Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T15:46:33.505Z Has data issue: false hasContentIssue false

Wavelet-based adaptive unsteady Reynolds-averaged turbulence modelling of external flows

Published online by Cambridge University Press:  05 January 2018

Giuliano De Stefano*
Affiliation:
Dipartimento di Ingegneria Industriale e dell’Informazione, Università della Campania, Aversa I-81031, Italy
Oleg V. Vasilyev*
Affiliation:
Skolkovo Institute of Science and Technology, Moscow 143026, Russia NorthWest Research Associates, Boulder, CO 80301, USA Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309, USA
Eric Brown-Dymkoski
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309, USA
*
Email addresses for correspondence: [email protected], [email protected], [email protected]
Email addresses for correspondence: [email protected], [email protected], [email protected]

Abstract

The recent development of the adaptive-anisotropic wavelet-collocation method, which incorporates the use of coordinate transforms, opens new horizons for wavelet-based simulations of wall-bounded turbulent flows. The new wavelet-based adaptive unsteady Reynolds-averaged Navier–Stokes approach for computational modelling of turbulent flows is presented. The proposed methodology that is integrated with anisotropic wavelet-based mesh refinement is demonstrated for a two-equation eddy-viscosity turbulence model. The performance of the method is assessed by conducting numerical simulations of the turbulent flow past a circular cylinder at subcritical Reynolds number. The present study demonstrates both the feasibility and the effectiveness of the new wavelet-based adaptive unsteady Reynolds-averaged turbulence modelling procedure for external flows.

