ISSN 0018-151X, High Temperature, 2008, Vol. 46, No. 3, pp. 296–300. © Pleiades Publishing, Ltd., 2008. Original Russian Text © A.V. Budin, V.A. Kolikov, F.G. Rutberg, 2008, published in Teplofizika Vysokikh Temperatur, Vol. 46, No. 3, 2008, pp. 331–335.

PLASMA INVESTIGATIONS

The Efficiency of Conversion of Energy in an Electric-Discharge Light-Gas Accelerator of Bodies A. V. Budin, V. A. Kolikov, and F. G. Rutberg Institute of Electrophysics and Electric Power, Russian Academy of Sciences, St. Petersburg, 191186 Russia e-mail: [email protected] Received November 1, 2006

Abstract—The results are given of investigation of the processes of energy transfer in a power supply-projectile system, which occur under conditions of acceleration of bodies by an electric-discharge light-gas accelerator with a caliber of 31.5 mm, and of the effect of the initial parameters of the working gas and a number of other factors on the efficiency of energy conversion. It is found that the efficiency of electric-discharge lightgas accelerator with the velocity of launching bodies ranging from 1800 to 6000 m/s is 6 to 19%; in a number of experiments, the efficiency reaches 23%. PACS numbers: 52.50.Nr, 52.80.-s DOI: 10.1134/S0018151X08030024

INTRODUCTION Investigations in the field of high-velocity launching of bodies using electric-discharge light-gas accelerators have been under way for almost fifty years [1]. Starting from the middle of the XX century, papers appear in which electric-discharge light-gas accelerators (their structures and supplies) are described [1], as well as the experimental data obtained using these accelerators [2, 3]. It was stated in some of these papers that the results obtained for the launching velocity and for the efficiency of acceleration differ significantly (they are lower) from predicted values. This was largely associated with the contamination of working gas (hydrogen, helium) by electrode erosion products; as a result, interest in accelerators of this type as a means of attaining high velocities of launching bodies was somewhat lost, as was demonstrated by the long absence of relevant publications. However, significant changes occurred by 1980s– 1990s in the approaches to raising the operating efficiency of accelerators of this type [4–6]. This is primarily associated with the fact that the correlation was found between the efficiency of the process of acceleration of bodies and the initial density of working gas. It is the objective of this study to determine the conditions which are conducive to attaining the maximal efficiency of conversion of the power supply energy to kinetic energy of the projectile.

the efficiency of acceleration of bodies was investigated in an electric-discharge light-gas accelerator with a caliber of 31.5 mm (Fig. 1). The accelerator had a barrel length of 4 m and a discharge chamber volume of 0.65–1.6 dm3; the working gas was hydrogen at a pressure of up to 42 MPa, with the projectile mass of 12 to 300 g. The electric-discharge accelerator was supplied from a capacitive power supply using a capacitor battery with a voltage of 10 kV and energy capacity of 6 MJ. The battery was divided into six identical autonomous modules, each connected to load via respective trigatron-type air dischargers. The discharge circuit characteristics were as follows: resistance of 1.5 mOhm, inductance of 0.25 µH, and wave impedance Z = 1.5 mOhm. The maximal discharge current could be as high as 2 MA (short-circuit current), the rate of current rise was in the range from 109 to 3.2 × 1010 A/s, and the pulse duration could vary from 250 µs to 2 ms.

EXPERIMENTAL SETUP The effect of the initial parameters of gas, the discharge chamber volume, the velocity and mass of projectiles, the degree of expansion of working gas etc. on

η = Wk/We.

ENERGY CONVERSION IN ELECTRIC-DISCHARGE ACCELERATOR Referred to as the efficiency η of an electric-discharge accelerator utilizing a capacitive energy storage as the power supply will be the ratio of kinetic energy of projectile Wk to electric energy We stored in the power supply, The process of energy conversion in the power supply-accelerator system takes three stages. 296

THE EFFICIENCY OF CONVERSION OF ENERGY 16

1

12

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2

7

6

9

14

8

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4

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15

Fig. 1. The discharge chamber of an electric-discharge light-gas accelerator: (1) chamber housing, (2) banding, (3) gas bleed-in channel, (4) diaphragm, (5) projectile, (6) current lead, (7) sealing ring, (8) anode insert, (9) nut, (10) cathode, (11) anode, (12) nut, (13) insulator, (14) initiating wire, (15) barrel, (16) nut.

