A three-dimensional supersonic boundary layer transition prediction method based on a neural network model

Abstract

The present invention provides a three-dimensional supersonic boundary layer transition prediction method based on a neural network model, belonging to the technical field of transition prediction. The method includes the following steps: S1. Obtain the flow field data of flat plates, blunt plates, and cones as the data samples of the neural network model; S2. Extract the characteristic parameters of the flow fields of flat plates, blunt plates, and cones under different working conditions; S3. Construct a neural network model to establish the relationship between the flow field characteristic parameters and the disturbance growth; S4. Calculate the flow field of a supersonic aircraft and extract the same flow field characteristic parameters as in S2; S5. Input the flow field characteristic parameters of the aircraft into the neural network model, output the disturbance growth rate of the supersonic aircraft, and then obtain the disturbance amplification factor by integrating the growth rate. When the disturbance amplification factor reaches e<supgt;7< / supgt;, it is predicted that transition occurs, solving the technical problem of low transition prediction efficiency in the prior art.

Description

Technical Field

[0001] The present application relates to a transition prediction method, in particular to a three-dimensional supersonic boundary layer transition prediction method based on a neural network model, and belongs to the technical field of transition prediction. Background Art

[0002] Transition is a flow phenomenon that characterizes the transition from laminar flow to turbulent flow. The transition problem is a widely concerned problem in the field of fluid mechanics and is also one of the unsolved problems. With the development of the aerospace industry, the research and development of supersonic aircraft is particularly crucial. In the supersonic flight state, the frictional drag on the aircraft can contribute up to 50% to the total drag, and the magnitude of the frictional drag is closely related to the flow state of the boundary layer. The frictional drag of the turbulent boundary layer is much greater than that of the laminar boundary layer. Therefore, for accurately calculating the drag of the aircraft, the prediction of the transition position is an important factor. In addition, the heat conduction capabilities of the laminar boundary layer and the turbulent boundary layer are also significantly different, and the prediction of the transition position is also important for thermal protection design.

[0003] Currently, the commonly used numerical simulation techniques for supersonic transition mainly include direct numerical simulation method (DNS), large eddy simulation (LES), intermittency factor transport model (RANS), and stability analysis method. DNS and LES methods are currently only used for the mechanism research of simple shapes due to their extremely large computational amounts. The intermittency factor transport model also brings a large computational amount and introduces large errors for aircraft with complex shapes. The most representative method in the stability analysis method is the eN method based on linear stability theory (LST), which is widely used in engineering practice. However, the eN method requires accurate boundary layer velocity and temperature profiles. In the three-dimensional boundary layer, there are complex flow phenomena such as separated flow and cross-flow vortices, which rely on high-precision numerical calculation methods. Moreover, the modal calculation of the three-dimensional boundary layer is more complex, and it is difficult to obtain the perturbation integral path. A global search for the initial eigenvalues is also required when solving the stability equation, which makes it time-consuming to use the stability analysis to calculate the perturbation growth.

[0004] From the current data, the research on transition prediction has become a key technology for aerospace development. However, the commonly used numerical simulation techniques for supersonic transition all require a large amount of time, and there is a lack of an efficient supersonic transition prediction method. Summary of the Invention

[0005] A brief overview of the present invention is given below to provide a basic understanding of certain aspects of the present invention. It should be understood that this overview is not an exhaustive overview of the present invention. It is not intended to identify the key or important parts of the present invention, nor is it intended to limit the scope of the present invention. Its purpose is only to present certain concepts in a simplified form as a prelude to the more detailed description to be discussed later.

[0006] In view of this, to solve the technical problem of low transition prediction efficiency in the existing technology, the present invention provides a three-dimensional supersonic boundary layer transition prediction method based on a neural network model.

[0007] Solution 1: A three-dimensional supersonic boundary layer transition prediction method based on a neural network model, comprising the following steps:

[0008] S1. Obtain flat plate, blunt plate, and cone flow field data as data samples for the neural network model;

[0009] S2. Extract characteristic parameters of the flat plate, blunt plate, and cone flow fields under different working conditions;

[0010] S3. Construct a neural network model to establish the relationship between the flow field characteristic parameters and the disturbance growth;

[0011] S4. Calculate the flow field of the supersonic aircraft and extract the same flow field characteristic parameters as in S2;

[0012] S5. Input the flow field characteristic parameters of the aircraft into the neural network model, output the disturbance growth rate of the supersonic aircraft, and then obtain the disturbance amplification factor by integrating the growth rate. When the disturbance amplification factor reaches e 7 a transition is predicted to occur, where e is the natural logarithm.

