Abstract

Experiments were performed to observe the growth of the turbulent, Rayleigh–Taylor unstable mixing layer generated between air and SF6, with an Atwood number of A=(ρ2ρ1)/(ρ2+ρ1)=0.64, where ρ1 and ρ2 are the densities of air and SF6, respectively. A nonconstant acceleration with an average value of 2300g0, where g0 is the acceleration due to gravity, was generated by interaction of the interface between the two gases with a rarefaction wave. Three-dimensional, multimode perturbations were generated on the diffuse interface, with a diffusion layer thickness of δ=3.6 mm, using a membraneless vertical oscillation technique, and 20 experiments were performed to establish a statistical ensemble. The average perturbation from this ensemble was extracted and used as input for a numerical simulation using the Lawrence Livermore National Laboratory (LLNL) Miranda code. Good qualitative agreement between the experiment and simulation was observed, while quantitative agreement was best at early to intermediate times. Several methods were used to extract the turbulent growth constant α from experiments and simulations while accounting for time varying acceleration. Experimental, average bubble and spike asymptotic self-similar growth rate values range from α=0.022 to α=0.032 depending on the method used, and accounting for variable acceleration. Values found from the simulations range from α=0.024 to α=0.041. Values of α measured in the experiments are lower than what are typically measured in the literature but are more in line with those found in recent simulations.

References

References
1.
Rayleigh
,
L.
,
1883
, “
Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density
,”
Proc. London Math Soc.
,
14
, pp.
170
177
.10.1112/plms/s1-14.1.170
2.
Taylor
,
G. I.
,
1950
, “
The Instability of Liquid Surfaces When Accelerated in a Direction Perpendicular to Their Planes 1
,”
Proc. R. Soc. A
,
201
, pp.
192
196
.https://royalsocietypublishing.org/doi/10.1098/rspa.1950.0052
3.
Hurricane
,
O. A.
,
Callahan
,
D. A.
,
Casey
,
D. T.
,
Celliers
,
P. M.
,
Cerjan
,
C.
,
Dewald
,
E. L.
,
Dittrich
,
T. R.
,
Döppner
,
T.
,
Hinkel
,
D. E.
,
Hopkins
,
L. F. B.
,
Kline
,
J. L.
,
Pape
,
S. L.
,
Ma
,
T.
,
MacPhee
,
A. G.
,
Milovich
,
J. L.
,
Pak
,
A.
,
Park
,
H.-S.
,
Patel
,
P. K.
,
Remington
,
B. A.
,
Salmonson
,
J. D.
,
Springer
,
P. T.
, and
Tommasini
,
R.
,
2014
, “
Fuel Gain Exceeding Unity in an Inertially Confined Fusion Implosion
,”
Nature
,
506
(
7488
), pp.
343
348
.10.1038/nature13008
4.
Town
,
R. P. J.
,
Delettrez
,
J. A.
,
Epstein
,
R.
,
Goncharov
,
V. N.
,
McCrory
,
R. L.
,
McKenty
,
P. W.
,
Short
,
R. W.
, and
Skupsky
,
S.
,
1999
, “
Direct-Drive Target Designs for the National Ignition Facility
,”
LLE Rev. Q.
,
79
, pp.
121
130
.https://www.lle.rochester.edu/media/publications/lle_review/documents/v79/79_01Direct.pdf
5.
Edwards
,
M. J.
,
Lindl
,
J. D.
,
Spears
,
B. K.
,
Weber
,
S. V.
,
Atherton
,
L. J.
,
Bleuel
,
D. L.
,
Bradley
,
D. K.
,
Callahan
,
D. A.
,
Cerjan
,
C. J.
,
Clark
,
D.
,
Collins
,
G. W.
,
Fair
,
J. E.
,
Fortner
,
R. J.
,
Glenzer
,
S. H.
,
Haan
,
S. W.
,
Hammel
,
B. A.
,
Hamza
,
A. V.
,
Hatchett
,
S. P.
,
Izumi
,
N.
,
Jacoby
,
B.
,
Jones
,
O. S.
,
Koch
,
J. A.
,
Kozioziemski
,
B. J.
,
Landen
,
O. L.
,
Lerche
,
R.
,
MacGowan
,
B. J.
,
MacKinnon
,
A. J.
,
Mapoles
,
E. R.
,
Marinak
,
M. M.
,
Moran
,
M.
,
Moses
,
E. I.
,
Munro
,
D. H.
,
Schneider
,
D. H.
,
Sepke
,
S. M.
,
Shaughnessy
,
D. A.
,
Springer
,
P. T.
,
Tommasini
,
R.
,
Bernstein
,
L.
,
Stoeffl
,
W.
,
Betti
,
R.
