Low-temperature plasma has been studied
because of its significant potential for high speed flow control [1-6] and for plasma
assisted combustion [7, 8] in aerospace science. The effects of different types
of electrical discharges on airflow and streamlined bodies are discussed widely
during the last three decades [1-4]. The main advantage of this control is the
small actuation time, which makes actuator effective in a wide frequency range
for gas-dynamic flows control from stationary flows to turbulent and separated
flows. Actuators are used to reduce surface friction, to influence the
laminar-turbulent transition, to the position of separation zones and shock
waves near the streamlined surface [2-6], to control the ignition of fuels and
combustion [4, 7].
When a pulse of energy is inserted into a
gas by an electric discharge, a rapid change in the state of the gas occurs in
the region of the discharge current leads to the formation and movement of
shock waves, pressure waves and rarefaction waves [2-4, 6, 8]. The main part of
the electrical energy of the discharges in the air goes to the excitation of
vibrational and electronic degrees of freedom of molecules [9]. A rather large
proportion of electrical energy goes into translational degrees of freedom of
gas molecules in the microsecond time interval [2-4]. The other part transforms
into thermal energy in the process of vibrational–translational relaxation
within several milliseconds [9]. The ion motion plays a key role in the plasma
dynamics in the boundary layer and the spatial distribution of input energy
release, as discussed in experimental and modeling studies [1, 2, 4]. Some
investigations focused on the shock wave generation in supersonic flow and the
plasma control of shock wave-boundary layer interaction [2, 3, 5, 6]. Dynamics
of discharges have not been studied in detail at operation in a high-speed
flow.
For the effective action on high-speed gas
flows, it is necessary to study the development of discharges in air flows,
determine the mechanism of their interaction with shock waves. The study of
plasma formations in a high-speed flow makes it possible to optimally solve
technological problems and problems in the field of plasma gas dynamics.
Moreover it is necessary to determine the structure of the supersonic flow
after discharge. In high-speed flows in the channels, the formation of
separation zones is possible when the boundary layer interacts with an oblique
shock wave [10, 11], and the search for methods for controlling such zones
remains relevant [12, 13], including the study of physical processes in the
plasma of nanosecond discharges discharge in an inhomogeneous flow [14, 15].
Nanosecond distributed surface sliding
discharge (plasma sheet) is a system of channels sliding over dielectric
surface [3, 6, 13]. The discharge enables to realize energy input in gas layer of
~0.5 mm near dielectric surface [3, 5] and can be used as an actuator for the
control of a near-surface flow [3, 6, 13]. The near-surface flow influences the
discharge channels [3, 6]. The interaction of vortex zone and the relaxing
plasma can lead to inhomogeneous discharge current [14, 15]. This study is
focused on the structure of a supersonic flow in a shock tube channel with
inclined shock wave and on the details of surface sliding discharge dynamics in
a supersonic airflow, which is important for understanding of the discharge
physics and processes of plasma-flow interaction. The experimental
visualization of the flow was realized based on high-speed shadowgraphy. The
dynamic of shock-wave structure of a supersonic flow when flowing around a
small obstacle was determined as well as the boundary layer on the wall and the
region of interaction of the boundary layer with an oblique shock wave. The
structure of the flow was analyzed after the initiation of a pulsed surface
sliding discharge in the region of intersection of an inclined shock wave and a
boundary layer.
The experiments were carried out on a shock
tube with a rectangular channel of 24
×
48 mm2
[3, 5]. Supersonic air flows with a speed of
660-1370 m/s were generated behind plane shock waves with Mach numbers M=2.5-5.2.
