Proceedings of the 7 th International Conference on HydroScience and Engineering Philadelphia, USA September 10-13, 2006 (ICHE 2006) ISBN:

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1 Proceedings of the 7 th International Conference on HydroScience and Engineering Philadelphia, USA September 10-13, 2006 (ICHE 2006) ISBN: Drexel University College of Engineering Drexel E-Repository and Archive (idea) Drexel University Libraries The following item is made available as a courtesy to scholars by the author(s) and Drexel University Library and may contain materials and content, including computer code and tags, artwork, text, graphics, images, and illustrations (Material) which may be protected by copyright law. Unless otherwise noted, the Material is made available for non profit and educational purposes, such as research, teaching and private study. For these limited purposes, you may reproduce (print, download or make copies) the Material without prior permission. All copies must include any copyright notice originally included with the Material. You must seek permission from the authors or copyright owners for all uses that are not allowed by fair use and other provisions of the U.S. Copyright Law. The responsibility for making an independent legal assessment and securing any necessary permission rests with persons desiring to reproduce or use the Material. Please direct questions to archives@drexel.edu

2 The 7 th Int. Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 Sep. 13, Philadelphia, USA 1 RANS SIMULATIONS AND LES OF FLOW OVER DUNES AT LOW RELATIVE SUBMERGENCE RATIOS Thorsten Stoesser 1, Dominic von Terzi 2, Wolfgang Rodi 3, Nils R. B. Olsen 4 ABSTRACT This paper assesses the quality of two Reynolds-Averaged Navier-Stokes (RANS) turbulence models for predicting the flow over two-dimensional dunes: the standard K-ω and the one-equation Spalart-Allmaras models. To this end a setup is chosen for which recent experimental mean flow data are available. Two different relative submergence ratios are considered: h/k=4 and h/k=5, where h is the water depth and k the dune height. The corresponding Reynolds numbers based on the mean bulk velocity and the water depth are Re h =36,000 and Re h =33,000, respectively. In addition, Large Eddy Simulations (LES) are performed to provide detailed reference data for the statistics of the turbulence. Comparisons of time-averaged velocities and streamlines, turbulent kinetic energy, and mean wall shear stresses along the dune bed are shown. 1. INTRODUCTION A flow of sufficient turbulence intensity generally initiates the motion of bed material in an alluvial channel. In the case of sand-bed rivers this motion usually results in dune or ripple formations at the channel bottom. The flow over dunes has been studied widely to understand the effect of bed shape on the flow and the mechanisms of bed and suspended load transport of sand bed rivers. However, compared to flow over smooth beds, mean flow characteristics, distributions of turbulent velocities, bed shear-stresses, and turbulence intensities differ significantly due to the bed deformation (e.g. McLean et al., 1999; Zedler and Street, 2001). A dune formation causes the overlying flow to separate at the dune crest, creating a large separation zone on the lee-side of the 1 Research Associate, Institute for Hydromechanics, Karlsruhe University, Karlsruhe, Germany (stoesser@ifh.uka.de) 2 Research Associate, Institute for Hydromechanics, Karlsruhe University, Karlsruhe, Germany (terzi@ifh.uka.de) 3 Professor, Institute for Hydromechanics, Karlsruhe University, Karlsruhe, Germany (rodi@ifh.uka.de) 4 Professor, The Norwegian Institute of Technology, Department of Hydraulic and Environmental Engineering, N-7491 Trondheim, Norway (nils.r.olsen@ntnu.no)