1. The conversion of energy We stored in the power supply to arc electric energy Wa. The efficiency of this stage is defined by the coefficient ηe = Wa/We. 2. The conversion of arc electric energy Wa to internal energy of working gas Wg. Its efficiency is characterized by the coefficient ηT equal to the ratio of increment of internal energy of working gas ∆Wg to arc electric energy Wa, ηT = ∆Wg/Wa. 3. The acceleration of projectile, in the process of which the internal energy of working gas Wg is converted to kinetic energy of projectile Wk. The efficiency of this process is characterized by the coefficient ηk = Wk/Wg. The accelerator efficiency may be determined as the product of these three coefficients, η = ηe × ηT × ηk. HIGH TEMPERATURE

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EXPERIMENTAL DATA The investigations resulted in obtaining the dependences of the coefficients of energy conversion on the initial parameters of working gas, the launching velocity and mass of bodies, the discharge chamber volume, and some other factors. The coefficient ηe is defined by the ratio of electric energy input to the arc Wa to electric energy We extracted from the power supply. The electric energy input to the arc Wa during time T is defined by the integral T

Wa =

∫ IU dt, a

0

where I is the arc current, and Ua is the voltage drop across the arc. In the case where the power supply is provided by a capacitor battery, We is determined by the formula

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η˝ 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

ηT 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 5

10

15

20

25

30

35

40 45 P0, MPa

Fig. 2. The coefficient of conversion of power supply energy to arc energy as a function of initial pressure of hydrogen P0.

( U init – U res ) -, W e = C ---------------------------2 2

2

where C is the capacity of the capacitor battery, Uinit is the initial voltage of the battery, and Ures is the residual voltage on the battery. Because the electric energy is released in the active component of arc resistance, the coefficient ηe may be further determined as ηe = 1 – Rc/(Rc + Ra), where Rc is the discharge circuit resistance, and Ra is the arc resistance. The investigation results demonstrate that the statistical mean value of process average resistance of pulsed arc burning in hydrogen at an initial pressure of ~40 MPa and current of ~1 MA is ~6 mOhm [7, 8]. The resistance of discharge circuit of capacitive storages of multimegajoule level of stored energy, designed for supplying arc loads, ranges from 0.1 mOhm (supply source of wind tunnel by McDonnell Douglas [8]) to 1.5 mOhm (resistance of discharge circuit of power supply employed in our investigations). The development of high-power capacitive supplies with a low resistance of discharge circuit is rather costly, because it requires a large amount of low-inductance high-current cable and other expensive materials. One of the main factors affecting the coefficient of conversion of battery energy to arc energy ηe is the initial pressure of working gas P0. One can see in Fig. 2 that ηe is a rising function of P0; in so doing, the average values of ηe in the range of initial hydrogen pressure from 5 to 42 MPa vary from 0.46 to 0.85, and its statistical mean value is ~0.7.

0

5

10

15

20

25

30

35

40 45 P0, MPa

Fig. 3. The coefficient of conversion of electric energy of the arc to internal energy of hydrogen as a function of initial pressure of hydrogen.

The coefficient ηT is determined as the ratio of increment of internal energy of working gas ∆Wg to energy input to the arc Wa; in so doing, ∆Wg may be estimated by the formula ∆Wg = [P(V – αmg) – P0V]/(k – 1), where P is the final gas pressure in the discharge chamber, V is the discharge chamber volume, mg is the mass of gas, P0 is the initial gas pressure, k is the adiabatic exponent, and α is covolume. The energy input to the arc Wa was determined by the oscillograms of current and voltage drop on the arc. The initial pressure of hydrogen P0 also affects the value of coefficient ηT. It follows from Fig. 3 that the average values of coefficient ηT at initial pressure of 20–42 MPa, which are typical of our experiments, amount to 0.7–0.9. Analysis of the experimental data revealed the increasing pattern of the dependence of the coefficient of conversion of electric energy of the arc to internal energy of hydrogen on the discharge chamber volume (Fig. 4). This may be explained by the increase in the mass of gas with increasing geometric dimensions of the chamber, which causes an increase in absorbed energy. The coefficient ηk is defined by the ratio of kinetic energy of projectile Wk = mv2/2, where m and v denote the mass and velocity of the body, to internal energy of gas Wg equal to the sum of initial internal energy of compressed gas Wg0 and its increment ∆Wg as a result of electric arc heating. The coefficient ηk depends on the velocity of launching bodies, on the mass of bodies, on the ratio of the mass HIGH TEMPERATURE

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THE EFFICIENCY OF CONVERSION OF ENERGY ηT 1.0

ηk 0.35

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0.25

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0.20 0.7 0.15 0.6

0.10

0.5 0.4 600

0.05 800

1000

0 1000

1200 1400 1600 Chamber volume, cm3

Fig. 4. The coefficient of conversion of electric energy of the arc to internal energy of hydrogen as a function of discharge chamber volume.

ηk 0.35

0.30

0.30

0.25

0.25

0.20

0.20

0.15

0.15

0.10

0.10

0.05

0.05 50

100

150

200

250

300

0

350 m, g

Fig. 6. The coefficient of conversion of internal energy of working gas to kinetic energy of projectiles as a function of their mass.

ηk 0.35

3000

4000

5000

6000

7000 v, m/s

Fig. 5. The coefficient of conversion of internal energy of working gas to kinetic energy of projectiles as a function of projectile velocity.

