Transition prediction method suitable for wide Mach domain of high-speed aircraft

Abstract

According to the transition prediction method suitable for the wide Mach domain of the high-speed aircraft provided by the invention, temperature and Mach number coupling correction is performed on key parameters in time scale modeling of a second mode of a transition mode, and simplified processing of a flow compression effect and a heat transfer process by traditional single parameter association is broken through; the influence of an incoming flow disturbance effect is embedded in the mode, and dynamic association between test environment parameters and transition triggering criteria is achieved; according to the improved mode, accurate prediction results are obtained on a plurality of examples with the Mach number range of 4.7-14, the research results provide a more reliable theoretical tool for aerodynamic configuration optimization of a high-speed aircraft with a wider speed range, and the method has important engineering guiding significance for thermal protection system design of a new-generation reusable aircraft.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of aerospace and computational fluid dynamics, and particularly relates to a transition prediction method suitable for a wide Mach number range of a high-speed aircraft. BACKGROUND

[0002] High-speed aircrafts show important application value in the field of space exploration, but their aerodynamic design faces severe challenges brought by extreme working environment. The process of boundary layer flow transition from laminar flow to turbulent flow directly affects the surface friction drag, heat flow distribution and aerodynamic stability of the aircraft, which makes transition prediction a key link of the design of the aircraft thermal protection system and the optimization of the aerodynamic shape.

[0003] Among the transition prediction methods, the RANS-based prediction method, which has both computational efficiency and computational accuracy and can greatly save manpower, material resources and financial resources, is still the most commonly used method in the engineering application field. The transition model based on RANS can be divided into two categories: based on empirical relationship and based on physical mechanism.

[0004] The most representative transition model based on empirical relationship is the transition model proposed by Menter and Langtry, etc. The mathematical form of the model is a standard scalar transport equation, which is fully compatible with the modern CFD solving framework. However, the initial transition model is based on incompressible flow, although many scholars have made compressible correction and improvement, but in fact the transition mechanism of hypersonic / supersonic speed is quite different from incompressible flow, and only numerical correction of incompressible transition model will make the transition model lose the physical meaning behind some transition phenomena, and it is also difficult to have good universality.

[0005] The core concept of the physical-based model is to model the non-turbulent (i.e. laminar) fluctuations before and in the transition zone, and the most representative one of which is the transition prediction model based on laminar fluctuation kinetic energy. The laminar kinetic energy model represents the non-turbulent fluctuation with an independent variable, i.e. laminar kinetic energy . Mayle and Schulz first proposed the transport equation to characterize the streamwise velocity fluctuations before transition. After that, some schemes proposed the transition model, which is established by merging the equation into the existing and turbulent flow through an additional source term. The model has strong bypass transition prediction ability, and its prediction ability for natural transition and separation bubble transition needs further research and improvement. Further research improves the transition model for hypersonic wall heat transfer, and extends the model to predict the transition dominated by distributed roughness.

[0006] In the previous research of the applicant's research group, a transition model compatible with modern CFD large-scale parallel computing is constructed based on the RANS framework. The evolution and instability of the disturbance are mainly modeled according to the Mack stability analysis conclusion for high-speed boundary layer, and a laminar fluctuating viscosity coefficient transport equation is constructed. The process of transition is described by an intermittent factor equation, and the turbulent flow part is calculated by using the classical SST turbulent flow model with compressible correction. After a large number of examples, the model can better simulate the boundary layer transition process under different transition mechanisms, and has good accuracy.

