Methods of gas-dynamic flows visualization using electric
discharges are widely used in plasma aerodynamics [1-5]. The discharges of various
types allow not only to organize flow control modes, but also to obtain
information about the flow structure [3-5]. Traditional visualization methods,
such as the direct shadowgraphy method, the schlieren method and the
interferometry, have effectiveness in studying supersonic flows in channels where
there are sharp changes in the parameters of the gas, including density and
refractive index [1, 2, 6].
In recent decades, visualization methods based on recording the
glow of various types of gas discharges have been developed [1, 3-6], in
addition to classical methods. These methods can be used at low gas pressures,
when the local intensity of the gas discharge plasma glow is directly related
to the magnitude of the reduced electric field and the gas density [4-7]. The interaction
of shock waves with bodies and boundary layers creates a complex flow field
(shocks, rarefaction zones, flow separation), which can affect the shape and
intensity of the discharge glow. Volume and surface discharges of nanosecond
duration, short compared to gas-dynamic times (~ 1 μs), allow
visualization of structural elements of high-speed flows, such as shock waves,
oblique shocks and other characteristic flow elements even at high flow
velocities [4-6]. In combination with classical methods, registration of gas
discharge glow can provide additional information about the three-dimensional
structure of a supersonic flow.
Nanosecond surface sliding discharge propagating along a
dielectric surface attracts attention due to its potential in plasma control of
high-speed flows. Sliding discharge forms a quasi-homogeneous plasma
distributed over the area of the dielectric [7, 8]. Compared to other types of
surface discharges, the sliding discharge creates a significantly wider plasma
zone, which makes it suitable for use in gas-dynamic flows [7, 9, 10].
The aim of the work was to study the distribution of the radiation
of a pulsed surface sliding discharge and the radiation of a combined volume
discharge in supersonic air flows with Mach numbers of 1.36-1.60, flowing
around an axisymmetric blunt body. Based on a comparison of the obtained images
and the results of shadowgraphy, the possibility of reconstructing the
three-dimensional structure of the gas-dynamic flow in the channel was
analyzed.
Experiments were carried out on a shock tube with a discharge
chamber of rectangular cross section 24×48 mm² (y×z) (Fig. 1).
Air at an initial pressure of 10–30 Torr was used as the working gas. A flow
with a plane shock wave was formed in the shock tube channel, followed by a
homogeneous co-current flow after rupture of the diaphragm [6, 7]. Supersonic
air flows with Mach numbers of 1.36–1.55 were generated behind the plane shock
waves with Mach numbers of 3.0–4.4. The uniform co-current flow behind the
shock wave had a duration of 200–500 μs. An axisymmetric body - a cylinder
with a spherical blunting, 7.5 mm in diameter and ~200 mm in length - was
mounted in the center of the discharge chamber at a zero angle of attack to the
oncoming flow. The nose part of the body, 15-25 mm long, was located inside the
discharge volume of 100 mm length of along the direction of the flow. Pressure
sensors connected to an oscilloscope were used to monitor the shock wave
velocity.
The direct shadowgraphy was used to visualize the flow in the
discharge chamber between the plane-parallel quartz side walls of the discharge
chamber [2, 6]. The optical scheme of the shadowgraphy included the formation
of a plane-parallel light beam passing through the studied area near the
streamlined body. A high-speed camera recorded shadowgraphy images at a
frequency of 150,000 frames per second. A laser with a wavelength of 532 nm was
used as a light source. The optical system formed a parallel beam of light ~40
mm wide, which passed through the quartz walls of the discharge chamber to
probe the flow field [6].
Fig. 1. Experimental setup and diagnostic equipment: 1 — shock
tube, 2 — discharge chamber, 3 — piezoelectric pressure sensors, 4 — discharge
switch, 5 — oscilloscope, 6 — photo camera/ICCD camera.
