Numerical Simulation for Gas-Liquid Two-Phase Free Turbulent Flow Based on Vortex in Cell Method

Abstract

This paper proposes a two-dimensional vortex method, based on Vortex in Cell method, for gas-liquid two-phase free turbulent flow. The behavior of vortex element and the bubble motion are calculated through the Lagrangian approach, while the change in the vorticity due to the bubble is analyzed in the computational grids resolving the flow field. Therefore, the numerical procedure corresponds to the Lagrangian-Eulerian method. The present method is applied to simulate the air-water bubbly flow around a square-section cylinder. The simulation demonstrates that the bubble entrainment into the Karman vortex and the resultant reduction for the strength of vortex are successfully captured by the method. It is also confirmed that the vortex shedding frequency and the pressure distribution on the cylinder are favorably compared with the measured results.

Numerical simulation of plane bubble plume by vortex method

“…∂φ ∂x = 0 on B 2 and B 3 (19) ψ z = 0 on B 1 , B 2 , and B 3 (20) On the upper boundary B 4 , the Sommerfeldt radiation condition is imposed [11]. The vortex element leaving the boundary B 4 is excluded from the calculation.…”

“…To extend the applicability of vortex method, one of the authors has proposed the vortex methods for gas-particle two-phase free turbulent flow [10][11][12], and applied the two-way coupling vortex methods to various free turbulent flows [13][14][15][16] as well as the particulate jet induced by free falling particles in quiescent air [17,18]. In a prior paper [19], the present authors have proposed a twodimensional vortex method for gas-liquid two-phase free turbulent flow. In this method, the bubble motion and the behaviour of vortex element are traced by the Lagrangian approach, while the change in the vorticity due to the bubble is computed by using the computational grids resolving the flow field.…”

“…In this method, the bubble motion and the behaviour of vortex element are traced by the Lagrangian approach, while the change in the vorticity due to the bubble is computed by using the computational grids resolving the flow field. The authors [19] applied the two-way coupling vortex method to simulate the flow around a rectangular cylinder mounted in a vertically upward bubbly flow. The phase distribution and the pressure distribution on the cylinder surface were favourably compared with the corresponding experimental results.…”

Vortex Simulation of the Bubbly Flow around a Hydrofoil

“…The authors [11] proposed a vortex method for gasliquid bubbly flow in a prior paper. The liquid vorticity field is discretized by vortex elements, and the behavior of vortex element and the bubble motion are simultaneously computed by the Lagrangian approach.…”

“…Therefore, it is usefully employed for the simulation of free turbulent flows, in which the large scale eddies play a dominant role. The authors applied the vortex method to simulate a bubbly flow around rectangular cylinder [11], a bubble-laden plane mixing layer [12], and a bubble-driven plume [13]. The simulations demonstrated that the interaction between the largescale eddies and the bubbles is successfully analyzed and that the simulated two-phase flow field is favorably compared with the corresponding experimental results.…”