Near-wall scaling for incompressible and compressible flows

Free access article

Issue		ESAIM: Proc. Volume 16, 2007 CEMRACS 2005 - Computational Aeroacoustics and Computational Fluid Dynamics in Turbulent Flows


Page(s)		114 - 132
DOI		http://dx.doi.org/10.1051/proc:2007015
Published online		02 March 2007

ESAIM: Proc., 2007, Vol. 16, pp. 114-132
DOI: 10.1051/proc:2007015

Near-wall scaling for incompressible and compressible flows

N. Peller¹, M. Manhart¹, M. Petrovan Boiarciuc² and C. Brun²

¹ Fachgebiet Hydromechanik, Technische Universität München, Arcisstrasse 21, 80333 München, Germany.
² Laboratoire de Mécanique et d'Energétique, Polytech'Orléans, 8 rue Léonard de Vinci, 45072 Orléans France.

n.peller@bv.tum.de
m.manhart@bv.tum.de
margareta.petrovan@univ-orleans.fr
christophe.brun@univ-orleans.fr

(Published online: 2 March 2007)

Abstract
The paper presents near-wall scaling in incompressible and compressible flows. It concentrates on flows with streamwise pressure gradients which render traditional scaling inapplicable. For incompressible flows a scaling for the velocity profiles is introduced based on both the friction velocity and the pressure gradient. For compressible flows a scaling is developed for the velocity and the temperature. This scaling is based on wall friction, pressure gradient and wall heat flux. We define two new parameters $\alpha$ and $\beta$ where $\alpha$ defines a measure for the ratio between wall friction and pressure gradient and $\beta$ defines the ratio between wall heat flux and pressure gradient. For zero pressure gradient flows the traditional scaling is recovered. A priori tests are performed by means of Direct Numerical Simulations (DNS). The compressible scaling is analyzed on channel flow with non-adiabatic walls and adverse pressure gradient. The incompressible scaling is analyzed on channel flow with periodic hill constrictions. Finally a wall model based on the new scaling is tested a posteriori by means of Large Eddy Simulation (LES).

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