The paper examines the influence of a piston motion on the gaseous motion set up by an explosion. This is a problem of relevance not only to explosions in which the remnants of the original explosive are present, but also by the application of the hypersonic similarity law, to the steady flow at high Mach number past a blunt-nosed object with increasing thickness. In the vicinity of the piston perturbation theory breaks down and matching techniques have to be employed. A solution is given in terms of a small parameter which essentially depends on the ratio of the speed of the piston to that of the shock. Some particular cases are discussed in which the piston motion plays a similar role to the counter pressure of the undisturbed gas.

The separation of a binary gas mixture for high feed flow rates such that the E¼ vertical shear layer is nonlinear is considered. Numerical solutions for the velocity field and the temperature within the centrifuge are computed using the method originally described by Bennetts & Hocking (1973). These solutions are inputs to the separation problem which is characterized by a concentration boundary layer also of width of O(E¼). Results are presented for a wide range of parameters and the effect of thermal drive strength is examined in detail. Surprisingly the numerical results indicate that the analytical solution for the separation factor given by Conlisk, Foster & Walker (1983) may be used far outside its strict asymptotic region of validity.

This report presents a numerical study of the two-dimensional, steady and inviscid flow of a perfect gas past wedge profiles with detached shock waves for free-stream Mach numbers between 1.05 and 1.44.

Utilizing the hodograph transformation, a boundary-value problem for the mixed flow is formulated in the hodograph plane and subsequently solved by a finite-difference scheme, iterating respectively between the elliptic and hyperbolic regions. The use of boundary-fitted coordinates and a graded lattice failed to achieve satisfactory results, owing to either convergence difficulties or numerical inaccuracies introduced through the coordinate generator. On the other hand, Cartesian coordinates presented no convergence problems and yielded accurate results.

After transforming the solution back to the physical plane, the flow field between the shock wave and the limiting Mach wave is determined. A comparison of the results with experiments and other theories shows a good agreement both for the pressure distribution on the wedge and for the shock stand-off distance.

Also of special interest is a quantitative comparison of the results with the small-disturbance theory (solution of the Tricomi equation) and the limiting case of the free-stream Mach number 1.

Moreover, an example of the flow past round-nosed wedges, with and without an angle of attack, is treated using the inverse method.

A general formulation is given for the dispersion of conservative tracers in steady flow in multi-connected channels. A multi-index is used to distinguish the different routes for tracer between the source and the observation position. For each route exact formulae are obtained for the time integral, time centroid, and cross-channel average of the temporal variance. The total concentration is the superposition of the contributions from the different routes.

A thermal-creep flow of a slightly rarefied gas induced axisymmetrically around two unequal spheres is studied on the basis of kinetic theory. The spheres, whose thermal conductivities are assumed to be identical with that of the gas, for simplicity, are placed in an infinite expanse of the gas at rest with a uniform temperature gradient at a far distance. Owing to the poor thermal conductivities of the spheres, a tangential temperature gradient is established on the surfaces, and this causes a thermal-creep flow in its direction. Consequently, the spheres experience forces in the opposite direction.

The flow considered here is a low-Reynolds-number flow in the ordinary fluid-dynamic sense (except for the Knudsen layer), and the solution is obtained in terms of bispherical coordinates, with respect to which the system of equations of Stokes type is well developed. The velocity field around the spheres and the forces acting on them are given explicitly. The results show the interesting feature that the smaller sphere experiences the minimum force at a value of the separation distance that depends on the radius ratio. This is in contrast with the case of the axisymmetric motion of two spheres treated by Stimson & Jeffery (1926) in ordinary fluid dynamics at low Reynolds number.

The ultimate velocities that the spheres would have under the action of the present thermal force when they are freely suspended are also obtained by utilizing the results for the forces of axisymmetric translational problems of two spheres at low Reynolds number. For a given temperature gradient in the gas, both spheres acquire larger velocities than those they would have if they were alone, and the smaller sphere tends to move faster than the larger one in the direction opposite to the temperature gradient.

Also presented, for completeness, are the results for the sphere–plane case and for the case of eccentric spheres, the solutions for which are derived as special cases of the preceding problem of two unequal spheres.

The transient effects generated when a shock wave is suddenly disturbed by a field of cellular vortices have been studied. Both the pressure disturbance on the shock and the local shock velocity are found to be strong functions of the cell geometry. Disturbances are resolved into transient components and sinusoidal components of constant amplitude. The transients are found to die out as t−3/2, t being the interaction time, except for one particular case of the cell geometry for which they diminish as t−1/2. Furthermore, the analysis indicates that the initial magnitude of the transient components may be quite appreciable in comparison with the sinusoidal component. The theory is extended to treat the convection through the shock of a single column of vortex cells.

An exact analytic solution is derived for the perturbation of a magnetic field while exposed to an immersed, axisymmetric, azimuthal, steady current source of arbitrary distribution in the presence of a slender, electrically conducting, independently permeated, compressible jet threading the axis of symmetry, subject to an equilibrium pressure balance. A further influence is the enclosure of the magnetic field by a coaxial cylindrical wall. The steady-state result invariably exhibits an infinite discrete superposition of axially decaying terms. In addition, there arise two admissible alternatives involving a fluid parameter λ (dependent on the flow speed, sound speed and both Alfvén speeds pertaining to the jet) together with a scale parameter χ(0) (equal to twice the ratio of the cross-sectional area of the jet to that of its externally enveloping field). Provided that λ exceeds χ(0), each element constituting the current distribution induces a stationary-wave contribution confined, as a consequence of an applied radiation condition, to the upstream domain, corresponding to an upstream-directed group velocity. However, if λ is exceeded by χ(0), this upstream wave is replaced by another decaying term, acting on both sides of every current constituent, like all other decaying terms.

The utility of piston theory as a means of solving insentropic two-dimensional aerodynamic problems has been aptly demonstrated by many writers in recent years. The present treatment removes the restriction of isentropic flows, extending the applicability of piston theory to flows with strong shocks. Sample calculations for a thin biconvex airfoil are carried out in which the local flow is assumed to be isentropic and non-isentropic. Comparison of the result is made with that of the shock expansion theory of Cole, Gazley & Williams (1956).

The results of tests on an axial-flow compressor stage designed to allow operation at unusually low axial clearances are presented. The axial clearance was varied between 1 and 33 % of the blade chord whilst the compressor was running, and the stage pressure rise showed a peak at a clearance around 4 % of blade chord. The pressure rise was 8 % higher at this clearance than at 33 % of chord, with no significant change in the stage efficiency. In addition, reducing the clearance was found under some conditions to bring the stage from a stalled to a fully unstalled state. The sound output of the stage was measured at all clearances, and the results show a significant increase in the high harmonics of the blade-passing frequency at low axial clearances.