Three-dimensional wake transition of rectangular cylinders and temporal prediction of flow patterns based on a machine learning algorithm

This study investigates the three-dimensional (3D) wake transition in unconfined flows over rectangular cylinders using direct numerical simulation (DNS). Two different cross-sectional aspect ratios (AR) and Reynolds numbers (Re) are scrutinized: AR = 0.5 at Re = 200 and AR = 3 at Re = 600. The investigation focuses on characterizing the flow patterns and forecasting their temporal evolution utilizing the proper orthogonal decomposition (POD) technique coupled with a long short-term memory (LSTM) network. The DNS results reveal the emergence of an ordered mode A for AR = 3, attributed to the stabilizing effect of the elongated AR. On the other hand, the case with a smaller AR (= 0.5) exhibits a mode-swapping regime characterized by modes A and B's distinct and simultaneous manifestation. The spanwise wavelengths of mode A and mode B are approximately 4.7 and 1.2 D for AR = 0.5, while the spanwise wavelength of mode A is 3.5 D for AR = 3. The POD serves as a dimensionality reduction technique, and LSTM facilitates temporal prediction. This algorithm demonstrates satisfactory performance in predicting the flow patterns, including the instabilities of modes A and B, across both transverse and spanwise directions. The employed algorithm adeptly predicts the pressure time series surrounding the cylinders. The duration for training the algorithm is only about 0.5% of the time required for DNS computations. This research, for the first time, demonstrates the effectiveness of the POD–LSTM algorithm in predicting complex 3D instantaneous wake transition patterns for flow past rectangular cylinders.