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TECHNICAL PAPERS

Large Eddy Simulation of Flow in a Stirred Tank

[+] Author and Article Information
H. S. Yoon

School of Mechanical Engineering, San 30 Chang Jeon Dong, Pusan National University, Kumjung-ku, Pusan 609–735, Korea

S. Balachandar

Department of Theoretical and Applied Mechanics, 216 Talbot Laboratory, University of Illinois, Urbana, IL 61801e-mail: s-bala@uiuc.edu

M. Y. Ha

School of Mechanical Engineering, San 30 Chang Jeon Dong, Pusan National University, Kamjung-ku, Pusan 609-735, Korea

K. Kar

Dow Chemical Company, 1776 Dow Center, Midland, MI 48674

J. Fluids Eng 125(3), 486-499 (Jun 09, 2003) (14 pages) doi:10.1115/1.1566046 History: Received August 17, 2001; Revised November 12, 2002; Online June 09, 2003
Copyright © 2003 by ASME
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References

Figures

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Schematic of the stirred tank with a typical six-blade Rushton impeller. The plan view shown at the bottom on the right is viewed up from under the tank.
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The velocity field on the curved θ–z surface at (r=1) obtained from the theoretical model of the impeller-induced flow (Yoon et al. 14). The parameters of the model are obtained such that the model provides the best approximation to the three-component stereo PIV measurement phase-averaged over 500 realizations. (a) In-plane velocity vector plot (a reference vector of magnitude equal to the blade tip velocity is provided) and (b) out-of-plane radial velocity contour. Only a 60 deg sector above the midplane (z>0) is shown and the thick vertical lines indicate the impeller blades.
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The z-location and the magnitude of the largest radial velocity measured at θ=20 deg and r=1 for the different realizations of the PIV measurement on the r-z plane, 17
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An instantaneous flow field over the entire r-z cross section of the tank at θ=30 deg for the fixed inflow model at Rem=4000. The grid resolution employed in the LES is much finer than what is shown above, where the resolution has been decreased to improve clarity.
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Frames (a) and (b) show a sequence of two frames, each separated by 1 nondimensional time unit, showing contours of radial velocity in the region close to the impeller on the r-z plane at θ=30 deg for the fixed inflow model. Frames (c) and (d) show the corresponding contours of axial velocity. Frames (e) and (f) are the same as frames (a) and (b), but for the oscillatory inflow model. In frames (a), (b), (e), and (f) there are eight contours ranging from −0.1 to 0.6 in steps of 0.1 and in frames (c) and (d) there are 11 contours ranging from −0.25 to 0.25 in steps of 0.05.
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The schematic of the (a) sinuous and (b) varicose instability of a jet flow. The dominant signature of the sinuous instability is the periodic (plus-minus) oscillation of the transverse velocity (frame (a)). The dominant signature of the varicose instability is the fluctuation in the longitudinal velocity about a positive mean (frame (b)). The sinuous and varicose disturbances, in a frame of reference moving with the local flow, correspond to staggered and in-line eddy patterns marked, A, B, etc.
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The time and θ-averaged nondimensional quantities from the dynamic large eddy simulation with fixed inflow model: (a) radial velocity contours (b) circumferential vorticity contours in the rotating frame of reference. The θ-averaged nondimensional quantities from the RANS simulation: (c) radial velocity contours (d) circumferential vorticity contours in the rotating frame of reference.
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The time-averaged nondimensional radial velocity as a function of the nondimensional radial distance from the blade tip (r=1) to the outer tank wall (r=3) along the midplane (z=0) at four selected azimuthal locations: (a) θ=0 deg, (b) 20 deg, (c) 30 deg, and (d) 40 deg. The LES results of the fixed and oscillatory inflow models are compared with those of RANS and the corresponding experimental measurements by Sharp et al. 17. Frame (e) compares the time and θ-averaged radial velocity from the fixed and oscillatory inflow LES simulations with those of Sharp et al. 17, Kim 28, Dong et al. 3, and Verzicco et al. 30.
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The contours of the time and θ-averaged nondimensional (a) radial velocity and (b) vorticity contours from the dynamic large eddy simulation with 20 deg oscillatory inflow model
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Tip vortex structure obtained for the θ=20 deg oscillatory inflow model at one instance in time (a) perspective view covering the 60 deg sector close to the impeller, (b) top view of the three-dimensional structure projected onto a horizontal plane
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Top view of the long time-averaged three-dimensional tip vortex structure obtained for the (a) 20 deg oscillatory and (b) fixed inflow models
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The top view of the time-averaged backbone of the three-dimensional tip vortex pair projected onto a horizontal plane. The results of the fixed and 20 deg oscillatory model LES are compared with the experimental measurements.
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The contours of time-averaged nondimensional (a) radial and (b) circumferential velocities on the z=0 midplane for the 20 deg oscillatory inflow model
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The time histories of nondimensional volume-averaged (a) resolved scale dissipation (εres), (b) subgrid scale dissipation (εsgs) for the fixed and 20 deg oscillatory inflow models
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The ratio of time and r-z plane-averaged nondimensional resolved scale dissipation (εres) and subgrid scale dissipation (εsgs) as a function of θ for the fixed and 20 deg oscillatory inflow models
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(a) The distribution of time and θ-averaged nondimensional subgrid scale dissipation for the 20 deg oscillatory model over the entire r-z plane, (b) the distribution of time and θ-averaged nondimensional subgrid scale dissipation in the region close to the blade tip for fixed inflow model and (c) for the 20 deg oscillatory model

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