Longitudinal Modal Analysis of a LOX-filled Tank Using the Virtual Mass Method

For liquid rocket engine(LRE)-based space launch vehicles, longitudinal instability, often referred to as the pogo phenomenon in the literature is predicted. In the building block of system-level task, accurate dynamic modeling of a fluid-filled tank is an essential. This paper attempts to apply the virtual mass method that accounts for the interaction of the vehicle structure and the enclosed liquid oxygen to LOX-filled tanks. The virtual mass method is applied in a modal analysis considering the hydroelastic effect of the launch vehicle tank. This method involves an analysis of the fluid in the tank in the form of mass matrix. To verify the accuracy of this method, the experimental modal data of a small hemispherical tank is used. Finally, the virtual mass method is applied to a 1/8-scale space shuttle external tank. In addition, the LOX tank bottom pressure in the external tank model is estimated. The LOX tank bottom pressure is the factor required for the coupling of the LOX tank with the propulsion system. The small hemispherical tank analysis provides relatively accurate results, and the 1/8-scale space shuttle external tank provides reasonable results. The LOX tank bottom pressure is also similar to that in the numerical results of a previous analysis.