Large eddy simulation of turbulent flow downstream of a backward-facing step

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1 Available online at Procedia Engineering 31 (01) 16 International Conference on Advances in Computational Modeling and Simulation Large eddy simulation of turbulent flow downstream of a backward-facing step Wenquan Wang a*, Lixiang Zang a, Yan Yan a a Faculty of Civil Engineering and Arcitecture, Kunming University of Science and Tecnology, Kunming , Cina Abstract large eddy simulation is used to predict turbulent flow in te separated and reattaced flow regions downstream of a backward-facing step.simulations were carried out at a Reynolds number of (based on te step eigt and te upstream centreline velocity) wit a cannel expansion ratio of 1.5. Two subgrid-scale models were tested, namely te dynamic eddy-viscosity, and te dynamic Vreman model. Bot models sowed good overall agreement wit available experimental data. It is conjectured tat te peak in tese fluctuations is caused by an impingement mecanism, in wic large eddies, originating in te sear layer, impact te wall just upstream of te mean reattacment location. 011 Publised by Elsevier Ltd. Selection and/or peer-review under responsibility of Kunming University of Science and Tecnology Open access under CC BY-NC-ND license. Keywords: Large eddy simulation; Dynamic global model; Turbulent flow; backward-facing step I Introduction Te separation and reattacment of turbulent flows are common features in engineering devices. Tey occur in many components of turbines, diffusers and combustors, as well as in external flows, including flows around buildings and aircraft. Reynolds-averaged turbulence modelling (witout significant tuning of te models) as been found to be generally incapable of an accurate prediction of te fluid dynamics and eat transfer in tese types of flow, of wic te backward-facing step is a well-studied, simplified example. * Corresponding autor. Tel.: ; fax: address: wwqquan@16.com Publised by Elsevier Ltd. doi: /j.proeng Open access under CC BY-NC-ND license.

2 Wenquan Wang et al. / Procedia Engineering 31 (01) In large eddy simulation (LES), te Smagorinsky subgrid-scale (SGS) eddy viscosity model wit a constant model coefficient as been widely used, especially due to its robustness and simplicity. However, te constant adopted for te Smagorinsky model coefficient is not universal. To overcome tis problem, a u filtered velocity i p filtered pressure S C s C m kinetic viscosity SGS stress tensor SGS strain-rate tensor caracteristic lengt scale of te largest SGS eddies Smagorinsky model coefficient. Vreman model coefficient caracteristic filter widt in te mt direction few approaces ave been proposed, e.g., dynamic localization model [] and Lagrangian dynamic model [3]. Te employments of tese models in actual LES ave proven teir applicability to complex flows [4]. Vreman [5] suggested a SGS eddy viscosity model denoted as te Vreman model wic guarantees teoretically zero SGS dissipation for various laminar sear flows. Tis property of te Vreman model is certainly superior to tat of te Smagorinsky model. Park et al.[6] recently sowed tat by a priori and a posteriori tests, te optimal Vreman model coefficient predicting accurate flow statistics is not universal and needs to be dynamically determined according to te flow. Tese dynamic global models successfully predicted various turbulent flows, suc as forced isotropic turbulence, turbulent cannel flow, flows over a circular cylinder and a spere, and flow over a simplified tree-dimensional model veicle [6,7]. Terefore, in te present study, we apply te Lagrangian dynamic model [3] and te dynamic global models based on te global equilibrium[6] to LES of turbulent flows in Francis turbine to furter test te capability of dynamic global model. Te present simulation aims to resolve two issues. First, large-eddy simulation are carried out at a Reynolds number ig enoug to allow for direct comparison wit experimental data. Second, te results of tese simulations are used to investigate te mecanisms of turbulent flow in te recirculation and reattacment zones. Numerical metod Applying a filter operation to te continuity equation and incompressible Navier-Stokes equations, te filtered equations are obtained as u j 0, (1) x j

