Numerical Study Of Lagrangian Coherent Structure In Two Dimensional Flow Field

With the rapid development of computing power and flow measurement technique,more and more discrete velocity field data sets can be obtained from numerical simulation or experimental measurement,which hide large amounts of information to be mined.Flow structure is one of the main approaches to describe flow field information.Coherent structure is a correlative structure in time and space of flow field,while Euler's coherent structure is mature,but some of them lack of objectivity.In order to solve this problem,scholars put forward Lagrangian Coherent structure(LCS).LCS is a material line which can affect the transport and mixing of flow field by dealing with discrete velocity field.This theory is based on the subject of dynamic system and originates from chaotic advection.By describing the deformation and the separation of particles,the material line which has special effect on flow field can be found.As the main tool of flow field analysis and flow visualization,LCS is of great significance to its research.Firstly,double gyre with analytic solution is analyzed to detect LCSs in the flow field,which is the validation of the program in this paper.The calculation method of Cauchy Green strain tensor and its invariants and the realization process of material advection in this paper are discussed.An easy-to-implement algorithm for identifying the finite-time Lyapunov exponent field(FTLE)ridge is proposed.Compared with the results of previous scholars,it is found that the algorithm can accurately solve the FTLE ridge.Geodetic theory can describe different types of LCSs in a universal way.All the solutions of LCSs in this paper are based on the calculation of geodesic theory.Three different methods of elliptic LCS are discussed.The method of adding Poincare cross section manually can not realize automatic identification and can not recognize all vortices.For the method of singularity identification using tensor lines,the singularity values are unstable and the results depend on integration time.The method of directly solving geodesic can avoid the above questions very well.However,to deal with denominator non-zero,some small vortices will be misreported and need to be filtered.The backward-time hyperbolic repelling LCS of the flow field is detected,and the shape is consistent with the tracer pattern.Vortex ring is a fundamental phenomenon in nature.In this paper,CFD is used to simulate the formation and evolution of vortex ring.The program correctness is verified using the ideal slug model and fluid topology structure.Through Lagrangian coherent structure,the vortex ring flow field is divided into three different regions: the irrotational potential flow region,the transition region and the vortex core region.Lagrangian coherent vortices are used as a boundary between transition region and vortex core region.Different regions have different characteristics.The vortex core with near-Gaussian vorticity distribution diffuses continuously.The transition region is composed of the shear layer injected from the piston and the fluid entrained in the periphery.The part of the fluid in the irrotational potential flow region will be entrained into the transition region by many lobes.Because the transition region has a strong time-varying properties,and the vortex core region is relatively stable.