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-dynamic 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, decreasing the condensation heat transfer coefficient, and increasing the thermal radiation coefficient. The cold-liquid viscosity and surface tension have a stabilizing effect, though this effect is negligibly small where the hot-liquid diameter is over 1mm. The analysis predicts the vapor explosion occurrence limits obtained experimentally by other researchers to within approximately 10K. 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 1K when the condensation heat transfer coefficient is over 10~4 W/m~2K and the hot-liquid temperature is lower than 2000°C.
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