Adaptive parameter identification method for SST turbulence model in shock wave boundary layer interference

Abstract

The invention discloses a self-adaptive parameter identification method for an SST turbulence model in shock wave boundary layer interference, and the method comprises the steps: S1, constructing a high-dimensional sample space according to a closed parameter interval range of the SST turbulence model under a determined working condition, carrying out the optimal Latin hypercube sampling, and uniformly obtaining the sample information in the whole space, and enabling the sample information to serve as an input parameter sample; s2, performing numerical simulation based on an input parameter sample and a determined working condition to form a model prior sample set; s3, according to the model prior sample set, constructing a flow field wall surface pressure prediction model under shock wave boundary layer interference based on an improved Bayesian neural network; and S4, based on the flow field wall surface pressure prediction model under the interference of the shock wave boundary layer, performing adaptive parameter identification on the SST turbulence model by adopting a particle swarm optimization algorithm to obtain the optimal closing parameter of the SST turbulence model for realizing the high-precision simulation of the flow field. According to the method, the numerical simulation precision and speed are improved, and technical support is provided for safe and reliable work of the scramjet engine in a complex environment.

Description

Technical Field

[0001] The invention belongs to the technical field of aerodynamics, and in particular relates to an adaptive parameter identification method of an SST turbulence model in shock wave boundary layer interference. Background Art

[0002] Shock wave / boundary layer interaction (SWBLI) is a common phenomenon involving complex flow structures. It has many effects on the flow and may cause a series of negative effects such as structural damage, aeroelasticity and thermal protection difficulties, intake airflow distortion, and even inlet failure. It is one of the most common challenges in fluid mechanics. Although identifying, understanding and controlling separated flows are essential in aerodynamics, predicting separated flows remains challenging. In terms of flow mechanism, SWBLI is mainly studied through precise and detailed means such as direct numerical simulation (DNS) and large eddy simulation (LES). These methods are accompanied by high-quality grids and unbearable computational costs. The Reynolds-averaged NS equations (RANS) have the advantages of strong robustness, high computational efficiency, and low requirements for computer hardware, and are widely used in practical engineering applications.

[0003] At present, most RANS models are based on the eddy viscosity hypothesis. The turbulence models developed from the 20th century to the present mainly include Spalart Allmaras (SA) model, model, model, Shear Stress Transport (SST) model, Baldwin-Lomax (BL) model, model, etc., and also include a series of other improved turbulence models, but the accuracy of each turbulence model depends on the actual problem. The model closure value in each turbulence model is calibrated by the model builder using data from simple flows. The closure coefficient value recommended by the model builder is usually called the nominal value. So far, there is no evidence that the nominal value performs well in all types of flows. Different types of flows should have different coefficient recommended values ​​to best match the turbulence model. Therefore, adjusting the closure coefficient value for a specific type of flow to improve the accuracy of numerical simulation has become one of the current research hotspots.

[0004] In the process of establishing the RANS model, some assumptions are introduced into the turbulence model, which leads to the uncertainty of numerical simulation. The uncertainty caused by the closure coefficient is called parameter uncertainty. The commonly used RANS models currently include one-equation models and two-equation models, such as the SA one-equation turbulence model, the BSL two-equation turbulence model and the SST two-equation turbulence model. The SA turbulence model has 11 closure coefficients, the BSL turbulence model has 8 closure coefficients, and the SST turbulence model has 9 closure coefficients. For simple flows, the closure coefficients of each turbulence model are selected according to the nominal value, and the obtained numerical simulation results are relatively ideal. However, for complex flows, the selection of nominal values ​​for calculation may result in large errors. Machine learning methods have been widely used in computational fluid dynamics. For a large number of posterior samples, it is time-consuming and unrealistic to perform CFD simulations on each set of parameters. In order to reduce the computational overhead, a machine learning proxy model is needed to reduce the computational cost. It is of great significance to explore complex flow mechanisms. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the adaptive parameter identification method of the SST turbulence model in the shock wave boundary layer interference provided by the present invention improves the accuracy and speed of numerical simulation, and provides technical support for the safe and reliable operation of scramjet engines in complex environments.

