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Conference on Turbulence and Interactions TI2006 May June Porquerolles France

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Niveau: Supérieur, Doctorat, Bac+8
Conference on Turbulence and Interactions TI2006, May 29 - June 2, 2006, Porquerolles, France SYMMETRY-PRESERVING REGULARIZATION MODELS OF TURBULENT CHANNEL FLOW Roel Verstappen Institute of Mathematics and Computing Science, University of Groningen P.O. Box 800, 9700 AV Groningen, The Netherlands, E-mail: ABSTRACT We consider regularizations of the convective term in the Navier-Stokes equations that preserve the con- servation and symmetry properties. These regularizations restrain the production of small scales of motion by vortex stretching in an unconditionally stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The regularization model is successfully tested for numerical simulations of fully-developed turbulent channel flow (Re?=180 and Re?=395). INTRODUCTION Most turbulent flows cannot be computed directly from the (incompressible) Navier-Stokes equa- tions, ∂tu + C(u, u) + D(u) +?p = 0, (1) because they possess far too many scales of motion. The computationally almost number- less small scales result from the convective term C(u, v) = (u ·?)v, which allows for the transfer of energy from scales as large as the flow domain to the smallest scales that can survive viscous dissipation.

  • between large

  • navier stokes equations

  • skew symmetry

  • large eddy

  • eddy simulation

  • symmetry-preserving regularization

  • local interaction


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Conference on Turbulence and Interactions TI2006, May 29  June 2, 2006, Porquerolles, France
SYMMETRYPRESERVING REGULARIZATION MODELS OF TURBULENT CHANNEL FLOW
Roel Verstappen
Institute of Mathematics and Computing Science, University of Groningen P.O. Box 800, 9700 AV Groningen, The Netherlands, Email: R.W.C.P.Verstappen@rug.nl
ABSTRACT We consider regularizations of the convective term in the NavierStokes equations that preserve the con servation and symmetry properties. These regularizations restrain the production of small scales of motion by vortex stretching in an unconditionally stable manner, meaning that the velocity cannot blow up in the energynorm (in 2D also: enstrophynorm). The regularization model is successfully tested for numerical simulations of fullydeveloped turbulent channel flow (Reτ=180 and Reτ=395).
INTRODUCTIONing modes of the NavierStokes solutionu. The first outstanding approach in this direction e Most turbulent flows cannot be computed directlygoes back to Leray [1], who took, u) = C(u from the (incompressible) NavierStokes equaC(u¯, u)and proved that a moderate filtering of tions, thetransport velocity is sufficient to regularize a turbulent flow. Here, the filtering operation is de tu+C(u, u) +D(u) +rp= 0,(1) noted by a bar; the residual will be indicated by a prime. The NavierStokesαmodel forms an other example of regularization modeling. In this because they possess far too many scales of e model, the convective term becomesCr(u, u) = motion. The computationally almost number Cr(u,¯u), whereCrdenotes the convective oper less small scales result from the convective term ator in rotational form:Cr(u, v) = (r ×u)×v. C(u, v) = (u∙ r)v,which allows for the transfer of energy from scales as large as the flow domain In largeeddy simulation, the NavierStokes to the smallest scales that can survive viscous equations are filtered spatially, and the resulting dissipation. In the quest for a dynamically less nonclosed term is modelled: complex mathematical formulation, we consider smooth approximations (regularizations) of the tu+C(u, u) +D(u) +rp=f(u),(3) nonlinearity: e tu+C(u, u) +D(u) +rp= 0.(2) wheref(u)represents the model. The regular e ization (2) falls in with this concept ifCis taken The regularized system (2) should be moresuch that amenable to solve numerically, while the leading e modes ofuhave to approximate the correspondC(u, u) =C(u, u)f(u).(4)