Two methods of analysis are developed for the unsteady wave flow through axial turbomachinery of high hub-tip ratio. In the first method, the machine is supposed to consist of an infinite number of small stages. Differential equations for the instantaneous values of flow properties are derived which may be solved directly or by the method of characteristics. Conditions for wave propagation are discussed. Secondly, a model is used in which actuator discs replace the stages and the flow is axial between the stages. This is a good approximation in many compressors in which the leaving angle from the stators is small. Again the method of characteristics may then be used for solving the equations of unsteady flow between the discs.

The stability of a two-dimensional wall jet was studied theoretically and experimentally. As a result of the linear stability calculation, it was found that one eigenmode is separated into two modes when the Reynolds number is large, and inside a neutral stable curve in the α, R-plane there exists another neutral curve enclosing a stable region. Experimental results of small disturbances were compared with calculated results; agreement between them was satisfactory. It was found, further, that subharmonics of a predominant disturbance velocity component appear in the non-linear region.

The paper develops and extends the calculation method of Stratford, for flows in which a Blasius type boundary layer reacts to a sharp unfavourable pressure gradient. Whereas even the more general of Stratford’s two formulae for predicting the position of boundary-layer separation is based primarily upon an interpolation between only three exact solutions of the boundary layer equations, the present proposals are based upon nine solutions covering a much wider range of conditions. Four of the solutions are for extremely sharp pressure gradients of the type studied by Stratford, and five are for more modest gradients. The method predicts the position of separation extremely accurately for each of these cases.

The method may also be used to predict the detailed distributions of skin friction, displacement thickness and momentum thickness, and does so both simply and accurately.

A class of dynamic sailplane winch-launch trajectory problems for maximum altitude is formulated. Numerical solutions are presented for representative values of maximum allowed lift coefficient and cable acceleration. The optimal trajectory is shown to consist of a climb-dive-climb sequence. An inequality constraint on cable retraction speed is also imposed and results in more realistic trajectories.

This paper presents results of an investigation of the wake flow of a series of two-dimensional bluff bodies with different boundary-layer separation angles. These results are compared with the results of an earlier investigation of a similar series of axisymmetric bodies. It is found that when the same length scales characterising the wakes that were proposed for the axisymmetric case are used in the current investigation, then there is good agreement between the two cases in the variation of the length scales with boundary-layer separation angle. The universal Strouhal number previously proposed for axisymmetric bodies is derived for the two-dimensional bodies under investigation and is found to remain a constant for the different bodies, but at a different numerical value from that found for the axisymmetric bodies.

Measured stability characteristics in a radial wall jet were compared with calculated results for a two-dimensional wall jet. It was found that the stability of the radial wall jet is similar in many respects to that of the two-dimensional wall jet. An exception is that the local amplification rate of the disturbance velocity is much higher than in the two-dimensional case. It was also found that quarter-harmonics appear in the non-linear region, as well as half-harmonics, and that their amplitude distributions show profiles similar to that of the fundamental component. Further, vortex patterns were visualised in water flow, and results corresponding to measurements in air flow and to the linear stability calculation were obtained.

An approximate method is presented for estimating the normal-force and pitching-moment characteristics (including the effects of wing-body interference) of wings mounted on bodies. A pair of wings placed side by side can be specified which, when operating at a certain angle of attack different from the geometrical angle of attack, have the same aerodynamic properties as the wings in the presence of the body. The equivalent wings and effective angle of attack are determined, and these enable the wing-body normal force and pitching moment to be estimated for wing-body combinations at angles of attack up to 90°. Comparisons made with the results of a specially conducted series of experiments on rectangular and delta planform wing-body combinations have provided gratifying supporting evidence for the theory.

Estimates are also made of the normal force and pitching moment produced by two cone-cylinder bodies over the angle of attack range 0° to 90°. These estimates, when added to the wing-body normal-force and pitching-moment estimates, have resulted in a set of longitudinal aerodynamic characteristics which are generally close to those found experimentally. The method appears to have application in the preliminary design phase for slewing missiles.

This Note proposes a restriction on possible solution procedures for thin-shock-layer theory. This restriction has been widely violated in solutions presented hitherto, although with negligible error apparently. Those cases are indicated where failure to apply the restriction leads to definite errors.

Measurements of static pressure across the boundary layer on the wall of a circular cylinder with flow parallel to its axis display wall-interference effects which exceed corrections due to turbulence by almost an order of magnitude. Two different types of static pressure probe were investigated and gave different pressure distributions in the same boundary layer.

