<div>Pressure-gain combustion in wave rotors offer the opportunity for substantial improvement in gas turbine efficiency and power, while controlling emissions with fuel flexibility, if provided rapid and reliable ignition of lean mixtures. In addition, tightening emission regulations and increasing availability of gas fuels for internal-combustion engines require more reliable ignition for ultra-lean operation to avoid high peak combustion temperature. Turbulent jet ignition (TJI) is able to address the ignition challenges of lean premixed combustion. Especially, the turbulent hot jet results in faster ignition penetration for wave rotor pressure-gain combustors that have high-frequency operation and fast-burn requirements. Controllability of TJI needs better understanding of the chemistry and fluid mechanics in the jet mixing region, particularly the estimation of ignition delay time and identifying the location of the ignition onset. </div><div>In the present work, numerical and analytical methods are employed to develop models capable of estimating the ignition characteristics that the turbulent hot jet exhibits as it is issued to a cold stoichiometric CH4-H2-Air mixture with varied fuel reactivity blends. Numerical models of the starting turbulent jet are developed by Reynolds-averaged and large-eddy simulation of Navier-Stokes and scalar transport equations in a high-resolution computational domain, with major focus on ignition of high-reactivity fuel blends in the jet near-field due to computational resource limitations. The chemical reactions are modeled using detailed chemistry by well-stirred and partially stirred reactor approaches. Numerical models describe the temporal evolution of jet mixture fraction, scalar dissipation rate, flow strain rate, and thermochemical quantities of the flow.</div><div>For faster estimation of ignition characteristics, analytical methods are developed to explicitly solve governing equations for the transient evolution of the near field and the leading vortex of the starting hot jet. First, the transient radial evolution of the turbulent shear-layer of a round transient jet is analytically investigated in the near-field of the nozzle, where the momentum potential core exists. The methods approximate the mixing and chemical processes in the jet shear and mixing layer. The momentum equation is integrated analytically, with a mixing-length turbulence model to represent the variation of effective viscosity due to the velocity gradients. The analytic predictions of the velocity field and mass entrainment rate of the jet are compared with numerical predictions and experimental findings. In addition, the transport equation of conserved scalars in the jet near-field is solved analytically for the history of the jet mixture fraction. This analytic solution for temperature and species is used, together with available models for instantaneous chemical induction time, to create an analytic ignition model that provides the time and radial location of the ignition onset.</div><div>Lastly, the ignition mechanism within the vortex ring, which leads the starting turbulent jet, is modeled using prior understanding about the mixing characteristics of the vortex. This mechanism is more relevant to low-reactivity fuel blends. Due to the presence of strong mixing at the large-scale, the vortex ring is treated as a homogeneous batch-reactor, which contains certain levels of the jet mixture fraction. This assumption provides the initial composition and temperature of the reactor in which ignition ensues. </div><div>This article-dissertation is developed as a collection of 4 articles published in peer-reviewed journals, one submitted article, and additional unpublished work. The study is laid out in 6 chapters with the following contributions:</div><div>Chapter 1: This chapter numerically investigates the three-dimensional behavior of a transient hot jet as modeled using the Reynolds-averaged turbulence flow. The study aims at providing an insight towards the role of mixing in the ignition progress and how the operating conditions such as fuel mixture and pre-chamber pressure ratio can influence the ignition success. An ignition prediction criterion is developed in this chapter, which helps to predict the ignition success under a broad range of operating conditions.</div><div>Chapter 2: In this chapter, the large-eddy simulation (LES) of hot jet ignition is reported in conjunction with detailed kinetics mechanism and adaptive-mesh refinement. The correlation between local values of mixture fraction gradient and ignition is discussed. Furthermore, the role of methane-hydrogen ratio on the heat release pattern is studied for two specific mixtures.</div><div>Chapter 3: The LES of CH4-H2-Air ignition is extended in this chapter to account for multivariable evaluation of ignition. Joint probability assessment of ignition explains the role of important scalars on the formation and growth of ignition. Also, the effect of CH4-H2 ratio on the spatial distribution of ignition is assessed and discussed.</div><div>Chapter 4: In this chapter, the rate of mass entrainment into the jet in the near-field region is studied. Characterization of the mass entrainment illuminates the understanding of mixing behavior of the starting turbulent jets. Through an exact solution of the momentum equation, this chapter includes a model of the diffusive transport in a round transient jet at high Reynolds numbers.</div><div>Chapter 5: This chapter proposes a method to evaluate the mass/heat exchange between a transient-turbulent jet and a quiescent environment. To analyze the transport phenomena in the jet near-field, the transient diffusion equation in cylindrical coordinates is explicitly solved and its solution is compared with the empirical findings. The transport solution then enables an ignition model to describe the spatiotemporal characteristics of ignition in the near-field.</div><div>Chapter 6: The development of ignition within the vortex ring of the transient jet is investigated in this chapter. The initiation, growth, and departure of the vortex ring are studied using the available empirical correlations and the LES. Using a perfectly-stirred, zero-dimensional representation of the vortex, chemical kinetic calculations provide estimates of ignition delay for various fuel mixtures.</div><div><br></div>

