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SPECIAL SECTION ON THE FLUID MECHANICS AND RHEOLOGY OF NONLINEAR MATERIALS AT THE MACRO, MICRO AND NANO SCALE

Swirling Flow of a Viscoelastic Fluid With Free Surface—Part II: Numerical Analysis With Extended Marker-and-Cell Method

[+] Author and Article Information
Bo Yu

Department of Oil and Gas Storage and Transportation Engineering, China University of Petroleum, Beijing, 102249, People’s Republic of China

Jinjia Wei

State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

Yasuo Kawaguchi1

Department of Mechanical Engineering, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 278-8510, Japan

1

Corresponding author.

J. Fluids Eng 128(1), 77-87 (Aug 20, 2005) (11 pages) doi:10.1115/1.2136929 History: Received June 25, 2004; Revised August 20, 2005

In Part I [Wei, 2004, 2004 ASME Int. Mech. Eng. Conference], we presented the experimental results for swirling flows of water and cetyltrimethyl ammonium chloride (CTAC) surfactant solution in a cylindrical vessel with a rotating disk located at the bottom for a Reynolds number of around 4.3×104 based on the viscosity of solvent. For the large Reynolds number, violent irregular instantaneous secondary flows at the meridional plane were observed by use of a particle image velocimetry system. Because of the limitations of our computer resources, we did not carry out direct numerical simulation for such a large Reynolds number. The LES and turbulence model are alternative methods, but a viscoelastic LES/turbulence model has not yet been developed for the surfactant solution. In this study, therefore, we limited our simulations to a laminar flow. The marker-and-cell method proposed for Newtonian flow was extended to the viscoelastic flow to track the free surface, and the effects of Weissenberg number and Froude number on the flow pattern and surface shape were studied. Although the Reynolds number is much smaller than that of the experiment, the major experimental observations, such as the inhibition of primary and secondary flows and the decrease of the dip of the free surface by the elasticity of the solution, were qualitatively reproduced in the numerical simulations.

Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sketch of the disk-cylinder swirling flow system

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Figure 7

Transient process of the development of the vortex of viscoelastic flow at Re=100, Fr=100, We=1.0, β=1.0, α=0, and a=1.0 from a static state

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Figure 8

Secondary flows at various Reynolds numbers with We=0.5, Fr=100, β=1.0, α=0, and a=1.0 for viscoelastic flow [(a), (b), and (c)] and Fr=100 and a=1.0 for Newtonian flow (d).

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Figure 9

Effect of Froude number on the free surface at Re=100, We=0.5, β=1.0, α=0.0, and a=1.0

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Figure 10

Secondary flow at Re=100, Fr=100, We=0.3, β=3.0, α=0.0, and a=1.0

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Figure 11

Secondary flows at various mobility factors and Re=100, We=1.0, Fr=100, β=1, and a=1.0

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Figure 12

Evolution of the minimal tangential velocity after the stop of the rotating disk

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Figure 13

Contours of the tangential velocity at Re=100, We=1, Fr=100, β=1, α=0.003, and a=1.0

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Figure 14

The evolution of the tangential velocities at different radial position after the stop of the rotating disk at Re=100, We=1, Fr=100, β=1, α=0.003, and a=1.0

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Figure 15

The evolution of the tangential velocities at different axial position after the stop of the rotating disk at Re=100, We=1, Fr=100, β=1, α=0.003, and a=1.0

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Figure 16

The relationship between rheological parameters and Quelleffekt, recoil, and drag reduction rate

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Figure 2

Secondary flow patterns of a confined swirling flow. (a) Inertia-driven vortex of Newtonian flow (Re=100 and a=1.0) and (b) elasticity-driven vortex of viscoelastic flow (Re=100, We=1.0, β=1.0, α=0 and a=1.0).

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Figure 3

The total normal pressure exerted on the top disk

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Figure 4

Secondary flows at various Weissenberg numbers and Re=100, Fr=100, β=1, α=0, and a=1.0

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Figure 5

Contours of the tangential velocity. (a) Newtonian fluid Re=100, Fr=100, and a=1.0; (b) We=0.3, Re=100, Fr=100, β=1, α=0 and a=1.0; and (c) We=1.0, Re=100, Fr=100, β=1, α=0, and a=1.0

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Figure 6

Tangential velocities at z=0.2

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