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Decomposition of the mean skin-friction drag in compressible turbulent channel flows

Published online by Cambridge University Press:  18 July 2019

Weipeng Li Open the ORCID record for Weipeng Li [Opens in a new window] ,
Yitong Fan ,
Davide Modesti Open the ORCID record for Davide Modesti [Opens in a new window]  and
Cheng Cheng
Weipeng Li*
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China Engineering Research Center of Gas Turbine and Civil Aero Engine, Ministry of Education, China
Yitong Fan
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China
Davide Modesti
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
Cheng Cheng
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China
*
†Email address for correspondence: [email protected]
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Abstract

The mean skin-friction drag in a wall-bounded turbulent flow can be decomposed into different physics-informed contributions based on the mean and statistical turbulence quantities across the wall layer. Following Renard & Deck’s study (J. Fluid Mech., vol. 790, 2016, pp. 339–367) on the skin-friction drag decomposition of incompressible wall-bounded turbulence, we extend their method to a compressible form and use it to investigate the effect of density and viscosity variations on skin-friction drag generation, using direct numerical simulation data of compressible turbulent channel flows. We use this novel decomposition to study the skin-friction contributions associated with the molecular viscous dissipation and the turbulent kinetic energy production and we investigate their dependence on Reynolds and Mach number. We show that, upon application of the compressibility transformation of Trettel & Larsson (Phys. Fluids, vol. 28, 2016, 026102), the skin-friction drag contributions can be only partially transformed into the equivalent incompressible ones, as additional terms appear representing deviations from the incompressible counterpart. Nevertheless, these additional contributions are found to be negligible at sufficiently large equivalent Reynolds number and low Mach number. Moreover, we derive an exact relationship between the wall heat flux coefficient and the skin-friction drag coefficient, which allows us to relate the wall heat flux to the skin-friction generation process.

JFM classification

Aerodynamics: High-speed flow Compressible Flows: Compressible boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , pp. 101 - 123
Copyright
© 2019 Cambridge University Press 

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