Transient three-dimensional side-loads analysis of a thrust-optimized parabolic nozzle during staging

The objective of this effort is to numerically investigate side-loads and correlative flow physics of a thrust-optimized parabolic nozzle during the fire-in-the-hole staging event. The three-dimension transient flow in nozzle is examined by the time-accurate numerical method with time-varying chamber pressure and separation gap width. The main properties (amplitude, phase position and frequency) of computed side-loads were also analyzed. The ordinary nozzle flow separation patterns, free shock separation (FSS) and restricted shock separation (RSS), were obtained. The transition processes from FSS to RSS and finally full flow during staging event were specially emphasized. As the simulation results presented, two types of asymmetric flow physics incur strong side-loads: random transition between FSS and partial quasi-RSS due to fish tailing effect of the supersonic jet, axial flow oscillation across the nozzle lip due to relative movement between supersonic jet and front edge of the lower stage. Side-loads caused by fish tailing effect and lip oscillation have equivalent maximum amplitudes but almost perpendicular directions, while the frequency of the former is much higher than that of the latter. The side-loads due to asymmetric flow separation in the thrust-optimized parabolic nozzle are significantly intensified by the obstruction of the lower-stage dome during the staging event. Therefore, the side-loads influence should be carefully considered in advanced upper-stage nozzle of thrust-optimized parabolic contour when involving with staging.