Shock Waves

, Volume 29, Issue 3, pp 415–426 | Cite as

Theoretical investigation of supersonic flow control by nonthermal DC discharge

  • F. SohbatzadehEmail author
  • M. Mehdipoor
  • S. Mirzanejhad
Original Article


This work describes a theoretical study on shock wave modification by the electrical discharge generated with a DC voltage. Weakly ionized and high-density assumptions for nonthermal plasma were examined to demonstrate heat and momentum transfer contributions in supersonic flow control. The momentum equation for the plasma electrons and ions was considered to evaluate the changes in the incident flow velocity by the plasma. The change in the incident flow temperature was studied by applying source terms arising from a weakly ionized and high-density plasma to the energy equation. It was concluded that the momentum transfer from a nonthermal plasma into the incoming supersonic flow was responsible for the increasing shock wave angle. On the other hand, a nonthermal plasma with a remarkably high ionization degree increases the incident flow temperature drastically, while a weakly ionized plasma has a negligible effect on flow temperature. Our numerical results show that the electric field distribution has a significant role in the plasma flow control mechanisms, suggesting a new tailoring parameter via cathode geometry. The results of this work are in good agreement with respective experimental validation data and can be used in plasma-based shock wave control apparatus.


Nonthermal plasma DC discharge Shock waves Flow control 



  1. 1.
    Raj, P., Mirandat, L.R., Seebass, A.R.: A cost-effective method for shock-free supercritical wing design. J. Aircr. 19(4), 283–289 (1982). CrossRefGoogle Scholar
  2. 2.
    Bur, R., Corbel, B., Délery, J.: Study of passive control in a transonic shock wave/boundary-layer interaction. AIAA J. 36(3), 394–400 (1998). CrossRefGoogle Scholar
  3. 3.
    Reneaux, J., Coustols, E.: Wave drug reduction technologies. Presented at the ONERA DLR Aerospace Symposium, Paris (1999)Google Scholar
  4. 4.
    Dufour, G., Rogier, F.: Numerical modeling of dielectric barrier discharge based plasma actuators for flow control: the COPAIER/CEDRE example. Aerosp. Lab J. 10, 1–13 (2015). Google Scholar
  5. 5.
    Chedevergne, F., Casalis, G., Léon, O., Forte, M., Laurendeau, F., Szulga, N., Vermeersch, O., Piot, E.: Applications of dielectric barrier discharges and plasma synthetic jet actuators at ONERA. Aerosp. Lab J. 10, 1–10 (2015). Google Scholar
  6. 6.
    Fomin, V.M., Tretyakov, P.K., Taran, J.P.: Flow control using various plasma and aerodynamic approaches (short review). Aerosp. Sci. Technol. 8(5), 411–421 (2004). CrossRefGoogle Scholar
  7. 7.
    Bletzinger, P., Ganguly, B.N., Van Wie, D., Garscadden, A.: Plasmas in high speed aerodynamics. J. Phys. D: Appl. Phys. 38(4), R33 (2005). CrossRefGoogle Scholar
  8. 8.
    Moreau, E.: Airflow control by non-thermal plasma actuators. J. Phys. D: Appl. Phys. 40(3), 605 (2007). CrossRefGoogle Scholar
  9. 9.
    Leonov, S.B.: Review of plasma-based methods for high-speed flow control. AIP Conf. Proc. 1376, 498–502 (2011). CrossRefGoogle Scholar
  10. 10.
    Wang, L., Luo, Z.B., Xia, Z.X., Liu, B., Deng, X.: Review of actuators for high speed active flow control. Sci. China Technol. Sci. 55(8), 2225–2240 (2012). CrossRefGoogle Scholar
  11. 11.
    Mishin, G., Mishin, G.: Experimental investigation of the flight of a sphere in weakly ionized air. In: 15th Applied Aerodynamics Conference, AIAA Paper 1997-2298 (1997).
  12. 12.
    Mishin, G.I., Serov, YuL, Yavor, I.P.: Flow around a sphere moving supersonically in a gas discharge plasma. Sov. Tech. Phys. Lett. 17, 413–416 (1991)Google Scholar
  13. 13.
    Wang, J., Li, Y., Xing, F.: Investigation on oblique shock wave control by arc discharge plasma in supersonic airflow. J. Appl. Phys. 106(7), 073307 (2009). CrossRefGoogle Scholar
  14. 14.
    Shneider, M.N.: Energy addition into hypersonic flow for drag reduction and steering. In: Atmospheric Pressure Weakly Ionized Plasmas for Energy Technologies, Flow Control and Materials Processing, 22–24 August 2011, Princeton (2011)Google Scholar
  15. 15.
    Satheesh, K., Jagadeesh, G.: Experimental investigations on the effect of energy deposition in hypersonic blunt body flow field. Shock Waves 18, 53–70 (2008). CrossRefGoogle Scholar
  16. 16.
    Cai, C., He, X.: Energy deposition/extraction effects on oblique shock waves over a wedge. AIAA J. 45(9), 2267–2272 (2007). CrossRefGoogle Scholar
  17. 17.
    Kulkarni, V., Hegde, G.M., Jagadeesh, G., Arunan, E., Reddy, K.P.J.: Aerodynamic drag reduction by heat addition into the shock layer for a large angle blunt cone in hypersonic flow. Phys. Fluids 20, 081703 (2008). CrossRefzbMATHGoogle Scholar