Type
JFM Papers
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Angot, P., Bruneau, C.-H. & Fabrie, P. 1999 A penalization method to take into account obstacles in incompressible viscous flows. Numer. Math. 81, 497520.Google Scholar
Beaudan, P. & Moin, P.1994 Numerical experiments on the flow past a circular cylinder at sub-critical Reynolds number. Tech. Rep. TF-62. Mechanical Engineering Department, Stanford University.Google Scholar
Brown-Dymkoski, E., Kasimov, N. & Vasilyev, O. V. 2014 A characteristic based volume penalization method for general evolution problems applied to compressible viscous flows. J. Comput. Phys. 262, 344357.Google Scholar
Brown-Dymkoski, E. & Vasilyev, O. V. 2017 Adaptive-anisotropic wavelet collocation method on general curvilinear coordinate systems. J. Comput. Phys. 333, 414426.Google Scholar
De Stefano, G., Goldstein, D. E. & Vasilyev, O. V. 2005 On the role of subgrid-scale coherent modes in large-eddy simulation. J. Fluid Mech. 525, 263274.Google Scholar
De Stefano, G., Nejadmalayeri, A. & Vasilyev, O. V. 2016 Wall-resolved wavelet-based adaptive large-eddy simulation of bluff-body flows with variable thresholding. J. Fluid Mech. 788, 303336.Google Scholar
De Stefano, G. & Vasilyev, O. V. 2012 A fully adaptive wavelet-based approach to homogeneous turbulence simulation. J. Fluid Mech. 695, 149172.Google Scholar
De Stefano, G. & Vasilyev, O. V. 2014 Wavelet-based adaptive simulations of three-dimensional flow past a square cylinder. J. Fluid Mech. 748, 433456.Google Scholar
Farge, M., Schneider, K. & Kevlahan, N. 1999 Non-Gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptive orthogonal wavelet basis. Phys. Fluids 11 (8), 21872201.Google Scholar
Freund, J. B. 1997 Proposed inflow/outflow boundary condition for direct computation of aerodynamic sound. AIAA J. 35 (4), 740742.Google Scholar
Fröhlich, J. & von Terzi, D. A. 2008 Hybrid LES/RANS methods for the simulation of turbulent flows. Prog. Aerosp. Sci. 44 (5), 349377.Google Scholar
Goldstein, D. E. & Vasilyev, O. V. 2004 Stochastic coherent adaptive large eddy simulation method. Phys. Fluids 16 (7), 24972513.Google Scholar
Kevlahan, N. K.-R. & Vasilyev, O. V. 2005 An adaptive wavelet collocation method for fluid–structure interaction at high Reynolds numbers. SIAM J. Sci. Comput. 26 (6), 18941915.Google Scholar
Kok, J. C. 2000 Resolving the dependence on freestream values for the k–𝜔 turbulence model. AIAA J. 38 (7), 12921295.Google Scholar
Kolmogorov, A. N. 1942 Equations of turbulent motions of an incompressible fluid. Izv. Akad. Nauk SSR Ser. Phys. 6 (1), 5658.Google Scholar
Kravchenko, A. G. & Moin, P. 2000 Numerical studies of flow over a circular cylinder at Re = 3900. Phys. Fluids 12 (2), 403417.Google Scholar
Menter, F. R. & Egorov, Y. 2010 The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 1. Theory and model description. Flow Turbul. Combust. 85, 113138.Google Scholar
Mittal, R. & Balachandar, S. 1995 Effect of three-dimensionality on the lift and drag of nominally two-dimensional cylinders. Phys. Fluids 7, 18411865.Google Scholar
Nejadmalayeri, A., Vezolainen, A., Brown-Dymkoski, E. & Vasilyev, O. V. 2015 Parallel adaptive wavelet collocation method for PDEs. J. Comput. Phys. 298, 237253.Google Scholar
Nejadmalayeri, A., Vezolainen, A., De Stefano, G. & Vasilyev, O. V. 2014 Fully adaptive turbulence simulations based on Lagrangian spatio-temporally varying wavelet thresholding. J. Fluid Mech. 749, 794817.Google Scholar
Norberg, C. 1994 An experimental investigation of the flow around a circular cylinder: influence of aspect ratio. J. Fluid Mech. 258, 287316.Google Scholar
Ong, L. & Wallace, J. 1996 The velocity field of the turbulent very near wake of a circular cylinder. Exp. Fluids 20, 441453.Google Scholar
Palkin, E., Mullyadzhanov, R. & Hanjalić, K. 2014 URANS and LES of a flow over a cylinder at Re = 3900. In Proceedings of 17th International Conference on the Methods of Aerophysical Research, June 30–July 6, 2014, Novosibirsk, pp. 18.Google Scholar
Palkin, E., Mullyadzhanov, R., Hadziabdić, M. & Hanjalić, K. 2016 Scrutinizing URANS in shedding flows: the case of cylinder in cross-flow in the subcritical regime. Flow Turbul. Combust. 97, 10171046.Google Scholar
Reina, G. P. & De Stefano, G. 2017 Computational evaluation of wind loads on sun-tracking ground-mounted photovoltaic panel arrays. J. Wind Engng Ind. Aerodyn. 170, 283293.Google Scholar
Saffman, P. G. 1970 A model for inhomogeneous turbulent flow. Proc. R. Soc. Lond. A 317 (1530), 417433.Google Scholar
Schneider, K. & Vasilyev, O. V. 2010 Wavelet methods in computational fluid dynamics. Annu. Rev. Fluid Mech. 42, 473503.Google Scholar
Spalart, P. R. & Rumsey, C. L. 2007 Effective inflow conditions for turbulence models in aerodynamic calculations. AIAA J. 45 (10), 25442553.Google Scholar
Travin, A., Shur, M., Strelets, M. & Spalart, P. 1999 Detached-eddy simulations past a circular cylinder. Flow Turbul. Combust. 63, 293313.Google Scholar
Vasilyev, O. V. 2003 Solving multi-dimensional evolution problems with localized structures using second generation wavelets. Intl J. Comput. Fluid Dyn. 17 (2), 151168 (special issue on High-Resolution methods in Computational Fluid Dynamics).Google Scholar
Vasilyev, O. V. & Bowman, C. 2000 Second generation wavelet collocation method for the solution of partial differential equations. J. Comput. Phys. 165, 660693.Google Scholar
Vasilyev, O. V. & Kevlahan, N. K.-R. 2002 Hybrid wavelet collocation: Brinkman penalization method for complex geometry flows. Intl J. Numer. Meth. Fluids 40, 531538.Google Scholar
Wilcox, D. C. 1988 Reassessment of the scale determining equation for advanced turbulence models. AIAA J. 26 (11), 12991310.Google Scholar
Wilcox, D. C.1993 A two-equation turbulence model for wall-bounded and free-shear flows. AIAA Paper 1993-2905.Google Scholar
Wilcox, D. C. 2008 Formulation of the k–𝜔 turbulence model revisited. AIAA J. 46 (11), 28232838.Google Scholar
Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477539.Google Scholar
Young, M. E. & Ooi, A. 2007 Comparative assessment of LES and URANS for flow over a cylinder at a Reynolds number of 3900. In 16th Australasian Fluid Mechanics Conference, pp. 10631070.Google Scholar