Spatially localized magnetoconvection

Numerical continuation is used to compute branches of time-independent, spatially localized convectons in an imposed vertical magnetic field focusing on values of the Chandrasekhar number Q in the range 10 < Q < 103. The calculations reveal that convectons initially grow by nucleating additional cells on either side, but with the build-up of field outside owing to flux expulsion, the convectons are able to transport more heat only by expanding the constituent cells. Thus, at large Q and large Rayleigh numbers, convectons consist of a small number of broad cells

An experimental investigation of the recirculation zone formed downstream of a forward facing step

An experimental investigation of the recirculation zone formed downstream of a forward facing step immersed in a turbulent boundary layer has been undertaken using particle image velocimetry. Bluff body flow is observed with the fixed separation point located at the leading edge of the step. The recirculation region dimensions are characterised over a range of Reynolds numbers (1400–19 000), with Reh based on the step height and the free stream velocity. Turbulent perturbations are produced in the free shear layer which develops between the recirculating flow close to the step and the free stream flow. Contour maps of amplification factor, streamwise perturbation velocity and Reynolds stresses are constructed, providing insight into optimal placement of structures within such topographical features. The mechanisms affecting the reattachment distance, namely the turbulent mixing within the boundary layer and the velocity deficit in the boundary layer, are discussed

Magnetohydrodynamic convectons

Numerical continuation is used to compute branches of spatially localized structures in convection in an imposed vertical magnetic field. In periodic domains with finite spatial period, these branches exhibit slanted snaking and consist of localized states of even and odd parity. The properties of these states are analysed and related to existing asymptotic approaches valid either at small amplitude (Cox and Matthews, Physica D, vol. 149, 2001, p. 210), or in the limit of small magnetic diffusivity (Dawes, J. Fluid Mech., vol. 570, 2007, p. 385). The transition to standard snaking with increasing domain size is explored

Weak-inertial flow between two rough surfaces

“Oseen–Poiseuille” equations are developed from an asymptotic formulation of the three-dimensional Navier–Stokes equations in order to study the influence of weak inertia on flows between rough surfaces. The impact of the first correction on macroscopic flow due to inertia has been determined by solving these equations numerically. From the numerical convergence of the asymptotic expansion to the three-dimensional Navier–Stokes flows, it is shown that, at the macroscopic scale, the quadratic correction to the Reynolds equation in the weak-inertial regime vanishes generalizing a similar result in porous media

Characterisation of a horizontal axis wind turbine’s tip and root vortices

The vortical near wake of a model horizontal axis wind turbine has been investigated experimentally in a water channel. The objective of this work is to study vortex interaction and stability of the helical vortex filaments within a horizontal axis wind turbine wake. The experimental model is a geometrically scaled version of the Tjæreborg wind turbine, which existed in western Denmark in the late 1980s. Here, the turbine was tested in both the upwind and downwind configurations. Qualitative flow visualisations using hydrogen bubble, particle streakline and planar laser-induced fluorescence techniques were combined with quantitative data measurements taken using planar particle image velocimetry. Vortices were identified using velocity gradient tensor invariants. Parameters that describe the helical vortex wake, such as the helicoidal pitch, and vortex circulation, were determined for three tip speed ratios. Particular attention is given here to the root vortex, which has been investigated minimally to date. Signatures of the coherent tip vortices are seen throughout the measurement domain; however, the signature of the root vortex is only evident much closer to the rotor plane, irrespective of the turbine configuration. It is postulated that the root vortex diffuses rapidly due to the effects of the turbine support geometries

The interaction between flow-induced vibration mechanisms of a square cylinder with varying angles of attack

This study examines the influence of angle of attack of a square section cylinder on the cylinder’s flow-induced vibration, where the direction of the vibration is transverse to the oncoming flow. Our experiments, which traversed the velocity–angle of attack parameter space in considerable breadth and depth, show that a low-mass ratio body can undergo combinations of both vortex-induced vibration and galloping. When the body has an angle of attack that makes it symmetric to the flow, such as when it assumes the square or diamond orientation, the two mechanisms remain independent. However, when symmetry is lost we find a mixed mode response with a new branch of vortex-induced oscillations that exceeds the amplitudes resulting from the two phenomena independently. The oscillations of this higher branch have amplitudes larger than the ‘upper branch’ of vortex-induced vibrations and at half the frequency. For velocities above this resonant region, the frequency splits into two diverging branches. Analysis of the amplitude response reveals that the transition between galloping and vortex-induced vibrations occurs over a narrow range of angle of incidence. Despite the rich set of states found in the parameter space the vortex shedding modes remain very similar to those found previously in vortex-induced vibration

Experimental vortex breakdown topology in a cylinder with a free surface.

The free surface flow in a circular cylinder driven by a rotating bottom disk is studied experimentally using particle image velocimetry. Results are compared with computational results assuming a stress-free surface. A dye visualization study by Spohn et al.. We confirm the existence of a transition where the top of the breakdown bubble crosses from the axis to the surface, which has previously only been found numerically. We employ a technique by Brøns et al

A numerical study of an inline oscillating cylinder in a free stream

Simulations of a cylinder undergoing externally controlled sinusoidal oscillations in the free stream direction have been performed. The frequency of oscillation was kept equal to the vortex shedding frequency from a fixed cylinder, while the amplitude of oscillation was varied, and the response of the flow measured. With varying amplitude, a rich series of dynamic responses was recorded. With increasing amplitude, these states included wakes similar to the Kármán vortex street, quasiperiodic oscillations interleaved with regions of synchronized periodicity (periodic on multiple oscillation cycles), a period-doubled state and chaotic oscillations. It is hypothesized that, for low to moderate amplitudes, the wake dynamics are controlled by vortex shedding at a global frequency, modified by the oscillation. This vortex shedding is frequency modulated by the driven oscillation and amplitude modulated by vortex interaction. Data are presented to support this hypothesis

Spatially localized binary fluid convection in a porous medium

The origin and properties of time-independent spatially localized binary fluid convection in a layer of porous material heated from below are studied. Different types of single and multipulse states are computed using numer- ical continuation and the results related to the presence of homoclinic snaking of single and multipulse states

Vortex-induced vibration of a square-section cylinder with incidence angle variation

Vortex-induced vibration (VIV) occurs when vortex shedding from a body results in fluctuating forces that, in turn, cause the body to vibrate. This can result in undesired large-amplitude vibrations leading to structural damage or catastrophic failure. While much has been done on the VIV of a circular cylinder less has been done on other canonical bluff bodies, such as rectangular cylinders. The present experimental work studied the VIV of a square cross-section cylinder in a water channel, with three different incidence angles (α 15 , 30 and 45 ). The influence of geometry on the body’s oscillation amplitude and frequency response, and its wake structure over a range of reduced velocity were investigated. The oscillations were measured at a low mass damping ratio of m ζ 0.013 , which was comparable to the circular cylinder system with m ζ 0.013 studied by Khalak & Williamson (1997)1. The comparison showed that the incidence angle change had a significant impact on amplitude response. For α 15 the maximum non-dimensional amplitude was A 1.11, 10% larger than the circular case, as shown in figure 1 (a). Asymmetric amplitudes with respect to the cylinder’s equilibrium position in still water were observed in α 15 and 30 cases, due to the one-sided nature of the mean lift force. Compared with the circular cyinder, the square cylinder locked on to the structural natural frequency in water over a smaller reduced velocity regime. An oscillation frequency drop was found in the α 15 case, during which the cylinder experienced its largest amplitude response. The wake structure for each case in the different flow regimes was determined using particle image velocimetry and will also be presented