I want to calculate that the N2 gas flow from slot at the wall injects transversely into the supersonic air main stream with K-Omega turbulence model, but I don't know how to deal with the bc on the injection slot for K-Omega turbulence model. All comments are welcomed! Thank you in advance.

hi. if the geometry of channel injection is defined then you can solve the channel of the jet injection with the main stram cross-flow and for the inlet of channel jet flow you can use uniform velocity profile your project is simillar of mine " compressible turbulent Jet Crossflow Interaction whith sevaral turbulence model(spc. k-e k-w and RSM)- application in gas turbine film-cooling smulation" i'm workinkg on this project since two yares ago

How do you set the k and w at the exit of inject? I have found many paper don't make clear this question. One AIAA paper says the turbulent viscous coefficient eqaul to laminar viscous coefficient and k is set by the experiment; Wilcox gived a formula for w at the mass injection but no information for the turbulent viscous coefficient and turbulent kinetic energy K in his famous book "Turbulence modeling in CFD", 1998. Can you give me some information in detail?

if you solve the channel jet with the main stream flow simultaneously there is no need to enforce any boundary condition at jet exit.