A transition prediction method suitable for wide mach number range of high speed vehicles

Abstract

This invention proposes a transition prediction method applicable to high-speed vehicles in a wide Mach range. It performs temperature and Mach number coupling correction on key parameters in the time-scale modeling of the second mode of the transition mode, overcoming the simplification of flow compression effects and heat transfer processes by traditional single-parameter correlation. The method embeds the influence of incoming flow disturbance effects into the model, achieving a dynamic correlation between experimental environment parameters and transition triggering criteria. The improved model achieves accurate prediction results in multiple calculations within the Mach number range of 4.7–14. The research results provide a more reliable theoretical tool for optimizing the aerodynamic shape of high-speed vehicles in a wider speed range and have significant engineering guiding significance for the design of thermal protection systems for next-generation reusable aircraft.

Description

Technical Field

[0001] This invention belongs to the fields of aerospace and computational fluid dynamics, and specifically relates to a transition prediction method applicable to the wide Mach domain of high-speed aircraft. Background Technology

[0002] High-speed aircraft have demonstrated significant application value in fields such as space exploration, but their aerodynamic design faces severe challenges from extreme operating environments. The transition process from laminar to turbulent flow in the boundary layer directly affects the surface friction drag, heat flux distribution, and aerodynamic stability of the aircraft, making transition prediction a key aspect of the design of the aircraft's thermal protection system and the optimization of its aerodynamic shape.

[0003] 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.

[0004] 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, the transition mechanism of supersonic / hypersonic flows is actually quite different from that of incompressible flows. Making numerical modifications only to incompressible transition modes will cause the transition modes to lose some of the physical meaning behind the transition phenomena and will also make it difficult to have good universality.

[0005] 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. Later, other solutions were proposed. 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. Further research has improved the model for supersonic wall heat transfer. Transition patterns are identified, and the patterns are extended to predictable distributed rough element-dominated transitions.

[0006] The applicant's research group previously constructed a system based on the RANS framework that is 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 have validated that this model can effectively simulate boundary layer transition processes under different transition mechanisms, demonstrating good accuracy.

[0007] However, as the operating conditions of modern aircraft expand into a wider Mach number range (Ma=5-12), the limitations of the aforementioned prediction methods—their inability to make accurate predictions simultaneously over a wider Mach number range—become apparent. Currently... The characterization of temperature and Mach number effects in the second-mode timescale construction of the Mack model is not yet complete, which limits the model's universality under varying Mach numbers and wall temperatures. Furthermore, the impact of differences in incoming flow disturbance levels in different wind tunnel and flight test environments on transition triggering has not been systematically incorporated into the prediction system, leading to certain calculation discrepancies between engineering applications and experimental results. Summary of the Invention

[0008] To address the problems existing in the prior art, this invention proposes a transition prediction method applicable to the wide Mach range of high-speed vehicles. The key parameters in the second-mode timescale modeling of the transition mode are corrected by coupling temperature and Mach number, breaking through the simplification of flow compression effect and heat transfer process by traditional single-parameter correlation. The influence of incoming flow disturbance effect is embedded in the model to realize the dynamic correlation between experimental environment parameters and transition triggering criteria. The improved model has achieved accurate prediction results in multiple examples in the Mach number range of 4.7-14. The research results provide a more reliable theoretical tool for the aerodynamic shape optimization of high-speed aircraft with a wider speed range, and have important engineering guiding significance for the design of thermal protection system of next-generation reusable aircraft.

[0009] The technical solution of this invention is as follows:

[0010] A transition prediction method applicable to the wide Mach range of high-speed vehicles includes the following steps:

[0011] 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;

[0012] S2: Stability theory analysis is performed on the second mode in the dominant transition mode. The non-local variables are localized using the boundary layer characteristic parameter database established in S1, and the time scale of the second mode is analyzed. Improve the key variables and establish a localized mathematical model;

[0013] S3: Based on the localized instability modes established in S2, establish the laminar pulsating viscosity coefficient transport equation and the intermittent factor transport equation;

[0014] S4: Couple the laminar pulsating viscosity coefficient transport equation and intermittent factor transport equation established in S3 with the SST turbulence model to establish... A four-equation turbulence-transition model was developed and embedded into an existing CFD solver.

