ISSN 10637842, Technical Physics, 2010, Vol. 55, No. 12, pp. 1760–1765. © Pleiades Publishing, Ltd., 2010. Original Russian Text © S.V. Bobashev, N.P. Mende, P.A. Popov, V.A. Sakharov, 2010, published in Zhurnal Tekhnicheskoі Fiziki, 2010, Vol. 80, No. 12, pp. 51–56.
GAS DISCHARGES, PLASMA
Experimental Investigation of Magnetohydrodynamic Action on a Heat Flux toward the Surface of a Model S. V. Bobashev, N. P. Mende, P. A. Popov, and V. A. Sakharov* Ioffe Physical–Technical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 21, St. Petersburg, 194021 Russia *email:
[email protected] Received April 26, 2010
Abstract—Experimental data for magnetohydrodynamic (MHD) action on a supersonic nitrogen flow about an axisymmetric model are presented. The experiments were carried out in the Big Shock Tube (Ioffe Phys ical–Technical Institute), at the end of which a test section equipped with a supersonic nozzle was mounted. A test conic model coupled with a cylinder is attached to the output cross section of the nozzle. A magnetic field is produced by a solenoid placed on the cylindrical part of the model through which a pulsed current due to an external voltage source discharging passes. Electrodes on the conic part of the model initiate a gas dis charge, which rotates about the axis of the model in the solenoidal magnetic field. The influence of the mag netic field on the gasdynamic pattern of the flow near the model and on the heat flux toward its surface is investigated. Schlieren patterns of the flow about the model, photographic scans of the discharge glow, and heat flux measurements are taken. It is found that the magnetic field has an effect on the gasdynamic pattern of the flow near the model and on the heat flux toward its surface. The dependence of MHD effects on the external voltage polarity is also revealed. DOI: 10.1134/S106378421012008X
INTRODUCTION Heat exchange between the fast flows of a weakly ionized gas and a solid surface is a subject of great importance in solving the problem of spacecraft reen try into the atmospheres of the Earth and other plan ets. As the velocities of flows near the surface increase, physical processes governing the amount and dynam ics of the heat flux toward the surface become more and more complicated. In recent years, the feasibility of active influence on a heat flux toward the surface of a vehicle using electromagnetic fields has attracted the attention of many researchers (see [1–5] and refer ences therein). Since a gas flow near the surface of fast objects may ionize, magnetohydrodynamic (MHD) methods are also among those that can be used for controlling heat exchange. The complicacy of the phenomenon necessitates a complex approach to study it. The importance of relevant experiments is difficult to overestimate in this case. Experiments on MHD control of the flow about a vehicle are carried out, as a rule, with sophisticated setups equipped with special facilities, for example, a plasmotron, providing a supersonic flow of a weakly ionized gas. A test model (usually simply shaped) is equipped with either permanent magnets or electro magnets. A shock tube with a supersonic nozzle is a relatively simple device serving for generation of hightempera ture gas flows. Usually, these flows arise when a shock wave reflects from the end face of the tube and the gas is accelerated in the adjacent nozzle. However, it is
rather difficult in this case to obtain a highconductiv ity supersonic plasma flow needed for effective MHD interaction at the exit of the nozzle. In 2002–2005, the authors of this work, on the initiative of Vasil’eva, car ried out experiments in which a supersonic weakly ionized xenon flowed about a model. Xenon was heated by a reflected shock wave to ~8000 K and then accelerated in a supersonic nozzle to a velocity corre sponding to M = 5. Unlike molecular gases, xenon exhibits a low recombination rate, as a result of which we managed to obtain a supersonic plasma flow with a degree of ionization of ~0.5% at the exit from the noz zle. However, the parameters of the plasma prevented an effective MHD influence on the flow. In this work, we propose a new approach to exper imentally modeling MHD effects in a supersonic flow about an axisymmetric model [6]. The idea of the approach consists in heating the gas in the shocked layer in front of the model by means of an electrical discharge. The discharge is initiated in a solenoidal magnetic field, which causes it to rotate about the model and forms a region with a hightemperature gas on its surface. EXPERIMENTAL SETUP Experiments on MHD action on a supersonic flow about an axisymmetric model were carried out in the Big Shock Tube (Ioffe Physical–Technical Institute) [7], the schematic of which is shown in Fig. 1. The shock tube with a channel 100 mm in diameter and
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Fig. 1. Schematic of the experimental setup and its test section.
