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Supercritical mixing of nitrogen is explored in a shear coaxial injector using detached eddy simulations with the Peng-Robinson equation of state. Computational results are processed and compared against experimental data. Time averaged results are shown to agree well with the experimental temperature profile near the tip of the injector. The transient flowfield is captured with shadowgraph images generated from the simulation and compared with the experimental images. Distinctive features of the shear coaxial flow are identified including high density inner core, the outer jet flow and shear layer between the outer injector fluid and the co-flow. These features are reasonably duplicated in the computational shadowgraph images. Shadowgraph images are found to depend on the distance of the screen from the fluid domain and therefore inferences drawn from such images are associated with this distance. Further, comparison of the shadowgraph images with a slice of the flowfield may not compare the same features and are found to be of limited use for the purpose of validation. Mixing length of the dense flow in the core of the injected fluid emphasizes this observation. Two acoustically excited cases: pressure node and pressure anti-node at the center plane of the jet are also studied in the same manner. The pressure anti-node case shows puffing behavior that does not significantly disrupt the inner core, while the pressure node case generates flapping motion which perceptibly shortens the core flow of the injected jet.