Void Fraction Effect on Added Mass in Bubbly Flow

Abstract

This paper proposes a relation for the added mass coefficient of spherical bubbles depending on void fraction based on results obtained by a semi-analytical method. This information is essential to completely characterize finely dispersed bubbly flows, where small spherical gas bubbles are present in a continuous liquid phase. Most of the closure relations for Euler-Euler or Euler-Lagrange models are obtained from experiments involving single bubbles. Their applicability to systems with high void fraction is therefore questionable. This paper uses solid harmonics to solve 3D potential flow around bubbles. Several configurations were calculated for different numbers of particles and spatial arrangements. Our results are compared with previous studies. Depending on the model proposed by previous authors, added mass forces could increase or decrease with the void fraction. This paper solves these discrepancies. The main purpose of this work is to develop simple formulas fitting our semi-analytical results. These simple formulas are suitable for further use, particularly as added mass models for multiphase flow averaged equations.