[0013] Preferably, the CFD is used to calculate the supersonic flat plate, blunt plate, and cone flow fields under different working conditions.

[0014] Preferably, the linear stability analysis method is used to obtain the disturbance growth rates corresponding to different flow field positions of the flat plate, blunt plate, and cone flow fields.

[0015] Preferably, the disturbance growth rate calculation method is as follows: Establish the NS equation and the state equation in a rectangular coordinate system:

[0016] ;

[0017] ;

[0018] ;

[0019] ;

[0020] ;

[0021] ;

[0022] Wherein, x, y, and z respectively represent the flow direction, normal direction, and spanwise direction in the Cartesian coordinate system, ρ represents density, u represents the flow velocity in the flow direction, v represents the flow velocity in the normal direction, w represents the flow velocity in the spanwise direction, T represents temperature, μ represents the viscosity coefficient, and the expression of the dissipation function Φ is: ;

[0023] Wherein, λ is the bulk viscosity coefficient, and its value is based on the Stokes hypothesis ;

[0024] For the internal flow field in the compressible boundary layer, dimensionless parameters are adopted. The reference length is taken, and the flow variables are referenced by the outer edge of the boundary layer , and the pressure is made dimensionless; the parallel flow hypothesis is introduced, and the vertical velocity component of the basic flow is ignored. At the same time, a three-dimensional small perturbation is superimposed on the basic flow, and the instantaneous flow field can be expressed as:

[0025] ;

[0026] For the three-dimensional supersonic transition problem, the form of the three-dimensional small perturbation is:

[0027] ;

[0028] Among them, represents the eigenvector of the perturbation, α and β respectively represent the wave numbers in the x direction and z direction, and ω represents the perturbation frequency.

[0029] Preferably, the dimensionless characteristic variables of the perturbation growth characteristics of the velocity type and temperature type are used as the flow field characteristic parameters.

[0030] Preferably, specifically, S3 is to select a neural network model based on radial basis functions, and select a Gaussian function as the basis function for training. Its expression is as follows:

[0031] ;

[0032] Among them, Vi represents the center point of the radial basis function, and Di represents the radial basis width of the radial basis function;

[0033] At the same time, a polynomial response surface model is combined for further fitting. Taking the second-order response surface model as an example, its expression is as follows:

[0034] ;

[0035] Among them, M represents the number of sample points, and α, β, and γ represent coefficients;

[0036] The order of the response surface model is selected based on the comprehensive determination of the number of sample points and the sample point dimension. The activation function is selected as the superposition combination of the Gaussian function and the polynomial response surface model. Its expression is as follows:

[0037] ;

[0038] Among them, M represents the number of sample points, represents the weight coefficient, represents the sample variable.

[0039] Solution 2: An electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the steps of a three-dimensional supersonic boundary layer transition prediction method based on a neural network model described in Solution 1 are implemented.

[0040] Solution 3: A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, a three-dimensional supersonic boundary layer transition prediction method based on a neural network model described in Solution 1 is implemented.

[0041] The beneficial effects of the present invention are as follows: By obtaining the flat plate, blunt plate, and cone flow field data as the data samples of the neural network model, extracting the flow field characteristic parameters, establishing the relationship between the flow field characteristic parameters and the disturbance growth, and using the flow field characteristic parameters to obtain the disturbance growth rate of the aircraft, the transition prediction method is realized; while ensuring the accuracy of the prediction result, the transition prediction efficiency is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation of the present application. In the drawings:

[0043] Figure 1 is a schematic flow chart of a three-dimensional supersonic boundary layer transition prediction method based on a neural network model;

[0044] Figure 2 is a schematic diagram of the transition prediction result. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0045] In order to make the technical solutions and advantages in the embodiments of the present application clearer and more understandable, the following further details the exemplary embodiments of the present application with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than an exhaustive list of all embodiments. It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0046] Embodiment 1: Refer to Figure 1 - Figure 2 to illustrate this embodiment. A three-dimensional supersonic boundary layer transition prediction method based on a neural network model includes the following steps:

[0047] S1. Obtain the flat plate, blunt plate, and conical flow field data as the data samples for the neural network model;

[0048] Use CFD to calculate the supersonic flat plate, blunt plate, and conical flow fields under different working conditions;

[0049] Use the linear stability analysis method to obtain the disturbance growth rates corresponding to different flow field positions of the flat plate, blunt plate, and conical flow fields.

