Jet in cross-flow (JICF) or transverse jet, is a broadly employed configuration in different environmental and industrial applications. In combustion applications specifically, cross-flow fuel injections are used in gas-turbine combustors and high-speed propulsion systems 1. It is also used to enhance fuel-air mixing in aerospace gas turbine for secondary fuel or dilution air injection 2, 3) and in stationary gas turbines for low NOx staged combustors 4. In high speed combustion systems, flames should be stabilized close to the jet exit while in low NOx gas turbines the flame stabilization occurs further downstream, thus the rate of fuel-oxidizer mixing are very important parameters in in fuel injection systems design 5 6.

The mixing and combustion in JICF are highly influenced by three-dimensional coherent vortical structures namely the horseshoe vortex, the wake vortex, the leading-edge and lee-side shear layer vortices and The counter-rotating vortex pair (CVP). The latter is the main vortical structures of JICF and persists in the jet far-field resulting in a better entrainment and mixing compared with a coflow jet 7-9.
The wide practical application, rich physics and its capability to use as a benchmark flow for mixing and combustion models validation, the turbulent non-reacting and reacting JICF has attracted the attention of great many studies. Comprehensive reviews of JICF studies are given in Refs. 2, 10-12. Non-reacting JICF’s are investigated both experimentally 13-20 and numerically 21-30. In these studies effect of some influencing parameters (such as jet to cross-flow density, velocity and momentum ratios, jet Reynolds number, jet arrays, jet nozzle, and jet swirl and pulsation) on the JICF vortical structures and flow and mixing characteristics have been investigated.
In comparison with non- reacting JICF, the theoretical and experimental studies considering reacting JICF are limited. Through experimental observations in reacting JICF 6, 31-43, Sullivan et al. 40 have investigated the reacting jets in a high-temperature vitiated cross-flow for a wide range of momentum ratios (0.75

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