The use of Gortler vortices in mixing enhancement and their presence in the supersonic turbulent boundary layer.

摘要

In this study, three main computational investigations were carried out. First, fluid-dynamically generated, owing to centrifugal instability, strongly nonlinear longitudinal vortices (Görtler vortices) were used to promote mixing enhancement in jets, as a novel concept, in place of explicit vortex generators, re-shaped, and lobed nozzle exits. Görtler vortices were allowed to develop, on a slightly concave wall, into their various nonlinear stages through selected cutoff length of the trailing edge prior to their release into a mixing layer. The entrainment properties of the Görtler vortices showed a significant increase in mixing enhancement and provided a guide for the selection of an optimal trailing edge cutoff, for fixed upstream conditions. In the second investigation, since nonlinear development of Görtler vortices leads to the production of unsteady secondary instability, for the mixing region, entrainment properties were compared with and without the secondary instabilities in order to access the latter's role in the mixing process. In order to achieve this, the nonlinear, three-dimensional parabolic equations for the total steady flow quantities, for wall bounded flow and in the mixing problem, were modified by the Reynolds stresses of the secondary instabilities; the latter, in turn, were solved via their respective nonlinear parabolic amplitude equations following spectral decomposition. Ascending number of spectral modes were taken into account. The results showed that secondary instability significantly helped in increasing the mixing enhancement. Finally, the compressibility effects on Görtler vortices in an adiabatic supersonic turbulent boundary layer, were linearly investigated. The linear solution for such a problem can be used as an appropriate initial condition in the study of the nonlinear development of Görtler vortices. By using appropriate scaling for a compressible turbulent boundary layer together with Morkovin's hypothesis, the nonlinear three-dimensional parabolic governing equations for Görtler vortices were obtained. The linearized disturbance equations were then obtained and solved numerically. The obtained stability diagrams were presented and interpreted. It was found that the flow became less stable as Mach number increased for turbulent boundary layer; this is due to the increase of the density and the effective viscosity destabilization effects as Mach number increases.