3 The 7 th Int. Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 Sep. 13, Philadelphia, USA 2 dune. Bordering the separation zone is a turbulent shear layer associated with the formation of large-scale eddies which travel downstream and towards the surface while dissipating. The flow reattaches approximately 4-6 dune heights downstream of the crest (Engel, 1981) and a new boundary layer is formed and grows as the flow accelerates towards the next dune crest. Numerous experimental studies were undertaken in the past in order to investigate the flow over dunes, most recently at the Iowa Institute of Hydraulic Research (IIHR) (Polatel, 2005), but also by Hyun et al. (2003), Maddux et al. (2003a,b), Lyn (1993) and Mierlo and Ruiter (1988) to name only a few. However, these experimental investigations are either of limited spatial resolution or are restricted to time-averaged quantities along selected measurement verticals. On the other hand, numerical simulations can provide a complete picture of the flow field and may be used to complement experimental investigations, to perform parametric studies or to explore fundamental physical mechanisms. Nevertheless, only a limited number of numerical studies of flow over dunes exist. Yoon and Patel (1996) presented calculations of the flow over dunes based on the solution of the Reynolds-Averaged Navier-Stokes (RANS) equations, and reported a good agreement between computed and measured time-averaged velocities. More recently, Patel and Lin (2004) showed results of both RANS computations and Large Eddy Simulations (LES) and compared mean velocities and turbulence statistics to those measured by Hyun et al. (2003). While they also concluded that a RANS model captures much of the mean velocity information, they observed that RANS computations seem to fail to model the effect of the large-scale flow structures on the turbulence statistics. Even though the available computing power and memory capacities of modern computers are rapidly increasing, LES is still restricted to moderate Reynolds numbers (11th ERCOFTAC/IAHR Workshop on Refined Turbulence Modelling, Chalmers University of Technology, 2005). This means that, for the computation of practical flow problems, engineers will have to rely on RANS methods as their standard simulation tool for the foreseeable future. Hence deficits of RANS computations need to be identified and, if possible, removed. In this paper, we present simulation results for channel flow over two-dimensional dunes at two different relative submergence ratios for the experimental setup of the Iowa Institute of Hydraulic Research. Large Eddy Simulation and RANS calculations using the K-ω and the oneequation Spalart-Allmaras model are performed and validated with experimental reference data where possible. The main goal is to assess the quality of the RANS simulations by comparison with the LES data. Shown are streamlines, velocities and the wall shear stresses along the dune bed for the mean flow field and contours and profiles of turbulent kinetic energy. 2. COMPUTATIONAL SETUP Geometry and boundary conditions were selected in analogy to laboratory experiments as reported by Polatel (2005). The dune height is k = 20 mm, which is defined as the distance between the highest and the lowest point of the dune geometry. The dune wavelength is λ = 400 mm, so that λ/k = 20, which is typical of many previous studies. Several water-depth-to-dune-height-ratios h/k were investigated, where h is the water depth above the dune trough. Results for h/k = 4 and h/k = 5 will be presented in the following. The results of the computations are compared with Laser Doppler Velocimetry (LDV) measurements taken at six verticals along the geometry as indicated in Figure 1. The Reynolds numbers based on the mean bulk velocity U b (obtained along vertical L1) and the dune height k are Re k = 9,000 for h/k = 4 and Re k = 6,600 for h/k = 5. The no-slip boundary condition is used on the dune surface. Periodic boundary conditions are applied in the streamwise and spanwise directions. The free surface is approximated as a flat plane of symmetry, i.e. a nostress condition is enforced. The streamwise extent of the computational domain is one dune length λ. For the three-dimensional LES, two water heights are chosen as the domain width. The computational domain and grids used for LES and RANS calculations are shown in Figure 1. For

