A fast prediction method for transonic buffeting flow field of airfoil based on deep neural network

Abstract

The present invention proposes a method for rapid prediction of airfoil transonic buffeting flow field based on a deep neural network, including generating an unsteady flow field sample set; constructing a neural network model for rapid prediction of unsteady flow field; training the constructed neural network model; and using the trained deep neural network for rapid prediction of unsteady flow field. The present invention uses flow field information based on a computational grid as input to a neural network model to predict flow field information at future moments. Compared with input based on images or uniform grids, it has a higher resolution under the same data volume standard, so that the model has a higher prediction accuracy. The present invention uses a simplified interpolation grid according to the flow field area of ​​interest, and interpolates the flow field parameters onto the grid for prediction of unsteady flow field. While ensuring the prediction accuracy of the unsteady flow field, it can minimize the number of data points and time consumption to improve efficiency.

Description

Technical Field

[0001] The present invention relates to the fields of deep learning and computational fluid dynamics, and specifically to a method for quickly predicting an airfoil transonic buffeting flow field based on a deep neural network. Background Art

[0002] Under transonic flow conditions, the interaction of shock wave / boundary layer separation may cause unstable motion of the entire flow field. This phenomenon is called transonic buffeting. In airfoil design, transonic buffeting is a very critical issue because the occurrence of buffeting limits the upper limit of airfoil performance. The buffeting phenomenon begins with the separation of the trailing edge flow caused by the interaction of the shock wave boundary layer. The flow field characteristics are manifested in the changes in the shock wave position and intensity, the separation of the post-wave flow, and the appearance and disappearance of the trailing edge shedding vortex. When the aircraft is flying at transonic speed, if it enters the buffeting initiation boundary, the pulsating pressure load caused by transonic buffeting will not only affect the aircraft's cruise performance and flight quality, but in severe cases it may cause aircraft structural fatigue and cause flight accidents. Therefore, it is necessary to develop an airfoil optimization design method that takes into account the buffeting problem to avoid or delay the occurrence of the buffeting phenomenon, thereby achieving an improvement in the comprehensive performance of the airfoil.

[0003] The mainstream airfoil design method now is the airfoil optimization design based on computational fluid dynamics (CFD). The main idea is to continuously adjust the initial airfoil through CFD calculation and optimization algorithm, and finally obtain the airfoil with the best target performance. However, the transonic buffeting flow field contains strong nonlinear flow structures such as separation vortex and shock wave. If it is directly numerically simulated during the optimization process, it will consume a lot of computing time and cost. At the same time, the current intelligent optimization algorithm requires a large number of CFD processes, which also reduces the optimization efficiency.

[0004] Therefore, researchers have proposed various aerodynamic reduced order models (ROM) based on CFD simulation data. ROM refers to the use of linear and nonlinear models to express the mapping relationship between input and output in complex aerodynamic systems. These methods, as proxy models for efficient calculation of fluid mechanics systems, have been widely used in aerospace and mechanical engineering. Typical representatives include Proper Orthogonal Decomposition (POD), Dynamic Mode Decompositon (DMD), Kriging model, support vector machine, artificial neural network, radial basis function, etc. Compared with numerical simulation, the reduced order model method greatly reduces the complexity of solving complex systems, improves the efficiency of modeling and solving, and maintains reasonable accuracy.

[0005] However, traditional reduced-order model methods also have some significant shortcomings. Most reduced-order models are based on linear methods, so it is difficult to capture nonlinear characteristics. At the same time, most of these methods are limited to the prediction of low-dimensional performance, such as aerodynamic coefficients and pressure distribution, and it is difficult to describe the complete flow field with high fidelity. In addition, these methods are sensitive to model parameters and are not easy to extend to high-dimensional design variables. Compared with the above methods, deep neural networks (DNNs) can easily handle high-dimensional design variables and have powerful processing capabilities for nonlinear problems, multi-scale problems, and problems containing time series information. They are expected to make up for the inherent shortcomings of traditional reduced-order models and are very suitable for modeling nonlinear dynamic systems. Reduced-order models are constructed to predict the transonic flutter flow field of airfoils to reduce the computational burden. Summary of the invention

[0006] For different flow states and flow problems, when constructing a prediction model based on deep learning, the issues that need to be paid attention to are also different. Different neural networks are also suitable for solving different types of problems due to their different construction ideas. Among them, convolutional neural networks are very suitable for modeling image and spatial data, and recurrent neural networks such as long short-term memory are suitable for modeling time series data. The airfoil flow field that undergoes transonic flutter has strong nonlinear characteristics in both time and space, and both convolutional neural networks and recurrent neural networks alone have certain limitations.