[0015] S5: The CFD solver in S4 is used to predict the laminar-turbulent transition of high-speed aircraft.

[0016] Furthermore, in S2, the second modal timescale The formula is:

[0017]

[0018] in These are the characteristic time-scale control coefficients for the second mode. The wavelength is the frequency at which the second mode perturbation is most unstable.

[0019] Furthermore, in S2, the wavelength of the most unstable frequency of the second-mode perturbation. Boundary layer thickness Twice the thickness of the boundary layer; Determined in the following ways:

[0020] Based on the boundary layer database established by 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 boundary layer thickness. With momentum thickness ratio A database showing the relationship between Mach number and wall temperature was used to fit the database, resulting in... Improved fitting formula:

[0021]

[0022]

[0023]

[0024] in The wall temperature, This refers to the temperature of the adiabatic wall surface.

[0025] Furthermore, momentum thickness Determined in the following ways:

[0026] Using the boundary layer database established by S1, the improved momentum thickness was obtained. The calculation formula is:

[0027]

[0028] in For the shear strain mode, The normal distance to the wall. For boundary layer edge velocity;

[0029]

[0030]

[0031]

[0032] in Momentum thickness correction factor:

[0033]

[0034] For density, For boundary layer edge density, For kinetic viscosity, The boundary layer edge dynamic viscosity.

[0035] Furthermore, the characteristic time scale control coefficient C6 of the second mode is determined according to the following formula:

[0036]

[0037]

[0038]

[0039] .

[0040] Beneficial effects

[0041] This invention proposes a transition prediction method applicable to a wide Mach range for hypersonic vehicles. To enable the transition prediction mode to have broader Mach number applicability and meet the requirements of modern aircraft design for multi-condition, high-precision prediction, this invention... The calculation method for key variables required for constructing the Mack second mode timescale in the transition-turbulence prediction model has been improved. To better reflect the overall flow characteristics of the boundary layer, the calculation of momentum thickness was corrected for temperature and Mach number effects. The correlation between boundary layer thickness and momentum thickness was recalibrated, taking into account the Mach number effect and the temperature effects of adiabatic and cooled / heated isothermal walls. To enhance the model's adaptability to different test environments, the influence of incoming flow disturbance was introduced. After the model improvement, its predictive capability was verified under multiple Mach number conditions using various wind tunnel test configurations. The results show that, compared with previous studies, the improved model can achieve high-precision transition position prediction over a wider Mach number range, fully demonstrating the rationality and accuracy of the improvements made in this invention, and providing a broader application basis for the aerodynamic design of high-speed aircraft.

[0042] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0043] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0044] Figure 1 This is a schematic diagram of the solution process of the method of the present invention.

[0045] Figure 2 This is a schematic diagram of the coordinate system used for boundary layer flow.

[0046] Figure 3 It is a 6 Mach straight conical mesh and boundary condition settings.

[0047] Figure 4 It is a comparison of the calculated and experimental transition positions of a Mach 6 straight circular cone at different Reynolds numbers.

[0048] Figure 5 It is a comparison between the calculated Mach 10 straight cone transition position and the experimental result.

[0049] Figure 6 This is a comparison between the calculated Mach 14 straight cone transition position and the experimental results. .

