A high-speed boundary layer transition prediction method capable of predicting heat flow overshoot phenomenon

Abstract

This invention belongs to the fields of aerospace and computational fluid dynamics, specifically a high-speed boundary layer transition prediction method for predicting thermal overshoot. This method corrects the time-scale control coefficients of the second mode characteristic of the transition mode, constructs an overshoot correction factor by combining the turbulent Mach number and the boundary layer edge Mach number, introduces a transition constraint factor and a new near-wall constraint factor to ensure that the correction only applies to the transition development region, and couples the overshoot correction factor with the intermittent factor transport equation in the form of a source term to achieve simulation and prediction of overshoot phenomena in the high-speed boundary layer. Verified by high-speed flat plate and conical examples, this invention can accurately reproduce the overshoot peak value and spatial distribution, and the prediction results agree well with experimental data without affecting the accuracy of transition position and length prediction. It can provide a reliable analytical tool for the thermal protection design and aerodynamic optimization of next-generation high-speed aircraft.

Description

Technical Field

[0001] This invention belongs to the field of computational fluid dynamics, specifically relating to a method for predicting high-speed boundary layer transition phenomena that can predict thermal overshoot. Background Technology

[0002] The transition from laminar to turbulent flow in the boundary layer directly affects the surface friction drag, heat flux distribution, and aerodynamic stability of an aircraft. This makes transition prediction a crucial aspect of aircraft thermal protection system design and aerodynamic shape optimization. Among transition prediction methods, RANS-based prediction methods, which combine computational efficiency and accuracy while significantly saving manpower, material resources, and financial resources, remain the most commonly used methods in engineering applications. RANS-based transition models can be divided into two main categories: those based on empirical relationships and those based on physical mechanisms.

[0003] The most representative transition model based on empirical relationships is proposed by Menter and Langtry et al. The transition model, mathematically represented by the standard scalar transport equations, is fully compatible with modern CFD solution frameworks. However, the initial... Transition modes are based on incompressible flows. Although many scholars have made compressible modifications and improvements to them, in fact, the ultra / high-speed transition mechanism is very different from that of incompressible flows. Simply making numerical modifications to the incompressible transition mode will cause the transition mode to lose some of the physical meaning behind the transition phenomena, and it will also be difficult to have good universality.

[0004] The core concept of physics-based models is to model non-turbulent (i.e., laminar) fluctuations before and during the transition. One of the most representative types is the transition prediction model based on the kinetic energy of laminar fluctuations. Laminar kinetic models use laminar kinetic energy as an independent variable to represent the non-turbulent fluctuations. To represent this. Mayle and Schulz first proposed a method to characterize the fluctuations in flow velocity before the transition. Transport equations were proposed by Walters and Leylek, and Walters and Cokljat. Transition pattern, which is achieved by... Equations merged into existing ones and In turbulent flow, an additional source term is used to establish the model. This model has strong predictive ability for bypass transition, but its predictive ability for natural transition and separated bubble transition needs further research and improvement. Qin et al. improved the model for supersonic wall heat transfer. Transition patterns: Liu et al. extended the pattern to predictable distributed rough element-dominated transitions.

[0005] The applicant's prior research, based on the RANS framework, constructed a system compatible with modern CFD massively parallel computing. The transition model, including the evolution and instability of disturbances, is primarily modeled based on Mack's stability analysis of high-speed boundary layers. A laminar pulsating viscosity coefficient transport equation is constructed, and the transition process is described by the intermittent factor equation. The turbulent part is calculated using the compressible modified SST classical turbulence model. Extensive numerical examples validate that this model can effectively simulate boundary layer transition processes under different transition mechanisms, demonstrating good accuracy. Qiao Lei et al. further developed this model by considering the three-dimensional high-speed boundary layer crossflow effect. The pattern makes this The model is better able to predict boundary layer crossflow transition.

