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Research Papers: Fundamental Issues and Canonical Flows

Characterization of Mixing in a Simple Paddle Mixer Using Experimentally Derived Velocity Fields

[+] Author and Article Information
Douglas Bohl

Akshey Mehta

 Department of Mechanical and Aeronautical Engineering, Clarkson University, 8 Clarkson Avenue, Potsdam, NY 13699aksheymehta@gmail.com

Naratip Santitissadeekorn

 Department of Mathematics, Clarkson University, 8 Clarkson Avenue, Potsdam, NY 13699santitn@unsw.edu.au

Erik Bollt

 Department of Mathematics, Clarkson University, 8 Clarkson Avenue, Potsdam, NY 13699bolltem@clarkson.edu

J. Fluids Eng 133(6), 061202 (Jun 16, 2011) (8 pages) doi:10.1115/1.4004086 History: Received February 22, 2011; Revised April 14, 2011; Published June 16, 2011; Online June 16, 2011

The flow field in a cylindrical container driven by a flat bladed impeller was investigated using particle image velocimetry (PIV). Three Reynolds numbers (0.02, 8, 108) were investigated for different impeller locations within the cylinder. The results showed that vortices were formed at the tips of the blades and rotated with the blades. As the blades were placed closer to the wall the vortices interacted with the induced boundary layer on the wall to enhance both regions of vorticity. Finite time lyapunov exponents (FTLE) were used to determine the lagrangian coherent structure (LCS) fields for the flow. These structures highlighted the regions where mixing occurred as well as barriers to fluid transport. Mixing was estimated using zero mass particles convected by numeric integration of the experimentally derived velocity fields. The mixing data confirmed the location of high mixing regions and barriers shown by the LCS analysis. The results indicated that mixing was enhanced within the region described by the blade motion as the blade was positioned closed to the cylinder wall. The mixing average within the entire tank was found to be largely independent of the blade location and flow Reynolds number.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of experimental apparatus

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Figure 2

Vorticity and velocity vectors for roff  = 0.55rw . Re = 8.

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Figure 3

Vorticity and velocity vectors for roff  = 0.55rw . Re = 108.

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Figure 4

Velocity and vorticity profiles as a function of blade offset for Re = 8, 108

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Figure 5

FTLE field for Re = 8 at 0.55rw blade offset

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Figure 6

FTLE fields versus blade offset for Re = 8 case

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Figure 7

Mean FTLE fields for Re = 8

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Figure 8

Normalized FTLE field as a function of integration time for Re = 8 and roff  = 0.55rw

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Figure 9

Maximum value in the FTLE field as a function of number of blade rotations. Re = 8, roff  = 0.55rw .

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Figure 10

Plot of virtual particle locations as a function of blade rotations for roff  = 0.17rw . Species noted by black or white colors, greys indicates mixed regions.

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Figure 11

Plot of virtual particle locations for ten blade rotations at roff  = 0.55rw . Species noted by black or white colors, greys indicates mixed regions.

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Figure 12

Plot of mixing ratios for Re = 8 case versus the number of blade rotations

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Figure 13

Comparison of mixing ratios after ten blade rotations for Re = 8 and 108

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