16 m in length has 1.5mlong highpressure chamber 1 equipped with an external electric heater. The pressure and temperature of the working gas, hydrogen, inside the chamber may amount to 50 MPa and 750 K, respectively. The highpressure chamber is separated from lowpressure channel 2 by a metallic diaphragm. The disruption of the diaphragm generates a shock wave propagating through the gas under study (nitro gen). One end of the lowpressure channel is terminated by 600mmlong test section 3 with a 210 × 75mm inner rectangular cross section. The test section has win dows 4 on side walls to observe the flow. The other end of the test section is connected to vacuum tank 5 with a volume of 6 m3. The test section was separated from the lowpres sure channel by a thin plastic diaphragm shutting the nozzle. When the shock wave reflected from the input end of the test section, the diaphragm broke down, giving rise to a flow through supersonic nozzle 6. The output crosssectional area of the nozzle measured 95 mm × 75 mm. Nitrogen was used as a working medium. The pressure, temperature, density, velocity, and Mach number of the supersonic nitrogen flow at the outlet of the nozzle were, respectively, ~4–5 kPa, ~600 K, ~0.025 kg/m3, ~2 km/s, and 4. The duration of the steady flow was about ~1.5 ms. Models 7 in the form of a 60° cone conjugated to a cylinder 32 mm in diameter were placed at the output cross section of the nozzle. The design of one of the models is shown in Fig. 2. Inside the model, coaxial magnetic core 1 made of steel with a low remnant magnetization is located. Magnetic coil 2 consisting of 16 turns of copper wire 1 mm in diameter is wound on the cylindrical part of the core. On the magnetic core, there is projection 3 along the cone–cylinder conjugation line, which is flush with the conical surface of the model. The outer surface of this projection serves as a ring electrode. The ring electrode is connected to one end of coil 2, and its other end is connected to the terminal of an external pulsed voltage source consisting of several LC ele ments. Before experiments, the source is charged up to TECHNICAL PHYSICS
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Fig. 2. Test model and the typical waveform of the dis charge current pulse.
a desired voltage. The other terminal of the source is connected to central electrode 4 on the axis of the model. The space between the central electrode and magnetic coil is filled with epoxy resin 5. The conical part of central electrode 4 and ring electrode 3 form a break (gap) in the discharge circuit of the pulsed volt age source. To close the discharge circuit, a short (~10–6 s) highvoltage discharge is initiated in this gap. This discharge, in turn, causes the pulsed voltage source to discharge for ~10–3 s. The typical waveform of the discharge current is shown in Fig. 2. The mag netic field induction calculated from the discharge current through the solenoid amounted to ~0.5 T near the ring electrode. Gas discharge 6 starts to rotate about the model in the solenoidal magnetic field of coil 2. In the experiments, we took Schlieren patterns of the flow about the model (the exposure time was 5 × 10–8 s) and of the timeintegrated discharge glow near the model and also photographed time scans of the discharge glow. The heat load was determined with sensor 7 placed on the cylindrical part of the model. This sensor [8] is a set of 0.2 × 0.2 × 6.0mm thermoelements connected in series. Each of them was cut from an anisotropic bismuth single crystal at a certain angle to one of its crystallographic axes. The thermoelements were arranged on a 4 × 6mm area in such a way that the electric currents in adjacent elements were directed opposite to each other. In this way, a high noise immu nity of the heat sensor was provided. The electric signal of the heat sensor is propor tional to the temperature difference between the work ing and rear surfaces of the thermoelement. The thick ness of the sensor (0.2 mm) is large enough for direct measurement of the heat flux with a characteristic time of ~1 ms. In this case, the amount of the heat flux can be determined provided that, first, the signal from the sensor is mathematically processed by solving the onedimensional heat equation [9], and, second, the initial signal is corrected with regard to warming of the sensor’s back surface. These procedures, while rather cumbersome, do not qualitatively distort measure
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ments. Therefore, we will conduct comparative analy sis of signals from the heat sensor for simplicity.