[0007] However, with the expansion of the working condition of modern aircraft to a wide Mach number domain (Ma=5-12), the limitation that the above prediction method cannot accurately predict in a wider Mach number range at the same time will be highlighted. At present The characterization of temperature effect and Mach number effect in the construction of the second mode time scale of the Mack model is not perfect, which limits the universality of the model under variable Mach number and wall temperature conditions. In addition, the influence of the difference in the disturbance level of the incoming flow in different wind tunnel test and flight test environments on the transition trigger has not been systematically included in the prediction system, resulting in a certain calculation deviation from the test results in engineering application. SUMMARY

[0008] In view of the problems existing in the prior art, the present application proposes a transition prediction method suitable for high-speed aircraft in a wide Mach number domain, which is characterized in that The key parameters in the modeling of the second mode time scale of the transition model are modified by coupling temperature and Mach number, breaking through the simplified processing of the flow compression effect and heat transfer process by traditional single parameter correlation. The influence of the incoming flow disturbance effect is embedded in the model to realize the dynamic correlation between the test environment parameters and the transition trigger criterion. The improved model has achieved accurate prediction results on multiple examples in the Mach number range of 4.7-14. The research results provide a more reliable theoretical tool for aerodynamic configuration optimization of high-speed aircraft in a wider speed domain, and have important engineering guiding significance for the thermal protection system design of new generation reusable aircraft.

[0009] The technical scheme of the present application is as follows:

[0010] A transition prediction method suitable for high-speed aircraft in a wide Mach number domain, comprising the following steps:

[0011] S1: A compressible Falkner-Skan-Cooke equation is solved to establish a compressible three-dimensional boundary layer characteristic parameter database, and the relationship between local and non-local variables in the required boundary layer is obtained;

[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, is the adiabatic wall temperature.

[0025] Further, the momentum thickness The momentum thickness is determined by the following way:

[0026] The improved momentum thickness is obtained by using the boundary layer database established by S1 The calculation formula is:

[0027]

[0028] Wherein is the shear strain module, is the wall normal distance, is the boundary layer edge velocity;

[0029]

[0030]

[0031]

[0032] Wherein is the momentum thickness correction factor:

[0033]

[0034] is the density, is the boundary layer edge density, is the dynamic viscosity, is the boundary layer edge dynamic viscosity.

[0035] Further, 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] The application provides a transition prediction method suitable for wide Mach number range of a hypersonic vehicle. The calculation method of the key variables required for the construction of the Mack second mode time scale in the transition-turbulence prediction mode is improved. In order to better reflect the overall flow characteristics of the boundary layer, the calculation of the momentum thickness is modified with the temperature and Mach number effects; the correlation between the boundary layer thickness and the momentum thickness is re-corrected by comprehensively considering the Mach number effect and the temperature effect of the adiabatic wall and the cooling / heating constant temperature wall; in order to enhance the adaptability of the mode to different test environments, the influence of the incoming flow disturbance effect is introduced. After the mode is improved, the prediction ability of the improved mode is verified under multiple Mach number conditions by using multiple wind tunnel test configurations. The results show that compared with the previous study, the improved mode can realize high-precision transition position prediction in a wider Mach number range, fully proving the rationality and accuracy of the improvements made in the application, and providing a more extensive application basis for the aerodynamic design of high-speed aircraft.

[0042] Additional aspects and advantages of the application will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following and / or can be learned by practice of the application. BRIEF DESCRIPTION OF DRAWINGS

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

[0044] Figure 1 is a schematic diagram of the flow of the method of the present application.

[0045] Figure 2 is a schematic diagram of the coordinate system adopted by the boundary layer flow.

[0046] Figure 3 is the 6 Mach straight cone grid and boundary condition setting.

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

[0048] Figure 5 is the comparison of the calculated and experimental transition positions of the 10 Mach straight cone.

[0049] Figure 6 is the comparison of the calculated and experimental transition positions of the 14 Mach straight cone, .

[0050] Figure 7 is the comparison of the calculated and experimental transition positions of the 14 Mach straight cone, . DETAILED DESCRIPTION

[0051] Embodiments of the application are described in detail below, which are exemplary and intended to explain the application, and cannot be understood as a limitation of the application.

