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Journal of Fluids Engineering | Volume 134 | Issue 4 | Flows in Complex Systems
Flows in Complex Systems

Numerical Investigations of Passive Scalar Transport in Turbulent Taylor-Couette Flows: Large Eddy Simulation Versus Direct Numerical Simulations

[+] Author and Article Information
Yacine Salhi

 USTHB, Physics Faculty, LMFTA, BP.32, 16111 Bab-Ezzouar, El-Alia Algiers, Algeria; Aero-Thermo-Mechanics Department, Université Libre de Bruxelles, CP 165/41, 50 Avenue F. D, Roosevelt, 1050 Brussels, Belgium

El-Khider Si-Ahmed

 USTHB, Physics Faculty, LMFTA, BP.32, 16111 Bab-Ezzouar, El-Alia Algiers, Algeria; GEPEA, CNRS, UMR 6144, CRTT, Université de Nantes, 37, Boulevard de l’Université BP 406, 44602 Saint-Nazaire Cedex, Franceel-khider.si-ahmed@univ-nantes.fr

Gérard Degrez

 Aero-Thermo-Mechanics Department, Université Libre de Bruxelles, CP 165/41, 50 Avenue F. D, Roosevelt, 1050 Brussels, Belgium

Jack Legrand

 GEPEA, CNRS, UMR 6144, CRTT,Université de Nantes, 37,Boulevard de l’Université BP 406, 44602 Saint-Nazaire Cedex, Francejack.legrand@univ-nantes.fr

J. Fluids Eng 134(4), 041105 (Apr 20, 2012) (10 pages) doi:10.1115/1.4006467 History: Received October 13, 2010; Revised March 16, 2012; Published April 20, 2012; Online April 20, 2012
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The highly turbulent flow occurring inside (electro)chemical reactors requires accurate simulation of scalar mixing if computational fluid dynamics (CFD) methods are to be used with confidence in design. This has motivated the present paper, which describes the implementation of a passive scalar transport equation into a hybrid spectral/finite-element code. Direct numerical simulations (DNS) and large eddy simulation (LES) were performed to study the effects of gravitational and centrifugal potentials on the stability of incom-pressible Taylor-Couette flow. The flow is confined between two concentric cylinders with an inner rotating cylinder while the outer one is at rest. The Navier-Stokes equations with the uncoupled convection–diffusion–reaction (CDR) equation are solved using a code named spectral/finite element large eddy simulations (SFELES) which is based on spectral development in one direction combined with a finite element discretization in the remaining directions. The performance of the LES code is validated with published DNS data for channel flow. Velocity and scalar statistics showed good agreement between the current LES predictions and DNS data. Special attention was given to the flow field, in the vicinity of Reynolds number of 68.2 with radii ratio of 0.5. The effect of Sc on the concentration peak is pointed out while the magnitude of heat transfer shows a dependence of the Prandtl number with an exponent of 0.375.
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Copyright © 2012 by American Society of Mechanical Engineers
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+Sketch of the reactor with Taylor-Couette geometry
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Sketch of the reactor with Taylor-Couette geometry
Figure 1

Sketch of the reactor with Taylor-Couette geometry

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+The rate of convergence plot for the developed code
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The rate of convergence plot for the developed code
Figure 2

The rate of convergence plot for the developed code

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+Mean streamwise velocity profiles using different grids
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Mean streamwise velocity profiles using different grids
Figure 3

Mean streamwise velocity profiles using different grids

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+Streamlines at different time steps: (a) cells start to form from the ends; (b) second groups of cells starts to form; (c) the inner cells start to form; (d) close to fully developed cells
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Streamlines at different time steps: (a) cells start to form from the ends; (b) second groups of cells starts to form; (c) the inner cells start to form; (d) close to fully developed cells
Figure 4

Streamlines at different time steps: (a) cells start to form from the ends; (b) second groups of cells starts to form; (c) the inner cells start to form; (d) close to fully developed cells

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+Streamlines for isothermal Taylor-Couette flow (a) Re = 30, (b) Re = 50, (c) Re = 60, (d) Re = 65 and (e) Re = 70.
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Streamlines for isothermal Taylor-Couette flow (a) Re = 30, (b) Re = 50, (c) Re = 60, (d) Re = 65 and (e) Re = 70.
Figure 5

Streamlines for isothermal Taylor-Couette flow (a) Re = 30, (b) Re = 50, (c) Re = 60, (d) Re = 65 and (e) Re = 70.

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+Heat and mass transfer variations on the outer cylinder for η=0.617. (Symbols: experimental data from Kataoka [21])
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Heat and mass transfer variations on the outer cylinder for η=0.617. (Symbols: experimental data from Kataoka [21])
Figure 6

Heat and mass transfer variations on the outer cylinder for η=0.617. (Symbols: experimental data from Kataoka [21])

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+Effect of Pr of heat transfer on the outer cylinder for Re=110, λz=1.88 and η=0.617
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Effect of Pr of heat transfer on the outer cylinder for Re=110, λz=1.88 and η=0.617
Figure 7

Effect of Pr of heat transfer on the outer cylinder for Re=110, λz=1.88 and η=0.617

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+Comparison of the numerical data with the empirical Eisenberg’s relation Eq. 24 at the Reynolds numbers 70 < Re < 10000. The dimensions of the reactor are: ri  = 6 mm, ro  = 35 mm, H = 50 mm.
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Comparison of the numerical data with the empirical Eisenberg’s relation Eq. 24 at the Reynolds numbers 70 < Re < 10000. The dimensions of the reactor are: ri  = 6 mm, ro  = 35 mm, H = 50 mm.
Figure 8

Comparison of the numerical data with the empirical Eisenberg’s relation Eq. 24 at the Reynolds numbers 70 < Re < 10000. The dimensions of the reactor are: ri  = 6 mm, ro  = 35 mm, H = 50 mm.

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+Sherwood number at the outer cylinder, Re= 3200
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Sherwood number at the outer cylinder, Re= 3200
Figure 9

Sherwood number at the outer cylinder, Re= 3200

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+Pipe flow - Comparison of velocity rms values
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Pipe flow - Comparison of velocity rms values
Figure 10

Pipe flow - Comparison of velocity rms values

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+Pipe flow - Comparison of scalar rms values
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Pipe flow - Comparison of scalar rms values
Figure 11

Pipe flow - Comparison of scalar rms values

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+Taylor-Couette flow - Fluctuating velocity and scalar for Sc = 0.7 and Sc = 5.0
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Taylor-Couette flow - Fluctuating velocity and scalar for Sc = 0.7 and Sc = 5.0
Figure 12

Taylor-Couette flow - Fluctuating velocity and scalar for Sc = 0.7 and Sc = 5.0

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+Taylor-Couette flow - RMS values of scalar for different Schmidt numbers
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Taylor-Couette flow - RMS values of scalar for different Schmidt numbers
Figure 13

Taylor-Couette flow - RMS values of scalar for different Schmidt numbers

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