Numerical integration is conducted for two-dimensional incompressible laminar flow over a 90° corner. Using Newton’s method, the Navier-Stokes equations are generated up toRe=2800, with the result that the corner generates a second bubble nearRe=800. There exist distinct patterns for the evolution of the pressure gradient and the position of a separation point. AsRe is increased the pressure gradient tends to approach zero over the recirculated region and shows sharper variations near the separation and reattachment points. Thus, these results confirm the free streamline model for separation proposed by Sychev.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
- i :
Index to denote the step number in ξ-direction
- I :
i at the downstream edge ξ=ξ m
- j :
Index to denote the step number in η-direction
- J :
j atη=η m
- M :
- p :
- Re :
- s :
Coordinate along the wall
- w :
x 1+iy 1
- x 1,y 1 :
Coordinate system inw-plane
- x, y :
Coordnate system inz-plane
- x s :
- z :
Normal component of ρ
- η m :
Displacement thickness of the boundary layer flow over a wedge
- η m :
η at the upper edge
Tangential component of ρ
- ε m :
ξ at the downstream edge
- T :
Wall shear defined as Eq. (14)
- Ψ m :
Ψ atη=η m
Batchelor, G.K. 1956a, “On Steady Laminar Flow with Closed Stream Lines at Large Reynolds Number”, JFM, Vol. 1, pp. 177–190.
Batchelor, G.K. 1956b, “A Proposal Concerning Laminar Wakes behind Bluff Bodies at Large Reynolds Number”, JFM, Vol. 1, pp. 388–398.
Dennis, S.C.R. and Chang, G.Z. 1970, “Numerical Solutions for Steady Flow past a Circular Cylinder at Reynolds Numbers up to 1000”, JFM, Vol. 42, pp. 471–485.
Fornberg, B. 1980, “A Numerical Study of Steady Viscous Flow past a Circular Cylinder”, JFM, Vol. 98, pp. 819–855.
Fornberg, B. 1986, “Steady Viscous Flow past a Circular Cylinder up to Reynolds Number 600”, J. Comp. Phys., Vol. 61, pp. 297–320.
Hildebrand, F. B., 1976, Advanced Calculus for Applications, second ed., Prentice-Hall, Inc., Englewood Cliffs, N. J., U.S.A., pp. 473–474.
Kaplun, S. 1954, “The Role of Coordinate Systems in Boundarylayer Theory”, ZAMP, Vol. 5, pp. 111–135.
Leal, L. G. 1973, “Steady Separated Flow in Linearly Decelerated Free Stream”, JFM, Vol. 59, pp. 513–535.
Patel, V.A. 1976, “Time-Dependent Solutions of the Viscous Incompressible Flow Past a Circular Cylinder by the Method of Series Truncation”, Computers and Fluids, Vol. 4, pp. 13–27.
Roache, P. J. 1975, “The LAD, NOS, and Split NOS Methods for the Steady-State Navier-Stokes Equations”, Computers and Fluids, Vol. 3, pp. 179–195.
Roache, P.J. and Ellis, M.A. 1975, “The BID Method for the Steady-State Navier-Stokes Equations”, Computers and Fluids, Vol. 3, pp. 305–320.
Smith, F. T. 1979, “Laminar Flow of an Incompressible Flow past a Bluff Body: The Separation, Reattachment, Eddy Properties and Drag”, JFM, Vol. 92, pp. 171–205.
Smith, F.T. 1982, “On the High Reynolds Number Theory of Laminar Flow”, IMA J. Appl. Math., Vol. 28, pp. 207–281.
Son, J.S. and Hanratty, T.T., 1969, “Numerical Solution for the Flow around a Circular Cylinder at Reynolds Numbers of 40, 200 and 500”, JFM, Vol. 35, pp. 369–386.
Suh, Y.K. 1986, “On Laminar Viscous Flow over a Corner”, Ph. D. Dissertation, State Univ. of New York at Buffalo, Buffalo, NY, U.S.A.
Sychev, V. V. 1972, “Laminar Separation”, Fluid Dynamics, Vol. 7, pp. 407–417.
Takami, H. and Keller, H., 1969, “Steady Two-Dimensional Viscous Flow of an Incompressible Fluid Past a Circular Cyliner”, High-speed of Computing in Dynamics, The Physics of Fluids Supplement II, pp. 51–56.
Walter, K. T. and Larsen, P.S. 1981, “The FON Method for the Steady-State Two-Dimensional Navier-Stokes Equations”, Computers and Fluids, Vol. 9, pp. 365–376.
About this article
Cite this article
Suh, Y.K., Park, C.K. Incompressible laminar flow near a corner of 90° angle. KSME Journal 1, 121–127 (1987). https://doi.org/10.1007/BF02971655
- Newton’s Method
- Second Bubble
- Boundary Layer
- Free Streamline Model