Experimental and numerical analysis of surrogate optimized de Laval nozzles in low-temperature supersonic flows

The design of de Laval nozzles for generating low-temperature (7–200 K), uniform supersonic jets for chemical kinetics experiments has traditionally relied on the Method of Characteristics (MOC). Our study addresses limitations and sources of unpredictability in conventional MOC-based design by introducing a surrogate based design optimization framework applicable across any CRESU (“Cinétique de Réaction en Écoulement Uniform”) apparatus. A free-form geometry parameterization with seven design variables is used to describe the nozzle, and an additional two are used for the operating conditions. The surrogate models are constructed using a global adaptive sampling strategy, enabling accurate prediction of kinetic jet parameters across a wide temperature range of 70–130 K. The proposed framework can be used to generate nozzle designs over many operating conditions and constraints, including flow temperature and experimental limitations, capabilities that are not achievable using traditional MOC-based approaches. The optimization of three nozzles reveals a trade-off governing low-temperature supersonic jet formation. Bell-shaped geometries generate supersonic flows that minimize shockwave magnitude across the jet, which are optimal for kinetic studies. The diameter of the isentropic core at the nozzle exit is strongly coupled to flow oscillations. Increasing the core thickness leads to a rapid increase in shockwave magnitude along the jet, while the maximum attainable core thickness decreases with increasing Mach number. The optimized nozzles are experimentally validated, with temperature fluctuations within 1 K of both surrogate predictions and numerical results. These findings demonstrate the coupling between critical parameters for kinetics studies, with implications for CRESU applications.