in the z-direction. For the local speed of sound, , , For measurement coefficients; S3.

3. Based on the boundary conditions, assign values ​​to the physical quantities on the basic flow virtual mesh and update the flow field attribute array; S3.

4. Depending on whether the shock capture format WENO is used, complete the calculation of the grid point template weight operator and construct the pre-calculated discrete operator library; S3.

5. Based on the original variable information of the basic flow, calculate the total energy, viscosity coefficient and thermal conductivity of the disturbed flow, and add them to the flow field attribute array.

5. The high-precision prediction method for the boundary transition of a supersonic vehicle according to claim 1, characterized in that, S4 specifically includes: S4.

1. Transform the original disturbance variables in the initial flow field into conserved variables. The expression is: in, For the perturbation flow density, velocity, and energy components, These are the basic flux density, velocity, and energy components. S4.

2. Solve for the inviscid flux of the perturbed flow, specifically the inviscid flux of the perturbed flow in the x, y, and z directions. , , The specific expression is: in, These are the pressures of the basic flow and the turbulent flow, respectively. S4.

3. Solve for the viscous flux of the disturbed flow, specifically the viscous flux of the disturbed flow in the x, y, and z directions. The specific expression is: in, and The viscosity coefficients of the basic flow and the disturbed flow are given. and These are the viscous stress terms for the basic flow and the disturbed flow, respectively. These are the linearized components of the viscous terms in the energy equation; S4.

4. Apply the disturbance flow excitation source term configured in S2; S4.

5. Update the conserved variables using an explicit time-progression format, combined with the time step; S4.

6. Based on the aforementioned boundary conditions, complete the boundary condition processing for the disturbed flow; S4.

7. Convert the updated conserved variables back to the original variables and output the perturbation flow field evolution data.

Images