Procedure for analyzing the friction-reducing effects of bubbles in a friction-reduced vessel

摘要

A method is provided for analyzing the effects of bubbles on skin-friction reduction in a ship cruising in a bubbly flow field. A shear stress decrement tau t, produced by a bubble in a flow field is obtained in a high frequency band region, in which a product of a bubble time-constant T and a turbulence frequency omega L in a flow field is sufficiently greater than 1, based on a resistive force DELTA Rv acting on a bubble derived from the bubble movements in a fluid flow direction along a ship surface and in a direction at right angles to a ship wall surface. Assuming that the shear stress decrement is generated by a decrease in a gas mixing length, an expression for the operative wall constant kappa 1 for bubbly flow including a parametric bubble diameter db is derived. Based on an expression relating the operative wall constant kappa 1 and a local friction factor Cf in bubbly flow, and an expression relating the normal wall constant kappa in non-bubbly flow and a local friction factor Cf0 in non-bubbly flow, an analytical solution is obtained for a skin-friction ratio Cf/Cf0.