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A technique for improving the numerical predictions of turbulent flows with the effect of streamline curvature is developed. Separated flows and the flow in a curved duct are examples of flow fields where streamline curvature plays a dominant role. New algebraic formulations for the eddy viscosity μt incorporating the k–ε turbulence model are proposed to account for various effects of streamline curvature. The loci of flow reversal (where axial velocities change signs) of the separated flows over various backward-facing steps are employed to test the capability of the proposed turbulence model in capturing the effect of local curvature. The inclusion of the effect of longitudinal curvature in the proposed turbulence model is validated by predicting the distributions of the longitudinal velocity and the static pressure in an S-bend duct and in 180 deg turn-around ducts. The numerical predictions of different curvature effects by the proposed turbulence models are also reported.

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The effect of exit geometry of a rectangular nozzle on the instability modes and mixing characteristics of under-expanded supersonic jets is computationally investigated. The unsteady three-dimensional viscous simulation is based on the Proteus code developed at NASA Glenn Research Center. A shock adaptive grid generator was developed to enhance the shock simulation. The nozzle aspect ratio for both plane and notched rectangular nozzles in this study is 5.0 and the fully expanded jet Mach number is 1.526. For the case of a plane rectangular nozzle, the ‘flapping’ oscillations, which are extensively observed in schlieren flow visualization and reported in acoustic measurements, are also captured in the presented computations. The flapping frequency in experimental measurements (7400 Hz) is closely predicted in the presented computations (7500 Hz). The symmetrical instability mode is also observed as viewed from the nozzle’s small and large dimensions at twice the flapping frequency. For the notched rectangular nozzle, the flapping oscillations ceased and instead a spanwise oscillation mode was observed as viewed from the nozzle’s large dimension. The instantaneous mass flowrate at nine jet widths downstream of the nozzle exit showed an increase of 8.5 per cent in mass flowrate in the jet emerging from the notched as compared to the plane rectangular nozzle.

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