A Note on Turbopump Blade Cavitation Compliance for the POGO Instability

Abstract

During the first or booster stage of flight many liquid-propellant rockets have experienced severe longitudinal vibrations caused by a closed loop interaction between the first longitudinal structural mode and the dynamics of the propulsion system. This, "POGO" instability, reviewed in Reference 1, has been the subject of intensive research since it was first encountered. One of the most important transients in the dynamic modelling of the propulsion system is the "cavitation compliance" of the turbopumps [3] defined as the negative of the derivative of the cavity and bubble volume in the pump and its suction line with respect to the section pressure. Thus, it describes the oscillatory source/sink behavior of the pump due to changes in the cavity volume. Past analyses [1, 2] have suggested dividing this compliance into two components corresponding to the two major types of pump cavitation, namely blade cavitation and back-flow cavitation. The purpose of this paper is to present some preliminary results of theoretical calculations of blade cavitation compliance. The most satisfactory starting point would be a theory for unsteady cavitating flow in a cascade. Whilst work on this is in progress at the present time, the low frequency or quasistatic approach based on existing steady flow theory is much simpler and in itself yields interesting results.

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