[0006] However, during high-speed boundary layer transition, overshoot, as an important flow characteristic, manifests as a transient, localized increase in the friction coefficient or thermal flux coefficient of the inner wall in the transition region. This phenomenon can severely impact the thermal protection design, stability, and flight safety of aircraft. However, currently... The intermittent factor transport equations of transition prediction models lack the intrinsic ability to characterize overshoot phenomena, resulting in significant shortcomings in accurately capturing the amplitude and morphology of overshoot within the transition region. Current models cannot reproduce the physical peaks caused by the intermittent, strongly nonlinear growth of laminar-turbulent flow during transition development, leading to biases in the prediction of local heat flux and frictional drag, and consequently affecting the comprehensive assessment of aircraft aerodynamic performance. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention proposes a high-speed boundary layer transition prediction method that can predict thermal overshoot. This method constructs an overshoot correction factor related to the flow state based on the correlation between the critical turbulent Mach number and the boundary layer edge Mach number, and then modifies this factor with… The intermittent factor transport equations of the transition mode are coupled to control the evolution of the intermittent factor in the overshoot region without affecting the prediction of the transition location and the fully turbulent region, thus introducing the physical basis for simulating the overshoot effect into the model. To ensure the overall consistency of the model predictions, the relevant model coefficients are simultaneously recalibrated. The improved model can effectively reproduce the overshoot peak value caused by the laminar-turbulent nonlinear development in the transition region in several typical high-speed boundary layer examples. The predicted friction and heat flux distributions are in good agreement with direct numerical simulation and wind tunnel test data. This invention provides a more reliable tool for the refined prediction of surface heat flux and friction of aircraft, and has clear engineering guiding significance for the aerodynamic thermal environment assessment and thermal protection design of high-speed aircraft.

[0008] The technical solution of this invention is:

[0009] A method for predicting high-speed boundary layer transition phenomena that can predict thermal overshoot includes the following steps:

[0010] S1: By solving the compressible Falkner-Skan-Cooke equation, a database of compressible three-dimensional boundary layer characteristic parameters is established to obtain the relationship between local and non-local variables within the desired boundary layer;

[0011] S2: A compressible 3D boundary layer feature parameter database established based on S1, localizing non-local variables and controlling the feature time scale coefficients of the second mode. Modifications were made to obtain entirely new feature time-scale control coefficients. This enables the second mode in the dominant transition mode to predict both the length of the transition region and the heat flow overshoot phenomenon. Based on the modified second mode, laminar pulsating viscosity coefficient transport equation and intermittent factor transport equation are established.

[0012] S3: Based on the turbulent Mach number within the boundary layer Mach number at the boundary layer edge Construct an overshoot correction factor that reflects the overshoot intensity. and in overshoot correction factor Introducing a transition restriction factor With the new near-wall region restriction factor Ensure overshoot correction factor It is only effective in the transition development zone and does not affect the prediction of the laminar and fully turbulent zones;

[0013] S4: The overshoot correction factor constructed in step S3 The source term is generated in the intermittent factor transport equation established in step S2. By coupling the two, an improved source term is obtained. This leads to the acquisition of a new intermittent factor transport equation;

[0014] S5: Couple the laminar pulsating viscosity coefficient transport equation established in S2 and the new intermittent factor transport equation coupled with the overshoot correction factor in S4 with the SST turbulence model to establish... A four-equation turbulence-transition model is constructed and embedded into an existing CFD solver capable of large-scale parallel computation; the CFD solver is then used to predict the laminar-turbulent transition of high-speed aircraft.

[0015] Furthermore, in step S2, the characteristic time scale control coefficients of the second mode are... The specific formula to be modified is as follows:

[0016]

[0017] In the formula, For the original The characteristic time-scale control coefficients of the second mode in the model. For free-flow turbulence, These are the revised characteristic time scale control coefficients; where, For the specific calculation method, please refer to the invention patent "A transition prediction method applicable to the wide Mach range of high-speed aircraft" with publication number CN121145697A.

[0018] Furthermore, in step S3, the overshoot correction factor is constructed. The formula is as follows:

[0019]

[0020] In the formula, As a transition limiting factor, It is a constant. For turbulent Mach number, This is the overshoot correction criterion. Furthermore, the expression for the overshoot correction criterion is as follows:

[0021]

[0022] In the formula, It is a constant, a constant The scores are 16.0, 80.0, and 7.00 respectively. It is the critical turbulent Mach number.

[0023] Furthermore, the turbulent Mach number within the boundary layer Calculated using turbulent kinetic energy and local sound speed:

[0024]

[0025] In the formula, For turbulent kinetic energy, The speed of sound in the local area.

