A comparative study is made of a recent theoretical approach to the problem of predicting the supersonic, turbulent base pressure and of the experimental evidence. The theory is based on the Chapman-Korst flow model of separated flows with a modified recompression process. Due allowance can be made for the presence of the initial boundary layer, with the limitation that its thickness must be less than about one step height at low Mach numbers, dropping to about one third of a step height at M=3·0. Fairly good agreement between the predicted and measured base pressure can be obtained although a predicted Reynolds number effect is not observed. The absence of this Reynolds number effect is. discussed in the light of recent experiments on flow mixing.

A rational method of lumping inertia forces by considering the equilibrium of the vibrating element has been developed. This method requires the selection of a suitable displacement distribution function over each element. The closer it is to the true mode shape, the better the result.

Considering a linear displacement distribution function over each element, the natural frequencies and mode shapes are obtained for transverse vibrations of a stretched string, torsional vibrations of a cantilever shaft (fixed at one end and free at the other) and transverse vibrations of a uniform cantilever beam. It is found that, even with a few elements, a reasonable accuracy can be obtained in the natural frequency, while the mode shapes are exact in the first two cases and almost exact in the third at the points considered.

In Appendix A, it is shown that, for the torsional vibration of a uniform cantilever shaft and with a linear displacement function over each element, this method gives exact mode shapes at the points considered, while the natural frequency is always an upper bound and the error follows an inverse square law when the number of elements considered is large.

In Appendix B, it is shown that a combination of this method with the conventional lumped mass method reduces the error in the natural frequency. The error follows an inverse fourth-power law when the number of elements considered is large and the mode shapes are exact at the points considered.

This method can incorporate better displacement distribution functions, to obtain better results and convergence, and can easily be adapted to the buckling of columns, the vibration of beam columns and forced vibrations, as well as more complicated problems such as the vibration or buckling of plates and shells.

Mixing systems have many applications in gas turbines and aircraft jet propulsion, e.g. mixing zones in combustion chambers, ejectors for jet lift thrust augmentors and supersonic propulsion systems. A further application similar to that of combustion chamber mixing is that of mixing the cold and hot exhausts of a bypass jet engine. These are both characterised by mixing at constant static pressure and approximately constant total pressure as opposed to the more general case of unequal pressures in ejector systems (Fig. 1).

The exhaust mixing process as used in Rolls-Royce bypass jet engines, e.g. Spey and Conway, enables the potential of the bypass principle, in terms of minimum weight and fuel consumption, to be exploited by a simple practical device.

This is achieved by mixing the two streams in a common duct of fairly short dimensions with a corrugated metal interface on the inlet side. The consideration of these practical systems forms the main topic of this paper.

Most hypervelocity tunnels presently make use of conical or wedge type nozzles which produce source-type flow non-uniformities in the test section. The present paper considers the effects of such free-stream non-uniformities on the flow fields about slender axisymmetric cones. The inviscid flow is considered within the framework of the Newtonian expansion procedure of Cole and simple expressions are obtained for the flow field properties in the shock layer. This inviscid analysis predicts that a free-stream gradient of a magnitude typical of present hypervelocity test facilities can cause sizeable reductions in surface pressure and increased shock-layer thickness at the aft end of long slender conical models. The cone pressure, accounting for the viscous-inviscid interaction, is obtained by applying the inviscid analysis in tangent-cone fashion to the effective body (i.e. physical cone plus boundary-layer displacement thickness). Cheng’s simple equation is used to approximate the hypersonic boundary-layer development. Large increases in the boundary-layer thickness at the aft end of the model are predicted as a consequence of the source flow effects. The analyses agree well with experimental measurements of surface pressure and boundary-layer thickness made on a 5° half-angle cone tested in the Republic 24 inch Longshot I hypervelocity shock tunnel.

The stress-concentration factor is calculated for an infinite plate in tension containing a doubly-symmetrical hole whose boundary consists of parts of three intersecting circles. A suggestion is made for modifying the results to apply to a strip.

A theoretical treatment is considered for the flow past slender wings in sudden plunging motion when leading-edge vortices are present. A form of slender-wing theory is used and, although the basis of the theory involves no restriction on compressibility, it has proved possible to make calculations only for an incompressible fluid.

Use is made of an analogy between the unsteady flow and related steady flows. In the incompressible case, an extension of the theory of Brown and Michael is given to determine the strength of the vortex and its path from the leading edge to the final steady-state position. A qualitative comparison with experiment is made of the instantaneous position of the vortex. In a typical case the lift is calculated to remain within one per cent of its final value after the vortex strength has reached 55 per cent of its final value.