Abstract A. Introduction - CiteSeerX

22nd AIAA Aerodynamic Measurement Technology and Ground Testing Conference

AIAA-2002-2703

INFLUENCE OF UPSTREAM PULSED ENERGY DEPOSITION ON A SHOCKWAVE STRUCUTRE IN SUPERSONIC FLOW Sohail H. Zaidi, M.N. Shneider, D.K. Mansfield, Y.Z. Ionikh, R.B. Miles Department of Mechanical and Aerospace Engineering Princeton University, Princeton, NJ 08540

Abstract A small-scale wind tunnel experiment has been performed to investigate the dynamics of the offbody energy addition upstream of an oblique shock wave generated by a wedge model. Off-body energy was simulated by laser-induced breakdown upstream the model in a Mach 2.4 flow. Laser pulses with the energy of about 350 mJ/pulse and with a pulse width of 10 ns were used to deposit the energy in the region of interest. The dynamics of the interaction were captured in both the schlieren and shadowgraphs images taken at 500,000 frames per second rates. In order to understand the complicated dynamics of the interaction between the thermal spot and its associated shockwave with the oblique shockwave from the model, computational calculations were performed. A two-dimensional, time-accurate Euler code was applied for this purpose. Good agreement between the theoretical and experimental results has been found. As expected, the laser-induced thermal spot indeed weakened the oblique shock. The images also show the dynamics of the interaction between shockwaves generated by the laser breakdown in the flow and the oblique shock, including reflections off the wedge body. The results from this near-field experiment can be used to optimize the energy addition for the practical applications including sonic boom reduction.

A. Introduction a) Energy Addition and Drag Reduction Several methods have been suggested to modify the external flowfield around a vehicle flying at supersonic speed. One very well known technique is the insertion of a physical spike extending forward from the blunt body nose [1]. Pressure drag on the body can drop up to 50% or more as a result of the generation of an additional conical oblique shock wave by the tip because it causes a substantial weakening of the normal bow shock wave in front of the blunt body nose. However there are certain problems associated with this technique which include reduction in off-design performance of the vehicle, the necessity to cool the spike and the additional frictional drag which occurs on the spike structure [2]. In recent years, energy addition has been proposed as another feasible way to reduce the drag on objects flying at supersonic speed. It has been demonstrated that a strong bow shock wave produced by a blunt body can become a more benign conical shock wave as a result of energy addition [3]. Various research groups

around the world have performed both experimental and theoretical estimates about the drag reduction in different aerodynamic conditions. In most cases, thermal energy has been added to heat the flow upstream the object under investigation. For example, a plasma arc torch with electric power up to 127 kW has been used by Toro et al. [4,5] who performed experiments in a Mach 10 flow. In this work a considerable reduction both in drag and surface heat transfer was observed as a result of the energy addition in the flow. In order to avoid the flow disturbances due to the physical presence of the electric torch, a “torchless” apparatus was employed by Bracken et al. [6] in a 24-inch hypersonic tunnel. An electric arc up to 75 kW was used in this work and experimental and computational results were compared to understand the loss mechanisms (radiation and circuit resistance losses) involved in the experiment. Figure 1 shows a typical Schlieren image from that work of the bow shock displacement as a result of energy addition upstream the blunt body [6]. In this case the energy addition (27 kW arc) spot was located at a distance corresponding to 60% of the diameter of the body. A comparison of experimental data to the predicted values reveals that in this case

1 American Institute of Aeronautics and Astronautics


27% of the arc power was deposited in the flow. In a similar work, Kuo et al. [7] conducted an experimental study of the plasma effects in the structure of an attached conical shock front appearing at the front end of the model in a Mach 2.5 flow. In this study a 60 degrees coneshaped model was employed. The tip and the body of the model were designed to function as two electrodes for the gaseous discharge. A 60 Hz self-sustained, diffuse arc discharge generated spray like plasma at the nose region of the model. The peak and average power for the plasma generation were less than 1.2 kW and 100 W, respectively. This revealed that plasma could cause the shock wave to move upstream with its shock front detached from the model. Shadow graph images of the flow also revealed that the front shock became more diffusive and had an increasing shock angle as heat was added to the flow. In addition to experimental work, several theoretical studies have been performed. Some of which have been used the experimental results to validate their models. A notable example is the work by Riggins et al.[8], who predicted a drag reduction to values as low as 30% of baseline drag (with no energy deposited in the flow) when energy was added upstream an object in a Mach 6.5 flow. A similar result was predicted for Mach 10 flows. An alternate way of creating a plasma in front of a bow shock is to use a powerful offboard or on-board microwave source. In the experiment performed by Beaulieu et al. [9], a free localized microwave discharge was generated upstream of a model in a Mach 1.4 flow. The microwave breakdown occurred at a peak power equal to 120-130 kW (900 Hz repetition rate, pulse duration 1.8 – 2.2 µs), where as the breakdown threshold was determined as 32-33 V/ cm Torr. A parabolic reflector was employed to focus the microwaves from the source which was located outside the wind tunnel. The schlieren method was employed to observe the shock wave and the influence of the energy addition in the flow. Time gating was used to obtain images of the shock wave in the front of the model. It was found that bow shock splitting began after 15-27 µs (relative to the microwave pulse), continued up to 130-150 µs and reappeared again after 150 µs. In the work carried out by Exton et al. [10], the generation of a plasma discharge in the near flow field ahead of a supersonic model was achieved by an on-board microwave source. The microwave source employed in this work had a

