Reduced-order modeling for turbulent wake of a finite wall-mounted square cylinder based on artificial neural network

Abstract

This study presents an artificial neural network and a proper orthogonal decomposition (POD)-based reduced-order model (ROM) of turbulent flow around a finite wall-mounted square cylinder. The proposed model is suitable for turbulent wake control applications, because it can predict the dynamics of the main features of the flow field with low computational cost. A long short-term memory neural network (LSTM NN) and a bidirectional long short-term memory neural network (BLSTM NN) are used to predict the temporal evolution of POD time coefficients at different sections along the height of the obstacle. The improved delayed detached-eddy simulation is performed to generate training datasets. Transfer learning is utilized in the training process by using the weights of the LSTM/BLSTM NN that are used to predict the POD time coefficients of the planes at lower elevations to initialize the weights of the networks at higher elevations along the height of the obstacle. The use of transfer learning results in a remarkable improvement in the prediction capability of LSTM/BLSTM NN compared with the one when the network is initialized with random weights. The BLSTM NN shows better results compared with the LSTM NN in terms of training and prediction error, indicating that the BLSTM-POD model is more suitable to be used as a ROM for predicting the turbulent wake. Furthermore, the temporal evolution of the time coefficients is carefully examined using the phase space plots and Poincaré sections. The results of using different lengths of the prediction time window show that the prediction error of the POD time coefficients increases as the prediction time window increases and the error increasing rate decreases with ranking of the POD modes.

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