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

Taylor-Couette Instabilities in Flows of Newtonian and Power-Law Liquids in the Presence of Partial Annulus Obstruction

[+] Author and Article Information
B. V. Loureiro, L. F. Azevedo

Department of Mechanical Engineering, Pontifícia Universidade Católica do Rio de Janeiro, Rua Marquês de São Vicente 225, Gávea, Rio de Janeiro, RJ, 22453-900, Brazil

P. R. de Souza Mendes1

Department of Mechanical Engineering, Pontifícia Universidade Católica do Rio de Janeiro, Rua Marquês de São Vicente 225, Gávea, Rio de Janeiro, RJ, 22453-900, Brazil

1

Corresponding author. Email: pmendes@mec.puc-rio.br

J. Fluids Eng. 128(1), 42-54 (Sep 29, 2005) (13 pages) doi:10.1115/1.2136930 History: Received September 20, 2004; Revised September 29, 2005

The flow inside a horizontal annulus due to the inner cylinder rotation is studied. The bottom of the annular space is partially blocked by a plate parallel to the axis of rotation, thereby destroying the circumferential symmetry of the annular space geometry. This flow configuration is encountered in the drilling process of horizontal petroleum wells, where a bed of cuttings is deposited at the bottom part of the annulus. The velocity field for this flow was obtained both numerically and experimentally. In the numerical work, the equations which govern the three-dimensional, laminar flow of both Newtonian and power-law liquids were solved via a finite-volume technique. In the experimental research, the instantaneous and time-averaged flow fields over two-dimensional meridional sections of the annular space were measured employing the particle image velocimetry (PIV) technique, also both for Newtonian and power-law liquids. Attention was focused on the determination of the onset of secondary flow in the form of distorted Taylor vortices. The results showed that the critical rotational Reynolds number is directly influenced by the degree of obstruction of the flow. The influence of the obstruction is more perceptible for Newtonian than for non-Newtonian liquids. The more severe is the obstruction, the larger is the critical Taylor number. The height of the obstruction also controls the width of the vortices. The calculated steady-state axial velocity profiles agreed well with the corresponding measurements. Transition values of the rotational Reynolds number are also well predicted by the computations. However, the measured and predicted values for the vortex size do not agree as well. Transverse flow maps revealed a complex interaction between the Taylor vortices and the zones of recirculating flow, for moderate to high degrees of flow obstruction.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Cross section of the partially obstructed annular space. Inner cylinder rotates counter-clockwise.

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Figure 2

Schematic view of the experimental setup

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Figure 3

Influence of dimensionless acceleration on critical Reynolds number for a Newtonian liquid. Experimental results.

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Figure 4

(a) Axial-to-tangent velocity norm ratio as a function of the rotational Reynolds number. (b) Derivative of the norm ratio as a function of the rotational Reynolds number (Newtonian liquid, h∕d=0.5).

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Figure 5

Critical Reynolds number as a function of the obstruction height

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Figure 6

Critical Reynolds number at the minimum gap as a function of the radius ratio at the minimum gap

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Figure 7

Vortex length as a function of obstruction height. Newtonian liquid.

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Figure 8

Axial velocity profiles for Taylor-vortex regime. Unobstructed annulus and Newtonian liquid. (a) Re=104. (b) Re=126.

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Figure 9

Axial velocity profiles for Taylor-vortex regime. Unobstructed annulus. n=0.406. Re≃1.8Rec.

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Figure 10

Velocity profile in the meridional planes 0 and 180deg for Taylor-vortex regime. Newtonian liquid. Re≃1.2Rec, h∕d=0.5.

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Figure 11

Velocity profile in the meridional plane 90deg for Taylor-vortex regime. Newtonian liquid. Re=109, h∕d=0.5.

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Figure 12

Velocity profile in the meridional plane 270deg for Taylor-vortex regime. Newtonian liquid. Re=109, h∕d=0.5.

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Figure 13

Velocity profile in the meridional planes (a) 0 and 180deg and (b) 90 and 270deg for Taylor-vortex regime. n=0.704. Re=69.5≃1.03Rec, h∕d=0.25.

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Figure 14

Velocity profile in the meridional planes (a) 0 and 180deg and (b) 90 and 270deg for Taylor-vortex regime. n=0.704. Re=80≃1.03Rec, h∕d=0.5.

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Figure 15

Velocity distribution in the r-z plane and vortex structure. Newtonian liquid. Re=85.6, h∕d=0.0, θ=0.

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Figure 16

Velocity distribution in the r-z plane and vortex structure. Newtonian liquid. Re=149h∕d=0.75, θ=0.

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Figure 17

Particle pathline as given by the numerical solution for a Newtonian liquid. h∕d=0.75, Re=149.

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Figure 18

Velocity distribution in the lower half of the cross section of the annular space (a) at the vortex-pair symmetry plane and (b) at the vortex midplane (upstream at left and downstream at right). Re=149, h∕d=0.75. Counter-clockwise cylinder rotation. Newtonian liquid.

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Figure 19

Shear stress distribution on the plate surface. (a) Re=87.2=0.99Rec. (b) Re=105.2=1.20Rec. (c) Complement of accumulated area (total area-accumulated area). h∕d=0.5. Newtonian liquid.

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Figure 20

Shear stress distribution on the plate surface. (a) Re=145.3=0.99Rec. (b) Re=175.6=1.20Rec. (c) Complement of accumulated area (total area-accumulated area). h∕d=0.75. Newtonian liquid.

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