Abstract
The unsteady interaction of plane-channel wall boundary layers with a supersonic inviscid flow is investigated. The flow regimes in which disturbances introduced by the boundary layer developing on one wall influence the boundary layer on the other wall are considered. The regime of relatively large pressure disturbance amplitudes generated near the nozzle outlet or by deforming the channel walls is studied. In these conditions, the interaction process is described by a system of Burgers equations with retarded arguments. Numerical solutions of this system are obtained for symmetric and antisymmetric perturbations of the channel walls.
Similar content being viewed by others
REFERENCES
H. S. Tsien and M. Finston, "Interaction between parallel streams of subsonic and supersonic velocity", J. Aero-naut. Sci., 16, No. 9, 515–528 (1949).
M. J. Lighthill, "Reflection of laminar boundary layer of a weak steady disturbance to a supersonic stream, ne-glecting viscosity and heat conduction," Quart. J. Mech. Appl. Math., 3, Pt 3, 303–325 (1950).
M. J. Lighthill, "On boundary layers and upstream influence. II Supersonic flows without separation" Proc. Roy. Soc. London. Ser. A, 217, No. 1131, 478–507 (1953).
V. Ya. Neiland, "Asymptotic problems of the theory of viscous supersonic flows," Trudy TsAGI, No. 1525, 1–125 (1974).
K. Stewartson, "Multistructured boundary layers on flat plates and related bodies," In: Advances in Applied Mechanics, 14, Acad. Press, New York, etc. (1974), pp. 145–239.
F. T. Smith, "Flow through constricted or dilated pipes and channels," Quart. J. Mech. Appl. Math., 29,Pt 3, 343–376 (1976).
F. T. Smith, "Upstream interactions in channels flows," J. Fluid Mech., 79, Pt 4, 631–655 (1977).
E. M. Nikolaeva and V. N. Trigub, "On the self-induced interaction of boundary layers in a plane channel," Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 4, 131–141 (1995).
E. V. Bogdanova and O. S. Ryzhov, "On free oscillations of a viscous incompressible fluid in a semi-infinite channel," Prikl. Matem. Mekh., 47, No. 1, 64–72 (1983).
A. I. Ruban and S. N. Timoshin, "On disturbance propagation in the boundary layer on plane-channel walls," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 74–79 (1986).
V. I. Zhuk and O. S. Ryzhov, "On locally inviscid disturbances in a boundary layer with self-induced pressure," Dokl. Akad. Nauk SSSR, 263, No. 1, 56–59 (1982).
V. I. Zhuk and S. P. Popov, "Modeling of nonlinear waves in boundary layers on the basis of the Burgers, Benjamin-Ono, and Korteweg-de Vries equations," Matem. Model., 2, No. 7, 96–109 (1990).
I. V. Savenkov, "Wave packets, resonant interactions, and soliton formation in inlet pipe flow," J. Fluid. Mech., 252, 1–30 (1993).
I. I. Lipatov and V. Ya. Neiland, "Towards a theory of unsteady separation and boundary layer interaction with a supersonic gas stream," Uchen. Zap. TsAGI, 18, No. 1, 36–49 (1987)
Rights and permissions
About this article
Cite this article
Dubinskii, S.V., Lipatov, I.I. On Disturbance Propagation in Internal-Flow Boundary Layers. Fluid Dynamics 39, 565–573 (2004). https://doi.org/10.1023/B:FLUI.0000045671.43477.c0
Issue Date:
DOI: https://doi.org/10.1023/B:FLUI.0000045671.43477.c0