Numerical methods to simulate viscous flow over solid objects are of much interest in a wide range of engineering applications. Numerical efficiency is a key consideration of using numerical methods. Immersed-boundary methods can effectively simulate flow around solid objects, as only simple Cartesian grids are needed without conforming to the shapes of the objects. An immersed-boundary method for viscous compressible flow around solid bodies is developed and validated in this study. The method used in this study is a modified version of the penalization method by modelling the solid bodies as porous media with a high flow resistivity with an infinite value for the rigid solids. The Navier–Stokes equations for compressible flow are for the fluid region, and modified Zwikker–Kosten (ZK) type of porous medium equations are for the momentum and energy equations in the solid bodies. These two sets of equations are solved simultaneously so that there is no need to specify the interface boundary conditions between the flow and the solid body. The forcing terms, which are formulated according to the porous medium model, are implemented in the immersed-boundary method to represent the effect of the solid boundaries in the flow. The formulation for compressible flow is different from that of the incompressible flow in which we only need to enforce the non-slip boundary condition without considering the density and energy equations. The third-order numerical scheme of and monotone upstream-centered scheme for conservation laws (MUSCL) is applied for the discretization of inviscid terms, and the fourth- order accurate centered finite-difference discretization is used for the viscous terms. The time integration is carried out by using a third-order TVD Runge-Kutta scheme. The order of accuracy of this simulation is analyzed in terms of grid size. According to the idea of upwind, the Rusanov-Riemann solver is used to provide a proper value of common flux. Two-dimensional flow over a cylinder is used as a test problem for the simulation. Flows with Reynolds number of 300 and Mach numbers of 0.3 and 1.2 are computed. The results show that the vortex shedding phenomenon is correctly captured at Mach number 0.3 and a shock wave structure can be seen at Mach number 1.2. The pressure coefficients and lift and drag coefficients calculated by the present method are compared with results from the body-fitted computation and literature. The reasonable agreement warrants the accuracy of the current immersed-boundary method used for compressible flow simulation.


An Immersed-Boundary Method for Simulation of Viscous Compressible Flow Around Solid Bodies

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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