Revision as of 08:31, 31 January 2011

Test Case

Brief Description of the Study Test Case

The case considered is the flow past a finite-height circular cylinder mounted on a flat plate for two height-to-diameter ratios h/D = 2.5 and 5.0. The parameters of the study and the dimensions of the cylinder are given in Table 1. The cylinder was placed in a water tunnel and the measurement section dimensions are provided in Fig. 2. The thickness of the approach- flow boundary layer was about 0.1 = h and the free-stream turbulence level was Tu ≈ 2%.

D (mm)	h (mm)	h/D	U_∞ (m/s)	Re = U_∞ D / ν
80	200	2.5	0.54	4.3×10⁴
40	200	5.0	0.54	2.2×10⁴

Table 1. Parameters in the experimental study

Figure 2. Experimental configuration for flow visualization and LDV measurements, from Palau-Salvador et al (2010)

Test Case Experiments

The experiments were carried out by Kappler (2002) in the closed high pressure water tunnel of the Institute for Hydromechanics at the University of Karlsruhe. The experiments are described in detail in Kappler (2002) and a link to the actual data is given in the reference. A short description is provided in Palau-Salvador et al (2010). The measurement section and the cylinder placed in it are shown in Fig. 2. Measurements of all three components of mean and fluctuating velocities were carried out with a 2D LDV in two consecutive steps. In the first step, the optical axis was oriented in the vertical direction, thus allowing determination of the velocity components u and v. In the second step, the optical system was reconfigured to point horizontally for simultaneous measurements of u and w (see also Fig. 2). The uncertainty in the velocity measurements was judged to be less than 5% of the inlet velocity for the mean and fluctuation values, with somewhat higher possible errors for the turbulent shear stress. Reference LDV measurements were performed without the cylinder in place in order to determine the boundary layer characteristics at different streamwise positions and the results are included in Kappler (2002). Prior to the LDV measurements, extensive flow visualizations were carried out for four cylinder configurations in the range h/D = 2.0 – 5.0. The results can also be found in Kappler (2002).

In addition to the components of mean and fluctuating velocities measured in various vertical and horizontal planes, and the visualizations of Kappler with dye-injection, some oil flow pictures showing the streamlines of the flow near the ground, along the cylinder walls and also the complex flow at the top of the cylinder are available from other studies at h/D = 2. Some of these results and the original references are included in Palau-Salvador et al (2010).

CFD Methods

The test cases considered here were only calculated by Palau-Salvador et al (2010) with LES and these calculations are described in detail in this paper. The LES employed the dynamic approach of Germano et al (1991) as modified by Lilly (1992) to model the subgrid-scale stresses. The model parameter c was regularized by averaging over the surrounding grid cells and imposing the subgrid-scale eddy viscosity to be larger than zero (Zang et al 1993). The contribution of the subgrid-scale stress is rather small in the simulations. The LES code MGLET originally developed at the Institute for Fluid Mechanics at the Technical University of Munich (Tremblay et al 2001) was employed to perform the large eddy simulations. This finite volume code uses a Cartesian grid and an immersed boundary method (Verzicco et al 2000) to represent the circular cylinder on this grid. The computational domain is sketched in Fig. 3 for the two cases considered; the height of the cylinder is constant and it is the diameter which varies giving different h/D ratios. 580 × 380 × 204 grid points were used for the h/D = 2.5 case and 516 × 252 × 204 grid points for the h/D = 5 case in streamwise, lateral and vertical directions respectively, yielding a total of 45 million grid points for the first case and 27 million grid points for the second one respectively. Around the cylinder, uniform distribution of grid cells was used in lateral and streamwise direction. Fig. 4 shows the grid in a horizontal and in a vertical plane indicating the refinement of the grid towards the cylinder and the ground plate. The mesh spacings around the cylinder in streamwise and lateral direction in wall units are in the range 2 – 6 while the vertical mesh sizes in wall units near the free end are around 1 – 3 and near the ground plate 2 – 5 in the vicinity of the cylinder. The time steps were such that the maximum CFL number was 0.83. At the outflow a convective condition was applied. At the ground plate and the cylinder walls the no-slip condition was used. The top wall and the side walls were treated as frictionless rigid lid so that the free slip condition was applied. At the inflow (x/h = −1.6) a u-velocity profile taken from the measurements was specified, v and w were set to zero and no fluctuations were imposed. Profiles of the u-velocity and the u-fluctuations in front of the cylinder were compared with measurements without the cylinder being present and reasonably good agreement was found even though in the LES fully realistic turbulence had not yet developed in the boundary layer (Palau-Salvador et al 2010).