Hypersonic boundary layer transition prediction method based on numerical solution of frequency domain NS equation

Abstract

This invention belongs to the field of hypersonic aerodynamics and discloses a method for predicting hypersonic boundary layer transition based on the numerical solution of the frequency domain Navier-Stokes equations. This method, through the assumption of small perturbations, linearly decomposes the hypersonic flow field into a steady flow field and a perturbed flow field. It eliminates the time differential terms in the time-domain Navier-Stokes equations using complex decomposition, transforming the time-domain Navier-Stokes equations into linear algebraic equations in complex space, thereby simplifying the solution and analysis of the time-domain Navier-Stokes equations. Specifically, it includes three stages: preprocessing, solver, and post-processing. The iterative solution of the frequency-domain Navier-Stokes equations in the solver is the core, including spatial discretization of the frequency-domain Navier-Stokes equations, iterative progression, implementation of boundary conditions, parallel data exchange, convergence judgment, and result output. The hypersonic boundary layer transition prediction method based on the numerical solution of the frequency-domain Navier-Stokes equations of this invention can balance computational efficiency and accuracy, and has practical engineering value.

Description

Technical Field

[0001] This invention belongs to the field of hypersonic aerodynamics, specifically relating to a method for predicting hypersonic boundary layer transition based on numerical solutions of the frequency domain Navier-Stokes equations. Background Technology

[0002] Hypersonic vehicles are prone to undergoing a transition process in the boundary layer, where laminar flow transitions into turbulent flow. This transition has a significant impact on the aerodynamics and thermal loads of the vehicle. Laminar and turbulent flow differ significantly in terms of frictional drag, heat exchange, noise, and mixing. The transition can cause the peak heat flux to be more than five times that of the laminar state, and it also leads to a sharp increase in surface frictional drag. This is one of the fundamental scientific problems restricting breakthroughs in hypersonic technology.

[0003] For hypersonic boundary layer transition problems, wind tunnel testing is an important tool for transition research. However, conventional wind tunnel test sections contain varying degrees of flow field noise, and the obtained hypersonic boundary layer development process and final transition location differ significantly from actual flight conditions. Furthermore, conventional wind tunnel tests cannot simultaneously reproduce key parameters such as total temperature, total pressure, and wall temperature ratio in hypersonic flight. Therefore, the reliability of boundary layer transition-related experimental data obtained from conventional wind tunnel tests is greatly reduced.

[0004] Given the complexity of the hypersonic boundary layer transition problem, researchers have developed various numerical methods to predict it. Among these, empirical correlation methods typically establish simple relationships between the transition and macroscopic physical quantities within the boundary layer. However, the resulting empirical expressions suffer from high uncertainty in their physical basis, lack universality, and are severely affected by a lack of experimental data. Prediction methods based on Reynolds-averaged Navier-Stokes (RANS) equations and transition models also exhibit uncertainties in predicting hypersonic boundary layer transition, with predictions heavily dependent on empirical parameters in the transition model. Direct numerical simulation (DNS) and large eddy simulation (LES) can cover all physical processes to the greatest extent possible, but their computational cost is enormous, currently limiting them to solving low Reynolds number problems. Prediction methods based on stability theory achieve a trade-off between computational efficiency and prediction accuracy, and are currently the mainstream methods for predicting transition locations. However, they still suffer from significant computational errors for complex two-dimensional or three-dimensional shapes.

[0005] Currently, there is an urgent need to develop a method for predicting hypersonic boundary layer transition based on the numerical solution of the frequency domain Navier-Stokes equations. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for predicting hypersonic boundary layer transition based on the numerical solution of the frequency domain Navier-Stokes equations, so as to overcome the defects of the prior art.

[0007] The hypersonic boundary layer transition prediction method based on the numerical solution of the frequency domain Navier-Stokes equations of the present invention includes the following: S10. Establish the frequency domain Navier-Stokes equations; S20. Establish a numerical solution approach for the frequency domain Navier-Stokes equations; S30. Perform numerical solutions to the Navier-Stokes equations in the frequency domain; S40. Perform iterative solution of the Navier-Stokes equations in the frequency domain.

