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Scaling and modelling of turbulence in variable property channel flows

Published online by Cambridge University Press:  15 June 2017

Rene Pecnik Open the ORCID record for Rene Pecnik [Opens in a new window]  and
Ashish Patel
Rene Pecnik*
Affiliation:
Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
Ashish Patel
Affiliation:
Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

We derive an alternative formulation of the turbulent kinetic energy equation for flows with strong near-wall density and viscosity gradients. The derivation is based on a scaling transformation of the Navier–Stokes equations using semi-local quantities. A budget analysis of the semi-locally scaled turbulent kinetic energy equation shows that, for several variable property low-Mach-number channel flows, the ‘leading-order effect’ of variable density and viscosity on turbulence in wall bounded flows can effectively be characterized by the semi-local Reynolds number. Moreover, if a turbulence model is solved in its semi-locally scaled form, we show that an excellent agreement with direct numerical simulations is obtained for both low- and high-Mach-number flows, where conventional modelling approaches fail.

JFM classification

Compressible Flows: Compressible boundary layers Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent boundary layers
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 823 , 25 July 2017 , R1
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Copyright
© 2017 Cambridge University Press 

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