[0050] Figure 7 This is a comparison between the calculated Mach 14 straight cone transition position and the experimental results. . Detailed Implementation

[0051] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0052] High-speed boundary layer transition prediction technology plays a crucial role in the aerodynamic and thermal protection design of high-speed aircraft, and its prediction accuracy directly affects the aerodynamic performance and safety of the aircraft. To enable the transition prediction mode to have a wider Mach number applicability and meet the requirements of modern aircraft design for multi-condition, high-precision prediction, this invention proposes a transition prediction method applicable to a wide Mach range for high-speed aircraft. The calculation method for key variables required for constructing the Mack second mode timescale in the transition-turbulence prediction model has been improved. To better reflect the overall flow characteristics of the boundary layer, a temperature correction was applied to the momentum thickness calculation. The correlation between boundary layer thickness and momentum thickness was recalibrated, taking into account Mach number effects and the temperature effects of adiabatic and cooled / heated isothermal walls. To enhance the model's adaptability to different experimental environments, the influence of incoming flow disturbances was introduced. After the model improvement, its predictive capability was verified using various wind tunnel configurations under multiple Mach number conditions. The results show that, compared with previous studies, the improved model can achieve high-precision transition position prediction over a wider Mach number range, fully demonstrating the rationality and accuracy of the improvements made in this invention, and providing a broader application basis for the aerodynamic design of high-speed aircraft.

[0053] like Figure 1 As shown, this embodiment employs a proposed transition prediction method applicable to the wide Mach range of high-speed vehicles to predict the transition positions on the surface of test models under various test environments, including the following steps:

[0054] 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 follows:

[0055] 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:

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] Definition as follows Figure 2In 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 the directions, where β is the pressure gradient factor, g is the gravitational acceleration, Pr is the Prandtl number, q is the ratio of the local total enthalpy to the total enthalpy at the boundary layer edge, and Ue is the boundary layer edge velocity. velocity in direction, The boundary layer edge sweep angle is T, where T is the temperature and M is the Mach number. 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:

[0062]

[0063]

[0064] Where u is the coordinate system The directional velocity component, w is The directional velocity component, where H is the total enthalpy.

[0065] Introducing the viscosity Sutherland formula to close the system of equations:

[0066]

[0067] 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.

[0068] 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.

[0069] S2 performs stability theory analysis on the second mode in the dominant transition mode, localizes non-local variables using the boundary layer characteristic parameter database established in S1, and analyzes the time scale of the second mode. Improve the key variables and establish a localized mathematical model;

[0070] 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:

[0071] Based on Mack's stability theory analysis and experimental observations, the most unstable frequency of Mack's second-mode perturbation is obtained as follows:

[0072]

[0073] in It is the wavelength of the most unstable frequency of Mack's second-mode perturbation. phase velocity

[0074]

[0075] The characteristic timescales of Mack's second mode are obtained as follows:

[0076]

[0077] In previous studies, the characteristic timescale control coefficient C6 of the second mode and the wavelength of the most unstable frequency of the second mode perturbation were... All values ​​are constants, which means previous studies were only applicable to specific wall temperatures and turbulence intensities, and also had priority in predicting high Mach number conditions. The characteristic timescale control coefficient C6 for the second mode and the wavelength of the most unstable frequency for the second mode perturbation are also considered. The modification is the core inventive point of this invention.

[0078] For the wavelength of the most unstable frequency of the second mode perturbation According to stability analysis, Boundary layer thickness Twice: Therefore, determining the boundary layer thickness That's the key.

[0079] Traditional boundary layer thickness According to the formula

[0080]

[0081] The calculation yielded, where For momentum thickness, This represents the Mach number at the edge of the boundary layer.

[0082] In this invention, based on the boundary layer database established by S1, the similarity solution of the three-dimensional compressible FSC boundary layer is solved by comprehensively considering the Mach number effect and the adiabatic and cooling / heating wall effects, thereby obtaining the boundary layer thickness. With momentum thickness ratio A database of the relationship between Mach number and wall temperature was created. The database was then fitted to obtain... Improved fitting formula:

[0083]

[0084]

[0085]

[0086] in The wall temperature, This refers to the temperature of the adiabatic wall surface.

