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 numberRe_θ> 6000. is made forRe_θ< 6000. It is found that κ = 0·40, the von Kármán constant forRe_θ> 6000, is replaced by Ω = 0·40 (Re_θ/6000)^⅛forRe_θ< 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 ε_M/ν are used to obtain a continuous expression for ε_M/ν as a function ofU⁺,V⁺_w, andRe_θfor the wall region. This expression is in reasonable agreement with the generated ε_M/ν blowing results and in less agreement with the unblown and suction results. Eddy viscosity and mixing length results confirm that ε_M/δ*U_∞∝ Ω²andl/δ ∝ Ω for the outer region and that ε_M/δ*U_∞andl/δ are substantially independent of blowing and moderate suction, as also reflected by the velocity defect representation for injection and suction.