An adaptive parameter identification method of SST turbulence model in shock boundary layer interaction

Abstract

The application discloses a kind of self-adapting parameter identification methods of SST turbulent model in shock wave boundary layer interference, comprising: S1, under the condition of determining, according to the closed parameter interval range of SST turbulent model, construct high-dimensional sample space, carry out optimal Latin hypercube sampling, uniformly obtain sample information in whole space as input parameter sample;S2, based on input parameter sample and the condition of determining, numerical simulation is carried out, and model prior sample set is formed;S3, according to model prior sample set, construct the flow field wall pressure prediction model under the shock wave boundary layer interference based on improved bayesian neural network;S4, based on the flow field wall pressure prediction model under the shock wave boundary layer interference, the particle swarm optimization algorithm is used to carry out self-adapting parameter identification to SST turbulent model, and the optimal closed parameter of SST turbulent model for realizing flow field high-precision simulation is obtained.The application improves the numerical simulation precision and speed, and provides technical support for the safe and reliable work of scramjet engine in complex environment.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of aerodynamics, and particularly relates to an adaptive parameter identification method of an SST turbulence model in shock boundary layer interference. BACKGROUND

[0002] Shock wave / boundary layer interaction (SWBLI) is a common phenomenon involving complex flow structures, which has multiple influences on the flow, and can produce structural damage, aerodynamic elasticity, and thermal protection difficulties, air intake flow distortion, and even cause air intake non-starting and a series of negative effects. It is one of the most common challenges in fluid mechanics. Although identifying, recognizing and controlling separated flow is essential in aerodynamics, predicting separated flow is still challenging. In terms of flow mechanism, SWBLI is mainly studied by precise and detailed methods such as direct numerical simulation (DNS) and large eddy simulation (LES). These methods are accompanied by high-quality grids and unbearable computing cost. Reynolds-averaged NS equation (RANS) has the advantages of strong robustness, high computing efficiency and low requirement for computer hardware, and is widely used in practical engineering applications.

[0003] At present, RANS models are mostly based on eddy viscosity hypothesis. From the development of turbulence models in the 20th century to now, the main turbulence models include Spalart Allmaras (SA) model, k- model, model, Shear Stress Transport (SST) model, Baldwin-Lomax (BL) model, model, etc., and a series of other improved turbulence models, but the accuracy of each turbulence model depends on the actual problem. The model closure value existing in each turbulence model is calibrated by the model builder using the data of simple flow. 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 flow. Different types of flow should have different coefficient recommendation values to best match the turbulence model. Therefore, adjusting the closure coefficient value of 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 in 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 at present mainly include one-equation model and two-equation model, such as SA one-equation turbulence model, BSL two-equation turbulence model and SST two-equation turbulence model. The closure coefficient of SA turbulence model has 11, the closure coefficient of BSL turbulence model has 8, and the closure coefficient of SST turbulence model has 9. For simple flow, the closure coefficient of each turbulence model is selected according to the nominal value, and the numerical simulation result obtained is ideal, but for complex flow, selecting the nominal value for calculation may have a large error. Machine learning method has been widely used in computational fluid dynamics. For a large number of posterior samples, CFD simulation is time-consuming and unrealistic for each group of parameters. In order to reduce the calculation cost, machine learning proxy model is needed to reduce the calculation cost. It is of great significance to explore the mechanism of complex flow. SUMMARY

[0005] In view of the above problems in the prior art, the adaptive parameter identification method of the SST turbulence model in the shock boundary layer interference provided by the present application improves the numerical simulation precision and speed, and provides technical support for the safe and reliable operation of the scramjet engine in complex environment.

[0006] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows: an adaptive parameter identification method of SST turbulence model in shock boundary layer interference, comprising the following steps:

[0007] S1. Under the determined working condition, a high-dimensional sample space is constructed according to the closure 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 whole space as input parameter samples;

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

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

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

[0011] Further, in the step S1, the working condition is determined according to the flow field channel configuration parameters and the incoming flow condition parameters;

[0012] The flow field passage configuration is a compression corner configuration, and parameters of the compression corner configuration include a compression corner size and a compression angle.

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

[0014] Further, in the step S1, the optimal Latin hypercube sampling is a sampling method obtained by improving a Latin hypercube sampling by using a minimum maximum distance criterion.