[0006] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: an adaptive parameter identification method of the SST turbulence model in shock wave boundary layer interference, comprising the following steps:

[0007] S1. Under certain working conditions, a high-dimensional sample space is constructed according to the closed parameter interval range of the SST turbulence model, and optimal Latin hypercube sampling is carried out in the high-dimensional sample space to uniformly obtain sample information in the entire space as input parameter samples;

[0008] S2. Based on the input parameter samples and the determined working conditions, numerical simulation is performed to form a model prior sample set;

[0009] S3. According to the model prior sample set, a wall pressure prediction model of the flow field under shock wave boundary layer interference based on the improved Bayesian neural network is constructed;

[0010] S4. Based on the wall pressure prediction model of the flow field under the interference of shock wave boundary layer, the particle swarm optimization algorithm is used to perform adaptive parameter identification of the SST turbulence model to obtain the optimal closure parameters of the SST turbulence model for high-precision simulation of the flow field.

[0011] Furthermore, in step S1, the operating conditions are determined according to the flow field channel configuration parameters and the incoming flow condition parameters;

[0012] The flow field channel configuration is a compression corner configuration, and its parameters include compression corner size and compression angle;

[0013] The incoming flow condition parameters include Mach number, boundary layer thickness, inlet total temperature and inlet total pressure.

[0014] Furthermore, in step S1, the optimal Latin hypercube sampling is a sampling method obtained by improving the Latin hypercube sampling by minimizing the maximum distance criterion;

[0015] Among them, the criterion for minimizing the maximum distance is: the distance between each sample in the high-dimensional sample space is taken as the maximum distance obtained in the high-dimensional sample space.

[0016] Furthermore, the step S2 includes the following sub-steps:

[0017] S21. Under a determined working condition, inputting the input parameter sample into a high-precision numerical simulation software for calculation to obtain RANS numerical simulation data;

[0018] S22. Perform data assimilation processing on the numerical simulation data to form a model prior sample set of multi-source data fusion.

[0019] Furthermore, the step S3 is specifically as follows:

[0020] The improved Bayesian neural network is used to learn the characteristic parameters of the model prior sample set, and the nonlinear mapping relationship between the SST turbulence model parameters and the flow field wall pressure is obtained. Then, the flow field wall pressure proxy model based on the improved Bayesian neural network is obtained. The model prior sample set is used to train the flow field wall pressure proxy model, and the flow field wall pressure prediction model under shock wave boundary layer interference is obtained.

[0021] Furthermore, the flow field wall pressure proxy model based on the improved Bayesian neural network is expressed as:

[0022]

[0023] In the formula, P(Y|X) represents the probability of outputting Y given input X, P(Y|X,ω) represents the probability distribution of outputting Y given weight ω and input X, P(D) represents the evidence probability, and E P(ω∣D) [P(Y|X,ω)] is the variational estimate of ∫P(Y|X,ω)P(ω|D)dω, where ω represents the internal parameters of the surrogate model.

[0024] Furthermore, the improved Bayesian neural network includes an input layer, a plurality of hidden layers and an output layer connected in sequence;

[0025] Hidden neurons in the hidden layer are connected with activation functions, and skip connections are used between adjacent hidden layers;

[0026] The input of the input layer is propagated to the output layer through the following formula:

[0027] Y k =f k (W k Y k*l +b k )

[0028] Where Y k represents the output of the kth layer, W k and b k represents the weight and bias of the kth layer, f k (·) represents the activation function of the k-th layer.

[0029] Furthermore, the loss function Loss of training the flow field wall pressure proxy model is:

[0030]

[0031] Where D KL [q(w|θ)||P(w)] represents the KL divergence between two probability distributions q(w|θ) and P(w), q(w|θ) represents the variational distribution in variational inference, and P(w) represents the prior distribution, which is the distribution of the neural network weight w when no data is observed. j represents the actual value of the jth sample, f(x j ) represents the predicted value of the jth sample, w represents the distribution probability of the parameter, θ represents the control parameter of the variational distribution q(w|θ), which determines the shape of the approximate posterior distribution, and x j Represents the input features of the j-th sample, the subscript j represents the j-th, and n represents the total number of samples.