4 The 7 th Int. Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 Sep. 13, Philadelphia, USA 3 LES, the grids consist of 416 x 170 (214) x 192 (160) cells for h/k = 4 (5) in the streamwise (x), spanwise (y) and vertical (z) directions, respectively. The cell spacing in terms of wall units is x + y + 15 and z + 1 (3) near the dune surface. For the RANS calculations, two-dimensional grids are used with the otherwise same resolution, except for the h/k = 4 case, where a coarser nearwall resolution of only z + 3 is employed due to a more benign grid stretching and the use of only 128 cells in the wall-normal direction. The results presented in the following are obtained using the finite volume flow solver LESOCC2 (Hinterberger, 2004) developed at the Institute for Hydromechanics at the University of Karlsruhe. It is an enhanced version of LESOCC (Breuer and Rodi, 1996) which also includes various RANS models. This simulation tool solves the incompressible, time-dependent, filtered Navier-Stokes equations on collocated, body-fitted, curvilinear, block-structured grids with the option of blockwise grid refinement. The Poisson equation for coupling the pressure to the velocity field is solved with the strongly implicit procedure (SIP) of Stone (1968). Momentum interpolation according to Rhie and Chow (1983) avoids decoupling of pressure and velocity. The diffusive fluxes are approximated with central differences of second-order accuracy. For the LES, secondorder central differences are also used for the discretisation of the convection fluxes and time discretisation is performed using a three-stage Runge-Kutta scheme. The subgrid-scale stresses appearing in the filtered Navier-Stokes equations are computed using the dynamic Smagorinsky model according to Germano et al. (1991). For the RANS calculations, an implicit scheme in time is employed and convective terms are computed using the monotonic HLPA scheme (Zhu, 1991), i.e. a second-order upwind scheme. The standard K-ω model (c.f. Wilcox, 1993) and the oneequation model of Spalart and Allmaras (1994) are used in order to compute the Reynolds stresses appearing in the RANS formulation. Since the time-averaged flow field is homogeneous in the lateral direction, the RANS computations are performed in two dimensions only. To ensure independence of the present results from a specific numerical scheme and its implementation, a second RANS solver of Olsen (2005) was used to repeat the K-ω model simulations and virtually the same results were obtained, such that these are not presented here. 3. RESULTS AND DISCUSSION 3.1 Mean Flow Field In Figure 2, streamlines are presented of the mean flow field over one wavelength of the dune resulting from the LES and RANS calculations for the h/k = 4 case. The flow separates at the dune crest, and reattaches just before the bed elevation increases towards the next crest. The flow recovers after a large recirculation zone, and develops a new boundary layer over the stoss-side of the next dune. LES and RANS calculations yield a very similar flow field with the RANS models predicting a slightly delayed reattachment of 5.5 and 6.0 dune heights for the K-ω and Spalart- Allmaras models, respectively, compared to 5.2 dune heights for the LES. However, these values lie within the error margins of the experiments (predicting reattachment between verticals L4 and L5, i.e. 5 < x/k < 6). A comparison of the mean streamwise velocity between LES, RANS and experiments for both submergence ratios is presented in Figures 3 and 4. Overall, agreement of all computations with the experiments is fairly good, except for verticals L4/5 in Figure 3 and L5/6 in Figure 4. The experimental data at L5 in Figure 4 shows a non-zero velocity at the wall which suggests that the lower data points might have been corrupted at post-processing. For the three other questionable verticals, the experimental data are inconsistent, since, for the plots shown here, all data were normalised with the bulk velocity at plane L1, hence, the consistently lower/higher values of

5 The 7 th Int. Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 Sep. 13, Philadelphia, USA 4 streamwise velocity in the experiments compared to the simulations at these locations corresponds to a violation of mass conservation. Again, RANS computations and LES yield very similar results, except for verticals L4 and L5, very close to reattachment, where the longer separated flow region in the RANS computation is responsible for the deviations observable near the wall. Also note a slightly larger slope at the inflection point in the shear layer of the LES profiles (L2-4). 3.2 Wall Shear Stress Figure 5 presents the distribution of the mean wall shear stress along the dune bed over one wavelength, for both the h/k = 4 and h/k = 5 submergence ratios. Since the first grid point is placed within the viscous sublayer the wall shear stress can be evaluated from the wall-normal gradient of the wall-tangential velocity. A qualitative match between RANS and LES results can be observed, however, as discussed before, the extent and the strength of the recirculation is slightly overpredicted by both RANS computations. The zero skin-friction at x = 2 corresponds to the lower corner in the step geometry whereas the one farther downstream represents flow reattachment. The strongest deviation of the RANS predictions from the LES data occurs in the redeveloping boundary layer after reattachment. Thereby the K-ω model yields a considerably larger wall shear stress in the reattached flow than both the LES and the Spalart-Allmaras model. 3.3 Turbulent Kinetic Energy As is shown in separate publications (Stoesser et al., 2005, 2006), for LES, the agreement of resolved turbulent normal stresses <u'u'>, <w'w'> and shear stresses <u'w'> with the experimental data is very satisfactory. Hence, the turbulent kinetic energy as predicted by the LES can be taken to evaluate the RANS models capabilities to predict the turbulence of this flow. For the h/k = 4 submergence ratio, the distribution of the resolved turbulent kinetic energy of the LES (with K = (<u'u'> + <v'v'> + <w'w'>) / 2 is compared in Figure 5 to the turbulent kinetic energy predicted by RANS simulations using the k-ω turbulence model (since the Spalart-Allmaras model does not provide this quantity). A detailed comparison at the selected measurement planes for both submergence ratios is provided in Figures 6 and 7. Most of the turbulence production occurs in the shear layer, where unsteady vortex rollers are generated due to a Kelvin-Helmholtz type instability. This is the region where the peak of the kinetic energy occurs. The rollers reattach at several dune heights downstream of the crest and are then swept towards the next crest generating a wake layer with a region of higher turbulence. The RANS model underpredicts the absolute value of the peak in the shear layer and its location appears farther downstream. Nevertheless, the shape and extent of the area of high turbulent kinetic energy are similar to what was computed using LES. Since it is the enhanced mixing of the large rollers which causes the flow to reattach in the mean, the delay and lower magnitude of the associated turbulence in the RANS computations explains the corresponding larger region of recirculating flow. Note that the production of turbulent kinetic energy in the K- equation is related to the slope of the mean velocity profile. For boundary and shear layers, the dominant contribution stems from the streamwise velocity. Therefore, the slightly too shallow slope predicted by the RANS calculations (see Section 3.1) is consistent with a lower production of turbulent kinetic energy which could explain the deficiencies. Note also the differences in the profiles in the near-wall region of the attached redeveloping boundary layer which is a consequence of the anisotropy in the normal Reynolds stresses, in particular a near-wall peak of <u'u'>, which can not be captured by the employed RANS models and which might well be the reason for the observed discrepancies in the prediction of the wall shear stress of the reattached flow (see