[0007] To this end, the present invention combines the performance advantages of two neural networks to construct a new hybrid neural network model for predicting the unsteady flow field of an airfoil. The model has both good temporal feature extraction capabilities and spatial feature extraction capabilities.

[0008] The invention proposes a method for fast prediction of airfoil transonic buffeting flow field based on deep neural network, which can quickly obtain flow field information at future moments under the condition of knowing the flow field information of a continuous finite number of equal time intervals, including the following steps:

[0009] Step 1: Generate an unsteady sample set; specifically, the following steps are included:

[0010] Step 1.1: Select the reference airfoil of the unsteady sample set, generate the airfoil computational grid using the elliptical partial differential equation, map the grid from the physical space to the computational space of a uniform rectangular grid in the plane through coordinate transformation, solve the unsteady flow field of the reference airfoil using the detached eddy simulation (DES) method, and output the flow field data (including pressure, density and velocity components) at a finite number of moments at a fixed time interval;

[0011] Step 1.2: Regenerate an interpolation grid according to the flow area concerned by the prediction problem, and interpolate the flow field information onto the grid as samples for training and testing;

[0012] Step 1.3: Normalize the sample data set and use the linear normalization method to linearly transform the interval of the sample data to [0, 1].

[0013] Step 2: Construct a neural network model for fast prediction of unsteady flow field;

[0014] The neural network model constructed for rapid prediction of unsteady flow fields is a hybrid neural network model, whose constituent modules include a Convlstm module, a convolution module and a deconvolution module; the Convlstm module includes a Convlstm layer, the convolution module sequentially includes a convolution layer, a BN layer and a ReLU layer, and the deconvolution module sequentially includes a deconvolution layer, a BN layer and a ReLU layer.

[0015] The neural network model uses four downsampling and four upsampling. The neural network parameters are adjusted to make the feature maps of the corresponding layers of upsampling (expansion path) and downsampling (contraction path) have the same shape. Skip connections are added between feature maps of the same dimension, and data fusion uses addition operation.

[0016] The input data of the neural network model is a four-dimensional matrix, which means: number of sequences × number of channels × height × width. The output data is a three-dimensional matrix, which means: number of channels × height × width. The number of sequences corresponds to the number of multi-moment flow fields, the number of channels corresponds to the number of variables in the multivariable flow field, and the height and width correspond to the size of the two-dimensional flow field.

[0017] Step 3: Train the constructed neural network model; use the mean square error loss (MSE) of the flow field parameters as the loss function, use the Adam optimizer and adaptive learning rate algorithm, and set the initial learning rate to 1×10 -3 , train the model, and the optimization goal is to minimize the loss function until the loss function of the training sample data set no longer decreases.

[0018] Step 4: Use the trained neural network model for rapid prediction of unsteady flow fields: Input the flow field information of a finite number of known continuous equal time intervals into the trained neural network to obtain the flow field information at future moments.

[0019] Beneficial Effects

[0020] Compared with the prior art, the present invention has the following advantages:

[0021] 1. The present invention uses flow field information based on a computational grid, including pressure, density, x-direction velocity component, and z-direction velocity component, as input to a neural network model to predict flow field information at future moments. Compared with input based on images or uniform grids, the present invention has a higher resolution under the same data volume standard, so that the model has a higher prediction accuracy.

[0022] 2. The present invention uses a simplified interpolation grid according to the flow field area of ​​concern to interpolate the flow field parameters onto the grid for prediction of unsteady flow fields. This can reduce the number of data points and time consumption as much as possible while ensuring the prediction accuracy of the unsteady flow field, thereby improving efficiency.

[0023] 3. The present invention combines ConvLSTM with U-net to construct a hybrid neural network model. Based on the powerful spatiotemporal information processing capability of ConvLSTM, U-Net further enhances the entire network's ability to extract spatiotemporal features, thereby improving the prediction accuracy of unsteady flow fields.