[0008] Furthermore, the frequency domain Navier-Stokes equation for S10 is as follows: ; In the formula: — Specific heat capacity of fluid at constant pressure, J / (kg•K); — Fluid thermal conductivity, W / (m•K); — Externally applied force, in N; — Externally applied heat, J; — Surface stress, Pa; — The work done by surface viscous forces on a fluid, in W; — Fluid velocity, m / s; — Fluid pressure, Pa; — Fluid temperature, K; — Fluid density, kg / m³ 3 ; — Gradient operator; — Subscript indicates the average quantity of a hypersonic steady flow field; — Superscript indicates the disturbance quantity corresponding to the average quantity of the hypersonic steady flow field; in, ; For operators, , , For the corresponding periodically changing physical quantity; In the frequency domain NS equations, the complex number solution method is used to eliminate the time differential terms in the time domain NS equations, transforming the frequency domain NS equations into linear algebraic equations in complex space, thus simplifying the solution and analysis of the frequency domain NS equations.

[0009] Furthermore, S20 includes the following steps: S21. Perform hypersonic steady flow field calculations; Using the continuity equation (1), momentum equation (2), and energy equation (3), considering only laminar flow, and with the model wall conditions being no-slip and adiabatic, the hypersonic steady flow field information, including the average velocity, was calculated. Mean pressure Average temperature and average density wait; S22. Perform hypersonic perturbation flow field calculations; Numerical solutions to the Navier-Stokes equations in the frequency domain were used. The model wall conditions were no-slip and adiabatic. To simulate the development of disturbances within the hypersonic boundary layer, plane wave disturbances of different frequencies were applied at the inlet, and the far field was a non-reflective boundary. The disturbance flow field information, including the disturbance velocity, was calculated. Disturbance pressure Disturbance temperature and perturbation density After the calculation is completed, the calculation results can be analyzed and compared using commonly used computational fluid dynamics post-processing software.

[0010] Furthermore, S30 includes the following steps: S31. Pre-processing stage; The computational domain is defined, the computational grid is generated and imported, the hypersonic inflow parameters are set and the steady flow field calculation is completed. The preprocessing stage uses a structured grid that supports single and multiple blocks. S32. Solver stage; The process includes two main steps: computation setup and equation solving. In the computation setup, the computational dimensions, continuation calculations, filtering, iteration parameters, and boundary conditions are set. In the equation solving module, the equation system is established and solved using a high-order spatial discretization scheme and frequency domain equation iterative solution. Data exchange and computational convergence judgment are also performed. In the post-processing stage, the results are output and analyzed. Visualization tools are used to analyze residual convergence curves, flow variable cloud maps, and aerodynamic characteristic data to verify the flow field results and study the flow characteristics.

[0011] Furthermore, S40 includes the following steps: The frequency domain NS equation iterative solution is used to solve the master frequency domain NS equation, including spatial discretization of the master frequency domain NS equation, iterative progress, boundary condition implementation, parallel data exchange, convergence judgment, and result output; the specific steps include reading in the boundary condition, adding the sound source, calculating the spatial derivative spatialDiff, calculating the flux and flux viscousFlux, calculating the gradient, calculating the divergence, exchanging data between different CPUs exchSol, and filtering the data.

[0012] The hypersonic boundary layer transition prediction method based on the frequency-domain Navier-Stokes equations of this invention uses the small perturbation assumption to linearly decompose the hypersonic flow field into a steady flow field and a perturbed flow field. It eliminates the time differential terms in the time-domain Navier-Stokes equations through complex decomposition, transforming the time-domain Navier-Stokes equations into linear algebraic equations in complex space, thereby simplifying the solution and analysis of the time-domain Navier-Stokes equations. Specifically, it includes three stages: preprocessing, solver, and post-processing. The iterative solution of the frequency-domain Navier-Stokes equations in the solver is the core, including spatial discretization of the frequency-domain Navier-Stokes equations, iterative progression, implementation of boundary conditions, parallel data exchange, convergence judgment, and result output.

[0013] The hypersonic boundary layer transition prediction method based on the frequency domain Navier-Stokes equations of the present invention has the following characteristics: 1. High computational efficiency; it can directly calculate the frequency components of periodic signals, avoiding the problem of long-term simulation required in time-domain methods; 2. High frequency resolution; it can clearly display the strength and distribution of each frequency component in the signal, making it suitable for analyzing the frequency characteristics of periodic flows; 3. Simplified computation: For linear or weakly nonlinear problems, linearization can greatly simplify the computation, avoiding the need for time-domain methods to deal with complex nonlinear equations.

