Linear Stability of the Supersonic Turbulent Boundary Layer to Görtler Vortices on a Concave Wall
In this paper, we linearly investigate the compressibility effects on Görtler vortices, caused by the centrifugal instability along a concave surface, in an adiabatic supersonic turbulent boundary layer. 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 are obtained. The linearized disturbance equations are then obtained and solved numerically using a fmite-difference method with deferred corrections. The obtained stability diagrams are presented and interpreted. It is found that the flow becomes less stable as Mach number increases for turbulent boundary layer; this is due to the increase of the density and the effective viscosity destabilization effects as Mach number increases.
KeywordsVortex Compressibility allO Tane
Unable to display preview. Download preview PDF.
- 2.Zakkay, V. and Calarese, W., NASA CR 2037, June 1972.Google Scholar
- 4.So, R.M.C. and Mellor, G.L, Aeron. Quart, Vol. 26, 1974, pp. 25–40.Google Scholar
- 5.Sandmayr, G., Deutsche Luft-und Raumfarhrt, 1966, pp. 66–41.Google Scholar
- 6.Lesieur, M., Comte, P., AGARD-R-819, 1997, pp.4. 1–4. 39.Google Scholar
- 9.Girgis, I.G., Ph.D. thesis, Brown University, 2000.Google Scholar
- 12.Harris, J. E., NASA TR R-368, Aug. 1971.Google Scholar