A Linear Stability Analysis of a Vapor Film in Terms of the Triggering of Vapor Explosions

A detailed analytical model to explain the vapor film collapse was developed to evaluate the occurrence conditions of self-triggering vapor explosions. The following conclusions were drawn based on linear stability analysis using the thermo-physical property of water, by linearizing and perturbing basic equations (Rayleigh-Lamb-Plesset's bubble momentum equation, the mass conservation equation, the state equation for ideal gas, and the Clausius-Clapeyron equation). The vapor film stabilizes with the reduction of the hot-liquid diameter, decrease of the condensation heat transfer coefficient, or increase of the thermal radiation coefficient. The cold-liquid viscosity and surface tension have a stabilizing effect, though this effect is negligibly small when the hot-liquid diameter is over 1 mm. The analysis predicts the vapor explosion occurrence limits obtained experimentally by other researchers within approximately 10 K. A simple correlation for the stability boundary is proposed by simplifying the above detailed model: the difference in cold-liquid temperature at the stability boundary between these models is less than 1 K when the condensation heat transfer coefficient is over 10⁴W/m²·K and the hot-liquid temperature is lower than 2,000°C.