Research On Hybrid Cartesian Grid Method For Simulating Unsteady Flows

In hybrid Cartesian grid method,the region near body is discretized by using body-fitted structured/unstructured grids,while the remaining computational domain is tessellated with generated Cartesian grids automatically.In this way,the treatment of boundaries in traditional Cartesian grid method is translated into how to deal with the communication of flow information on the interfaces between two different meshes.This method combines the advantages of structured/unstructured grid and Cartesian grid,so it has wide applications in handling problems involving complex geometries,complex flow features and unsteady flow phenomena.The difficulties of Hybrid Cartesian grid method lies in the fast grid generation and the communication between different grids.Nowadays,the hybrid grid method could be applied to simulate many kinds of steady flows.But for the simulation of unsteady flows,it still requires to be further developed.In this thesis,much effort is devoted to study the details of hybrid Cartesian grid method and its applications for simulation of viscous and unsteady flows.Firstly,how to generate the hybrid Cartesian grid is studied.Through the investigation of Hole-map and Cut-Paste method that are often used in Overset methods,a new inverse way of hybrid Cartesian grid generation is developed and the idea of "Donor cell" is employed to implement the communication of flow information on interfaces.An alternating digital tree(ADT)algorithm is introduced to accelerate the grid generation as well as the donor cell searching,and an ADT based efficient method for calculation wall distance is also investigated.Based on the proposed hybrid grid,a finite volume solver is developed for flows at all speeds governed by the Faver Reynolds averaged Navier-Stokes(RANS)equations combined with adaptive mesh refinement and preconditioning method.In the present work,several cases about mesh generation around complex geometries as well as the simulation of many typical steady and viscous flows are presented to show the robustness and effectiveness of the proposed Hybrid Cartesian grid generation method and the corresponding flow solver.Secondly,the hybrid Cartesian grid method is then extended to simulate unsteady flows around fixed boundary.The dynamic adaptive mesh refinement,the implicit dual-time stepping LU-SGS approach and the unsteady preconditioning method are developed for unsteady simulation.Then the detached eddy simulation(DES)based on the SST k-? turbulence model is investigated for 3-D massively separated flows at high Reynolds numbers.During unsteady simulations,the near wall body-fitted grids are fixed,whilst the off-body Cartesian grids are adapted dynamically based on flow features.As a consequence,the complex flow phenomena could be captured more accurately.DES coupled with the unsteady hybrid Cartesian grid method is applied in the vortex breakdown of low speed flow over a 70-degree delta wing and separation flows around a 6:1 prolate spheroid.These two established numerical results indicate that the proposed method is very suited for massively separated vortex dominated flows.Finally,in order to expand the application range of the unsteady hybrid Cartesian grid method,it is further developed for solving moving boundary problems.The off-body background Cartesian grid is adapted or refreshed based on the distance to interface,and the "donor cell" method for steady flows is extended to simulate 2-D unsteady moving boundary flows.Numerical results,such as flow past a rotating circular cylinder,flow past a pitching airfoil with small amplitude,dynamic stall problem of an airfoil,and flapping airfoil problem,show the accuracy and efficiency of this treatment.When the current method is coupled with rigid moving equations,a store separation process is simulated.The result shows that the proposed method is also suited for problems involving large-scale moving boundaries.For 3-D moving boundary problems,the interpolated treatment of Overset method is investigated to handle the communication of different grids,the hovering of Caradonna-Tung rotor wing based on unsteady hybrid Cartesian grid method is simulated to show its ability for handling 3-D moving boundary problems.