[0052] High-speed boundary layer transition prediction technology plays a vital role in the aerodynamic and thermal protection design of high-speed vehicles, and its prediction accuracy is directly related to the aerodynamic performance and safety of the vehicle. In order to make the transition prediction model have a wider Mach number applicability to meet the requirements of modern vehicle design for multi-working condition and high-precision prediction, the present application proposes a transition prediction method suitable for wide Mach number range of high-speed vehicles, which is used to predict the transition position of the surface of a test model in various test environments. The calculation method of the key variables required for constructing the time scale of Mack's second mode in the transition-turbulence prediction model is improved. The calculation of momentum thickness is temperature corrected to better reflect the overall flow characteristics of the boundary layer; the correlation between the boundary layer thickness and the momentum thickness is re-corrected by considering the Mach number effect and the temperature effect of the adiabatic wall and the cooling / heating constant temperature wall; and the influence of the incoming flow disturbance effect is introduced to enhance the adaptability of the model to different test environments. After the improvement of the model, the prediction ability of the improved model is verified under multiple Mach number conditions using multiple wind tunnel test configurations. The results show that compared with previous studies, the improved model can achieve high-precision transition position prediction in a wider Mach number range, fully proving the rationality and accuracy of the improvements made in the present application, and providing a more extensive application basis for high-speed vehicle aerodynamic design.

[0053] As shown in Figure 1 , the present embodiment adopts a transition prediction method suitable for wide Mach number range of high-speed vehicles to predict the transition position of the surface of a test model in various test environments, including the following steps:

[0054] S1, a compressible Falkner-Skan-Cooke (FSC) equation is solved to establish a compressible three-dimensional boundary layer characteristic parameter database, and the relationship between the required local and non-local variables in the boundary layer is obtained. This step has been disclosed in previous studies, and the details are as follows:

[0055] The FSC equation is a simplified form of the N-S equation in the boundary layer, and the FSC equation is expressed as only depending on local variables and geometric parameters, as follows

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] Definition as Figure 2The coordinate system shown in the figure, , is a fixed plane rectangular coordinate system, and the dashed line represents a curvilinear coordinate system, is the direction of the combined velocity of the boundary layer edge, is perpendicular to the direction, wherein is the density, is the dynamic viscosity, is the ratio of the velocity in the local direction to the velocity in the boundary layer edge direction, β is the pressure gradient factor, g is the acceleration of gravity, Pr is the Prandtl number, q is the ratio of the local total enthalpy to the total enthalpy of the boundary layer edge, Ue is the velocity in the boundary layer edge direction, is the sweep angle behind the boundary layer edge, T is the temperature, M is the Mach number, is the specific heat ratio, and the superscript denotes the derivative, and the subscript e represents the value of the boundary layer edge. In the above equation, the expressions of the parameters , β, g, q, , m are as follows:

[0062]

[0063]

[0064] wherein u is the velocity component in the direction of the coordinate system, w is the velocity component in the direction, and H is the total enthalpy.

[0065] The viscous Sutherland formula is introduced to close the equation set:

[0066]

[0067] wherein is the Sutherland constant, the value is 110.4K, T is the temperature, is the dynamic viscosity, and the subscript e represents the value of the boundary layer edge.

[0068] The velocity profile and the temperature profile in the boundary layer are obtained by solving the FSC equation, and the required characteristic parameters, such as the boundary layer thickness, the boundary layer momentum thickness, and the boundary layer displacement thickness, are further obtained through the velocity profile and the temperature profile. Different Mach numbers, pressure gradients, and wall temperatures are used to solve the FSC equation, and the obtained characteristic parameters are stored to obtain a database of characteristic parameters of a compressible three-dimensional boundary layer.

[0069] S2, stability theory analysis is performed on the second mode in the dominant transition mode, the non-local variable is localized by using the boundary layer characteristic parameter database established in S1, and the key variable of the time scale of the second mode is improved to establish a localized mathematical model

[0070] The dominant transition mode is Mack's first mode, Mack's second mode and cross-flow mode. The modeling process of the three modes has been disclosed in previous studies. The modeling process of the second mode is as follows:

[0071] According to Mack's stability theory analysis and experimental observation, the most unstable frequency of Mack's second mode disturbance is obtained as follows:

[0072]

[0073] wherein is the wavelength of the most unstable frequency of Mack's second mode disturbance, is the phase velocity

[0074]

[0075] The characteristic time scale of Mack's second mode is obtained as follows:

[0076]

[0077] In previous studies, the characteristic time scale control coefficient C6 of the second mode and the wavelength of the most unstable frequency of the second mode disturbance are constant, which leads to the fact that previous studies are only applicable to specific wall temperature and specific turbulence conditions, and the prediction ability for high Mach number conditions is also preferential. The modification of the characteristic time scale control coefficient C6 of the second mode and the wavelength of the most unstable frequency of the second mode disturbance is the core of the present application.