[0032] Furthermore, in step S4, the formula for adaptive parameter identification of the SST turbulence model using the particle swarm optimization algorithm is:

[0033] ν id (k+1)=ν id (k)+c1r1[p id (k)-x id (k)]+c2r2[p gd (k)-x id (k)]

[0034] x id (k+1)=x id (k)+ν id (k+1)

[0035]

[0036] p gd (k) = min{p 1d (k),...,p id (k)},i∈N

[0037] Where, ν id (k+1) and ν id (k) represents the velocity of the dth dimension of the i-th particle at the k+1th iteration and the kth iteration, p id (k) represents the individual optimal position of the dth dimension of the i-th particle in a total of k iterations, x id (k) and x id (k+1) represents the position of the dth dimension of the i-th particle at the k-th iteration and the k+1-th iteration, p id (k) and p id (k+1) represents the individual optimal position of the dth dimension of the i-th particle in a total of k iterations and the k+1th iteration, p gd (k) represents the global optimal position of the dth dimension of the entire population in a total of k iterations, f(·) represents the fitness function, c1 and c2 represent learning factors, r1 and r2 represent random numbers between [0,1], and N is the population size.

[0038] The beneficial effects of the present invention are:

[0039] (1) The present invention can meet the demand for high-precision numerical simulation of supersonic flow in shock wave boundary layer interference by combining machine learning, fluid mechanics and scramjet engine technology, using data obtained from ground pulse combustion wind tunnels and high-precision numerical simulation software to construct pressure and flow field data sets, and realize adaptive parameter identification of turbulence models through machine learning technology.

[0040] (2) The present invention improves the accuracy and speed of numerical simulation, and provides technical support for the safe and reliable operation of supersonic flow field numerical simulation in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A flow chart of the adaptive parameter identification method of the SST turbulence model in shock wave boundary layer interference provided by the present invention.

[0042] Figure 2 This is a diagram of the improved Bayesian neural network structure provided by the present invention. DETAILED DESCRIPTION

[0043] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0044] The embodiment of the present invention provides an adaptive parameter identification method for the SST turbulence model in shock wave boundary layer interference, such as Figure 1 As shown, the following steps are included:

[0045] S1. Under certain working conditions, a high-dimensional sample space is constructed according to the closed parameter interval range of the SST turbulence model, and optimal Latin hypercube sampling is carried out in the high-dimensional sample space to uniformly obtain sample information in the entire space as input parameter samples;

[0046] S2. Based on the input parameter samples and the determined working conditions, numerical simulation is performed to form a model prior sample set;

[0047] S3. According to the model prior sample set, a wall pressure prediction model of the flow field under shock wave boundary layer interference based on the improved Bayesian neural network is constructed;

[0048] S4. Based on the wall pressure prediction model of the flow field under the interference of shock wave boundary layer, the particle swarm optimization algorithm is used to perform adaptive parameter identification of the SST turbulence model to obtain the optimal closure parameters of the SST turbulence model for high-precision simulation of the flow field.

[0049] In step S1 of the embodiment of the present invention, the operating conditions are determined according to the flow field channel configuration parameters and the incoming flow condition parameters; the flow field channel configuration is a compression corner configuration, and its parameters include the compression corner size and the compression angle; the incoming flow condition parameters include the Mach number, the boundary layer thickness, the inlet total temperature and the inlet total pressure.

[0050] In an optional embodiment of the present invention, the Mach number is 2.85, the boundary thickness is 21.5 mm, the total temperature is 99.8 K, the total pressure is 23526.0 Pa, and the compression corner angle is 24°.

