A series of experiments have been conducted on a bleed hole array spanning the width of the Cambridge University Engineering Department supersonic wind tunnel at Mach numbers of 1.8 and 2.5. The wind tunnel was run with varying levels of suction, and the flow structure over the bleed array was subsequently mapped with a laser Doppler velocimetry system at a resolution of 0.25 hole diameters or better. The same wind-tunnel setup was simulated using the OVERFLOW Navier-Stokes equation solver. The information obtained was used primarily in qualitative comparisons of flow patterns. Overall good agreement was found in the definition of the expansion fan and barrier shock pattern produced by flow entering the normal holes, as well as three-dimensional flow patterns. Both studies agreed well in terms of measured mass flow rates, to within 1% of the boundary-layer mass flow. The presence of the barrier shock standing off the downstream edge of the bleed holes corresponded with a jet of upward flow, which may provide a mechanism for the generation of streamwise vortices.

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A series of experiments have been conducted on an array of bleed holes spanning the width of the CUED supersonic wind tunnel at Mach numbers of 1.8 and 2.5. The wind tunnel was run with varying levels of suction, and the resulting flow structure over the bleed array was subsequently mapped with a Laser Doppler Velocimetry (LDV) system at a resolution of 0.25 hole diameters or better. The same wind tunnel setup was also simulated using the OVERFLOW Navier-Stokes equation solver. Overall good agreement was found in the definition of the expansion fan and barrier shock pattern produced by flow entering the normal holes, with the production of streamwise vorticity noted in both CFD and experimental studies. The proposed mechanism of vorticity generation is an effect of the barrier shock standing off from the rear edge of each bleed hole, and is predicted by CFD to increase in strength as Mach number increases, as well as when the vorticity is produced by a single hole, rather than an array. Both studies found that vorticity decreases as suction strength is reduced, however the experimental study showed the vortices persist farther downstream than predicted by CFD.

The Harmonic Balance method is well suited for analyzing unsteadiness in turbomachinery flows comprised of a few dominant frequencies. A harmonic condition is imposed on the temporal derivatives through a Fourier transform operation. The solution is then reinterpreted as a time-domain problem, where several instances of time (lying within the largest period) are solved for simultaneously with the enforcement of the time-harmonic condition providing coupling between time instances. A discontinuous Galerkin discretization is used together with overset grids to provide higher-order spatial accuracy and flexibility in representing complex geometry. In this work, the discontinuous Galerkin infrastructure is extended for unsteady problems with a Harmonic Balance method and a Diagonally Implicit Runge-Kutta time-integrator. Verification results are presented for both time integration approaches in addition to results for a turbine blade with unsteadiness driven by a prescribed unsteady inlet boundary condition. Comparisons of results from the Harmonic Balance and Diagonally Implicit Runge-Kutta approaches are very close, with some small discrepancies that require further investigation. Significantly, rapid convergence from the Newton solver is obtained for the Harmonic Balance approach applied to the Euler equations for the turbine blade problem. Solutions converged by 8–10 orders of magnitude are obtained in between 5 and 16 Newton steps.

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