Vortex Identification Method Based On The Right Real Schur Form Of Velocity Gradient And Numerical Simulation Of Laminar Flows With New Flow Theory

Velocity gradient is the basis of many vortex identification methods,such as Q criterion,? criterion,?2 criterion,?ci criterion,and ? criterion.Most of them are based on Helmholtz decomposition to decompose velocity gradients into strain rate and rotation rate,who perform the analysis or design of various invariants.In recent years,it has become a hot research to identify vortex based on the complex eigenvalues of the velocity gradient.Among them,He Feng et al.introduced the quadruple decomposition of velocity gradient tensor and proposed the concept of canonical rotation.Liu Chaoqun and others further explored the characteristic information of the velocity gradient,proposed an effective algorithm for Liutex(canonical rotation),and gave the accordingly vortex identification methods.This analysis shows that they are all real Schur forms of velocity gradients based on the left eigenproblem of ?v.In this context,this paper focuses on the vortex identification method based on right Schur form of velocity gradient.In addition,Professor Wennan Zou proposed a new flow theory based on the sliding characteristics and built in the bending and torsion field.This paper carried out numerical research on this.The main results and conclusions are as follows:1.This article proposes a vortex identification method based on the right real Schur form of the velocity gradient,and comprehensively discusses the tensor decomposition representation and geometric meaning of the real Schur form of the velocity gradient;by the way of image display,the two Schur forms' similarities and differences are compared.At the same time,according to the definition of local streamline,the streamline equations in the two representations are derived respectively.2.A program for solving the components of the left and right real Schur form and corresponding canonical frames is compiled to verify the accuracy of its streamline equation and the quantitative relationship between the left and right decompositions;mainly through the DNS data of the turbulent boundary layer,compare the effect of the vortex identification method based on the right real Schur form with the left the other.3.Through Fluent's UDF(User Defined Function),by adding the source term to the N-S equation,the numerical simulation under the degenerate form(laminar flow)of the new flow theory is finally realized.Finally,taking the flow around a cylinder as an example,the phenomenon under the new theory is discussed.The above work improves the characteristic decomposition of the velocity gradient under the canonical frame and provides a reference for the flow deformation model;the new theory of flow laminar simulation provides reference and basis for the subsequent numerical simulation of laminar flow.