Analytic Solution for the Phase Change in a Suddenly Pressurized Liquid-Vapor System
To prevent boil-off of a cryogenic liquid in a nonperfectly insulated container, it is necessary to pressurize the ullage region. This is most conveniently accomplished by introducing a small quantity of gas at an elevated temperature. The amount of pressurizing gas required is inversely proportional to the temperature at which it enters the tank, since the pressurization requirement manifests itself as an energy requirement. The introduction of pressurant has two effects on the liquid-vapor system: it raises the interface temperature to the saturation temperature corresponding to the elevated ullage pressure, and it increases the vapor temperature. The liquid-vapor system, if isolated, will adjust to this nonequilibrium condition by transferring thermal energy from the vapor to the liquid. However, unlike two solids at different temperatures in thermal contact, the controlling temperature difference is not governed by the initial liquid and vapor temperatures alone. It is the interface temperature that controls the net heat flow into the liquid or vapor. Any imbalance of heat flow across the liquid-vapor interface is accounted for by a phase change, i.e., by energy being released at the interface by condensation or absorbed by evaporation.
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