An experimental adaptation of the well-known laser-Doppler anemometry technique is developed for measuring the velocity and concentration profiles in concentrated suspension flows. To circumvent the problem of optical turbidity, the refractive indices of the solid and liquid phases are closely matched. The residual turbidity, owing to small mismatches of the refractive indices, as well as impurities in the particles, allows a Doppler signal to be detected when a particle passes through the scattering volume. By counting the number of Doppler signals in a period of time, the local volume fraction is also measured.

This new technique is utilized to study concentrated suspension flows in a rectangular channel. The general behavior of the suspension is that the velocity profile is blunted while the concentration profile has a maximum near the centre. Comparisons are made with theoretical predictions based on the shear-induced particle migration theory.

The application of Lighthill's acoustic analogy to the generation of sound by rotating surfaces with supersonic speeds results in radiation integrals in which the stationary points of the phase function – that describes the sapce-time distance between each source point and a fixed observation point – have variable positions and coalesce at a caustic in the space of source points. Here, the leading term in the asymptotic expansion of the corresponding Green's function at this caustic is calculated, both in the time and the frequency domains, and it is shown that the radiation generated by volume sources, which are steady in the uniformly rotating blade-fixed frame, has an amplitude that does not obey the spherical spreading law, i.e. does not fall off like RP–1 with the radial distance RP away from the source. Within a finite solid angle, depending on the extent of the source distribution, the amplitude of this newly identified sound decays like RP–½, so that it is stronger in the far field than any previously studied element. That this is not incompatible with the conservation of energy is because the emission time intervals associated with the volume elements of the source distribution which contribute towards the non-spherically decaying component of the radiation are by a large (RP-dependent) factor greater than the time intervals during which the signals generated by these elements are received. The contributing source elements are those whose positions at the retarded time coincide witht the locus of singularities of the Green's function, i.e. with the one-dimensional locus of points, fixed in the rotating frame, which approach the observer with the wave speed and zero acceleration along the radiation direction. Because the signals received at two neighbouring instants in time arise from distinct, coherently radiating filamentary parts of the source which have both different extents and different strengths, the resulting overall waveform in the far zone consists of the superposition of a (continuous) set of narrow subpulses with uneven amplitudes. These subpulses are narrower the larger the distance from the source.

The differences between the new results and those of the earlier works in the literature are shown to arise from the error terms in the far-field and high-frequency approximations, approximations that are inappropriate for volume sources moving supersonically.

Calculations have been performed for the inviscid hypervelocity flow of nitrogen past a 15° semi-angle sharp cone at an incidence of 30°, at an enthalpy sufficiently high to produce dissociation/recombination chemistry downstream of the bow shock wave. A spatially second-order-accurate scheme for the numerical solution of the inviscid Euler equations was used combined with the Lighthill–Freeman model of the non-equilibrium ideal dissociating gas. The computational method has been used as a ‘numerical wind tunnel’ in order to gain understanding of the interaction between the gas dynamics and the finite-rate gas chemistry. Inviscid flow has been considered to ensure that the only physical lengthscales in the flow are those associated with the chemical reactions. It was found that a chemical lengthscale Ls based on the local dissociation length behind the shock on the windward plane of symmetry is an important governing parameter of the flow. However, as the flow lengthscale becomes large and the flow approaches the limiting case of equilibrium chemistry, Ls is not the dominant chemical lengthscale. This is particularly true of the leeward flow, which contains a shock–vortex structure. A simple modelling technique has been used to determine a more appropriate lengthscale, Lr, t, for the leeward flow as the equilibrium limit is approached. This lengthscale is based on the expected equilibrium conditions behind the cross-flow shock.

A cylinder is subjected to frequency-modulated (FM) excitation and the structure of its wake is characterized in terms of the modulation frequency and the frequency deviation. It is possible to destabilize or restabilize the degree of organization of the vortical structures in the near wake and thereby substantially manipulate the spectral content, relative to the case of purely sinusoidal excitation. These processes of destabilization and restabilization are attainable by varying the frequency deviation while holding the modulation frequency constant or vice versa. A phase-locked periodicity of the nearwake response is attainable at the period of the modulation frequency, as well as at double its period. This phase-locked periodicity, or lack of it, is related to the degree of organization of the wake. The structure of the far wake is strongly dependent upon the nature of the near wake modification. Either coherent or destabilized wake structure can be induced in the far wake, at a given value of nominal excitation frequency, by employing appropriate FM excitation.

