Stability of Vapor Film in Subcooled Film Boiling on a Sphere

Abstract

The previously proposed linear stability theory of vapor film in subcooled film boiling on a sphere was generalized to take account of the interaction between the base flow and the perturbed component. A disturbance of standing wave type was assumed to be superimposed on the base flows of the surrounding liquid and the vapor film. For the surrounding liquid, the wave equation was applied to the whole region including the boundary layer and the energy equation was solved analytically by introducing a simplifying assumption. For the vapor film, the basic equations were solved by the integral method. By use of the compatibility conditions at the liquid-vapor interface, the solutions for the surrounding liquid and the vapor film were combined to yield an algebraic relation among the vapor film thickness, the order of disturbance and the complex amplification factor of the disturbance. The numerical solutions of the critical vapor film thickness at which the real part of the complex amplification factor was equal to zero were obtained for the disturbances of the orders of 0, 1 and 2. The numerical results indicated that the vapor film was most unstable for the disturbance of the 0-th order (i.e., uniform disturbance). The calculated value of the critical vapor film thickness for the uniform disturbance compared well with the average vapor film thickness at the minimum-heat-flux point obtained from the immersion cooling experiments of spheres in water at high liquid subcoolings.