SPECTRAL ELEMENT STABILITY ANALYSIS OF VORTICAL FLOWS
The scope of the present study is to demonstrate the use of spectral/hp-element methods in understanding the global instability mechanisms of vortex dominated flows. Using a BiGlobal stability analysis, analytically constructed and numerically evaluated base flows have been investigated, with the leading eigenvalues obtained by the Arnoldi algorithm. Subsequently, Direct Numerical Simulation (DNS) was used to investigate the non-linear development of an unstable Batchelor vortex. It was found that a spiral-type instability, if allowed to develop in an axially unconstrained manner, leads to an axial loss of energy and the formation of a stagnation point.
KeywordsDirect Numerical Simulation Stagnation Point Vortex Breakdown Spectral Element Method Vortical Flow
Unable to display preview. Download preview PDF.
- Abid, M. and Brachet, M.E. (1998). Direct numerical simulations of the Batchelor trailing vortex by a spectral element method. Physics of Fluids, 10(2).Google Scholar
- Ash, R.L. and Khorrami, M.R. (1995). Vortex stability. In Green, S.I., editor, Fluid Vortices, pages 317–372. Kluwer Academic Publishers.Google Scholar
- Barkley, D. and Tuckerman, L.S. (2000). Bifurcation analysis for timesteppers. In Doedel, E. and Tuckerman, L.S., editors, Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems, pages 466–543. Springer, New York.Google Scholar
- Crouch, J.D., Garbaruk, A., Shur, M., and Strelets, M. (2004). Predicting unsteady buffet onset using RANS solutions. TM 2004–212913, NASA.Google Scholar
- Leibovich, S. (1978). The structure of vortex breakdown. Annual Reiew of Fluid Mechanics, 10:221–246.Google Scholar
- Lessen, M., Singh, P.J., and Paillet, F. (1974). The stability of a trailing line vortex: Part 1 - inviscid theory. Journal of Fluid Mechanics, 63:753–763.Google Scholar
- Squire, H.B. (1960). Analysis of the vortex breakdown phenomenon, part I. Report No. 102, Aeronautics Department, Imperial College, London.Google Scholar