10. LASER ENERGY DEPOSITION IN QUIESCENT AIR AND INTERSECTING SHOCKS

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1 10. LASER ENERGY DEPOSITION IN QUIESCENT AIR AND INTERSECTING SHOCKS H. Yan 1, R. Adelgren 2, G. Elliott 3, D. Knight 4 Rutgers - The State University of New Jersey Mechanical and Aerospace Engineering Piscataway, N.J , USA T. Beutner Air Force Office of Scientific Research801 N. Randolph St.Arlington, VA M. Ivanov 5, A. Kudryavtsev 6, D. Khotyanovsky 7 Institute of Theoretical and Applied MechanicsSiberian Branch of the Russian Academy of SciencesNovosibirsk , Russia Abstract. This paper presents a combined experimental and computational study of the effects of a single laser energy pulse in two flow configurations. The first study examines a single laser pulse in quiescent air. It is conducted to examine the principle features of the laser pulse. A Gaussian profile is proposed for the initial temperature distribution. Real gas effects are not considered. The second study is an asymmetric laser pulse in symmetric intersecting shocks with freestream Mach number of It is studied to determine the capability of laser energy deposition to reduce the extent of the Mach stem. Introduction The design of high performance supersonic and hypersonic air vehicles requires careful attention to aerodynamic flow control. Energy deposition as a means of global flow control including drag reduction and modification of vehicle aerodynamic forces and moments has been studied experimentally and numerically [1-5]. On the other hand, since the aerodynamic performance of high speed vehicles is often controlled by highly localized fluid dynamic phenomena, attention has been directed towards local flow control, in which small scale energy addition system is intended to control local flow phenomena, e.g., reducing peak surface pressure and heat transfer, modifying separation regions, changing the shock structure. For example, Adelgren et al [6] measured a 30% reduction of peak surface pressure for an Edney IV interaction at Mach 3.5 using energy deposition. Leonov et al [7] demonstrated a significant change in the shock structure for transonic flow past an NACA 0014 airfoil using electric arc discharge. The crossing shock wave interaction is a fundamental phenomenon in high speed flight. For example, a scramjet powered hypersonic vehicle (Fig.1) may utilize shock interactions to decelerate the flow field in the inlets. The intersection of two symmetric oblique shock waves (shown in Fig.2) may result in either a Regular Reflection (RR) or Mach Reflection (MR) depending on the incoming Mach number M and shock angle as illustrated in Fig.3. For shock angles greater than the shock detachment angle D, only a Mach Reflection is possible. The shock detachment angle D is readily determined from the oblique shock relations. Fig.1. Hypersonic vehicle. Von Neumann [8] proved the existence of a dual solution domain, defined by an angle N (denoted the von Neumann angle) and the detachment angle D with N D, wherein either 1 Research Associate, Dept. of Mechanical and Aerospace Engineering. 2 Major, USAF, Dept. of Mechanical and Aerospace Engineering. 13 Professor, Dept. of Mechanical and Aerospace Engineering. 4 Professor, Dept. of Mechanical and Aerospace Engineering. 5 Head, Computational Aerodynamics Laboratory. 6 Senior Scientist, Computational Aerodynamics Laboratory 7 Research Scientist, Computational Aerodynamics Laboratory 68

