Research On Cartesian Grid Method For Simulating Complex Flows

The hybrid Cartesian grid method could solve the wall boundary problems with high Reynolds number,due to its characteristic that body-fitted structured grids are generated around the geometries,while the background Cartesian grids are used in the other region.A searching technique for the donor cells is adopted to transfer the data between these two types of grid system.Meanwhile,due to the body-fitted structured grids can move rigidly along with the geometry boundary,and the background Cartesian grids only need to be adjusted slightly,which makes the hybrid Cartesian grid method has inherent advantages to simulate the unsteady moving boundary problems,and avoids the geometric conservation law problems emerging in deforming grid method.This paper is devoted to developing an adaptive hybrid Cartesian grid generation approach and flow field calculation methods.The accuracy and conservation problems caused by the introduction of the interface are studied firstly.Secondly,a cell-centered third-order U-MUSCL scheme which is applicable to the hybrid Cartesian grid method is proposed.Finally,coupled with the hybrid Cartesian grid method,it is applied to the numerical investigations of some complex flow problems.The research contents and achievements of the thesis include the following parts:(1)An adaptive hybrid Cartesian grid generation method and its corresponding cell-centered finite volume flow field solution method are developed,then the properties of hybrid Cartesian grid's interfaces are studied.The hybrid Cartesian grid can not only deal with the viscous flow problems with high Reynolds number,but also make the two sets of grids as a whole by searching the donor cell at the interface,so only one set of solving algorithms are needed to solve the problems.In addition,the hybrid Cartesian grid method is applied to the simulation of moving boundary unsteady problems,and the flow field solution method is extended to solve the unsteady Arbitrary Lagranian Eulerian equation.In the study of interfacial properties,the numerical cases of accuracy test are shown that the cell gradients calculated by the Green-Gauss method will reduce the accuracy near the interfaces greatly,and the least square method can improve this problem effectively.After that,the problem about moving shock and vortex crossing the interfaces is studied.It is found that fast shock can smoothly cross the interfaces without hindrance,slow shock will be blocked at the interfaces and can't cross.Vortex can pass through the interfaces successfully and its strength is affected little.In order to solve the problem of slow shock blocking at the interfaces,a new interfaces interpolation method is proposed.This method is only slightly modified from the original method about searching donor cell,and retains the convenience and overall solution characteristics of original method.The problem of slow shock being blocked has been solved by this method.(2)The research of high-order numerical algorithm based on hybrid Cartesian grid is carried out.A new third-order U-MUSCL scheme by cell-vertex is extended to the cell-centered grid and applied to hybrid Cartesian grid.This numerical scheme does not need to construct interpolation templates and add extra degrees-of-freedom within cells.Theoretical analysis and numerical cases are shown that the scheme can even achieve fourth-order accuracy when the coefficients are chosen properly.At the same time,the numerical vortex keeping case is used to prove that the scheme has low dissipation,and its ability to maintain vortex is equivalent to that of the second-order scheme which adopt sixteen times mesh numbers in two dimension problem.(3)Numerical simulations of complex flow problems with complex flow phenomena such as shock waves and vortexes are carried out.The adaptive hybrid Cartesian grid method,cell-centered third-order U-MUSCL scheme,implicit LU-SGS double time steps method(to unsteady problem)and SST-DDES model are used to simulate some complex flow problems.By the cases of unsteady flow around a two-dimensional cylinder and viscous flow around a three-dimensional spheroid of 6:1,the capturing ability of the hybrid Cartesian grid coupled cell-centered third-order U-MUSCL scheme for shedding vortexes and separating vortexes is verified.In addition,by the cases of NACA0012 airfoil,ONERA M6 wing and DLR-F6wing-body,the grid adaptive technique based on flow field characteristics is verified.During the iteration process,the shock waves and vortexes in these complex flows are accurately captured by the adaptive refinement and coarsening of grid.(4)Numerical simulation about three-dimensional rotating flow problems are carried out.Weiss-Smith precondition method is applied to the hybrid Cartesian grid flow field solution algorithm,so that the algorithm can solve the problems with both compressible and incompressible flow regions,which lays a foundation for the simulation of three-dimensional rotating flow problems.Then the rotating coordinate system method is used to transform the three-dimensional unsteady rotation problems into quasi-steady problems,which saves computing resources and improves computing efficiency.These above methods are intergrated to simulate the three-dimensional rotational flow of wind turbine blades and helicopter rotors.In the numerical simulation of Phase VI blades,with the increase of inflow velocity,the hybrid Cartesian grid method developed in the doctoral thesis successfully simulates the development of the transverse flow region along the blade development direction,that is the separation process on the leeward side.And this method also captures the development process of tip and root vortices downstream of the blade.In the Caradonna-Tung rotor calculation,the Cartesian grid adaptive technique is adopted to capture the tip vortexes of the rotor in hover.