[0024] 4. The present invention aims to construct and train a neural network for the transonic buffeting flow field of an airfoil, which is highly targeted and can quickly and accurately predict the transonic buffeting flow field of an airfoil.

[0025] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0027] Figure 1 Schematic diagram of the structure of the deep neural network for rapid prediction of unsteady flow field of the present invention

[0028] Figure 2 This is the computational grid for the flow around an airfoil. (a) is the overall grid view, and (b) is a local magnified view.

[0029] Figure 3 This is the interpolation grid used for neural network training. (a) is the full view of the grid, and (b) is a local magnified view.

[0030] Figure 4It is the prediction effect of the flow field at a certain moment of the flow around the airfoil with flutter phenomenon. (a) is the pressure of the airfoil flow field calculated by CFD, (b) is the pressure of the airfoil flow field predicted by the deep learning model, (c) is the error of the pressure of the airfoil flow field predicted by the deep learning model, (d) is the density of the airfoil flow field calculated by CFD, (e) is the density of the airfoil flow field predicted by the deep learning model, (f) is the error of the density of the airfoil flow field predicted by the deep learning model, (g) is the x-direction velocity component of the airfoil flow field calculated by CFD, (h) is the x-direction velocity component of the airfoil flow field predicted by the deep learning model, (i) is the error of the x-direction velocity component of the airfoil flow field predicted by the deep learning model, (j) is the z-direction velocity component of the airfoil flow field calculated by CFD, (k) is the z-direction velocity component of the airfoil flow field predicted by the deep learning model, and (l) is the error of the z-direction velocity component of the airfoil flow field predicted by the deep learning model. DETAILED DESCRIPTION

[0031] Embodiments of the present invention are described in detail below. The embodiments are exemplary and intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0032] The method for rapid prediction of airfoil transonic buffeting flow field based on deep neural network described in this embodiment includes generating an unsteady flow field sample set; constructing a neural network model for rapid prediction of unsteady flow field; training the constructed neural network model; and using the trained deep neural network for rapid prediction of unsteady flow field. The specific steps are as follows:

[0033] Step 1: Generate an unsteady flow field sample set:

[0034] 1) The detached eddy simulation (DES) method is used to simulate the transonic turbulent flow field of the supercritical airfoil OAT15A with a chord length of 0.23 m. The calculation state is as follows: Re = 13.04 × 10 6 , Ma=0.73,α=3.5°,T ∞ =487.98R, set the time step to Δt=5.189×10 -6 s. The computational grid adopts CH structured grid, with 657 points distributed around the airfoil, which are encrypted at the leading and trailing edges and the middle of the upper surface of the airfoil. The height of the first layer of the boundary layer is set to 4.6×10 -7 m, the global and local distribution diagram of the computational grid is shown in Figure 2 As shown. The boundary conditions of the object surface are adiabatic and no-slip wall, and the turbulence model adopts the SST turbulence model. A complete flow field is saved every 10 time steps, and the full flow field at 2000 periodic regular moments is extracted.

[0035] 2) Regenerate an interpolation grid according to the flow field structure and model training requirements, and interpolate the flow field information onto the grid as samples for training and testing. Figure 3 Shown is a schematic diagram of the global and local distribution of the interpolation grid used for neural network training, where the sizes of the two grid blocks are 245×89 and 61×221 respectively.

[0036] 3) Normalize the sample data set and use the linear normalization method to linearly transform the interval of the sample data to [0,1].

[0037] Step 2: Construct a neural network model for fast prediction of unsteady flow field:

[0038] 1) Construct a hybrid neural network model, whose components include ConvLSTM module, convolution module and deconvolution module. The model uses four downsampling and four upsampling. By adjusting the neural network parameters, the feature maps of the corresponding layers of upsampling (expansion path) and downsampling (contraction path) have the same shape, and skip connections are added between feature maps of the same dimension. Data fusion uses addition operation.

[0039] The convolution module of the model contains a convolution layer, a BN layer and a ReLU layer in sequence, the deconvolution module contains a deconvolution layer, a BN layer and a ReLU layer in sequence, and a Convlstm module includes a Convlstm layer.

[0040] 2) The input data of the neural network is a four-dimensional matrix, which means: number of sequences × number of channels × height and width, and its output data is a three-dimensional matrix, which means: number of channels × height × width. The number of sequences corresponds to the number of multi-time flow fields, the number of channels corresponds to the number of variables in the multivariable flow field, and the height and width correspond to the size of the two-dimensional flow field.