[0051] In step S1 of the embodiment of the present invention, the optimal Latin hypercube sampling is a sampling method obtained by improving the Latin hypercube sampling by minimizing the maximum distance criterion;

[0052] Among them, the criterion for minimizing the maximum distance is: the distance between each sample in the high-dimensional sample space is taken as the maximum distance obtained in the high-dimensional sample space, which is expressed as:

[0053] min 1≤ij≤n,i≠j d(xi ,x j )

[0054] In the formula, x i ,x j are the i-th and j-th samples respectively, d(x i ,x j ) is the distance between two samples.

[0055] The optimal Latin hypercube sampling method in this embodiment is used for uniform, random, and orthogonal sampling in the input parameter sample space region, and can obtain a large amount of model information with relatively few points, and has good space filling and balance.

[0056] Step S2 of the embodiment of the present invention includes the following sub-steps:

[0057] S21. Under a determined working condition, inputting the input parameter sample into a high-precision numerical simulation software for calculation to obtain RANS numerical simulation data;

[0058] Among them, the numerical simulation data include flow field wall pressure, friction coefficient, velocity distribution and density distribution, etc.

[0059] S22. Perform data assimilation processing on the numerical simulation data to form a model prior sample set of multi-source data fusion.

[0060] Step S3 of the embodiment of the present invention is specifically:

[0061] The improved Bayesian neural network is used to learn the characteristic parameters of the model prior sample set, and the nonlinear mapping relationship between the SST turbulence model parameters and the flow field wall pressure is obtained. Then, the flow field wall pressure proxy model based on the improved Bayesian neural network is obtained. The model prior sample set is used to train the flow field wall pressure proxy model, and the flow field wall pressure prediction model under shock wave boundary layer interference is obtained.

[0062] Specifically, the flow field wall pressure proxy model based on the improved Bayesian neural network in this embodiment is expressed as:

[0063]

[0064] In the formula, P(Y|X) represents the probability of outputting Y given input X, P(Y|X,ω) represents the probability distribution of outputting Y given weight ω and input X, P(D) represents the evidence probability, and E P(ω∣D) [P(Y|X,ω)] is the variational estimate of ∫P(Y|X,ω)P(ω|D)dω, where ω represents the internal parameters of the surrogate model.

[0065] In this embodiment, if Figure 2As shown in the figure, the improved Bayesian neural network includes an input layer, several hidden layers and an output layer connected in sequence; wherein, the hidden neurons in the hidden layer are connected with an activation function, and jump connections are used between adjacent hidden layers; the input of the input layer is propagated to the output layer through the following formula:

[0066] Y k =f k (W k Y k*l +b k )

[0067] Where Y k represents the output of the kth layer, W k and b k represents the weight and bias of the kth layer, f k (·) represents the activation function of the k-th layer.

[0068] Specifically, the number of neurons in the input layer and the output layer depends on the size of the input and output, and the number of neurons in the hidden layer is defined by the user based on experience. In order to increase its nonlinear fitting ability, an activation function is connected after the hidden layer neurons.

[0069] In this embodiment, the training process can be divided into three steps: forward propagation, loss function calculation and back propagation. In the output layer, the predicted value Y obtained by forward propagation is used pred With the actual value Y actual The error between the two is used to measure the prediction effect. The error value depends on the loss function. Once the loss function is calculated, it will be back-propagated. During the back-propagation process, the gradient descent is used to update the parameters to complete the model training.

[0070] In this embodiment, an improved Bayesian neural network is proposed, and RMSE is introduced and used in combination with the uncertainty estimation unique to the Bayesian method. RMSE itself only focuses on the average error of the prediction point. By considering the root mean square error and uncertainty estimation at the same time, the prediction ability and stability of the model can be more comprehensively evaluated and compared. To provide more comprehensive and reliable support for decision-making in practical applications, the loss function Loss of the flow field wall pressure proxy model is:

[0071]

[0072] Where D KL [q(w|θ)||P(w)] represents the KL divergence between two probability distributions q(w|θ) and P(w), q(w|θ) represents the variational distribution in variational inference, and P(w) represents the prior distribution, which is the distribution of the neural network weight w when no data is observed. j represents the actual value of the jth sample, f(xj ) represents the predicted value of the jth sample, w represents the distribution probability of the parameter, θ represents the control parameter of the variational distribution q(w|θ), which determines the shape of the approximate posterior distribution, and x j Represents the input features of the j-th sample, the subscript j represents the j-th, and n represents the total number of samples.

