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EXAMINATION OF NEAR-WALL SCALING FOR TURBULENT BOUNDARY LAYERS WITH ADVERSE PRESSURE GRADIENT

Nikolaus Peller
Fachgebiet Hydromechanik, Technische Universität München Arcisstrasse 21, D-80333 München, Germany

Michael Manhart
Fachgebiet Hydromechanik, Technische Universitat München, Arcisstrasse 21, 80333 München, Germany

Margareta Petrovan Boiarciuc
Polytech'Orleans/LME, 8 rue Léonard de Vinci, 45072 Orleans CEDEX 2, France

Christophe Brun
Laboratoire d'Etudes Géophysiques et Industrielles/MoST, BP 53, 38041 Grenoble CEDEX 9, France

Sinopsis

Based on earlier work in Peller et al. (2005) and Manhart et al. (2006) we further investigate the behaviour of an extended scaling for turbulent flows including a streamwise pressure gradient. The scaling is based on a combination of the friction velocity Uτ and the pressure velocity Up leading to a combined velocity scale Uτp. The influence of pressure gradient with respect to wall friction is quantifi ed by a non-dimensional parameter α = Uτ/Uτp ∈ [0; 1]. We investigate Reynolds, convective and pressure terms within the streamwise momentum balance as well as the viscous and turbulent stresses, based on DNS of two types of separated flows. We find good agreement in the profi les when they are ploted in extended wall normal coordinates for positions characterized by a similar α value. In most cases we can con rm the assumption of a constant streamwise pressure gradient in wall normal direction, except when curvature e ffects are present, which modifi es the pressure gradient distribution. For a given we observe universal behaviour for the velocity profi les that shows very good agreement over a complete recirculation region. Accordingly, the terms in the momentum balances agree well and this gives hope to describe universal behaviour of e.g. Reynolds terms depending on the parameter α.