P. J. Thomas

On the influence of the Basset history force on the motion of a particle through a fluid

A parameter study on the development of the Basset integral appearing in the equation of motion of a particle moving through a fluid is presented. The particle motion is investigated numerically for the flow across an aerodynamic shock. It is found that, for this type of flow, the Basset history force acting upon the particle described by the Basset integral can be many times larger than the viscous drag in the immediate shock region. It is demonstrated how this force affects the particle motion across the shock for different particles. Nevertheless, the results obtained show that it is justified to neglect the Basset integral for the theoretical description of the motion of the types of particles commonly used in flow measurement tracer techniques for the type of flow considered here.

The observation of the simultaneous development of a long- and a short-wave instability mode on a vortex pair

Experiments on the stability of vortex pairs are described. The vortices (ratio of length to core diameter L/c of up to 300) were generated at the edge of a flat plate rotating about a horizontal axis in water. The vortex pairs were found to be unstable, displaying two distinct modes of instability. For the first time, as far as it is known to the authors, a long-wave as well as a short-wave mode of instability were observed to develop simultaneously on such a vortex pair. Experiments involving single vortices show that these do not develop any instability whatsoever. The wavelengths of the developing instability modes on the investigated vortex pairs are compared to theoretical predictions

Fine structure of granular banding in two-phase rimming flow

Solid–liquid two-phase flow inside a partially filled horizontally rotating cylinder is investigated. We document the observation of a new, secondary banding pattern developing in the flow when the solid phase comes out of suspension to accumulate as regularly spaced, circumferential bands on the inner cylinder wall. This secondary pattern, the fine structure, is superposed on the primary pattern which we previously described [O. A. M. Boote and P. J. Thomas, Phys. Fluids 11, 2020 (1999)]. The fine structure is characterized by each of the primary bands adopting a compound structure consisting of three individual, narrower secondary bands. New results on the influence of the physical properties of the solid phase on transitions between characteristic flow states are briefly discussed. It is reported that state-transition boundaries in the phase plane and the wavelength of the primary instability are insensitive to particle size and shape while there exist influences due to the particle density.

Effects of granular additives on transition boundaries between flow states of rimming flows

An experimental study of the rimming flow established inside a partially fluid-filled cylinder rotating around a horizontal axis of rotation is described. For the first time effects of granular additives on transition boundaries between flow states adopted by the fluid for different experimental conditions are studied. For the granule-free fluid and low filling levels we confirm results of previous authors showing that the ratio of viscous stresses and gravitational force remains constant along the transition boundaries considered. For higher filling levels our new data indicate, however, that the gravitational force becomes increasingly more important. For the solid–liquid two-phase flow our data reveal that even small amounts of granular additives can have a significant effect on a suitable parameter defined to characterize the transition boundaries. Granular additives can lead to the stabilization of states and to the extension of the parameter range over which certain states can be observed. It is sho...

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...

Rotating gravity currents: small-scale and large-scale laboratory experiments and a geostrophic model

Laboratory experiments simulating gravity-driven coastal surface currents produced by estuarine fresh-water discharges into the ocean are discussed. The currents are generated inside a rotating tank filled with salt water by the continuous release of buoyant fresh water from a small source at the fluid surface. The height, the width and the length of the currents are studied as a function of the background rotation rate, the volumetric discharge rate and the density difference at the source. Two complementary experimental data sets are discussed and compared with each other. One set of experiments was carried out in a tank of diameter 1 m on a small-scale rotating turntable. The second set of experiments was conducted at the large-scale Coriolis Facility (LEGI, Grenoble) which has a tank of diameter 13 m. A simple geostrophic model predicting the current height, width and propagation velocity is developed. The experiments and the model are compared with each other in terms of a set of non-dimensional parameters identified in the theoretical analysis of the problem. These parameters enable the corresponding data of the large-scale and the small-scale experiments to be collapsed onto a single line. Good agreement between the model and the experiments is found.

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.

The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer

A theoretical study investigating the effects of both anisotropic and isotropic surface roughness on the convective stability of the boundary-layer flow over a rotating disk is described. Surface roughness is modelled using a partial-slip approach, which yields steady-flow profiles for the relevant velocity components of the boundary-layer flow which are a departure from the classic von Karman solution for a smooth disk. These are then subjected to a linear stability analysis to reveal how roughness affects the stability characteristics of the inviscid Type I (or cross-flow) instability and the viscous Type II instability that arise in the rotating disk boundary layer. Stationary modes are studied and both anisotropic (concentric grooves and radial grooves) and isotropic (general) roughness are shown to have a stabilizing effect on the Type I instability. For the viscous Type II instability, it was found that a disk with concentric grooves has a strongly destabilizing effect, whereas a disk with radial grooves or general isotropic roughness has a stabilizing effect on this mode. In order to extract possible underlying physical mechanisms behind the effects of roughness, and in order to reconfirm the results of the linear stability analysis, an integral energy equation for three-dimensional disturbances to the undisturbed three-dimensional boundary-layer flow is used. For anisotropic roughness, the stabilizing effect on the Type I mode is brought about by reductions in energy production in the boundary layer, whilst the destabilizing effect of concentric grooves on the Type II mode results from a reduction in energy dissipation. For isotropic roughness, both modes are stabilized by combinations of reduced energy production and increased dissipation.

Evolution of ultrasonic impulses in chains of spheres using resonant excitation

It is demonstrated that broad-bandwidth ultrasonic signals containing frequency components in excess of 200 kHz can be created in spherical chains using harmonic excitation at 73 kHz. Multiple reflections created a periodic waveform containing both harmonics and sub-harmonics of the original forcing frequency, due to non-linear Hertzian contact. These discrete frequencies represented some of the many allowed non-linear normal modes of vibration of the whole chain. Excitation at a single fixed frequency could thus be used to produce wide-bandwidth impulses for different lengths of spherical chains. Experimental results were in good agreement with theoretical predictions.

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

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 is 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 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.