Study on Ex-Vessel Cooling of RPV: Model Analysis of Critical Heat Flux on Inclined Plate Facing Downward and Development to Hemispherical Surface

The cooling of the Ex-vessel in Light-Water-Reactors has been proposed to maintain reactor vessel integrity during severe accident. The critical heat flux — CHF — from the underside of down-facing convex surfaces, like hemispheres, is important to the assessment of the cooling. The authors examined CHFs on inclined plates under saturated boiling experimentally, focusing on the effect of the inclination angle on the CHF and characteristic length and velocity of coalesced bubbles near the heater at the CHF. In this study, the critical heat fluxes on the inclined plates in saturated boiling were investigated analytically by using the macrolayer model and the Kelvin-Helmholtz instability, based on our previous experimental report. Furthermore, the present model was developed for the CHF on a hemispheric surface. In the present model, the most dangerous wavelength and propagative velocity of the wave in the Kelvin-Helmholtz instability for ideal fluid with vapor flow of finite thickness and surface tension on liquid-vapor interface were calculated to determine the length and the velocity of the coalesced bubble on the heating surface at CHF. The time covered over the heater with the bubble was estimated as the calculated value with the length divided by the velocity. The predictions of the present CHF model by using the macrolayer model for CHF and the Kelvin-Helmholtz instability for the characteristic values of the coalesced bubble agree well with previous experimental data for CHF on inclined plates with 30 to 180 degree in orientation. Furthermore, the present model given as a function of the inclination angle relative to the horizontal downward plate was extended to CHF on a hemispheric surface. The CHFs obtained by the present model are in qualitative agreement with experimental data on hemispheres reported by some investigators.