The response of a turbulent boundary layer to a step change in surface roughness. Part 2. Rough-to-smooth

Abstract

An experimental study of the structure of the internal layer which grows down-stream from a rough-to-smooth surface change shows it to be essentially different from that studied by Antonia & Luxton (1971 b) for the case of a smooth-to-rough perturbation. The rate of growth of the internal layer is less than that for the smooth-to-rough step and it appears that the more intense initial rough-wall flow dictates the rate of diffusion of the disturbance for a considerable distance. Inside the internal layer the mixing lengthIis increased relative to the equilibrium distributionI=KY.A turbulent energy budget shows that the advection is comparable with the production or dissipation, whilst there seems to be some diffusion of energy into the internal-layer region close to the wall. The boundary layer, as a whole, recovers much more slowly following a rough-to-smooth change than following a smooth-to-rough change, and at the last measuring station (16 boundary-layer thicknesses from the start of the smooth surface) the distributions of mean velocity and Reynolds shear stress are far from self-preserving.

New perspectives on the impulsive roughness-perturbation of a turbulent boundary layer

“…The internal-layer growth can also be measured dimensionally (without scaling), and it is found that δ 1 ∼ x 0.3 and δ 2 ∼ x 0.1 , such that the exponent of the dimensional growth rate for the second internal layer is approximately half that of the first internal layer, consistent with the findings of Antonia & Luxton (1971a) and Antonia & Luxton (1972), who reported growth rates of δ 1 ∼ x 0.7 and δ 2 ∼ x 0.4 . It is worth noting that for the outer-scaled internal-layer growth, Pearson et al (1997) also observed roughly the same exponents for the two internal-layer boundaries, δ 1 /δ ∼ (x/δ) 0.15 and δ 2 /δ ∼ (x/δ) 0.17 .…”

“…Antonia & Luxton (1971a) reported M S → R = −4.6 and M R → S = 5.8; Andreopoulos & Wood (1982) reported M S → R = −3.67 and M R → S = 4.34 (although it is worth noting that there appears to be a sign error in their results which, if corrected, would result in M R → S = 2.86). The smooth to rough transition is expected to have a stronger roughness step, since the corresponding velocity deficit should be greater than the velocity deficit once recovery is underway downstream; this expectation is met by both the current results and the corrected results from Andreopoulos & Wood (1982); Antonia & Luxton (1972) do not formally report their rough-to-smooth step strength, but a value for their study is reported by Andreopoulos & Wood (but perhaps with the same sign error?) which is not amenable to simple correction.…”

“…For the transition from a smooth to rough surface (S → R) studied by Antonia & Luxton (1971a), the return to equilibrium was monitored by the development of an internal layer corresponding to the adjustment of the flow to the new boundary condition, which started at the roughness transition point and grew quickly to the edge of the boundary layer itself, thereby reestablishing equilibrium in the flow field. The transition from a rough to smooth wall condition (R → S) showed significantly slower growth of the corresponding internal layer, and the restoration of equilibrium was not observed even 16δ downstream in a second experimental study by Antonia & Luxton (1972), where δ refers to the mean boundary layer thickness measured at 99% of the free stream velocity. Subsequently, the problem of a spatial impulse of roughness on an otherwise smooth boundary was considered by Andreopoulos & Wood (1982), since it provided an opportunity to isolate the influence of the roughness in a patch short enough to avoid establishment of equilibrium.…”

An experimental investigation of wall pressure fluctuations beneath non-equilibrium turbulent flows

“…In the following discussion, the characteristics of turbulence profiles measured downstream of reattachment will be compared to those In the study of Antonia and Luxton (1972), a rough-to-smooth step change in surface roughness, the region of excess turbulence stress is not as dramatic as for an impulsive change in surface roughness. Antonia and Luxton (1972) found that the mean velocity profiles, when plotted in the form of U/U, versus y 11 2 , followed a half-power line near the wall and then followed another half-power line, but of IN different slope, further out in the boundary layer.…”

Characteristics of a Turbulent Boundary Layer Perturbed by Spatially-Impulsive Dynamic Roughness

“…The transition from a rough to smooth wall condition showed significantly slower growth of the corresponding internal layer and experimentally the restoration of equilibrium was never observed. 6 Subsequently, the problem of a spatial impulse of roughness on an otherwise smooth boundary was considered by Andreopoulos and Wood,7 since it provided an opportunity to isolate the influence of the roughness in a patch short enough to avoid establishment of equilibrium. In this way, the additional length scale of the roughness was introduced to the turbulent boundary layer and the response of the boundary layer could be observed downstream independent of the continued presence of the roughness itself.…”