P. W. Carpenter

An experimental study of boundary-layer transition over a rotating, compliant disk

An experimental study is described which investigates the laminar-turbulent transition of the boundary layer over rigid and compliant disks rotating under water. Hot-film data are presented and analyzed to produce neutral-stability curves. It appears to be the first time that such data has become available for a compliant disk. Our experiments employing a rigid disk essentially confirm the results of previous authors. For the flow over the compliant disk the turbulence levels in the transitional and fully turbulent flow regimes are found to be considerably lower than the corresponding levels for the rigid disk. The analysis of our experimental data suggests that wall compliance has a stabilizing influence in the frequency range associated with the Type I cross-flow instability. Nevertheless, compliance is found to have an overall destabilizing effect on the boundary-layer flow. This results in a substantially lower transitional Reynolds number compared to the case of the rigid disk. The experimental obser...

Laminar-turbulent boundary-layer transition over a rough rotating disk

Boundary-layer transition over a disk spinning under water is investigated. Transitional Reynolds numbers, Rec, and associated boundary-layer velocity profiles are determined from flow-visualizations and hot-film measurements, respectively. The value of Rec and the velocity profiles are studied as a function of the disk’s surface roughness. It is found that transition over rough disks occurs in a similar fashion to that over smooth disks, i.e., abruptly and axisymmetrically at well-defined radii. Wall roughness has little effect on Rec until a threshold relative roughness is reached. Above the threshold Rec decreases sharply. The decrease is consistent with the drop one expects for our flow for the absolute instability discovered by Lingwood [J. Fluid Mech. 299, 17 (1995); 314, 373 (1996); 331, 405 (1997)]. This indicates that the Lingwood absolute instability may continue to play a major role in the transition process even for large relative roughness.

Effects of wall compliance on the laminar–turbulent transition of torsional Couette flow

Torsional Couette flow between a rotating disk and a stationary wall is studied experimentally. The surface of the disk is either rigid or covered with a compliant coating. The influence of wall compliance on characteristic flow instabilities and on the laminar–turbulent flow transition is investigated. Data obtained from analysing flow visualizations are discussed. It is found that wall compliance favours two of the three characteristic wave patterns associated with the transition process and broadens the parameter regime in which these patterns are observed. The results for the effects of wall compliance on the third pattern are inconclusive. However, the experiments indicate that the third pattern is not a primary constituent of the laminar–turbulent transition process of torsional Couette flow.

A wave driver theory for vortical waves propagating across junctions with application to those between rigid and compliant walls

A theory is described for propagation of vortical waves across alternate rigid and compliant panels. The structure in the fluid side at the junction of panels is a highly vortical narrow viscous structure which is idealized as a wave driver. The wave driver is modelled as a ‘half source cum half sink’. The incoming wave terminates into this structure and the outgoing wave emanates from it. The model is described by half Fourier–Laplace transforms respectively for the upstream and downstream sides of the junction. The cases below cutoff and above cutoff frequencies are studied. The theory completely reproduces the direct numerical simulation results of Davies & Carpenter (J. Fluid Mech., vol. 335, 1997, p. 361). Particularly, the jumps across the junction in the kinetic energy integral, the vorticity integral and other related quantities as obtained in the work of Davies & Carpenter are completely reproduced. Also, some important new concepts emerge, notable amongst which is the concept of the pseudo group velocity.

Wave Propagation in Flows Across Junctions Between Rigid and Flexible Walls

The generic problem considered is the propagation of vortical waves across junctions between one wave-bearing medium and another. It is assumed that the eigensolutions are known for the corresponding spatially homogeneous problems. The task is how to determine the amplitudes of the reflected and transmitted waves given the amplitude of the incident wave. In general, there may be more than one incident, reflected or transmitted wave. It is shown how this sort of problem may be solved in terms of the homogeneous eigensolutions by drawing an analogy between the junction and a wave-driver. The particular illustrative problem studied is that of a Tollmien-Schlichting wave, propagating along a rigid-walled channel flow, that is incident on a section of the channel where the walls consist of compliant panels. It is shown how the wave system over the compliant panels and the amplitude of the Tollmien-Schlichting wave leaving the compliant section may be determined in terms of the incident wave. The technique developed for this problem is considered to be generic.Copyright