1. INTRODUCTION
In many problems associated with fast compression processes of
matter, the situation arises when a material of less density (light
material) and a more dense material (heavy material) have a contact
surface and are accelerated. In case of constant acceleration, the
contact surface is to be subjected to the action of the
Rayleigh–Taylor instability (RTI). If the pulsed acceleration
(e.g., at the passage of shock waves) takes place, then any contact
surface is unstable, because the Richtmyer–Meshkov instability
(RMI) arises.
The instability implies that any small perturbation has a tendency to
unlimited growth, interpenetration of material occurs, shear turbulence
breaks up structures into smaller-scale structures, and a turbulent
mixing zone (TMZ) develops. The evolution of instabilities on the
contact surface of different density media exerts an influence on the
dynamics of the compression, and restricts the limiting value of
compression and the dynamics of subsequent processes.
The determining parameter that takes into account the gravitational
turbulent mixing influence is the turbulent mixing zone width, which
depends on the density ratio of different density media, the duration
of the instability, and so forth. In a number of problems, taking into
account compressibility on both sides of the contact surface becomes
important.
Under laboratory conditions, the investigation of RTI and arising
gravitational turbulent mixing (GTM) is performed using different
density liquid and gaseous media at the installations EKAP and SOM. The
installation OSA makes it possible to investigate different kinds of
instability (RTI, RMI) by using three replaceable drivers for these
purposes. The distinctive feature of the experiments is the usage of
the controlled separating membrane, making it possible to form the
evolution process of GTM of different gases with preset initial
conditions.
The aim of the present work is to perform experiments by using the
shock tube OSA creating RTI and to apply the controlled separating
membrane for these investigations.
2. SETUP OF EXPERIMENTS
For performing experiments regarding the gravitational turbulent
mixing investigation the scheme presented in Figure
1 was used.
Physical scheme of the experiments setup.
The 0 < x < x1 region is filled up
with the compressed gas and represents a high pressure chamber. From
the rest of the shock tube, part the chamber is separated by a light
piston, which is found at the point x =
x1. The x1 < x <
x2 region is filled up with a light working gas 1
of density ρ1 and represents the low pressure chamber.
The x > x2 region is filled up with a
heavy working gas 2 of density ρ2 and represents a
measuring chamber by which the mixing process imaging is performed. In
the point x = x2 the separating membrane
is found that prevents the mixing of working gases during the
experiment preparation. At the specified instant of time, the
separating membrane is destroyed into pieces of definite size by the
external force. The installation operates as follows. At the instant of
time t = t0, the piston begins to move
with constant acceleration in the positive direction of the x
axis under the action of the compressed gas in the high-pressure
chamber. From the piston a compression wave begins to propagate in the
positive direction of the x axis with velocity
C1, where C1 is the sound
velocity in the working gas 1. At the instant of time t =
(x2 −
x1)/C1 the compression wave
arrives at the interface of gases x = x2.
At the same time, the external destructive force is applied to the
separating membrane, and the contact boundary between gases begins to
be accelerated. As the contact boundary, acceleration profile slightly
decreases and the pressure gradient in the compression wave is directed
oppositely to the density gradient at the contact boundary, and
conditions are created for the RTI occurrence.
Figure 2 shows the functional scheme of the
installation OSA. The total height of the installation amounts to ≈5
m. In the upper part of the installation, the high-pressure chamber is
located. It is a thick-walled vessel consisting of three parts
connected by flanges. The operating pressure in the chamber is up to 2
MPa. At the upper flange of the high-pressure chamber there is the
emergency valve of pressure drop and pipelines for gas inlet and
outlet. The high-pressure chamber is separated from the remainder of
the shock tube by an aluminum membrane.
Functional scheme of the installation OSA.
The membrane thickness is 1 mm or 0.5 mm and determines the limiting
pressure of the gas in the reservoir. For the membrane destruction at
the specified instant of time, a strong electric explosion is used. A
sliding contact in the form of a metal needle touches the membrane in
the center. The needle is connected to the positive pole of the
capacitor bank by means of cables, whereas the membrane is connected to
the negative pole. At the instant of time t =
t0, the pulse of current burns through the aluminum
membrane in the center. Gas begins to flow out of the reservoir and
opens the membrane completely. The gas flow passes through the conical
part of the transitional section and begins to push a plastic piston.
In the compression wave, the pressure profile and amplitude depend on
the piston mass. Under the action of the compressed gas, the piston
moves with acceleration along the section with a light gas. The section
with a light gas is filled up with gas of density ρ1.
The internal cross section of the light gas section is equal to 138
× 138 mm2, but the length amounts to 500 mm. The
contact boundary acceleration profile depends on the light gas section.
The further the contact boundary of gases is from the piston, the more
the acceleration differs from the constant one and approaches a
delta-shaped one.
Prior to the execution of the experiment, the section with a light
gas is filled up with the working gas of density ρ1
through the gas inlet system. Simultaneously, the measuring chamber is
filled up with the working gas of density ρ2 through the
gas inlet system. The gas inlet system controls the extent of purity of
working gases. Between the light gas section and the measuring chamber
the controlled separating membrane is located. It is designed to
prevent the mixing of working gases during the experiment
preparation.
The controlled measuring membrane is an interweaved grid of
microconductors, 20 μm in diameter and spaced 4 mm apart. A liquid
soap film solution is applied to this grid. The film thickness amounts
to ≈1 μm. At the specified instant of time, the electric current
is passed through the grid. Microconductors are heated, and the liquid
film begins to be destroyed into the pieces with the typical scale
λ ≈ 4 mm in the places of contact with microconductors. Then the
surface tension forces tighten the pieces of liquid film into small
balls that act as initial perturbations at the contact boundary of
working gases. When the compression wave reaches the boundary between
gases, the contact boundary begins to be accelerated. As acceleration
is directed from the light gas to the heavy one, the conditions are
created for the gravitational turbulent mixing zone evolution.