[0078] For the wavelength of the most unstable frequency of the second mode disturbance , according to the stability analysis, is twice the thickness of the boundary layer : Therefore, it is determined that the thickness of the boundary layer is critical.

[0079] The traditional thickness of the boundary layer is calculated according to the formula

[0080]

[0081] , wherein is the 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 improving the boundary layer thickness and the momentum thickness The wavelength of the most unstable frequency of the second mode disturbance is improved The prediction ability of the transition model in high Mach number conditions is enhanced.

[0100] For the characteristic time scale control coefficient C6 of the second mode, a number of wind tunnel and flight test examples are used for calibration and fitting, and the incoming flow disturbance effect is introduced to better cope with different wall temperatures and turbulence degrees, and the main process is as follows:

[0101] To enhance the adaptability of the model to different wind tunnel environments and flight environments, the present application introduces the influence of incoming flow disturbance effect. Turbulence degree as a physical quantity to characterize the quality of flow field or the degree of free incoming flow disturbance has an important influence on the transition position of the test model. The huge difference in turbulence degree between ground wind tunnel test and flight test is also the main reason for the large data divergence between them. There are facts that show that there is a certain correlation between wind tunnel noise and turbulence degree, and in the hypersonic condition, the correlation between noise and turbulence degree can reach more than 80%.

[0102] In wind tunnel test, the noise level of wind tunnel is usually obtained by measuring pressure fluctuation. Among them, the noise level percentage (Noise Level, NL) is a way to quantitatively describe the noise level of wind tunnel, which is defined as follows

[0103]

[0104] Where the time-averaged pressure p and the root mean square fluctuation pressure p rms are defined as follows

[0105]

[0106]

[0107] Where is the instantaneous pressure at a certain spatial position.

[0108] The fitting curves of the noise levels of different wind tunnels at home and abroad, NASA LaRC 20 Inch (M=6) and AEDC Tunnle 9, are as follows

[0109]

[0110]

[0111] There are also studies by discussing the characteristics of various hyperbolic waves in Euler system, focusing on the essential relationship between fluctuating pressure and fluctuating velocity in the sound field, and theoretically obtaining the relationship between sound pressure level and sound-induced turbulence:

[0112]

[0113] Wherein, The specific heat ratio of the gas is represented by Cp / Cv, The free stream Mach number is represented by M. The present invention uses To quantify the environmental disturbance intensity. Its calculation depends on the measurement of the environmental noise level (pressure fluctuation intensity). If the environmental noise level can be explicitly provided, the turbulence intensity level can be calculated or interpolated using the above formula. In the absence of environmental pressure fluctuation intensity information, reasonable estimates must be made. For example, a typical low environmental disturbance intensity under flight conditions is usually assigned a value of 0.01%. If it is operated in a wind tunnel where the environmental disturbance intensity is unknown, a reasonable estimate can be made by analogy to the closest comparable wind tunnel experiment.

[0114] Finally, the second modal scale control coefficient C6 is calibrated by several wind tunnel and flight experiment examples, and according to the calibration results, the influence of turbulence intensity is introduced into the second modal scale control coefficient C6:

[0115]

[0116]

[0117]

[0118]

[0119] In this embodiment, the second modal scale control coefficient C6 of the 6 Mach straight cone model tested in the NASA Langley 6 Mach anechoic wind tunnel is selected for calibration, and the coefficients of the improved model and the improved model are 0.3375 and 2.0250 respectively. After the calibration of the coefficient C6, the 11.3 Mach sharp double cone and the 14 Mach example are selected for verification. The verification results show that the improved model before the improvement cannot calculate the transition phenomenon, and the calculated results of the improved model after the improvement are in good agreement with the experiments. Therefore, the prediction effect of the improved model for higher Mach number examples has been obviously improved, which proves the effectiveness of the improvement made by the present invention.