[0041] Step 3: Train the constructed neural network model;

[0042] 1) Divide the sample set into training samples and test samples, with the ratio of training samples to test samples being 4:1.

[0043] 2) The mean square error (MSE) of the flow field parameters (pressure, density, x-direction velocity component, z-direction velocity component) is used as the loss function, and the Adam optimizer and adaptive learning rate algorithm are used. The initial learning rate is set to 1×10 -3 , train the model, and the optimization goal is to minimize the loss function until the loss function of the training sample data set no longer decreases.

[0044] Step 4: Use the trained deep neural network for rapid prediction of unsteady flow fields.

[0045] By inputting the flow field information of a finite number of equal time intervals into the trained neural network, the flow field information at the future moment can be obtained. The mean absolute error (MAE) of most samples in the training set is less than 0.002, and the mean absolute error (MAE) of most samples in the test set is less than 0.006, which has a high prediction accuracy, indicating that the U-ConvLSTM we constructed has good spatiotemporal feature extraction capabilities. The prediction effect of the transonic buffeting flow field at a certain moment is as follows: Figure 4 shown.

[0046] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. A method for rapid prediction of airfoil transonic buffeting flow field based on deep neural network, characterized in that: The following steps are involved: Step 1: Generate an unsteady sample set: Step 1.1: Select the reference airfoil of the unsteady sample set and generate the airfoil computational grid. Through coordinate transformation, map the grid from the physical space to the computational space of a uniform rectangular grid in the plane, solve the unsteady flow field of the reference airfoil, and output the flow field data of a finite number of moments at a fixed time interval. Step 1.2: Regenerate an interpolation grid according to the flow area concerned by the prediction problem, and interpolate the flow field information onto the grid as samples for training and testing; Step 1.3: Normalize the sample data set using a linear normalization method to linearly transform the sample data interval to [0, 1]; Step 2: Construct a neural network model for fast prediction of unsteady flow field: A hybrid neural network model is used to construct a neural network model for rapid prediction of unsteady flow fields; the hybrid neural network model includes a Convlstm module, a convolution module and a deconvolution module; the Convlstm module includes a Convlstm layer, the convolution module includes a convolution layer, a BN layer and a ReLU layer in sequence, and the deconvolution module includes a deconvolution layer, a BN layer and a ReLU layer in sequence; The hybrid neural network model uses four downsampling and four upsampling. The neural network parameters are adjusted so that the feature maps of the corresponding layers of upsampling and downsampling have the same shape. Skip connections are added between feature maps of the same dimension. Data fusion uses addition operation. The input data of the hybrid neural network model is a four-dimensional matrix, which means: number of sequences × number of channels × height × width, and the output data is a three-dimensional matrix, which means: number of channels × height × width, the number of sequences corresponds to the number of multi-time flow fields, the number of channels corresponds to the number of variables in the multivariable flow field, and the height and width correspond to the size of the two-dimensional flow field; Step 3: Train the constructed neural network model; Step 4: Use the trained neural network model for rapid prediction of unsteady flow fields: Input the flow field information of a finite number of known continuous equal time intervals into the trained neural network model to obtain the flow field information at future moments.

2. According to claim 1, a method for rapid prediction of airfoil transonic buffeting flow field based on deep neural network, characterized in that: In step 1.1, the airfoil computational grid is generated using an elliptical partial differential equation, and the unsteady flow field of the benchmark airfoil is solved using the detached vortex simulation method.

3. According to claim 1, a method for rapid prediction of airfoil transonic buffeting flow field based on deep neural network, characterized in that: In step 1.1, the output flow field data includes pressure, density and velocity components.

4. According to claim 3, a method for rapid prediction of airfoil transonic buffeting flow field based on deep neural network is characterized in that: In step 3, the sample data set is first divided into training samples and test samples, with a ratio of 4:

1. The root mean square loss of flow field parameters is used as the loss function, and the Adam optimizer and adaptive learning rate algorithm are used. The initial learning rate is set to 1×10 -3 , train the model, and the optimization goal is to minimize the loss function until the loss function of the training sample data set no longer decreases, and obtain a trained neural network model.

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