Shocked Water Layer Experiments
In the conceptual design of inertial fusion energy (IFE) reactors, the
chamber walls require protection from high energy X-rays that occur during
the fusion reaction. Liquid layer(s) or jets of a breeding material,
such as Flibe (Li2BeF4), have been proposed in
several protection schemes. Following the initial interaction of the
x-rays with the liquid, it is essential to understand the shock
hydrodynamics associated with the liquid layer break-up and the shock
acceleration of the layer and its effect as it impinges on the reactor
chambers' first wall. Liquid layer break-up is important to
understand when analyzing the chamber's vacuum clearing system, and also,
the amount of break-up has an effect on the pressure loading on the first
Figure 1 is a schematic of an experiment conducted at the WiSTL.
A horizontal water layer (blue) is placed in the vertical shock tube and
is supported by a thin Mylar film and equal-spaced nylon filaments
spanning the width of the shock tube. A shock wave with speed W
travels down the shock tube having accelerated the shocked gas behind it
(yellow) to a particle velocity up. The shock wave
interacts with the water and a shock is reflected off the upper surface of
the water layer (WR) and a shock is transmitted (WT)
and the water accelerates with a velocity ur. The
initially flat layer begins to break up and spread out, as noted by the
layer thickening and the wavy surfaces, and is accelerated into the test
section where it can be imaged through the circular window. At later
times, the transmitted shock wave reflects off the end-wall of the shock
tube and is accelerated back up with a velocity WTR, and
in the final image, a shock is transmitted through the layer and travels
back up the shock tube.
Fig. 1 The shock wave-water layer interaction.
Studying the break-up of the water layer, due to the shock interaction,
is accomplished through several imaging techniques: shadowgraphy
(Fig. 2) , planar light sheet (Fig. 3), front-lit high speed
cinematography (2 megabyte avi), and X-ray transmission (Fig. 4). In each
of the experimental image montages shown, only one image is obtained per
experiment so adjacent images have been obtained in successive
In shadowgraphy, a collimated, pulsed, light beam is
steered through the large quartz windows on each side of the shock tube
onto a screen. At the onset of the experiment the camera shutter is
opened, and when the water sheet is in the test section, the light source
is pulsed. The first of the three images in Fig. 2 is the leading
edge of the water sheet, initially flat and 6.4 mm thick, 1.32 ms after it
has been accelerated by a M=2.68 shock wave. The transmitted
shock wave is also seen at the bottom of the viewing area (since this
imaging senses the second spatial derivative of density
gradients.) The initially flat layer has undergone a severe
amount of break-up and the lack of left-right symmetry is notable.
Arcs seen as dark lines are very weak shocks reflected off a small gap in
the shock tube wall. In the later time images at 1.43 and 1.47 ms,
the water layer is observed moving downward with a bulk velocity while
further break-up at the leading edge is observed.
Three images from a planar light sheet imaging campaign are shown in
Fig. 3. A
laser beam is projected up through a window in the bottom of the shock
tube, parallel to a window surface, and the leading edge of the water
layer is imaged by reflecting light into the camera. Qualitatively,
the amount of break-up for this lower Mach number (2.14) and thicker water
sheet (12.8 mm) experiment is similar to the shadowgraph images; however,
more detail is seen at the leading edge and a gray scale, somewhat
proportional to the density, is observed at 2.62 ms.
|Fig. 2 Shadowgraph images of the water layer break-up.
|Fig. 3 Planar light sheet images of the water layer break-up.
Figure 4 shows a
series of 4 X-ray for an initially flat 12.8 mm thick water sheet
subjected to a M=2.12 shock wave. The quartz windows have been
replaced by smaller, thin carbon fiber windows that are optically opaque
but appear transmissive to X-rays (150 keV maximum, 70 ns pulse). A fluorescent screen, on the
opposite side of the shock tube than the X-ray head, is excited by the
transmitted X-rays and the image is captured with a digital
camera. Figure four is arranged so the leading edge of the
disrupted water sheet is on the bottom, the trailing edge on the top, and
the bulk of the water is in the middle two images. By constructing
the image in this way, the overall water density distribution can be
obtained in four separate experiments because the water layer has
stretched out to over 20 cm (20 times the initial thickness) in the 3.2 ms
volume fraction images have been obtained from the actual X-ray images
(through a detailed calibration process) and the regions with no water are
black, while the regions with a high volume fraction of water are
light. A region of interest is shown as a tall, narrow rectangular
box and this is used to construct the linear volume fraction through the
layer. This integration technique allows for a reconstruction of the
average water volume fraction throughout the entire thickness. A
peak volume fraction of 22% is observed at 8 cm above the leading edge of the
layer, and then the density decreases at a slower rate than it was
steepened and ripples are observed in this trailing edge portion.
Although the leading edge experiences significant break-up, as seen in
Figs. 2 and 3, it is evident from the X-ray image analysis that there is
even more break-up at the trailing edge of the layer.
|Fig. 4 X-ray images of the water layer converted to volume
fraction (left) and the linear water volume fraction in the
rectangular-boxed region of interest (right).
The end-wall peak pressures measured in the experiment are shown
in Fig. 5.
These pressures are not due to the transmitted shock wave (WT),
but instead, are due to the momentum of the water layer compressing
to a zero velocity at the end-wall of the shock tube. These pressure
are typically much higher than would be associated with the reflected
shock wave. The thicker water layer, 12.8 mm versus 6.4 mm,
typically results in a higher value of the peak pressure, as would be
expected for more mass, and therefore, more momentum. A new
analytical model (one-dimensional) for predicting the peak pressure
(labeled P5) is compared with the experimental data. The isentropic
model is generally considered to calculated a conservative value of the
peak pressure, however, at M=2.2, there are data that fall above
the model. A most significant result of these experiments are the
extremely high pressures associated with the water layer acceleration from
a strong shock wave. In the IFE reaction, the shock strengths could
me much higher (up to M=20) and therefore, the hydrodynamic shock
loading on the chambers first wall needs to be a fundamental consideration
in the design.
Fig. 5 End-wall pressure as a function of Mach number.