Generalized stability theory of vapor film in subcooled film boiling on a sphere

The previously proposed stability theory of vapor film in subcooled film boiling on a sphere was generalized to take account of interaction between base flow and perturbed components. A disturbance of standing wave type was assumed to be superimposed on the base flows of surrounding liquid and 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 an integral method. By use of 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 disturbance. The numerical solutions of critical vapor film thickness at which the real part of complex amplification factor was equal to zero were obtained for the disturbances of the zeroth, first and second orders. The numerical results indicated that the vapor film was most unstable for the disturbance of the zeroth 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.