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

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.

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

“…Turbulent flow topology in supersonic boundary layer with wall heat transfer was investigated in Sharma, Shadloo and Hadjadj (2019). Decomposition of the mean skin-friction drag in compressible turbulent channel flows was studied in Li, Fang, Modesti and Cheng (2019b).…”

Contributions of different scales of turbulent motions to the mean wall-shear stress in open channel flows at low-to-moderate Reynolds numbers

“…50 % for aircraft, 90 % for submarine, etc. Gad-el-Hak 1994;Fan, Cheng & Li 2019a;Li et al 2019), but also exhibits close relevance to wall surface morphology (such as bed load transport in rivers, wind-blown sand movement in desert, etc.). Given the essential significance, sustained research efforts have been made to determine τ w (Winter 1979;Haritonidis 1989;Klewicki et al 2007;Walker 2014;Cierpka, Rossi & Köhler 2015;Rathakrishnan 2017;Vinuesa & Örlü 2017, etc.…”

“…treating the power of τ w as an energy transfer from the wall to the fluid through viscous dissipation (C f 1,RD ) and turbulent kinetic energy (TKE) production (C f 2,RD ). The RD identity as well as its modifications/extensions have also been widely used: CCFs (Agostini & Leschziner 2019;Fan et al 2019a); zero/adverse pressure gradient TBLs (Renard & Deck 2016, 2017Fan, Li & Pirozzoli 2019b;Senthil et al 2020); compressible CCFs (Li et al 2019); compressible TBLs (Fan et al 2019b); viscoelastic CCFs (Zhang et al 2020), etc. Almost at the same time that the RD identity was proposed, Yoon et al (2016) presented another decomposition method.…”

“…Gad-el-Hak 1994; Fan, Cheng & Li 2019 a ; Li et al. 2019), but also exhibits close relevance to wall surface morphology (such as bed load transport in rivers, wind-blown sand movement in desert, etc. ).…”

On the structure of streamwise wall-shear stress fluctuations in turbulent channel flows

“…2018; Fan, Cheng & Li 2019 a ; Fan, Li & Pirozzoli 2019 b ; Li et al. 2019) and active/passive control approaches (Gose et al. 2018; Yao, Chen & Hussain 2018; Li & Liu 2019; Yao & Hussain 2019), to date, very few works have investigated the features of wall-shear stress fluctuations and their associated dynamics.…”