When a boundary layer on a surface encounters an obstacle, the fluid near to the surface has lower momentum than the fluid further away and therefore stagnates at a lower pressure on the obstacle The variation in stagnation pressure on the leading edge of the obstacle induces a downflow along the leading edge towards the surface, giving rise to the "horseshoe vortex" which wraps around the obstacle and trails downstream from it This type of flow may be found in many physical situations In the environmental field there are the examples of wind around buildings, and scouring of a river bed around bridge piers. In the field of aeronautical and marine engineering, important examples are the cases of flow around the junction of a wing with the fuselage of an aircract, or flow around a fin-hull junction in a submarine

The latter case has been the motivation behind the present work The horseshoe vortex around a fin of a submarine causes velocity variations in the wake which can give rise to unsteady forces on the propeller For optimal design of the propeller it is necessary to have detailed knowledge of the flow conditions there, and hence of the wakes of the fins. The study described in this chapter concerns the numerical prediction of the horseshoe-vortex flow around a symmetrical aerofoil mounted on a flat plate, which is an idealized case of the fin-hull junction, the principal difference being the lack of lateral curvature m the surface The study is of course relevant also to wing-fuselage junctions in aircraft

The problem is an interesting one numerically, being a case where simple geometry and boundary conditions give rise to a complex flow structure

DESCRIPTION OF THE PROBLEM

The geometry considered is a NACA 0017 symmetrical aerofoil, with a chord of 0 45 m, mounted normally on a flat plate The upstream boundary is placed 036 m in front of the leading edge The Reynolds number is 2 x 106 The incoming flow has a boundary layer of thickness 009 m, with a distribution following a 1/107th power law The downstream boundary is placed 135 m behind the trailing edge. The arrangement is shown in Figure 1(Fig. 1 is available in full paper).

MATHEMATICAL FORMULATION

To determine the flow field around the aerofoil, a set of partial differential equations must be solved, together with the appropriate algebraic relations and boundary conditions These differential equations are the mass-conservation equation and the Navier-Stokes momentum equations (time averaged) The k-e turbulence model (Launder and Spalding, 1974) is used, and therefore additional conservation equations are solved for turbulence kinetic energy and for the dissipation rate of turbulence energy These equations can all be expressed in the following general form

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