[0087] Regarding momentum thickness The traditional calculation formula is

[0088]

[0089]

[0090] However, under hypersonic conditions, due to the significant temperature difference between the boundary layer edge and the bottom layer, this invention addresses the momentum thickness... Further improvements will be made to better reflect the overall flow characteristics of the boundary layer:

[0091] Using the boundary layer database established by S1, the improved momentum thickness was obtained. The calculation formula is:

[0092]

[0093] in For the shear strain mode, The normal distance to the wall. For boundary layer edge velocity;

[0094]

[0095]

[0096]

[0097] Momentum thickness correction factor:

[0098]

[0099] By measuring the boundary layer thickness With momentum thickness Improvements were made to achieve the wavelength of the most unstable frequency of the second-mode perturbation. The improvements enhanced the predictive ability of the transition model under high Mach conditions.

[0100] As for the characteristic time scale control coefficient C6 of the second mode, it was calibrated and fitted using several wind tunnel and flight test examples. The incoming flow disturbance effect was introduced to better cope with different wall temperatures and turbulence intensities. The main process is as follows:

[0101] To enhance the model's adaptability to different wind tunnel and flight environments, this invention introduces the influence of incoming flow disturbance. Turbulence intensity, as a physical quantity characterizing flow field quality or the degree of free flow disturbance, has a significant impact on the transition position of the experimental model. The significant difference in turbulence intensity between ground wind tunnel tests and flight experiments is also the main reason for the large data divergence between the two. Factual research has shown that there is a specific correlation between wind tunnel noise and turbulence intensity, and under hypersonic conditions, the correlation between noise and turbulence intensity can reach over 80%.

[0102] In wind tunnel testing, the noise level of the wind tunnel is usually obtained by measuring pressure fluctuations. Noise Level (NL) is one way to quantitatively describe the noise level of a wind tunnel, and its definition is as follows:

[0103]

[0104] Wherein is the time-averaged pressure p and the root mean square pulsating pressure p rms Defined as follows

[0105]

[0106]

[0107] in It refers to the instantaneous pressure at a certain spatial location.

[0108] The fitting curves for the noise levels of different wind tunnels at home and abroad, using NASA LaRC 20 Inch (M=6) and AEDC Tunnel 9, are shown in the following formula.

[0109]

[0110]

[0111] Other studies have discussed various hyperbolic wave characteristics in the Euler system, focusing on the essential relationship between fluctuating pressure and fluctuating velocity in the flow field sound waves, and theoretically derived the relationship between sound pressure level and acoustic turbulence intensity:

[0112]

[0113] in, Indicates the specific heat ratio of a gas. This represents the free-flowing Mach number. This invention employs... This is used to quantify the intensity of environmental disturbances. Its calculation depends on the measurement of the ambient noise level (pressure pulsation intensity). If the ambient noise level can be explicitly provided, the turbulence intensity level can be calculated using the above formula or by interpolation. In the absence of information on ambient pressure pulsation intensity, a reasonable estimate must be made. For example, a typical low ambient disturbance intensity under flight conditions is usually assigned a value of 0.01%. If operating in a wind tunnel where the ambient disturbance intensity is unknown, a reasonable estimate can be obtained by analogy with the closest comparable wind tunnel experiment.

[0114] Finally, the second modal scale control coefficient C6 was calibrated using several wind tunnel and flight test examples. Based on the calibration results, the influence of turbulence intensity was introduced into the second modal scale control coefficient C6.

[0115]

[0116]

[0117]

[0118]

[0119] In this embodiment, the scale control coefficient C6 of the second mode of the model was calibrated using a Mach 6 straight cone tested in NASA's Langley Mach 6 silent wind tunnel. The coefficients of the unmodified model and the modified model were 0.3375 and 2.0250, respectively. After calibration of coefficient C6, Mach 11.3 pointed double cone and Mach 14 examples were selected for verification. The verification results showed that the unmodified examples could not calculate the transition phenomenon, while the results calculated by the modified model were in good agreement with the experiments. Therefore, the modified model significantly improved the prediction performance for higher Mach number examples, proving the effectiveness of the improvements made in this invention.

