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Research Papers: Fundamental Issues and Canonical Flows

Numerical Investigation of the Three-Dimensional Pressure Distribution in Taylor Couette Flow

[+] Author and Article Information
David Shina Adebayo

Department of Engineering,
University of Leicester,
University Road,
Leicester LE1 7RH, UK
e-mail: dsa5@le.ac.uk

Aldo Rona

Department of Engineering,
University of Leicester,
University Road,
Leicester LE1 7RH, UK
e-mail: ar45@le.ac.uk

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 31, 2016; final manuscript received May 10, 2017; published online August 8, 2017. Assoc. Editor: Daniel Livescu.

J. Fluids Eng 139(11), 111201 (Aug 08, 2017) (10 pages) Paper No: FE-16-1714; doi: 10.1115/1.4037083 History: Received October 31, 2016; Revised May 10, 2017

An investigation is conducted on the flow in a moderately wide gap between an inner rotating shaft and an outer coaxial fixed tube, with stationary end-walls, by three-dimensional Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD), using the realizable kε  model. This approach provides three-dimensional spatial distributions of static and dynamic pressures that are not directly measurable in experiment by conventional nonintrusive optics-based techniques. The nonuniform pressure main features on the axial and meridional planes appear to be driven by the radial momentum equilibrium of the flow, which is characterized by axisymmetric Taylor vortices over the Taylor number range 2.35×106Ta6.47×106. Regularly spaced static and dynamic pressure maxima on the stationary cylinder wall follow the axial stacking of the Taylor vortices and line up with the vortex-induced radial outflow documented in previous work. This new detailed understanding has potential for application to the design of a vertical turbine pump head. Aligning the location where the gauge static pressure (GSP) maximum occurs with the central axis of the delivery pipe could improve the head delivery, the pump mechanical efficiency, the system operation, and control costs.

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Figures

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Fig. 1

(a) Hexahedral computational mesh structure and (b) computational mesh detail at the end-wall. One mesh point every two in X, r, and θ has been plotted for clarity.

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Fig. 2

Radial velocity profiles at r=Ri+0.500d for three different levels of computational mesh refinement for test cases: (a) Γ = 7.81 and (b) Γ = 11.36. (⋄) Mesh type 1, (◻) mesh type 2, and (⊹) mesh type 3.

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Fig. 3

Normalized (a) axial and (b) radial velocity profiles from PIV and CFD at the constant radial positions r=Ri+0.125d and r=Ri+0.500d on the meridional plane at θ=−0.5π, with the PIV error band. Γ = 7.81.

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Fig. 4

Normalized velocity vectors in the meridional plane of the annulus for test cases: (a) Γ= 7.81 and (b) Γ = 11.36. The reference velocity vector is 0.5 ΩRi.

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Fig. 5

Velocity vectors on different axial planes normalized byΩRi: (a) X/Ri = 0.05, Γ = 7.81, (b) X/Ri = 0.92, Γ = 7.81, (c) X/Ri = 1.47, Γ = 7.81, (d) X/Ri = 1.41, Γ = 11.36, (e) X/Ri = 1.84, Γ = 11.36, and (f) X/Ri = 9.95, Γ = 11.36

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Fig. 6

Normalized gauge static pressure profiles in the meridional plane at constant radial positions: (⊹) r=Ri+0.045d, (⋄) r=Ri+0.500d, and (◻) r=Ri+0.955d for the test cases (a) Γ = 7.81 and (b) Γ = 11.36. (−)  θ=0.5π and (- -) θ=−0.5π.

Grahic Jump Location
Fig. 7

Normalized dynamic pressure profiles in the meridional plane at constant radial positions: (⊹) r=Ri+0.045d, (⋄) r=Ri+0.500d, and (◻) r=Ri+0.955d for the test cases (a) Γ = 7.81 and (b) Γ  = 11.36. (−) θ=0.5π and (- -) θ=−0.5π.

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Fig. 8

Azimuthal profiles of normalized dynamic pressure atdifferent radii on selected axial planes for the test cases:(a)Γ = 7.81 and (b) Γ = 11.36. (⊹) r=Ri+0.045d, (⋄) r=Ri+0.500d, and (◻) r=Ri+0.955d.

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Fig. 9

Normalized gauge static pressure profiles on different axial planes at θ=−0.5π: (a) Γ = 7.81 and (b) Γ = 11.36

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Fig. 10

Normalized dynamic pressure profiles on different axial planes at θ=−0.5π: (a) Γ = 7.81 and (b) Γ = 11.36

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