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Research Papers: Multiphase Flows

The Tilted Rocket Rig: A Rayleigh–Taylor Test Case for RANS Models1

[+] Author and Article Information
Nicholas A. Denissen

Los Alamos National Laboratory,
Los Alamos, NM 87545
e-mail: denissen@lanl.gov

Bertrand Rollin, Jon M. Reisner, Malcolm J. Andrews

Los Alamos National Laboratory,
Los Alamos, NM 87545

1The United States Government retains and by accepting the article for publication, the publisher 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.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 2, 2013; final manuscript received May 13, 2014; published online July 9, 2014. Assoc. Editor: Oleg Schilling.

J. Fluids Eng 136(9), 091301 (Jul 09, 2014) (13 pages) Paper No: FE-13-1290; doi: 10.1115/1.4027776 History: Received May 02, 2013; Revised May 13, 2014

Reynolds-Averaged Navier–Stokes (RANS) models remain the most common design tool in a wide variety of fluid mixing applications. This includes variable-density turbulent mixing as occurs in inertial confinement fusion. The present work extends validation of the BHR-2 RANS model for variable-density turbulence to a two-dimensional Rayleigh–Taylor test case, the “tilted-rig.” The combined effects of bulk fluid motion and turbulence model behavior are discussed, and several quantities of interest are shown to demonstrate the capability of a four-equation turbulence model to describe this type of two-dimensional turbulent mixing. More generally, the tilted-rig test problem is shown to be a useful exercise for RANS model validation.

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References

Figures

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Fig. 1

Acceleration profile from Ref. [11]

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Fig. 2

Mix region from the experiment (left), RANS (center), and ILES (right). Simulation mix regions visualized by 4f1f2 at t = 60 ms (τ = 1.74). Gray scale range is from [0:1]. The overall structure of the mixing region in the RANS and ILES is comparable to the experiment. (All experimental images ©British Crown Owned Copyright 2012/AWE).

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Fig. 3

Contours of heavy fluid volume fraction (f1) for RANS (left) and ILES (right) at t = 45 ms (τ = 1.26). Volume fraction contours are [0.025 0.3, 0.7, 0.975].

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Fig. 4

Contours of heavy fluid volume fraction (f1) for RANS (left) and ILES (right) at t = 60 ms (τ = 1.74). Volume fraction contours are [0.025 0.3, 0.7, 0.975] The RANS contours are closer together on the heavy side indicating larger asymmetry than the ILES.

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Fig. 5

Heavy fluid volume fraction (f1) along the centerline showing the difference in mixture fraction on the heavy side of the interface. (a) Volume fraction: t = 45 and (b) volume fraction: t = 60

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Fig. 6

Contours of turbulent kinetic energy K for RANS (left) and ILES (right) at t = 45 ms. Contours are [0.025 0.3, 0.7, 0.975] of the maximum RANS value; this saturates the ILES. The maximum values are K = 1.124 for the RANS and K = 1.538 for the ILES. Note the elevated levels of K on the spike (left) and bubble (right) side seen in the ILES are captured by the RANS.

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Fig. 7

Contours of turbulent kinetic energy K for RANS (left) and ILES (right) at t = 60 ms. Contours are [0.025 0.3, 0.7, 0.975] of the maximum RANS value; this saturates the ILES. The maximum values are K = 2.114 for the RANS and K = 3.109 for the ILES.

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Fig. 8

Contours of vertical turbulent mass-flux velocity az for RANS (left) and ILES (right) at t = 45 ms. Contours are [0.025 0.3, 0.7, 0.975] of the maximum RANS value; this saturates the ILES. The maximum values are az = 0.138 for the RANS and az = 0.5 for the ILES. The low-level contours are comparable, but the RANS underpredicts the centerline values. Note also the intermittency of the ILES.

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Fig. 9

Contours of vertical turbulent mass-flux velocity az for RANS (left) and ILES (right) at t = 60 ms. Contours are [0.025 0.3, 0.7, 0.975] of the maximum RANS value; this saturates the ILES. The maximum values are az = 0.184 for the RANS and az = 0.66 for the ILES. The RANS captures the structure of the LES but not the peak values along the center of the mix layer. The ILES shows significant intermittency with regions that are comparable to RANS near regions with much stronger turbulent mass flux.

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Fig. 10

Contours of the density-specific volume correlation b for RANS (left) and ILES (right) at t = 45 ms. Contours are [0.025 0.3, 0.7, 0.975] of the maximum RANS value; this saturates the ILES. The maximum values are b = 0.064 for the RANS and b = 0.182 for the ILES. The contours of b are much more constant along the mixing layer than other terms.

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Fig. 11

Contours of density-specific volume correlation b for RANS (left) and ILES (right) at t = 60 ms. Contours are [0.025 0.3, 0.7, 0.975] of the maximum RANS value; this saturates the ILES. The peak values are b = 0.063 for the RANS and b = 0.202 for the ILES. The ILES shows significant intermittency in this quantity as well.

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Fig. 12

Comparison of gradient diffusion model (left) for the horizontal turbulent mass-flux velocity (ax) and the transport model of BHR (center) and ILES (right) at t = 45 ms. Colors are values of ax and contour lines are [0.025,0.5,0.975] of the heavy fluid volume fraction to show the center and edges of the mixing layer. Note the countergradient flux in the top half of the mix layer.

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Fig. 13

Global quantities versus nondimensional time (τ) for FLAG-BHR2, viscous ILES (RTI3D-V), inviscid ILES (RTI3D-I), square domain DNS (DNS-TP), experimental box dimensions DNS (DNS-Exp), and experiment. (a) bubble height, (b) spike height, (c) mix width, (d) tilt angle, (e) TKE–linear scale, and (f) TKE–log scale.

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Fig. 14

Energy budget for the tilt rig RANS simulation. Symbols are terms computed directly from the code, line is the computed change in energy based on Eq. (9) demonstrating energy conservation. (a) Potential, kinetic, total, and predicted energy and (b) turbulent kinetic and internal energy. Oscillations in the internal energy are artifacts of the compressible nature of the simulations.

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Fig. 15

Integrated mix mass and numerical mix mass from coarse and fine resolution calculations, and an alternative remap strategy. (a) Mix mass (g) and (b) mix mass fraction. By all times discussed, numerical mix is a small fraction of the total.

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