Reduced-Order Model Using the Machine Learning Technique in a Free Round Jet in Transition from Laminar to Turbulent Region

Since the reduced-order model techniques can reduce the computational burden of numerical simulation while retaining the most important features of flow physics, the reduced-order model plays a crucial role in the optimization and control for the unforced round jet flow. In this work, a deep neural network method or neural ordinary differential equation (ODE) was applied to the reduced-order model for a free round jet. In this model, the output or proper orthogonal decomposition (POD) coefficient of the reduced-order model is calculated using an ODE solver. The method is exemplified for classic shear flow such as a jet and numerically demonstrated for a round jet generated by large-eddy simulation (LES). The Reynolds number Re of the round jet is calculated based on the diameter of nozzle exit D and averaged streamwise velocity along the spanwise distribution. The reduced-order model accurately reconstructs the free jet velocity field based on the original snapshots. These results revealed that the employment of neural ODEs will significantly improve the availability and efficiently of the reduced-order model, which may supply crucial instruction on future studies using the reduced-order model improved by machine learning algorithms. We expect the proposed method to be applicable for a model-based flow control in future.