[0026] Furthermore, the critical turbulent Mach number For the Mach number at the boundary layer edge Functions:

[0027] .

[0028] Furthermore, the Mach number at the boundary layer edge It is obtained by calculating using the following expression:

[0029]

[0030]

[0031]

[0032] In the formula, constant , The boundary layer edge flow velocity, For the free flow velocity, The speed of sound at the edge of the boundary layer. For the speed of free flow, For local pressure, For free flow pressure, For free flow density.

[0033] Furthermore, transition limiting factor The expression for the overshoot correction used to prevent the influence of overshoot on the transition position is as follows:

[0034]

[0035] In the formula, The viscosity ratio is , where For turbulent kinetic energy, For specific dissipation rate, It is the molecular viscosity coefficient; The new near-wall restriction factor is introduced to limit Langtry's... The corrections are limited to the near-wall region of the turbulent flow, and their calculations are based on "Qiao Lei, Bai Junqiang, Hua Jun, et al. γ-Re θt Improvement and Validation of Transition Model [J]. Journal of Aerospace Power, 2015, 30(10):2488-2497”, the specific formula is as follows:

[0036]

[0037] In the formula, The viscosity base correction factor for Langtry is calculated as follows:

[0038]

[0039]

[0040] In the formula, As an intermediate variable, For density, Let be the kinetic viscosity, and d be the minimum distance from the wall. It is the specific dissipation rate;

[0041] The boundary layer constraint factor is calculated as follows:

[0042]

[0043] In the formula, For local turbulence intensity, As an intermittent factor, It relates to turbulent kinetic energy and local velocity, and is calculated using the following formula:

[0044]

[0045] In the formula, For turbulent kinetic energy, Q is the local velocity; intermediate variables , , The specific calculation expression is as follows:

[0046]

[0047]

[0048]

[0049] In the formula, constant The value is 50.0, where S is the modulus of shear strain. The modulus of vorticity. Let be the viscosity ratio of the free flow, and d be the minimum distance from the wall. This represents the boundary layer thickness.

[0050] Furthermore, in step S4, the overshoot correction factor constructed in step S3 is... The generation of source terms in the intermittent factor transport equation The preceding intermittent factor Multiplying them together yields the improved source term. The destructive source term remains unchanged; the improved generating source term... for:

[0051]

[0052] In the formula, For local density, It is a constant. For switching functions, Let S be the interval factor, and S be the magnitude of the shear strain; where S is a constant. The value is set to 0.64, while the calculation methods for the other parameters remain unchanged; the improved source term is then used. Substituting these equations into the intermittent factor transport equation established in step S2 yields a new intermittent factor transport equation.

[0053] The simulation principle of the new intermittent factor transport equation, which includes an overshoot correction factor, for overshoot is as follows: During the transition from laminar to turbulent flow, the intermittent factor increases from 0 to 1; in the fully turbulent region, the intermittent factor remains at its maximum value of 1, at which point the intermittent factor source term... Close; when the transition process occurs, It decreases in the overshoot region and remains constant at 1 in other regions; this correction delays the intermittent factor source term. The shutdown allows the intermittent factor to continue to increase in the overshoot region while remaining normal in other regions, thus simulating the overshoot phenomenon.

[0054] Beneficial effects:

[0055] This invention proposes a high-speed boundary layer transition prediction method that can predict thermal overshoot. Addressing the limitation of existing transition prediction models in failing to simulate wall friction and thermal flow (overshoot) during transition, this method constructs an overshoot correction factor related to the flow state based on the correlation between the critical turbulent Mach number and the boundary layer edge Mach number. This factor is then compared with… The intermittent factor transport equations of the transition mode are coupled to control the evolution of the intermittent factor in the overshoot region without affecting the prediction of the transition position and the fully turbulent region, thus introducing the physical basis for simulating the overshoot effect into the model. To ensure the overall consistency of the model predictions, the relevant model coefficients are simultaneously recalibrated. The improved model was systematically verified on high-speed flat plate and conical configurations. The results show that, compared with the original model and existing methods, the peak values ​​and spatial distributions of frictional drag and heat flux overshoot predicted by this invention are in good agreement with direct numerical simulation and wind tunnel test data, and do not affect the prediction accuracy of the transition initiation position and transition length. This invention can provide a more reliable simulation tool for the refined prediction of heat flux and frictional drag on the surface of aircraft, and has important engineering application value for the optimization of aerodynamic shape and the design of thermal protection systems for high-speed aircraft. Attached Figure Description

