Skip to main content Accessibility help
×
Home

Numerical and asymptotic solutions for merging flow through a channel with an upstream splitter plate

  • H. Badr (a1), S. C. R. Dennis (a2), S. Bates (a3) and F. T. Smith (a3)

Abstract

A numerical and analytical study is described for the divided flow field produced when the flows in two equal parallel channels, separated upstream by an aligned splitter plate, join together to form a single channel beyond the enclosed trailing edge of the plate. On the numerical side the second-order-accurate finite-difference scheme is based on a modified procedure to preserve accuracy and iterative convergence at higher Reynolds numbers R. Account is taken also of the influence of the boundedness of the computational domain and of the irregular behaviour of the flow solution at the trailing edge. The numerical solutions are presented for values of R up to 1000. On the analytical side the asymptotic structure of the solution for large R is governed mainly by a long $O(R^{\frac{1}{7}})$ relative lengthscale upstream and beyond the trailing edge. This is followed by a longer O(R) scale far downstream, but effects of practical significance also arise on the nominally tiny scale of O(R−½). Comparisons between the numerical and the asymptotic results for the wall shear stresses and the wake centreline velocity are made, and overall the agreement seems reasonable. The use of comparisons is believed to strengthen the value of both the numerical and the analytical approaches for these flows.

Copyright

References

Hide All
Bates, S. 1978 Ph.D. thesis, University of London.
Bramley, J. S. & Dennis, S. C. R. 1982a The calculation of eigenvalues for the stationary perturbation of Poiseuille flow. J. Comp. Phys. 47, 179.
Bramley, J. S. & Dennis, S. C. R. 1982b A numerical treatment of two-dimensional flow in a branching channel. In Lecture Notes in Physics vol. 170, p. 155. Springer.
Bramley, J. S. & Dennis, S. C. R. 1984 The numerical solution of two-dimensional flow in a branching channel. Comp. Fluids (to appear).
Daniels, P. G. 1974 Numerical and asymptotic solutions for the supersonic flow near the trailing edge of a flat plate. Q. J. Mech. Appl. Maths 27, 175.
Dennis, S. C. R. & Hudson, J. D. 1978 A difference method for solving the Navier-Stokes equations. In Numerical Methods in Laminar and Turbulent Flow, p. 69. Pentech.
Dennis, S. C. R. & Smith, F. T. 1980 Steady flow in a channel with a symmetrical constriction in the form of a step. Proc. R. Soc. Lond. A 372, 392.
Dijkstra, D. 1974 Ph.D. thesis, University of Groningen.
Goldstein, S. 1930 Concerning some solutions of the boundary-layer equations in hydrodynamics. Proc. Camb. Phil. Soc. 26, 1.
Hakkinen, R. J. & Rott, N. 1965 Similar solutions for merging shear flows. AIAA J. 3, 1553.
Pedley, T. J. 1980 The Fluid Mechanics of Large Blood Vessels. Cambridge University Press.
Smith, F. T. 1976 Flow through constricted or dilated pipes and channels. Part 2. Q. J. Mech. Appl. Maths 29, 365.
Smith, F. T. 1977a Steady motion through a branching tube. Proc. R. Soc. Lond. A 355, 167.
Smith, F. T. 1977b Upstream interactions in channel flows. J. Fluid Mech. 79, 631.
Smith, F. T. 1978 A note on a wall jet negotiating a trailing edge. Q. J. Mech. Appl. Maths 31, 473.
Smith, F. T. & Dennis, S. C. R. 1981 Injection from a finite section of a flat plate placed parallel to a uniform stream. J. Engng Maths 15, 267.
Smith, F. T. & Duck, P. W. 1980 On the severe nonsymmetric constriction, curving or cornering of channel flows. J. Fluid Mech. 98, 727.
Smith, F. T. & Stewartson, K. 1973 On slot-injection into a supersonic laminar boundary layer. Proc. R. Soc. Lond. A 322, 1.
Stewartson, K. 1970 On supersonic laminar boundary layers near convex corners. Proc. R. Soc. Lond. A 319, 289.
Van Dyke, M. 1970 Entry flow in a channel. J. Fluid Mech. 44, 813.
Wilson, S. 1971 Entry flow in a channel. Part 2. J. Fluid Mech. 46, 787.
Woods, L. C. 1954 A note on the numerical solution of fourth order differential equations. Aero. Q. 5, 176.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Numerical and asymptotic solutions for merging flow through a channel with an upstream splitter plate

  • H. Badr (a1), S. C. R. Dennis (a2), S. Bates (a3) and F. T. Smith (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.