Simulation and force modeling for a submarine with a hull + sail configuration in a steady turn
University of New Brunswick
The effect of turning on a submarine in a hull and sail (H+S) configuration is investigated by RANS based numerical simulations at a fixed Reynolds number of 23×10 6 . The two geometric parameters in the problem are (i) the turning ratio, given by R/ℓ, where R is the turning radius of the hull center of buoyancy and ℓ is the hull length. The turning ratio is varied from 1 to 10 covering a full range of turns from very tight ones where the submarine turns within a hull length to ten times hull length (which can also be seen to be an asymptotic approximation of ∼ ∞). (ii) the pivot point of the submarine is assumed to be at λp/ℓ = 0.25 where λp is the distance of the pivot point from the nose of the submarine. Kinematic constraints fix the yaw angle for the center of buoyancy for a given turning ratio (the local yaw angle varies along the hull length for a submarine in a turn). The resulting forces and moments which include both in-plane yaw forces and also out-of-plane pitch forces are obtained and compared to the analytical models used in DSSP, (see Mackay ) showing fair agreement. In general, it has been found that the axial drag force, the yaw force and the pitch forces increase with the tightness of the turn. However, the behavior of the moments is more complex and while the roll moment increases monotonically with the tightness of the turn, the pitch and yaw moments show an initial increase and then fall as the turn is made tighter with a peak at R/ℓ ∼ 1.5. Parametric studies have been run to investigate the effect of sail height Sh/ℓ and the pivot point location λp/ℓ. A reduced sail height, predictably, reduces the yaw force and moment. The effect of pivot point position is more complicated because as it approaches the center of buoyancy, the entire sail experiences negative incidence resulting in a reversal of the direction of the yaw force on the sail.