The flow Mach numbers reached M1=1.70, the Reynolds numbers of the
flows were ~ 105
at a density of 0.01-0.15 kg/m3. The
thickness of the laminar boundary layer on the channel walls did not exceed 1
mm [5]. Two side walls of the test chamber of the shock tube were
plane-parallel quartz glasses 170 mm long, which made it possible to carry out
optical diagnostics (Fig. 1). On the lower and upper walls of the discharge
chamber, electrodes of surface sliding discharges 100 mm long with an inter-electrode
distance of 30 mm were located. A synchronizing system from signals of
piezoelectric pressure sensors in the shock tube channel made it possible to
initiate a discharge at a given time of gas dynamic process. In the
experiments, a surface sliding discharge of nanosecond duration was initiated
on the upper wall of the discharge chamber 80–800
μ
s after the initial shock wave passed the obstacle. The development
of the discharge in the region of interaction of an inclined shock wave with
the boundary layer and the gas-dynamic flow field after the discharge were
investigated. Photo registration was carried out and 9-frame registration of
the discharge radiation was carried out with a K011 BIFO ICCD camera. Emission
spectra and the discharge current were recorded.
High-speed shadowgraphy was used to study the plane shock wave diffraction on
obstacle and the flow pattern evolution prior to and after the pulse surface
sliding discharge.
Figure 1.
Experimental setup: 1 – driver section, 2 –
driven section, 3 - helium, 4 - diaphragm section, 5 - pressure sensors, 6 -
discharge chamber, 7 - dump tank, 8 – vacuum pump, 9 - oscilloscopes, 10 -
discharge triggering unit, 11 - delay generator, 12 - shunt, 13 - spectrometer,
14 - photo cameras, 15 - shadowgraphy optics, 16 - high-speed video camera, 17
- PC.
The optical scheme of the direct
shadowgraphy consists of a laser light source, diverging and collimating
lenses, and a prism (Fig. 2). The lenses formed a plane-parallel light beam ~
40 mm in diameter. The prism was placed so that the beam passed through the
discharge chamber perpendicular to the quartz glasses and hit the CCD matrix of
the high-speed video camera. The light source was a continuous wave laser (532
nm). Shadowgraph images of the gas-dynamic flow field were recorded with a high-speed
video camera with a frame rate of 150,000 frames per second. The frame exposure
was 1
μs,
the image size on the matrix was
256×144 pixels. Experimental shadowgraph images were processed with
background subtraction. Then the images were processed with the intensity
scanning program in different directions to obtain quantitative information about
the motion of shock-wave structures.
Figure 2.
Direct shadowgraphy arrangement: 1
-
laser; 2-4
-
diverging
lenses; 5
-
collimating lens; 6
-
prism; 7
-
quartz
glasses; 8
-
discharge chamber; 9
-
high-speed video camera.
A dielectric obstacle in the form of a
parallelepiped with dimensions of 48,0
´
6,2
´
1,9 mm3
is located on the lower wall of the discharge
chamber at a distance of 30 mm from the beginning of the electrodes (Fig. 3,
a). The long part of the obstacle was perpendicular to the walls of the
chamber. High-speed shadowgraphy of the flow field in the discharge chamber was
carried out at all stages of its development from the beginning of diffraction
of the initial plane shock wave on the obstacle to the end of a homogeneous co-current
flow behind the initial shock wave.
Quasi-stationary flow around the obstacle
was formed after the diffraction of the initial plane shock wave by the
obstacle. Figure 3 b shows a sequence of images of the flow field in a channel
with total length of about 80 mm (channel height is 24 mm). Each image is
composed of shadowgraph images from three separate experiments. The high
repeatability of the processes under the same initial conditions makes it
possible to reconstruct the flow field. Two upper images show the initial
stages of diffraction of a plane shock wave, corresponding to the moments of
time up to 20 μs from the moment the shock wave touches the leading edge
of the obstacle. The upper part of the initial plane shock wave moves to the
right, and the diffracted part of shock front moves to the left of the
obstacle. At the unsteady stage of the flow up to 200 μs, an oblique shock
wave forms behind the bottom of the obstacle and disturbances in front of the
obstacle (images 4-6). The images 7-9 corresponds to the quasi-stationary stage
of the flow with the steady-state positions of the shock waves in the channel.
