Similarity Behavior in Transitional Boundary Layers Over a Range of Adverse Pressure Gradients and Turbulence Levels

Abstract

Boundary layer transition has been investigated experimentally under low, moderate and high free-stream turbulence levels and varying adverse pressure gradients. Under high turbulence levels and adverse pressure gradients a pronounced subtransition was present. A strong degree of similarity in intermittency distributions was observed, for all conditions, when the Narasimha procedure for determination of transition inception was used. Effects of free-stream turbulence on the velocity profile are particularly strong for the laminar boundary layer upstream of the transition region. This could reflect the influence of the turbulence on the shear stress distribution throughout the layer and this matter needs further attention. The velocity profiles in wall coordinates undershoot the turbulent wall layer asymptote near the wall over most of the transition region. The rapidity with which transition occurs under adverse pressure gradients produces strong lag effects on the velocity profile; the starting turbulent boundary layer velocity profile may depart significantly from local equilibrium conditions. The practice of deriving integral properties and skin friction for transitional boundary layers by a linear combination of laminar and turbulent values for equilibrium layers is inconsistent with the observed lag effects. The velocity profile responds sufficiently slowly to the perturbation imposed by transition that much of the anticipated drop in form factor will not have occurred prior to the completion of transition. This calls into question both experimental techniques which rely on measured form factor to characterize transition and boundary layer calculations which rely on local equilibrium assumptions in the vicinity of transition.

Simplified Approach to Predicting Rough Surface Transition

“…For the smooth vane suction surface transition occurs in regions where the pressure gradient is very negative. At this Reynolds number the pressure gradient at the start of transition for the smooth surface is more negative than the pressure gradient data of Gostelow et al [41], which was used by Solomon et al [33] to determine the value of the spot production parameter, N. The length of transition is very sensitive to negative pressure gradients. Figure 4a shows that an abrupt smooth suction surface transition was calculated for the 8% turbulence level.…”

“…The transition length would increase if N were limited to a smaller value. The data of Gostelow and Walker [42] strongly indicate that extrapolating the correlation of Gostelow et al [41] to more negative pressure gradients would overestimate the value for N. At the lower turbulence intensity, figure 4b, the start of suction surface transition is at an even more negative pressure gradient, because the critical Reynolds number for the start of transition is increased. At the lower pressure gradient the rapid increase in intermittency is appropriate.…”

Measurements in a Transitional Boundary Layer With Görtler Vortices

“…. Gostelow and Walker (1991) showed that the agreement is also good for adverse pressure gradient cases on flat plates. The present data indicate that the theory does not always hold when curvature effects are introduced.…”

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 1 — Mean Quantities

“…The results of Walker and Gostelow (1989) indicate that the shape factor, H, is close to the local equilibrium turbulent flow value at the 99% intermittency point for the zero-pressuregradient case, but it increasingly exceeds this value as the pressure gradient becomes more adverse, which suggests the possibility that the shape factor may not be settled at the 99% intermittency point. Gostelow and Walker (1991) evaluated their transitional skinfriction values by using the relationship C f = (1-F) CfIam + I'Cf,mrb. The skin-friction value at the onset of transition was determined in the near-wall region by linear extrapolation of U + = Y+ , and the skin-friction value at transition completion was obtained by using ti K/p = 0.0464(v/U^S) 0'21U" 212.…”