[0050] The calculation method of the disturbance growth rate is as follows.

[0051] 1) Establish the NS equation and state equation in the Cartesian coordinate system:

[0052] ;

[0053] ;

[0054] ;

[0055] ;

[0056] ;

[0057] ;

[0058] In the formula, x, y, and z respectively represent the flow direction, normal direction, and spanwise direction in the Cartesian coordinate system, ρ represents the density, u represents the flow direction velocity, v represents the normal direction velocity, w represents the spanwise direction velocity, T represents the temperature, μ represents the viscosity coefficient, and the expression of the dissipation function Φ is:

[0059] ;

[0060] In the formula, λ is the bulk viscosity coefficient, and its value is based on the Stokes hypothesis ;

[0061] For the internal flow field in the compressible boundary layer, dimensionless parameters are adopted. Take the reference length , and the flow variables use the outer edge of the boundary layer as the reference quantity , and the pressure is dimensionlessized with ; Introduce the parallel flow hypothesis, ignore the vertical velocity component of the basic flow, and at the same time, superimpose three-dimensional small disturbances on the basic flow. The instantaneous flow field can be expressed as:

[0062]

[0063] For the three-dimensional supersonic transition problem, the form of the three-dimensional small disturbance is:

[0064]

[0065] Among them, represents the eigenvector of the perturbation, α and β represent the wave numbers in the x - direction and z - direction respectively, and ω represents the perturbation frequency.

[0066] S2. Extract the characteristic parameters of the flow fields of the flat plate, blunt plate, and cone under different working conditions;

[0067] Take the dimensionless characteristic variables of the perturbation growth characteristics of the velocity type and temperature type as the flow field characteristic parameters

[0068] S3. Construct a neural network model to establish the relationship between the flow field characteristic parameters and the perturbation growth;

[0069] Select a neural network model based on the radial basis function, select the Gaussian function as the basis function for training, and its expression is as follows:

[0070]

[0071] Among them, Vi represents the center point of the radial basis function, and Di represents the radial basis width of the radial basis function;

[0072] At the same time, combine the polynomial response surface model for further fitting. Taking the second - order response surface model as an example, its expression is as follows:

[0073]

[0074] Among them, M represents the number of sample points, and α, β, γ represent coefficients;

[0075] The order of the response surface model is selected based on the comprehensive determination of the number of sample points and the dimension of the sample points. The activation function is selected as the superposition combination of the Gaussian function and the polynomial response surface model, and its expression is as follows:

[0076]

[0077] Among them, M represents the number of sample points, represents the weight coefficient, represents the sample variable.

[0078] S4. Calculate the flow field of the supersonic aircraft and extract the same flow field characteristic parameters as in S2;

[0079] S5. Input the flow field characteristic parameters of the aircraft into the neural network model, output the perturbation growth rate of the supersonic aircraft, and then obtain the perturbation amplification factor by integrating the growth rate. When the perturbation amplification factor reaches e 7 it is predicted that transition occurs, where e is the natural logarithm.

[0080] The following further illustrates a three - dimensional supersonic boundary - layer transition prediction method based on a neural network model proposed in this embodiment by predicting the transition position of a supersonic swept - wing airfoil;

[0081] S1. Calculate the three-dimensional compressible blunt plate under different working conditions as samples. The specific calculation conditions are shown in Table 1:

[0082] Table 1

[0083]

[0084] Calculate the flow field of the three-dimensional compressible blunt plate, and use the linear stability analysis method to solve the disturbance growth rate;

[0085] S2. Select the following dimensionless parameters as the characteristic parameters of the boundary layer flow field and input them into the neural network model for training, namely the Reynolds number of the boundary layer thickness , Mach number Ma, and shape factor H, the ratio of the thickness at the maximum cross-flow velocity to the nominal thickness , the maximum cross-flow velocity , wall temperature ratio .

[0086] S3. Based on the radial basis function as the neural network model, establish the relationship between the characteristic parameters and the disturbance growth rate;

[0087] ;

[0088] S4. Calculate the flow field of the supersonic swept wing and extract the flow field characteristic parameters shown in S2. The calculated relevant parameters are shown in Table 2:

[0089] Table 2

[0090]

[0091] S5. Use the existing neural network model in S3 to predict the transition position of the supersonic swept wing. The transition prediction results are as Figure 2 shown.