[0015] The minimum maximum distance criterion is that distances between all samples in a high-dimensional sample space are all taken as a maximum distance taken in the high-dimensional sample space.

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

[0017] S21, under a determined working condition, inputting the input parameter sample into high-precision numerical simulation software to calculate and obtain RANS numerical simulation data;

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

[0019] Further, the step S3 is specifically:

[0020] Using the improved Bayesian neural network to learn feature parameters of the model prior sample set, obtaining a nonlinear mapping relationship between SST turbulent model parameters and flow field wall surface pressure, and then obtaining a flow field wall surface pressure proxy model based on the improved Bayesian neural network, using the model prior sample set to train the flow field wall surface pressure proxy model, and obtaining a flow field wall surface pressure prediction model under shock boundary layer interference.

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

[0022]

[0023] In the formula, P(Y|X) represents a probability of output Y under a given input X, P(Y|X,ω) represents a probability distribution of output Y under a given weight ω and input X, P(D) represents an evidence probability, E P(ω∣D) [P(Y|X,ω)] is a variational estimation of ∫P(Y|X,ω)P(ω|D)dω, and ω represents an internal parameter of the proxy model.

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

[0025] The hidden neurons in the hidden layers are connected to activation functions, and skip connections are used between adjacent hidden layers.

[0026] The input to the input layer propagates to the output layer using the following formula:

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

[0028] In the formula, Y k W represents the output of the k-th layer. k and b k f represents the weights and biases of the k-th layer. k (·) represents the activation function of the k-th layer.

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

[0030]

[0031] In the formula, D KL [q(w|θ)||P(w)] represents the KL divergence between two probability distributions q(w|θ) and P(w), where q(w|θ) represents the variational distribution in variational inference, and P(w) represents the prior distribution, the distribution of the neural network weights w when no data has been observed. j Let f(x) represent the actual value of the j-th sample. j Let q(w|θ) represent the predicted value of the j-th sample, w represent the probability distribution of the parameter, θ represent the control parameter of the variational distribution q(w|θ), which determines the shape of the approximate posterior distribution, and x represent the predicted value of the j-th sample. j Let j represent the input feature of the j-th sample, where j indicates the j-th sample 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 as follows:

[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] In the formula, ν id (k+1) and ν id (k) represents the velocity of the d-th dimension of the i-th particle in the (k+1)-th and k-th iterations, p id (k) represents the optimal position of the i-th particle in the d-th dimension across k iterations, x id (k) and x id (k+1) represents the position of the d-th dimension of the i-th particle in the k-th and k+1-th iterations, p id (k) and p id (k+1) represents the optimal position of the d-th dimension of the i-th particle in the k-th and k+1-th iterations, p gd (k) represents the global optimal position of the entire population in the d-th dimension during 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 this invention are as follows:

[0039] (1) This invention addresses the need for high-precision numerical simulation of supersonic flow in shock wave boundary layer interference. By combining machine learning, fluid mechanics and scramjet engine technology, and using data obtained from ground pulse combustion wind tunnel and high-precision numerical simulation software, pressure and flow field datasets are constructed, and adaptive parameter identification of turbulence models is achieved through machine learning technology.

[0040] (2) This 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. Attached Figure Description

[0041] Figure 1 The flowchart shows the adaptive parameter identification method for the SST turbulence model in shock wave boundary layer disturbance provided by this invention.

[0042] Figure 2 The improved Bayesian neural network structure diagram provided by this invention. Detailed Implementation

[0043] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0044] This invention provides an adaptive parameter identification method for an SST turbulence model in shock wave boundary layer disturbance, such as... Figure 1 As shown, it includes the following steps:

[0045] S1. Under a given operating condition, construct a high-dimensional sample space based on the range of the closed parameter interval of the SST turbulence model. Perform optimal Latin hypercube sampling within the high-dimensional sample space to uniformly acquire sample information throughout 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. Based on the model's prior sample set, construct a flow field wall pressure prediction model based on an improved Bayesian neural network under shock wave boundary layer disturbance.

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

[0049] In step S1 of this embodiment of the 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 compression angle; the incoming flow condition parameters include Mach number, boundary layer thickness, inlet total temperature and 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 this embodiment of the invention, the optimal Latin hypercube sampling is a sampling method that is improved by using the maximum distance minimization criterion based on Latin hypercube sampling.

