title: Study of supersonic nozzle flows in low-pressure environments: starting jets and lunar plume-surface interactions
Creators: name: Cao, Ziqu
Publisher: name: University of Glasgow
Year: 2023

description: Supersonic nozzle flows play an important role in aerospace engineering, e.g. controlling motions, attitudes, and orbits of space vehicles using various propulsion systems. Supersonic nozzle flows include free nozzle flows and restricted nozzle flows, such as plume-surface interactions if a surface obstructs the flow propagation. When compressed gas is discharged from a nozzle into a low-pressure environment in the case of free nozzle flows, the shock wave diffracts around the nozzle lip and a vortex loop forms. These phenomena have attracted much attention in the continuum flow regime, but how the shock diffraction and vortex behave under rarefied flow conditions has received less attention. Understanding transient flow in rarefied conditions is helpful for increasing thrust vector control and avoiding potential contamination and erosion of spacecraft surfaces. Furthermore, comprehending plume-surface interactions is critical for the design of lander modules and future bases on bodies such as the moon, as it is necessary to anticipate surface erosion patterns and the transport of displaced regolith material. Extraterrestrial conditions are difficult to recreate experimentally (e.g. the effects of low gravity, strong radiation and extreme temperature difference). Available numerical techniques for modelling regolith entrainment and subsequent movement suffer from limited accessibility and different levels of sophistication. In this thesis, a design for an open-ended shock tube connected to a vacuum chamber is presented. This is used to release a shockwave into a low-pressure environment and study the subsequent vortex ring formation as the gas diffracts around the shocktube exit. Schlieren visualisation and pressure measurements of the vortex ring formation are conducted. The flow structure degenerates through a decrease in the strength of the embedded shock waves and an increase in their thickness, and the counter-rotating vortex ring when the environmental pressure decreases. The existence of the vortex ring is confirmed through spectral analysis when the environmental pressure is as low as 1.0kPa. Due to limitations with experimental measurement equipment and techniques, the shock wave diffraction problem should be complemented with numerical techniques. A program to generate ensemble-averaged direct simulation Monte Carlo (DSMC) results is designed. Computational fluid dynamics (CFD) and ensemble-averaged DSMC methods are implemented to simulate the formation of a two-dimensional vortex loop due to shock wave diffraction around a 90◦ corner. The influence of the Mach number and rarefaction on the development and growth of the vortex loop are studied. A concept, called rorticity, was used to investigate the transient structures of vortex loops. The simplification of the internal structure of vortex loops and postponement of the vortex loop formation due to the increase of the rarefaction level are confirmed. Two properties from the decomposition equation of vorticity to quantify the vortex strength; rorticity flux (i.e. representing the vortex rotational strength), and the shear vector flux (i.e. representing the vortex shear movement strength), are derived. A mutual transformation relationship between the rorticity and shear vectors has been identified, suggesting that this concept can be employed to better explain vortex flow phenomena. It is found that the increase of the Knudsen number thickens the Knudsen layer, causing the failure of the generation of the vortex sheet and the subsequent formation of vortex loops. A new solver based on dsmcFoamPlus – rarefiedMultiphaseFoam, is developed for solving rarefied multiphase flows. The solver is extended to include a two-way coupling model and a particle phase change model. Additionally, the solid stochastic collison model and the multiphase nparticle-in-cell (MPPIC) method for solving dilute and dense granular flows, respectively, have been implemented in the new solver. The models mentioned are rigorously benchmarked against analytical solutions and previous results in the literature. The benchmarking results of the two-way coupling method show excellent agreement with analytical results. The results of a reproduced uniform gas-solid flow and a purely gravity-controlled granular flow sedimentation agree well with previous numerical results in the literature. A solid particle is allowed to experience a physical and continuous phase change and diameter variation using the updated phase change model. Finally, the rarefiedMultiphaseFoam solver is used to simulate two lunar plume-surface interaction (PSI) cases using the stochastic collision model and the MPPIC method, respectively. Both methods are applied to a scaled down version of the Apollo era lunar module descent engine and comparisons are made between the two simulation results. The results show that the transient effects are essential to both the gas and solid phase evolution and the entrained dust particles significantly influence the evolution of the gas flow. In the PSI simulations, the MPPIC method is more reliable than the stochastic collision method because it takes enduring contacts and the close-packing limit into account. Furthermore, it is identified that the breakdown of the locally free-molecular flow assumption has a significant impact on the solid particle temperatures.