Velocity of cavitation bubbles in uniform flowfield high and low Reynolds number

Abstract

AGASEOUS bubble caused by the tip cavitation of a propeller blade operating in a uniform flowfield environment experiences a drag force in relation to its angular velocity and a thrust force in the axial direction. In this paper, a mathematical model is presented that studies propagation of the gaseous bubble at low and high Reynolds number cases. The temporal and the spatial profile velocity variations are presented. The time constants involved in both regimes are obtained. The velocity variations are shown to be exponential for the low Reynolds number case and algebraic for the high Reynolds number case. Contents When a propeller operates in an underwater environment at high revolutions, cavitation will occur. Three different types of cavitation can occur: 1) hub cavitation, 2) blade cavitation, and 3) tip cavitation. In this paper, tip cavitation will be considered. Tip cavitation produces tip vortices of entrained gases that propagate downstream in a helical motion. The rate at which the cavitation gases propagate downstream is a function of propeller geometry, flowfield, and the geometry of the cavitation gases. The three different types of cavitation that can exist are 1) individual spherical bubbles of equal size, 2) individual bubbles of different sizes, and 3) train of gas shaped in cylindrical form. In this paper, it will be assumed that the cavitation bubbles are spherical and the shape does not change as a function of time. The motion of air bubbles in a fluid has been investigated by a variety of authors with numerous articles being presented by Lauterborn.1 Individual gaseous bubbles will be assumed to be moving in a flowfield, and interactions between successive bubbles will be neglected. The bubble is assumed to move with velocity V, whereas the flowfield has a velocity U. The effect of the added mass and the mass of the displaced fluid have to be considered in the general governing equation. The governing equation of motion is the conservation of momentum equation as given by Newman2 dV dV