Scaling of oxygen-methane reacting coaxial jets using x-ray fluorescence to measure mixture fraction

Abstract

Stoichiometric mixing length Ls of reacting coaxial jet flames is a critical scaling parameter for liquid rocket engine combustors. Previous studies have shown that Ls for shear coaxial flames can be scaled like their nonreacting counterparts using a nondimensional momentum flux ratio J. In addition, stoichiometric mixing lengths of reacting and nonreacting coaxial jets collapse upon a single line by altering J using an effective outer flow gas density. This effective density is calculated from a modified version of the equivalence principle, originally developed by Tacina and Dahm [1, 2] and accounts for the effects of heat release on mixing. However, previous studies also required a second nonphysical scaling constant Sc for the reacting jets, which is not predicted by the equivalence principle [3]. It was originally hypothesized that Sc is attributed to the limitation of hydroxyl (OH) planar laser-induced fluorescence, which only infers Ls. Direct quantitative measurement of conserved scalar fields using conventional optical diagnostics is difficult due to the lack of a tracer that easily fluoresces, survives high temperature oxygen flames, and is not dominated by quenching effects. To measure a conserved scalar field, this work implements x-ray fluorescence of Kr and Ar tracers to obtain quantitative mixture fraction fields. From these mixture fraction fields, stoichiometric mixing lengths for two CH4/O2 flames are calculated and scaled against nonreacting coaxial mixing lengths using the equivalence principle. By directly measuring the stoichiometric mixing length, it is established that the additional constant is a byproduct of the OH measurement technique and the equivalence principle fully captures the scaling. Comparison with high-fidelity simulation of the flame further supports this conclusion. In addition to further strengthening this scaling method, this work represents the first use of x-ray fluorescence to make quantitative conserved scalar measurements in turbulent flames.