The motion of a solid piston between the driver and test gases in a closed shock tube is studied. In particular, the piston stopping distance, i.e. the total length required to bring the piston to a stop, is calculated for various experimental conditions. Before the stop, the moving piston compresses the test gas, at first with its induced shock and then further with its own kinetic energy through the successive shock reflections. Thus, the moving piston can produce a reservoir of compressed gas with higher enthalpy than a shock of similar strength without the piston. Normal shock-wave theory for an ideal gas is used until the first reflected shock meets the piston. The subsequent shock reflections are approximated by a continuous compression in thermodynamic equilibrium. The calculated values for the piston stopping distance are found to compare favourably with the available experimental data, indicating that the approximations used are reasonable. Peak pressure and temperature of the compressed test gas are computed, and the effect of bleeding the gas reservoir through a nozzle is also included.

The repetitive pattern of buckling, common to most theoretical analyses, is shown to be itself unstable. An approximate but very simple analysis is presented to describe the true buckling behaviour.

From an investigation of published experimental results, it appears that three types of propagating stall cells occur on isolated blade rows. On stationary blade rows, and rotating rows which have the highest blade incidence at the tip, the speed of propagation seems to depend on a parameter based on the blade section near the leading edge, and in some experiments marked changes in this speed have been observed to coincide with changes in the form of stall on the individual blades. For rotating rows with the highest incidence at root or mid-section the speed of stall propagation lies within a fairly limited range and shows no dependence on the blade geometry. When the incidence is increased well beyond that at which stall first occurs, the stall cell pattern on most rotating rows changes from multiple cells to one or two of very large amplitude, with a marked change in speed of propagation.

A simple method of calculating the flow in turbo-machines with flared annuli is given. Approximate solutions are derived for the compressible swirling flow between the blade rows. Originally received February 1964.

Numerical solutions are obtained for the one-dimensional radial flow of a compressible fluid between parallel discs. A general discussion of the variations of pressure, density, velocity and temperature along the radius of the disc is then given. The present investigation covers both subsonic and supersonic flows, a range not previously covered in the literature.

The paper provides relationships between the buckling resistance of clamped transversely stiffened plates and the flexural rigidity of the stiffeners for various values of the ratio of torsional rigidity to flexural rigidity. Results are presented for four different stiffener spacings.

An integral part of the study of supersonic combustion is the investigation of supersonic turbulent mixing of dissimilar fluids. Experimental results obtained in the course of investigating the turbulent mixing zone between supersonic streams of CO3 and air are presented. Good correlation between observation and available theories has been obtained in terms of the parameter ξ=σy/x. The correlating parameter σ defines the spreading rate of the mixing zone. The available theories, though not developed for these specific conditions, are shown to be applicable to the turbulent mixing of supersonic streams.

The correlating parameter σ was determined for three different combinations of internal and external flow Mach numbers. The values found for σ were 18, 16·3, 15·3 for constant external Mach number 1·62 and internal Mach number 1·62, 1·53, 1·47 respectively. The magnitudes of σ showed the expected trend, that is the higher value implies the least divergence of the mixing boundaries.

The reasonable agreement with experiment and the simplicity of application of the momentum integral form of solution would appear to favour the use of this approach for the theoretical prediction of the mixing conditions.

Donnell type equilibrium and stability equations are derived for stiffened thin conical shells. The stiffeners are considered closely spaced and are therefore assumed to be “distributed” over the whole surface of the shell. In the proposed theory the stiffeners and their spacing may vary in any prescribed manner, but here only equal and equally spaced stiffeners are dealt with. The force- and moment-strain relations of the combined stiffener-sheet cross section are determined by the assumption of identical normal strains at the contact surface of stiffener and sheet.

The stability equations are solved for general instability under hydrostatic pressure by the method of virtual displacements. The solution used earlier for unstiffened conical shells, which satisfies some of the boundary conditions of simple supports only approximately, is again applied here. The effect of this incomplete compliance with boundary conditions is shown to be negligible by consideration of “boundary work”. The solution proposed for stiffened conical shells involves the concepts of “correcting coefficients” and minimisation of corresponding “error loads”.

Typical examples are analysed and the effect of eccentricity of stiffeners is investigated. Simplified approximate formulae for the critical pressure of frame-stiffened conical shells are also proposed.

A method of deriving the finite-difference equations to be applied at or near flexural discontinuities in plates subjected to bending is suggested. Such equations are presented for the case when a plate consists of two regions of different flexural rigidities, the boundary between the regions being formed by straight lines meeting at right angles.

The heat of ablation of glassy materials can be improved by surface-active agents. The degree of improvement is more pronounced at high flight velocities and depends strongly on the coefficient of diffusion in the liquid layer. The analysis is carried out near the stagnation point of blunt bodies for steady state ablation.

The growth of a line vortex with time and the spread of a trailing vortex behind a wing due to turbulence are considered. It is shown that the eddy viscosity for this type of motion may be taken to be proportional to the circulation round the vortex and the solution is then similar to the solution for the growth of a vortex in laminar flow. The method is applied to calculate the distance behind a wing for which the trailing vortices will touch one another.