An alternative method of treating the boundary conditions for wing and body flow problems is developed and a detailed analysis for the flow around two-dimensional aerofoils is given. The basis of the method is the concept of an analytic continuation of the exterior flow to give a fictitious interior flow and a modified problem which can be solved using the ideas of thin-wing theory. The detailed analysis for flows described by the linear Prandtl-Glauert potential equation is given. The results obtained for several examples are satisfactory. The application of the theory to continuous and discontinuous transonic flows is outlined.

The paper suggests a simple method of generating intermittent reservoir conditions for an intermittent, cryogenic wind tunnel. Approximate performance estimates are given and it is recommended that further studies be made because this type of tunnel could be valuable in increasing the opportunities for research at high Reynolds numbers.

An algorithm is described for solving the partial differential equations governing inviscid, incompressible, irrotational and axisymmetric flow in order to obtain duct wall shapes from prescribed wall velocity distributions. Equations of motion are formulated with distances from and along the axis of symmetry as dependent variables. A velocity potential and Stokes stream function are employed as independent variables. A numerical method based on the iterative solution of finite-difference equations on a non-uniform mesh is presented. The residuals obtained from calculations with differing mesh sizes, for the two examples described, indicate that the proposed method gives satisfactory solutions to the specified design problem.

Based on computing efficiency, a comparison is made of three different ways of representing the chordwise variation of bound vorticity for use in panel methods. Because of expense, the two-dimensional analogues of the three-dimensional models were used and the results assumed to hold in both situations. A constant panel of vorticity is found to have inherent difficulties which make it unattractive to use. A linearly varying vorticity model is found to be best but a model using line vortices is almost as good and, moreover, simpler to use.

Results obtained by hot-wire measurements in a turbulent jet are presented for the cases where the jet issues into a co-flowing free stream and, for comparison, where the jet issues into quiescent air. The results obtained in the former show some agreement with other workers, but they are more extensive, including measurements of microscales and macroscales. The results also suggest that the presence of a free stream reduces the rate of decay of the longitudinal turbulent component of velocity, which has the effect of increasing the skewness of the eddy structure.

Following a brief introduction, an examination is presented of the factors which define fracture toughness, resistance-curve relationships and the extent of stable crack extension in thin-sheet failure. Tests have been performed on three aluminium alloys to establish the variations in the shape of resistance curves, using both compliance-indicated and measured absolute values of crack length in compact tension specimens and centre crack sheets. The results show that both the toughness and the resistance curves of the two specimen types are different and that these differences cannot be explained wholly by consideration of crack tip plastic zone sizes.

Evidence is presented to show that the universal law of the wall has a wider range of validity than the assumption l = ky, with k a universal constant. If an effective value of k is defined for the wall region its value is shown to vary between wide limits, and keff can be correlated with other parameters describing the flow in the wall region.

A free-vortex flow over a stationary disc produces a boundary layer on the surface which proceeds inwards towards the centre under the action of the imposed radial pressure gradient. Close to the centre the boundary layer leaves the surface to form a rising core. The present paper uses a control-volume approach and earlier calculations of laminar boundary-layer development on the disc to determine the characteristics of the core-formation process.

An improved technique for the use of a five-hole yaw probe has been used in determining velocity, vorticity and pressure distributions over a transverse plane five chords downstream of a lifting wing. A well-defined tip vortex is shown to exist, together with a vortex sheet which contains a significant proportion of the total vorticity. The vorticity distribution is compared with that predicted by the calculation of vortex sheet roll-up using a two-dimensional array of line vortices. Good agreement is obtained, and the validity of using time steps large enough to inhibit the chaotic motion found in some calculations of this type is demonstrated. The structure of the tip vortex is found to be well described by the turbulent vortex model of Hoffman and Joubert.

If a canopy is idealised as a cylinder with one end open to the free-stream flow, and the other end closed, then the internal flow during inflation is given by a simple analytic function. In this note the function is derived and then the internal pressures and corresponding forces associated with inflation are determined. It is found that, in addition to ram pressure and the von Kármán “virtual mass” terms in the pressure equations, there are other transient terms associated with radial velocity and acceleration.

An approximate analysis of conditions at separation produced by turbulent boundary-layer/shock-wave interaction is presented for swept, cylindrically symmetric flows. An integral boundary-layer prediction method is used, incorporating Johnston crossflow profiles. The results indicate a marked reduction in pressure rise required to produce separation as sweep is increased. At low Reynolds numbers the skin friction at separation is inferred to be small, whereas at higher Reynolds numbers the presence of a vigorous streamwise flow may be detected. In the limiting case of zero sweep, or two-dimensional flow, predictions using the approximate analysis are shown to compare well with experimental results of pressure rise to separation.