Stability of spinning spacecraft containing shallow pool of liquid under thrust

Abstract

A well-known flight nutation instability observed with spinning spacecraft under the thrust of a solid rocket motor is examined. A shallow pool of molten slag trapped in the aft motor chamber is represented by a linearized hydrodynamic coupled finite element model. The frequency of the dominant retrograde swirl mode of the uncoupled liquid is found to intersect the spacecraft nutation frequency during the anomalous flight and is the suspected cause of instability. With no effects of internal gas flow the coupled model predicts the onset of instability only at the very end of the burn. However, if the equilibrium liquid shape is deformed slightly more outboard, as suggested by a previously predicted recirculating gas flow in the motor chamber, then the model is capable of matching the onset of nutation growth observed in flight. The subsequent nutation growth amplitude profile is also matched. However, the nutation frequency of the linear model deviates from the flight value as the burn progresses. For a prolate spinner, high spin speed, low thrust and large slag axial offset are the conditions for instability; for an oblate spinner the destabilizing conditions are opposite.