<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>