Potential flow around a deforming bubble in a Venturi

The differential pressure between the entrance and throat of a Venturi will fluctuate if the liquid flowing through the Venturi contains bubbles. This paper reports computations of the pressure fluctuation due to the passage of a single bubble. The liquid is assumed inviscid and its velocity, assume d irrotational, is computed by means of a boundary integral technique. The liquid velocity at the entrance to the Venturi is assumed constant and unif orm across the pipe, as is the pressure at the outlet. The bubble is initia lly far upstream of the Venturi and moves with velocity equal to that of th e liquid. Buoyancy is neglected. If the bubble is sufficiently small that i nteractions with the Venturi walls may be neglected, a simple one-dimension al model for the bubble velocity is in good agreement with the full boundar y integral computations. The differential pressure (taken to be positive) d ecreases when the bubble enters the converging section of the Venturi, and then increases to a value higher than for liquid alone as the bubble passes the pressure measurement position within the throat. The changes can be es timated using the one-dimensional model, if the bubble is small. The bubble is initially spherical (due to surface tension) but is perturbed by the lo w pressure within the Venturi throat. In the absence of viscosity, the bubb le oscillates after leaving the Venturi. The quadrupole oscillations of the bubble are similar in frequency to those of a bubble in unbounded fluid; t he frequency of the monopole oscillations is modified by the presence of th e pipe walls. Numerical results for the frequency of monopole oscillations of a bubble in a uniform tube of finite length are in good agreement with a nalytic predictions, as is the computed drift of the oscillating bubble. (C ) 2000 Elsevier Science Ltd. All rights reserved.