[0056] Figure 1 This is a schematic diagram of the solution process of the method of the present invention;

[0057] Figure 2 This is a schematic diagram of the coordinate system used for boundary layer flow;

[0058] Figure 3 It is a comparison between the calculated Mach 2.25 plate transition position and the experimental result;

[0059] Figure 4 It is a Mach 6 conical mesh and boundary condition settings;

[0060] Figure 5 It is a comparison of the calculated and experimental transition positions of the Mach 6 straight cone at different Reynolds numbers. Detailed Implementation

[0061] To better understand the solutions of the present invention, embodiments of the present invention are described in detail below with reference to the accompanying drawings. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0062] like Figure 1 As shown, this embodiment uses a high-speed boundary layer transition prediction method proposed in this invention to predict the overshoot phenomenon during the transition process of test model surfaces under various test environments. The method includes the following steps:

[0063] S1: By solving the compressible Falkner-Skan-Cooke (FSC) equations, a compressible 3D boundary layer characteristic parameter database is established to obtain the relationship between local and non-local variables within the desired boundary layer; this step has been disclosed in previous studies, as detailed below:

[0064] The FSC equations are a simplified form of the NS equations in the boundary layer. The FSC equations are expressed as depending only on local variables and geometric parameters, as follows:

[0065]

[0066]

[0067]

[0068]

[0069]

[0070] Definition as follows Figure 2 In the coordinate system shown, , The first line represents a fixed Cartesian coordinate system, while the dashed line represents a curvilinear coordinate system. The direction of the resultant velocity at the boundary layer edge. and The direction is perpendicular, among which For density, For kinetic viscosity, For the local velocity in direction and boundary layer edge The ratio of velocities in different directions, where β is the pressure gradient factor and g is the acceleration due to gravity. For Prandtl numbers, It is the ratio of the local total enthalpy to the total enthalpy at the boundary layer edge. Boundary layer edge velocity in direction, The boundary layer edge sweep angle is T, where T is the temperature and M is the Mach number. For specific heat ratio, superscript Let denote the derivative, and the subscript 'e' represents the value at the boundary layer edge. In the above equation, the parameters... ,β,g,q, The expression for m is:

[0071]

[0072]

[0073] in In the coordinate system Directional velocity component, for Directional velocity component, Total enthalpy.

[0074] Introducing the viscosity Sutherland formula to close the system of equations:

[0075]

[0076] in Here, is the Satland constant, with a value of 110.4 K, and T is the temperature. The value represents the kinetic viscosity, and the subscript 'e' indicates the value at the boundary layer edge.

[0077] Solving the FSC equations yields the velocity and temperature profiles within the boundary layer. These profiles are then used to derive the desired characteristic parameters: boundary layer thickness, boundary layer momentum thickness, and boundary layer displacement thickness. The FSC equations are solved by iterating through different Mach numbers, pressure gradients, and wall temperatures. The resulting characteristic parameters are stored to create a compressible three-dimensional boundary layer characteristic parameter database.

[0078] S2: A compressible 3D boundary layer feature parameter database established based on S1, localizing non-local variables and controlling the feature time scale coefficients of the second mode. Modifications were made to obtain entirely new feature time-scale control coefficients. This enables the second mode in the dominant transition mode to predict both the length of the transition region and the heat flow overshoot phenomenon. Based on the modified second mode, laminar pulsating viscosity coefficient transport equation and intermittent factor transport equation are established.