ther from the conic surface and its front is slightly curved compared with the case of the unperturbed flow (Fig. 3a). The patterns of the flows about the models with and without the magnetic core (Figs. 3b, 3c) also differ noticeably. The discharge glow in these patterns is also considerably different (the glow is more intense near the model with the core) although the electric power spent on maintenance of the discharge was the same in both cases. Finally, the patterns of the flow behind the shock wave also differ: turbulence near the model without the core (Fig. 3c) is less pronounced. Having analyzed the Schlieren patterns of the supersonic nitrogen flows with M = 4 about two differ ent models, we found that the flow is affected more strongly in the case of the model with the core, when the magnetic induction near the ring electrode attained 0.7 T. Therefore, the model with the core can be considered as the most promising for the MHD action on a supersonic flow and for respective investi gations.
RESULTS AND DISCUSSION Influence of the Magnetic Field In the above approach to experimental modeling, we take into account two physical processes: Joule heat release and the action of the ponderomotive force on the gas discharge. The heat release depends mainly on the current through the plasma, and the pondero motive force depends on this current and on the mag netic field strength. To elucidate the role of a magnetic field in the MHD action on a supersonic flow, we used two models of the same geometry, in one of which a magnetic core was absent. The core increases the magnetic induction approximately by a factor of 1.5, all other conditions being equal. In the absence of the magnetic core, a brass ring served as a ring electrode. The brass ring was placed at the same place along the line of cone–cylin der conjugation. To suppress the effect of eddy cur rents when switching a pulsed magnetic field, a notch was made on the ring electrode along its generatrix. The discharge current during experiments remained the same to maintain the heat release at a constant level. Figure 3 shows three Schlieren patterns of the steady supersonic nitrogen flow about the models in the (a) absence (the electromagnetic device was inac tive) and (b, c) presence of the MHD action. Figures 3b and 3c correspond to the flows with and without the magnetic core, respectively. The Schlieren patterns were taken with an exposure time of ~50 ns. The bright areas near the conical surface of the model in Figs. 3b and 3c correspond to the regions of discharge rotation. These regions, exposed throughout the experiment (~10–3 s), shed light on the form of the discharge near the surface of the model. It is distinctly seen that, in the presence of the MHD action (Figs. 3b, 3c), the bow shock wave is far
Influence of the Ring Electrode Polarity on the Discharge Dynamics In the experiments with the model having a mag netic core, we found that the rotation frequency of the discharge and the signal from the heat sensor depend on the polarity of the ring electrode connected to the voltage source. When the polarity of the voltage source reverses, so does the sense of the discharge current through the magnetic coil, because the discharge and coil constitute a series discharge circuit of the source. The direction of the ponderomotive force remains invariable. Since the ring electrode is near the magnetic coil, where the magnetic induction and electromagnetic force reach a maximum, it seems reasonable to con sider processes taking place near the ring electrode. The rotation frequency of the discharge was mea sured with a ZhFR2 waiting photorecorder. The dis charge glow was recorded from the area of the conic surface along the generatrix. The image of the glow was limited by a slit diaphragm 1 mm in width, which was parallel to the cone generatrix, and was moved over the photofilm with a preset velocity to calculate the average rotation frequency of the gas discharge. In the experiments, the parameters of the super sonic flow and the discharge currents were kept con stant. Figure 4 demonstrates two photographic scans corresponding to different polarities of the ring elec trode: at the top, the ring electrode is a cathode; at the bottom, it serves as an anode. The shown fragments of the scans correspond to the steady flow. The time in the photographs varies from left to right along the hor izontal. The vertical coincides with the direction along the cone generatrix. Processing of the photographic scans showed that the average rotation frequency of the discharge is about 30 kHz, when the ring electrode is a cathode,
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Fig. 3. Schlieren patterns of the supersonic flow about the models in the (a) absence and (b, c) presence of MHD action on the model (b) with and (c) without the magnetic core.
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Fig. 4. Photographic scans of the discharge glow when the ring electrode is negatively (upper photograph) and posi tively charged (lower photograph). Letters R and C on the left indicate the positions of the ring and central elec trodes, respectively, on the cone generatrix.
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Fig. 6. Time variation of signals from the heat sensor for discharge current Imax = (1) 1.3 and (2) 1.5 kA when the ring electrode is a cathode.