6 The 7 th Int. Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 Sep. 13, Philadelphia, USA 5 Section 3.2). Whether enhanced turbulence models, e.g. full Reynolds stress closures, could alleviate these problems requires further testing. 4. CONCLUSIONS In this paper we presented simulation results for channel flow over two-dimensional periodic dunes at two different relative submergence ratios for a given experimental setup. Large Eddy Simulations were compared with RANS calculations using the K-ω and the one-equation Spalart- Allmaras models and the experimental reference data. Time-averaged velocity fields calculated by both turbulence modelling approaches show good agreement with the experimental data and even more so with each other. All major features of the turbulent flow over dunes are correctly predicted. However, LES provides additional turbulence quantities, in agreement with the experiments, including the turbulent kinetic energy. The Spalart-Allmaras model could not provide K, whereas the K-ω model yielded the correct shape and order of magnitude of the turbulent kinetic energy profiles, but with consistently lower values of maximum kinetic energy and a delay in the location of the absolute maximum. ACKNOWLEDGEMENTS This work is part of research funded by the German Research Foundation (DFG) under project number Ro 558/29-1. Computer time was provided by the Scientific Supercomputing Center (SSCK) at the University of Karlsruhe, Germany. The support of Dr. Jan Wissink for generation of the computational grids is gratefully acknowledged. The authors are indebted to Ceyda Polatel for kindly providing the data of the experiments performed at the Iowa Institute of Hydraulic Research (IIHR). REFERENCES Breuer, M., Rodi, W. (1996). Large Eddy Simulation of Complex Turbulent Flows of Practical Interest. In: Notes on Numerical Fluid Mech., Flow Simulations with High Performance Computers II. Ed.: Hirschel, E. H. Vieweg, Braunschweig, pp Engel, P. (1981). Length of flow separation over dunes. J. Hydraul. Div. Am. Soc. Civ. Eng., 107 (10), pp Germano, M., Piomelli U., Moin P., Cabot W.H. (1991). A dynamic subgrid-scale eddy viscosity model. Physics of Fluids, 3 (7), pp Hinterberger, C. (2004). Dreidimensionale und tiefengemittelte Large-Eddy-Simulation von Flachwasserströmungen. Ph.D. thesis, University of Karlsruhe. Hyun, B.S., Balachandar, R., Yu, K., Patel, V.C. (2003). Assessment of PIV to measure mean velocity and turbulence in water flow. Exp. in Fluids, 35, pp Lyn, D.A. (1993). Turbulence measurements in open-channel flows over artificial bed forms. J. Hydraulic. Eng., 119 (3), pp Maddux, T.B., Nelson, J.M., McLean, S.R. (2003a). Turbulent flow over 3D dunes. I: Free surface and flow response. J. Geophys. Res., 108 (F1). Maddux, T.B., McLean, S.R., Nelson, J.M. (2003b). Turbulent flow over 3D dunes. II: Fluid and bed stresses. J. Geophys. Res., 108 (F1).

