Destabilization of Film Boiling Due to Arrival of a Pressure Shock: Part II—Analytical

Vapor explosions are believed to be triggered by the rapid collapse of film boiling of coolant in contact with molten fuel, probably due to local pressure waves from an initially small interaction. In Part I of this work the heat transfer during the first two ms after passage of a shock past a hot nickel tube surrounded by subcooled Freon-113 or ethanol was studied. The following important results were obtained: (1) The peak heat flux exhibits a maximum of a heater surface temperature of 280–350° C, depending upon the strength of the shock. This is well above the critical temperature, so that nucleation considerations are irrelevant. (2) The maximum of the peak heat flux envelope depends upon the shock ΔP, indicating that only partial contact is made upon collapse of the vapor film. (3) The collapse is rapid (1–2 frame at 5000 f/s), and is produced by relatively weak shocks (ΔP = 2–3 atm.). In the present work, the vapor film collapse is studied analytically, in order to obtain additional insight into the mechanism. A Lagrangian transformation due to Hamill and Bankoff is introduced to immobilize the moving boundary, and a polynomial temperature distribution in the transformed mass variable is assumed in the vapor region, as well as in the liquid region. This leads to a set of coupled nonlinear ordinary differential equations in the three regions, which are solved numerically. Two models were developed: (1) A detailed model, taking into account the Knudsen layers at the vapor-liquid and vapor-solid interfaces, and (2) a simplified model, in which these layers were neglected, and a linear temperature profile in the Lagrangian vapor phase variable was assumed. It is found that the initial vapor mass is a key variable determining whether collapse is achieved. In practice, this is a stochastic variable due to bubble departure, which explains the observed heat flux data scatter. The analytical results are in general agreement with the experimental data.