Analytical Description of an Axisymmetric Supercavitation Bubble in a Viscous Flow

One of the basic elements which characterizes flow regimes, is viscosity. This element has typically been neglected in research on supercavitational flows, describing and predicting supercavitation bubbles geometry and formation using non-viscous potential flows. Arguing that the viscosity effect is much smaller than the inertial effect at high flow speeds, the viscosity has been ignored and the only parameter for modeling the flow has been the cavitation number. However, for some situations and conditions, the viscosity was found to be significant and crucial for the bubble geometry and formation, especially at the supercavitation bubble detachment point, hence some investigations based on numerical calculations have taken viscosity into account. This paper presents an analytical model of an axisymmetric supercavitation bubble in a viscous flow according to Serebryakov annular model for calculation of axisymmetric cavity flows. Viscosity effect on the bubble geometry is suggested, and an analysis for validation and examination is presented as well. The results show the change of the bubble formation from past models due to the viscosity, and offer a more accurate description of the bubble geometry close to the detachment point. Moreover, the slenderness parameter is calculated and presented for supercavitation bubbles in a viscous flow together with its dependency on Reynolds number and the cavitation number. The analysis reveals that the slenderness parameter increases with increasing both the cavitation number and Reynolds number, where the latter has a substantial effect.