[0014] The hypersonic boundary layer transition prediction method based on frequency domain Navier-Stokes equations linearizes periodic perturbation flows and solves them in the frequency domain. By directly extracting the frequency components of periodic signals, it simplifies the solution process for complex flow problems, balances computational efficiency and accuracy, and achieves efficient prediction of linear evolution in hypersonic boundary layer transition processes, thus possessing practical engineering value. Attached Figure Description

[0015] Figure 1 This is a schematic diagram illustrating the numerical solution process for the frequency domain Navier-Stokes equations in this invention. Figure 2 This is a flowchart of the numerical solution process for the frequency domain Navier-Stokes equations in this invention. Figure 3 This is a flowchart of the iterative solution of the frequency domain Navier-Stokes equations in this invention; Figure 4 A schematic diagram illustrating the boundary conditions for the perturbation flow field in the example of a flat plate. Figure 5 The calculation results of disturbance pressure at different frequencies on the outer wall surface of the flat plate in the example are shown. Figure 6 The numerical solution of the frequency domain Navier-Stokes equations obtained in the example is compared with the results of different calculation methods. Detailed Implementation

[0016] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0017] The hypersonic boundary layer transition prediction method based on the numerical solution of the frequency domain Navier-Stokes equations of the present invention includes the following: S10. Establish the frequency domain Navier-Stokes equations; S20. Establish a numerical solution approach for the frequency domain Navier-Stokes equations; S30. Perform numerical solutions to the Navier-Stokes equations in the frequency domain; S40. Perform iterative solution of the Navier-Stokes equations in the frequency domain.

[0018] Furthermore, the derivation process of the frequency domain NS equation for S10 is as follows: Hypersonic flow follows three fundamental physical laws: the law of conservation of mass, the law of conservation of momentum, and the law of conservation of energy, which correspond to the continuity equation (1), the momentum equation (2), and the energy equation (3), respectively. These three equations, together with the gas law, constitute the Navier-Stokes equations: ; In the formula: — Specific heat capacity of fluid at constant pressure, J / (kg•K); — Fluid thermal conductivity, W / (m•K); — Time, s; — Externally applied force, in N; — Externally applied heat, J; — Surface stress, Pa; — The work done by surface viscous forces on a fluid, in W; — Fluid velocity, m / s; — Fluid pressure, Pa; — Fluid temperature, K; — Fluid density, kg / m³ 3 ; — Gradient operator; The constitutive equation in the above formula is: ; In the formula: — Identity matrix; — Dynamic viscosity and volume viscosity, Pa∙s; — Bulk viscosity coefficient, Pa∙s; To analyze the effect of small external disturbances on the hypersonic flow field, the hypersonic flow field is decomposed into a steady-state flow field and a small-disturbance flow field, with the source term also decomposed accordingly: ; In the formula: — Subscript indicates the average quantity of a hypersonic steady flow field; — Superscript indicates the disturbance quantity corresponding to the average quantity of the hypersonic steady flow field; Substituting equation (6) into the continuity equation (1), momentum equation (2), and energy equation (3), respectively, subtracting the steady-state flow field equation, and neglecting the higher-order terms of the disturbance, we obtain the time-domain linear Navier-Stokes equations: ; The constitutive equation in the above formula is: ; The propagation of disturbances in hypersonic flow fields has wave-like characteristics. Therefore, performing linear Navier-Stokes equations in the frequency domain has significant advantages. On the one hand, the physical meaning will be clearer, and on the other hand, the subsequent numerical calculations can be significantly reduced. With the help of The operator enables the conversion between the time domain and the frequency domain; It has the following characteristics: , , Let be the corresponding periodically changing physical quantity; when the disturbance in the hypersonic flow field undergoes simple harmonic oscillation, the disturbance field and source term are written in the following form: ; Substituting equation (9) into the continuity equation (1), momentum equation (2), and energy equation (3) respectively, and subtracting the steady-state flow field equation, we can cancel out... After neglecting the higher-order terms of the perturbation, the frequency-domain linear Navier-Stokes equations can be obtained: ; It can be seen that in the frequency domain NS equation (10), the time differential term in the time domain NS equation (7) is eliminated by using the complex number solution method, and the frequency domain NS equation (10) is transformed into a linear algebraic equation in the complex space, which simplifies the solution and analysis of the frequency domain NS equation (10).

