Plasma Chemistry and Plasma Processing

, Volume 38, Issue 3, pp 557–571 | Cite as

DC Discharge Electronic Non-equilibrium Effects Investigations on a M = 2 Rarefied Supersonic Flow Over a Flat Plate

  • Sabrina Hamdoun
  • Bachir Liani
  • Amina Ait Oumeziane
  • Jean-Denis Parisse
Original Paper
  • 24 Downloads

Abstract

This work aims at studying the effects of a low-pressure Argon discharge (P = 0.5 Torr) on a supersonic Argon flow (M = 2) around a flat plate. The observed phenomena during high speed-flow control with a plasma discharge are exhaustively described. The present investigation is of great interest not only to aviation but also to numerous other areas like the wind power industry. The computations have been carried out using the DC discharge and the High Mach Number Flow Comsol Multiphysics modules. To simulate the DC discharge, chemical reactions near the cathode region along with their corresponding Townsend coefficients need to be defined. The latter are calculated using the Bolsig + computer code. The other reactions cross sections are imported from the LXCAT data base. The imported data are used to calculate the reactions rates. The plasma discharge effects on the rarefied supersonic flow are described using a 2D hydrodynamical model under the Drift–Diffusion approximation. The hydrodynamical model was validated by comparing its results for a supersonic air flow with experiments. The main results on an Argon supersonic flow coupled to an Argon discharge show an increase in the pitot pressure and the shock angle.

Keywords

Plasma actuators Glow discharge Supersonic flow COMSOL multiphysics 

List of symbols

Roman

De

Diffusivity (m2 s−1)

Dε

Energy diffusivity (m2 s−1)

\(\overrightarrow {E}\)

Electric field vector (V s−1)

e

Elementary charge (C)

Rε

Energy loss from all reactions (V m−3 s−1)

Et

Total energy per unit of volume (J m−3)

\(\overrightarrow {{f_{e} }}\)

Electrical force density vector (N m−3)

\(\overline{\overline{I}}\)

Unit tensor (1)

K

Stress tensor (Pa)

kj

Rate coefficient of the reaction (m3 s−1)

Ls

Slip length (m)

n

Normal projection (1)

ne

Electron density (m−3)

nε

Electron energy density (V m−3)

Ni

ith Species number density (m−3)

ni

Ions density (m−3)

Nn

Total neutral number density (m−3)

nt

Total density (kg m−3)

Pi

Partial pressure of the ith species (Pa)

P

Total pressure (Pa)

\(\overrightarrow {q}\)

The heat flux (W m−2)

T

Temperature of the flow (K)

t

Time (s)

Te

Electron temperature (V)

tp

Tangential projection (1)

u

Tangential velocity (m s−1)

uw,t

Tangential velocity near to the wall (m s−1)

\(\overrightarrow {V}\)

Velocity (m s−1)

We

Electron source term (m−3 s−1)

X

Distance according to the x-coordinates (m)

xj

Mole fraction of the target species for reaction j (1)

Y

Distance according to the y-coordinates (m)

Zi

The ith species electrical charge (1)

Greek

α

Shock angle (°)

αv

Accommodation coefficient (1)

\(\Delta \varepsilon_{j}\)

Energy loss from reaction j (V)

ε0

Vacuum permittivity (F m−1)

\(\overline{\varepsilon }\)

Mean electron energy (V)

\(\varGamma_{e}\)

Electron flux density (m−2 s−1)

\(\varGamma_{\varepsilon }\)

Electron energy flux (V m−2 s−1)

λ

Mean free path (m)

μ

Viscosity (Pa s)

μe

Electron mobility (m2 V−1 s−1)

με

Energy mobility (m2 V−1 s−1)

ρ

Density of the flow (kg m−3)

σT

Thermal tangential jump (1)

\(\overline{\overline{\tau }}\)

Viscous stress tensor (Pa)

τn,t

Tangential stress (Pa)

