Numerical study of rising bubbles with path instability using conservative level-set and adaptive mesh refinement

Abstract

This paper focuses on three-dimensional direct numerical simulations of rising bubbles in the wobbling regime, and the study of its dynamical behavior for Eötvös number 1 ≤ Eo ≤ 10 and Morton number 1e−11 ≤ M ≤ 1e−9. The computational methodology is based on a mass Conservative Level-Set method, whereas the spatial discretization of the computational domain employs an Adaptive Mesh Refinement strategy for the reduction of computational resources. The Navier–Stokes equations are discretized using the finite-volume approach on a collocated unstructured mesh; the pressure-velocity coupling is solved using a classical fractional-step projection method. This methodology is applied to a series of verification and validation tests, which are compared with experiments and numerical results from the literature. Finally, buoyancy bubbles rising in the wobbling regime are researched at moderate to high Reynolds numbers (100 < Re < 3000). Terminal Reynolds number, drag coefficient and frequency of path oscillations are compared with empirical correlations and numerical studies from the literature. Results show the discharge of alternate oppositely-oriented hairpin vortex structures. Moreover, depending on the characteristics numbers of the system, different path features, bubble shape, and vortical structures in the wake are reported.