MODIFICATION OF FLOW AROUND A CIRCULAR CYLINDER USING POROUS MEDIA

Flow around a circular cylinder having a porous surface is studied numerically by means of direct numerical simulation (DNS) and large eddy simulation (LES). The flow in the porous media is represented by a spatially-averaged (i.e., macroscopic) model. The parameters of the most effective porous media are found from a two-dimensional parametric test at the Reynolds number, based on the free stream velocity and the diameter of cylinder, of Re = 1000. The lift force fluctuation is notably reduced in the case of thicker porous surface. The DNS of three-dimensional flow at Re = 1000 reveals that the porous surface works to stabilize the shear layer. The LES at a very high Reynolds number (Re = 105) shows that the vortex shedding is completely suppressed by the porous media, which supports the experimental observation by Sueki et al. (2007). Simulations at different Reynolds numbers show that the stabilization effect works better at higher Reynolds numbers. INTRODUCTION Vortex shedding from a circular cylinder causes many engineering problems, such as noise, large drag and oscillation due to the lift force, which in the worst case yield breakage of instruments. In order to resolve these problems, flow control around a circular cylinder has been studied by many researchers (Choi et al., 2008). Recently, Sueki et al. (2007) investigated the effect of porous media fitted around a cylinder aiming at noise reduction of pantograph and achieved considerable reduction of noise. Its mechanism was explored by the same group using the PIV measurement (Takaishi et al., 2007): they observed apparent modification of the downstream wake. These results suggest that the porous media is an effective control device for flow around a bluff body. Toward the use of porous media in industral applications, one should further accumulate the knowledge about its effect on the flow, including the dependency to various design parameters and the detailed mechanism of flow modification. Therefore, in the present study, we perform simulation of flow around a circular cylinder having a porous surface by means of direct numerical simulation (DNS) and large eddy simulation (LES). First, we perform a parametric test for two-dimensional (2D) flow at the Reynolds number, based on the free stream velocity and the diameter of cylinder, of Re = 1000, and the flow fields in some selected cases are analyzed in detail. Subsequently, three-dimensional (3D) simulation is performed at Re = 1000 in order to investigate the 3D effect. Moreover, the simulation is performed for a lower Reynolds number (Re = 100) and a higher Reynolds number (Re = 105) in order to clarify the Reynolds number dependency. NUMERICAL DETAILS We consider the flow around a circular cylinder having a porous surface. Various simulation methods have been proposed to treat the flow faced on porous surface: 1. direct method, in which the complex geometry of porous media is treated directly (Martys and Chen, 1996); 2. method of boundary condition, which uses an artificial boundary condition mimicking the effect of porous surface (Jiménez et al., 2001); 3. macroscopic flow model, which uses a volume-averaged equation in the porous media (Bruneau and Mortazavi, 2004). In this study, we adopt the last method to avoid numerical complexity and to study the effect of porous media thickness. The momentum equation for an isothermal, incompressible flow including that in the porous media is given by (Hsu and Cheng, 1990): ∂u⃗ ∂t + ∇ ( u⃗ · u⃗ φ ) = −∇p + 1 Re ∇u⃗ + K⃗ , (1) where K⃗ = − φ ReDa u⃗ − 1.75 √ 150 1 √ Da u⃗|u⃗| √ φ . (2) Equation (1) is developed from the assumption that the porous media is made of mono-dispersed sphere particles. The permeability, k, is made dimensionless by using the cylinder diameter D to be expressed by the Darcy number, Da = k/D2. The permeability is related to the porosity, φ and the particle diameter, dp, through k = φdp a(1 − φ)2 . (3) Figure 1: Flow configuration. Note that, since Eq. (1) reduces to the conventional NavierStokes equation outside the porous media, the interface between the porous media and flow outside can be solved without any additional treatment. Throughout the present study, the surrounding porous media are assumed to have uniform thickness, permeability, and porosity. Two different thicknesses are considered: 20% and 50% of whole radius (i.e., d = 0.2R and d = 0.5R). The simulation code is based on the DNS code in the cylindrical coordinate system by Fukagata and Kasagi