Interaction of bodies in free surface with consideration of cross-flow

Abstract

This paper examines the side-force and induced drag on two thin bodies in arbitrary separation, stagger, and Froude number. The cross-flow induced by the interaction between two bodies is addressed by placing a doublet sheet on the body center-plane and the wake. The coupled integral equations for the doublet strength are then solved, subjected to the body boundary conditions and Kutta condition at the trailing edges. The doublet strength is affected by camber of body surface, yawed angle, and the thickness of neighboring body. It has been shown in this paper that the cross-flow induced by the thickness of neighboring body is negligible, compared with yaw angle effect. For a pair of bodies with a small separation and zero stagger, the side-force experienced by each body can be thirty percent larger than that without interaction at certain Froude numbers. However, the total side-force on the two-body system only has a few percent variation and is not sensitive to the separation due to force cancelation. For two bodies with non-zero staggers, the total side-force and induced drag referring to their zero-stagger values are antisymmetric with respect to the stagger. At high Froude numbers, the two bodies interact strongly at large staggers, while at lower Froude numbers, strong interaction occurs at small staggers. The total drag experienced by the two-body system is dominated by the wave drag at medium Froude numbers, and by side-force induced drag at high Froude numbers.