8/3/2019 John M. Budzinski, Robert F. Benjamin and Jeffrey W.
Jacobs- Influence of initial conditions on the flow patterns of
a
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Influence of initial conditions on the flow patterns of a
shock-acceleratedthin fluid layer
John M. Budzinski and Robert F. BenjaminDynamic Experimentation
Division, Los Alamos National Labo ratory Los Alamos, New Mexico
87545
Jeffrey W. JacobsDepartment of Aerospace and Mechanical
Engineering, University of Arizona, lkson, Arizona 85 721
(Received 5 May 1994; accepted 22 July 1994)
Previous observations of three flow patterns generated by shock
acceleration of a thin perturbed,fluid layer are now correlated
with asymmetries in the initial conditions. Using a different
diagnostic(planar laser Rayleigh scattering) than the previous
experiments, upstream mushrooms, downstreammushrooms, and sinuous
patterns are still observed. For each experiment the initial
perturbationamplitude on one side of the layer can either be
larger, smaller, or the same as the amplitude on theother side, as
observed with two images per experiment, and these differences lead
to the formationof the different patterns.
This study is directed toward a better understanding ofthe flow
of an accelerated heavy layer imbedded betweenlower-density fluids.
As an example, this phenomenon may
occur in inertial confinement fusion targets when the
abla-tively driven impulse causes implosion of a
fuel-containingshell. A potential difficulty is the mixing of shell
materialwith the fuel, as a consequence of interfacial fluid
instability.
A shock-accelerated layer involves the Richtmyer-Meshkov (RM)
instabilityr of each interface between fluidsof different density.
A perturbed interface between two fluidssubjected to a normal,
impulsive acceleration is unstable anddistorts after the
interaction. If the downstream fluid isdenser than the upstream
fluid the perturbation grows. How-ever, if the upstream fluid is
denser than the downstreamfluid, the perturbation first reverses
phase and then grows,
and the original peaks in the perturbation will become
thevalleys and the valleys will become the peaks. In both casesthe
early-time growth rate is constant and proportional to theamplitude
of the initial perturbation. At later times thegrowth rate
decreases, and mushroom shapes form from thepeaks in the distorting
interface.
We study a shock interaction with a layer of heavy gasbounded on
both sides by a lighter gas, where both interfacesof the layer have
nearly sinusoidal perturbations. Previousresearch34 observed that
three distinct flow patterns evolvefrom similar initial conditions,
and speculated that differ-ences in initial conditions might
influence which flow pattern
occurs during each event. These experiments observed onlythe
dynamic flow condition for each event at one preset timebecause of
limitations that precluded multiple image acqui-sition. We now
report experiments where both initial anddynamic flow conditions
are recorded for each event. Thesame three flows are observed, and
have a strong correlationwith asymmetries in the initial flow
profile.
The present experiments use planar laser Rayleigh scat-tering
(PLRS) to capture two frames per event, but use thesame shock tube
and test section as in the earlier work.3*4Our PLRS images clearly
show regions of high SF, concen-tration because SF6 scatters about
six times more light thanair. Iwo pulsed dye lasers illuminate the
test region with
coplanar sheets of laser light, and a cooled CCD camerarecords
each image. We convert the images to maps of SF,concentration by
calibrating the system with scattering from
pure air and pure SF,.The nozzle above the test section produces
a vertically
flowing, laminar gas jet6 (i.e., the gas curtain) with a
varicosecross section and diffuse boundaries; the wavelength is
about6 mm and the peak-to-peak amplitude is up to 2 mm on eachside.
This flow system has been shown to produce a two-dimensional flo~.~
The shock tube is fired when the gas cur-tain appears to be stable
as observed with a real timeschlieren system, and drives a Mach 1.2
shock wave in air.Small, unsteady, uncontrollable fluctuations in
the SF, flowcause asymmetries which vary from experiment to
experi-ment and are correlated with the three different shock-
accelerated flows. We find that the thicker regions of thelayer
contain about 50% SF, and the thinner regions about40% SF,. The SF,
concentration across the layer width hasan approximately Gaussian
profile.
We observe the same three patterns after a Mach 1.2shock
interaction as seen in the earlier work, and find thatasymmetries
in the initial condition correlate with the threepostshock flow
patterns in over 90% of the lOO+ experi-ments performed. Typical
examples of the initial and dy-namic conditions for the three flow
patterns are shown inFig. 1, where the initial condition was taken
about 100 wbefore the shock interaction and the dynamic condition
at
400-450 ,us after the shock interaction. Upstream mush-rooms
formed in about 46% of the experiments, a sinuouspattern formed in
about 41% of the experiments, and down-stream mushrooms developed
in 13% of the experiments.Mostly we find that an upstream mushroom
pattern developswhen the perturbations on the upstream side (i.e.,
on the sidefirst interacting with the shock wave) are larger than
the per-turbations on the downstream side. A sinuous pattern
formswhen the perturbations on the downstream side are about
thesame or slightly larger than upstream side. A downstreammushroom
develops when the perturbation on the down-stream side is much
larger than the perturbation on the up-stream side. About 8% of the
experimental images were
3510 Phys. Fluids 6 (ll), November 1994
1070-6631/94/6(11)/3510/3/$6.00 @ 1994 American Institute of
Physics
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8/3/2019 John M. Budzinski, Robert F. Benjamin and Jeffrey W.