Indiana University-Purdue University Indianapolis (IUPUI) / Investigations of a constant-volume combustor ignited by a penetrating transient jet (a puff) of hot reactive gas have been conducted in order to provide vital data for designing wave rotor combustors. In a wave rotor combustor, a cylindrical drum with an array of channels arranged around the axis spins at a high rpm to generate high-temperature and high-pressure product gas. The hot-gas jet ignition method has been employed to initiate combustion in the channels. This study aims at experimentally investigating the ignition delay time of a premixed combustible mixture in a rectangular, constant-volume chamber, representing one channel of the wave rotor drum. The ignition process may be influenced by the multiple factors: the equivalence ratio, temperature, and the composition of the fuel mixture, the temperature and composition of the jet gas, and the peak mass flow rate of the jet (which depends on diaphragm rupture pressure). In this study, the main mixture is at room temperature. The jet composition and temperature are determined by its source in a pre-chamber with a hydrogen-methane mixture with an equivalent ratio of 1.1, and a fuel mixture ratio of 50:50 (CH4:H2 by volume). The rupture pressure of a diaphragm in the pre-chamber, which is related to the mass flow rate and temperature of the hot jet, can be controlled by varying the number of indentations in the diaphragm. The main chamber composition is varied, with the use of four equivalence ratios (1.0, 0.8, 0.6, and 0.4) and two fuel mixture ratios (50:50, and 30:70 of CH4:H2 by volume). The sudden start of the jet upon rupture of the diaphragm causes a shock wave that precedes the jet and travels along the channel and back after reflection. The shock strength has an important role in fast ignition since the pressure and the temperature are increased after the shock. The reflected shock pressure was examined in order to check the variation of the shock strength. However, it is revealed that the shock strength becomes attenuated compared with the theoretical pressure of the reflected shock. The gap between theoretical and measured pressures increases with the increase of the Mach number of the initial shock. Ignition delay times are obtained using pressure records from two dynamic pressure transducers installed on the main chamber, as well as high-speed videography using flame incandescence and Schileren imaging. The ignition delay time is defined in this research as the time interval from the diaphragm rupture moment to the ignition moment of the air/fuel mixture in the main chamber. Previous researchers used the averaged ignition delay time because the diaphragm rupture moment is elusive considering the structure of the chamber. In this research, the diaphragm rupture moment is estimated based on the initial shock speed and the longitudinal length of the main chamber, and validated with the high-speed video images such that the error between the estimation time and the measured time is within 0.5%. Ignition delay times decrease with an increase in the amount of hydrogen in the fuel mixture, the amount of mass of the hot-jet gases from the pre-chamber, and with a decrease in the equivalence ratio. A Schlieren system has been established to visualize the characteristics of the shock wave, and the flame front. Schlieren photography shows the density gradient of a subject with sharp contrast, including steep density gradients, such as the flame edge and the shock wave. The flame propagation, gas oscillation, and the shock wave speed are measured using the Schlieren system. An image processing code using MATLAB has been developed for measuring the flame front movement from Schlieren images. The trend of the maximum pressure in the main chamber with respect to the equivalence ratio and the fuel mixture ratio describes that the equivalence ratio 0.8 shows the highest maximum pressure, and the fuel ratio 50:50 condition reveals lower maximum pressure in the main chamber than the 30:70 condition. After the combustion occurs, the frequency of the pressure oscillation by the traversing pressure wave increases compared to the frequency before ignition, showing a similar trend with the maximum pressure in the chamber. The frequency is the fastest at the equivalence ratio of 0.8, and the slowest at a ratio of 0.4. The fuel ratio 30:70 cases show slightly faster frequencies than 50:50 cases. Two different combustion behaviors, fast and slow combustion, are observed, and respective characteristics are discussed. The frequency of the flame front oscillation well matches with that of the pressure oscillation, and it seems that the pressure waves drive the flame fronts considering the pressure oscillation frequency is somewhat faster. Lastly, a feedback mechanism between the shock and the flame is suggested to explain the fast combustion in a constant volume chamber with the shock-flame interactions.