,
Boehly
,
T. R.
,
Sangster
,
T. C.
,
Glebov
,
V. Y.
,
McKenty
,
P. W.
,
Regan
,
S. P.
,
Edgell
,
D. H.
,
Knauer
,
J. P.
,
Stoeckl
,
C.
,
Harding
,
D. R.
,
Batha
,
S.
,
Grim
,
G.
,
Herrmann
,
H. W.
,
Kyrala
,
G.
,
Wilke
,
M.
,
Wilson
,
D. C.
,
Frenje
,
J.
,
Petrasso
,
R.
,
Moreno
,
K.
,
Huang
,
H.
,
Chen
,
K. C.
,
Giraldez
,
E.
,
Kilkenny
,
J. D.
,
Mauldin
,
M.
,
Hein
,
N.
,
Hoppe
,
M.
,
Nikroo
,
A.
, and
Leeper
,
R. J.
,
2011
, “
The Experimental Plan for Cryogenic Layered Target Implosions on the National Ignition Facility—The Inertial Confinement Approach to Fusion
,”
Phys. Plasmas
,
18
(
5
), p.
051003
.10.1063/1.3592173
6.
Andrews
,
M. J.
, and
Dalziel
,
S. B.
,
2010
, “
Small Atwood Number Rayleigh–Taylor Experiments
,”
Philos. Trans. R. Soc. A
,
368
(
1916
), pp.
1663
1679
.10.1098/rsta.2010.0007
7.
Read
,
K. I.
, and
Youngs
,
D. L.
,
1983
, “
Experimental Investigation of Turbulent Mixing by Rayleigh–Taylor Instability
,”
AWRE, Aldermaston
,
Reading, UK
, Report No. O11/83, pp.
1
59
.
8.
Dimonte
,
G.
, and
Schneider
,
M.
,
1996
, “
Turbulent Rayleigh–Taylor Instability Experiments With Variable Acceleration
,”
Phys. Rev. E
,
54
(
4
), pp.
3740
3743
.10.1103/PhysRevE.54.3740
9.
Waddell
,
J. T.
,
Niederhaus
,
C. E.
, and
Jacobs
,
J. W.
,
2001
, “
Experimental Study of Rayleigh–Taylor Instability: Low Atwood Number Liquid Systems With Single-Mode Initial Perturbations
,”
Phys. Fluids
,
13
(
5
), pp.
1263
1273
.10.1063/1.1359762
10.
Read
,
K. I.
,
1984
, “
Turbulent Mixing by Rayleigh–Taylor Instability
,”
Physica D
,
12
(
1–3
), pp.
45
48
.10.1016/0167-2789(84)90513-X
11.
Burrows
,
K. D.
,
Read
,
K. I.
, and
Youngs
,
D. L.
,
1984
, “
Experimental Investigation of Turbulent Mixing by Rayleigh–Taylor Instability II
,”
AWRE, Aldermaston
,
Reading, UK
, Report No. O22/84, pp.
1
60
.
12.
Smeeton
,
V. S.
, and
Youngs
,
D. L.
,
1988
, “
Experimental Investigation of Turbulent Mixing by Rayleigh–Taylor Instability III
,”
AWRE, Aldermaston
,
Reading, UK
, Report No. O35/87, pp.
1
72
.
13.
Dimonte
,
G.
, and
Schneider
,
M.
,
2000
, “
Density Ratio Dependence of Rayleigh–Taylor Mixing for Sustained and Impulsive Acceleration Histories
,”
Phys. Fluids
,
12
(
2
), pp.
304
321
.10.1063/1.870309
14.
Wilkinson
,
J. P.
, and
Jacobs
,
J. W.
,
2007
, “
Experimental Study of the Single-Model Three-Dimensional Rayleigh–Taylor Instability
,”
Phys. Fluids
,
19
(
12
), p.
124102
.10.1063/1.2813548
15.
Olson
,
D. H.
, and
Jacobs
,
J. W.
,
2009
, “
Experimental Study of Rayleigh–Taylor Instability With a Complex Initial Perturbation
,”
Phys. Fluids
,
21
(
3
), p.
034103
.10.1063/1.3085811
16.
Mokler
,
M. J.
,
2013
, “
Incompressible Miscible and Immiscible Experiments on the Rayleigh-Taylor Instability Using Planar Laser Induced Fluorescence Visualization
,”
Master's thesis
, The University of Arizona, Tucson, AZ.
17.
Banerjee
,
A.
, and
Andrews
,
M. J.
,
2006
, “
Statistically Steady Measurements of Rayleigh–Taylor Mixing in a Gas Channel
,”
Phys. Fluids
,
18
(
3
), 035107.10.1063/1.2185687
18.
Banerjee
,
A.