Figure 3 shows the characteristic
photographic images of the separating membrane destruction process at
different instants of time. In this figure, microconductors are denoted
by number 1, liquid film pieces by number 2, the microconductor with
the liquid film around it by number 3. From this figure it is seen that
after the current pulse is applied to the grid, the liquid film begins
to separate from the microconductors and then, under the action of the
surface tension forces, it is tightened into a drop.
Characteristic photographic images of the liquid film destruction
process.
The measuring section is located beyond the block with the separating
membrane. It is filled with working gas of density ρ2.
The measuring chamber has two transparent walls of high-quality optical
glass. This makes it possible to perform the photographic record of the
turbulent mixing zone by means of a Schlieren (photograph) technique.
If it is necessary to investigate the late stages of the turbulent
mixing process, then an additional chamber of low pressure is mounted
between the block of the controlled separating membrane and the
measuring section. After the measuring chamber the low pressure
chamber, 260 mm in length, is found. It is also filled up with the
working gas of density ρ2.
This chamber is necessary so that the reflected compression wave does
not exert an influence on the photographic record of the turbulent
mixing zone. After terminating the photographic record and passing of
the piston into the low-pressure chamber, it is necessary to slow down
the piston. For this purpose, the special outlet section is designed.
When the piston passes into the low-pressure chamber its velocity is
≈100–150 m/s. The gas being pushed by the piston ruptures
the outlet membrane, which is located between the measuring chamber and
the outlet section. The gas pressure ahead of the piston becomes
gradually higher than the pressure behind the piston, and the latter
begins to decelerate. When the piston moves along the outlet section,
the pressure of the decelerating gas increases. To decrease the
acceleration of retardation and to prevent reverse motion of the
piston, it is necessary to release gas from the inlet section into the
atmosphere. For this purpose, in the outlet section there are exhaust
windows in which the membranes of lavsan are found. When reaching the
ultimate strength, the membranes are ruptured and gas gets into
atmosphere. The rubber shock absorber located at the bottom of the
outlet section is designed to cancel the residual speed of the
piston.
Imaging of the flow arising at the contact surface (CS) of two
different density gases after its acceleration was carried out through
the apertures in the measuring section by the Schlieren device
IAB–451. The device is consistent with the high-speed camera VFU,
operating in the mode of a time magnifier. Illumination was carried out
by a flash lamp. The light pulse duration was equal to 4 ms. The flash
lamp, the camera VFU-1, and the phenomenon itself were synchronized in
such a way that the phenomenon registration was performed at the
required stage of evolution. The optical method to image transparent
inhomogeneities is based on the dependence of the refractive index of
gases on density.
3. DISCUSSION OF RESULTS
In the present work Ar (density ρ = 1.78 kg/m3)
and Kr gas (density ρ = 3.7 kg/m3) were used as
working gases. The density ratio for the given pair of gases n
= 2.1, but the Atwood number A = (ρ2 −
ρ1)/(ρ2 + ρ1) for the
given pair of gases was equal to A = 0.35. For these
experiments, the acceleration of the contact boundary of gases amounted
to g ≈ 40000 m/s2. The photographic record
of the turbulent mixing process was carried out when changing the
parameter S = gt2/2 from 0.1 m to 0.5
m.
Figure 4 shows the characteristic
photographic records of the gravitational turbulent mixing process. The
turbulent mixing zone is seen in photos in the form of a wide dark
band. It is seen that the zone width is increased with time, but the
zone itself is mixing downwards. For the correct determination of the
image scale, reference benchmarks are set before the measuring chamber
glasses.
Characteristic photographic records of the gravitational turbulent
mixing process.
Figure 5 shows the dependence of the
turbulent mixing zone width on the parameter S for the pair of
gases Ar–Kr. The conditions of self-similarity for the given
experiment are carried out at S ≥ 100 mm.
Dependence of the turbulent mixing zone width on the parameter
S for the pair of gases Ar–Kr.
It means that the turbulent mixing zone growth does not depend on the
initial conditions on the contact boundary of gases. All the totality
of experimental points at S ≥ 100 mm can be described by
the formula L = 4αAS, where the parameter
S = gt2/2 is the contact boundary
displacement, A = (ρ2 −
ρ1)/(ρ2 + ρ1) is the
Atwood number, and α is the dimensionless velocity of turbulent
mixing. On the basis of experimental results the constant α = 0.04
has been determined.
4. CONCLUSION
In the present work, the Rayleigh–Taylor instability for
gaseous media was studied. Ar and Kr were used as working gases.
Density ratio ρ2 /ρ1 was taken to be
equal to 2.1, but the Atwood number A = (ρ1
− ρ2)/(ρ1 + ρ2)
was equal to 0.35.
At the initial instant of time, different density gases being
investigated were located in the shock tube and were sepa-rated by the
controlled separating membrane. Then the separating membrane was
destroyed by the external force into small-scale fragments with a
typical size λ ≈ 4 mm.
The contact boundary of gases was accelerated by means of a
compression wave, which was generated by an accelerating piston. The
initial acceleration of the contact boundary of gases amounted to
≈40,000 m/s2.
According to the results of experiments, the dependencies of the
turbulent mixing zone width on the contact boundary displacement
S were constructed. The parameter S was changed from
100 mm to 500 mm. At the self-similar stage of the turbulent mixing
evolution, the dimensionless velocity of turbulent mixing α was
determined to be equal to 0.04.
