By considering the equations of motion it has been shown that the flow in the outer part of a two-dimensional, curved, turbulent wall jet is approximately self-preserving if the ratio of jet thickness to wall radius of curvature is constant along the jet. This condition is satisfied for a jet blowing over a surface of logarithmic spiral profile, for which the radius of curvature R increases linearly with distance s along the wall.

Measurements of velocity profiles and rates of growth of wall jets for surfaces with curvature ratios and 1 are presented. These are compared with solutions obtained using an eddy viscosity theory, and with the flow of jets round circular cylinders. The measured jets are found to be approximately self-preserving in form, and to have rates of growth which are much larger than the jets on circular cylinders with corresponding values of s/R.

The paper deals with a class of shock-wave systems that are of importance in the design and operation of supersonic intakes. It is shown that, when n− 1 wedge shocks, all of the same family, meet at a point, together with a tail shock and a bow shock, then the equations of motion which describe the flow near the shock confluence or junction are reducible to a polynomial equation of degree 10. Numerical results are obtained for the special case of the four-shock confluence and it is shown that, the number of solutions of physical interest, m4, may be 0, 2 or 4. It is found that the m4=0 solution can be interpreted physically in three different ways. These are a Guderley type flow, a confluence of three shocks with a Prandtl-Meyer expansion fan or the appearance of a shock system containing more than one confluence point. The methods developed also permit the discussion of multi-confluence wave systems and a number of examples are given. Finally, the Prandtl-Meyer compression fan is brought within the scope of the method by approximating it with a system of shock waves of weak intensity and minimum entropy.

A theoretical study is made of the aerodynamics of wings executing simple harmonic oscillations. The wings considered are slender and infinite-simally thin; they may have curved leading edges and be cambered, but their cross sections must be straight lines. The value of the reduced frequency is assumed to be such that the flow is governed by the two-dimensional Laplace equation.

Leading-edge separation is simulated by a line vortex joined to the leading edge by a cut. The strength and position of the vortex and the values of the generalised forces can be determined by the theory. Results have been calculated for flat delta wings and a flat gothic wing; they are in reasonable agreement with experiment.

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.

The paper treats the general problem of the response to multiple random excitation of a system having n degrees of freedom. Analysis is developed which connects the spectral density matrix of a set of generalised coordinates with that of corresponding generalised forces, and makes explicit the contributions of the various normal modes. The case of two degrees of freedom is considered in detail. The importance of cross-correlations between modes is shown by determining their effects on spectra and on mean-square response.

This paper presents an approach to the determination of structural member sizes to provide minimum weight under a number of load conditions consistent with specified limitations on stress and displacement. The procedure amalgamates the disciplines of matrix displacement analysis and operations research into a scheme suitable for automatic digital computation.

This paper presents the application to a number of structural design problems of a procedure for determining minimum weight member sizes. Included are examples of trussed and stiffened plate structures and experience with computational times for a wide range of problem sizes.

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.

Jet drag, defined as the form drag associated with jet entrainment in otherwise inviscid fluid, has been analysed by replacing a two-dimensional incompressible jet with a suitable continuous distribution of sinks. Exact solutions for the jet drag, with the flow incompressible and the jet turbulent, are presented for uncambered struts of various shapes (including an ellipse and a circular cylinder), various thickness ratios, and with blowing slots of various widths in both quiescent and uniform streaming flow. In uniform streaming flow the jet is blowing in the direction of the external flow. The extension of the theory to cross-stream blowing (as in the jet flap) is discussed.

The present theory compares favourably with the few available experimental results when the ratio of jet velocity to streaming-flow velocity is sufficiently large.

Experiments are described on the interaction of the shock wave generated by a wedge in a supersonic wind tunnel with the turbulent boundary layer on the side wall. It is shown that the onset of separation appears to be largely affected by the action of streamwise vorticity in the interaction region. A simple approximate theory based on this concept shows reasonable agreement with the experimental results. Comparisons have been made with two-dimensional interactions of normal shocks and boundary layers, but they did not produce any conclusive results.

A simple general expression is obtained for the rate of change of generalised aerodynamic damping coefficients with respect to frequency parameter in the limit as frequency tends to zero. The expression is directly proportional to aspect ratio and does not depend explicitly on Mach number. The result is consistent with calculated pitching derivatives from finite-frequency theory.

This extension of quasi-steady theory is applied to determine the leading transient term of the asymptotic expansion for large time of generalised forces due to an indicial upwash field. The expansion has direct relevance to the use of quasi-steady aerodynamic derivatives in the field of stability and control.

A study of shock tube operation with free-piston compression of the driver gas is presented. It is shown theoretically and experimentally that shock Mach numbers exceeding 30 in air may be obtained with an apparatus of moderate size. The operating limitations imposed by the maximum pressures allowed in the apparatus, by the ratio of the volume of the shock tube to the volume of the compression tube, and by the maximum pressure available for driving the piston are all explored theoretically. The compression process is studied experimentally, and results for three different compression tubes are used to indicate empirical rules for maximising the efficiency of the compression process. Streak photographs of the movement of the luminous gas behind the shock wave in a 1 in diameter shock tube are used to demonstrate the quality of the shock-wave motion produced.

This paper contains a theoretical study for an idealised ground effect wing, both tips of which are close to the ground. The wing is assumed to be a simple semicircular lifting line in a transverse plane and the fluid is assumed incompressible and inviscid. When the gap between the tips and the ground tends to zero, the flow velocity through it becomes infinite. This fact is unrealistic and seems to be the reason why the theoretical ground effect is in error.

An approximate method is presented for the calculation of heat transfer rates to cooled turbine blades. The method is based on a combination and extension of methods which have been developed in recent years for the calculation of the skin friction and heat transfer coefficients on wings in high speed flight. The use of the method is demonstrated by application to a specific cascade for which an experimental determination of overall heat transfer coefficient is known. Very close agreement with the experimental results is found over the range of Reynolds number tested. The calculated distribution of local heat transfer coefficient indicates that local pressure gradients have a marked effect on the heat transfer. A first-order estimate of the effect of blade cooling on the rate of mass flow through a blade passage shows that an increase of the order of one per cent in the mass flow rate may be obtained by a reasonable degree of blade cooling.

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.

Non-symmetric response of elastic shells to localised impact loads is studied. Closed-form solutions for the response to four particular kinds of pulse shapes are given. Experimentally measured values of the strain response of a cylinder to impact loads are obtained which compare satisfactorily with theoretical predicted values.

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.

The paper presents a solution of the non-linear problem of the deformation of slender rectangular plates which are stiffened along their edges by elastically compressible stiffeners flexible in the plane of the plate. The webplate is assumed to be simply-supported along its contour. Numerical results showing the effect of flexural and normal rigidity of stiffeners are given for a square webplate loaded by shear and compression.

The possible steady rates of roll of an aeroplane are determined in the case when inertia cross-coupling is present. This phenomenon not only changes the simple linear relationship between aileron angle and rate of roll, but may lead to more than one possible rate of roll for a given aileron angle. Simplified equations of motion are given for the cases in which the rolling takes place (a) from level flight, (b) during a pull-out manoeuvre. In both cases, these equations, which are non-linear, are solved numerically for typical examples. The static stability of the possible steady motions is considered in detail, and the dynamic stability is determined in the numerical examples.