2 Reconstruction Flux Algorithm Time Integration Table 1. Numerical Method ITAM RU 4th order of MUSCL 1st and 3nd order of MUSCL Harten-Lax-van Leer-Einfeldt 2nd exact Godunov's 3rd Runge-Kutta 2nd Runge-Kutta a RR or MR can occur and are stable to infinitesimal perturbations [9]. The dual solution domain exists for M > 2.2 (for =1.4) and is important for hypersonic flight (Fig.4). The difference in the downstream static pressure between a Regular Reflection and Mach Reflection can be significant. For example, at Mach 5 and =35 (i.e., midway between N and D ), the stagnation pressure ratio across the RR is 349% greater than the MR. Consequently, the ability to control the transition from RR to MR (and the reverse) is important for scramjet propulsion. for MR RR equals N. Experiments and numerical simulations by Ivanov and his colleagues [9,11-13] confirmed the hysteresis model of Hornung et al [10]. Fig.4. Dual solution domain Fig.2. Crossing shock boundary layer interaction The objective of this combined computational and experimental study is to propose a proper initial condition for the laser energy spot, to demonstrate the blast wave structure in the quiescent air and further to determine the capability of laser energy deposition to reduce the extent of the Mach stem in a Mach Reflection. Numerical Methodology Fig.3. Regular and Mach reflection Hornung et al [10] proposed a specific model for hysteresis within the dual solution domain. For increasing (beginning with < N, i.e., a RR), Hornung et al proposed that the forward F transition angle tr for RR MR equals D. For decreasing (beginning with > D, i.e., a MR), they proposed that the backwards transition angle Two different numerical methods are employed to simulate the laser induced blast wave propagation in the quiescent air. The first approach is used by Institute of Theoretical and Applied Mechanics (ITAM). The second approach is presented by Rutgers University (RU). The details are presented in Table 1. Experimental Facilities The intersecting shock experiments were performed in the Mach 3.45 supersonic wind tunnel of the Rutgers Gas Dynamics and Laser Diagnostics Laboratory (Fig.5). The tunnel is a blow-down facility with compressed air supplied from high pressure (16.6MPa) air storage tanks with a capacity of 8m 3. Three four-stage compressors and a regenerative air dryer are 69

3 Table 2. Test Conditions Pressure for quiescent air, p s MPa Stagnation pressure for intersecting shocks, p s MPa Temperature for quiescent air, T s 295 K Stagnation temperature for intersecting shocks, T s 293 K Laser perturbation focal volume, V 0 3 mm 3 Laser beam incidence energy for quiescent air, E 112 mj/pulse Laser beam incidence energy for intersecting shocks, E 317 mj/pulse employed. The test section is 15.2cm 15.2cm, and the total test time is several minutes per day. Test section stagnation pressure can be set in the range of 0.55 to 4.8MPa, with a typical value of 1.0MPa, and the stagnation temperature is ambient (typically 290 deg K). The Reynolds number per meter is used with an injection seeded Nd:YAG laser frequency doubled with a wavelength of 532nm. This imaging laser, passed through sheet forming optics, illuminated the flow field region (Fig.6). Fig.6. Schematic of test apparatus for Rayleigh scattering images Fig.5. Rutgers Supersonic Wind Tunnel A short duration (10ns) laser pulse is generated using a Nd:YAG laser ( =532nm). The laser beam (1cm diameter) is focused through a lens (typically 100mm focal length) to a small volume (typically 1-3mm 3 ). The laser pulse repetition rate is 10Hz. Schlieren visualization was performed using a xenon ashlamp with 1 s pulse duration. The schlieren image is captured on a CCD camera and digitized. At typical tunnel stagnation conditions, the freestream velocity is 640m/s, yielding an effective flow transit distance of 0.64mm during the schlieren pulse. The typical model dimensions (in the cross sectional plane) is 25.4mm. Thus, the schlieren image is effectively instantaneous; however, the image is optically integrated in the spanwise direction due to the inherent nature of schlieren, and typically multiple images are ensemble averaged at the same time delay following the laser pulse. Flow visualization of the blast wave, created from the laser induced breakdown in quiescent air, was obtained by a Rayleigh scattering technique [14-16]. A molecular iodine filter was The imaging laser sheet was aligned with the focal region (the spark location) of the second Nd:YAG laser such that the sheet passed through the center of the spark. A Princeton Instruments integrated charge couple device camera was used to record the filtered Rayleigh scattering images of the flow region at time delays ranging from 5 to 40 us. For these time delays, the blast wave was observed propagating away from the spark. A Stanford Research Systems pulse generator was used to control the time delay between the laser spark, the laser sheet, and the camera. Since the pulse widths of the lasers are 10ns, the time delay between the imaging laser sheet and the laser spark can be controlled on the order of 10ns. The images were phase averaged and measurements were made of the radial position versus time for the blast wave. The Rayleigh scattering flow visualization technique basically consists of a molecular filter with absorption wells located within the frequency range of the imaging laser. This molecular filter is placed in front of the receiving optics to modify the frequency spectrum of the scattering signal from the imaged flow region. The imaging laser, i.e. the laser sheet, can be tuned to the absorption wells of the molecule within the filter (iodine for these tests). Unwanted scattering from the walls, windows, background, etc. is absorbed while the Doppler shifted Rayleigh scattering from the 70