A surface sliding discharge with an area of 30×100 mm²
(z×x) was initiated on the lower wall of the discharge chamber at a pulse
voltage of 25 kV; the discharge current was 1-2 kA [7]. A special electrical
circuit was used to form a combined volume discharge. The discharge included
two surface sliding discharges on the upper and lower walls of the discharge chamber,
located at a distance of 24 mm from each other [11]. When a pulse voltage was
applied, the sliding discharges formed the upper and lower plasma electrodes,
providing preionization of the volume with ultraviolet radiation. During pulsed
discharge, a volume breakdown of the gas occurred, the discharge current
reached 1 kA. The duration of the discharge current was ~500 ns.
In the experiments, discharges of two types were realized at
different stages of the flow after the shock wave passed the bow of the body
until the end of the co-current flow. The discharges initiated by a pulse delay
generator relative to the passage of the shock wave through a piezoelectric
pressure sensor in the shock tube channel (Fig. 1). Pressure sensors connected
to an oscilloscope were used to monitor the shock wave velocity.
The discharge glow was recorded through quartz windows of the
discharge chamber at different angles (the exposure time corresponded to the
discharge emission time in the visible spectral range); and by ICCD camera with
nanosecond resolution. The glow of the surface sliding discharge on the lower
wall was recorded at a large angle of inclination to the discharge plane. The
discharges emission in air at high electric fields is determined mainly by the
bands of the second positive system of molecular nitrogen with a maximum in the
ultraviolet range [7, 10, 12]. The photo images were processed using a graphic
editor to improve the sharpness and contrast. A comparison of the discharge
glow images and the corresponding shadowgraphy patterns of the flow was carried
out to reveal a relationship between the discharge plasma emission and the
structure of the gas-dynamic flow near the streamlined body in the channel.
High-speed shadowgraphy showed the formation of a complex system
of shock waves during the supersonic flow around the body in the discharge
chamber, the areas of boundary layer separation. After the shock wave passes
the nose of the blunt body and diffraction occurs, a stationary flow with a bow
shock wave is formed. The stationary flow was formed for 30-50 μs during
the diffraction and continued for up to 500 μs within the duration of a
homogeneous co-current flow under experimental conditions. After the end of the
stationary stage, the flow was reconstructed with a change in the shock-wave
configuration. The transition to the non-stationary phase occurred after the
end of the co-current flow or after the arrival of reflected shock waves moving
towards the flow.
Fig. 2. Shadowgraphy image of supersonic flow elements around a streamlined body: 1 — flow, 2 — bow shock wave, 2* — inclined
shock waves, 3 — position of separation zone. Flow Mach number is 1.60, density
is 0.10 kg/m3. The region of applied pulsed voltage is highlighted
in color.
Fig. 2 shows a shadowgraphy image of the flow around a body at the
steady stage of flow, including the bow shock wave, oblique shock waves,
reflected shock waves from the channel walls and from the body. These shock
waves interacted with the boundary layers formed on the walls of the discharge
chamber.
The glow of the surface sliding discharge in quiescent air is
relatively uniform, with some filamentation appearing with gas density increase
(Fig. 3a). The discharge glow distribution in supersonic flows shows a distinct
correlation with the gas-dynamic structure of the near-surface flow (Figs.
3b–d). Local radiation of the discharge plasma is associated with the local
concentration of excited gas molecules [9, 13], which depends on the electron
concentration and, accordingly, the magnitude of the reduced electric field E/N
(E is the electric field strength, N is the concentration of gas molecules)
[13]. Photo images of the glow instantly visualize the flow structure.
Fragments b, c, and d of Fig. 3 show images of the discharge glow initiated at
various stages of the supersonic flow around the body.
All of the images show a curved line of intersection between
the discharge plane and the bow shock of the streamlined body. This line
separates the region of uniform glow in the flow from the high-density region
behind the bow shock, where no glow is observed. At each point of the
near-surface air layer, electron avalanches develop simultaneously and
high-energy electrons excite nitrogen molecules that emit photons. In the
high-density region, ionization does not occur, and glow is absent.