Jacobs- Influence of initial conditions on the flow patterns of
a
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Just AfterShock
Early time150p.WC
Later time450psec
FIG. 1. Composite of images from three typical experiments
showing theinitial and dynamic condi tion on each experiment. The
shock wave movesleft to right. Th e distance shown in the figure
between the initial and dy-namic condi tion of each pair is
considerably l ess than the actual distance inthe experiment. Each
pair of initial and dynamic conditi on was recorded onthe same
event. (a) Sinuous, dynamic image recorded at ~450 p after theshock
interaction; (b) upstream mushroom, dynamic image t=450 F;
(c)downstream mushr oom, dynamic image t = 400 w.
anomalous and did not follow the correlation describedabove.
The postshock flow pattern was classified visually as oneof the
three flow patterns based on the asymmetries presen tin the spacing
of the pattern lobes and the SF, mass distri-bution, using the
criteria described in Fig. 2. The preciseperiodicity shown in the
patterns in Fig. 2 was usually notpresent in the data;
irregularities often occurred as shown inthe typical data, Fig.
1.
When the initial conditions fell be tween those that pro-duced
one of the standard patterns, typically the postshockpattern had
characteristics of more than one pattern. Whenthe initial
conditions had a downstream perturbation that wasnot large enough
to produce a full downstream mushroom,and yet not small enough to
produce a pure sinuous pattern,then by 0.45 ms after the shock
interaction, well-defined
stems and caps would not be present, but the pattern wouldhave
some characteristics of the early-time downstre ammushroom pattern.
For example, the dimension a in Fig. 2would be greater than b, but
not to the extent as found in thedevelopment of a standard
downstream mushroom. This pat-tern was categorized as one of the
41% sinuous patterns.
We also find that the upstream mushrooms are alignedwith the
thicker parts of the initial layer whereas the down-stream
mushrooms are aligned with the thinner regions. Thusin the early
development of downstream mushrooms, theheavy fluid moves laterally
(i.e., normal to the shock direc-tion) from the thicker to the
thinner regions; there is lesslateral movement of the heavy fluid
during the early devel-
MSb d
FIG. 2. Differences in the different patterns throughout their
development
and a simple model to explain why they might occur. (a) Sinuous
pattern:perturbations are about equal on both sides of the layer,
at early timesa-b,at latter times c-e,d--f, and the SF6 is evenly
distributed throughout thelayer. Just after the shock interaction
the center of vorticity (shown by thecircular arrows) is roughly in
the center of the layer inducing the sinuouspattern to develop. (b)
Upstream mushroom pattern: The initial upstreamperturbation a
mplitude is larger than the downstream, at early times b>a,
atlater times d>e, cb, at later times df. The highest SF,
concentrations and most ofthe SF, ma ss is in th e mushroom caps.
Just after the shock interaction mostof the vorticity is to the
right of the layer. As the vorticity entrains the fluidthe
mushrooms form.
opment of upstream mushrooms. When a sinuous patternforms the
downstream lobes are aligned with the thin regionsof the initial
layer and the upstream lobes are aligned withthe thicker
regions.
Our interpretation of these flow patterns is based on
aone-dimensional (1-D) calculation, Richtmyer-Meshkov in-stability,
and vortex dynamics. The wave dynamics of theinteraction of a
planar shock wave with a layer is complexbecause of multiple
wave-interface interactions. The wavesreverberate within the heavy
layer after the initial interac-
tions that produce a Mach 1.3 shock wave in the SF6 and aMach
1.17 shock in the air downstream of the layer. Theinterfaces attain
the same velocity after a few reverberations.
The observed nonlinear Bow patterns can be
interpretedqualitatively as the independent RM-instability growth
ofeach interface, followed by strong coupling in the
nonlineargrowth regime. Richtmyers impulse model reasonably
pre-dicts the early-time growth rate of a single interface
(shownrecently in analyses7s). For our layer, the coupling
betweeninterfaces is initially weak7 when perturbation amplitudes a
resmall, so the growth of each interface occurs independently.The
impulse model predicts that the ratio of growth rates of
the interfaces is equal to the ratio of initial perturbation
am-Phys. Fluids, Vol. 6, No. 11, November 1994 Letters 3511
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