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maximum peak power of 425 kW with a .001 duty cycle. The microwave pulses were square wave shaped with a maximum duration of 3.5 µs. It was found that for a thin plasma, there is no noticeable difference in the shock standoff distance or shape whether the plasma is present or not. In fact time-averaged schlieren images reveal that the shock from the plasma is reflected by the bow shock and then propagates towards the model. The main precursor plasma was very thin, highly reflective and had no observable effect on the bow shock. It was suggested that in future work the spatial and temporal size of the plasma should be increased to obtain a better deposition of energy into the flow and to increase the interaction with the shock wave. Methods of minimizing the plasma reflectance and increasing the absorption were discussed. Another important step in shock wave mitigation was taken by Tretjakov et al. [11] who were the first to use a stable optical discharge in a supersonic flow. In their study a CO2 laser (2.5-100 kHz) was used to focus energy in front of a cylindrical model with an apex angle of 60 degrees. In a Mach 2 argon flow behind the discharge region, which was 5-7 mm in length, a heated wake was formed with a diameter of roughly 5mm. Shadowgraph images of the flow around the model when the discharge was pulsing with a frequency of 50 kHz, are shown in figure 2. The experiment demonstrate that the position of the bow shock wave is spread out when the energy is added. It was found that the changes in the shock structure became more visible as the discharge position was moved towards the body. b) Energy Reduction

Addition

and

Sonic

Boom

Shockwaves generated by a supersonic object produce a sonic boom on the ground and concern about boom formation has been the main obstacle in the development of supersonic/hypersonic vehicles. For a supersonic aircraft, the near-field shock structure is a complex array of shock waves that originates from various parts of the aircraft. In the far-field these shock waves coalesce and produce a “N” shape pressure signature on the ground. Figure 3 shows a typical ground signature of a jet sonic boom [12]. Sonic boom is a far-field phenomenon and therefore it does not follow necessarily that the attenuation or complete destruction of the shocks in the near filed will



eliminate or even reduce the sonic boom. Previously suggested methods to reduce the sonic boom include exceptionally long aircraft [13], underwing thermal gradients [14] and high speed oscillation of flight velocity [15]. Current work focuses mainly on the development of long, thin aircraft because the other methods seem unrealistic due to practical considerations. Energy addition is an alternate approach to overcome these practical problems. It has been argued that upstream energy addition to supersonic vehicle may weaken the shockwave and may prove to be a useful approach to suppress the sonic boom on the ground. Recent work related to DARPA’s Quiet Supersonic Platform Program, which was conducted at Princeton, addressed these issues in a greater detail. The details of this project have been presented by Miles et al. [16]. The results indicated that steady state off-body energy addition can reduce the far-field signature primarily by suppressing the far-field coalescence of the various shock waves originating from the various parts of the vehicle [16]. The present paper contains follow-on work to that project. New theoretical and experimental results which investigate the influence of upstream pulsed energy deposition on a shock wave structure in the near-field of a model in a Mach 2.4 flow are presented. Both theoretical and experimental approaches have been adopted to investigate the complex dynamics of interaction of the entropy spot resulting from the pulsed energy deposition in the flow, with the shock wave generated from the model. The following sections describe both the experimental and theoretical approaches adopted in this study in a greater detail.

B. Computational Modeling Computational modeling was performed to investigate the dynamic effects of energy addition upstream the shock wave produced by a model in the flow. Theoretical work was conducted at the flow conditions used for the experimental studies [M = 2.4, p0 = 1 atm, T0 = 136 K, γ = 1.4 (Ideal gas)]. In the wind tunnel experiment a wedge of 15 mm length and a 20° inclusive angle was used to generate the required shock wave in the flow. However, a diamond shaped model was used in the modeling whose front-half had the dimensions of the wedge

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employed in the experiment. The main reason for using a diamond shaped model was to avoid the flow instabilities generated at the sharp trailing edge of the wedge and to simplify the computational calculations. A laser spark produced the cylindrical shock wave and a rarefied thermal spot that moved together downstream with the flow. The energy deposition region was assumed to have a cylindrical shape and a gaussian distribution in the (x,z) plane with effective radius (reff) of 0.125 cm. In the experiment the laser pulse energy focused in the flow was about 350 mJ/pulse. A 40% coupling efficiency was assumed that corresponds to Q0 = 0.137 J/cm where Q0 is the total heat dissipated by the flow per unit length in a direction normal to the flow stream. The dynamic effects of energy addition were investigated using a time marching two dimensional Euler-code. The set of Euler equations in cartesian coordinates together with ideal gas equation of state were used in the form given below:

∂ ∂ ∂ U+ X+ Z=H ∂t ∂x ∂z

ρ ρu U= , ρv e

ρu ρu 2 + p X = , ρuv (e + p)u

(1)

ρv ρuv Z= , ρv 2 + p ( e + p )v

0 H=

0 0 p

(2) p = (g-1)ρ

(3)

e = ρ[e+(u2+v2)/2]

(4)

where ρ and p denote the gas density and pressure, respectively, u , v are the x and z velocity components, e is the total energy of the gas per unit volume, and e is the internal energy per unit mass. P ( x, z , t ) is the power density of the source of energy released in (W/m3). Computations were performed by 2nd order MacCormack method [17] on a rectangular grid. The physical coordinates (x , z ) were transformed into (x , z ) following transformation:

according to the

x=x z = z / z b ( x),


z ∈ [0,1]

(5)


where zb (x ) is the coordinate along the upper boundary of the region of computation. On the wedge surface the velocity component normal to the wedge surface was assumed to be zero. As τ pulse