Three-Dimensional Numerical Study of the Conical Nozzle Side Loads during Staging

Abstract

The objective of this paper is to numerically investigate the three-dimensional side loads and associated flow physics of a conical nozzle during the fire-in-the-hole staging event of the multistage rocket. The transient flow in nozzle is examined by a three-dimensional time-accurate numerical method with the start-up process of the upper-stage motor and the prescribed nominal separating motion of the lower stage. The impacts of asymmetric lateral motion due to non-nominal staging movement on the nozzle side loads are also numerically analyzed. These motion deviations include the relative angle between axes of two stages, relative lateral displacement between two stages, superposition of relative angle with relative lateral displacement, and angle of thrust vector control. As presented in the simulation results, the flow separation in nozzle is significantly prolonged and intensified by the obstruction of the lower stage. With the location of shockwave reflection approaching the dome of lower stage, the nozzle flow structure experiences two different, stable free shock separation (FSS) patterns. The transition from the first pattern to the second pattern results in the flow oscillation and the side loads peak. The staging motion deviations result in not only the enlarged nozzle side loads, but also a sustained unidirectional effect that may influence the flight stability of the upper stage. An essential ingredient driving the flow unsteadiness and asymmetry is related to the asymmetric reverse supersonic flow deflected by the dome and skirt corner of lower stage. Lastly, the flight data of maximum lateral force during staging of Scout’s stage I and stage II is discussed and compared with the computed results in the article.