[0052] The minimization of maximum distance criterion is as follows: 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 For the i-th and j-th samples respectively, d(x) i ,x j ) represents the distance between the two samples.

[0055] The optimal Latin hypercube sampling method in this embodiment is used to uniformly, randomly, and orthogonally sample within the input parameter sample space region. It can obtain a large amount of model information with relatively few points and has good space filling and balance.

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

[0057] S21. Under a given operating condition, input the sample of input parameters into a high-precision numerical simulation software for calculation to obtain RANS numerical simulation data.

[0058] The numerical simulation data includes wall pressure, friction coefficient, velocity distribution, and density distribution in the flow field.

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

[0060] Step S3 in this embodiment of the invention is specifically as follows:

[0061] By using an improved Bayesian neural network to learn the feature parameters of the model prior sample set, the nonlinear mapping relationship between the SST turbulence model parameters and the flow field wall pressure is obtained, and then a flow field wall pressure surrogate model based on the improved Bayesian neural network is obtained. The flow field wall pressure surrogate model is trained using the model prior sample set to obtain a flow field wall pressure prediction model under shock wave boundary layer interference.

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

[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, as Figure 2As shown, the improved Bayesian neural network includes an input layer, several hidden layers, and an output layer connected sequentially. Each hidden neuron in the hidden layer is followed by an activation function, and skip connections are used between adjacent hidden layers. The input to the input layer propagates to the output layer using the following formula:

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

[0067] In the formula, Y k W represents the output of the k-th layer. k and b k f represents the weights and biases of the k-th layer. k (·) represents the activation function of the k-th layer.

[0068] Specifically, the number of neurons in the input and output layers depends on the size of the input and output, while the number of neurons in the hidden layer is defined by the user based on experience. In order to increase its nonlinear fitting ability, activation functions are also 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 backpropagation. In the output layer, the predicted value Y obtained through forward propagation is used... pred Compared with the actual value Y actual The error between the two is used to measure the prediction performance. The error value depends on the loss function. Once the loss function is calculated, it will be backpropagated. During backpropagation, gradient descent is used to update the parameters, thereby completing the model training.

[0070] In this embodiment, an improved Bayesian neural network is proposed, which combines RMSE with the uncertainty estimation unique to Bayesian methods. RMSE itself only focuses on the average error of the prediction points. By simultaneously considering the root mean square error and uncertainty estimation, the predictive ability and stability of the model can be more comprehensively evaluated and compared. This provides more comprehensive and reliable support for decision-making in practical applications. The loss function Loss for training the flow field wall pressure surrogate model is:

[0071]

[0072] In the formula, D KL [q(w|θ)||P(w)] represents the KL divergence between two probability distributions q(w|θ) and P(w), where q(w|θ) represents the variational distribution in variational inference, and P(w) represents the prior distribution, the distribution of the neural network weights w when no data has been observed. j Let f(x) represent the actual value of the j-th sample.j Let q(w|θ) represent the predicted value of the j-th sample, w represent the probability distribution of the parameter, θ represent the control parameter of the variational distribution q(w|θ), which determines the shape of the approximate posterior distribution, and x represent the predicted value of the j-th sample. j Let j represent the input feature of the j-th sample, where j indicates the j-th sample and n represents the total number of samples.

[0073] In step S4 of this embodiment, the particle swarm optimization (PSO) algorithm is used to adaptively identify the parameters of the SST turbulence model. The basic principle of PSO is that a swarm of particles randomly searches for the optimal solution in the solution space of the optimization problem. The most effective strategy is to find the individual particle closest to the optimal solution in the swarm and search for it, thereby obtaining the optimal parameters. In this embodiment, the formula for the PSO algorithm 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] In the formula, ν id (k+1) and ν id (k) represents the velocity of the d-th dimension of the i-th particle in the (k+1)-th and k-th iterations, p id (k) represents the optimal position of the i-th particle in the d-th dimension across k iterations, x id (k) and x id (k+1) represents the position of the d-th dimension of the i-th particle in the k-th and k+1-th iterations, p id (k) and p id (k+1) represents the optimal position of the d-th dimension of the i-th particle in the k-th and k+1-th iterations, p gd (k) represents the global optimal position of the entire population in the d-th dimension during 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 this embodiment of the invention, the optimal closure parameters of the SST turbulence model obtained by adaptive parameter identification are used for actual simulation in high-speed internal and external flow coupling numerical simulation software, which comprehensively improves the accuracy of turbulence parameter identification under supersonic shock wave boundary layer interference and lays the foundation for high-precision calculation in the numerical simulation process.

