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European Journal of Applied Sciences – Vol. 9, No. 4
Publication Date: August 25, 2021
DOI:10.14738/aivp.94.10779. Kuo, S. P. (2021). Air Plasma Mitigation of Shock Wave. European Journal of Applied Sciences, 9(4). 228-244.
Services for Science and Education – United Kingdom
Air Plasma Mitigation of Shock Wave
Spencer P. Kuo
Department of Electrical & Computer Engineering,
New York University-Tandon School of Engineering, Brooklyn, NY, USA
ABSTRACT
Theory is presented to show that shock wave structure can be modified via
interacting with an air plasma plume generated symmetrically in front of a shock
wave generator. Electron jet in the plasma plume deflects the impinging airflow via
momentum transfer collisions. Symmetrical deflection makes it easy to satisfy the
conservation of transverse momentum between the airflow and plasma. The charge
transfer between N2+ and N2 randomizes the impinging airflow to increase the
deflection angle. The flow deflection increases the effective cone angle of the shock
generator; as the effective cone angle exceeds a critical value, the shock becomes
detached and faded. Experiments were conducted in a Mach 2.5 wind tunnel to
mitigate shock wave via air plasma deflection. A non-thermal air plasma was
symmetrically generated, in front of a wind tunnel model by on-board 60 Hz
periodic electric arc discharge, as a deflector for shock wave mitigation. The results
show a transformation of the shock from a well-defined attached shock into a highly
curved shock structure, which has increased shock angle and appears in diffused
form. Shown in a sequence with increasing discharge intensity, the transformed
curve shock in front of the model moves upstream to become detached with
increasing standoff distance from the model and is eliminated when the discharge
is near the peak. The steady of the incoming flow during the discharge cycle is
manifested by the repetition of the baseline shock front. The experimental
observations confirm the theory and efficacy of this air plasma mitigator.
Keywords: Shock Wave Mitigation; Air Plasma Deflector; Shadowgraph; Drag Reduction;
Wind Tunnel; Electric Discharge.
INTRODUCTION
Shock wave appears in the form of a steep pressure gradient. It introduces a discontinuity in
the flow properties at the shock front location. The background pressure behind the shock front
increases considerably, leading to significant enhancement of the flow drag and friction on the
spacecraft. Thus, the design for supersonic aircraft tends to choose slender shapes to reduce
the drag and cooling requirements. This is an engineering tradeoff between volumetric and fuel
consumption efficiencies and this tradeoff significantly increases the operating cost of
commercial supersonic aircraft. Shock wave also produces sonic booms. The noise issue raises
environmental concerns, which have precluded routine commercial supersonic flight over land.
There are considerable theoretical and experimental studies comprehend shock waves in
super-sonic flows [1] and various approaches to reduce shock wave drag to a supersonic
spacecraft have been explored. A physical spike [2] is currently used to move shock wave
upstream from the spacecraft. It improves the aspect ratio of a blunt body to reduce shock wave
drag. Further mitigation of shock wave impact, shock wave formation around a supersonic
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Kuo, S. P. (2021). Air Plasma Mitigation of Shock Wave. European Journal of Applied Sciences, 9(4). 228-244.
URL: http://dx.doi.org/10.14738/aivp.94.10779
spacecraft must be attenuated or even eliminated. It has the payoff that the fuel consumption
is reduced, and smaller propulsion system can provide the same cruise speed.
Thermal energy deposition in front of a flying body to perturb the incoming flow and shock
wave formation has been studied [3]-[7]. Heating of the background air in front of a flying body
essentially reduces the Mach number of the impinging airflow to the body. As a result, the
formed shock is weakened and has an increased shock angle (i.e., moving the shock front
upstream). This approach must elevate the gas temperature significantly to effectively reduce
the wave drag and shock noise. However, the energy gain from drag reduction is not enough to
make up the injected heating energy [5]. Although this is not a practical approach for drag
reduction purposes, it can be a feasible approach for sonic boom attenuation [3].
