Abstract
The flow in a pipe of circular cross-section which is coiled in a circle is studied, the pressure gradient along the pipe varying sinusoidally in time with frequency ω. The radius of the pipeais assumed small in relation to the radius of curvature of its axisR. Of special interest is the secondary flow generated by centrifugal effects in the plane of the cross-section of the pipe, and an asymptotic theory is developed for small values of the parameter β = (2ν/ωa2)½, where ν is the kinematic viscosity of the fluid. The secondary flow is found to be governed by a Reynolds number$R_s = \overline{W}^2a/R \omega\nu$, where$\overline{W}$is a typical velocity along the axis of the pipe, and asymptotic theories are developed for both small and large values of this parameter. For sufficiently small values of β it is found that the secondary flow in the interior of the pipe is in the opposite sense to that predicted for a steady pressure gradient, and this is verified qualitatively by an experiment described at the end of the paper.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference14 articles.
1. Batchelor, G. K. 1956 J. Fluid Mech. 1,177–90.
2. Barua, S. N. 1963 Quart. J. Mech. Appl. Math. 16,61–77.
3. Dean, W. R. 1928 Phil. Mag. (7)5,673–95.
4. McConalogue, D. J. & Srivastava, R. S. 1968 Proc. Roy. Soc A307,37–53.
5. Harper, J. F. & Moore, D. W. 1968 J. Fluid Mech. 32,367–91.
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