It was recently stated by Cockrell, Diamond and Jones(1) that attempts to correlate diffuser loss coefficients with the inlet boundary layer momentum thickness were generally unsatisfactory. In particular, it had proved impossible to align various results from diffuser tests which had been made with differing inlet flow conditions. The two methods of thickening the diffuser inlet boundary layer, using either

(a) a length of parallel pipe, or

(b) screen rings at inlet to the diffuser

led to a corresponding variation in diffuser performance.

The conclusion was drawn that “the manner by which an inlet boundary layer has been thickened is as significant in determining diffuser performance as is the thickness of the layer. No satisfactory inlet flow parameter is at present known”.

This contribution from Livesey and Turner is of considerable interest. Following work by Horlock and Lewis(1) on the flow of an inviscid fluid through a diffuser from which an analytic solution was obtained, the present authors show that such a solution is only significant if the boundary layer at entry to the diffuser is in equilibrium. Non-equilibrium profiles in pipes, such as those produced using short inlet lengths or gauzes, will continue to change their state beyond the plane of measurement and so will influence the state of flow through whatever pipe component succeeds them. Our work at the University of Leicester accords with this.

Most investigators into the characteristics of fluid flow through diffusers have used methods of analysis based on the Karman Momentum Equation (e.g. Spence and Norbury; Ross and Fraser; Schlichting). The pressure rise which would accompany the tendency of an inlet profile to achieve its equilibrium state is not considered part of the diffusion process, although the corresponding pressure rise occurring in a downstream pipe length, as the outlet boundary layer velocity profile regains its equilibrium state, is recognised and is calculable.

This is an extension of the design method described in ref. 1 to the compressible flow in integral nozzles comprising both subsonic (contraction) and supersonic (effusor) parts. The nozzles are axially symmetric and will be considered as isentropic convertors of low speed high enthalpy inviscid gas to a high speed, relatively low enthalpy state, heat transfer effects being ignored. The key advantage of the method over existing hybrid design methods(2'3'4'5) is that no assumption is made as to conditions in the “sonic” throat region before expansion in the effusor, the design being integral from low speed inlet to high speed outlet. A slight disadvantage of the method is that of ref 1, namely that a nozzle of an ideally infinite extent has to be truncated both at inlet and outlet. However, for a given nozzle length this limitation can be biased towards the relatively insensitive low subsonic inlet to benefit correspondingly outlet conditions to the extent that it should be possible to make the maximum variation from the mean in the cross-sectional speed at outlet less than 0.01 per cent. The method is being applied to design integral hypersonic nozzle units for the projected small intermittent hypersonic facility in the Department of Aeronautics and Space Technology. This tunnel will have a nominal working-section diameter of 2 in and the flow will be accelerated from low speed (about 20 ft/sec) at inlet to Mach numbers of either 5, 6, or 7 at outlet to the working section using three alternative nozzles.

This third technical note, on the background of the author's Main Lecture to the Society(1), illustrates the application of the technique given in ref. 2 on a simple example, and develops the basic ideas further, with particular reference to the effect of reinforcing flanges and initial loads, as may arise through differential thermal straining. A more ambitious example demonstrating the improvement achieved by the new triangle appears in ref. 1.

Over the last five years or so both in the USA (especially by the active group at Berkeley under R. W. Clough(7) ) and the UK, there have been a number of attempts to incorporate the plane triangular element under bending and membrane action into a general matrix displacement analysis of shells. All investigators stressed the positive aspects of the triangular element, which arise from its adaptability to any geometrical form of the shell, but noted at the same time some serious shortcomings due to a partial satisfaction of the kinematic compatibility conditions at the boundary. Thus we have within the Matrix Displacement Method the rather unusual example of a type of element whose deficiency with respect to kinematic compatibility does not automatically ensure convergence to the exact result as the number of elements is increased.