Mass transport under partially reflected waves in a rectangular channel is studied. The effects of sidewalls on the mass transport velocity pattern are the focus of this paper. The mass transport velocity is governed by a nonlinear transport equation for the second-order mean vorticity and the continuity equation of the Eulerian mean velocity. The wave slope, ka, and the Stokes boundary-layer thickness, k (ν/σ)½, are assumed to be of the same order of magnitude. Therefore convection and diffusion are equally important. For the three-dimensional problem, the generation of second-order vorticity due to stretching and rotation of a vorticity line is also included. With appropriate boundary conditions derived from the Stokes boundary layers adjacent to the free surface, the sidewalls and the bottom, the boundary value problem is solved by a vorticity-vector potential formulation; the mass transport is, in gneral, represented by the sum of the gradient of a scalar potential and the curl of a vector potential. In the present case, however, the scalar potential is trivial and is set equal to zero. Because the physical problem is periodic in the streamwise direction (the direction of wave propagation), a Fourier spectral method is used to solve for the vorticity, the scalar potential and the vector potential. Numerical solutions are obtained for different reflection coefficients, wave slopes, and channel cross-sectional geometry.

Inviscid, adiabatic, one-dimensional flow of a conducting gas in the presence of crossed electric and magnetic fields is investigated for the case where the magnetic field is generated by the current being supplied to the gas. The electrode geometry and the connections to the electrical power supply are such that the magnetic field falls to zero at the downstream end of the MHD duct. The analysis allows for magnetic Reynolds number rm to be anywhere in the range 0 to ∞ The main part of the investigation is restricted to consideration of ducts with constant spacing between electrodes.

The way in which the density of the gas varies along the duct with the changing magnetic field is analysed generally and the results are then applied to the case where gas is fed to the MHD duct from high pressure in a plenum chamber and where the duct exhausts to a region of negligible pressure. If the flow is choked by the converging entry to the duct and the magnetic Reynolds number is moderate to high, the main electromagnetic effect is for the j × B forces to accelerate the gas to supersonic speeds. As rm is reduced, ohmic heating becomes more important, and it may cause the flow to be choked at exit from the duct, giving rise to a reduction in mass flow. For certain ranges of rm and ratio of initial magnetic pressure to plenum-chamber pressure the flow may choke at a sonic point within the duct itself, while accelerating from subsonic to supersonic through the point.

Some illustrative examples of how properties vary with distance along the duct have been computed and the consequences of the analysis for MHD thrusters are explored. The magnetic forces will augment thrust per unit cross-sectional area, the essential measure of this being the drop in magnetic pressure along the duct, but there is an upper limit on the ratio of magnetic pressure to plenum-chamber pressure for flows to be possible. Flow at low magnetic Reynolds number is favoured if the object is to increase specific thrust by reducing mass flow through the duct.

Measurements of the boundary layer on an effectively infinite rotating disk in a quiescent environment are described for Reynolds numbers up to Reδ2 = 6000. The mean flow properties were found to resemble a ‘typical’ three-dimensional crossflow, while some aspects of the turbulence measurements were significantly different from two-dimensional boundary layers that are turned. Notably, the ratio of the shear stress vector magnitude to the turbulent kinetic energy was found to be at a maximum near the wall, instead of being locally depressed as in a turned two-dimensional boundary layer. Also, the shear stress and the mean strain rate vectors were found to be more closely aligned than would be expected in a flow with this degree of crossflow. Two-point velocity correlation measurements exhibited strong asymmetries which are impossible in a two-dimensional boundary layer. Using conditional sampling, the velocity field surrounding strong Reynolds stress events was partially mapped. These data were studied in the light of the structural model of Robinson (1991), and a hypothesis describing the effect of cross-stream shear on Reynolds stress events is developed.

We study the dynamic sof gas or vapour bubbles when the volume mode of oscillation is coupled with one of the shape modes through quadratic resonance. In particular, the frequency ratio of the volume mode and the shape mode is assumed to be close to two-to-one. The analysis is based upon the use of a two-timescale asymptotic approximation, combined with domain perturbation theory. The viscous effect of the fluid is included by using a rigorous treatment of weak viscosity. Through solvability conditions, amplitude equations governing the slow-timescale dynamics of the resonant modes are obtained. Bifurcation analysis of these amplitude equations reveals interesting phenomena. When volume oscillations are forced by oscillations of the external pressure, we find that the volume mode may lose stability for sufficiently large amplitudes of oscillation, and this instability may lead to chaotic oscillations of both the volume and the shape modes. However, we find that for chaos to occur, a critical degree of detuning is required between the shape and volume modes, in the sense that their natural frequencies must differ by more than a critical value. When a shape mode is forced by oscillations of anisotropic components of the external pressure, we find that chaos can occur even for exact resonance of the two modes. The physical significance of this result is also given.

