Near-wall scaling for incompressible and compressible flows

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.

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

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 α and β where α defines a measure for the ratio between wall friction and pressure gradient and β 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).