This paper compares the performance of eight Reynolds-Averaged Navier–Stokes (RANS) two-equation turbulence models and two sub-grid scale (SGS) large eddy simulation (LES) models in the scenario of unsteady flow around a finite circular cylinder at an aspect ratio (AR) of 1.0 and a Reynolds number of Re=20000. It is found that, among all the eight RANS turbulence models considered, the K-Omega-SST model (viz. SST-V2003) developed by Menter et al.[1, 2] possesses the best overall performance (being closest to the numerical results of the two LES models considered, which can be deemed as the quasi-exact solution in view of the very fine computational mesh employed by the two LES models in this study) in terms of the mean surface pressure coefficient distribution (i.e. Cp), the mean drag coefficient (i.e. Cd), the mean streamline profiles in some characteristic planes (such as the mid-height plane and the symmetry plane of the cylinder) and the distribution of mean bed-shear-stress amplification on the bottom wall.
The experimental and numerical study on the complex three-dimensional flow structures around a bluff body remains one of the most active areas of research in fundamental fluid dynamics over the past decades, mainly due to the extensive presence of such flows in nature and engineering applications, such as the wind field around high-rise buildings, the pollutant transport around chimney stacks, the aerodynamics force on cooling towers, the flow field around offshore structures, the heat exchange on electronic circuit boards, and so on [3-6]. Although many earlier studies focused on the analysis of the flow past a nominally infinite two-dimensional (2D) circular or square cylinder, recently most attentions have been paid to the unsteady flow around finite-height cylinders [7-12], with one end immersed in the free stream (viz. the free end) and the other end mounted on a flat wall (viz. the base end), which are more consistent with the structures in reality. Correspondingly, due to the combined influence of the downwash flow from the free end and the boundary layer near the bottom wall, the three-dimensional (3D) flow structure around a finite cylinder is usually much more complicated than that behind an infinite one.
It can be concluded from the existing literature that all the following six factors can have some effects on the flow structure around a finite-height cylinder [6-8]: 1). the turbulence intensity of the approaching flow; 2). the cross-section shape of the cylinder; 3). the Re number (viz. Re=UD/ν, where D is the characteristic width of the cylinder, U is the free stream velocity, and ν is the fluid’s kinematic viscosity.); 4). the boundary-layer thickness on the bottom wall relative to the cylinder height (viz. δ/h); 5). the ratio of the cylinder height to the characteristic width of the cylinder (viz. AR=h/D); 6). the blockage ratio of the channel (viz. β1=h/H and β2=D/B, where H and B are the height and width of the channel or the computational domain, respectively.). On one hand, the respective effect extent of the aforementioned factors may vary significantly from each other when it comes to a specific condition. On the other hand, in view of multiple influencing factors and complex flow field under this circumstance, in the past, researchers often only discuss one or two factors’ influence in each article for simplifying the problem, therefore, the integrated effect of simultaneously changing several parameters remain to be investigated in the future.
Considering that high Reynolds numbers always result in very complicated vortex structures in the wake of a finite circular cylinder (especially when mounted on a non-slip bottom wall), this paper presents a detailed discussion on the flow around a finite circular cylinder with AR=1 at a relatively high Re numbers (viz. 20000). The purpose of this study is to quantitatively and qualitatively make a detailed comparison of different turbulence models when it comes to the mean pressure coefficient profile Cp in the mid-height plane of the cylinder, the mean drag coefficient Cd of the cylinder, the time-averaged velocity and pressure fields, and the distribution of mean bed-shear-stress amplification on the bottom wall.
2. Configuration and Numerical Model
2.1 Test Configuration
A similar geometric configuration as that used by Zhang et al. [6, 8] is employed in this study. As illustrated in Fig. 1, a finite circular cylinder with a non-dimensional width of D=1 and a nondimensional height of h=1 is vertically mounted on a plane boundary, and the (streamwise) length, (transverse) width and (spanwise) height of the computational domain are, respectively, L=30D, W=22D and H=2D (which gives an area blockage ratio of 2.27%). Further, the junction section between the cylinder and the bottom wall is centered at the origin of the coordinate system, which means that the inlet boundary is located at 10D upstream of the cylinder and the outlet boundary is situated at 20D downstream of the cylinder (i.e. L1=10D, L2=20D).
2.2 Governing Equations
2.2.1. RANS models.
The unsteady 3D Reynolds-averaged Navier-Stokes (RANS) equations employed in this study can be obtained by taking ensemble average of instantaneous mass and momentum conservation equations for incompressible and isothermal flows, as shown in the following.
2.3. Boundary Conditions and Numerical Schemes
Four kinds of boundary conditions are involved:
1. Inlet: For the velocity field, a fixed uniform velocity is prescribed (i.e. I u =1, I v =wI =0), and, for the pressure field, the zero-gradient condition is imposed (i.e. 0 Ip n ).
2. Outlet: For the velocity field, the convective outflow boundary condition is adopted: (11) where denotes all the three velocity components (viz. u, v and w), and c u is the advective velocity at the outlet boundary. For the pressure field, the homogeneous Dirichlet condition is utilized at the outlet boundary (i.e. p=0).
3. Bottom wall and the surface of the obstacle: No-slip impermeable boundary condition is prescribed for the velocity field (i.e. u=v=w=0), and the zero-gradient condition is employed for the pressure field.
4. Top and lateral boundaries of the computational domain: Free-slip condition is prescribed, which means that the velocity component normal to the boundary is zero (i.e. 0 b u ) and the normal gradients of both the pressure and the tangential velocity component are zero (i.e. // 0 b b u n p n , where b// u is the tangential velocity component).