7 The 7 th Int. Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 Sep. 13, Philadelphia, USA 6 McLean, S.R., Wolfe, S.R., Nelson, J.M. (1999). Spatially averaged flow over a wavy boundary revisited. J. Geophys. Res., 104 (C7), pp Mierlo, M.C.L.M., de Ruiter, J.C.C. (1988). Turbulence measurements above artificial dunes. Rept. Q789, Delft Hydr. Lab., Delft, The Netherlands. Olsen, N.R.B. (2005). SSIIM User s Manual. Department of Hydraulic and Environmental Engineering, The Norwegian University of Science and Technology. < Patel, V.C., Lin, C.L. (2004). Turbulence modeling in flow over a dune with special reference to free surface and bed roughness effects. Proc. of the 6 th Int. Conf. on Hydroscience and Engineering (ICHE-2004), May 30-June 3, 2004, Brisbane, Australia. Polatel, C. (2005). Personal Communication. Rhie, C.M., Chow, W.L. (1983). Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J., 21 (11), pp Spalart, P.R., Allmaras, S.R. (1994). A one-equation turbulence model for aerodynamic flows. La Recherche Aérospatiale, 1, pp Stoesser, T., Rodi, W., Polatel, C., Patel, V.C., Muste, M. (2005). Large Eddy Simulations of flow over two-dimensional dunes. Proc. XXXI IAHR Congress, Seoul, Korea. Stoesser, T., Braun, C., Garcia-Villalba, M., Rodi, W. (2006). Turbulence structures in flow over two-dimensional dunes. Submitted to J. Hydraul. Eng. Stone, H.L. (1968). Iterative Solution of Implicit Approximation of Multi-dimensional Partial Differential Equations. SIAM J. Numerical Analysis. No. 3. Yoon, J.Y., Patel. V.C. (1999). Numerical model of turbulent flow over sand dune. J. Hydraul. Eng., 122, pp Wilcox, D.C. (1993). Turbulence modeling for CFD. DCW industries, p. 84. Zedler, E.A., Street, R.L. (2001). Large Eddy Simulation of sediment transport: Currents over ripples. J. Hydraul. Eng., 127 (6), pp Zhu, J. (1991). Low diffusive and oscillation-free convection scheme. Comm. Appl. Num. Meth. 7, pp

8 The 7 th Int. Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 Sep. 13, Philadelphia, USA 7 FIGURES Figure 1 Location of the LDA measurement verticals (L1-6) and computational grids for LES (top) and RANS calculations (centre) for h/k=4 and both LES and RANS calculations for h/k=5 (bottom); every 5 th point shown for clarity.

9 The 7 th Int. Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 Sep. 13, Philadelphia, USA 8 Figure 2 Mean streamlines for h/k=4: LES (top), K-ω (centre) and Spalart-Allmaras (bottom) RANS models; the red arrow indicates the reattachment point (location of zero skin friction).

10 The 7 th Int. Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 Sep. 13, Philadelphia, USA 9 Figure 3 Comparison of mean streamwise velocities along the six measurements verticals for h/k=4.

11 The 7 th Int. Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 Sep. 13, Philadelphia, USA 10 Figure 4 Comparison of mean streamwise velocities along the six measurements verticals for h/k=5.

12 The 7 th Int. Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 Sep. 13, Philadelphia, USA 11 Figure 5 Distribution of mean wall shear stress along the dune bed for h/k=4 (left) and h/k=5 (right). Figure 6 Contours of the turbulent kinetic energy for h/k=4: LES (top, only resolved part) and K-ω RANS model (bottom).

13 The 7 th Int. Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 Sep. 13, Philadelphia, USA 12 Figure 7 Comparison of turbulent kinetic energy along the six measurements verticals for h/k=4.

14 The 7 th Int. Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 Sep. 13, Philadelphia, USA 13 Figure 8 Comparison of turbulent kinetic energy along the six measurements verticals for h/k=5.