ηk 0.35

0

2000

1

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7

8

9 10 mp/mg

Fig. 7. The coefficient of conversion of internal energy of gas to kinetic energy of projectile as a function of the ratio of projectile mass mp to mass of gas mg.

Efficiency, % 25

1 0.30

20 2

0.25

15 0.20

3 10

0.15

5

0.10 0.05 2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0 ε

Fig. 8. The coefficient of conversion of internal energy of gas to kinetic energy of projectile as a function of degree of expansion of gas for different masses of projectiles: (1) 100–300 g, (2) 50–100 g, (3) 15–50 g. HIGH TEMPERATURE

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0 1000

2000

3000

4000

5000

6000 v, m/s

Fig. 9. The accelerator efficiency as a function of velocity of launching bodies.

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of projectile to the mass of working gas, and on the degree of expansion of working gas. The dependence of ηk on the launching velocity v is given in Fig. 5. This dependence is decreasing, with the average value of ηk in the range of velocities from 1800 to 6000 m/s varying from 0.25 to 0.08. In experiments with bodies of a mass of ~300 g, the value of ηk was 0.28–0.29. The dependence of ηk on the mass of projectiles is given in Fig. 6. The dependence is increasing and, with a mass in excess of 200 g, asymptotically approaches the value of 0.3. Figure 7 gives ηk as a function of the ratio of the mass of projectile mp to mass of working gas mg. The dependence is increasing and, with mp/mg > 7.0, asymptotically approaches the value of 0.32; in so doing, the average values of ηk vary from 0.1 to 0.32 in the range of variation of mp/mg from 0.21 to 8.9. Figure 8 gives ηk as a function of the degree of expansion of working gas ε = (Vch + Vb)/Vch, where Vch is the discharge chamber volume and Vb is the barrel volume, for different values of projectile mass mp. The experimentally obtained dependence of the accelerator efficiency η = ηe × ηT × ηk on the velocity of launching bodies is given in Fig. 9. The dependence is decreasing, with the statistical mean value of efficiency in the velocity range from 1800 to 6000 m/s ranging from 6 to 19%; in a number of experiments with superheavy projectiles, the efficiency reached 20– 23%. CONCLUSIONS The coefficients are determined of energy transfer from a capacitive power supply to the arc, from the arc to internal energy of working gas, and from internal energy of working gas to kinetic energy of projectiles, as well as their dependences on the initial pressure of working gas, velocity of bodies, discharge chamber volume, and a number of other parameters. The average efficiency of electric-discharge light-gas accelerator at velocities ranging from 1800 to 6000 m/s is 6 to 19%;

in a number of experiments, the efficiency reached 20– 23%. ACKNOWLEDGMENTS This study was supported by the Presidium of the Russian Academy of Sciences (Program P-09 on Investigation of Matter under Extreme Conditions), by the Russian Foundation for Basic Research (project nos. 05-02-16033 and 05-08-01125), and by the Russian Foundation of Agency for Science and Innovations (State Contract no. 02.445.11.7384). REFERENCES 1. Stollenwerk, E.J. and Perry, R.W., AGARDograph, 1959, no. 32, p. 200. 2. Lecont, K., High-Velocity Launching, in Fizika bystroprotekayushchikh protsessov (The Physics of Fast Processes), Moscow: Mir, 1971, vol. 2, p. 247 (Russ. transl.). 3. Clemens, P. and Kingeri, M., Development of Measurement Techniques for Hypersonic Ballistic Facilities, in Tekhnika giperzvukovykh issledovanii (Hypersonic Investigation Techniques), Moscow: Mir, 1964, p. 124. 4. Massey, D.W., Tidman, D.A., Goldstein, S., and Napier, P., Experiments with a 0.5 Megajoule Electric Gun System for Fairing Hypervelocity Projectiles from Plasma Cartridges, Final report GTD 86-1. GT Devices, Alexandria, VA, 1986. 5. Rutberg, Ph.G., Glukhov, A.M., Kolikov, V.A., and Levchenko, B.P., Electrical Light Gas Gun as an Effective Hypervelocity Launcher, 6th Int. Conf. on Megagauss Magnetic Field Generation and Related Topics, Albuquerque, 1992, p. 182. 6. Budin, A.V., Levchenko, B.P., Leont’ev, V.V. et al., Zh. Tekh. Fiz., 1994, vol. 64, no. 9, p. 86. 7. Budin, A.V., Kolikov, V.A., and Rutberg, Ph.G., IEEE Trans. Plasma Sci., 2006, vol. 34, no. 4, p. 1553. 8. Rothert, R. and Sivier, K., Hypersonic Impulse Wind Tunnel with Energy Store of 7 MJ, in Tekhnika giperzvukovykh issledovanii (Hypersonic Investigation Techniques), Moscow: Mir, 1964, p. 282.

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