[0073] In step S4 of the embodiment of the present invention, a particle swarm optimization algorithm is used to perform adaptive parameter identification on the SST turbulence model. The basic principle of the particle swarm optimization (PSO) algorithm is: a group of particles randomly search for the optimal solution in the solution space of the optimization problem. The most effective strategy is to search for the individual closest to the optimal solution in the particle swarm, and then obtain the optimal parameters. In this embodiment, the particle swarm optimization algorithm formula is:

[0074] ν id (k+1)=ν id (k)+c1r1[p id (k)-x id (k)]+c2r2[p gd (k)-x id (k)]

[0075] x id (k+1)=x id (k)+ν id (k+1)

[0076]

[0077] p gd (k) = min{p 1d (k),...,p id (k)},i∈N

[0078] Where, ν id (k+1) and ν id (k) represents the velocity of the dth dimension of the i-th particle at the k+1th iteration and the kth iteration, p id (k) represents the individual optimal position of the dth dimension of the i-th particle in a total of k iterations, x id (k) and x id (k+1) represents the position of the dth dimension of the i-th particle at the k-th iteration and the k+1-th iteration, p id (k) and p id (k+1) represents the individual optimal position of the dth dimension of the i-th particle in a total of k iterations and the k+1th iteration, p gd (k) represents the global optimal position of the dth dimension of the entire population in a total of k iterations, f(·) represents the fitness function, c1 and c2 represent learning factors, r1 and r2 represent random numbers between [0,1], and N is the population size.

[0079] In step S4 of the embodiment of the present invention, the optimal closure parameters of the SST turbulence model obtained based on adaptive parameter identification are actually simulated in high-speed internal and external flow coupling numerical simulation software to comprehensively improve the accuracy of turbulence parameter identification under supersonic shock wave boundary layer interference, laying the foundation for high-precision calculation work in the numerical simulation process.

[0080] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0081] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. An adaptive parameter identification method for the SST turbulence model in shock wave boundary layer interference, characterized in that: The following steps are involved: S1. Under certain working conditions, a high-dimensional sample space is constructed according to the closed parameter interval range of the SST turbulence model, and optimal Latin hypercube sampling is carried out in the high-dimensional sample space to uniformly obtain sample information in the entire space as input parameter samples; S2. Based on the input parameter samples and the determined working conditions, numerical simulation is performed to form a model prior sample set; S3. According to the model prior sample set, a wall pressure prediction model of the flow field under shock wave boundary layer interference based on improved Bayesian neural network is constructed; S4. Based on the wall pressure prediction model of the flow field under the interference of shock wave boundary layer, the particle swarm optimization algorithm is used to perform adaptive parameter identification of the SST turbulence model to obtain the optimal closure parameters of the SST turbulence model for high-precision simulation of the flow field.

2. The method for adaptive parameter identification of the SST turbulence model in shock wave boundary layer interference according to claim 1, characterized in that: In the step S1, the working condition is determined according to the flow field channel configuration parameters and the incoming flow condition parameters; The flow field channel configuration is a compression corner configuration, and its parameters include compression corner size and compression angle; The incoming flow condition parameters include Mach number, boundary layer thickness, inlet total temperature and inlet total pressure.

3. The method for adaptive parameter identification of the SST turbulence model in shock wave boundary layer interference according to claim 1, characterized in that: In step S1, the optimal Latin hypercube sampling is a sampling method obtained by improving the Latin hypercube sampling by minimizing the maximum distance criterion; Among them, the criterion for minimizing the maximum distance is: the distance between each sample in the high-dimensional sample space is taken as the maximum distance obtained in the high-dimensional sample space.

