Steady Flow Structures and Pressure Drops in Wavy-Walled Tubes

[+] Author and Article Information
M. E. Ralph

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 9EW, England

J. Fluids Eng 109(3), 255-261 (Sep 01, 1987) (7 pages) doi:10.1115/1.3242656 History: Received August 08, 1986; Online October 26, 2009


Solutions of the Navier-Stokes equations for steady axisymmetric flows in tubes with sinusoidal walls were obtained numerically, for Reynolds numbers (based on the tube radius and mean velocity at a constriction) up to 500, and for varying depth and wavelength of the wall perturbations. Results for the highest Reynolds numbers showed features suggestive of the boundary layer theory of Smith [23]. In the other Reynolds number limit, it has been found that creeping flow solutions can exhibit flow reversal if the perturbation depth is large enough. Experimentally measured pressure drops for a particular tube geometry were in agreement with computed predictions up to a Reynolds number of about 300, where transitional effects began to disturb the experiments. The dimensionless mean pressure gradient was found to decrease with increasing Reynolds number, although the rate of decrease was less rapid than in a straight-walled tube. Numerical results showed that the mean pressure gradient decreases as both the perturbation wavelength and depth increase, with the higher Reynolds number flows tending to be more influenced by the wavelength and the lower Reynolds number flows more affected by the depth.

Copyright © 1987 by ASME
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