Computational Fluid Dynamics Analysis and Optimisation of Laval Nozzles for Low Temperature Kinetics

CRESU (“Cinétique de Réaction en Écoulement") is an experimental approach used to investigate gas phase reaction kinetics and is employed by research groups worldwide.~This technique is used to study the temperature and pressure dependence of the reaction rate coefficient of reaction pathways that occur in low-temperature (7 - 200 K) environments, such as the interstellar media or planetary atmospheres. Reactions at low temperatures can exhibit non-Arrhenius behaviour and are pathways to complex organic molecules, which are fundamental in understanding and modelling the chemical evolution of the universe. Experimentally, low temperatures are achieved by expanding an inert bath gas through a Laval nozzle to form a thermalized, collimated supersonic jet, which is coupled with laser spectroscopy systems to study reaction kinetics. Laval nozzles used in CRESU have been designed exclusively using an analytical technique known as the Method of Characteristics (MOC) since its early development. Nozzles designed using this approach can struggle to operate at the correct design temperature and achieve the flow uniformity necessary for accurate kinetic studies. It often requires multiple design iterations to produce a suitable nozzle design, which is time consuming, tedious and inefficient. Furthermore, it requires the nozzle to be manufactured and tested experimentally before performance can be determined. The first part of this research investigates computational modelling techniques to predict low-temperature, low-pressure supersonic jets used in CRESU, focusing on model choice, boundary condition sensitivity, unsteady jet behaviour, manufacturing techniques and influence of experimental geometry to illustrate robustness in model choices. The numerical predictions are validated using two different experimental apparatuses from research groups at the University of Leeds and the University of Birmingham. To improve the current MOC nozzle design workflow, an automation framework was developed to rapidly perform Computational Fluid Dynamics (CFD) on any Laval nozzle, with the ability to change nozzle geometry, operating conditions and bath gas. The toolbox has been rigorously tested with experimental data across a range of Mach numbers and bath gases, showing steady state CFD can be used to accurately predict global jet quantities within 5 - 10 K of experimental measurements. The second part of this research involves using CFD based data driven optimisation techniques instead of the MOC to improve Laval nozzle design for kinetics. This study details the development of a novel global design optimisation framework that utilises a free form design approach for the Laval nozzle, and a novel technique to obtain the isentropic core length.~The optimisation framework uses surrogate modelling techniques, including Kriging and neural networks, coupled with exploratory adaptive sampling to generate robust and globally accurate predictive meta models. The framework has been used to design Laval nozzles between 70 - 130 K, which were validated experimentally, providing up to a 75\% improvement in flow uniformity compared to the existing MOC nozzles for the same operating temperature. The framework has also been used to deigns nozzles operating at higher temperatures than previously achieved in these groups. Lastly, CFD is used to enhance chemical kinetic studies, this includes understanding the blockage effect of a Pitot tube in the flow, which is used to evaluate jet performance experimentally, improving pressure dependent kinetics, and understanding the temperature history of the reactants along the jet during a kinetic study to investigate the impact of the boundary layer on kinetic measurements. This highlights the usefulness of incorporating CFD into the CRESU workflow, and future applications of CFD within the field.

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