Study On The Interaction Between The Rigid Body And Fluid Using Projected Immersed Boundary Method

Nonlinear dynamic fluid-structure coupling problem is the most challenging content in both engineering and academic field. By the modern numerical technique, researches on the interaction between the structural vibration and the uNavier-Stokesteady flow field is of great importance for the avoidance of the structural resonance induced by the fluid so that it can enhance the reliability and safety of the structure. In fluid structure interaction (FSI) fields, there are many problems involving the interaction between the rigid body and the fluid. When the rigid body has large movement, it would be a potential challenge for the ordinary FSI method based on the dynamic gird technique, for example, the mesh dynamic update, the mesh control of boundary layer.But FSI based on the immersed boundary method (IBM) doesn’t need to update the grids, which shows huge advantages in the FSI calculation including large movement. According to this, Both the model and numerical strategy for interaction between the rigid body and the fluid based on projection IBM are established, and the corresponding program is also written with VC++language. The validation for the program is carried out by the basic numerical example of the flow over circular cylinder. Furthermore, the distribution characteristics of the vortex caused by the flow over the double column in series and parallel are analyzed and some meaningful conclusions are obtained. There are five chapters altogether, and the main content are list below:(1) A projection IBM and the numerical technique to deal with the interaction between the fluid and rigid body is proposed. In this algorithm, the projection step method is used to realize the decoupling of the velocity and the pressure terms in the incompressible Newtonian fluid governing equation added movement source term. At the same time, in the process of solving the pressure, it composes a set of pressure Poisson equation which contains mixed boundary condition,which is identical to the real physical boundary condition of the solving process and is different from the conventional boundary condition in which the pressure gradient is set as zero.(2) In space discretization, a general expression for advection terms is used, which can be alternative to be Quick, central difference, second order up-winding or the Fromm schemes by changing the parameter CF.And for diffusion terms, the central difference scheme is used. In time discretization, the Euler method is adopted.The volume ratio to caulate the movement source term.which is calculated by Romberg algorithm effectively.(3) After the Poisson equation is discreted, due to the noNavier-Stokesingularity and the unsymmetry of the large sparse linear equation set, the open function library UMFPACK is used for fast solving. When transferring the coefficient matrix and the right end vector, the function library Eigen to optimize the data structure is adoped, which decreases the storage space, finally realize the fast solving and meantime keep the robustness.(4) According to the numerical method in this essay, the reliability of solving the incompressible Naver-Stokes equation and the projection IBM are validated by the basic numerical examples of the2-D Channel flow and flow over circular cylinder. The corresponding numerical calculation program is written by C++language. For flow over circular cylinder, the distribution of the velocity field and the pressure field, as well as the votex structure are analyzed in different Reynolds numbers.(5) Using projection IBM, it analyzes the vortex distribution of the double column in series and parallel. What’s more, the dynamic circumferential flow characteristics in different Reynolds numbers, blocking ratio and distance between two cylinders are given.