4 molecules in the imaged flow field is shifted and thermally broadened outside of the molecular absorption well. If the Doppler shift is small (due to the optical arrangement), planar images are obtained of the qualitative density and temperature variations. The intensity variations of the images recorded are proportional to a first approximation to the flow field density. Thus, the blast wave was clearly observed in the filtered Rayleigh scattering images. A typical z-path schlieren system was used for flow visualization of the laser induced breakdown in quiescent air in addition to the filtered Rayleigh scattering technique. However, a novel technique was designed and used for the schlieren ash source. The ash for the schlieren image was generated by a focused laser discharge on the end of 1mm diameter 2% thoriated tungsten welding rod in a cavity with blowing Argon. The pulse duration of this schlieren light source was 10ns with a 2ns jitter. This pulse duration and jitter are a three order of magnitude improvement when compared to the same characteristics of the xenon ash lamp. The schlieren image was captured and digitized with a CCD camera and PC system. The pressure changes caused by the laser spark induced blast wave were recorded with a Kistler model 211B5 piezoelectric pressure transducer with 50mV/psi sensitivity. The transducer was mounted in a probe positioned on a radius from the spark centroid. The probe, in turn, was mounted on a translation stage used to control the probe position. A Kistler 5126A piezotron coupler signal conditioner processed the transducer signal, and the data was recorded on a laptop PC connected via a National Instruments GPIB-PCMI card and HP 500 MHz oscilloscope. The test conditions for the quiescent air and intersecting shocks cases are listed in Table 2 and Table 3. Table 3. Wedge parameters Wedge length, w 25.4 mm Wedge span, b mm Wedge separation, 2g mm Mach number, M 3.45 Quiescent Air Two individual computations were completed at ITAM and RU. In the first calculation done at ITAM, the 3D unsteady Euler equations were solved. A uniform cartesian grid was used and the resolution was 0.3mm. The second simulation performed at RU was a one dimensional calculation in the spherical polar coordinate system. The grid resolution is 0.03mm which can resolve the focal volume of 3mm 3 more accurately than the first simulation. For both computations, the ambient condition is temperature T=293K, density =1.28kg/m 3 and freestream velocity U=0. The laser energy addition is modeled as a temperature variation and the breakdown of air is not considered in this paper. Baker 17 noted that the blast front tends to become spherical in shape with increasing distance from the origin independently of any finite source shape. This phenomenon is also demonstrated in our FRS images which show a fairly spherical blast wave after t=6 s in Figs.7. Note that the line in the center is residual emission from the spark. A plasma formed by the cascade release of electrons absorbs energy rapidly and propagates along the focal axis towards the laser source forming a tear drop shape. A blast wave formed by the formation of the plasma and rapid expansion of gas in the focal region propagates into the surrounding gas and is nearly spherical after certain time which is dependent mainly on the energy level. The lower the energy level is, the less time is needed. Fig.7. Laser pulse at t=5 s Results and Discussion The flow structures of a single laser pulse in two flow configurations are investigated. The first case is the laser induced blast wave propagation in the quiescent air. The second one is an asymmetric laser pulse for unsteady shocks at a freestream Mach number of Consequently, we propose a spherically symmetric initial temperature distribution to model the laser energy pulse assuming the energy is added instantaneously at constant volume (therefore the density is constant) and the gas is ideal. The temperature variation using a Gaussian profile can be written as 71

