A Dual-‐Mesh Framework for Turbulence Modeling:Application to Flow Around a Circular Cylinder Heng Xiao, Yoshiyuki Sakai and Patrick JennyInstitute of Fluid Dynamics, ETH Zurich, Switzerland1. IntroductionLarge-Eddy Simulation (LES) has gained popularity and successes in the pastdecades, particularly for free-shear flows. However, the high computational costin wall-bounded flows is still a major hurdle for the application of LES inindustrial and practical flows.To overcome this difficulty, various hybrid LES/RANS approaches have beendeveloped, where RANS (Reynolds-averaged Navier-Stokes) equations are solvedin the near-wall region while LES is only conducted in the free-shear region awayfrom the wall [Fröhlich and von Terzi 2008]. One of the methods to address thisissue is a consistent framework for turbulence modeling, where the filtered andReynolds-averaged equations are solved simultaneously in the entire domain[Xiao and Jenny 2011]. To ensure consistency between the two solutions,additional drift terms are added to the corresponding equations. This approachleads to very clean conditions at the LES/RANS interfaces. According to thisframework, a hybrid solver for incompressible turbulent flows has beenimplemented based on the open source CFD platform OpenFOAM [OpenFOAM2011] taking advantage of its existing LES and RANS solvers as well as its fieldoperation capabilities. The solver has been tested on plane channel flows andflow over periodic hills. To further validate the new simulation framework, theflow around a circular cylinder is investigated with the hybrid solver in this study.The major difficulties related to this flow include the coherent structures and theflow-dependent separation location, which pose challenges for both LES andRANS. By combining the advantages of LES and RANS, we expect to addressthese difficulties.
22. ResultsFor this study, various different cylinder-diameter Reynolds number (Re D ) weretested. For this report, only the results from Re D = 3.6 x10 6 are shown, mainly dueto the availability of reference data to compare with. In fact, it is one of the majordifficulties to study such complex flows, e.g. flow around a circular cylinder,because rigorous DNS and/or experiment data for such flows are sparse.In the hybrid simulations, LES and RANS have different grid resolutionrequirements. To have better predictions around the cylinder wall with RANS, thewall-normal grid-resolution for the method needs to be sufficiently fine (y + ≈ 1 forthe first grid points), while the resolutions in other directions are relatively coarse.On the other hand, the LES grid needs to be fine enough in streamwise as well asspanwise direction to resolve a broad range of turbulent flow structures, but can berelatively coarse in wall-normal direction near the wall. See Fig. 1 for the LESand RANS grids used in this study.For flows with high Reynolds number, such as our case of Re D = 3.6 x10 6 , theturbulent flow behind the cylinder should be fully developed and no clearindication of large scale periodic oscillations, so-called Kármán vortex street,should be visible. It is, however, commonly known that if the simulation does notresolve the near-wall turbulence properly, an artificial Kármán vortex street mayappear [Catalano et al. 2003]. This is indeed the case for our pure LESsimulation, which does not have enough resolution around the cylinder wall (Fig.2 left). The inadequate resolution has been significantly improved by applying thehybrid method (Fig. 2 right), which produced much finer turbulent structures aswell as narrower wake width. The better resolved wake contribute well to predictthe drag force applied on the cylinder, by correctly representing the “drag-crisis”due to the flow separations behind the cylinder correctly. The hybrid method alsoshowed better performance for the pressure distribution around the wall surface(see Fig. 3).3. ConclusionA hybrid LES/RANS solver with dual-mesh framework has been successfullyused to simulate the flow past a circular cylinder. Our study showed that thehybrid method has the ability to reduce the wall-resolution requirement for theLES mesh, such as the complex flow applications that has been investigated. Inthe context of the positive results from the periodic hill cases that has beeninvestigated in earlier studies, it is confirmed that the hybrid framework works
3very well for flows with separations. This is an encouraging observation showinggreat potential of the methods for industrial applications.AcknowledgementThe work has been performed under the HPC-EUROPA2 project (project number:228398) with the support of the European Commission - Capacities Area -Research Infrastructures.ReferencesH. Xiao and P. Jenny. A Consistent Dual-Mesh Framework for Hybrid LES/RANS Modeling.Journal of Computational Physics, 231 (2012) 1848-1865.J. Froehlich and D. von Terzi. Hybrid LES/RANS methods for the simulation of turbulent flows.Progress in Aerospace Sciences, 44(5):349–377, 2008.OpenCFD Ltd. The open source CFD toolbox, 2011. URL www.openfoam.com.P. Catalano,M. Wang, G. Iaccarino and P. Moin. Numerical simulation of the flow around a circular cylinderat high Reynolds numbers. International Journal of Heat and Fluid Flow, 24:463-469, 2003.E. Achenbach, Distribution of local pressure and skin friction around a circular cylinder in crossflowup to Re = 5x10 6 , Journal of Fluid Mechanics, vol. 34, pp. 625-639, (1968).P. Catalano, M. Wang, G. Iaccarino and P. Moin. Numerical simulation of the flow around acircular cylinder at high Reynolds numbers. International Journal of Heat and Fluid Flow,24:463-469, 2003.Figures:Fig. 1. The meshes used for the LES (left) and the RANS (right). The spanwise direction withuniform spacing is not shown.
4Fig. 2. Instantaneous vorticity distribution from the pure LES (left) and the hybrid LES/RANSsimulations (right).Fig. 3. Surface pressure distribution from the pure LES (blue dots) and hybrid LES/RANS (reddots). Clear improvement compared to the experimental data [Achenbach 1968] was observed.