DOI: 10.1615/TSFP9
SELF-PRESERVATION IN ZERO PRESSURE GRADIENT TURBULENT BOUNDARY LAYERS
要約
Starting with the Navier-Stokes Equation (NSE), we derived the conditions for self-preservation (SP) in a zeropressure gradient (ZPG) turbulent boundary layer. The analysis showed that it is strictly not possible to obtain SP in a ZPG turbulent boundary layer, unless the viscous term is eliminated from the NSE. This can be achieved in a smooth wall boundary layer only when the Reynolds number (Re) approaches infinity. In the case of rough walls, it is noted that the viscous effects can be compensated by surface roughness and therefore, SP is achievable, irrespective of Re. In this case, SP analysis showed that velocity scale (u*) must be constant and the length scale (l) should vary linearly with streamwise distance (x). These SP conditions are tested using experimental data taken over a similar streamwise fetch on a smooth wall and several types of rough walls. It is observed that complete SP in a ZPG turbulent boundary layer is possible when the roughness height (k) increases linearly with x, where both the SP constraints (u* = Uτ = constant and l = δ ∝ x) are met. In the present rough wall study, Uτ is observed to remain practically constant in x and δ ~ x and appears to be the next best candidate for achieving SP.