5 2 2 r r T T 0 0e (1) where T 0, the peak temperature variation is determined by the total energy deposited 2 r 2 sin c Tdrd d E v (2) where c v is the specific heat at constant volume. Substituting (1) into the above equation and integrating E T 0 3/ 2 3 r0 c (3) v where r 0 is related to the initial radius R 0 of the laser spot obtained from the laser perturbation focal 4 3 volume V 0 = R 0 and set to be R0 /2. From Eq. (1), 3 T will reach 2% of the maximum temperature amplitude T 0 at r=r 0. In this case, only one energy level of E=112mJ is used. E T 0 3/ 2 3 r0 c (4) v The results from ITAM and RU show good agreement with experimental fit given in Adelgren [18] (r(t)= t , where t is in seconds and r in meters) except in the region very close to the origin, where no experimental data are available. If taking into account the energy absorption rate, the result from RU with =0.7 exhibits closer agreement with experiment. The measurement of the absorption rate in experiment is considerably difficult because of the scattering of the laser beam. By fitting the profile of shock wave radius vs time, an approximate absorption rate can be obtained numerically. For strong shock wave (M s 2 >>1, where M s =V s /a, and M s, V s and a are the shock Mach number, shock velocity and ambient speed of sound, respectively.), Taylor [19] proposed a Taylor's similarity solution at the early stage of the air explosion, r(t)=at 0.4 where A is the function of input energy and ambient density. The blast wave in our case doesn't behave in accordance with the Taylor's similarity solution by comparing the exponent in the experimental data _t. The reason may be explained from Fig.9. As a blast wave is propagated through the air, it weakens rapidly and decreases in shock velocity until it is propagating at essentially the speed of sound shown in Fig.9. The Mach number at t=5 s, which is the first time record in our experiment is about 1.6. This doesn't qualify for the application of the Taylor's solution. Fig.8. Shock wave radius vs time The blast wave propagates into the ambient air. The position of the leading front of the blast wave (shock wave) varying with time is shown in Fig.8. The position of the blast front is determined by locating the maximum pressure along the radial distance from the center of the source. Considering not all of the laser energy is absorbed and some of the energy is reflected, transmitted, scattered and emitted by the plasma, the absorption rate is introduced as =E a /E, where E a is the absorbed energy and E is the total input energy. Therefore, Eq. (3) becomes Fig.9. Shock Mach number vs time 72

6 Fig.10. Density vs radius Fig.13. Velocity vs radius Fig.11. Pressure vs radius The flow still exhibits the similar structures discontinuous increase in pressure, density and temperature when the shock wave passes through shown in Figs.10, 11, 12 and 13. As a blast wave is propagated through the air, the peaks of the density, pressure and velocity move further away from the center and decrease with time. The size of the high temperature region induced by laser energy stays almost constant. When the laser energy is deposited and subsequently the blast wave is formed, the density and pressure rise to their peaks abruptly. The flow is accelerated by the passage of the blast front. Then the pressure decays and drops below ambient. A reversed flow shown in Fig.13 is formed by the adverse pressure gradient. Finally, the pressure is recovered to the ambient value. Figs.14, 15, 16 and 17 present the propagation of the blast wave with Fig.12. Temperature vs radius Fig.14. Density vs time 73

7 time at four different radii. At r=5mm located inside the high temperature region shown in Fig.12, the temperature and velocity show the similar distribution with the peak decreasing in increasing the distance from the center of the spot. Fig.15. Pressure vs time Fig.18. Pressure vs time at E =58 mj Fig.16. Temperature vs time Fig.19. Pressure vs time at E =112 mj Fig.17. Velocity vs time The profiles of pressure vs time at r=7.1mm with two different energy levels are shown in Figs.18 and 19. The standard deviations for both energy levels are 1%, 5% and 4% for upstream, peak and downstream as indicated in the figure, respectively. The comparison with the preliminary experiment is fairly good in terms of shock position. The reason for the discrepancy in peak pressure between computation and experiment is under investigation. The blast wave generated by the laser spot with higher energy level propagates faster than the lower energy level. The response 74

8 time of the pressure transducer in terms of the rise time of the pressure is within only 2 s delayed for both energy levels. Intersecting Shocks The wedges at M =3.45 with a single laser pulse are studied experimentally and numerically. The experimental results are shown and the numerical simulation is in progress. The chronological sequence of schlieren images for a laser pulse above the centerline for wedges is shown in Figs.21 to 25 where each image is an ensemble of three to eight experiments. The undisturbed flowfield (Fig.20) displays a distinct Mach stem at the intersection of the Fig.20. No perturbation Fig.23. t=60 s Fig.21. t=10 s Fig.24. t=70 s Fig.22. t=30 s Fig.25. t=90 s 75

