Published in Journal of Propulsion and Power, Volume 32, Issue 5, July 18, 2016, pages 1298-1301.
The definitive version is available at https://doi.org/10.2514/1.B36059.
The use of a thrust-optimized contour (TOC) for the supersonic nozzle in a rocket engine will inherently maximize the propulsive efficiency and payload capacity of the entire launch system. A TOC can be approximated using a skewed parabola, commonly referred to as a thrust-optimized parabola (TOP), and the TOP contour can be manipulated to avoid undesirable flow separation during low-altitude operation by increasing the static wall pressure at the expense of thrust (approximately 0.1 0.2%). For this reason, a TOP design is often used in nozzles with a high area ratio, such as those used in the Vulcain and Vulcain 2 corestage engines, and suggests that ensuring full-flowing operation at low-altitude conditions can be considered a nozzle design requirement. Unfortunately, any thrust-optimized nozzle may excite an undesirable shift between a free shock separation (FSS) and restricted shock separation (RSS) mode during engine startup and shutdown.
The shift between an FSS and an RSS flowregimewas first noticed during operation of the high-area-ratio J2-S engine, and the RSS condition consequently was deemed responsible for inducing high structural loading to the nozzle walls. However, it was later found that the highest levels of side loading were, in fact, caused by the transition process to and from the RSS flow condition, as opposed to the RSS phenomenon itself. Because the precise flow mechanisms that drive the transition to and from the RSS condition are still not fully understood, the structural loading that occurs as a result of RSS appears to currently be accepted as a design consideration in core-stage rocket nozzles.
A nozzle contour that was capable of suppressing the RSS flow condition itself would inherently prevent the transition to and from RSS and, therefore, decrease the structural loading that occurs during these transition phases. For a net benefit to be realized, the resulting nozzle must produce an equal or greater thrust coefficient compared to the existing design, as well as avoid flow separation during low-altitude operation. In this paper, a set of equivalent thrust-optimized nozzle contours have been produced using an arc-based design method to determine if the suppression of RSS could be achieved by manipulating the contour geometry. The subscale Volvo S1 TOP nozzle that was designed by Volvo Aero Corporation (now GKN Aerospace Engine Systems) was selected as the test case due to the availability of experimental data that captures the transition from FSS to RSS and to ensure that a positive result may be applicable to a full-scale rocket engine, because this nozzle has been shown to possess equivalent flow characteristics to the core-stage Vulcain engine nozzle.
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