Transpired turbulent boundary layers: a general strategy for RANS turbulence models

ABSTRACT

Transpired boundary layers are of major interest for many industrial applications. Although well described, there is no turbulence model specifically dedicated to the prediction of boundary layers for both blowing and suction configurations. Revisiting closure relations of turbulence models, a general strategy was established to recover Stevenson's law of the wall that described the behaviour of transpired boundary layers in the wall region. The methodology is applied to the $k-\omega$ SST turbulence model and compared to Wilcox's correction, only applicable to blowing cases. A version of the proposed correction, more suited to RANS solvers, was also derived. Several experimental boundary layer configurations with blowing or suction were computed using both versions of the correction. The good agreements observed on all cases prove the relevance and the efficiency of the present strategy.

Abbreviations: l: mixing length; u: longitudinal velocity component; v: wall-normalvelocity component; $u^{\prime }$: longitudinal velocity fluctuation; $v^{\prime }$: wall-normal velocityfluctuation; x: longitudinal direction; y: wall-normal direction; k: turbulent kineticenergy; ω: specific dissipation; ${\delta }_1$: displacement thickness; τ: shear stress; ρ: density; ν: kinematic viscosity; ${\nu }_t$: eddy viscosity; μ: dynamic viscosity; κ: Kàrmàn constant; ${}^{+}$:superscript for dimensionless wall quantities; ${}_w$: subscript for quantities at the wall; $⟨⟩$:Reynolds average

KEYWORDS:

• Transpired boundary layers
• blowing
• suction
• turbulence models

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

François Chedevergne  http://orcid.org/0000-0003-3634-8482