[0019] Furthermore, such as Figure 1 As shown, S20 includes the following steps: S21. Perform hypersonic steady flow field calculations; Using the continuity equation (1), momentum equation (2), and energy equation (3), considering only laminar flow, and with the model wall conditions being no-slip and adiabatic, the hypersonic steady flow field information, including the average velocity, was calculated. Mean pressure Average temperature and average density wait; S22. Perform hypersonic perturbation flow field calculations; Numerical solutions to the Navier-Stokes equations in the frequency domain were used. The model wall conditions were no-slip and adiabatic. To simulate the development of disturbances within the hypersonic boundary layer, plane wave disturbances of different frequencies were applied at the inlet, and the far field was a non-reflective boundary. The disturbance flow field information, including the disturbance velocity, was calculated. Disturbance pressure Disturbance temperature and perturbation density After the calculation is completed, the calculation results can be analyzed and compared using commonly used computational fluid dynamics post-processing software.

[0020] Furthermore, such as Figure 2 As shown, S30 includes the following steps: S31. Pre-processing stage; The computational domain is defined, the computational grid is generated and read in, the hypersonic incoming flow parameters are set and the steady flow field calculation is completed. Since the numerical solution of the frequency domain Navier-Stokes equations is computationally intensive, a structured grid that supports single and multiple blocks is adopted in the preprocessing stage to improve the efficiency of parallel computing. S32. Solver stage; The process includes two main steps: computation setup and equation solving. In the computation setup, the computational dimensions, continuation calculations, filtering, iteration parameters, and boundary conditions are set. In the equation solving module, the equation system is established and solved using a high-order spatial discretization scheme and frequency domain equation iterative solution. Data exchange and computational convergence judgment are also performed. In the post-processing stage, the results are output and analyzed. Visualization tools are used to analyze residual convergence curves, flow variable cloud maps, and aerodynamic characteristic data to verify the flow field results and study the flow characteristics.

[0021] Furthermore, such as Figure 3 As shown, S40 includes the following steps: The frequency domain NS equation iterative solution is used to solve the master frequency domain NS equation, including spatial discretization of the master frequency domain NS equation, iterative progress, boundary condition implementation, parallel data exchange, convergence judgment, and result output; the specific steps include reading in the boundary condition, adding the sound source, calculating the spatial derivative spatialDiff, calculating the flux and flux viscousFlux, calculating the gradient, calculating the divergence, exchanging data between different CPUs exchSol, and filtering the data.

[0022] Example: This example uses a two-dimensional hypersonic flat plate as an example to illustrate how to carry out hypersonic boundary layer transition prediction based on the numerical solution of the frequency domain Navier-Stokes equations.

[0023] The flat plate has an external length of 1100mm, and the free flow velocity, temperature and pressure are 705.093m / s, 61.111K and 646.3Pa, respectively. The corresponding sound velocity is 156.7m / s and the Mach number is 4.5. The surface of the flat plate is a non-slip insulating wall.

[0024] Figure 4 A schematic diagram showing the boundary conditions for the perturbation flow field of the flat plate is provided. The computational domain is set to [-250 ~ 1350mm] × 500mm. To ensure that the leading edge corners of the flat plate are easily handled, [the following is omitted]. x = [-250 ~ 0mm] and x = [1100 ~ 1200mm] is set as the symmetrical boundary. x = [0 ~ 1100mm] is set as a solid wall condition. The left boundary is the acoustic disturbance inlet, and the acoustic amplitude is set to free flow pressure / 1000, i.e., 0.646Pa. The right region... x = [1200 ~ 1350mm] is the perturbation wave adsorption layer, and the upper boundary is the external field non-reflection boundary. The computational domain grid is 1500×150, and 1100 points are distributed on the flat plate wall. The grid spacing of the first layer in the wall normal is 0.005mm.

[0025] Figure 5 The results show the calculated disturbance pressure at different frequencies along the flat plate wall. As the flow progresses downstream, the amplitude of the disturbance pressure gradually increases, and due to the increase in boundary layer thickness, the frequency of the peak disturbance pressure gradually decreases. The disturbance pressure amplitude increases most rapidly at the 70kHz frequency. x Growth begins at approximately 800mm, and... x The amplitude reaches its peak at approximately 1000mm.

[0026] Figure 6 This paper compares the results of numerical solutions to the Navier-Stokes equations in the frequency domain with those of different calculation methods. The frictional resistance calculation in the numerical solution of the Navier-Stokes equations in the frequency domain considers the perturbation growth at a frequency of 70 kHz. Figure 6 The paper also presents direct numerical simulation (DNS), laminar flow models, and turbulent flow models. The calculation results show that the frictional resistance obtained by this invention is generally consistent with the DNS results, although the transition position is slightly later.

