TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B · 1995 · 30 citations · 0 references
EngineeringOcean EngineeringComputational Fluid DynamicsFluid DynamicsFluid MechanicsBubble DynamicsFlow ModelingTransient Flow AnalysisViscous FlowBubble Drag ForceBubble FlowDragDrag CoefficientFluid Constitutive EquationsNatural CirculationTransient FlowTwo-fluid Model
In the previous report, we proposed constitutive equations for a drag coefficient, CD, of a single bubble in a stagnant liquid. Applicability of the proposed CD to transient flow was examined in this report based on the relaxation time required for a stationary bubble to reach the terminal condition. As a result, it was confirmed that the bubble will reach the terminal condition after traveling a distance almost equal to 2d where d is the bubble diameter. Hence, we can apply the proposed CD to transient flow provided that the whole flow field does not change much while the bubble moves the distance about 2d. Then, the proposed CD was modified so as to be applicable to a swarm of bubbles. The modification was carried out using an empirical correlation for drift velocity of the swarm and balance of forces acting on a bubble in the swarm. Comparisons between measured and calculated transient bubble-induced natural circulation were conducted to verify the modified CD. The calculation was carried out using a two-fluid model with the modified CD. It was confirmed that the modified CD can give good predictions.