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High‐Reynolds‐number effects on turbulent scalings in compressible channel flow
Author(s) -
Modesti Davide,
Bernardini Matteo,
Pirozzoli Sergio
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510235
Subject(s) - reynolds number , turbulence , mach number , mechanics , compressibility , magnetic reynolds number , physics , supersonic speed , reynolds stress equation model , reynolds decomposition , reynolds stress , mathematics , direct numerical simulation , reynolds averaged navier–stokes equations , statistical physics , reynolds equation , k epsilon turbulence model , k omega turbulence model
The effect of the Reynolds number in a supersonic isothermal channel flow is studied using a direct numerical simulation (DNS). The bulk Mach number based on the wall temperature is 1.5, and the bulk Reynolds number is increased up to Re τ ≈ 1000. The use of van Driest velocity transformation in the presence of heated walls has been questioned due to the poor accuracy at low Reynolds number. For this reason alternative transformations of the velocity profile and turbulence statistics have been proposed, as, for instance, semi‐local scalings. We show that the van Driest transformation recovers its accuracy as the Reynolds number is increased. The Reynolds stresses collapse on the incompressible ones, when properly scaled with density, and very good agreement with the incompressible stresses is found in the outer layer. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)