Spanwise length and mesh resolution effects on simulated flow around a 5:1 rectangular cylinder

Highlights

• Elaborate LES simulations are conducted for a 5:1 rectangular cylinder at Re ​= ​4 ​× ​10⁴.

• The effects of cylinder length and mesh size on flow features are comprehensively investigated.

• The simulation cases of L ​= ​2.5D and δz ​= ​0.025D, 0.0125D are firstly attempted in this study.

• The LES simulation results show good agreements with the experimental data.

Abstract

For a 5:1 rectangular cylinder, the large eddy simulations (LES) are carried out to systematically evaluate the influences of the cylinder spanwise length (L) and spanwise mesh size (δz) on the aerodynamic forces, spanwise-averaged quantities, and flow features. The L varies from 10D to 2.5D, and δz varies from 0.1D to 0.0125D, where D is the cylinder depth. The new simulation cases of L ​= ​2.5D and δz ​= ​0.025D, 0.0125D are firstly attempted in this study. Some flow details are unveiled through flow visualization and spanwise correlation functions of the surface pressure. The simulation accuracy is validated through the comparisons of the surface pressure, velocity profile in wake region, and relative phase angle distributions on the cylinder top face with the available experimental results. It was found that the influence of L is in general insignificant, while δz has more significant effects on the surface pressure fluctuation, main separation bubble size, and 3D flow features. In consideration of both simulation accuracy and computation time, 2.5D and 0.025D are recommended for the selections of L and δz, respectively. The results based on the more refined grids in this study could serve as references for evaluating the accuracies of other numerical simulations.

Introduction

The aerodynamic characteristics of rectangular cylinders provide good references for many engineering structures, such as high-rise buildings and bridge decks, and thus has gained wide attentions. As is known, the flows around rectangular cylinders are highly turbulent and heavily dependent on the chord-to-depth ratio, or the aspect ratio B/D, where B and D are the cylinder width and depth, respectively. According to Parker and Welsh (1983), for rectangular cylinders with 3.2 ​< ​B/D ​< ​7.6, the separated shear layers from the leading edge roll up and periodically reattach to the cylinder lateral faces. Unlike the classical Karman-type vortex shedding of a circular or square cylinder, the vortex shedding behavior in this case is triggered by the “impinging shear-layer instability” (Rockwell and Naudascher, 1979; Nakamura et al., 1991; Ohya et al., 1992), i.e., the alternatively impinging of shear-layers onto the cylinder trailing edge. Accompanied by the shear-layer impinging instability is the periodical fluctuating force acting on the cylinder, which may induce the potential vortex-induced vibration (VIV) or flutters. Due to the flow regime complexity, the aerodynamics of cylinders with aspect ratio in this range are expected to be more sensitive to some parameters and are more challenging to be captured. For this reason, a benchmark study on the aerodynamics of a 5:1 rectangular cylinder (BARC) has been launched in 2008 during the 6th International Colloquium on Bluff Body Aerodynamics and Applications (BBAA6). Since then, a variety of wind tunnel tests (Bartoli et al., 2011; Bronkhorst et al., 2011; Schewe, 2013; Liu et al., 2013; Haan et al., 2016; Mannini et al., 2017) and computational fluid dynamics (CFD) simulation studies (Bruno et al., 2010&2012; Mannini et al., 2011, Mannini et al., 2019; Nguyen et al., 2015; Patruno et al., 2016; Ricci et al., 2017; Mariotti et al., 2017; Cimarelli et al., 2018a, 2018b, 2019) were carried out aiming at reproducing and analyzing the flows around a 5:1 rectangular cylinder.

Bruno et al. (2014) summarized and compared the results obtained from the experimental and CFD studies during the first four years of BARC activity. Good agreement can be found in terms of near wake flow, base pressure, and consequently the drag coefficient. However, significant dispersions were highlighted with regard to flow features and pressure distributions along the cylinder lateral sides, even for the time-averaged values, indicating the high sensitivity of the flow feature to experimental conditions and CFD simulation setups. During wind tunnel tests, the imperfect geometry shape, non-null angle of attack, and inevitable free-stream turbulence are all underlying factors influencing the results. For the CFD simulations, however, these parameters can be accurately set, and it is just the simulation accuracy that matters.

