Characteristics of turbulent boundary layers at low Reynolds numbers with and without transpiration

Abstract

An extension to Coles's (1956) ‘law of the wall–law of the wake’ formulation for incompressible unblown boundary layers with momentum thickness Reynolds numberReθ> 6000. is made forReθ< 6000. It is found that κ = 0·40, the von Kármán constant forReθ> 6000, is replaced by Ω = 0·40 (Reθ/6000)⅛forReθ< 6000. Based upon the data of Simpson (1967) this formulation is extended to injection and undersucked (dθ/dx> 0) flows in ‘law of the wall’ and ‘velocity-defect’ representations. This law of the wall for the logarithmic turbulent region and Reichardt's sublayer variation of εM/ν are used to obtain a continuous expression for εM/ν as a function ofU+,V+w, andReθfor the wall region. This expression is in reasonable agreement with the generated εM/ν blowing results and in less agreement with the unblown and suction results. Eddy viscosity and mixing length results confirm that εM/δ*U∞∝ Ω2andl/δ ∝ Ω for the outer region and that εM/δ*U∞andl/δ are substantially independent of blowing and moderate suction, as also reflected by the velocity defect representation for injection and suction.