| Author: | Yang, Tao |
| Title: | Theoretical and computational investigations of flame-vortex and droplet-surface dynamics |
| Advisors: | Ma, Yuan (ME) Zhang, Peng (ME) |
| Degree: | Ph.D. |
| Year: | 2025 |
| Department: | Department of Mechanical Engineering |
| Pages: | xxxiv, 263 pages : color illustrations |
| Language: | English |
| Abstract: | The thesis consists of two parts, with Part I on flame-vortex dynamics and Part II on droplet-surface impact dynamics. Specifically, the vortex-dynamics interactions and synchronization modes of single-, dual-, triple-, and octa-flickering diffusion flames were investigated computationally and theoretically in Part 1, while the splash and complete rebound of droplets impacting on the surface was modelled theoretically based on the previous experimental findings in Part 2. These works are conducive to studying spray flames. Flickering flames are bridges between flame dynamics and vortex dynamics, which is a powerful analysis approach in fluid mechanics and deserves more attention from the combustion community. Turbulence characterizes multi-scale vortex interaction and is hardly bypassed to deeply understand turbulent flames, in which multi-scale chemical reactions are coupled with vortices. Flickering flames facilitate the experimental, numerical, and theoretical studies of unsteady flames, as they retain the intrinsically unsteady nature of turbulent flames but contain richer physics than laminar flames. In the thesis, the main studies and achievements of flickering flame are summarized as follows: 1. Flickering buoyant diffusion methane flames in weakly rotatory flows were computationally and theoretically investigated. One notable computational discovery is the nonlinear increase in flicker frequency with the nondimensional rotational intensity R (up to 0.24), correlating with the nondimensional circumferential circulation. This finding aligns with prior experimental evidence suggesting that rotatory flows can amplify flame flickering to a certain degree. Drawing on a vortex-dynamical comprehension of flickering flames, where flame flickering results from the periodic shedding of buoyancy-induced toroidal vortices, a scaling theory was developed for flickering buoyant diffusion flames in weakly rotatory flows. This theory posits that the rise in flicker frequency f follows the scaling relation ( f - f0 ) ∝ R², a proposition that closely mirrors the computational findings. Moreover, the presence of external rotatory flow in physics augments the radial pressure gradient around the flame, with the significant baroclinic effect of ∇p × ∇p serving as an additional factor fueling the growth of toroidal vortices, thereby accelerating their periodic shedding. 2. Small-scale flickering buoyant diffusion flames in externally swirling flows were computationally investigated, with emphasis on identifying and characterizing various distinct dynamical behaviours of the flames. A one-step reaction mechanism is utilized to explore the impact of finite rate chemistry on flame flicker. By adjusting the external swirling flow conditions (the intensity R and the inlet angle α), six flame modes, including flickering flame, oscillating flame, steady flame, lifted flame, spiral flame, and flame with a vortex bubble, were computationally identified in both physical and phase spaces. Observing the phase portraits and their differences in distinct modes could help identify the dynamical behaviours of flames and understand complex phenomena. 3. Anti-phase and in-phase flickering modes of dual buoyant diffusion flames were numerically investigated and theoretically analyzed. The mode transition was found to rely on the inner-side shear layers between two flames, of which the crucial role resembles the von Karman vortex street in the wake of a bluff body. A unified regime nomogram in the parameter space of the normalized frequency and the newly defined flame Reynolds number was obtained and verified by present simulations and the previous experiments. 4. Triple flickering buoyant diffusion flames of methane gas in an equilateral triangle arrangement, regarded as a nonlinear dynamical system of interconnected oscillators, were computationally investigated. For the first time, the study successfully replicated four distinct dynamical modes: in-phase, death, rotation, and partially in-phase, which were interpreted through the perspective of vortex interaction, with a specific emphasis on vorticity reconnection and vortex-induced flow. This work well establishes a connection between vortex dynamics and the nonlinear dynamics of the triple-flame system, which could be essential in comprehending more extensive dynamic systems involving multiple flickering flames. 5. A series of circular arrays of octuple flickering laminar buoyant diffusion flames were investigated in computational and modelling manners to understand their collective behaviours. In the work, five distinct dynamical modes, such as the merged, in-phase mode, rotation, flickering death, partially flickering death, and anti-phase modes, were identified and interpreted from the perspective of vortex dynamics. A unified regime diagram was obtained in terms of f/f0 and of a combined Reynolds-number-like parameter αGr¹/². The bifurcation transition from the in-phase mode and the anti-phase mode to the totally or partially flickering death occurs at αGr¹/² = 655 ± 55. In addition, a toy model of identical Stuart-Landau oscillators with time-delay coupling was utilized to mimic the collective dynamics of multiple flame systems, bringing out a great capability of reproducing the general features and collective modes. The physical model based on vortex-dynamics mechanisms and the toy model of Stuart-Landau oscillators both provide valuable insights into the behaviour of complex coupled oscillatory systems. Modelling droplet-surface impact plays an important role in the numerical simulation of many industrial devices, such as inkjet printing, spray coating, nuclear installation, and bipropellant rocket engines. The droplet impact on a solid surface involves rich phenomena of gas-liquid-solid three-phase interplays, of which understanding is crucial for optimizing processes in various applications. Droplet impact facilitates the experimental, numerical, and theoretical studies of fluid dynamics. In the thesis, the main studies and achievements of droplet impact are summarized as follows: 6. The splash in low-Oh region and the receding breakup in high-Oh region were analyzed qualitatively based on the unbalanced forces acting on the rim of the spreading or receding liquid film. A semi-empirical correlation of splash threshold is proposed and well fits the experimental results from previous and present studies over a wide range of liquid viscosity. When the surface is high temperature (TW), three sub-patterns of thin-sheet splash were unified in the three-dimensional phase diagram of Oh - We - TW. For the transition surface temperature TW,cr from thin-sheet splash to deposition, a scaling correlation of TW,cr/T0∼We³/² is derived based on the analysis of the temperature-dependent destabilizing force on the levitated lamella and agrees well with the experimental data. 7. A practically useful model of droplet splashing on a smooth solid surface was established by unifying many previous experimental data for different liquids, droplet sizes, droplet velocities, and ambient pressures. Specifically, a scaling law of the splash threshold comprising the physical properties of the impacting liquid and the surrounding gas was derived from the instabilities of the spreading liquid sheet and the entrapping air film. The resulting correlation between two combinations of non-dimensional parameters ΠL = Re¹/²Oh² and ΠG = ηKn⁻¹ (Re, Oh, Kn, and η are the Reynolds, Ohnesorge, and Knudsen numbers and the gas-to-liquid viscosity ratio) agrees well with the previous splashing criteria that are either limited to narrow parametric ranges or expressed by piecewise fitting formulas. 8. The fluctuating recovery coefficient of oscillating droplets rebounding completely from non-superhydrophobic surfaces was theoretically interpreted and modelled. A physical understanding is that the inevitable oscillation of a large droplet in freely falling makes the impacting droplet shape slightly deviate from being spherical and in turn affects the interaction between the droplet and the surface. A theoretical model of oscillating droplet rebound is proposed and well fits the present experiments over a wide range of We. In the concluding chapter, potential research directions are suggested to extend those addressed in the thesis. |
| Rights: | All rights reserved |
| Access: | open access |
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