[0079] The dominant transition modes are Mack's first mode, Mack's second mode, and the transverse flow mode. The process of modeling these three modes has been disclosed in previous studies. The modeling process for the second mode is as follows:

[0080] Based on Mack's stability theory analysis and experimental observations, the most unstable frequency of Mack's second-mode perturbation is obtained as follows:

[0081]

[0082] in It is the wavelength of the most unstable frequency of Mack's second-mode perturbation. Phase velocity:

[0083]

[0084] The characteristic timescales of Mack's second mode are obtained as follows:

[0085]

[0086] in, These are the characteristic time-scale control coefficients for the second mode. The most unstable frequency of the second mode perturbation. For the specific calculation method, please refer to the invention patent "A transition prediction method applicable to the wide Mach domain of high-speed aircraft" with publication number CN121145697A.

[0087] In previous studies, the characteristic timescale control coefficient C6 of the second mode was calibrated using several wind tunnel and flight experiment examples, enabling the model to be applicable to wide Mach domain simulations. However, it was still not suitable for simulating thermal flow overshoot. To enable the model to reasonably predict the length of the transition zone while also predicting thermal flow overshoot, the method of this invention is based on the free-flow turbulence intensity of the characteristic timescale control coefficient of the second mode. The specific formula to be modified is as follows:

[0088]

[0089] In the formula, For the original The characteristic time-scale control coefficients of the second mode in the model. For free-flow turbulence, These are the revised characteristic time scale control coefficients.

[0090] In this embodiment, based on the compressible three-dimensional boundary layer characteristic parameter database established in S1, and by comprehensively considering the Mach number effect and the adiabatic and cooling / heating wall effects, the similarity solution of the three-dimensional compressible FSC boundary layer is solved to obtain the ratio of boundary layer thickness to momentum thickness. A database of the relationship between Mach number and wall temperature was created. The database was then fitted to obtain... Improved fitting formula:

[0091]

[0092]

[0093]

[0094] in The wall temperature, This refers to the temperature of the adiabatic wall surface.

[0095] By solving the FSC boundary layer similarity solution, we can conclude that the momentum, thickness, and Reynolds number are... With vorticity, thickness, and Reynolds number The maximum value of has the following relationship:

[0096]

[0097] in,

[0098]

[0099]

[0100] .

[0101] The transport equations for laminar pulsating viscosity coefficient and intermittent factor are established; this process has been disclosed in previous studies, and the specific steps are as follows:

[0102] The transport equation for laminar pulsating viscosity is established, and its form is as follows:

[0103]

[0104] in, and These are the source terms for laminar pulsating viscosity and the source term for rupture, respectively, and their specific expressions are as follows:

[0105]

[0106]

[0107] To combine the first, second, and transverse instability modes within the hypersonic boundary layer, the total time scale of laminar fluctuations is set as follows:

[0108]

[0109]

[0110] , , Corresponding to the first, second, and crossflow mode time scales, respectively. The relative Mach number, The speed of sound.

[0111] The intermittent factor transport equation is established, and its form is as follows:

[0112]

[0113] in, and These are the source term and the destruction term of the intermittent factor equation, respectively, and their specific expressions are as follows:

[0114]

[0115]

[0116] Where C3=80.0, C4=0.06 and C5=50.0 are model constants. The modulus of vorticity. The switching function that generates the source term. The main control point is the starting point of the entire transition process, and its calculation is as follows:

[0117]

[0118] in, To suppress the destructive source terms in the laminar bottom layer and the outer boundary layer of the boundary layer, it is defined as follows:

[0119]

[0120] in, The laminar pulsating viscosity coefficient, The molecular viscosity coefficient, These are model coefficients. This refers to the viscosity ratio.

[0121] S3: Based on the compressible three-dimensional boundary layer characteristic parameter database established in S1, the physical mechanism of overshoot phenomenon accompanying the transition process is analyzed, and its nonlinear correlation with the intermittent development of turbulence is identified; based on the turbulent Mach number within the boundary layer... Mach number at the boundary layer edge Construct an overshoot correction factor that reflects the overshoot intensity. and in overshoot correction factor Introducing a transition restriction factor With the new near-wall region restriction factor This ensures that the correction factor is only effective in the transition development zone and does not affect the predictions in the laminar and fully turbulent zones.

[0122] In this embodiment, the constructed overshoot correction factor The formula is as follows:

[0123]

[0124] In the formula, As a transition limiting factor, It is a constant. For turbulent Mach number, The overshoot correction criterion is expressed as follows:

[0125]

[0126] In the formula, It is a constant, a constant The scores are 16.0, 80.0, and 7.00 respectively.

