Linear and nonlinear nonlocal instability analyses for two-dimensional laminar separation bubbles
The linear and nonlinear instability properties of steady laminar two-dimensional incompressible boundary-layer flows with thin separation bubbles are analyzed by means of nonlocal instability theory based on the parabolized stability equations (PSE). The results are compared to data from a direct numerical simulation (DNS). Good to excellent agreement is found in the linear as well as the moderately nonlinear regime, clearly demonstrating that PSE methods are an appropriate instability analysis tool for this type of flow as well. Moreover, a vortexshedding Strouhal number available in literature and reportedly being independent of Reynolds number and pressure gradient is verified. This Strouhal number, obtained by time-accurate Navier-Stokes simulations, is in line with the Strouhal numbers of the most amplified two-dimensional disturbances obtained from the instability analysis of the two laminar separated flows considered here.
Unable to display preview. Download preview PDF.
- 1.Allen, T., Riley, N. (1995) Absolute and convective instabilities in separation bubbles. Aero. J. 99, 439–448Google Scholar
- 3.Bestek, H., Gruber, K., Fasel, H. (1989) Self-excited unsteadiness of laminar separation bubbles caused by natural transition. In: Proc. Conf. on the Prediction and exploitation of Separated Flows, 18–20 Oct. 1989Google Scholar
- 5.Hein, S., Bertolotti, F. P., Simen, M., Hanifi, A., Henningson, D. (1994) Linear nonlocal instability analysis — the linear NOLOT code —. DLR IB 223–94 A56Google Scholar
- 6.Hein, S., Theofilis, V., Dallmann, U. (1998) Unsteadiness and three-dimensionality of steady two-dimensional laminar separation bubbles as result of linear instability mechanisms. DLR-IB 223–98 A39, Aug. 1998Google Scholar
- 8.Rist, U., Maucher, U. (1994) Direct numerical simulation of 2–D and 3–D instability waves in a laminar separation bubble. In: AGARD–CP–551 Application of Direct and Large Eddy Simulation to Transition and Turbulence, 34–1–34–7Google Scholar
- 9.Rist, U., Maucher, U., Wagner, S. (1996) Direct numerical simulation of some fundamental problems related to transition in laminar separation bubbles. In: Proc. Computational Fluid Dynamics Conf. ECCOMAS ‘86, 319–325Google Scholar
- 10.Theofilis, V., Hein, S., Dallmann, U. (2000) On the origins of unsteadiness and three-dimensionality in a laminar separation bubble. Phil. Trans. Roy. Soc. London A (to appear)Google Scholar