In this paper, we consider the evolution of an initially small voidage disturbance in a gas-fluidized bed. Using a one-dimensional model proposed by Needham & Merkin (1983), Crighton (1991) has shown that weakly nonlinear waves of voidage propagate according to the Korteweg–de Vries equation with perturbation terms which can be either amplifying or dissipative, depending on the sign of a coefficient. Here, we investigate the unstable side of the threshold and examine the growth of a single KdV voidage soliton, following its development through several different regimes. As the size of the soliton increases, KdV remains the leading-order equation for some time, but the perturbation terms change, thereby altering the dependence of the amplitude on time. Eventually the disturbance attains a finite amplitude and corresponds to a fully nonlinear solitary wave solution. This matches back directly onto the KdV soliton and tends exponentially to a limiting size. We interpret the series of large-amplitude localized pulses of voidage formed in this way from initial disturbances as corresponding to the ‘voidage slugs’ observed in gas fluidization in narrow tubes.

The instability of the surface of discontinuity separating two streams of immiscible constant-density fluids is studied experimentally and theoretically near onset when surface tension effects are significant. Following Thorpe's original idea, a tube filled with two immiscible fluids is tilted at an angle and returned to its horizontal position to produce a nearly constant velocity difference between both streams that can be varied continuously across threshold. In order to control the wavenumber near onset, the flow is spatially forced by periodically distributing small obstacles on the upper side of the tank. When the kinematic viscosities of each fluid are nearly equal, ones observes two counter-propagating waves of equal amplitude, which cannot be explained from a vortex sheet model. A linear stability analysis of a density discontinuity embedded within a piecewise-linear velocity profile demonstrates that such waves are Holmboe modes associated with the diffusive layers above and below the interface. Good agreement is obtained between the measured and predicted values of the critical velocity difference, propagation velocity and growth factors of the waves. The instability analysis of the asymmetric velocity profile reveals that the breaking of reflectional symmetry gives rise to a single propagating wave near onset. When the kinematic viscosities of each fluid differ, the first destabilized wave is observed to propagate in the same direction as the less-viscous fluid, in agreement with the theoretical results, and the dominant direction of propagation can be manipulated by adjusting the viscosities accordingly.

This paper applies two theoretical wave models, namely the generalized channel Boussinesq (gcB) and the channel Korteweg–de Vries (cKdV) models (Teng & Wu 1992) to investigate the evolution, transmission and reflection of long water waves propagating in a convergent–divergent channel of arbitrary cross-section. A new simplified version of the gcB model is introduced based on neglecting the higher-order derivatives of channel variations. This simplification preserves the mass conservation property of the original gcB model, yet greatly facilitates applications and clarifies the effect of channel cross-section. A critical comparative study between the gcB and cKdV models is then pursued for predicting the evolution of long waves in variable channels. Regarding the integral properties, the gcB model is shown to conserve mass exactly whereas the cKdV model, being limited to unidirectional waves only, violates the mass conservation law by a significant margin and bears no waves which are reflected due to changes in channel cross-sectional area. Although theoretically both models imply adiabatic invariance for the wave energy, the gcB model exhibits numerically a greater accuracy than the cKdV model in conserving wave energy. In general, the gcB model is found to have excellent conservation properties and can be applied to predict both transmitted and reflected waves simultaneously. It also broadly agrees well with the experiments. A result of basic interest is that in spite of the weakness in conserving total mass and energy, the cKdV model is found to predict the transmitted waves in good agreement with the gcB model and with the experimental data available.

We consider the continuous separation process of a monodispersed suspension flowing axially through a rotating circular cylinder. This stationary problem can be regarded as a basic flow case of rotating mixtures in conjunction with previous studies of time-dependent flows like spin-up and batch settling in a cylinder. The ‘mixture model’ for two-phase flow is used to formulate the problem, which is solved in the range of small Ekman and Rossby numbers by asymptotic analytical methods and by a numerical code. The gradual separation of the axially injected suspension is manifested as a stationary stratification of the mixture which induces a swirl component of the velocity, in analogy with the thermal wind in the Earth's atmosphere. The presence of the azimuthal motion and induced secondary flow due to Ekman-layer pumping clearly influences the character of the stratification. Analytical and numerical results are in excellent agreement.

The energetics of oscillating lifting surfaces in two and three dimensions is calculated by the use of integral conservation laws in inviscid incompressible flow for general and harmonic transverse oscillations. Wing deformations are prescribed as a function of time and total thrust is calculated from the momentum theorem, and energy loss rate due to vortex shedding in the wake is calculated from the principle of conservation of mechanical energy. Total power required to maintain the oscillations and hydro-dynamic efficiency are also determined. In two dimensions, the results are obtained in closed form. In three dimensions, the distribution of vorticity on the lifting surface is also required as input to the calculations. Therefore, unsteady lifting-surface theory must be used as well. The analysis is applicable to oscillating lifting surfaces of arbitrary planform, aspect ratio and reduced frequency and does not require calculation of the leading-edge thrust.