[0127] Turbulent Mach Number within the Boundary Layer Calculated using turbulent kinetic energy and local sound speed:

[0128]

[0129] In the formula, For turbulent kinetic energy, The speed of sound in the local area;

[0130] Critical turbulent Mach number For the Mach number at the boundary layer edge Functions:

[0131]

[0132] boundary layer edge Mach number It is obtained by calculating using the following expression:

[0133]

[0134]

[0135]

[0136] In the formula, constant , The boundary layer edge flow velocity, For the free flow velocity, The speed of sound at the edge of the boundary layer. For the speed of free flow, For local pressure, For free flow pressure, For free flow density.

[0137] Transition limiting factor The expression for the overshoot correction used to prevent the influence of overshoot on the transition position is as follows:

[0138]

[0139] In the formula, The viscosity ratio is , where For turbulent kinetic energy, For specific dissipation rate, It is the molecular viscosity coefficient; The new near-wall restriction factor is introduced to limit Langtry's... The corrections are limited to the near-wall region of the turbulent flow, and their calculations are based on "Qiao Lei, Bai Junqiang, Hua Jun, et al. γ-Re θt Improvement and Validation of Transition Model [J]. Journal of Aerospace Power, 2015, 30(10):2488-2497”, the specific formula is as follows:

[0140]

[0141] In the formula, The viscosity base correction factor for Langtry is calculated as follows:

[0142]

[0143]

[0144] In the formula, As an intermediate variable, For density, Let be the kinetic viscosity, and d be the minimum distance from the wall. It is the specific dissipation rate;

[0145] The boundary layer constraint factor is calculated as follows:

[0146]

[0147] In the formula, For local turbulence intensity, As an intermittent factor, It relates to turbulent kinetic energy and local velocity, and is calculated using the following formula:

[0148]

[0149] In the formula, For turbulent kinetic energy, Q is the local velocity; intermediate variables , , The specific calculation expression is as follows:

[0150]

[0151]

[0152] In the formula, constant The value is 50.0, where S is the modulus of shear strain. The modulus of vorticity. Let be the viscosity ratio of the free flow, and d be the minimum distance from the wall. This represents the boundary layer thickness.

[0153] S4: The overshoot correction factor constructed in step S3 The source term is generated in the intermittent factor transport equation established in step S2. By coupling the two, an improved source term is obtained. This leads to the acquisition of a new intermittent factor transport equation;

[0154] In this embodiment, the specific process of obtaining the new intermittent factor transport equation is as follows:

[0155] The overshoot correction factor constructed in step S3 The source term is generated in the intermittent factor transport equation established in step S2. The preceding intermittent factor Multiplying them together yields the improved source term. The destructive source term remains unchanged; the improved generating source term... for:

[0156]

[0157] In the formula, For local density, It is a constant. For switching functions, Let S be the interval factor, and S be the magnitude of the shear strain; where S is a constant. The value of 0.64 was obtained through experimental calibration, while the calculation methods for the other parameters remained unchanged; the improved generation source term was used. Substituting these equations into the intermittent factor transport equation established in step S2, we obtain the new intermittent factor transport equation.

[0158] The simulation principle of the new intermittent factor transport equation, which includes an overshoot correction factor, for overshoot is as follows: During the transition from laminar to turbulent flow, the intermittent factor increases from 0 to 1; in the fully turbulent region, the intermittent factor remains at its maximum value of 1, at which point the intermittent factor source term... Close; when the transition process occurs, It decreases in the overshoot region and remains constant at 1 in other regions; this correction delays the intermittent factor source term. The shutdown allows the intermittent factor to continue to increase in the overshoot region while remaining normal in other regions, thus simulating the overshoot phenomenon.

