# Calculations for a cylindrical electric arc with allowance for energy transfer by radiation with the hydrogen at a pressure of 100 atm

## Abstract

An approximate method is described for the consideration of energy transfer by radiation during the utilization of real properties of a gas (in particular, the frequency-dependent absorption coefficient under conditions of local thermal equilibrium). With increasing pressure, it becomes necessary to take self-absorption into account over almost the entire frequency spectrum.

Calculations are carried out for a wall-stabilized cylindrical electric arc in hydrogen as an example for a pressure of 100 atm and channel radii of 0.3, 1, and 3 cm at values of current strength up to the order of 10 A. The strong effect of radiation on the current-voltage characteristic of the arc, the gas temperature, and the nature of its distribution over the arc radius is demonstrated.

The process of energy transfer by radiation plays a significant and sometimes predominant role in the thermal balance of electric arcs with high current strengths [1–9]. Calculations have been performed for cylindrical arcs in atmospheres of argon and hydrogen [5, 7] with allowance for energy transfer by radiation and for atmospheric pressure in which case the gas is essentially transparent to radiation. Approximate estimates were obtained for the self-absorbed portion of the radiation.

The role played by radiation increases with increasing current strength, arc radius, and pressure, while self-absorption in this process extends over an increasingly large region of the spectrum. Hence, calculations must be carried out for the arc if conditions are such that the gas in the arc does not transmit radiation.

In [10–13], an approximate method was developed for taking into account energy transfer by radiation in the presence of intense selfabsorption as applied to heat transfer problems under conditions of local thermal equilibrium with allowance for the variation of the absorption coefficient as a function of the frequency. The conditions for local thermal equilibrium in an arc passing through an argon or hydrogen atmosphere are fulfilled for pressures greater than atmospheric pressure and for current strengths greater than ∼10 A [14–16], The results of [10–12] were used as the foundation for calculations based on an electric arc in argon at atmospheric pressure, under which conditions, self-absorption affects only the transitions to the ground state. The part played by radiation in the heat transfer process is smaller than the part played in the energy transfer by conduction. Calculations confirmed the results of [5, 7].

The role of energy transfer by radiation in the energy balance of the arc increases with increasing pressure, while in turn, the role of the continuous spectrum increases for the radiation. The results of calculations performed for a wall-stabilized arc burning in an atmosphere of hydrogen at a pressure of 100 atm are given in the present paper. In this case, almost the entire energy supply is lost by radiation. The approximate method of accounting for energy transfer by radiation is demonstrated by an example.

## Keywords

Heat Transfer Energy Transfer Approximate Method Heat Transfer Process Current Strength## Notation