[0120] S3, based on the localized instability modes established in S2, establishes the laminar pulsating viscosity coefficient transport equation and the intermittent factor transport equation; this process has been disclosed in previous studies, and the specific process is as follows:

[0121] The transport equation for laminar pulsating viscosity is established, and its form is as follows:

[0122] ∂ ( rn L ) ∂ t + ∂ ( u j rn L ) ∂ x j = P n L − E n L + ∂ ∂ x j [ s 1 r ( n + s m L n L ) ∂ n L ∂ x j ]

[0123] 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:

[0124]

[0125]

[0126] 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:

[0127]

[0128]

[0129] , , Corresponding to the first, second, and crossflow mode time scales, respectively. The relative Mach number, The speed of sound.

[0130] The intermittent factor transport equation is established, and its form is as follows:

[0131] ∂ ( r c ) ∂ t + ∂ ( r u j c ) ∂ x j = P c − E c + ∂ ∂ x j [ ( m + m t ) ∂ c ∂ x j ]

[0132] in, and These are the source term and the destruction term of the intermittent factor equation, respectively, and their specific expressions are as follows:

[0133] P c = r C 3 F onset ( 1 − c ) [ − ln ( 1 − c ) ] 1 3 S

[0134]

[0135] 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:

[0136]

[0137] 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:

[0138] F turbid = exp [ − ( 0 . 25 R T ) 4 ]

[0139] in, The laminar pulsating viscosity coefficient, The molecular viscosity coefficient, These are model coefficients. This refers to the viscosity ratio.

[0140] S4, couples the laminar pulsating viscosity coefficient transport equation and the intermittent factor transport equation established in S3 with the SST turbulence model to establish... A four-equation turbulence-transition model is used, and this model is embedded into an existing CFD solver capable of large-scale parallel computation. In this embodiment, the CFD solver is NASA's open-source CFD code CFL3D. This process has been disclosed in previous research, and the specific process is as follows:

[0141] The turbulence model obtained by coupling the transport equations for the laminar fluctuating viscosity coefficient and the intermittent factor transport equations obtained in step S3 with the turbulent kinetic energy generation source term and the destruction source term of the MenterSST turbulence model is as follows:

[0142] ∂ ( r k ) ∂ t + r ∂ ( u j k ) ∂ x j = P k − D k + P c c + ∂ ∂ x j [ ( m + s k m t ) ∂ k ∂ x j ]

[0143] ∂ ( r oh ) ∂ t + ∂ ( r u j oh ) ∂ x j = α t t i j ∂ u i ∂ x j − ( 1 + M t 2 ) β r oh 2 + ∂ ∂ x j [ ( m + s oh m t ) ∂ oh ∂ x j ] + 2 ( 1 − F 1 ) r s oh 2 oh ∂ k ∂ x j ∂ oh ∂ x j

[0144]

[0145]

[0146]

[0147] M t The Mach number representing turbulence is defined as follows: , where 'a' represents the local speed of sound.

[0148] S5 uses the CFD solver from S4 to predict the laminar-turbulent transition of a high-speed aircraft. The specific 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 the 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.

[0149] Calculation example 1:

[0150] 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 3 Set the numerical solution method and parameters, and solve in parallel until convergence.

[0151] Figure 4 The dimensionless thermal conductivity coefficients at three Reynolds numbers were compared between model predictions and experimental measurements. 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 Fay and Riddell's stagnation temperature calculation formula. As shown in the figure, the phenomenon of increased heat flux due to transition is consistent with the experiment, proving the rationality of the second-mode modeling and improvement.

[0152] Calculation example 2:

[0153] This example performs a numerical simulation of a right circular cone with a semi-cone angle of 7° and a speed of Mach 10. The model dimensions are as follows: semi-cone angle 7°, base diameter D. b =0.381m, head radius R n =0.152mm. The experimental study was conducted by Marineau EC et al. in wind tunnel No. 9 at the Air Force Arnold Engineering Development Center (AEDC). The calculation condition selected in this example uses Mach number. Reynolds number , , The calculated free-flow turbulence intensity .