[0080] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0081] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. An adaptive parameter identification method for SST turbulence model in shock boundary layer interaction, characterized in that, The method comprises the following steps: S1. Under a determined working condition, a high-dimensional sample space is constructed according to a SST turbulence model closed parameter interval range, and optimal Latin hypercube sampling is carried out in the high-dimensional sample space to uniformly obtain sample information in the whole space as input parameter samples; S2. Based on the input parameter samples and the determined working condition, numerical simulation is carried out to form a model prior sample set; The data of the numerical simulation comprises flow field wall surface pressure, friction coefficient, velocity distribution and density distribution; S3. According to the model prior sample set, a flow field wall surface pressure prediction model under shock boundary layer interference is constructed based on an improved Bayesian neural network; S4. Based on the flow field wall surface pressure prediction model under shock boundary layer interference, a particle swarm optimization algorithm is used to carry out adaptive parameter identification on the SST turbulence model to obtain optimal closed parameters of the SST turbulence model for realizing high-precision simulation of the flow field; The step S3 specifically comprises: An improved Bayesian neural network is used to learn the characteristic parameters of the model prior sample set to obtain a nonlinear mapping relationship between the SST turbulence model parameters and the flow field wall surface pressure, and then a flow field wall surface pressure proxy model based on the improved Bayesian neural network is obtained, the flow field wall surface pressure proxy model is trained using the model prior sample set, and a flow field wall surface pressure prediction model under shock boundary layer interference is obtained; The flow field wall surface pressure proxy model based on the improved Bayesian neural network is expressed as: where, denotes the probability of output Y given input X, denotes the probability distribution of output Y given input X and weights , denotes the evidence probability, is the variational estimate of , denotes the internal parameters of the surrogate model.

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

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

4. The adaptive parameter identification method of SST turbulence model in shock boundary layer interaction according to claim 1, characterized in that, The step S2 comprises the following steps: S21. Under the determined working condition, the input parameter samples are input into high-precision numerical simulation software to calculate and obtain RANS numerical simulation data; S22. The numerical simulation data is subjected to data assimilation processing to form a model prior sample set of multi-source data fusion.

5. The adaptive parameter identification method of SST turbulence model in shock boundary layer interaction according to claim 1, characterized in that, The improved Bayesian neural network comprises an input layer, a plurality of hidden layers and an output layer connected in sequence; The hidden neurons in the hidden layers are connected with an activation function after the hidden neurons, and the adjacent hidden layers are connected by a skip connection; The input of the input layer is propagated to the output layer by the following formula: wherein, represents the output of the k layer, and represents the weight and bias of the k layer, represents the activation function of the k layer.

6. The adaptive parameter identification method of SST turbulence model in shock boundary layer interaction according to claim 1, characterized in that, Loss function for training the flow field wall surface pressure proxy model is: In the formula, [ || ] represents two probability distributions , KL divergence between them This represents the variational distribution in variational inference. This represents the prior distribution, the distribution of the neural network weights w when no data has been observed. Indicates the first j The actual value of each sample Indicates the first j The predicted value for each sample, This represents the probability distribution of the parameter. Represents variational distribution The control parameters determine the shape of the approximate posterior distribution. Indicates the first j Input features of each sample, subscript j Indicates the j-th element. n This represents the total number of samples.

7. The adaptive parameter identification method of SST turbulence model in shock boundary layer interaction according to claim 1, characterized in that, In the step S4, the formula for using the particle swarm optimization algorithm to carry out adaptive parameter identification on the SST turbulence model is: wherein and denotes the dimension of the particle at the th iteration and the th iteration, denotes the i dimension of the particle at the individual best position in a total of iterations, and denotes the dimension of the particle at the th iteration and the th iteration, and denotes the i dimension of the particle at the individual best position in a total of iterations and the th iteration, denotes the global best position of the dimension of the entire population in a total of iterations, denotes the fitness function, , denotes the learning factor, , denotes a random number between [0, 1], N is the population size.

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