[0120] S3, based on the local instability mode established in S2, the transport equation of laminar fluctuating viscosity coefficient and the intermittency factor transport equation are established; this process has been disclosed in previous studies, and the specific process is as follows:

[0121] The transport equation of laminar fluctuating viscosity coefficient is established, which is as follows:

[0122] ∂ ( p v L ) ∂ t + ∂ ( u j p v L ) ∂ x j = P v L − E v L + ∂ ∂ x j [ s 1 p ( v + s m L v L ) ∂ v L ∂ x j ]

[0123] where, and are the generation and destruction source terms of the laminar fluctuation viscosity coefficient, respectively, and their specific expressions are:

[0124]

[0125]

[0126] To combine the first, second, and cross-flow instability modes in the hypersonic boundary layer, the total time scale of the laminar fluctuation is set as:

[0127]

[0128]

[0129] , , correspond to the first, second, and cross-flow mode time scales, respectively, is the relative Mach number, is the acoustic speed.

[0130] The intermittent factor transport equation is established, which is as follows:

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

[0132] where, and are the generation and destruction source terms of the intermittent factor equation, respectively, and their specific expressions are:

[0133] P g = p C 3 F onset ( 1 − g ) [ − ln ( 1 − g ) ] 1 3 S

[0134]

[0135] where C3=80.0, C4=0.06, and C5=50.0 are model constants, is the modulus of vorticity. The switch function of the generation source term mainly controls the starting point of the entire transition process, which is calculated as follows:

[0136]

[0137] where, In order to suppress the destruction source term in the boundary layer laminar bottom layer and the boundary layer outside the boundary layer, is defined as:

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

[0139] where, is the laminar pulsating viscosity coefficient, is the molecular viscosity coefficient, is the model coefficient, is the viscosity ratio.

[0140] S4, the laminar pulsating viscosity coefficient transport equation and the intermittency factor transport equation established in S3 are coupled with the SST turbulence model to establish a four-equation turbulence-transition model, and the above model is embedded in the existing CFD solver capable of large-scale parallel computing, in this embodiment, the CFD solver is the open source CFD code CFL3D of NASA. This process has been disclosed in previous studies, and the specific process is as follows:

[0141] The turbulence model after coupling the laminar pulsating viscosity coefficient transport equation and the intermittency factor transport equation obtained in step S3 with the turbulent energy generation source term and the destruction source term of the Menter SST turbulence model is as follows:

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

[0143] ∂ ( w p ) ∂ t + ∂ ( w u j t ) ∂ x j = α t p i j ∂ u i ∂ x j − ( 1 + M t 2 ) β w m 2 + ∂ ∂ x j [ ( s + w m w t ) ∂ p ∂ x j ] + 2 ( 1 − F 1 ) s w w 2 w ∂ k ∂ x j ∂ Figure 3 ∂ x j

[0144]

[0145]

[0146]

[0147] M t represents the turbulent Mach number, which is defined as , and a represents the local sound speed.

[0148] S5, the CFD solver in S4 is used to predict the laminar-turbulent transition of a high-speed aircraft. The specific numerical solution method can use the finite volume method, in which the inviscid flux is discretized by the FDS (Flux Difference Splitting) format of Roe, the viscous flux is discretized by the central difference format, and the time advancement is performed by the approximate factorization method. In the calculation, the multi-grid and grid sequence technology are used to accelerate the convergence, and large-scale parallel computing is performed based on the MPI (Message Passing Interface) parallel strategy.

