| Author: | Li, Xin |
| Title: | Richtmyer–Meshkov instability of shock-induced double-layer gas cylinders |
| Advisors: | Hao, Jiaao (AAE) Wen, Chih-yung (AAE) |
| Degree: | Ph.D. |
| Year: | 2025 |
| Subject: | Gas cylinders Fluid dynamics -- Mathematical models Stability -- Mathematical models Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Aeronautical and Aviation Engineering |
| Pages: | xxi, 115 pages : color illustrations |
| Language: | English |
| Abstract: | Richtmyer-Meshkov (RM) instability arises due to the baroclinic and pressure perturbation mechanisms when a perturbed density interface is impulsively accelerated. The perturbation on the interface will result in the generation of secondary instabilities and the formation of massive small-scale vortices, which in turn cause turbulent mixing. RM instability in inert and reactive gas mixture finds widespread applications in various engineering fields, including dust cloud explosions, scramjet engines and multiphase combustion in propulsion systems. The evolution of an inert double-layer gas cylinder under various Mach numbers and Atwood numbers is studied numerically. Regarding the effects of varying Mach numbers (M = 1.27, 1.5, 1.7, and 2.1), a bulge is generated near the upstream pole of the outer cylinder due to the impingement of a reflected shock wave, which promotes the formation of an upstream jet for M ≥ 1.5. At a higher Mach number, the evolution of the jet is suppressed under the influence of a higher pressure upstream of the jet head. The compressibility effects are quantified by the widths and heights of the gas cylinders. The mechanism behind vorticity evolution is investigated using the vorticity transport equation. The dilatation and baroclinic terms play a dominant role in the dynamics of vorticity production. Higher Mach numbers amplify the dilatation, baroclinic and viscosity terms, thereby promoting the development of RM instability. In terms of Atwood number effects, two types of gas layer configurations are considered: an A/B/A-type gas layer (where the densities in the surroundings, gas ring, and inner cylinder are denoted as A, B, and A) and an A/B/C-type gas layer (where the densities in the surroundings, gas ring, and inner cylinder are denoted as A, B, and C). The Atwood number is associated with nonlinear acoustic effects, and the sign of A results in a significant variation in the wave patterns. For the scenarios of A/B/A-type gas layer (A1 = 0.50, 0.39, 0.19, and −0.20, where A1 is the Atwood number for the first layer), the development of vortex pairs slows down with the decreasing Atwood numbers when A1 > 0. The widths and heights of the outer and inner cylinders keep steady at a later phase of the evolution. Vortex pairs emerge and propagate in both upstream and downstream directions from the outer interface for A1 = −0.20. For the scenarios of A/B/C-type gas layer (A2 = −0.50, −0.25, −0.06, 0.06 and 0.17, where A2 is the Atwood number for the second layer), secondary vortex pairs emerge at the downstream interface of the outer cylinder following the interaction of a high-pressure triple point with the downstream interface, while a downstream jet is formed due to the generation of a notably higher-pressure zone after the transmitted shock wave traverses the convergence point when A2 < 0. Higher Atwood numbers amplify the dilatation, baroclinic and viscosity terms and induce RM instability for A1 > 0, while the increase in the magnitude of the Atwood number in the inner gas cylinder primarily enhances vorticity transport during the stage when the first transmitted shock passes through the inner cylinder. The net circulation can be predicted by the linear superposition of Samtaney and Zabusky (SZ) and Picone and Boris (PB) models. Analysis of the mean mass fraction histories of the outer and inner cylinders shows that increased mixing of ambient gas into the gas ring leads to the dilution of SF₆ and promotes gas mixing as the Mach number and the magnitude of Atwood number rises, especially when the incident shock wave passes over the gas cylinder. The evolution of a reactive double-layer gas cylinder under various Mach numbers and radius ratios is studied numerically. Regarding the effects of varying Mach numbers (M = 2.13, 2.3, 2.5 and 2.9), a deflagration wave is initiated, propagating at subsonic speed and reaching the UI1 in the long-term evolution at Mach 2.13. As the Mach number increases, the ignition time occurs earlier, followed by a detonation wave. The incident shock wave ignites the gas mixture at the upstream pole of the outer cylinder at higher Mach numbers. The distributions of pressure, temperature, and hydrogen mass fraction at the reaction front suggest that deflagration-to-detonation transition (DDT) occurs after ignition at Mach numbers of 2.3 and 2.5. The evolution of the gas cylinder is analyzed quantitatively by evaluating the transverse bubble diameter and bubble area. Combustion completeness is used to quantitatively describe the ignition process. Regarding the molecular mixing fraction, the slope of curves in the inert scenarios rises with increasing Mach numbers, as stronger shock intensities enhance vorticity production and accelerate the growth of RM instability. The reactive scenarios exhibit different behaviours, where the mixing fraction is generally suppressed due to vortex cancellation. Regarding the effects of varying radius ratios (λ = 0.25, 0.5 and 0.75), a hot spot forms near the downstream interface of the outer cylinder due to high pressure and temperature from the triple point. When λ increases to 0.75, a second hot spot appears near the upstream interface of the inner cylinder. The distribution of pressure, temperature, and hydrogen mass fraction at the reaction front indicates that DDT occurs after the generation of the first hot spot. Following the second hot spot, a detonation wave propagates upstream towards the outer interface. Intense heat release following ignition causes an expansion in the outer diameter and the area of the gas ring, while compressing the inner diameter and inner gas area. Detonation results in a more rapid increase in combustion completeness compared to deflagration, which quantifies the ignition process. Regarding vorticity and mixing fraction, the magnitude of net vorticity decreases, and its rate of decrease slows after ignition as the radius ratio increases. Additionally, the mixing fraction for the outer interface increases with increasing radius ratios in both reactive and inert gas cylinders but remains lower in reactive cylinders compared to inert counterpart after ignition. |
| Rights: | All rights reserved |
| Access: | open access |
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