Investigation of conjugate circular arcs in rocket nozzle contour design

The use of conjugate circular arcs in rocket nozzle contour design has been investigated by numerically comparing three existing sub-scale nozzles to a range of equivalent arc-based contour designs. Three performance measures were considered when comparing nozzle designs: thrust coefficient, nozzle exit wall pressure, and a transition between flow separation regimes during the engine start-up phase. In each case, an equivalent arc-based contour produced an increase in the thrust coefficient and exit wall pressure of up to 0.4 and 40% respectively, in addition to suppressing the transition between a free and restricted shock separation regime. A general approach to arc-based nozzle contour design has also been presented to outline a rapid and repeatable process for generating sub-scale arc-based contours with an exit Mach number of 3.8–5.4 and a length between 60 and 100% of a 15\(^{\circ }\) conical nozzle. The findings suggest that conjugate circular arcs may represent a viable approach for producing sub-scale rocket nozzle contours, and that a further investigation is warranted between arc-based and existing full-scale rocket nozzles.