Water-Tank Studies of Separating Flow Over Rough Hills

Abstract

The present work investigates the lower boundary condition for flows over a steep, rough hill. Simple asymptotic arguments together with the mixing-length hypothesis are used to derive a local analytical solution that is tested against three different flow conditions. In all, 36 velocity profiles are compared with the proposed expression. The experiments were carried out in a water channel and velocity measurements were made through laser Doppler anemometry. The extent of separated flow was made to vary as a function of the roughness and the Reynolds number. The analysis includes regions of attached as well as separated flow. In particular, the solution of Stratford is studied at the points of separation and re-attachment and found to apply equally well in rough walls.

Note on a Parametric Relation for Separating Flow over a Rough Hill

“…The excessive level of complexity involved in the description of both subjects has usually forced workers to approach the problem individually. Recently, Loureiro et al (2008) proposed a new treatment for the lower boundary condition that, in principle, can be used in regions of attached and separated flows over rough surfaces. The specification of wall functions to represent near-wall turbulence is particularly helpful for flows over rough surfaces, since the fine-scale complexities generated by the flow around roughness elements cannot be resolved even in the present day environment of optimized algorithms and high computing power.…”

“…The treatment of Loureiro et al (2008) is not susceptible to the deficiencies encountered by the classical logarithmic law of the wall. Close to a separation point, the proposed solution reduces to the square-root law of Stratford (1959).…”

“…In Loureiro et al (2008), the additive parameter of the law of the wall formulation, C, is parametrized by considering the limiting form of the proposed solution as τ w (1/ρ)∂ x p. The implication is that C is written in terms of u * , (1/ρ)∂ x p, z 0 and the von Kármán constant, (= 0.4). The clear attractiveness of this approach is the possibility of defining C from, as mentioned before, the vast collection of z 0 values that appears in literature.…”

“…The purpose of the present work is to investigate in detail the validity of the new treatment of Loureiro et al (2008) for the lower boundary condition through direct numerical simulation (DNS) and experimental data. In particular, the behaviour of the additive parameter C in regions of attached as well as separated flow is investigated with the help of global optimization algorithms based on direct search methods.…”

Feasible domain of Walker's unsteady wall-layer model for the velocity profile in turbulent flows

“…(2) is that it becomes undetermined at a point of flow separation, x s , since u τ = 0. Also note that, at this point, pressure changes greatly across the boundary layer, implying that p e is not an appropriate reference parameter at the wall (Stratford (1959), Silva Freire (2009, 2011), Loureiro et al (2008)). …”