[0027] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. For those skilled in the art, all features disclosed in the present invention, or all steps in all methods or processes disclosed, except for mutually exclusive features and / or steps, can be combined in any way without departing from the principles of the present invention. The present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method for predicting hypersonic boundary layer transition based on numerical solution of the frequency domain Navier-Stokes equations, characterized in that, The prediction method includes the following: S10. Establish the frequency domain Navier-Stokes equations; S20. Establish a numerical solution approach for the frequency domain Navier-Stokes equations; S30. Perform numerical solutions to the Navier-Stokes equations in the frequency domain; S40. Perform iterative solution of the Navier-Stokes equations in the frequency domain.

2. The hypersonic boundary layer transition prediction method based on numerical solution of the frequency domain Navier-Stokes equations according to claim 1, characterized in that, The frequency domain Navier-Stokes equation for S10 is as follows: ； In the formula: — Specific heat capacity of fluid at constant pressure, J / (kg•K); — Fluid thermal conductivity, W / (m•K); — Externally applied force, in N; — Externally applied heat, J; — Surface stress, Pa; — The work done by surface viscous forces on a fluid, in W; — Fluid velocity, m / s; — Fluid pressure, Pa; — Fluid temperature, K; — Fluid density, kg / m³ 3 ; — Gradient operator; — Subscript indicates the average quantity of a hypersonic steady flow field; — Superscript indicates the disturbance quantity corresponding to the average quantity of the hypersonic steady flow field; in, ; For operators, , , For the corresponding periodically changing physical quantity; In the frequency domain NS equations, the complex number solution method is used to eliminate the time differential terms in the time domain NS equations, transforming the frequency domain NS equations into linear algebraic equations in complex space, thus simplifying the solution and analysis of the frequency domain NS equations.

3. The hypersonic boundary layer transition prediction method based on numerical solution of the frequency domain Navier-Stokes equations according to claim 2, characterized in that, S20 includes the following steps: S21. Perform hypersonic steady flow field calculations; Using the continuity equation (1), momentum equation (2), and energy equation (3), considering only laminar flow, and with the model wall conditions being no-slip and adiabatic, the hypersonic steady flow field information, including the average velocity, was calculated. Mean pressure Average temperature and average density wait; S22. Perform hypersonic perturbation flow field calculations; Numerical solutions to the Navier-Stokes equations in the frequency domain were used. The model wall conditions were no-slip and adiabatic. To simulate the development of disturbances within the hypersonic boundary layer, plane wave disturbances of different frequencies were applied at the inlet, and the far field was a non-reflective boundary. The disturbance flow field information, including the disturbance velocity, was calculated. Disturbance pressure Disturbance temperature and perturbation density After the calculation is completed, the calculation results can be analyzed and compared using commonly used computational fluid dynamics post-processing software.

4. The hypersonic boundary layer transition prediction method based on numerical solution of the frequency domain Navier-Stokes equations according to claim 3, characterized in that, S30 includes the following steps: S31. Pre-processing stage; The computational domain is defined, the computational grid is generated and imported, the hypersonic inflow parameters are set and the steady flow field calculation is completed. The preprocessing stage uses a structured grid that supports single and multiple blocks. S32. Solver stage; The process includes two main steps: computation setup and equation solving. In the computation setup, the computational dimensions, continuation calculations, filtering, iteration parameters, and boundary conditions are set. In the equation solving module, the equation system is established and solved using a high-order spatial discretization scheme and frequency domain equation iterative solution. Data exchange and computational convergence judgment are also performed. In the post-processing stage, the results are output and analyzed. Visualization tools are used to analyze residual convergence curves, flow variable cloud maps, and aerodynamic characteristic data to verify the flow field results and study the flow characteristics.

5. The hypersonic boundary layer transition prediction method based on numerical solution of the frequency domain Navier-Stokes equations according to claim 4, characterized in that, S40 includes the following steps: The frequency domain NS equation iterative solution is used to solve the master frequency domain NS equation, including spatial discretization of the master frequency domain NS equation, iterative progress, boundary condition implementation, parallel data exchange, convergence judgment, and result output; the specific steps include reading in the boundary condition, adding the sound source, calculating the spatial derivative spatialDiff, calculating the flux and flux viscousFlux, calculating the gradient, calculating the divergence, exchanging data between different CPUs exchSol, and filtering the data.

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