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Fundamental Issues and Canonical Flows

Can the Dean number Alone Characterize Flow Similarity in Differently Bent Tubes?

[+] Author and Article Information
Krzysztof Cieślicki

Laboratory of Bioflows,  Institute of Automatic Control and Robotics, Warsaw University of Technology, 02-525 Warsaw, Poland

Adam Piechna1

Laboratory of Bioflows,  Institute of Automatic Control and Robotics, Warsaw University of Technology, 02-525 Warsaw, Polandadam.piechna@gmail.com

1

Corresponding author.

J. Fluids Eng 134(5), 051205 (May 22, 2012) (6 pages) doi:10.1115/1.4006417 History: Received June 06, 2011; Revised March 19, 2012; Published May 18, 2012; Online May 22, 2012

Although flows of fluids in curved channels belong to a classical problem of fluid dynamics, most publications are restricted to investigations of flows in tube coils, or in single bends. This paper presents experimental and numerical (CFD) results concerning Newtonian flows in a set of multiple S-type bends of various orientations. Investigations were conducted for a wide range of Re values (0–3500) and for a significant curvature ratio lying between 0.05 and 0.29, which corresponds to De value falling within the range 0.02–1200. A coiled tube was also examined and treated as the reference geometry. It was shown, that despite a completely different velocity pattern, the nonlinear dependence of normalized flow resistance of wavy tubes and coiled tube of the same curvature ratio overlap within a significant range of De. A novel, close phenomenological formula to estimate the nonlinear flow resistance of tortuous tube in a wide range of De was proposed and compared with those in the literature. The conditions were also determined in which the De might be the only dimensionless group that characterizes such flows.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Four considered tubes’ configurations. Dimensions of the sine-type tubes are shown on the right-bottom drawing.

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Figure 2

The experimental setup

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Figure 3

(a) Discretization of computational flow domain. The fine mesh lying within the boundary layer is marked out. (b) Results of the mesh convergence test. Fine reference mesh and mesh with optimal cell density are marked out.

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Figure 4

Experimental and numerical plots of hydraulic resistance of examined tubes, RC = J/Q, against Re obtained for models: (a) sinA; (b) sinB; (c) sin3D; (d) coil. Solid lines denote the best fit approximations of experimental points obtained from the introduced Eq. 1a. Images denote normalized velocity magnitude at characteristic cross section of a particular model for four Re values.

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Figure 5

Relative flow resistance of all experimental models against De. Solid line is plotted according to Eq. 1,1ab. The Dashed line refers to equation of hyperbole’s asymptote (see A2 in the appendix).

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Figure 6

The relations of flow resistance ratio versus the curvature ratio for constant values of De

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Figure 7

Comparison of the literature analytical (2) and asymptotic solutions to our experimental and CFD results (for δ = 0.074) for low range of De. Our best fit relation 1 and 1 is marked by solid bold line.

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