Influence of Surface Roughness on the Second Order Transport of Turbulence in Non-Equilibrium Boundary Layers

The concentration distribution of massive dilute species (e.g. aerosols, heavy vapours, etc.) carried in a gas stream in non-isothermal boundary layers is studied in the large-Schmidt-number limit, Sc[Gt ]1, including the cross-mass-transport by thermal diffusion (Ludwig–Soret effect). In self-similar laminar boundary layers, the mass fraction distribution of the dilute species is governed by a second-order ordinary differential equation whose solution becomes a singular perturbation problem when Sc[Gt ]1. Depending on the sign of the temperature gradient, the solutions exhibit different qualitative behaviour. First, when the thermal diffusion transport is directed toward the wall, the boundary layer can be divided into two separated regions: an outer region characterized by the cooperation of advection and thermal diffusion and an inner region in the vicinity of the wall, where Brownian diffusion accommodates the mass fraction to the value required by the boundary condition at the wall. Secondly, when the thermal diffusion transport is directed away from the wall, thus competing with the advective transport, both effects balance each other at some intermediate value of the similarity variable and a thin intermediate diffusive layer separating two outer regions should be considered around this location. The character of the outer solutions changes sharply across this thin layer, which corresponds to a second-order regular turning point of the differential mass transport equation. In the outer zone from the inner layer down to the wall, exponentially small terms must be considered to account for the diffusive leakage of the massive species. In the inner zone, the equation is solved in terms of the Whittaker function and the whole mass fraction distribution is determined by matching with the outer solutions. The distinguished limit of Brownian diffusion with a weak thermal diffusion is also analysed and shown to match the two cases mentioned above.

Download Full-text

Reply to Mellor’s comments on “Stability of algebraic non-equilibrium second-order closure models” (Ocean Modelling 3 (2001) 33–50)

Ocean Modelling ◽

10.1016/s1463-5003(02)00059-8 ◽

2003 ◽

Vol 5 (3) ◽

pp. 291-293 ◽

Cited By ~ 4

Author(s):

Eric Deleersnijder ◽

Hans Burchard

Keyword(s):

Second Order ◽

Ocean Modelling ◽

Closure Models ◽

Non Equilibrium

Download Full-text

SECOND-ORDER EFFECTS IN LAMINAR BOUNDARY LAYERS

AIAA Journal ◽

10.2514/3.1462 ◽

1963 ◽

Vol 1 (1) ◽

pp. 33-40 ◽

Cited By ~ 25

Author(s):

STEPHEN H. MASLEN

Keyword(s):

Boundary Layers ◽

Second Order ◽

Order Effects ◽

Laminar Boundary Layers ◽

Second Order Effects

Download Full-text

Surface roughness effects in turbulent boundary layers

Experiments in Fluids ◽

10.1007/s003480050370 ◽

1999 ◽

Vol 27 (5) ◽

pp. 450-460 ◽

Cited By ~ 280

Author(s):

P.-Å. Krogstadt ◽

R.A. Antonia

Keyword(s):

Surface Roughness ◽

Boundary Layers ◽

Turbulent Boundary Layers ◽

Roughness Effects

Download Full-text

Measurements in adverse-pressure-gradient turbulent boundary layers with a step change in surface roughness

Journal of Fluid Mechanics ◽

10.1017/s0022112075002200 ◽

1975 ◽

Vol 70 (3) ◽

pp. 573-593 ◽

Cited By ~ 19

Author(s):

W. H. Schofield

Keyword(s):

Surface Roughness ◽

Pressure Gradient ◽

Boundary Layers ◽

Leading Edge ◽

Adverse Pressure Gradient ◽

Turbulent Boundary Layers ◽

Step Change ◽

Internal Layer ◽

Mean Velocity ◽

Law Of The Wall

The response of turbulent boundary layers to sudden changes in surface roughness under adverse-pressure-gradient conditions has been studied experimentally. The roughness used was in the ‘d’ type array of Perry, Schofield & Joubert (1969). Two cases of a rough-to-smooth change in surface roughness were considered in the same arbitrary adverse pressure gradient. The two cases differed in the distance of the surface discontinuity from the leading edge and gave two sets of flow conditions for the establishment and growth of the internal layer which develops downstream from a change in surface roughness. These conditions were in turn different from those in the zero-pressure-gradient experiments of Antonia & Luxton. The results suggest that the growth of the new internal layer depends solely on the new conditions at the wall and scales with the local roughness length of that wall. Mean velocity profiles in the region after the step change in roughness were accurately described by Coles’ law of the wall-law of the wake combination, which contrasts with the zero-pressure-gradient results of Antonia & Luxton. The skin-friction coefficient after the step change in roughness did not overshoot the equilibrium distribution but made a slow adjustment downstream of the step. Comparisons of mean profiles indicate that similar defect profile shapes are produced in layers with arbitrary adverse pressure gradients at positions where the values of Clauser's equilibrium parameter β (= δ*τ−10dp/dx) are similar, provided that the pressure-gradient history and local values of the pressure gradient are also similar.

Download Full-text