Application of Realizability and Shock Unsteadiness to k-ε Simulations of Under-Expanded Axisymmetric Supersonic Free Jets

An explicit cell-centered finite volume solver coupled to a k-epsilon turbulence model corrected for structural compressibility fails to satisfactorily predict the behavior of under-expanded supersonic jets exhausting into still air, because the model does not properly account for the turbulence/shock wave interaction. Two approaches are examined: imposing a realizability constraint and taking into account shock unsteadiness effects. Although both corrections yield better agreement with experimental data of under-expanded jets, the realizability constraint yields better results than the shock unsteadiness correction.