Simulation of Flow around a Surface-mounted Square-section Cylinder of Aspect Ratio Four You Qin Wang 1, Peter L. Jackson 2 and Jueyi Sui 2 1 High Performance Computing Laboratory, College of Science and Management, the University Of Northern British Columbia, Prince George, BC, Canada V2N 4Z9 2 Environment Science & Engineering Program, College of Science and Management, the University Of Northern British Columbia, Prince George, BC, Canada V2N 4Z9 Email: yqwang@unbc.ca ABSTRACT The Reynolds Stress Model (RSM) and Detached Eddy Simulation (DES) are used to study the turbulent flow around a surface-mounted square cylinder of aspect ratio h/d=4 at a Reynolds number of 13,041. The performances of the RSM and DES are evaluated by comparing their simulation results against experimental measurements. Both models successfully reproduced the primary flow, as well as the three-dimensional large-scale vortex structure in the wake of finite wall-mounted body. However, RSM produces better predictions in both mean velocity and root-mean-square velocity than DES. The Strouhal number obtained by statistical analysis of the streamwise drag coefficient on the top wall of the cylinder is 0.1 by RSM, which matches the value obtained by experimental study carried out under a similar flow condition with the same geometry. 1. INTRODUCTION The flow around an infinite square cylinder has a two-dimensional nature and is typically characterized by von Karman vortex shedding [1]. In contrast to the infinite case, the flow behind a surface-mounted square cylinder is more complex since the wake is characterized by the interaction of three types of vortices, namely, tip vortices, spanwise vortices and horseshoe vortices. Turbulent flow around a wallmounted cube [1]-[7] has received more attention than the flow around a surface-mounted square cylinder of aspect ratio h/d >1. Wang et. al. [8]-[9] have reported an experimental study with h/d ranging from 3-7. Meanwhile, experimental investigation conducted by Bourgeois [10]-[11] focused on one aspect ratio of h/d=4. So far, only a few numerical investigations have been done for the h/d >1 case. Becker et. al. [12] have studied the case with h/d=6 at Reynolds number of 1.25x10 4. However, very limited information about their numerical approach and numerical solution has been provided in their published work. Recently LES was used to study the turbulent flow around a surface-mounted square cylinder of aspect ratio h/d = 3 and 5 at a relatively low Reynolds number of Re=500 by Einian et. al. [13]-[15]. In the present study, both RSM and DES were used to simulate the flow around a surfacemounted square cylinder of aspect ratio h/d = 4 at Reynolds number of Re=13041. The goal of this work is to evaluate the performance of these two models and to search for a numerical approach which could provide a reasonably accurate prediction of flow characteristics. The detailed information from simulations can complement experimental measurements to improve fundamental understanding of the flow structure and dynamics. 2. SIMULATION OVERVIEW In the following section, the computational grid and domain, numerical method, and the boundary conditions are summarized. More detailed information regarding both RSM and DES used in the present study can be found in [16]-[17]. The problem under consideration involves flow over a surface-mounted square cylinder of aspect ratio h/d=4 in an open-section wind tunnel. The study case was originally posted at the 20th Annual Conference of the Computational Fluid Dynamics Society of Canada (CFD2012) as a challenge exercise. The experimental results obtained by Particle Image Velocimetry (PIV) were provided by Bourgeois et. al. [10]-[11] for code validation and performance
assessment. The calculations were performed at a Reynolds number of 13,041 based on the width of square cylinder d and free-stream velocity U, using the computational fluid dynamics code FLUENT (fluent 6.2.16). The simulation domain was set to be 0.762m x 0.1778m x 0.127m, and the free stream turbulence intensity was set at 0.8%, the same as in the experimental set up. The no-slip boundary condition was used at the bottom edge, and the symmetrical condition was used at the top edge, and both side edges. A pressure-outlet boundary condition was used to define the static pressure at the flow outlet. The grid consists of 487,085 cells with a maximum volume of 8.70 x 10-8 m 3, and it was generated having a thin boundary layer around the cylinder walls. A segregated solution approach using the SIMPLE algorithm was used. At least 4000 time steps were used to obtain the time-averaged results, and convergence was declared when the maximum scaled residuals were less than 10-4 for the velocity equations, and 10-3 for all other equations. of two foci by RSM. Figs 2-4 indicate that the results obtained by RSM match well with the experimental measurements, including the dipole-type mean streamline pattern