There are lots of factors affecting the simulation accuracy, among which the turbulence modelling method is the most fundamental one. Although the two-dimensional (2D) Reynolds-averaged Navier-Stokes equations (RANS) turbulence model is more affordable for engineering practice and the accuracy is acceptable in terms of the mean drag coefficient, Mannini et al. (2011) and Patruno et al. (2016) found that the 2D RANS model always overestimates the separation bubble size and the pressure fluctuation on the lateral faces. The influences of RANS turbulence modelling method and turbulence parameters were systematically studied by Witteveen et al. (2015) and Mariotti et al. (2016) through uncertainty quantification and stochastic sensitivity analysis. Compared with the 2D RANS simulation, the three-dimensional (3D) large eddy simulation (LES) and detached eddy simulation (DES) are expected to give more accurate results and consequently gain more applications, although they need higher computational costs. In addition, Cimarelli et al. (2018a) conducted a direct numerical simulation (DNS) study at moderately high Reynolds number (Re ​= ​3000), which can serve as a reference for the validation of other CFD studies.

The computational domain size also influences the simulation results. Bruno et al. (2014) concluded that the distance of the cylinder from the inlet boundary and from each of the lateral boundary should be larger than 20D, where D is the cylinder depth. However, the requirement of the spanwise domain size, i.e., the cylinder length (L), is not very clear up to now. Ideally, the cylinder length should be large enough to make the spanwise correlation of the quantity of interest close to zero. Nevertheless, validating the accuracy of the simulated spanwise correlation coefficient itself is not an easy task. In fact, Mannini et al. (2011) found that the spanwise correlations of cylinder surface pressure show significant reductions when L increases from 5D to 10D, while Bruno et al. (2012) came to a different conclusion that the simulation results of L ​= ​5D, 10D, 20D are very close. Besides, the selection of L should also consider the incoming flow turbulence properties. Ricci et al. (2017) found that the ratio of the inflow turbulence integral length scale to L significantly affects the simulation results. It is useful to find an appropriate L in consideration of both simulation accuracy and computational cost. It is a pending issue to verify the feasibility of using a shorter L. The case of L ​= ​2.5D has never been attempted in previous studies.

Apart from the turbulence model and computational domain size, the computational mesh resolution is another important factor affecting the simulation accuracy. In LES simulation, the large-scale energetic eddies are directly solved, while the isotropic eddies with scale smaller than the mesh size are modelled into the equations of the large-scale eddies. Unfortunately, the computational cost is still not affordable for a real LES simulation within the BARC subject and most of the existing LES studies are actually very-large-eddy simulations. In this case, a sensitivity study of the simulation results to grid refinement is essential. Due to the simplicity of the geometry of the BARC cylinder, and in order to maintain grid orthogonality, the generated 3D mesh is usually structured in the spanwise direction. In addition, the mesh in spanwise direction is usually much coarser than in the other two directions in the near-wall region. Tamura et al. (1998) suggested that the spanwise grid size (δz) should not be larger than 0.1D to simulate the bulk flow parameters. Later, Bruno et al. (2012) further decreased δz to 0.05D and found that the results of δz ​= ​0.1D and δz ​= ​0.05D show large discrepancies. In virtue of this scenario, we further decrease δz to 0.025D and 0.0125D values to unveil its influence on the simulation results.

In all, it is well acknowledged that there are some modelling parameters that might affect the simulated flow around the cylinder. Nevertheless, how and to what extent will these parameters influence the simulation results, and what are the most suitable choices to get a good balance between the simulation accuracy and computational costs, are not very clear yet. Based on this reality, this study intends to systematically investigate the influences of L and δz on the simulated flows around the 5:1 rectangular cylinder based on LES simulations, with focuses on smooth incoming flow and null angle of attack condition. Much finer grids are adopted in both streamwise and spanwise directions compared with other studies (δz decreased to 0.0125D and up to 60 million total grids). Besides, the possibility to replace a length L of 5D or larger with a length of 2.5D will also be explored to reduce the computational cost. More flow details are expected to be unveiled based on the fine simulation and the results could serve as a reference for evaluating the simulation accuracy of other similar simulations.

The rest of this paper is organized in the following manner. Section 2 introduces the numerical model including the turbulence model, computational domain, mesh arrangements, and simulation cases. Section 3 reports the simulated aerodynamic forces. Then, the spanwise-averaged and 3D flow features are analyzed in section 4 and section 5, respectively. Finally, some conclusions are drawn in section 6.