At the initial stage of flow formation (Fig. 3b) clearly visible
the region of intersection between the bow shock in front of the body and the
boundary layer. In this area, the discharge glow has a characteristic rounding
that followed by a region of absent glow. A bright glow in the right part of
the image appears in the separation zone at the edge of the discharge gap. At
this stage the boundary layer on the walls of the discharge chamber remains
laminar (Fig. 3b); at later stages the flow becomes turbulent [14]. Boundary
layer state affects the glow characteristics of the surface sliding discharge,
as seen in the uniform flow upstream (Fig. 3g, left). The boundary layer state
also influences the formation of a low-density region due to interaction with
an oblique shock wave with intense discharge glow is observed in the right part
of the image (Figs. 3b–d).
The area without discharge glow becomes wider which corresponds to
the stationary flow pattern observed in the shadowgraph images (Figs. 3c, d).
The bright discharge glow region is located in a low-density zone formed by the
interaction of an oblique shock wave with the turbulent boundary layer [7, 15].
The transition to the unsteady gas-dynamic regime is characterized by
changes in the position and shape of the bow shock. The glow distribution in
the flow region upstream of the body also changes and the discharge glow in the
separation zone is modified.
Comparison of the shadowgraphy frames with discharge glow images
demonstrates a clear relationship between the location of gas-dynamic
inhomogeneities and the spatial glow distribution of the surface sliding
discharge plasma. In flows with sharp density gradients the ionization rate
increases in regions of low density concentrating the discharge current in
localized channels [7, 15]. Low-density areas in the boundary layer are
effectively visualized accordingly by the glow of the surface sliding
discharge. Thus, the spatial glow distribution of the surface sliding discharge
serves as a "map" of the near-surface flow structure: the plasma
emission is intense in regions of rarefaction or strong density gradients
associated with gas-dynamic structures in the supersonic flow.
Fig. 3. Surface sliding discharge glow (left) and corresponding
shadowgraphy images of the flow field (right) in quiescent air (a) and in
supersonic flows with Mach number 1.54 (b–d). Air density is 0.09 kg/m³.
Discharge initiated 31 µs (b), 42 µs (c), 54 µs (d) after shock wave diffraction.
The
discharge radiation of the nanosecond volume discharge in still air exhibits a
high uniformity [11, 13]. A series of photo images of the discharge glow in
supersonic flows around the model (Fig. 4) enabled analysis of its spatial
distribution, which is correlated to the specific features of discharge
current. The volume discharge radiation in the uniform freestream supersonic flow
remains largely homogeneous. However, the radiation is absent in the volume
between the bow shock wave and the nose of the model. Further downstream, the
intensity of the volume discharge radiation noticeably decreases. The
distribution of surface sliding discharges glow in the near-wall regions also
shows nonuniformity. The surface glow remains uniform upstream of the bow shock
front; it disappears in the area of increased density immediately behind the
bow shock and becomes more intense in areas where oblique shock waves interact
with the boundary layer (Figs. 4 and 5). Thus, the spatial distribution of
discharge radiation effectively visualizes the density field in the flow.
Regions of lower gas density, where the electron concentration is correspondingly
higher, produce more intense radiation, whereas areas of higher density are
characterized by reduced discharge emission intensity.
Digital processing of the discharge photo images has demonstrated
that the radiation distribution enables highly accurate determination of the
position and shape of the bow shock front, as well as other features of the
shock-wave configuration.
Fig. 4. Photo
images of discharge during steady supersonic flow around the model at a Mach
number of 1.55 (density 0.07 kg/m³), captured from different viewing
angles.
Figure 5, a present a photo image of the
nanosecond volume discharge at the steady stage of supersonic flow around the
body. The spatial distribution of the discharge radiation is clearly linked to
the shock-wave configuration illustrated in the three-dimensional flow diagram
around the axisymmetric model (Fig. 5, b). The bow shock smoothly envelopes the
body while a system of oblique compression waves develops around it, including
waves reflected from the channel walls and the surface of the model. These flow
structures remain stable during the steady stage when the discharge was
initiated and its glow was recorded (Fig. 5, a).