9 incident shock waves as expected. The blast wave and laser spot interacts initially with the upper oblique shock wave (Figs.21 to 22) causing an upstream deflection of the oblique shock. This deflection eventually reaches the Mach stem (Fig.23) causing a reduction in the height of the Mach stem. The variation in height of the Mach stem with time is shown in Fig.26. The Mach stem decreases monotonically to 20% of its original height, and then returns to its original height. Conclusion Fig.26. Mach stem height vs t (22 22 ) This paper presents a combined numerical and experimental study of a single laser pulse in quiescent air and the intersecting shocks at a Mach number of 3.45 with a single asymmetric laser energy deposition. A Gaussian profile is proposed for the initial temperature distribution due to the laser energy deposition. A good agreement with experiment is achieved in the profile of the shock radius vs time. The experimental results for laser energy deposition upstream of intersecting shocks show the apparent decrease of the height of the Mach stem when the blast wave passes through the Mach stem. Acknowledgements This research is supported by AFOSR under Grant No. F monitored by John Schmisseur and Steve Walker. References 1. Levin, V. and Terent'eva, L., Supersonic Flow Over a Cone with Heat Release in the Neighborhood of the Apex, Mekhanika Zhidkosti i Gaza, No.2, pp (1993). 2. Myrabo, L. and Raizer, Y., Laser-induced Air Spike for Advanced Transatmospheric Vehicles, AIAA Paper No (1994). 3. Riggins, D., Nelson, H. and Johnson, E., Blunt Body Wave Drag Reduction Using Focused Energy Deposition, AIAA J., Vol.37, No.4, pp (1999). 4. Toro, P., Myrabo, L. and Nagamatsu, H., Pressure Investigation of the Hypersonic 'Directed Energy Air Spike' Inlet at Mach Number 10 up to 70kW, AIAA Paper No (1998). 5. Tretyakov, P., Garanin, A., Kraynev, V., Tupikin, A. and Yakovlev, V., Investigation of Local Laser Energy Release Influence on Supersonic Flow by Methods of Aerophysical Experiments, International Conference on Methods of Aerophysical Research, Novosibirsk, Russia, pp (1996). 6. Adelgren, R., Elliot, G., Knight, D., Zheltovodov, A. and Beutner, T., Energy Deposition in Supersonic Flows, AIAA Paper No (2001). 7. Leonov, S., Bityurin, V. Savischenko, N., Yuriev, A. and Gromov, V., Influence of Surface Electrical Discharge on Friction of Plate in Subsonic and Transonic Airfoil, AIAA Paper No (2001). 8. Von Neumann, J., in Collected Works, Vol. 6, 1963, pp , Pergamon Press (originally published in 1943). 9. Ivanov, M., Markelov, G., Kudryavtsev, A. and Gimelshein, S., Numerical Analysis of Shock Wave Reflection Transition in Steady Flows, AIAA J., Vol.36, No.11, pp (1998). 10. Hornung, H., Oertel, H. and Sandeman, R., Transition to Mach Re ection of Shock Waves in Steady and Pseudosteady Flow With and Without Relaxation J. Fluid Mechanics, Vol. 90, pp (1979). 11. Ivanov, M., Gimelshein, S. and Beylich, A., Hysteresis Effect in Stationary Re ection of Shock Waves, Physics of Fluids, Vol.7, pp (1995). 12. Ivanov, M., Beylich, A., Gimelshein, S. and Markelov, G., Numerical Investigation of Shock Wave Re ection Problems in Steady Flows 20th International Symposium on Shock Waves, pp (1996). 13. Ivanov, M., Khotyanovsky, D., Kudryavtsev, A. and Nikiforov, S., Experimental Study of 3D Shock Wave Configurations During RR MR Transition, 23rd International Symposium on Shock Waves (2001). 76

10 14. Miles, R.B. and Lempert, W.R., Flow Diagonostics in Unseeded Air, AIAA paper (1990). 15. Elliott, G. S. and Beutner, T., Molecular Filter Based Planar Doppler Velocimetry, Progress in Aerospace Sciences, Vol.35, pp (1999). 16. Elliott, G.S., Boguszko, M. and Carter, C., Filtered Rayleigh Scattering: Toward Multiple Property Measurements, AIAA paper (2001). 17. Baker, W.E., Explosions in Air University of Texas Press, Austin and London (1973). 18. Adelgren, R., Boguszko, M. and Elliott, G., Experimental Summary Report Shock Propagation Measurements for Nd:YAG Laser Induced Breakdown in Quiescent Air, Dept of Mechanical and Aerospace Engineering, Rutgers University, October (2001). 19. Taylor, G.I., The Formation of a Blast Wave by a Very Intense Explosion: I Theoretical Discussion, Proc.Roy.Soc., 201, pp (1950). 77