Stability analysis of interface of two-phase flow with heat and mass transfer using viscous potential flow

Abstract

The nonlinear stability analysis of film boiling of gas-liquid interface with heat and mass transfer in annular concentric cylinder is studied with viscous potential flow(VPF). The viscous potential flow or purely irrotational viscous fluid flow presented by Joseph, is an new hydrodynamic theory which includes viscosity in irrotational potential flow with viscous normal stress through boundary condition. And the VCVPF(viscous correction viscous potential flow) analysis, modified theory of viscous potential flow which includes interface shear stress to VPF is also considered. In linear hydrodynamic stability analysis, capillary and Kelvin-Helmholtz instability of gas-liquid interface with heat and mass transfer in annular concentric cylinder is studied. A new dispersion relation is obtained including effects of surface tension, heat and mass transfer, phase change and viscosity using viscous potential flow. From the new dispersion relation of capillary instability, it is shown that the heat and mass transfer on film boiling in specified vapor fraction stabilize the vapor-liquid interface. Additionally, the viscosity of vapor-liquid decreases the maximum growth rate and related wave number. And the dimensionless numbers which arise in this phase change problem are identified and their effect on the marginal stability curves, the maximum growth rate and related wave number and critical wave number for unstable flow are computed and compared with inviscid potential flow. The dimensionless numbers governing this potential flow are the density and dynamic and kinematic viscosity ratios, the vapor fraction, the Ohnesorge number and a phase change parameter proportional to the ratio of the heat flux to latent heat. All of the effects of these dimensionless numbers are computed with neutral curve, which shows the variation of critical wave number. From the study of neutral curve with various dimensionless numbers, it is identified that there’s marginal stability reg...