,
Kraft
,
W. N.
, and
Andrews
,
M. J.
,
2010
, “
Detailed Measurements of a Statistically Steady Rayleigh–Taylor Mixing Layer From Small to High Atwood Numbers
,”
J. Fluid Mech.
,
659
, pp.
127
190
.10.1017/S0022112010002351
19.
Akula
,
B.
,
Suchandra
,
P.
,
Mikhaeil
,
M.
, and
Ranjan
,
D.
,
2017
, “
Dynamics of Unstably Stratified Free Shear Flows: An Experimental Investigation of Coupled Kelvin–Helmholtz and Rayleigh–Taylor Instability
,”
J. Fluid Mech.
,
816
, pp.
619
660
.10.1017/jfm.2017.95
20.
Zaytsev
,
S. G.
,
Krivets
,
V. V.
,
Mazilin
,
I. M.
,
Titov
,
S. N.
,
Chebotareva
,
E. I.
,
Nikishin
,
V. V.
,
Tishkin
,
V. F.
,
Bouquet
,
S.
, and
Haas
,
J.-F.
,
2003
, “
Evolution of the Rayleigh–Taylor Instability in the Mixing Zone Between Gases of Different Densities in a Field of Variable Acceleration
,”
Laser Particle Beams
,
21
(
3
), pp.
393
402
.10.1017/S0263034603213173
21.
Youngs
,
D. L.
,
1984
, “
Numerical Simulation of Turbulent Mixing by Rayleigh–Taylor Instability
,”
Physica D
,
12
(
1–3
), pp.
32
44
.10.1016/0167-2789(84)90512-8
22.
Cabot
,
W. H.
, and
Cook
,
A. W.
,
2006
, “
Reynolds Number Effects on Rayleigh-Taylor Instability With Possible Implications for Type-Ia Supernovae
,”
Nat. Phys.
,
2
(
8
), pp.
562
568
.10.1038/nphys361
23.
Aslangil
,
D.
,
Banerjee
,
A.
, and
Lawrie
,
A. G. W.
,
2016
, “
Numerical Investigation of Initial Condition Effects on Rayleigh–Taylor Instability With Acceleration Reversals
,”
Phys. Rev. E
,
94
(
5
), p.
053114
.10.1103/PhysRevE.94.053114
24.
Ramaprabhu
,
P.
,
Karkhanis
,
V.
, and
Lawrie
,
A. G. W.
,
2013
, “
The Rayleigh–Taylor Instability Driven by an Accel-Decel-Accel Profile
,”
Phys. Fluids
,
25
(
11
), p.
115104
.10.1063/1.4829765
25.
Glimm
,
J.
, and
Li
,
X. L.
,
1988
, “
Validation of the Sharp-Wheeler Bubble Merger Model From Experimental and Computational Data
,”
Phys. Fluids
,
31
(
8
), pp.
2077
2085
.10.1063/1.866660
26.
Jones
,
M. A.
, and
Jacobs
,
J. W.
,
1997
, “
A Membraneless Experiment for the Study of Richtmyer–Meshkov Instability of a Shock-Accelerated Gas Interface
,”
Phys. Fluids
,
9
(
10
), pp.
3078
3085
.10.1063/1.869416
27.
Morgan
,
R. V.
,
2014
, “
Experiments on the Rarefaction Wave Driven Rayleigh-Taylor Instability
,” Ph.D. dissertation,
The University of Arizona
,
Tucson, AZ
.
28.
Morgan
,
R. V.
,
Likhachev
,
O. A.
, and
Jacobs
,
J. W.
,
2016
, “
Rarefaction-Driven Rayleigh-Taylor Instability—Part 1: Diffuse-Interface Linear Stability Measurements and Theory
,”
J. Fluid Mech.
,
791
, pp.
34
60
.10.1017/jfm.2016.46
29.
Morgan
,
R. V.
,
Cabot
,
W.
,
Greenough
,
J. A.
, and
Jacobs
,
J. W.
,
2018
, “
Rarefaction-Driven Rayleigh-Taylor Instability—Part 2: Experiments and Simulations in the Nonlinear Regime
,”
J. Fluid Mech.
,
838
, pp.
320
355
.10.1017/jfm.2017.893
30.
Jacobs
,
J. W.
,
Krivets
,
V. V.
,
Tsiklashvili
,
V.
, and
Likhachev
,
O. A.
,
2013
, “
Experiments on the Richtmyer–Meshkov Instability With an Imposed, Random Initial Perturbation
,”
Shock Waves
,
23
(
4
), pp.
407
413
.10.1007/s00193-013-0436-9
31.
Settles
,
G. S.
,
2001
,
Schlieren and Shadowgraph Techniques
,
Springer
,
Berlin
.
