This paper is concerned with a numerical analysis of axisymmetric gas-particle two-phase flows. Underexpanded supersonic free-jet flows and supersonic flows around a truncated cylinder of gas-particle mixtures are solved numerically on the super computer Fujitsu VP-400. The gas phase is treated as a continuum medium, and the particle phase is treated partly as a discrete one. The particle cloud is divided into a large number of small clouds. In each cloud, the particles are approximated to have the same velocity and temperature. The particle flow field is obtained by following these individual clouds separately in the whole computational domain. In estimating the momentum and heat transfer rates from the particle phase to the gas phase, the contributions from these clouds are averaged over some volume whose characteristic length is small compared with the characteristic length of the flow field but large compared with that of the clouds. The results so obtained reveal that the flow characteristics of the gas-particle mixtures are widely different from those of the dust-free gas at many points.

The inertial migration of a small sphere in a Poiseuille flow is calculated for the case when the channel Reynolds number is of order unity. The equilibrium position is found to move towards the wall as the Reynolds number increases. The migration velocity is found to increase more slowly than quadratically. These results are compared with the experiments of Segré & Silberberg (1962 a, b).

An asymptotic theory describes the stationary instability of convective flow between differentially heated vertical planes at large Prandtl numbers. The theory is concerned with the structure for A [Gt ] 1 where A is a Rayleigh number based on the horizontal temperature difference and the distance between the planes. As such it is relevant to the instability of flow in a vertical slot of aspect ratio h [Gt ] 1 where the convective regime corresponds to order-one values of a non-dimensional parameter γ which partly depends on the vertical temperature gradient generated in the slot and can be approximated by γ4 = A/8h. Instability is shown to set in at a critical value of γ that compares well with experimental observation. The lower branch of the neutral curve conforms to a boundary-layer type approximation while the upper branch has a critical-layer structure midway between the planes which becomes fully developed as the first reversal of the vertical velocity of the base flow is encountered near the centreline.

The secondary flow patterns induced by a differentially rotating lid in a partially filled, rapidly rotating, tapered cylinder have been investigated. Using a new laser-Doppler velocimeter system capable of making measurements in the rotor frame of reference, the radial dependence of the azimuthal and axial velocity components was measured at two axial positions in the rotor. A linear, asymptotic analysis and a finite-difference simulation were made for comparison. The latter was performed on a boundary-fitted computational mesh so that the slanted rotor wall and the sagging free surface could be accommodated in the model. The agreement between the experimental and numerical results was excellent for the azimuthal velocity component and good for the axial component. Of particular interest is the modified E½ boundary layer on the slanted wall, a feature which is not present with a vertical sidewall.

Preliminary tests have been carried out on short circular cylinders with both ends free. Drag force is measured across the range 6 × 104 < Re < 2.6 × 105 for cylinders of length to diameter ratio L/D between 1 and 10. The effect of hemispherical ends is also investigated. A kind of periodic vortex shedding is found in the range 2 < L/D < 8. The oil-film surface flow visualization shows that the ‘eyes’ near the free ends (regions of low pressure) gradually disappear as L/D is reduced to 3. An asymmetric flow pattern is established for very short cylinders (L/D < 3). The detailed measurements of pressure distribution along and across models shows asymmetries of minimum and base pressures along the span. The asymmetric flow produces yawing and rolling moments which are also measured.

The European Mechanics Colloquium number 237 was held at the Institut de Mécanique Statistique de la Turbulence (Université d'Aix-Marseille II) from 18 to 21 July 1988. This was the first meeting to consider the influence of density variations on turbulent flows for both non-reacting and reacting flows in a variety of configurations. Several new experiments, computational models and theoretical analyses were presented for non-reacting flows. All these approaches showed the marked effects of density variations on coherent structures in turbulent shear flows. It was found that the approximate models used for turbulent Reynolds stresses in homogeneous flows do not need to be changed for the mean flow field but predictions for variances and correlations are still rather uncertain: in fact experimental results providing such information in variable-density flows are rare. The special problem of measuring turbulence in flows with density variations was discussed. In the discussions it was agreed that there are in fact strong similarities in the effects of density gradients on the dynamics of non-reacting flows and reacting flows despite the differences in the distributions of density gradients. Participants at the meeting from industry emphasized the importance of these flows to many different kinds of industrial and environmental problems.