MATHEMATICAL MODEL FOR SIMULATING THE EFFECT OF INTERFACE MOTION ON ULLAGE PRESSURE IN A CRYOGENIC PROPELLANT TANK

The interface motion in a cryogenic propellant tank during the vehicle lift-off and in the accent phase disturbs the thermally stratified layer and results in variation of tank pressure and liquid temperature. A 1D mathematical model is developed here that can be used as a tool for engineering analysis of the effect of the sloshing/interface motion in cryogenic fluid. The model considers the ullage volume as a multicomponent gas mixture, and the pressure history predicted through this method matches with the flight data (within ± 8%). The mathematical model reported in this paper incorporates the effect of interface motion by taking a multiplication factor (sloshing Nusselt number) for the liquid conductivity near the interface, which represents the effect of liquid mixing due to sloshing. The sloshing Nusselt number and Reynold number correlation proposed by the experimental work of Ludwig et al. (2013) [Ludwig, C., Dreyer, M.E., and Hopfinger, E.J., Pressure Variations in a Cryogenic Liquid Storage Tank Subjected to Periodic Excitations, Int. J. Heat Mass Transf., vol. 66, pp. 223-234, 2013.] is referred to here to estimate the heat transfer between the liquid and the interface. A parametric study is carried out by simulating the different types of slosh waves which can be generated inside the tank and the pressure collapse in each case is compared. It is found that the pressure collapse caused by stable planar waves is much less compared to collapse caused by breaking or swirl waves at the interface. The model reported here can be used along with results of ground testing (Nu<sub>s</sub> ) for predicting the pressure drop due to liquid sloshing in a cryogenic tank for a given flight disturbance profile.