Abstract
In this paper we consider a fully developed turbulent flow in a round pipe with a small inner annulus. The diameter of the inner annulus is less than 10% of the diameter of the outer pipe. As a consequence, the surface area of the inner pipe compared to the outer pipe is small. The friction exerted by the wall on the flow is proportional to the surface area and the wall shear stress. Due to the small surface area of the inner annulus the additional stress on the flow due to the presence of the annulus may expected to be negligible. However, it will be shown that the inner annulus drastically changes the flow patterns and gives rise to unexpected scaling properties. In previous studies (Chung et al., Int J Heat Fluid Flow 23:426–440, 2002; Churchill and Chan, AIChE J 41:2513–2521, 1995) it was argued that radial position of the point of zero shear stress does not coincide with the radial location of the point of maximum axial velocity. In our direct numerical simulations we observe a coincidence of these points within the numerical accuracy of our model. It is shown that the velocity profile close to the inner annulus is logarithmic.
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References
Eggels, J.G.M., Unger, F., Weiss, M.H., Westerweel, J. Friedrich, R., Nieuwstadt, F.T.M.: Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J. Fluid Mech. 268, 175–209 (1994)
Chung, S.Y., Rhee, G.h., Sung, H.J.: Direct numerical simulation of turbulent concentric annular pipe flow, Part 1: flow field. Int. J. Heat Fluid Flow 23, 426–440 (2002)
Rehme, K.: Turbulent flow in smooth concentric annuli with small radius ratios. J. Fluid Mech. 64, 263–287 (1974)
Kaneda, M., Yu, B., Ozoe, H., Churchill, S.W.: The characteristics of turbulet flow and convection in concentric circular annuli, Part I: flow. Int. J. Heat Mass Transfer 46, 5045–5057 (2003)
Brighton, J.A., Jones, J.B.: Fully developed turbulent flow in annuli. J. Basic Eng. 86, 835–844 (1964)
Quarmby, A.: An analysis of turbulent flow in concentric annuli. Appl. Sci. Res. 19, 250–273 (1968)
Churchill, S.W., Chan, C.: Turbulent flow in channels in terms of local turbulent shear and normal stresses. AIChE J. 41, 2513–2521 (1995)
Nouri, J.M., Umur, H, Whitelaw, J.H.: Flow of Newtonian and non-Newtonian fluids in concentric and eccentric annuli. J. Fluid Mech. 253, 617–641 (1993)
Mochizuki, S., Nieuwstadt, F.T.M.: Reynolds number-dependence of the maximum in the streamwise velocity fluctuations in wall turbulence. Exp. Fluids 21, 218–226 (1996)
Hinze, J.O.: Turbulent flow regions with shear stress and mean velocity gradient of opposite sign. Appl. Sci. Res. 22, 163–175 (1970)
Neves, J.C., Moin, P., Moser, R.D.: Effects of convex transverse curvature on wall-bounded turbulence. Part 1. The velocity and vorticity. J. Fluid Mech. 272, 349–381 (1994)
Pope, S.B: (2003) Turbulent Flows. Cambridge University Press
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Boersma, B.J., Breugem, WP. Numerical Simulation of Turbulent Flow in Concentric Annuli. Flow Turbulence Combust 86, 113–127 (2011). https://doi.org/10.1007/s10494-010-9295-y
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DOI: https://doi.org/10.1007/s10494-010-9295-y