3 18 Wenquan Wang et al. / Procedia Engineering 31 (01) 16 ui p u u uu, () t xj xi x j xj x i xj were ui, p and are te filtered velocity, te filtered pressure and te kinetic viscosity respectively, uu uu te SGS stress tensor. A standard Smagorinsky model for SGS stresses is written as: kk t S, (3) 3 C S S 1. (4) t s Were S is te SGS strain-rate tensor, te caracteristic lengt scale of te largest SGS eddies and C s is te Smagorinsky model coefficient. 1 LM Cs, (5) M M were L uu uu, M S S S S, and te caret () denotes a quantity filtered using te test filter and denotes te instantaneous averaging over omogeneous direction (denoted as DSSG ereinafter). On te oter and, te Vreman model [6] determines t in te following form: II t C, (6) u j, (7) x i II , (8) 3 mmimj m1, (9) were C is te Vreman model coefficient and m is te caracteristic filter widt in te mt direction. were C is te Vreman model coefficient and m is te caracteristic filter widt in te mt direction. Te dynamic global model based on te Germano identity suggested by Park et al. [6] denoted as 1 LM V C (10) M M Were V L uu uu (11)

4 Wenquan Wang et al. / Procedia Engineering 31 (01) M II S II Were denotes te instantaneous volume average and / is assumed. We call tis model as te V dynamic Vreman model wit te Germano identity (denoted as DVMG ereinafter). Note tat tis global constant C is te function of time only. Altoug te dynamic procedure to get te model coefficient is similar to tat of DSM, DVMG requires no omogeneous direction in te flow field for averaging. (1) 3 Computational details Te simulation was carried out in te same configuration as te experiments of Vogel and Eaton [8]. Furter data on tese experiments are presented in [9, 10]. A scematic layout of te simulation domain is sown in Fig. 1. Te cannel expansion ratio was 1.5, wit a Reynolds number of (based on te freestream velocity and step eigt, ). Te experiment was carried out wit an inflow condition consisting of two developing boundary layers separated by a relatively undisturbed core. Tese boundary layers ad a measured tickness of / =1.1. Te total domain size used for te computations was 5 3, wic included an entry lengt of. A grid containing nodes was used, wic was stretced in te wall-normal and streamwise directions using yperbolic tangent functions to cluster grid points at te step edge and in te wall boundary layers. Te grid stretcing can be observed in Fig. 1. Due to te need to supply a time-varying turbulent inflow condition, a time-series obtained from a separate periodic cannel flow simulation was used at te inflow plane. A forcing metod [11] was used to force te periodic cannel flow simulation to matc te experimental results for te mean and fluctuations of streamwise velocity. A convective boundary condition [1] was used at te exit plane. Statistics were averaged in te omogeneous spanwise direction and over 60 flow-troug times. Fig. 1 Computational geometry wit computational grid 4 Rresults and discussion Tab. 1 summarizes te time-averaged mean reattacment lengts obtained for te two grid simulations, te simulation of Akselvoll and Moin [13] and te experimental data. Te present results using te dynamic

5 0 Wenquan Wang et al. / Procedia Engineering 31 (01) 16 model containing nodes and te results obtained by Akselvoll and Moin [13] are witin te estimated experimental error bounds. Tab. 1. Mean reattacment lengts x/ Deviation from experiment[10] Experiment[10] LES [13] % Present, LES, FVM, Grid( ) % Te computed coefficient of friction along te lower wall is compared to te experimental results in Fig.. Te coefficient of friction is defined as Cf w Uc, were w is te sear stress at te wall and U c is te freestream velocity. Tere are no known differences between te two grid simulations. Te results sow a similar agreement wit te experimental results as te simulations by Akselvoll and Moin [13]: good agreement upstream of x/ = and from reattacment to x/ = 16, but poor agreement in bot te recirculation zone and downstream of x/ = 16. Te reason for te poor agreement downstream of x/ = 16 is probably te effect of te outflow boundary condition. In te recirculation zone, it is unclear wy all te LES simulations predict a larger negative value of C f. Akselvoll and Moin [13] noted tat tis could be caused by eiter te inflow generation metod used or by inadequate grid resolution in tis region. Fig. 3 sows te mean streamwise velocity at a number of locations downstream of te step. Bot grid simulations sow generally good agreement wit te experimental results wit te major differences occurring downstream of reattacment and in te recirculation region. Te DVMG model results sow a sligtly stronger reversed flow in te recirculation zone comparing wit te DSGS model, but bot model simulations sow generally a little lower of te experimental results. Near reattacment region bot subgrid-scale models sow smaller velocities tan te experiments, wic it is attributed to te flow gaining momentum as it passes downstream (due to side-wall boundary-layer growt) in te experiments, owever, downstream of reattacment region, te LES results of bot model are sowed tat velocities are good agreement wit te experimental results in tis region. Te primary discrepancy wit te experimental results is in te recirculation region (at x/=3. and 5.9), were bot subgrid-scale models predict a weaker backflow <C f > Present 19x18x18 Akselvoll and Moin [13] Adams et al [10] x/ Fig. Coefficient of friction along te lower wall