[0149] Example 1: ​

[0150] The 6 Mach straight cone case completed by Horvath et al. in NASA Langley Research Center 6 Mach anechoic wind tunnel is chosen as the example. The free stream Mach number , and the wall temperature is constant . The calculated turbulent intensity is . The axisymmetric geometry of the zero angle of attack cone is calculated by using a quarter cone. The computational grid is arranged in the streamwise, circumferential and wall normal directions with 401, 101 and 201 grids respectively. The height of the first layer of the boundary layer is , which ensures . The grid and boundary conditions are shown in Figure 4 . The numerical solution method and parameters are set, and parallel solution is performed until convergence.

[0151] Figure 5 The dimensionless heat transfer coefficients at three Reynolds numbers are compared between the predicted results and the experimental measurements . The heat transfer coefficient is defined as , where is the wall heat flux; and are the enthalpies of the theoretical adiabatic wall and the physical wall respectively; is the reference heat flux value obtained by the Fay and Riddell stagnation temperature calculation formula. As shown in the figure, the phenomenon of heat flux increase due to transition is consistent with the experiment, which proves the rationality of the second mode modeling and improvement.

[0152] Example 2:

[0153] This example is a numerical simulation of a 10 Mach straight cone with a half cone angle of 7°. The model size is as follows: half cone angle 7°, bottom diameter D b = 0.381 m, head radius R n = 0.152 mm. The experimental study was conducted by Marineau E C et al. in Air Force Arnold Engineering Development Center (AEDC) No. 9 wind tunnel. The Mach number , Reynolds number , , , the calculated free stream turbulent intensity is .

[0154] The computational grid is arranged in the streamwise, circumferential and wall normal directions with 785, 132 and 98 grids respectively. The height of the first layer of the boundary layer is 1 × 10 −5 mm, and the growth rate is 1.1, which ensures The grid region is sufficient to fully contain the characteristic flow field phenomena such as oblique shock, and can capture the details in the flow and boundary layer changes. At the same time, the calculation grid is verified for grid convergence, and the results show that the grid convergence has been established. The inlet condition is Riemann boundary, the outlet condition is extrapolation boundary, and the wall condition is no-slip adiabatic wall. The numerical solving method and parameters are set, and parallel solving is performed until convergence. Figure 6 The distribution of the calculated surface Stanton number is shown.

[0155] Example 3

[0156] This example is a numerical simulation of a straight circular cone at 14 Mach with a half cone angle of 7° and different attack angles. The experimental study was conducted by Marineau E C et al. in the Air Force Arnold Engineering Development Center (AEDC) No. 9 wind tunnel, and the model, grid and boundary condition setting are the same as the above 10 Mach straight cone. The calculation conditions of this example are selected as the free stream Mach number , the Reynolds number and , , , the calculated free stream turbulence .

[0157] ​ For comparison of the calculated surface Stanton number and the experiment, the transition position is in good agreement with the experiment, which proves the rationality and effectiveness of the improvement made by the present application.

[0158] In summary, the transition prediction method suitable for wide Mach number range of high-speed aircraft proposed by the present application can accurately predict the transition position of different models in different test environments, and has accurate prediction effect for examples in wide Mach number range. It can be used to guide the design of high-speed aircraft.

[0159] Although the embodiments of the present application have been shown and described above, it should be understood that the above-mentioned embodiments are exemplary and should not be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above-mentioned embodiments without departing from the principles and purposes of the present application within the scope of the present application.

Claims

1. A transition prediction method applicable to the wide Mach range of high-speed vehicles, 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: 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; 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.

2. The transition prediction method applicable to the wide Mach range of high-speed vehicles according to claim 1, characterized in that: In S2, the second modal time scale The formula is: 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.

3. The transition prediction method applicable to the wide Mach range of high-speed vehicles according to claim 2, characterized in that: 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: 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, This refers to the temperature of the adiabatic wall surface.

4. The transition prediction method applicable to the wide Mach range of high-speed vehicles according to claim 3, characterized in that: 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.

5. The transition prediction method applicable to the wide Mach range of high-speed vehicles according to claim 2, characterized in that: The characteristic time scale control coefficient C6 of the second mode is determined according to the following formula: 。

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