  18. 18.
    Yu, F.M., Lin, M.S.: Investigation of a planar shock on a body loaded with low temperature plasmas. Shock Waves 2, 1425–1430 (2009). CrossRefGoogle Scholar
  19. 19.
    Marconi, F.: An investigation of tailored upstream heating for sonic boom and drag reduction. AIAA Paper 1998-333 (1998).
  20. 20.
    Riggins, D., Nelson, H.F., Johnson, E.: Blunt-body wave drag reduction using focused energy deposition. AIAA J. 37(4), 460–467 (1999). CrossRefGoogle Scholar
  21. 21.
    Kremeyer, K., Sebastian, K.A., Shu, C.-W.: Computational study of shock mitigation and drag reduction by pulsed energy lines. AIAA J. 44(8), 1720–1731 (2006). CrossRefGoogle Scholar
  22. 22.
    Miles, R.B., Macheret, S.O., Martinelli, L., Murray, R., Shneider, M., Ionikh, Y.Z.: Plasma control of shock waves in aerodynamics and sonic boom mitigation. Proceedings of the 32nd AIAA Plasmadynamics and Lasers Conference, AIAA Paper 2001-3062 (2001).
  23. 23.
    Khorunzehenko, V., Roupassov, D., Starikovskii, A.: Hypersonic flow and shock wave structure control by low temperature nonequilibrium plasma of gas discharge. AIAA Paper 2002-3569 (2002).
  24. 24.
    Bœuf, J.P., Pitchford, L.C.: Electrohydrodynamic force and aerodynamic flow acceleration in surface dielectric barrier discharge. J. Appl. Phys. 97, 103307 (2005). CrossRefGoogle Scholar
  25. 25.
    Boeuf, J.P., Lagmich, Y., Unfer, T., Callegari, T., Pitchford, L.C.: Electrohydrodynamic force in dielectric barrier discharge plasma actuators. J. Phys. D: Appl. Phys. 40(3), 652–662 (2007). CrossRefGoogle Scholar
  26. 26.
    Unfer, T., Boeuf, J.P.: Modelling of a nanosecond surface discharge actuator. J. Phys. D: Appl. Phys. 42, 194017 (2009). CrossRefGoogle Scholar
  27. 27.
    Kuo, S.P., Kalkhoran, I.M., Bivolaru, D., Orlick, L.: Observation of shock wave elimination by a plasma in a Mach-2.5 flow. Phys. Plasmas 7(5), 1345–1348 (2000). CrossRefGoogle Scholar
  28. 28.
    Kuo, S.P., Bivolaru, D.: Plasma effect on shock waves in a supersonic flow. Phys. Plasmas 8(7), 3258 (2001). CrossRefGoogle Scholar
  29. 29.
    Kuo, S.P.: Conditions and a physical mechanism for plasma mitigation of shock wave in a supersonic flow. Phys. Scr. 70, 161–165 (2004). CrossRefGoogle Scholar
  30. 30.
    Kuo, S.P., Kuo, S.S.: A physical mechanism of nonthermal plasma effect on shock wave. Phys. Plasmas 12, 012315 (2005). CrossRefGoogle Scholar
  31. 31.
    Kuo, S.P.: Shock wave modification by a plasma spike: experiment and theory. Phys. Scr. 71, 535–539 (2005). CrossRefGoogle Scholar
  32. 32.
    Kuo, S.P.: Plasma mitigation of shock wave: experiments and theory. Shock Waves 17, 225–239 (2007). CrossRefGoogle Scholar
  33. 33.
    Shin, J., Clemens, N.T., Raja, L.L.: Schlieren imaging of flow actuation produced by direct-current surface glow discharge in supersonic flows. IEEE Trans. Plasma Sci. 36(4), 1316–1317 (2008). CrossRefGoogle Scholar
  34. 34.
    Raizer, Yu.P.: Gas Discharge Physics. Springer, Berlin (1991)Google Scholar
  35. 35.
    Surzhikov, S.T.: Computational Physics of Electric Discharges in Gas Flows, vol. 7. Walter de Gruyter, Berlin (2013)zbMATHGoogle Scholar
  36. 36.
    Anderson Jr., J.D.: Modern Compressible Flow. McGraw-Hill, New York (1990)Google Scholar
  37. 37.
    Burm, K.T.A.L., Goedheer, W.J., Schram, D.C.: The isentropic exponent in plasmas. Phys. Plasmas 6(6), 2622–2627 (1999). CrossRefGoogle Scholar
  38. 38.
    Moisan, M., Pelletier, J.: Physics of Collisional Plasmas. Springer, Berlin (2006). Google Scholar
  39. 39.
    Menier, E., Leger, L., Depussay, E., Lago, V., Artana, G.: Effect of a DC discharge on the supersonic rarefied air flow over a flat plate. J. Phys. D: Appl. Phys. 40, 695–701 (2007). CrossRefGoogle Scholar
  40. 40.
    Yano, R., Contini, V., Ploenjes, E., Palm, P., Merriman, S., Aihal, S., Adamovich, I., Lempert, W., Subramaniam, V., Rich, J.W.: Supersonic nonequilibrium plasma wind-tunnel measurements of shock modification and flow visualization. AIAA J. 38(10), 1879–1888 (2000). CrossRefGoogle Scholar
  41. 41.
    Merriman, S., Ploenjes, E., Palm, P., Adamovich, I.V.: Shock wave control by nonequilibrium plasmas in cold supersonic gas flows. AIAA J. 39(8), 1547–1552 (2001). CrossRefGoogle Scholar
  42. 42.
    Leonov, S., Bityurin, V., Savelkin, K., Yarantsev, D.: Effect of electrical discharge on separation processes and shocks position in supersonic airflow. In: 40th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA Paper 2002-355 (2002).

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Atomic and Molecular Physics Department, Faculty of Basic SciencesUniversity of MazandaranBabolsarIran
  2. 2.Department of Physics, Faculty of ScienceGonbad Kavous UniversityGonbad KavousIran

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