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A numerical description of heterogeneous propellant combustion enables us to examine the spatial and temporal fluctuations in the flow field arising from the heterogeneity. Particular focus is placed on the fluctuations in a zone intermediate between the combustion field (where reaction is important) and the chamber flow domain, for these define boundary conditions for simulations of the turbulent chamber flow. The statistics of the temperature field and the normal velocity field are described, and characteristic length scales and time scales are identified. The length scales are small compared to any relevant length scale of the chamber flow, and so the boundary conditions for this flow at any mesh point are statistically independent of those at any other mesh point. But the temporal correlations at a fixed point are significant, and affect the nature of the chamber flow in a variety of ways. We describe the fluctuations in the head-end pressure that arise because of them, and contrast these results with those calculated using a white-noise assumption.

We examine small deviations from axial symmetry in a solid-propellant rocket motor, and describe a ‘bath-tub-vortex’ effect, in which substantial axial vorticity is generated in a neighbourhood of the chamber centreline. The unperturbed flow field is essentially inviscid at modest Reynolds numbers, even at the chamber walls, as has long been known, but the inviscid perturbed flow is singular at the centreline, and viscous terms are required to regularize it. We examine perturbations sufficiently small that a linear analysis is valid everywhere (εRe small, where ε is a measure of the perturbation amplitude and Re is a Reynolds number), and larger perturbations in which a nonlinear patch is created near the centreline of radius O(√ε). Our results provide an explanation of swirl experimentally observed by others, and a cautionary note for those concerned with numerical simulations of these flows, whether laminar or turbulent.

The ignition of lean H2/air mixtures under microgravity (μg) conditions can lead to the formation of spherical premixed flames (flame balls) with small Péclet number (Pe). A central question concerning these structures is the existence of appropriate stationary stable solutions of the combustion equations. In this paper we examine an individual flame ball that is suspended in a fluid whose velocity far from the flame is steady and varies linearly in space. Detailed results are obtained for simple shear flows and simple straining flows, both axisymmetric and plane.Convection enhances the flux of heat from the flame and the flux of mixture to the flame, but because the Lewis number (Le) is less than unity the relative impact on the former is greater than on the latter. Consequently, there is a net loss of energy from the flame to the far field, and if large enough this will quench the flame. For values of shear or strain less than the quenching value there are two possible stationary solutions, but one of these is unstable to spherically symmetric disturbances of the flame ball. The radius of the other solution is unbounded as Pe goes to zero. Examination of a class of three-dimensional disturbances reveals no additional instability when the energy losses are due only to convection, but sufficiently large flame balls are unstable when volumetric heat losses from radiation are accounted for. This last result is in agreement with previous results that have been obtained for zero Pe, albeit with inadequate accounting for the flow field generated by the perturbations.

We consider the deformation of a thin thread of viscous liquid (viscida) as its ends are slowly moved together. Equations are deduced which are capable of describing the motion of the thread when the displacement of the axis from a straight line is either on the scale of the thread thickness (problem 1) or on the much larger scale of the thread length (problem 2). In the former case it is shown analytically that an arbitrary initial displacement evolves in such a way that, as the appropriately scaled time τ becomes large, the first mode of the disturbance emerges in a dominant role with an amplitude that is proportional to τ½ and independent of the initial amplitude. This provides the initial condition for problem 2, for which a numerical description is obtained.In addition, we analyse the situation when the ends of the viscida are slowly pulled apart. In this case the high frequency end of the spectrum dominates as an arbitrary disturbance decays.

The unsteady creeping motion of a thin sheet of viscous liquid as it advances over a gently sloping dry bed is examined. Attention is focused on the motion of the leading edge under various influences and four problems are discussed. In the first problem the fluid is travelling down an open channel formed by two straight parallel retaining walls placed perpendicular to an inclined plane. When the channel axis is parallel to the fall line there is a progressive-wave solution with a straight leading edge, but inclination of the axis generates distortions and these are calculated. In the second problem a sheet with a straight leading edge travelling over an inclined plane penetrates a region where the bed is uneven, and the subsequent deformation of the leading edge is followed. The third problem considers the flow down an open channel of circular cross-section (a partially filled pipe) and the time-dependent shape of the leading edge is calculated. The fourth problem is that of flow down an inclined plane with a single curved retaining wall. These problems are all analysed by assuming that a length characteristic of the geometry is large compared with the fluid depth divided by the bed slope, and all the solutions display extreme sensitivity to the data.

This paper is an investigation of MHD boundary layers in a transverse magnetic field when the magnetic Reynolds number (Rm) is small. The main purpose is to understand something about the suppression of separation by a strong magnetic field, with particular emphasis on the behaviour near a rear stagnation point. Given anO(1) inviscid flow it is shown that there is a critical value ofN, the interaction parameter, to completely suppress separation. This value is one half that proposed by Leibovich (1967), a discrepancy that is due to the non-regularity of the boundary-layer equations at a rear stagnation point, a possibility that Leibovich did not consider in his solution. Model linear equations suggest the true role of Leibovich's solution. The possibility of a viscous wake leaving the rear stagnation point is considered and it is suggested that one doesnotarise from vorticity generated in the boundary layer.