[0159] S5: Couple the laminar pulsating viscosity coefficient transport equation established in S2 and the new intermittent factor transport equation coupled with the overshoot correction factor in S4 with the SST turbulence model to establish... A four-equation turbulence-transition model is constructed and embedded into an existing CFD solver capable of large-scale parallel computation. This CFD solver is then used to predict the laminar-turbulent transition of a high-speed aircraft. In this embodiment, the CFD solver is NASA's open-source CFD code, CFL3D. This process has been disclosed in previous studies, and the specific steps are as follows:

[0160] The turbulence model obtained by coupling the transport equation for the laminar fluctuating viscosity coefficient obtained in step S2, the new intermittent factor transport equation obtained in step S4, and the turbulent kinetic energy generation source term and destruction source term of the Menter SST turbulence model is as follows:

[0161]

[0162]

[0163]

[0164]

[0165]

[0166] M t The Mach number representing turbulence is defined as follows: , where 'a' represents the local speed of sound.

[0167] The aforementioned CFD solver is used to predict the laminar-turbulent transition of a high-speed aircraft. Specifically, the numerical solution method employs the finite volume method, where inviscid flux is discretized using Roe's FDS (Flux Difference Splitting) scheme, viscous flux is discretized using a central difference scheme, and time propagation is achieved using the approximate factorization method. Multigrid and grid sequence techniques are used to accelerate convergence, and large-scale parallel computation is performed based on the MPI (Message Passing Interface) parallel strategy.

[0168] Calculation example 1:

[0169] For the Mach 2.25 high-speed flat plate example, the reference data for this example is: The results of the direct numerical simulation. Experimental conditions, incoming Mach number. Reynolds number Re ∞ =2.5×10⁷ / m, incoming flow temperature is The inflow turbulence intensity is 0.132%, and the wall temperature is an adiabatic wall. The viscosity ratio is set as follows: It can ensure the attenuation level distribution of turbulent fluctuations outside the boundary layer.

[0170] Figure 3 The comparison between the calculated surface friction coefficient after overshoot correction and the original model shows that the model after overshoot correction has the ability to predict overshoot, and the overshoot peak value agrees well with the experimental results. Overshoot correction factor. The corrective effect gradually strengthens in the transition region and then gradually disappears. This mechanism does not affect the transition location or the friction coefficient in the turbulent region.

[0171] Calculation example 2:

[0172] For the Mach 6 straight cone simulation completed by Horvath et al. in the Mach 6 silent wind tunnel at NASA Langley Research Center, the free-flow Mach number... The wall temperature is constant. The calculated turbulence intensity is: For a cone with zero angle of attack and an axisymmetric geometry, a quarter cone is used for calculation. The computational mesh is arranged with 401, 101, and 201 meshes in the flow direction, circumferential direction, and wall normal direction, respectively. The height of the first boundary layer is... This ensured For mesh and boundary condition settings, see [link to mesh settings]. Figure 4 Set the numerical solution method and parameters, and solve in parallel until convergence.

[0173] Figure 5 The model predictions and experimental measurements of dimensionless thermal conductivity at four Reynolds numbers were compared. The thermal conductivity coefficient is defined as... ,in It is heat flow over the wall; and These are the enthalpies of the theoretical adiabatic wall and the physical wall, respectively. The reference heat flux value is obtained from the stagnation temperature calculation formula of Fay and Riddell. As shown in the figure, the modified model achieves good simulation of overshoot, proving the effectiveness of the improvement.

[0174] In summary, the high-speed boundary layer transition prediction method proposed in this invention can accurately predict the overshoot phenomenon in the transition process of different models under different test environments. It can significantly improve the model's ability to predict the fine structure of the transition region and can be performed in large-scale parallelism. This invention provides a more reliable tool for the refined prediction of surface heat flux and friction of aircraft, and has clear engineering guiding significance for the aerodynamic thermal environment assessment and thermal protection design of aircraft.

