Separated flows exist on submersibles at large angles of incidence such as occur, for example, during turns at high speed and emergency recovery actions. They significantly affect the hydrodynamic forces and moments and consequently the manoeuvring performance A knowledge of these hydrodynamic loads is a prerequisite to determining the safe manoeuvring limits of the vehicle, simulating manoeuvres on a crew trainer and assessing new designs.

A traditional procedure for obtaining manoeuvnng data is to test a scale model in a towing tank or on a rotating arm (Gertler, 1972, Burcher, 1972) and measure the hydro-dynamic loads unposed during a variety of steady and oscillatory motions Polynomial functions are derived which express the components of the force and moment in terms of the vehicle's velocity components. This method has been relied on for more than twenty years but has several limitations, notably the long programme of runs - the results of which may be overtaken by design changes - flow interference from the towing strut, and the fact that the polynomial functions are not clearly defined and measurements are made only with lateral or longtudinal motion (not both simultaneously as occurs during a manoeuvre) Some of these limitations can be overcome by using a free-running model and system identification techniques (Tinker et al, 1979) but these require high quality instrumentation in order to identify a comprehensive model of the dynamics

Numerical simulation avoids lengthy programmes of model tests and provides data during the early design process Lloyd (1983) has developed a method for computing submerged trajectories in which the separated flow from the hull is represented by a par of longtudinal votices whose strength and position are determined empirically from tests on a particular body of revolution This gives satisfactory results for longtudinal manoeuvres but unreliable results when simulating turns The latter aspect is the subject of current development by Lloyd (1986) The method assumes the hull to have a circular section and therefore cannot predict the out-of-plane force which occurs during a turn.

This chapter describes a numerical method for calculating the separated flow over a submersible at an angle of incidence with reduced empirical dependence The flow field (Fig. 1 is available in full paper) and the hydrodynamic loads are computed directly from the geometric description of the hull and appendages The techniques employed have been adapted from those developed for missiles and aeroplanes for which there is an abundant published literature

The flow field around a manoeuvnng submersible is very complex Figure 1 shows the principal feature of the flow based upon flow visualization tests around slender bodies and lifting surfaces at incidence Tip and root vortices trail from all the appendages when these are at an angle of incidence to the flow The boundary layer on the hull separates to form strong primary vortices on the leeward side of the hull Additional weaker vortices may arise from concave hull surfaces and protuberances.

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