[0092] The required calculation time is shown in Table 3,

[0093] Table 3

[0094]

[0095] Although the present invention has been described in terms of a limited number of embodiments, those skilled in the art of this technology will appreciate that other embodiments can be envisioned within the scope of the present invention as thus described. In addition, it should be noted that the language used in this specification has been principally selected for readability and instructional purposes rather than to limit or define the subject matter of the invention. Accordingly, many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the appended claims. For the scope of the present invention, the disclosure of the present invention is illustrative, not restrictive, and the scope of the present invention is defined by the appended claims.

Claims

1. A three-dimensional supersonic boundary layer transition prediction method based on a neural network model, characterized in that It includes the following steps: S1. Obtain the flat plate, blunt plate, and cone flow field data as the data samples of the neural network model, and use the linear stability analysis method to obtain the disturbance growth rates corresponding to different flow field positions of the flat plate, blunt plate, and cone flow fields; S2. Extract the flow field characteristic parameters of the flat plate, blunt plate, and cone under different working conditions; S3. Construct a neural network model to establish the relationship between the flow field characteristic parameters and the disturbance growth. The neural network model is a neural network model based on radial basis functions; S4. Calculate the flow field of the supersonic aircraft and extract the same flow field characteristic parameters as in S2; S5. Input the flow field characteristic parameters of the aircraft into the neural network model, output the disturbance growth rate of the supersonic aircraft, and then obtain the disturbance amplification factor by integrating the growth rate. When the disturbance amplification factor reaches e 7 , it is predicted that transition occurs, where e is the natural logarithm.

2. The three-dimensional supersonic boundary layer transition prediction method based on a neural network model according to claim 1, wherein Use CFD to calculate the supersonic flat plate, blunt plate, and cone flow fields under different working conditions.

3. The three-dimensional supersonic boundary layer transition prediction method based on a neural network model according to claim 1, wherein, The disturbance growth rate calculation method is as follows: Establish the NS equation and state equation in the rectangular coordinate system: p = ρRT Where x, y, and z respectively represent the flow direction, normal direction, and spanwise direction in the Cartesian coordinate system, ρ represents the density, u represents the flow direction velocity, v represents the normal direction velocity, w represents the spanwise direction velocity, T represents the temperature, μ represents the viscosity coefficient, and the expression of the dissipation function Φ is: where λ is the coefficient of bulk dilatational viscosity, and its value is based on the Stokes hypothesis For the internal flow field in a compressible boundary layer, dimensionless parameters are adopted, and the reference length is taken The flow variables use the outer edge of the boundary layer as the reference quantity U e , T e , ρ e , μ e , k e , the pressure is made dimensionless; the parallel flow assumption is introduced, the vertical velocity component of the basic flow is ignored, and at the same time, a three-dimensional small perturbation is superimposed on the basic flow. The instantaneous flow field is expressed as: q(x, y, z, t) = q0(y) + q'(x, y, z, t) For the three-dimensional supersonic transition problem, the form of the three-dimensional small disturbance is: Among them, represents the eigenvector of the perturbation, α and β respectively represent the wave numbers in the x - direction and z - direction, and ω represents the perturbation frequency.

4. The three-dimensional supersonic boundary layer transition prediction method based on a neural network model according to claim 3, wherein Take the dimensionless characteristic variables of the disturbance growth characteristics of the velocity type and temperature type as the flow field characteristic parameters.

5. The three-dimensional supersonic boundary layer transition prediction method based on a neural network model according to claim 1, characterized in that, In S3, the Gaussian function is selected as the basis function for training, and its expression is as follows: Among them, Vi represents the center point of the radial basis function, and Di represents the radial basis width of the radial basis function; At the same time, combine the polynomial response surface model for further fitting. Taking the second-order response surface model as an example, its expression is as follows: Among them, M represents the number of sample points, and α, β, and γ represent coefficients; The order of the response surface model is selected based on the comprehensive determination of the number of sample points and the dimension of the sample points. Select the activation function as the superposition combination of the Gaussian function and the polynomial response surface model, and its expression is as follows: Among them, M represents the number of sample points, ω i represents the weight coefficient, and n represents the sample variable.

6. An electronic device, characterized in that, It includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it implements the steps of a three-dimensional supersonic boundary layer transition prediction method based on a neural network model as claimed in claim 1 or 2 or 3 or 4 or 5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements a three-dimensional supersonic boundary layer transition prediction method based on a neural network model as claimed in claim 1 or 2 or 3 or 4 or 5.

Images