Summary
The effect of localized suction/injection through two slots, with Gaussian wall velocity distribution, on the spatial inviscid stability of a compressible two-dimensional boundary layer on a slender cone is investigated. The solution of the basic flow and the stability equations are achieved by an efficient spectral numerical technique. Making use of this technique, the effect of localized suction/injection on the growth rates and frequencies of the first two unstable modes is studied, and the obtained results are presented graphically followed by discussion.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Mack, L. M.: Boundary-layer stability theory. In: Special course on stability and transition of laminar flow (Michel, R., ed.), 3-1 3-81, Special course on stability and transition of laminar flows, VKI, Brussels, 1984, AGARD Report No. 709 (1984).
Reed, H., Saric, W. S., Arnal, D.: Linear stability theory applied to boundary layers. Ann. Rev. Fluid Mech.28, 389–428 (1996).
Duck, P. W.: The inviscid axisymmetric stability of the supersonic flow along a circular cylinder. J. Fluid Mech.214, 611–637 (1990).
Duck, P. W., Shaw, S. J.: The inviscid stability of supersonic flow past a sharp cone. Theoret. & Comput. Fluid Dynamics2, 139–163 (1990).
Shaw, S. J., Duck, P. W.: The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies. Phys. Fluids A4, 1541–1557 (1992).
Karabis, A., Shaw, S. J.,Theofilis, V., Kafoussias, N.: The inviscid instability of supersonic flow along a sharp slender cone. DLR ReportIB 223-99 A10 (1999).
Karabis, A., Shaw, S. J., Theofilis, V.: On the inviscid spatial instability of supersonic boundary layer flow along bodies of revolution. In: Proceedings of the IUTAM symposium on laminar-turbulent transition (Saric, W., Fasel, H., eds.), IUTAM Symposium on Laminar-Turbulent Transition, Sedona, AZ, 1999 (forthcoming).
Boyd, J. P.: Complex coordinate methods for hydrodynamic instabilities and Sturm-Liouville eigenproblems with an interior singularity. J. Comp. Phys.57, 454–471 (1985).
Arnal, D.: Control of laminar-turbulent transition for skin friction drag reduction. In: Control of flow instabilities and unsteady flows (Meier, G. E. A., Schnerr, G. H., eds.), pp. 119–153. CISM Courses and Lectures No. 369, CISM 1996.
Joslin, R. D.: Overview of laminar flow control, NASA/TP-1998-208705 (1998).
Al-Maaitah, A. A., Nayfeh, A. H., Masad, J.: Effect of suction on the stability of supersonic boundary layers. Part I—Second-mode waves & Part II—First-mode waves. ASME J. Fluids Eng.113, 591–601 (1990).
Mack, L. M.: On inviscid acoustic mode instability in supersonic shear flows. In: Numerical and physical aspects of aerodynamic flows (Cebeci, T. ed.). Fourth Symposium on Numerical and Physical Aspects of Aerodynamic Flows, Long Beach, CA., 1989. Berlin Heidelberg New York: Springer 1990.
Saric, W. S., Reed, H. L.: Effect of suction and weak mass injection on boundary layer transition. AIAA J.24, 383–389 (1986).
Nayfeh, A. H., Reed, H. L.: Stability of flow over axisymmetric bodies with porous suction strips. Phys. Fluids28, 2990–2998 (1985).
Theofilis, V.: On the resolution of critical flow regions in inviscid linear and nonlinear instability calculations. J. Eng. Math.34, 111–129 (1998).
Canuto, C., Hussaini, M. Y., Quarteroni, A., Zang, T. A.: Spectral methods in fluid dynamics. Berlin Heidelberg: Springer 1988.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Karabis, A., Kafoussias, N. The effect of distributed suction/injection on the spatial linear inviscid instability of a supersonic boundary layer past a slender cone. Acta Mechanica 152, 109–119 (2001). https://doi.org/10.1007/BF01176948
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01176948