[0175] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for predicting high-speed boundary layer transition phenomena that can predict thermal overshoot, characterized in that: Includes the following steps: S1: By solving the compressible Falkner-Skan-Cooke equation, a database of compressible three-dimensional boundary layer characteristic parameters is established to obtain the relationship between local and non-local variables within the desired boundary layer; S2: A compressible 3D boundary layer feature parameter database established based on S1, localizing non-local variables and controlling the feature time scale coefficients of the second mode. Modifications were made to obtain entirely new feature time-scale control coefficients. This enables the second mode in the dominant transition mode to predict both the length of the transition region and the heat flow overshoot phenomenon. Based on the modified second mode, laminar pulsating viscosity coefficient transport equation and intermittent factor transport equation are established. Among them, the characteristic time scale control coefficients for the second mode The specific formula to be modified is as follows: In the formula, For the original The characteristic time-scale control coefficients of the second mode in the model. For free-flow turbulence, These are the modified, entirely new feature timescale control coefficients; S3: Based on the turbulent Mach number within the boundary layer Mach number at the boundary layer edge Construct an overshoot correction factor that reflects the overshoot intensity. and in overshoot correction factor Introducing a transition restriction factor With the new near-wall region restriction factor Ensure overshoot correction factor It is only effective in the transition development zone and does not affect the prediction of the laminar and fully turbulent zones; wherein the constructed overshoot correction factor The formula is as follows: wherein is a transition limiting factor, is a preset constant, is a turbulent Mach number, is an overshoot correction criterion; S4: The overshoot correction factor constructed in step S3 The generation source term in the intermittent factor transport equation established in step S2 By coupling, an improved source term is obtained. This leads to the acquisition of a new intermittent factor transport equation; S5: The laminar pulsating viscosity coefficient transport equation established in S2 and the overshoot correction factor in S4 are coupled together. The new intermittent factor transport equation is coupled with the SST turbulence model to establish A four-equation turbulence-transition model is constructed and embedded into an existing CFD solver; the CFD solver is then used to predict the laminar-turbulent transition of a high-speed aircraft.

2. The method of claim 1, wherein the method is a method of predicting a high-speed boundary layer transition that is capable of predicting a heat flux overshoot phenomenon. The overshoot correction criterion expression is as follows: In the formula, All are preset constants. It is the critical turbulent Mach number.

3. The method of claim 1, wherein the method is a method of predicting a high-speed boundary layer transition that is capable of predicting a heat flux overshoot phenomenon. Turbulent Mach number within the boundary layer Obtained by calculation of turbulent kinetic energy and local sound speed: wherein is the turbulent kinetic energy, is the local sound speed.

4. The method for predicting high-speed boundary layer transition based on predictable thermal overshoot as described in claim 2, characterized in that: Critical turbulent Mach number is a function of the boundary layer edge Mach number : 。 5. The method for predicting high-speed boundary layer transition based on the predictable thermal overshoot phenomenon according to claim 4, characterized in that: Boundary layer edge Mach number Computed by the following expression: In the formula, As a preset constant, The boundary layer edge flow velocity, For the free flow velocity, The speed of sound at the edge of the boundary layer. For the speed of free flow, For local pressure, For free flow pressure, For free flow density.

6. The method for predicting high-speed boundary layer transition based on the predictable thermal overshoot phenomenon according to claim 1, characterized in that: Transition limiting factor The expression is as follows: wherein is the viscous ratio, wherein is the turbulent kinetic energy, is the specific dissipation rate, is the molecular viscosity coefficient; is a new near-wall region limiter introduced, which is specified as follows: wherein is the Langtry viscous sublayer correction factor, is the boundary layer limiter.

7. The method for predicting high-speed boundary layer transition phenomena according to claim 6, characterized in that: Langtry's viscous sublayer correction factor The calculation expression is as follows: wherein is an intermediate variable, is the density, is the dynamic viscosity, d is the minimum distance from the wall, is the specific dissipation rate; Boundary layer limiting factor The computational expression for the boundary layer limiting factor is as follows: wherein is the local turbulence intensity, is the intermittency factor, is related to the turbulent kinetic energy and the local velocity and is calculated by wherein is the turbulent kinetic energy, Q is the local velocity; the intermediate variable , , The calculation expression of is as follows: where the constant is 50.0, S is the modulus of shear strain, is the modulus of vorticity, is the free-stream viscosity ratio, d is the minimum distance from the wall, is the boundary layer thickness.

8. The method for predicting high-speed boundary layer transition based on the predictable thermal overshoot phenomenon according to claim 1, characterized in that: In step S4, the improved source item is generated is: In the formula, is the local density, is a constant, is a switch function, is a intermittency factor, S is the modulus of shear strain; wherein, the constant is taken as 0.64, and the calculation method of the remaining parameters remains unchanged; the improved generation source term is substituted into the intermittency factor transport equation established in step S2, that is, a new intermittency factor transport equation is obtained.

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