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Time-dependent viscous flow in a straight channel

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Abstract

An infinite straight channel, filled with an incompressible viscous fluid, is closed at one end by a piston. This is set in motion with finite acceleration and then maintained at constant velocity until the flow pattern in the fluid reaches a steady state. The development of velocity profiles, stream lines, and streak lines is investigated by direct numerical solution of the complete Navier Stokes equations. It is found that the nonconvex velocity profiles found in previous work on steady-state problems appear from the beginning, and their development is studied. In the downstream region alternative methods can be used which serve as a check on the accuracy of the numerical procedures. The asymptotic behaviour downstream is studied in some detail.

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Abbreviations

a :

acceleration of piston

f(t):

nondimensional distance travelled by piston up to time t

2l :

width of channel

p :

pressure (in units of ρu 20 )

R :

Reynolds number, lu 0/ν

t 0 :

time during which piston is accelerated

u 0 :

final velocity of piston

(u, v):

(x, y) components of fluid velocity (relative to piston, in units of u 0)

x :

distance measured downstream from piston (in units of l)

y :

distance from central axis of channel (in units of l)

ζ :

vorticity

ρ :

density of fluid

ν :

kinematic viscosity

ψ :

stream function

References

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Authors and Affiliations

  1. Dept. of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel

    N. Liron & J. Gillis

Authors
  1. N. Liron
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  2. J. Gillis
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Liron, N., Gillis, J. Time-dependent viscous flow in a straight channel. Appl. Sci. Res. 23, 243–268 (1971). https://doi.org/10.1007/BF00413202

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  • DOI: https://doi.org/10.1007/BF00413202

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