- ρ and T
gas density and temperature, respectively

- u
velocity

- c
_{p} heat capacity of the gas at constant pressure

- χ
coefficient of thermal conductivity

- σ
coefficient of electrical conductivity

- x and r
cylindrical coordinates

- r
_{0} channel radius

- I
current strength

- E
electric field strength

*u*_{ν}°equilibrium value of radiation energy density

*u*_{ν}value of radiation energy density

- ν
radiation frequency

- ϕ
divergence of energy flux density transported by radiation

- k
_{ν} absorption coefficient

- c
speed of light

- ɛ
_{i} emissivity of the i-th region of the spectrum

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## References

- 1.H. W. Emmons and R. I. Land, “Poiseuille plasma experiment,” Phys. Fluids, vol. 5, no. 12, pp. 1489–1500, 1962.Google Scholar
- 2.G. Schmitz and H. T. Patt, “Die Bestimmung von Material funktionen, eines Stickstoffplasma bei Atmospharendruck bis 15 000° K.” Zs. Fhys., vol. 171, no. 4. pp. 449, 1963.Google Scholar
- 3.E. I. Asinovskii and A. V. Kirillin, “Experimental determination of the thermal-conductivity coefficient of an argon plasma,” Teplofizika vysokikh temperatur, vol. 3, no. 5, pp. 677–685, 1965.Google Scholar
- 4.Yu. R. Knyazev, R. V. Mitin, V. I. Petrenko, and E. S. Borovik, “Emission of a high-pressure argon arc,” ZhTF, vol. 34, no. 7. pp. 1224–1230, 1964.Google Scholar
- 5.V. N. Vetlutskii, A. T. Onufriev, and V. G. Sevast'yanenko, “Calculations for a cylindrical electric arc with allowance for energy transport by radiation,” collection: Low-Temperature Plasma, Proceedings of International Symposium on the Properties and Applications of Low-Temperature Plasma at the 20-th International Congress on Theoretical and Applied Chemistry, Moscow, June 15–17, 1965, [in Russian], Mir, pp. 395–407, 1967.Google Scholar
- 6.N. N. Ogurtsovat and I, V. Podmoshenskii, “Capillary discharge as a plasma source for quantitative analysis,” collection: Low-Temperature Plasma [in Russian], Mir, pp. 432–441, 1967.Google Scholar
- 7.V. N. Vetlutskii, A. T. Onufriev, and V. G. Sevast'yanenko, “Calculations for a wall-stabilized argon arc with account for radiative energy transfer,” PMTF [Journal of Applied Mechanics and Technical Physics], no. 4, pp. 71, 1965.Google Scholar
- 8.E. A. Romishevskii, “Boundary layers and stabilized gas discharge for diffuse radiation,” Inzh. Zh., vol. 2, no. 1, pp. 170–174, 1962.Google Scholar
- 9.Yu. R. Knyazev, E. S. Borovik, R. V. Mitin, and V. I. Petrenko, “Pulsed high-pressure arc in helium and hydrogen,” ZhTF, vol. 37, no. 3, pp. 528–532, 1967.Google Scholar
- 10.A. T. Onufriev and V. G. Sevast'yanenko, “Radiative transfer in spectral lines with self-absorption,” PMTF [Journal of Applied Mechanics and Technical Physics], no. 2, pp. 122, 1966.Google Scholar
- 11.A. T. Onufriev and V. G. Sevast'yanenko, “Calculations for energy transport by radiation in spectral lines,” PMTF [Journal of Applied Mechanics and Technical Physics], no. 1, pp. 125, 1967.Google Scholar
- 12.A. T. Onufriev and V. G. Sevast'yanenko, “The influence of radiation energy transport accounting for self-absorption on the heat transfer process for an electric arc in turbulent argon flow.” Proceed 3-rd International Heat Transfer Conference, Chicago, Illinois, 1966, vol. 5; American Institute Chemical Engrs., N. Y., 1966.Google Scholar
- 13.I. S. Voronina, V. P. Zamuraev, and V. G. Sevast'yanenko, “Calculations for energy transport by radiation in the continuous spectrum with allowance for the changes in the absorption coefficient with respect to frequency in the presence of self-absorption,” PMTF [Journal of Applied Mechanics and Technical Physics], no. 1, 1968.Google Scholar
- 14.V. N. Kolesnikov, “Arc discharge in inert gases,” Tr. FIAN, vol. 30, pp. 66–158, 1964.Google Scholar
- 15.A. N. Lagar'kov, “Conditions for the applicability of local thermodynamic equilibrium,” Teplofizika vysokikh temperatur, vol. 4, no. 3, pp. 305, 1966.Google Scholar
- 16.V. S. Vorob'ev, “Influence of self-absorption of radiation on the deviation from thermodynamic equilibrium,” Teplofizika vysokikh temperatur, vol. 4, no. 4, pp. 494, 1966.Google Scholar
- 17.G. I. Marchuk, Methods of Calculations for Nuclear Reactors [in Russian], Gosatomizdat, Moscow, 1961.Google Scholar
- 18.L. M. Biberman and G. E. Norman, “Continuous spectra of atomic gases and plasmas,” Usp. fiz. n., vol. 91, no. 2, pp. 193, 1967.Google Scholar
- 19.I. I. Sobel'man, Introduction to the Theory of Atomic Spectra [in Russian], Fizmatgiz, Moscow, 1963.Google Scholar