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Control of Unsteady Flows

Simulations were carried out for the unsteady separated-reattaching flow and associated heat transfer over a long rectangular plate subjected to an oscillatory inlet velocity, U=Uo(1+Ap×SIN(2πfpt)). The two-dimensional simulations were performed at a Reynolds number of 1,000 by solving the time-dependent Navier-Stokes and energy equation using a finite volume method. The computations were performed on a 300x100 grid, using centered second-order accurate spatial discretization, and a third-order time-stepping scheme. The effect of forcing was investigated by exploring the response of the flow over a range of frequencies up to the 60th harmonic of the natural vortex shedding frequencies and for velocity perturbation amplitudes up to 20% of the free stream. Forcing of the flow is found to radically alter the dynamics of the flow and results in significantly higher local heat transfer rates.

The unperturbed flow at Re = 1,000 displays an inherently unsteady behaviour as reported in several experimental and numerical studies.The flow pattern for the unperturbed base case is illustrated in this figure.The instantaneous vorticity field shows the separated shear layer and the typical cycle of vortex formation and shedding. This typical flow pattern is repeated in a quasi-periodic fashion, with occasional vortex merging taking place.

By applying a Fast Fourier Transform (FFT) to vertical velocity component signals along an horizontal line close to the plate surface, it is possible to analyze the evolution of the amplitude of the fundamental frequency of the flow. The dominant frequencies associated with the large scale structures were determined from velocity spectra evaluated at each grid point along the streamwise direction; the resulting variation  of the dominant frequency with the streamwise direction is shown in the top figure. The bottom figure shows the spectral amplitudes corresponding to each location and dominant frequency. The largest energy fluctuations are clearly associated with shedding of vorticity at a characteristic frequency fn=0.14. Harmonics of this frequency were selected as forcing frequencies in the simulations with oscillatory inflow.

The left figures  show instantaneous flow patterns for the high amplitude case Ap=0.2 at various frequencies fp. As the forcing frequency increases, the vortices in the tail end of the separated shear layer start to diffuse more rapidly and the shear layer stabilizes and becomes quasi-stationary. The onset of this stabilization mechanism occurs further upstream with increasing forcing frequency. By fp =9fn, the flow is quasi-steady over most of the plate and the shear layer behaves as a steady laminar shear layer. Its lower growth rate results in delayed interaction with the surface of the plate and, hence, delayed reattachment resulting in a very large separation region. At yet higher frequencies, fp > 12.5fn, a string of smaller size vortices are still shed from the leading edge. These are convected along the outer edge of the shear layer without penetrating the recirculation zone. This has been experimentally observed. The flow is then governed by two regimes: forcing which controls the flow in the vicinity of leading edge of the blunt plate, and shear layer instability, as in the unperturbed case, which take place farther downstream.

This study was carried out at the University of Victoria (BC, Canada) during the Post-Doctoral studies of Dr Latif Bouhadji.