Physics-Inspired Machine Learning Methods For Flow Field Around A Bluff Body

The flow around a bluff body is a common flow phenomenon in civil,ocean,mechanical,aerospace and other engineering fields.It involves the complex interaction of boundary layer,free shear layer and wake.The measurement of flow field is the basis of analyzing flow separation and reattachment,flow instability and transition,and clarifying flow mechanism encountered in bluff body problems.In the past few decades,with the deepening of the research on bluff body wake,a large number of experimental and numerical simulation data have been produced,which can be regarded as the analytical or numerical solutions of the governing Navier-Stokes equations.How to make full use of the existing flow measurement and simulation data to develop fast and accurate flow field prediction algorithms or directly solve the governing Navier-Stokes equations to obtain the flow field are the key scientific issues in the study of flow around a bluff body.Based on the deep learning theory,the present study makes full use of the flow physical characteristics of large-scale high-dimensional flow data;proposes a fast reconstruction and prediction algorithm of flow field around a bluff body;then investigates a new flow solution method.Firstly,a deep learning method for time-resolved reconstruction of flow field around a bluff body is investigated.Aiming at the problem of low sampling frequency in traditional particle image velocimetry system,inspired by Taylor's freezing hypothesis,the nonlinear velocity spatial-temporal correlation function is introduced to theoretically deduce the relationship between the POD coefficient of flow field and the velocity time history of a few discrete measurement points in the flow field;based on this,a bi-directional recurrent neural network architecture is designed to learn the functional relationship between the velocity of some discrete measuring points with high sampling frequency and the POD coefficient of the flow field,so as to reconstruct the time-resolved flow field.When training the neural network,the early termination strategy is used to prevent the model from over fitting,and the flow field around a cylinder at subcritical regime is employed to verify the proposed method.Secondly,the convolutional-neural-network model for flow field around a cylinder is investigated.Based on close correlation among Reynolds stress,vortex length and base pressure in the wake of a bluff body and the characteristics of convolutional layer and pooling layer,a fusion convolutional neural network composed of paths with and without pool layer is used to establish the relationship between pressure on the surface and velocity field around the bluff body.The effectiveness of the model is verified by modeling the flow field around a cylinder at subcritical regime.Thirdly,a physics-informed neural network method for solving incompressible Navier-Stokes equations is investigated.Considering two different mathematical forms of Navier-Stokes equations,the velocity-pressure form and the vorticity-velocity form,a deep neural network for solving incompressible Navier-Stokes equations is investigated.Its effectiveness is verified by systematic simulations of different laminar flow conditions and turbulent channel flow.The influence of spatial sampling point distribution and weight coefficients in the loss function on the solution accuracy is studied,and the empirical convergence rate of the network solution is given.Then physics-informed neural network methods for ill-posed problems with incomplete or noisy boundary conditions and some inverse problems are investigated.And a new framework for integrating physics with neural networks is explored.Finally,a general framework for solution of differential equations in fluid mechanics based on deep reinforcement learning is investigated.A general method for solving differential equations using neural networks is given,and reinforcement learning is employed to guide the solving process.The transfer learning characteristic between the solution of different time steps are studied.In order to speed up the solution process of Navier-Stokes equation,the initial parameters of the policy networks for solving equations with higher Reynolds numbers are transferred from those for solving equations of lower Reynolds numbers.