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and about 15 kHz for the inverse polarity. It should also be noted that the rotation frequency of the dis charge depends on the ambient gas pressure. This is indicated by measurements taken in quiescent air [6]. An interesting result was obtained when measuring the thermal action on the cylindrical part of the model at opposite polarities of the voltage source. In this series of experiments, we compared signals from the heat sensor for two values of the discharge current under opposite polarities of the voltage source. When the discharge current is varied, the duration of the cur rent pulse remains almost the same and only its ampli tude changes. Therefore, the maximum value of the discharge current, Imax, will be taken as its quantitative characteristic. Figure 5 shows signals from the heat sensor under the conditions of discharge current variation when the ring electrode is used as an anode. It follows from this figure that, when the discharge current increases by 15%, the signal grows twofold on average. During the experiment, the signal from the sensor continuously varies. Note also that the pulsation frequency in curve 2 is approximately equal to 15 kHz, which agrees with the value measured from the photographic scan. TECHNICAL PHYSICS
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5 Fig. 7. Schematic of the setup for recording the movement of the cathode spot.
Figure 6 plots signals from the sensor for the same values of the discharge current when the ring electrode is a cathode. Unlike the previous case, the signal decreases twofold when the discharge current increases. These experiments show that one can reduce the heat load on the surface using a magnetic field. Such an impressive influence of the magnetic field on the supersonic flow pattern and thermal action cannot be explained in terms of the adopted physical model (including electric heating and action of the ponderomotive force) and suggests the presence of another mechanism. The physics of nearelectrode processes in a gas discharge and, in particular, the mechanism behind the motion of the cathode spot have been subjects of fundamental research [10–13] and touched upon in many publications. However, no generally accepted explanation of some properties of
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Fig. 8. Form of the discharge at time instants of (a) 0.1, (b) 0.2, (c) 0.6, and (d) 0.8 ms when the anode spot (upper row) and cathode spot (lower row) moves over the ring electrode.
the cathode spot, such as its reverse motion in a tangen tial magnetic field [10], has been proposed until now. To elucidate the role of nearelectrode processes influencing the dynamics of the gas discharge, we con ducted additional experiments using the model with the magnetic core using a HSFCPro (PCO AG, Kelheim, Germany) highspeed digital camera. The schematic of the setup is shown in Fig. 7. Highspeed digital camera 1, which has three record ing channels and makes it possible to get six 1280 × 1024pixel electronic images with a desired exposure time, is connected to PC 2. Test chamber 3 has obser vation window 4 and vacuum system 5 providing a desired pressure. Test model 6 was placed in the cham ber in such a way that photos were taken from the front end of its conical part. Since the gas discharge in the supersonic flow considered is pressed against the con ical surface by the shock wave (Fig. 3), the action of the flow on the model was simulated by covering its conical part by glass funnel 7 with an expansion angle equal to the apex angle of a cone outlined by the shock front in the supersonic flow about the model. The pressure in the test chamber was 20 kPa, which was roughly equal to the pressure in the shock layer in the supersonic flow. Naturally, such an approach does not exactly simulate conditions in the supersonic flow; however, it enabled us to reveal main factors governing the dynamics of a gas discharge in a magnetic field. Figure 8 shows the Schlieren images of the dis charge taken using the HSFCPro camera at various time instants (the exposure time is 10–6 s). The pat terns demonstrate that the discharge has a spiral form. In the lower images, the spiral is longer and more uni formly distributed over the conic surface than in the upper patterns. Note that the patterns in the lower row show several cathode spots.
