Abstract
The reduced-order model can accurately and efficiently predict unsteady problems in many aerospace engineering applications. The traditional reduced-order model based on proper orthogonal decomposition (POD) and Galerkin projection has poor robustness and large error in predicting complex problems. In this paper, a reduced-order model combining POD and deep learning is proposed to predict cavity flow oscillations under different flow conditions. Firstly, POD modes and corresponding coefficients are obtained by POD. Then, two deep learning frameworks, including multilayer perceptron (MLP) and long short-term memory (LSTM) neural networks, are used to predict the future POD coefficients, respectively. Finally, the cavity flow oscillations across multi-Mach numbers are predicted by the POD modes and the future coefficients. The results show that both of these frameworks can accurately predict cavity flow oscillations when the flow conditions change, and the time cost is reduced by order of magnitude. In addition, due to the performance of LSTM is better than that of MLP, its calculation speed is faster.
Highlights
The cavity flow oscillations are numerically simulated by direct numerical simulation (DNS). e flow chart of the reduced-order model (ROM) for cavity flow oscillations is shown in Figure 4. e goal of this work is to combine proper orthogonal decomposition (POD) and deep learning to predict cavity flow oscillations across multi-Mach numbers. e specific process of this method can be divided into five steps: (1) Select the cavity velocity fields at Ma 0.51, 0.52 to be used as the training datasets and velocity fields at Ma 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6 to be used as the test datasets
A reduced-order model based on POD and deep learning was established for predicting cavity flow oscillations across multiple Mach numbers. e specific conclusions are concluded as follows: (i) After the POD analysis of the numerical simulation data, the first 13 POD modes were extracted, which occupy 99.9% of the energy. e POD modal structures at Ma 0.51, 0.6 are qualitatively similar, so the deep learning method can accurately learn their common features
(ii) By comparing the predicted coefficients with the actual POD coefficients, it is found that the multilayer perceptron (MLP) and long shortterm memory (LSTM) frameworks can accurately predict the POD coefficients, but there are some small oscillations in the coefficients predicted by the MLP framework
Summary
Cavity flow oscillations exist in many aerospace engineering fields [1,2,3,4], such as weapon bays [5, 6] and landing gears [7, 8]. e physical mechanism in a cavity is complex. e shear layer above the cavity generates a vortex, which collides with the trailing wall to generate sound waves. e generated sound waves radiate forward and continue to excite the shear layer to generate new vortices. is process causes intense pressure oscillations in the cavity. e study of oscillation characteristics in the cavity is helpful to understand the mechanism of cavity noise and suppress cavity noise. erefore, the cavity flow oscillation issue has received more and more attention [9,10,11]. e experimental investigations of cavity flow oscillations are usually carried out in wind tunnels or water tunnels. e maintenance of experimental equipment and the complexity of working conditions require many costs, while computational fluid dynamics (CFD) can effectively solve this problem. E maintenance of experimental equipment and the complexity of working conditions require many costs, while computational fluid dynamics (CFD) can effectively solve this problem. E shear layer above the cavity generates a vortex, which collides with the trailing wall to generate sound waves. It fundamentally changes the design process of aerospace vehicles and effectively reduces the number of experiments and deeply understands the physical mechanism. It can effectively extract the main characteristics of the flow field and provide a theoretical basis for analyzing the mechanism and oscillation characteristics of complex systems
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