6 Wenquan Wang et al. / Procedia Engineering 31 (01) DVMG Model (grid: 19x18x18) DSSG Model (grid: 19x18x18) Exp. Adams et al [10] y/ 4 3 x/=-1 x/=3. x/=5.9 x/=7. x/= <u>/u C Fig.3 Compared wit mean streamwise velocity profiles between computation and experiment 5 Conclusion In te present study, Vreman model is as a basic eddy viscosity model, and te dynamic approac based on te global equilibrium between te subgrid-scale dissipation and te viscous dissipation wit a global model coefficient are applied to large eddy simulation of turbulent flow in te separated and reattaced flow regions downstream of a backward-facing step. Distributions of skin friction coefficient, streamwise velocity profile and mean reattaced lengt are gained, wic is good overall agreement wit available experimental data and suggested tat te SGS model based on te global equilibrium is valid for turbulent flow in complex geometries. Acknowledgements Te autors tank te National Natural Science Foundation of Cina (NSFC) [Grant no and ], te Natural Science Foundation of Yunnan Province of Cina (Grant no. 009ZC035M and 008GA07) for financial support of tis researc. References [1] Nie JH, Armaly BF. Reverse flow regions in tree-dimensional backward-facing step flow. Int J Heat Mass Transfer 004; 47 (): [] Gosal S, Lund TS, Moin P, Akselvoll K. A dynamic localization model for large-eddy simulation of turbulent flows. J Fluid Mec 1995; 86: 955. [3] Meneveau C, Lund TS, and Cabot WH. A Lagrangian dynamic subgrid-scale model of turbulence. J Fluid Mec 1996; 319: [4] Moin P. Advances in large eddy simulation metodology for complex flows. Int J Heat Fluid Flow 00; 3: [5] Vreman AW. An eddy-viscosity subgrid-scale model for turbulent sear flow:algebraic teory and applications. Pys Fluids 004; 16: [6] Park N, Lee S, Lee J, Coi H. A dynamic subgrid-scale eddy viscosity model wit a global model coefficient. Pys Fluids

7 Wenquan Wang et al. / Procedia Engineering 31 (01) ; 18: [7] Lee J, Coi H. Proceedings of te Sixt International Symposium on Turbulence and Sear Flow Penomena (TSFP, Seoul, 009), p [8] Vogel JC, Eaton J.K. Combined eat transfer and fluid dynamic measurements downstream of a backward facing step. J Heat Transfer 1985; 107: 999. [9] Vogel JC. Heat transfer and fluid mecanics measurements in te turbulent reattacing flow beind a backward-facing step, PD Tesis, Stanford University, 1984 [10] Adams EW, Jonston JP, Eaton JK. Experiments on te structure of turbulent reattacing flow Tecnical Report MD-43 Termosciences Division, Department of Mecanical Engineering, Stanford University, [11] Pierce CD, Moin P. Metod for generating equilibrium swirling inflow conditions. AIAA J 1998; 36: [1] Orlanski I. A simple boundary condition for unbounded yperbolic flows. J Comput Pys 1976; 1: 569. [13] Akselvoll K, Moin P. Large eddy simulation of turbulent confined coannular jets and turbulent flow over a backward facing step, Tecnical Report TF-63, Department of Mecanical Engineering, Stanford University, 1995.