A homogeneous distribution of volume
discharge radiation is observed in the uniform supersonic flow upstream of the
bow shock, which clearly visualizes the curved front of the shock wave.
However, the volume discharge glow is absent in the region between the bow
shock and the oblique compression waves. The intensity of the volume glow
decreases further downstream in the flow separation zone.
Fig. 5. Photographic image of discharge radiation during
steady-state supersonic flow around the model at a Mach number of 1.52 (density
0.09 kg/m³) (a), and three-dimensional flow scheme around the axisymmetric
model (b): 1 — airflow; 2 — bow shock wave; 2* — oblique shock waves; 3 — flow
separation zone; 4 — sliding surface discharges radiation; 5 — volume discharge
radiation.
Sliding surface discharges glow on the
upper and lower walls visualizes the flow within the boundary layers and in
regions where oblique compression waves interact with the boundary layer. In
these areas, lower gas density is accompanied by higher electron concentration,
resulting in intensified surface discharge radiation. As turbulence develops
within the boundary layers, local density fluctuations near the walls lead to
increased glow intensity in low-density regions (Fig. 5, a). Therefore,
the spatial distribution of discharge glow is highly sensitive to small-scale
flow inhomogeneities.
Photo recording of the glow of nanosecond surface sliding
discharge and combined volume discharge in supersonic air flows showed good
prospects for visualizing the structure of supersonic flows in a channel.
Recording of discharges radiation with ICCD camera with nanosecond resolution
showed that the duration of the glow of the volume phase of the combined volume
discharge does not exceed 300 ns, and the afterglow of surface sliding
discharges can last up to 1000 ns. With such exposure times of photo images,
the flow elements do not have time to shift, which allows visualizing the
structure of the shock-wave configuration in front of the streamlined body
instantly.
Comparison of photo images and shadowgraphy images provided
information for revealing the three-dimensional structure of the flow. Gas
discharge visualization by the volume discharge allows obtaining information
about the structure of the flow in volume, unlike two-dimensional shadowgraphy
images. Since the total plasma volume emits radiation, registration can be
carried out at different angles and from different perspectives. This allows
restoring a three-dimensional picture of the supersonic flow and identifying
details that cannot be determined by classical optical methods. This approach
is especially valuable for analyzing complex gas-dynamic structures, such as
areas of interaction of shock waves, separation zones and turbulent formations
in the flow.
An experimental study of a non-uniform supersonic flow in a
channel around a blunt body was carried out by recording the radiation of a
surface sliding discharge and a combined volume discharge of nanosecond
duration and by the direct shadowgraphy. It was shown that the mode of the
discharge current and the spatial distribution of the glow of a nanosecond
surface sliding discharge are closely related to the gas-dynamic structure of
the near-surface non-uniform flow. The discharge current can be localized in
areas of low density, mainly in the zones of interaction of shock waves with
the boundary layer. The correlation between the discharge glow and the position
of shock waves, inclined shock waves, and boundaries of separation regions
demonstrates the possibility of using a pulsed surface sliding discharge as a
diagnostic tool for visualizing near-surface gas flows. The spatial
distribution of the glow of a surface sliding discharge allows visualizing
turbulent structures in the boundary layer of a supersonic flow.
The use of a nanosecond combined volume discharge for an optical
diagnostic has shown its high efficiency in studying the spatial structure of a
supersonic flow. A complex method combining the recording of discharge glow and
high-speed shadowgraphy has made it possible to obtain detailed information on
the flow structure, including shock waves, oblique shock waves, and areas of
their interaction with boundary layers. The results of the work confirm the
prospects for further use of these methods in plasma aerodynamics and can
contribute to improving approaches to diagnostics and control of supersonic
flow around bodies.
The obtained experimental results also make it possible to make
clear the mechanisms of the relationship between the characteristics of
nanosecond discharges with the local structure of high-speed flows and
shock-wave configurations, as well as to determine ways to optimize
new-generation plasma actuators.
The study was conducted under the state
assignment of Lomonosov Moscow State University.
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