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Research Papers: Fundamental Issues and Canonical Flows

Computational Studies of Two-Dimensional Rayleigh-Taylor Driven Mixing for a Tilted-Rig

[+] Author and Article Information
Malcolm J. Andrews

MS F644,
Los Alamos National Laboratory,
Los Alamos, NM 875454
e-mail: mandrews@lanl.gov

David L. Youngs

AWE,
Aldermaston, RG7 4PR, UK
e-mail: david.youngs@awe.co.uk

Daniel Livescu

MS D413,
Los Alamos National Laboratory,
Los Alamos, NM 875454
e-mail: Livescu@lanl.gov

Tie Wei

Department of Mechanical Engineering,
New Mexico Tech,
Socorro, NM 87801
e-mail: twei@nmt.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 12, 2013; final manuscript received April 29, 2014; published online July 9, 2014. Assoc. Editor: Dimitris Drikakis.

The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.

J. Fluids Eng 136(9), 091212 (Jul 09, 2014) (14 pages) Paper No: FE-13-1553; doi: 10.1115/1.4027587 History: Received September 12, 2013; Revised April 29, 2014

A time-dependent, incompressible, turbulent mixing problem, referred here to as the “tilted-rig,” is defined, based results from an experiment that involved the introduction of a large-scale overturning motion, with a superposed localized Rayleigh-Taylor (RT) driven mixing. The problem serves to examine the development of RT turbulent mixing while being strained by a large-scale two-dimensional confined motion. Care is taken to define the problem in detail so others might use the definition, and the results, to help develop advanced models of buoyancy driven mixing in complex flows. Aside from a careful definition, the problem has been solved using two different implicit-large-Eddy-simulations (ILES) based codes, and with a direct numerical simulations (DNS) code. Two-dimensional and one-dimensional mix metrics are defined, and then used to examine the development of the mixing region, and the overall evolution of the flow. Comparison of simulations with experiment reveals that large-scale overturning can be well captured in all the simulations, similarly central mix widths, and spike/bubble sidewall penetrations are also in good agreement. A comparison between the different simulation methodologies, ILES and DNS, reveals an overall good agreement between mix metrics such as the amount of molecular mixing. The DNS simulations reveal a dependency on Reynolds number that merits further experimental work.

Copyright © 2014 by ASME
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Figures

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Fig. 3

Boundary conditions; (a) is for left/right free-slip and (b) is for equivalent left/right cyclic – note saw-tooth of density interface

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Fig. 2

Experiment 110 (a) and experiment 115 (b); British Crown Owned Copyright 2014/AWE

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Fig. 1

Schematic of the tilted-rig experiment

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Fig. 4

Acceleration history for experiment 110

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Fig. 5

Layzer equation model: bubble and spike distances for experiment 110

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Fig. 17

CFDNS tilt-angle (degrees) at different Rep values

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Fig. 7

Experiment 110. Stages selected for comparison with numerical simulations

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Fig. 12

(a) RTI3D volume fraction distributions at 45 ms, 60 ms, and 71 ms using a 512 × 512 × 768 mesh with contour levels of 0.025, 0.3, 0.7, 0.975. (b) RTI3D volume fraction distributions at 45 ms, 60 ms, and 71 ms using a 320 × 320 × 480 mesh with contour levels of 0.025, 0.3, 0.7, 0.975.

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Fig. 13

(a) RTI3D “b” distributions at t = 45 ms, 60 ms and 71 ms using a 512 × 512 × 768 mesh and (b) RTI3D “b” distributions at t = 45 ms, 60 ms and 71 ms using a 320 × 320 × 480 mesh

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Fig. 8

TURMOIL integral mix widths of Eq. (10)

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Fig. 9

TURMOIL sidewall bubble and spike positions, Hb, Hs versus τ

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Fig. 10

TURMOIL volume fraction distributions at τ = 1.741: (a) 300 × 300 × 480 meshes, (b) 300 × 300 × 1200 meshes (clipped image), and (c) 600 × 600 × 960 meshes. Contour levels 0.025, 0.3, 0.7, and 0.975.

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Fig. 11

TURMOIL results for 600 × 600 × 960 meshes at τ = 1.741. (a) molecular mixing parameter, θ and (b) turbulence kinetic energy, k, scale maximum = 0.033 cm2/ms2

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Fig. 14

RTI3D sidewall bubble and spike positions, Hb, Hs versus τ for 320 × 320 × 480 and 512 × 512 × 768 meshes

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Fig. 15

RTI3D tilt-angle (β) versus τ for 320 × 320 × 480 and 512 × 512 × 768 meshes

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Fig. 16

CFDNS side wall bubble and spike heights and 6 × W at different Rep values

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Fig. 22

CFDNS turbulent kinetic energy (m2/s2) at (a) t = 1.256 and (b) τ = 1.741

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Fig. 23

CFDNS molecular mix parameter at (a) τ = 1.256 and (b) τ = 1.741

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Fig. 24

CFDNS density specific volume correlation b at (a) τ = 1.256 and (b) τ = 1.741

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Fig. 25

Comparison of global molecular mixing with CFDNS Rep = 14000

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Fig. 18

Turbulent kinetic energy for the CFDNS cases

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Fig. 19

Total kinetic energy for the CFDNS cases

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Fig. 20

Global mix parameter, Θ, for the CFDNS cases

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Fig. 21

CFDNS f1 contours at (a) τ = 1.256 and (b) t = 1.741

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