N. Riley

Non-uniform slot injection into a laminar boundary layer

SummarySlot injection into a laminar boundary layer in both supersonic and subsonic flow is considered. The blowing rates are sufficiently large to provoke an interaction between the boundary layer and outer inviscid flow, and this interaction is accounted for by triple-deck theory. The non-uniform nature of the blowing velocity models the channel flow from which the injection takes place.

High Reynolds number flows with closed streamlines

SummaryIn this paper we consider high Reynolds number flows with closed streamliness within which an inviscid region of uniform vorticity is separated from the containing boundary by viscous boundary layers. From numerical solutions of the boundary-layer equations we are able to determine that value of the core vorticity for which inviscid core and boundary layer are compatible.

Unsteady fully-developed flow in a curved pipe

It is shown that the boundary layer which develops from rest in a loosely coiled pipe of circular cross-section, following the imposition of a constant pressure gradient, terminates in singular behaviour at the inside bend after a finite time. This singularity of the boundary-layer equations is interpreted as an eruption of boundary-layer fluid into the interior or core flow. This result complements earlier work by Stewartson et al. [1] who consider the steady inlet flow to a curved pipe at high Dean number. In that case a singularity also develops, now at a finite distance from the entrance at the inside bend, which is again interpreted in terms of a boundary-layer collision or eruption.

Unsteady free convection from a heated sphere at high Grashof number

SummaryThe free-convective boundary-layer flow over the surface of a sphere whose temperature is suddenly raised to a value greater than its surroundings is considered. Numerical solutions of the boundary-layer equations are presented which give a complete description of the flow and which confirm the appearance of a singularity in the solution at the upper pole after a finite time.

Inviscid fluid flow around a submerged circular cylinder induced by free-surface travelling waves

We consider the fluid flow induced when free-surface travelling waves pass over a submerged circular cylinder. Perturbation methods are used to formulate a sequence of potential problems that are solved using a Boundary Element method. Favourable comparison is made, where possible, with earlier work. Attention is focused, primarily, upon the time-averaged flow about the cylinder.

On flows with closed streamlines

SummaryIn this paper we present numerical solutions of the steady, two-dimensional Navier-Stokes equations for an incompressible fluid, for the flow in a plane elliptical region driven by the motion of its boundary. As the Reynolds number increases a core region in which the vorticity is uniform emerges, and a favourable comparison is possible with results obtained in the high-Reynolds-number limit.

Separation from a smooth surface in a slender conical flow

SummaryHigh Reynolds number flow of an incompressible fluid past a smooth surface in a slender conical flow is considered. Attention is focused upon the flow properties in the neighbourhood of the separation line. The analysis incorporates the results of a recent inviscid-flow investigation by Smith [1], and the ideas of Sychev [2] for flow separation in two dimensions.

The three-dimensional boundary layer on a yawed body of revolution

A three-dimensional boundary layer calculation is carried out for the flow over a semi-infinite circular cylinder which is placed at a small angle of incidence to an oncoming uniform stream. To elucidate the details of the flow both a spectral and a finite difference method of solution has been employed. The results show that separation of ‘open’ type on a body of revolution is characterized by a line of Goldstein singularities that originates, spontaneously, at a finite distance from the nose of the body.

Free convection from a vertical cooling fibre

We study the free-convective boundary-layer flow that is induced when a slender circular cylinder emerges from an orifice and moves vertically downwards. We demonstrate, by numerical solution of the equations, that the boundary-layer solution develops a singularity at a finite point, where the limiting form of solution is as predicted by Kuiken [3] for an analogous two-dimensional flow.

Prediction of leading-edge vortex behaviour to supplement the suction analogy

SummaryAn analytical treatment is presented which permits the prediction of the strength and path of leading-edge vortices on thin wings of delta-like planform from a knowledge of the behaviour of the linearized approximation to the attached flow past the wing. This supplements the leading-edge suction analogy, which predicts the forces and moments acting on the wing from the same input. The fundamental assumption is that the vortex lies close to the leading edge. It is represented by a single line-vortex and the presentation is confined to low-speed flow and plane wings. The treatment is independent of the way the basic attached flow is calculated. Results are shown for two simple planforms, using inputs from three-dimensional lifting-surface theory and from slender-body theory.