In the last image, the shock-wave configuration is modified and moves to the
left after the end of the uniform co-current flow and the arrival of
rarefaction waves. Boundary layers are formed on the channel walls in the flow
behind a plane shock wave. First, the boundary layer is laminar, then it
becomes turbulent at a certain distance from the shock front [5].
|
|
|
a
|
|
|
|
b
|
Figure 3.
(a) Schematic of a steady shock-wave
configuration; (b) The sequence of shadowgraph images of flow field after the
interaction of plane shock wave with obstacle. Shadowgraph images are taken for
initial shock wave number 3.50, initial pressure 25 torr. The zero-time
corresponds to the moment when the initial plane shock wave contacts the obstacle
(yellow rectangular on the lower wall).
Analysis of high-speed imaging showed that
the formation of a quasi-stationary flow occurs within 90-150
μ
s after the plane shock wave passes the obstacle. Its duration is
about 150-500
μs,
which corresponds to
numerical simulation
[15]. The total
duration of a homogeneous co-current flow behind a plane shock wave is 180-650
μs
depending on the Mach number of the initial shock wave (Fig. 4 a).
An inclined shock wave forms behind the obstacle and interacts with the
boundary layer on the upper wall of the discharge chamber. The angle of
inclination of the shock wave is from 35 to 43 degrees in experiments depending
on the flow Mach number. Reflection of an inclined shock wave from the boundary
layer depends on the Mach number of the flow
M1
and the boundary layer, as seen in the shadow images. Figure 4 b
shows the increased near-wall flow regions of interaction of a laminar and
turbulent boundary layer with an oblique shock wave of 5
´
12 mm2
in size. It is seen that the thickness of the laminar boundary layer is less
than 0.5 mm, and the thickness of the turbulent boundary layer does not exceed
1 mm. Interaction with the boundary layer can be with separation of the flow or
without separation [6-8].
In both cases, a region of
low density is formed [15].
Figure
4.
a) Duration of a
homogeneous co-current flow in the shock tube depending on the Mach number of
shock wave: 1 – theory [16], 2 – experiment; b) shadowgraph images of the
oblique shock wave interacting with a laminar boundary layer (top) and
turbulent boundary layer (bottom). The zero-time corresponds to the moment when
the initial plane shock wave contacts the obstacle.
A surface sliding discharge was initiated
in experiments at a pulse voltage of 22-25 kV. The discharge current was ~ 1
kA, the current duration was less than 500 ns. The main energy input to the gas
occurs within 150 ns, i.e. almost instantaneously compared to the
characteristic gas-dynamic time. Significant energy input into a thin gas layer
leads to the formation of shock waves from the channels [3]. The short duration
of the discharge (~ 100 ns) and the small thickness of the plasma layer,
comparable to the thickness of the boundary layer in the shock tube (~ 1 mm),
make it possible to act almost instantly on the near-wall flow in a supersonic
flow.
The development of a pulsed discharge is
determined by the local value of the reduced electric field
E/N (E
is the electric field strength,
N
is the concentration of molecules), on
which the plasma conductivity and discharge current depend [9]. Therefore, in
an inhomogeneous air flow with an oblique shock wave, a surface sliding
discharge develops as a single channel located in a region of low density
formed during the interaction of an oblique shock wave with the boundary layer
(Fig. 5 c, d), [15]. In experimental photo images, the discharge channel looks
like an intensively emitting band about 10 mm wide. The image in Fig. 5 d obviously
shows the clear boundaries of the discharge channel.
The emission spectrum of the discharge in the flow is characterized
by a high intensity of the continuum, indicating a high concentration of
electrons [15].
Figure 5.
Photo images of a surface sliding
discharge in motionless air at 0.05 kg/m3
(a) and at 0.25
kg/m3
density (b) and
of discharge in supersonic air flow with inclined
shock wave
(c, d) at flow Mach
number 1.27 and 0.15 kg/m3
density.
The image (d) was registered through an optical filter
that transmits radiation with a wavelength of 405 nm. Arrows indicate the flow direction.
