A method of broad applicability is presented which can be used to obtain solutions to problems involving a phase change. The solution in one of the phases is specified as a known single-phase solution; an inverse analysis then determines the solution for the other phase. Two problems are studied: The first yields the similarity solution for the planar geometry and the second gives the exact solution to a more general problem. Convergence is shown and error bounds are given. The method can accommodate convection, heat generation, variable properties, nonplanar, and multidimensional systems.

<p>The stability and liftoff characteristics of a nitrogen (N₂) diluted hydrogen (H₂) jet flame in a vitiated co-flow are investigated experimentally with particular attention focused on regimes where multiple stabilization mechanisms are active. Information gleaned from this research is instrumental for informing modeling approaches in flame transition situations when both autoignition and flame propagation influence combustion characteristics. Stability regime diagrams which outline the conditions under which the flame is attached, lifted, blown-out, and unsteady are experimentally developed and explored. The lifted regime is further characterized in determining liftoff height dependence on N₂ dilution, jet velocity, and co-flow equivalence ratio (or essentially, co-flow temperature). A strong sensitivity of liftoff height to N₂ dilution, jet velocity, and co-flow equivalence ratio is observed. Liftoff heights predicted by Kalghatgi’s correlation are unable to capture the effects of N₂ dilution on liftoff height for the heated co-flow cases. A uniquely formulated Damköhler number, where the chemical time scale is based on flame propagation rather than autoignition, was therefore developed which acceptably captures the effects of jet velocity, nitrogen dilution and environment temperature on liftoff height. Satisfactory agreement between the correlation results indicate that stabilization is dominated by propagation, and prior studies with similar flames, such as the research of Muñiz and Mungal (1997) indicate that the propagating flame is likely tribrachial.</p>

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