Hostname: page-component-6bf8c574d5-956mj Total loading time: 0 Render date: 2025-02-20T20:21:43.739Z Has data issue: false hasContentIssue false
  • English
  • Français

Inviscid Batchelor-model flow past an airfoil with a vortex trapped in a cavity

Published online by Cambridge University Press:  26 April 2006

A. V. Bunyakin ,
S. I. Chernyshenko  and
G. Yu. Stepanov
A. V. Bunyakin
Affiliation:
Department of Applied Mathematics, Krasnodar Polytechnic Institute, 350072 Krasnodar, Russia
S. I. Chernyshenko
Affiliation:
Institute of Mechanics, Moscow University, 119899 Moscow, Russia
G. Yu. Stepanov
Affiliation:
Institute of Mechanics, Moscow University, 119899 Moscow, Russia
Get access Rights & Permissions [Opens in a new window]

Abstract

An efficient method of constructing inviscid Batchelor-model flows is developed. The method is based on an analytic continuation of the potential part of the flow into the closed-streamline vortex region. Numerical solutions are presented for Batchelor-model flows past airfoils with cavities. With the airfoil and dividing streamline shape, the eddy vorticity, and the jump in the Bernoulli constant across the eddy boundary given, the program calculates the corresponding cavity shape and the entire flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 323 , 25 September 1996 , pp. 367 - 376
Copyright
© 1996 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abrashkin, A. A. & Yakubovich, E. I. 1988 Flow past a non-uniformity of a plane surface with formation of attached vortex. Zh. Prikl. Mekh. Tekhn. Fiz. No. 5, 81–84 (in Russian).Google Scholar
Batchelor, G. K. 1956a On steady laminar flow with closed streamlines at large Reynolds number. J. Fluid Mech. 1, 177–190.Google Scholar
Batchelor, G. K. 1956b A proposal concerning laminar wakes behind bluff bodies at large Reynolds number. J. Fluid Mech. 1, 388–398.Google Scholar
Chernyshenko, S. I. 1984 Calculation of low-viscosity flows with separation by means of Batchelor's model. Fluid Dyn. 19(2), 206–210. (Izv. Akad. Nauk SSSR. Mekh. Zhidk. Gaza No. 2, 40–45, in Russian.)Google Scholar
Chernyshenko, S. I. 1988 The asymptotic form of the stationary separated circumference of a body at high Reynolds number. Appl. Math. Mech. 52(6), 746. (Prikl. Matem. Mekh. 52 No. 6, 958–966, in Russian.)Google Scholar
Chernyshenko, S. I. 1991 Separated flow over a backward-facing step whose height is much greater than the thickness of the lower sublayer of the interaction zone. Fluid Dyn. 26(4), 496–501. (Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza (No. 4, 25–30, in Russian.)Google Scholar
Chernyshenko, S. 1993 Stratified Sadovskii flow in a channel. J. Fluid Mech. 250, 423–431.Google Scholar
Chernyshenko, S. I. 1995 Stabilization of trapped vortices by alternating blowing—suction. Phys. Fluids. 7, 802–807.Google Scholar
Chernyshenko, S. I. & Castro, I. P. 1993 High-Reynolds-number asymptotics of the steady flow through a row of bluff bodies. J. Fluid Mech. 257, 421–449.Google Scholar
Gol'dshtik, M. A. 1981 Vortex Flows. Novosibirsk: Nauka (in Russian).
Kuethe, A. M. & Chow, C. Y. 1986 Foundation of Aerodynamics. Bases of Aerodynamic Design. John Wiley & Sons.
Moore, D. W., Saffman, P. G. & Tanveer, S. 1988 The calculation of some Batchelor flows: The Sadovskii vortex and rotational corner flow. Phys. Fluids 31, 978–990.Google Scholar
Prandtl, L. 1905 Über Flüssigkeitsbewegung beu sehr kleiner Reibung. In Vehr. d. III. Intern. Math.–Kongr., Heidelberg, 1904, pp. 484–491. Leipzig: Teubner.
Sadovskii, V. S. 1971 Vortex regions in a potential stream with a jump in Bernoulli's constant across the boundary. Appl. Math. Mech. 35, 729. (Prikl. Matem. Mekh. 35(5), 773–779, in Russian.)Google Scholar
Shabat, A. B. 1963 On two sewing problems. Dok. Akad. Nauk SSSR 150(6), 1242–1245 (in Russian).Google Scholar
Smith, F. T. 1979 Laminar flow of an incompressible fluid past a bluff body: the separation, reattachment, eddy properties and drag. J. Fluid Mech. 92, 171–205.Google Scholar
Turfus, C. 1993 Prandtl—Batchelor flow past a flat plate at normal incidence in a channel — inviscid analysis. J. Fluid Mech. 249, 59–72.Google Scholar
Wu, J. M. & Wu, J. Z. 1992 Vortex lift at a very high angle of attack with massively separated unsteady flow. In: Fluid Dynamic of High Angle of Attack. IUTAM Symp. Tokyo, Japan, September 13–17, 1992 (ed. R. Kawamura & Y. Aihara), p. 34. Springer.