The duration of the discharge glow was
determined on the basis of registration with a 9-frame ICCD camera. Fig. 6 a, b
shows photo images and 9-frame images of the discharge in motionless air and in
a flow with an oblique shock wave. The glow time of the discharge channel in
the flow is more than 4 μs. Fig. 6 c shows the time dependences of the
glow intensity and the current waveform. After the end of the discharge
current, the afterglow of the current channel is observed with a decay time of
~ 2 μs.
|
|
|
c
|
Figure 6.
ICCD images of surface
sliding discharge in motionless air at 0.085
kg/m3
density (a) and
in supersonic flow with
inclined shock wave
(b) at
flow Mach number 1.27 and 0.15 kg/m3
density.
ICCD images were taken with exposure times
of 100 ns. Time intervals between frames were 100 ns (a) and 500 ns (b).
Time dependences of discharge radiation
intensity (c) in air flow (1) and in
motionless
air (2),
discharge current waveforms in air flow (3) and in
motionless
air (4).
Shadowgraphy imaging of the flow field
after the discharge shows a shock wave propagation in the flow from the
discharge channel, the front shape of which is close to semi-cylindrical at the
initial stage of motion. Shock wave moves downward, away from the channel, and
shifts to the right in the direction of the flow, rapidly damping (Fig. 7 a).
Different velocities of the wave front parts lead to a change in the shape of
the front over time. The movement of the shock wave significantly changes the
structure of the flow in the discharge chamber. A heat trace is formed from the
discharge region, which propagates in the boundary layer.
It has been experimentally established
that
the discharge regime as well as shock wave dynamics depend on the Mach number
of the flow and the type of interaction of the oblique shock wave with the
boundary layer.
Shadowgraphy images were processed to obtain information on horizontal
and vertical motion of the shock wave generated by the discharge channel. To
determine the vertical displacement, the vertical coordinate of the shock front
point located at the greatest distance from the upper edge of the image was
taken. Figure 7 b shows the result of processing high-speed images obtained in
different experiments of discharge initiation in air flows with Mach numbers of
1.27. It is seen that the dynamics of the vertical motion of the generated
shock wave has good repeatability. The vertical velocity of the shock front
during the first 7
μs
is about 1100 m/s, then
falls to 700 m/s. The intensity of the shock wave depends on the magnitude of
the current and the geometry of the region of discharge current, which, in
turn, depends on the type of interaction of the oblique shock wave with the boundary
layer. Within ~ 100
μs,
the flow pattern in the
channel changes; then the quasi-stationary shock-wave flow configuration with
an oblique shock wave is restored.
|
|
|
à
|
|
|
|
b
|
Figure
7.
The
sequence of shadowgraph images of flow field after the discharge (a) and the
time dependence of vertical displacement of
shock wave from discharge channel (b).
Shadowgraph images are taken for flow Mach number 1.27
and 0.15 kg/m3
density.
The zero-time corresponds to the moment of
discharge. The flow is from left to right.
The spatial structure of a supersonic flow
with an oblique shock wave upon initiation of a nanosecond surface sliding
discharge in the discharge chamber of a shock tube is studied experimentally
using high-speed shadowgraphy at a frequency of up to 150,000 frames per
second. Investigation of the flow field was carried out in supersonic flows at
Mach numbers of 1.20-1.68. Digital processing of sequences of obtained
shadowgraph images showed that the shock-wave structure of the flow remains
disturbed for more than 100
μs.
Thus, supersonic
flow with an oblique shock wave in the channel is affected by the movement of
the shock waves generated by the discharge. The shock wave dynamics depends on
the Mach number of the flow and the discharge parameters. The implementation of
such an effect on the flow, taking into account the development of a surface
sliding discharge in high-speed flows, can be used to control flows.
Altogether, the obtained result can serve as a base for simulating the real
time disturbed flow associated with movement of the shock wave generated by the
discharge channel and studying downstream events.
The work was supported by RFBR grant
19-08-00661.
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