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High-Reynolds-number effects in supersonic turbulent channel flow

DOI: 10.1615/ICHMT.2015.THMT-15.810
pages 403-406

D. Modesti
Dipartimento di Ingegneria Meccanica e Aerospaziale, 'Sapienza' University Via Eudossiana 18, 00184 Roma, Italy

Matteo Bernardini
Department of Mechanical and Aerospace Engineering, Sapienza University of Rome via Eudossiana 18, Rome, 00184, Italy

Sergio Pirozzoli
Dipartimento di Meccanica e Aeronautica, Universita di Roma 'La Sapienza' Via Eudossiana 18, 00184 Roma, Italy


The effect of the Reynolds number in a compressible isothermal channel flow is investigated through a series of direct numerical simulations (DNS). The bulk Mach number based on the wall temperature is kept fixed at 1.5, and the bulk Reynolds number is increased up to Reτ ~ 1000. Previous work at lower Reynolds number confirmed the validity of Morkovin's hypothesis but questioned the use of van Driest velocity transformation in the presence of heated walls. 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.

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