32.
Cook
,
A. W.
, and
Cabot
,
W.
,
2004
, “
A High-Wavenumber Viscosity for High-Resolution Numerical Methods
,”
J. Comp. Phys.
,
195
(
2
), pp.
594
601
.10.1016/j.jcp.2003.10.012
33.
Cook
,
A. W.
, and
Cabot
,
W.
,
2005
, “
Hyperviscosity for Shock-Turbulence Interactions
,”
J. Comp. Phys.
,
203
(
2
), pp.
379
385
.10.1016/j.jcp.2004.09.011
34.
Cook
,
A. W.
,
2007
, “
Artificial Fluid Properties for Large-Eddy Simulation of Compressible Turbulent Mixing
,”
Phys. Fluids
,
19
(
5
), p.
055103
.10.1063/1.2728937
35.
Cheng
,
B. C.
,
Glimm
,
J.
, and
Sharp
,
D. H.
,
2002
, “
A Three-Dimensional Renormalization Group Bubble Merger Model for Rayleigh–Taylor Mixing
,”
Phys. Fluids
,
18
, p.
074101
.https://aip.scitation.org/doi/10.1063/1.1460942
36.
Wieland
,
S. A.
,
Hamlington
,
P. E.
,
Reckinger
,
S. J.
, and
Livescu
,
D.
,
2019
, “
Effects of Isothermal Stratification Strength on Vorticity Dynamics for Single-Mode Compressible Rayleigh–Taylor Instability
,”
Phys. Rev. Fluids
,
4
(
9
), p.
093905
.10.1103/PhysRevFluids.4.093905
37.
Cook
,
A. W.
, and
Dimotakis
,
P. E.
,
2001
, “
Transition Stages of Rayleigh–Taylor Instability Between Miscible Fluids
,”
J. Fluid Mech.
,
443
, pp.
69
99
.10.1017/S0022112001005377
38.
Ristorcelli
,
J. R.
, and
Clark
,
T. T.
,
2004
, “
Rayleigh–Taylor Turbulence: Self-Similar Analysis and Direct Numerical Simulations
,”
J. Fluid Mech.
,
507
, pp.
213
253
.10.1017/S0022112004008286
39.
Jacobs
,
J. W.
, and
Dalziel
,
S. B.
,
2005
, “
Rayleigh–Taylor Instability in Complex Stratifications
,”
J. Fluid Mech.
,
542
(
1
), pp.
251
279
.10.1017/S0022112005006336
40.
Roberts
,
M. S.
,
2012
, “
Experiments and Simulations on the Incompressible, Rayleigh–Taylor Instability With Small Wavelength Perturbations
,”
The University of Arizona
,
Tucson, AZ
.
41.
Mokler
,
M. J.
,
2013
, “
Incompressible Miscible and Immiscible Experiments on the Rayleigh–Taylor Instability Using Planar Laser Induced Fluorescence Visualization
,”
The University of Arizona
,
Tucson, AZ
.
42.
Roberts
,
M. S.
, and
Jacobs
,
J. W.
,
2016
, “
The Effects of Forced Small Wavelength Finite Bandwidth Initial Perturbations and Miscibility on the Turbulent Rayleigh–Taylor Instability
,”
J. Fluid Mech.
,
787
, pp.
50
83
.10.1017/jfm.2015.599
43.
Dalziel
,
S. B.
,
Linden
,
P. F.
, and
Youngs
,
D. L.
,
1999
, “
Self-Similarity and Internal Structure Induced by Rayleigh–Taylor Instability
,”
J. Fluid Mech.
,
399
, pp.
1
48
.10.1017/S002211209900614X
44.
Andrews
,
M. J.
, and
Spalding
,
D. B.
,
1990
, “
A Simple Experiment to Investigate Two-Dimensional Mixing by Rayleigh–Taylor Instability
,”
Phys. Fluids A
,
2
(
6
), pp.
922
927
.10.1063/1.857652
45.
Ramaprabhu
,
P.
, and
Andrews
,
M. J.
,
2004
, “
Experimental Investigation of Rayleigh–Taylor Mixing at Small Atwood Numbers
,”
J. Fluid Mech.
,
502
, pp.
233
271
.10.1017/S0022112003007419
46.
Tsiklashvili
,
V.
,
Romero-Colio
,
P. E.
,
Likhachev
,
O. A.
, and
Jacobs
,
J. W.
,
2012
, “
An Experimental Study of Small Atwood Number Rayleigh–Taylor Instability Using the Magnetic Levitation of Paramagnetic Fluids
,”
Phys. Fluids
,
24
(
5
), p.
052106
.10.1063/1.4721898
This content is only available via PDF.
You do not currently have access to this content.