From the sequence of the images, it can be noticed that, when the ring electrode is an anode (upper row), the discharge rotates clockwise according to the direc tion of the ponderomotive force. In the case when the cathode spot moves over the ring electrode (lower row), the discharge rotates counterclockwise, i.e., opposite to the direction of the ponderomotive force. It is remembered that, when the polarity of the ring electrode changes, the direction of the ponderomotive force remains unchanged because the directions of the discharge current and magnetic field change simulta neously. Thus, based on the data of the additional experi ments, we can argue that the dynamics of the gas dis charge in a solenoidal magnetic field is largely gov erned by the motion of the cathode spot over the sur face of the ring electrode. CONCLUSIONS Experiments with a supersonic flow about models equipped with an embedded electromagnetic device were carried out aimed at studying the influence of MHD effects on the gasdynamic flow pattern and thermal load on the model’s surface. From the exper imental data, the following conclusions can be drawn. (1) The dynamics of the gas discharge near the con ical part of the model is mainly governed by processes near the ring electrode, since the magnetic induction is maximal in this region of the flow. (2) The magnetic field strength appreciably influ ences the dynamics of the gas discharge. The velocity of discharge rotation about the model increases with increasing magnetic field induction. (3) It is found that the efficiency of MHD action on the gasdynamic pattern near the model depends on the TECHNICAL PHYSICS
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polarity of the ring electrode. When the ring electrode is a cathode, the influence of the gas discharge on the flow is much stronger. (4) If the ring electrode is a cathode, the dynamics of the gas discharge is governed not only by the pon deromotive force and ohmic heating but also by the motion of the cathode spot in the tangential magnetic field. In this case, the cathode spot moves over the electrode surface in the direction opposite to the action of the ponderomotive force. (5) The configuration when the ring electrode serves as a cathode seems to increase the efficiency of MHD action on the heat flux toward the surface. It is experimentally found that the thermal load on the model decreases when the discharge current and the magnetic induction rise. ACKNOWLEDGMENTS The work is supported by the European Office of Aerospace Research & Development (ISTC project no. 3475), program no. P049 at the Presidium of the Russian Academy of Sciences, and federal program “Scientific Brainpower and Pedagogical Staff of Inno vative Russia” (state contract no. 02.740.11.0201). REFERENCES 1. C. Glass, “NonContinuum Hypersonic Shock Inter actions on a Simulated Airbreathing Engine Cowl,” in Proceedings of the 36th AIAA Thermophysics Conference, Orlando, Florida, 2003; AIAAPap., No. 20033772 (2003). 2. J. S. Shang, Prog. Aerosp. Sci. 37, 1 (2001).
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3. J. Poggie and D. V. Gaitonde, Phys. Fluids 14, 1720 (2002). 4. V. A. Bityurin, V. Yu. Velikodny, A. I. Klimov, S. V. Leo nov, and V. G. Potebnya, in Proceedings of the 30th AIAA Plasmadynamics and Laser Conference, Norfolk, 1999; AIAA Pap., No. 993533. 5. Y. Golovachov, Y. Kurakin, A. Schmidt, and D. Van Wie, in Proceedings of the 41st Aerospace Science Meeting and Exhibition, Reno, 2003; AIAAPap., No. 2003171. 6. V. A. Sakharov, N. P. Mende, S. V. Bobashev, and D. M. Van Wie, Pis’ma Zh. Tekh. Fiz. 32 (14), 40 (2006) [Tech. Phys. Lett. 32, 621 (2006)]. 7. V. G. Maslennikov and V. A. Sakharov, Zh. Tekh. Fiz. 67 (11), 88 (1997) [Tech. Phys. 42, 1322 (1997)]. 8. N. P. Divin, A. V. Mitiakov, V. Y. Mitiakov, and S. Z. Sapozhnikov, “Universal Sensor for Measuring Shear Stress, Mass Flow or Velocity of a Fluid or Gas, for Determining a Number of Drops, or Detecting Drip or Leakage,” EP Patent No. 1223411 (July 17, 2002). 9. B. I. Reznikov, N. P. Mende, P. A. Popov, V. A. Sakha rov, and A. S. Shteinberg, Pis’ma Zh. Tekh. Fiz. 34 (15), 49 (2008) [Tech. Phys. Lett. 34, 656 (2008)]. 10. I. G. Kesaev, Cathode Processes in Electric Arcs (Nauka, Moscow, 1968) [in Russian]. 11. V. I. Rakhovskii, Physical Bases of Services of Electric Current in Vacuum (Nauka, Moscow, 1970) [in Rus sian]. 12. G. A. Mesyats, Ectons (Nauka, Yekaterinburg, 1993), Chap. 1 [in Russian]. 13. J. M. Lafferty, Vacuum Arcs: Theory and Application (Wiley, New York, 1980; Mir, Moscow, 1982). Translated by N. Mende