Shock-tube experiments showed the impact of non-thermal plasma on the shock wave
structures. Several wind tunnel experiments further explored the non-thermal (and non- equilibrium) plasma effects on shock wave mitigation. In the wind tunnel experiment
conducted by Gordeev et al. [8], a high Z conducting wire, inside the chamber of a cone-cylinder
model, was exploded off electrical short circuit; a high-pressure metal vapor (high Z) plasma
was produced and injected into the upstream supersonic flow through a nozzle. A significant
drag reduction, which was too large to be accounted for by the thermal effect alone, was
measured. In the subsequent wind tunnel experiments [9]-[17], electric discharges were
applied to generate plasmas in the supersonic flows to interact with the shock waves. The
results showed that the shock front increased dispersion in its structure and/or the standoff
distance from the model when the plasma was generated either off-board or on-board ahead of
a model. Computational and experimental studies [18] indicated that an added magnetic field
could strengthen the arc plasma to further weaken the shock wave. Microwave discharge is
another way to generate non-thermal plasma, so far, the microwave plasma projected on-board
was still too weak to introduce any visible effect on the shock wave in a hypersonic flow [19].
Theory shows that the shock wave angle and the shock structure depend on the cone angle of
the wind tunnel model, and on the Mach number and the deflection angle of the incoming flow
[1]. In the present study, the cone angle of the wind tunnel model and the Mach number of the
incoming flow are fixed, an on-board plasma deflector is introduced to study shock structure
modification by the flow deflection [20]. The polarity of the applied voltage enables electron
plasma to be accelerated in the upstream direction by the applied electric field, it forms a
plasma deflector in the upstream region to deflect incoming flow through elastic collisions. Ion
plasma also affects the incoming flow, but via a different (non-equilibrium) process. Ions
moving through their own gas are subject to charge transfer to the neutral gas, which is a
predominant inelastic collision process in the low ion energy regime [21]. An ion becomes a
neutral particle after the charge transfer, but retains its velocity, which is typically low. Thus,
these particles do not contribute to the shock wave formation. The ions converted from neutrals
through charge-transfer are collected by the cathode and do not contribute to the shock wave
generation either. The shock of the deflected flow is expected to have a larger shock angle (than
that of the baseline one) and a modified structure, representing a weaker shock.
In Section 2, Taylor-Maccoll theory for a normally incident supersonic flow over a cone is
generalized to the case of obliquely incident flow as a basis to describe plasma mitigation
mechanism. A plasma deflector generated by an electric discharge is modeled and the flow
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European Journal of Applied Sciences (EJAS) Vol. 9, Issue 4, August-2021
Services for Science and Education – United Kingdom
deflection by this deflector is formulated in Section 3. Numerical illustration of the plasma
deflection effect is also presented in Section 3. Wind tunnel experimental results to
demonstrate shock mitigation by a plasma deflector, generated by 60 Hz periodic arc discharge,
are presented in Section 4. In Section 5, a summary of the work is given, and conclusion remarks
are drawn.
GENERATION OF TAYLOR-MACCOLL THEORY
In the Case of Parallel Flow
A supersonic flow propagates parallel to the cone axis from the left toward a cone. In the steady
state, a conic shock front signified by a step pressure jump is formed to separate the flow into
regions 1 and 2 of distinct entropies as sketched in Figure 1 with q¢ = 0. In the figure, the cone
is placed horizontally (along the z-axis); thus, the flow velocity V1 in region 1 is along the z
(cone’s) axis, i.e., �! = V!�%" = V! (�%# cosb - �%q sinb), where �%# and �%q are unit vectors in the
radial and poloidal directions of the spherical coordinate system, the origin is at the tip of the
cone. The flow has a Mach number �!. The conic shock wave angle b is to be determined. In
region 2 immediately behind the shock front, the flow has a deflection angle d with Mach
number M2 and velocity �$ = V$[�%# cos(b − d) - �%q sin(b − d)].
Figure 1: Geometric relations of the supersonic flow velocity at the discontinuity across the
shock front of a cone.
Across a conic shock front (similar to across an oblique shock front), the continuity conditions
of the flow at the discontinuity interface include: 1) the continuity of the flow, i.e., r!V! sinb =
r$V$ sin(b − d) where r is the mass density of the flow; and 2) the preservation of the
tangential component (i.e., �%# component) of the flow velocity, i.e., V! cosb = V$ cos(b − d).
The continuity, momentum, and energy equations show that the changes across the shock front
are governed by the normal component of the free stream velocity, which is represented in
terms of the normal component of the upstream Mach number �%! = �!sinb. The normal
component of the downstream Mach number is obtained to be [1]
�%$
$ = �%!
$ + 2/(� − 1)
[2�/(� − 1)]�%!
$ − 1 (1)