at mid-span, the characteristic of low aspect ratio obstacles. (a) DES 3. RESULTS AND DISCUSSION Selected results obtained by both RSM and DES are presented in Figs. 1-8 below. Fig. 1 shows the timeaveraged streamlines in a symmetry plane parallel to the approach flow located at the centerline of the cylinder with the contour of the mean streamwise velocity. Notably, RSM reproduced better prediction in the mean streamwise velocity and time-averaged streamlines than DES did. The saddle point marked by the symbol + in the Figs. 1(b) and 1(c) results from interaction between downwash and upwash flows. This type of saddle point often occurs when the aspect ratio h/d is sufficient large such that the flow over the top of the square cylinder does not attach to the ground surface. The time-averaged streamlines plotted in Fig. 1(a) shows that there is an absence of appreciable upwash flow from the ground plane; this is consistent with the flow around a finite cylinder of low aspect ratio, i.e., where h/d is less than the critical value [15]. Figs. 2 and 3 show the time-averaged streamlines and mean steamwise velocity contours in two different horizontal sections of the wake behind the square cylinder. At z/d=1.0, the recirculation zone behind the square cylinder obtained by DES is larger than the recirculation zones obtained by RSM and PIV. In fact, the results obtained by DES indicate that the wake tends to become larger and stronger near the lower half of the cylinder. At z/d=2.0, an important difference in the streamline patterns obtained by DES and RSM is that there are four foci by DES, instead (c) PIV solutions from [10] Figure 1. Comparison of mean streamwise velocity and the time-averaged streamline at y/d=0. Mean velocity and root-mean-square velocity obtained by DES and RSM at z/d=2.0, and y/d=- 0.0877 are compared with PIV solutions in Fig. 4. It is observed that although both models underpredicted the root-mean-square streamwise velocity, overall RSM produced better predictions in both mean velocity and root-mean-square velocity than DES, especially for the root-mean-square spanwise velocity.
(a) DES (a) DES (c) PIV solutions from [10] Figure 2. Comparison of mean velocity at z/d=1.0. (c) PIV solutions from [10] Figure 3. Comparison of mean velocity at z/d=2.0.
(a) Streamwise mean velocity Instantaneous streamlines and instantaneous vertical vorticity contours in three different horizontal sections obtained by both DES and RSM are plotted in Fig. 5 and Fig. 6, respectively. The stream-ribbons of the instantaneous velocity obtained by both DES and RSM are plotted in Fig. 7. The plots indicate that the flow structure predicted by RSM is highly threedimensional due to the interaction of the downwash flow, upwash flow and the spanwise vortex shedding. However, near the upper half of the cylinder, flow structure predicted by DES is dominated by downwash flow, and the axis of the back vortex is almost parallel to the y axis (the spanwise coordinate). (b) Spanwise mean velocity The frequency spectra of the streamwise drag force coefficient is shown in Fig. 8. The drag coefficient was taken on the top wall of the square cylinder and the frequency has been converted to a Strouhal number. The Strouhal number obtained by RSM is 0.1 which is consistent with the experimental observations [10]. Two Strouhal numbers are obtained by DES. In the power spectrum distribution, the first peak is 0.05, and the second peak is 0.1, its harmonic. 4. CONCLUSIONS (c) Root-mean-square streamwise velocity The DES and RSM in FLUENT were used to predict the flow around a surface-mounted finite square cylinder at Reynolds number of 13041. Overall, the predicted mean velocity and turbulence quantities in the present study are in good agreement with measurement data provided by CFD society of Canada (http://www.cfdcanada.ca/challenge/data), as well as reported in the literature [10]-[11]. RSM produces better predictions than DES of both mean velocity and root-mean-square velocity. It captured most flow features including the vortex shedding frequency. The numerical solutions indicate that the flow behind the square cylinder is surprisingly complex. It is highly three-dimensional due to the interaction of the downwash flow, upwash flow and the spanwise vortex shedding. ACKNOWLEDGEMENTS (d) Root-mean-square spanwise velocity Figure 4. Mean and root-mean-square velocity profiles at z/d=2.0. Computing infrastructure for this work was provided by grants from the Canada Foundation for Innovation, BC Knowledge Development Fund, SGI Canada and donors to the University of Northern British Columbia.
(a) z/d=1.0 (a) z/d=1.0 (b) z/d=2.0 (b) z/d=2.0 (c) z/d=3.0 Figure 5. Instantaneous streamlines and vertical vorticity contours in three sections as predicted by DES. (c) z/d=3.0 Figure 6. Instantaneous streamlines and vertical vorticity contours in three sections as predicted by RSM.
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