Study of the numerical instabilities in Lagrangian tracking of bubbles and particles in two-phase flow

In the context of the Lagrange approach, used in numerical simulations of two-phase flow, the discrete elements that constitute the dispersed phase are tracked through the fluctuating fluid field by solving their equations of motion. It has been shown previously [Lain, S., & Goz, M. F. (2000). Instabilities in numerical simulations of dispersed two-phase flow. Mechanical Research Communication 27,475; Lain, S., & Goz, M. F. (200 1). Numerical instabilities in bubble tracking in two-phase flow simulations. International Journal of Bifurcation and Chaos, 11 (4), 1169] that widely used discretization methods for integrating the particle equation of motion in bubbly flows may lead to artificial instabilities and, eventually, yield spurious oscillations and chaotic behavior via period-doubling bifurcations. The purpose of this paper is the extension of these previous investigations to consider dispersed two-phase flow laden with solid particles, which can be heavier or lighter than the fluid in which they are immersed. As a result, the numerical techniques applied to integrate the particle or bubble equation of motion are quite stable in the case of heavy particles but must be used very carefully when applied to the tracking of bubbles or light solid particles in a fluid. In addition, sound criteria are established for choosing optimal time steps to simultaneously avoid numerical instabilities and guarantee code efficiency, in contrast to the usual but naive trial and error approach. (C) 2004 Elsevier Ltd. All rights reserved.