[0154] The computational grid is arranged with 785, 132, and 98 grids in the flow direction, circumferential direction, and wall normal direction, respectively. The first boundary layer has a height of 1×10⁻⁶. −5 mm, growth rate 1.1, guaranteed The given grid region is sufficient to fully encompass characteristic flow field phenomena such as oblique shock waves, and can capture details of the flow and boundary layer changes. Furthermore, the computational grid has undergone convergence verification, and the results show that the grid convergence has been established. The inlet condition is a Riemann boundary, the outlet condition is an extrapolated boundary, and the wall condition is a no-slip adiabatic wall. Numerical solution methods and parameters are set, and parallel solutions are implemented until convergence. Figure 5 The distribution of the calculated Stanton number on the surface is shown.

[0155] Calculation example 3:

[0156] This example presents a numerical simulation of a right circular cone at Mach 14 with a half-cone angle of 7° and different angles of attack. The experimental study was conducted by Marineau EC et al. in Wind Tunnel No. 9 at the Air Force Arnold Engineering Development Center (AEDC). The model, mesh, and boundary conditions were identical to those used for the aforementioned Mach 10 right circular cone. The calculation case for this example uses a free-flow Mach number. Reynolds number and , , The calculated free-flow turbulence intensity .

[0157] Figure 6 The calculated Stanton number was compared with the experimental result. The transition position matched the experimental result well, which proved the rationality and effectiveness of the improvement made in this invention.

[0158] In summary, the transition prediction method proposed in this invention, applicable to the wide Mach range of high-speed aircraft, can accurately predict the transition positions of different models under different test environments. It also has accurate prediction results for examples with a wide Mach range. It can be performed in large-scale parallel processing, ensuring prediction accuracy while greatly improving computational efficiency. It can be used to guide the design of high-speed aircraft.

[0159] 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 transition prediction method suitable for use in a wide Mach number regime of a high speed vehicle, characterized by: 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: Stability theory analysis is performed on the second mode in the dominant transition mode. The non-local variables are localized using the boundary layer characteristic parameter database established in S1, and the time scale of the second mode is analyzed. Improve the key variables and establish a localized mathematical model; Second modal time scale The formula is: in These are the characteristic time-scale control coefficients for the second mode. The most unstable frequency of the second-mode perturbation: in For phase velocity, It is the wavelength of the most unstable frequency of the second-mode perturbation, taken as the boundary layer thickness. Twice the thickness of the boundary layer; Determined in the following ways: Based on the boundary layer database established by 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 boundary layer thickness. With momentum thickness ratio A database showing the relationship between Mach number and wall temperature was used to fit the database, resulting in... Improved fitting formula: in The wall temperature, The temperature of the insulating wall surface. The Mach number at the edge of the boundary layer; Momentum Thickness Determined in the following ways: Using the boundary layer database established by S1, the improved momentum thickness was obtained. The calculation formula is: in For the shear strain mode, The normal distance to the wall. For boundary layer edge velocity; in Momentum thickness correction factor: For density, For boundary layer edge density, For kinetic viscosity, The boundary layer edge dynamic viscosity; The characteristic time scale control coefficient C6 of the second mode is determined according to the following formula: in Indicates the intensity of environmental disturbance; S3: Based on the localized instability modes established in S2, establish the laminar pulsating viscosity coefficient transport equation and the intermittent factor transport equation; S4: Couple the laminar pulsating viscosity coefficient transport equation and intermittent factor transport equation established in S3 with the SST turbulence model to establish... A four-equation turbulence-transition model was developed and embedded into an existing CFD solver. S5: The CFD solver in S4 is used to predict the laminar-turbulent transition of high-speed aircraft.

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