Hejlesen, Mads Mølholm

Larsen, Allan

Rasmussen, Johannes Tophøj

Walther, Jens Honore

Online Research Database In Technology

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Downloaded from orbit.dtu.dk on: Dec 20, 2017Turbulence modelling in the two-dimensional vortex-in-cell methodHejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Larsen, Allan; Walther, Jens HonorePublication date:2012Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Hejlesen, M. M., Rasmussen, J. T., Larsen, A., & Walther, J. H. (2012). Turbulence modelling in the two-dimensional vortex-in-cell method. Abstract from IUTAM Symposium on Particle Methods in Fluid Mechanics,Kgs.Lyngby, Denmark.Turbulence modelling in the two-dimensional vortex-in-cell methodMads M. Hejleseny, Johannes T. Rasmusseny, Allan Larsen], Jens H. WaltheryzyTechnical University of Denmark ]COWI Consulting Engineers A/SKgs. Lyngby, Denmark Kgs. Lyngby, Denmarkmmhej@mek.dtu.dk ALN@cowi.dkzComputational Science and Engineering Laboratory, ETHZu¨rich, Switzerlandwalther@mavt.ethz.chKeywords: CFD, unsteady flow computation, vortex-in-cell method, turbulence modelling.ABSTRACTIn bridge aerodynamics, particle based vortex methods are used extensively to calculate the aerody-namic forces and flow field around bridge cross sections due to its stability and efficiency. So far theapplied vortex methods have modelled the flow without employing an explicit model for unresolved tur-bulence scales. The hybrid vortex-in-cell (VIC) method offers a highly efficient particle-mesh algorithmthat combines Lagrangian and Eulerian schemes to discretise different parts of the governing equationand thereby exploits the strength of each scheme. One of the benefits of the VIC method is its abilityto efficiently solve transport equations. This is used in the present study to implement transport basedturbulence models. The main focus of the study is implementing the Spalart-Allmaras (SA) turbulencemodel [1] by an unsteady RANS approach. Additionally, a selection of LES models have been imple-mented, including the Lagrangian dynamic eddy viscosity (LDEV) model [2] and a transport model forthe kinetic turbulent energy. Even though 2D LES turbulence modelling lack physical merit, due to thenon-existing vortex stretching, reasonable results using LES have been presented in literature e.g. [3].The 2D LES models are however only used as a basis of comparison and as a step towards a future3D implementation. The applied 2D VIC method is a further development of of the multi-resolutionVIC method presented in [4], where a novel high order Poisson solver is implemented based on fastFourier transforms subject to free space boundary conditions. By exploiting the linearity of the Poissonequation, high grid resolution is achieved using particle and mesh patches of different resolution. Solidboundaries are implemented by a Brinkman penalisation [5] using an explicit split-step algorithm. Theturbulence models are implemented by solving the eddy viscosity transport equation similarly to thevorticity equation by convecting the eddy viscosity along with the particles.Figure 1: The simulated flow around a square cylinder using the Spalart-Allmaras turbulence modelwith an inflow condition of the eddy viscosity. Left: vorticity field. Right: modelled eddy viscosity.-0.50-0.250.000.250.500.751.000 1 2 3 4 5 6 7uUx=DFigure 2: Wake profile of the time averaged horizontal velocity u for the different models. Presentresults: ——: SA, ——: LDEV, ——: turbulence energy equation. Experimental results:  Lyn et al.[7]. Other 2D numerical results:——: LES Bouris et al. [3], - - - - and – – – –: RANS Bosch et al. [6]As shown in figure 1, the implemented turbulence model is validated by simulating the highly separatedflow around a square cylinder at Re = UD= = 22:000, where D is the height/length of the cylinderand  is the kinematic viscosity of the fluid. The resulting mean flow shows an overall good agreementwith experimental data [7] as seen in fig. 2. The SAmodel captures the mean back-flow in the near wakeof the cylinder while still maintaining a good result in the far wake. The calculated drag coefficients isfound to be approximately 10% higher than what is reported in experimental publications. The calcu-lated vortex shedding frequency of the SA model is found to be around 20% too high. This is believed tobe caused by the averaging of a general vortex shedding pattern which leads to a single vortex sheddinginstead of a double pairwise shedding, which is observed in experiments. The LES models (not shown)are found to capture the pairwise vortex shedding pattern and identify multiple shedding frequencies.References[1] P.R. Spalart, S.R. Allmaras: A one-equation turbulence model for aerodynamic flows. Rech.Aerospatiale, 1(1994), 5–21.[2] C. Meneveau, T. S. Lund, W. H. Cabot. A Lagrangian dynamic subgrid-scale model of turbulence.J.Fluid Mech., 319(1996),353–385[3] D. Bouris, G. Bergeles: 2D LES of vortex shedding from a square cylinder. J. Wind Eng. Ind.Aerodyn., 80(1999),31–46.[4] J.T. Rasmussen, G.-H. Cottet, J.H. Walther: A multiresolution remeshed particle vortex methodusing patches. J. Comput. Phys., 230(2011), 6742–6755.[5] P. Angot, C. -H. Bruneau, P. Fabrie: A penalization method to take into account obstacles inincompressible viscous flows. Numer. Math. 81(1999),497–520[6] G. Bosch, W. Rodi: Simulation of vortex shedding past a square cylinder with different turbulencemodels. Int. J. Numer. Meth. Fluids, 28(1998),601–616.[7] D.A. Lyn, S. Einav, W. Rodi, J.-H. Park: A laser-Doppler velocimetry study of ensemble-averagedcharacteristics of the turbulent near wake of a square cylinder. J.Fluid Mech., 304(1995),285–319.

Turbulence modelling in the two-dimensional vortex-in-cell method

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Turbulence modelling in the two-dimensional vortex-in-cell method

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