On the stability of von Kármán rotating-disk boundary layers with radial anisotropic surface roughness

Abstract

We summarise results of a theoretical study investigating the distinct convective instability properties of steady boundary-layer flow over rough rotating disks. A generic roughness pattern of concentric circles with sinusoidal surface undulations in the radial direction is considered. The goal is to compare predictions obtained by means of two alternative, and fundamentally different, modelling approaches for surface roughness for the first time. The motivating rationale being to identify commonalities and isolate results that might potentially represent artefacts associated with the particular methodologies underlying one of the two modelling approaches.The most significant result of practical relevance obtained is that both approaches predict overall stabilising effects on the Type I instability mode of rotating disk flow. This mode leads to transition of the rotating-disk boundary layer and, more generally, the transition of boundary-layers with a cross-flow profile. Stabilisation of the Type 1 mode means that it may be possible to exploit surface roughness for laminar-flow control in boundary layers with a cross-flow component. However, we also find differences between the two sets of model predictions, some subtle and some substantial. These will represent criteria for establishing which of the two alternative approaches is more suitable to correctly describe experimental data when these become available.

The effect of surface roughness on rotor-stator cavity flows

“…The combined effects of h * r , α * i = (α * r , α * θ , α * z ), and the shape function are important factors to uniquely determine the type of the roughness, and the different combinations provide a mechanism to simulate many different roughness types. This sensitivity to the precise form of the roughness was also demonstrated by Garrett et al 15 Figure 13 shows the variation in the entrainment coefficient under different α * and h * r values. An increase in either α * or h * r shows an increase in K from K ≈ 0.35 for smooth boundary layers.…”

“…However, in general, there may be situations where the effects of roughness are no longer negligible. For example, Zoueshtiagh et al, 12 and Harris et al, 13 Cooper et al, 14 and Garrett et al 15 conducted investigations into the transition of von Kármán-type boundary layers over rough rotating disks. All investigations agree that surface roughness has only a minor influence on the transition process up to a certain level of roughness, but beyond this, the flow is significantly stabilised via a reduction in the critical Reynolds number Re c for the onset of the dominant Type I mode.…”

Quantifying non-Newtonian effects in rotating boundary-layer flows

“…Some minor discrepancies were found in the values of the type II critical Reynolds numbers. However, as noted by Garrett et al [20], the determination of this mode is strongly dependent on the choice of numerical solution method, whereas the type I mode appears not to be. In this study we choose to report the results owing from our transformed variables method.…”

Quantitative Kinetic Analysis of a PdAu3Alloy Catalyst for Oxygen Electro-Reduction

“…The integration domain is discretized by a uniform lattice of N ρ × N ζ points and the spatial increments are given by ρ = (x end − ρ 1 )/(N ρ − 1), ζ = x end /(N ζ − 1). For RRDE simulations with a nonuniform lattice see, 31 where a Chebyshev polynomial discretization was used. The time derivatives in the field equations are set to zero, which corresponds to the limit t → ∞, since we are interested in the steady state only.…”

“…In this respect, Cooper et al tested different roughness models, 30 and a review on the topic can be found in Ref. 31.…”