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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)