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Research Papers: Multiphase Flows

Numerical Simulation and Proper Orthogonal Decomposition of the Flow in a Counter-Flow T-Junction

[+] Author and Article Information
E. Merzari

e-mail: emerzari@anl.gov

P. Fischer

Argonne National Laboratory,
Argonne, IL 60439

It actually is the turbulent kinetic energy in the midplane, the out of plane component is not included.

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 20, 2012; final manuscript received March 18, 2013; published online July 11, 2013. Assoc. Editor: Zvi Rusak.

This manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE - AC02 - 06CH11357. The U.S. Government retains for itself, and others acting on its behalf, a paid - up nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government.

J. Fluids Eng 135(9), 091304 (Jul 11, 2013) (13 pages) Paper No: FE-12-1401; doi: 10.1115/1.4024059 History: Received August 20, 2012; Revised March 18, 2013

Large eddy simulations (LES) of the turbulent mixing in a T-junction have been carried out with the spectral element code Nek5000 at two inlet velocity ratios. Numerical results have been compared with an available experiment. Proper orthogonal decomposition (POD) has then been used to identify the most energetic modes of turbulence for both the velocity and temperature fields. Since POD was also performed on the experiment particle image velocimetry (PIV) data, a further means of verification and validation was available. The structure of the numerical POD modes and the time histories of the projection of each mode on the velocity field offer additional insight into the physics of turbulence in T-junctions. In particular, in the case of identical inlet velocities (T-junction velocity ratio equal to 1.0) the dynamics appears to be richer than might be expected and additional diagonal modes are present.

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Figures

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Fig. 1

(a) Layout of a counter-flow type T-junction with the dimensions of the computational domain in millimeters; (b) cyclic boundaries and inlet boundary conditions. The outlet is scaled in figure for clear illustration.

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Fig. 2

Cross section of the mesh employed for the VR = 1.0 case. Spatial coordinates units are in mm.

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Fig. 3

Instantaneous scalar distribution s at VR = 3.0; (a) three-dimensional plot (scalar distribution at the wall), (b) T-junction mid-section (z = 0), (c) volume rendering. spatial coordinates units are in mm.

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Fig. 4

Instantaneous scalar distribution s at VR = 1.0; (a) T-junction mid-section (z = 0), (b)–(c) streamwise normal section (y = −1.5 L) at two different time steps. Spatial coordinates units are in mm.

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Fig. 5

Comparison between LES data and the data of Gavrilakis et al. for the streamwise velocity profile at z = 0. Re = 3000.

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Fig. 6

Vector plot of the Reynolds averaged velocity field at the midplane z = 0 for VR = 1.0

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Fig. 7

Reynolds averaged y-velocity, VR = 3.0, a profile at z = 0, y = –L; (b) profile at z = 0, y = −2.5 L. Values normalized by the mixing bulk velocity (the boundary conditions in the experiment were different from the simulation the high stream was at the negative x coordinates and characterized by s = 0. The experimental data presented has been rotated).

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Fig. 8

Reynolds averaged y-velocity, VR = 1.0, a profile at z = 0, y = –L/2; (b) profile at z = 0, y = −1.5 L. Values normalized by the mixing bulk velocity.

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Fig. 9

Reynolds averaged x-velocity, VR = 1.0, at z = 0, y = –L/2, values normalized by the mixing bulk velocity

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Fig. 10

Turbulent kinetic energy for the case VR = 1.0. Profile at z = 0, y = –L/2, values normalized by the square of the mixing bulk velocity.

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Fig. 11

Rms of the y-velocity, VR = 1.0, component in the plane z = 0. Values normalized by the mixing bulk velocity.

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Fig. 12

Rms of the y-velocity component, VR = 3.0, a profile at z = 0, y = −1.5 L, (b) profile at z = 0, y = −2.5 L. Values normalized by the mixing bulk velocity (the boundary conditions in the experiment were different from the simulation, the high stream was at the negative x coordinates and characterized by s = 0. The experimental data presented has been rotated). The experimental data in Fig. 13 has therefore been rotated and subtracted to 1 to match the computational conditions).

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Fig. 13

Distribution of the mixing scalar s and rms of the mixing scalar, VR = 3.0. (a) Profile of the mixing scalar s at z = 0, y = –L/2. (b) Profile of the mixing scalar s at z = 0, y = −1.5 L. (c) Profile of the rms of mixing scalar s at z = 0, y = –L/2. (d) Profile of the rms of the mixing scalar s at z = 0, y = −1.5 L (the boundary conditions in the experiment were different from the simulation, the high stream was at the negative x coordinates and characterized by s = 0. The experimental data presented has been rotated and subtracted to 1 to match the computational conditions).

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Fig. 15

POD energy distribution as a function of the mode number: (a) first 500 modes normalized by the total energy for each case, (b) first 10 modes normalized by the total energy for each case, (c) first 10 modes normalized by the energy of case VR = 3

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Fig. 16

POD eigenfunctions at VR = 1.0. Vector plots in the plane at y = –L, (a) Mode 1, (b) Mode 3. Spatial coordinates units are in mm.

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Fig. 17

POD eigenfunctions for the scalar s at VR = 1.0. Contour plots in the plane at y = –L, (a) Mode 1, (b) Mode 3. Spatial coordinates units are in mm.

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Fig. 18

POD eigenfunctions for VR = 3.0. Contour plots and Vector plots in the plane at y = –L, (a) scalar s eigenmode 1, (b) velocity eigenmode 1, (c) scalar s eigenmode 2, (d) velocity eigenmode 2. Spatial coordinates units are in mm.

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Fig. 19

Projection of the velocity fluctuation among the first five modes for case VR = 3

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Fig. 14

λ2 isosurfaces. (a) VR = 3.0 multiple isosurfaces. (b) VR = 3.0 detail. (c) VR = 1.0 detailed isosurfaces at the junction.

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