4. The method for adaptive parameter identification of the SST turbulence model in shock wave boundary layer interference according to claim 1, characterized in that: The step S2 comprises the following sub-steps: S21. Under a determined working condition, inputting the input parameter sample into a high-precision numerical simulation software for calculation to obtain RANS numerical simulation data; S22. Perform data assimilation processing on the numerical simulation data to form a model prior sample set of multi-source data fusion.

5. The method for adaptive parameter identification of the SST turbulence model in shock wave boundary layer interference according to claim 1, characterized in that: The step S3 is specifically as follows: The improved Bayesian neural network is used to learn the characteristic parameters of the model prior sample set, and the nonlinear mapping relationship between the SST turbulence model parameters and the flow field wall pressure is obtained. Then, the flow field wall pressure proxy model based on the improved Bayesian neural network is obtained. The model prior sample set is used to train the flow field wall pressure proxy model, and the flow field wall pressure prediction model under shock wave boundary layer interference is obtained.

6. The method for adaptive parameter identification of the SST turbulence model in shock wave boundary layer interference according to claim 5, characterized in that: The flow field wall pressure proxy model based on the improved Bayesian neural network is expressed as: In the formula, P(Y|X) represents the probability of outputting Y given input X, P(Y|X,ω) represents the probability distribution of outputting Y given weight ω and input X, P(D) represents the evidence probability, and E P(ω∣D) [P(Y|X,ω)] is the variational estimate of ∫P(Y|X,ω)P(ω|D)dω, where ω represents the internal parameters of the surrogate model.

7. The method for adaptive parameter identification of the SST turbulence model in shock wave boundary layer interference according to claim 5, characterized in that: The improved Bayesian neural network includes an input layer, a plurality of hidden layers and an output layer connected in sequence; Hidden neurons in the hidden layer are connected with activation functions, and skip connections are used between adjacent hidden layers; The input of the input layer is propagated to the output layer through the following formula: Y k =f k (W k Y k*l +b k ) Where Y k represents the output of the kth layer, W k and b k represents the weight and bias of the kth layer, f k (·) represents the activation function of the k-th layer.

8. The method for adaptive parameter identification of the SST turbulence model in shock wave boundary layer interference according to claim 5, characterized in that: The loss function Loss for training the flow field wall pressure proxy model is: Where D KL [q(w|θ)||P(w)] represents the KL divergence between two probability distributions q(w|θ) and P(w), q(w|θ) represents the variational distribution in variational inference, and P(w) represents the prior distribution, which is the distribution of the neural network weight w when no data is observed. j represents the actual value of the jth sample, f(x j ) represents the predicted value of the jth sample, w represents the distribution probability of the parameter, θ represents the control parameter of the variational distribution q(w|θ), which determines the shape of the approximate posterior distribution, and x j Represents the input features of the j-th sample, the subscript j represents the j-th, and n represents the total number of samples.

9. The adaptive parameter identification method of the SST turbulence model in shock wave boundary layer interference according to claim 1 is characterized in that: In step S4, the formula for adaptive parameter identification of the SST turbulence model using the particle swarm optimization algorithm is: ν id (k+1)=ν id (k)+c1r1[p id (k)-x id (k)]+c2r2[p gd (k)-x id (k)] x id (k+1)=x id (k)+ν id (k+1) on gd (k)=min{p 1d (k),...,p id (k)},i∈N Where, ν id (k+1) and ν id (k) represents the velocity of the dth dimension of the i-th particle at the k+1th iteration and the kth iteration, p id (k) represents the individual optimal position of the dth dimension of the i-th particle in a total of k iterations, x id (k) and x id (k+1) represents the position of the dth dimension of the i-th particle at the k-th iteration and the k+1-th iteration, p id (k) and p id (k+1) represents the individual optimal position of the dth dimension of the i-th particle in a total of k iterations and the k+1th iteration, p gd (k) represents the global optimal position of the dth dimension of the entire population in a total of k iterations, f(·) represents the fitness function, c1 and c2 represent learning factors, r1 and r2 represent random numbers between [0,1], and N is the population size.

Images