Abbreviations

EEDF

Electron energy distribution function

References

  1. 1.
    Corke T, Cavalieri D (1997) Controlled experiments on instabilities and transition to turbulence in supersonic boundary layers. In: 28th Fluid dynamics conference, p 1817Google Scholar
  2. 2.
    Merriman S, Ploenjes E, Palm P, Adamovich IV (2001) Shock control by nonequilibrium plasmas in cold supersonic gas flows. AIAA J 39(8):1547–1552.  https://doi.org/10.2514/2.1479 CrossRefGoogle Scholar
  3. 3.
    Moreau E (2007) Airflow control by non-thermal plasma actuators. J Phys D Appl Phys 40(3):605CrossRefGoogle Scholar
  4. 4.
    Ganiev YC, Gordeev V, Krasilnikov A, Lagutin V, Otmennikov V, Panasenko A (2000) Aerodynamic drag reduction by plasma and hot-gas injection. J Thermophys Heat Transf 14(1):10–17CrossRefGoogle Scholar
  5. 5.
    Bletzinger P, Ganguly B, Garscadden A (2005) Influence of dielectric barrier discharges on low Mach number shock waves at low to medium pressures. J Appl Phys 97(11):113303CrossRefGoogle Scholar
  6. 6.
    Bletzinger P, Ganguly B, Van Wie D, Garscadden A (2005) Plasmas in high speed aerodynamics. J Phys D Appl Phys 38(4):R33CrossRefGoogle Scholar
  7. 7.
    Ganguly B, Bletzinger P, Garscadden A (1997) Shock wave damping and dispersion in nonequilibrium low pressure argon plasmas. Phys Lett A 230(3–4):218–222CrossRefGoogle Scholar
  8. 8.
    Kuo S, Bivolaru D (2001) Plasma effect on shock waves in a supersonic flow. Phys Plasmas 8(7):3258–3264CrossRefGoogle Scholar
  9. 9.
    Lowry H, Stepanek C, Crosswy L, Sherrouse P, Smith M (1999) Shock structure of a spherical projectile in weakly ionized air. Arnold Engineering Development Center Arnold AFS TNGoogle Scholar
  10. 10.
    Mishin G (1997) Experimental investigation of the flight of a sphere in weakly ionized air. AIAA Paper 2298Google Scholar
  11. 11.
    Lapushkina TA, Erofeev AV, Ponyaev SA, Bobashev SV (2009) Supersonic flow of a nonequilibirum gas-discharge plasma around a body. Tech Phys 54(6):840–848CrossRefGoogle Scholar
  12. 12.
    Gnemmi P, Charon R, Dupéroux JP, George A (2008) Feasibility study for steering a supersonic projectile by plasma actuator. AIAA J 46(6):1307–1317CrossRefGoogle Scholar
  13. 13.
    Palm P, Meyer R, Plonjes E, Rich JW, Adamovich IV (2003) Nonequilibrium radio frequency discharge plasma effect on conical shock wave: M = 2.5 flow. AIAA J 41(3):465–537CrossRefGoogle Scholar
  14. 14.
    Parisse JD, Léger L, Depussay E, Lago V, Burtshell Y (2009) Comparison between Mach 2 rarefied airflow modification by an electrical discharge and numerical simulation of airflow modification by a surface heating. Phys Fluids 21:106103CrossRefGoogle Scholar
  15. 15.
    Parisse JD, Lago V (2013) Shock modification induced by a DC discharge: numerical and experimental study. Int J Aerodyn 3 (1/2/3)Google Scholar
  16. 16.
    Parisse JD, Kudryavtsev AN, Lago V (2015) Mach 2 rarefied airflow over a plate submitted to a DC discharge: surface temperature gradient investigation. Int J Eng Syst Model Simul 7(4):271–278Google Scholar
  17. 17.
    Joussot R, Lago V, Parisse JD (2015) Quantification of the effect of surface heating on shock wave modification by a plasma actuator in a low-density supersonic flow over a flat plate. Exp Fluids 56(5):102CrossRefGoogle Scholar
  18. 18.
    Liu X, He W, Yang F, Wang H, Liao R, Xiao H (2012) Numerical simulation and experimental validation of a direct current air corona discharge under atmospheric pressure. Chin Phys B 21(7):075201CrossRefGoogle Scholar
  19. 19.
    Bogdanov EA, Demidov VI, Kudryavtsev AA, Saifutdinov AI (2015) Is the negative glow plasma of a direct current glow discharge negatively charged? Phys Plasmas 22:024501CrossRefGoogle Scholar
  20. 20.
    Aoki K, Takata S, Aikawa H, Golse F (2001) A rarefied gas flow caused by a discontinuous wall temperature. Phys Fluids 13(9):2645–2661CrossRefGoogle Scholar
  21. 21.
    Hagelaar G, Pitchford L (2005) Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models. Plasma Sources Sci Technol 14(4):722CrossRefGoogle Scholar
  22. 22.
    Bogaerts A, Gijbels R (1995) Modeling of metastable argon atoms in a direct-current glow discharge. Phys Rev A 52(5):3743CrossRefGoogle Scholar
  23. 23.
    Rafatov I, Bogdanov E, Kudryavtsev A (2012) On the accuracy and reliability of different fluid models of the direct current glow discharge. Phys Plasmas 19(3):033502CrossRefGoogle Scholar
  24. 24.
    COMSOL Multiphysics documentation. Plasma module users guideGoogle Scholar
  25. 25.
    Joussot R, Lago V, Parisse JD (2014) Efficiency of plasma actuator ionization in shock wave modification in a rarefied supersonic flow over a flat plate. In: Proceedings of the 29th international symposium on rarefied gas dynamics, AIP Conference Proceedings, vol 1628, pp 1146–1153Google Scholar
  26. 26.
    Coumar S, Joussot R, Parisse JD, Lago V (2016) Influence of a plasma actuator on aerodynamic forces over a flat plate interacting with a rarefied Mach 2 flow. Int J Numer Meth Heat Fluid Flow 26(7):2081–2100CrossRefGoogle Scholar
  27. 27.
    Mahadevan S, Raja LL (2012) Simulation of direct-current surface plasma discharges in air for supersonic flow control. AIAA J 50(2):325–337CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Sabrina Hamdoun
    • 1
  • Bachir Liani
    • 1
  • Amina Ait Oumeziane
    • 2
  • Jean-Denis Parisse
    • 3
  1. 1.Laboratoire de Physique ThéoriqueAbou Beker Belkaid UniversityTlemcenAlgeria
  2. 2.IUSTI, UMR CNRS 7343Aix-Marseille UniversityMarseilleFrance
  3. 3.French Air Force School Salon de ProvenceSalon-de-ProvenceFrance

Personalised recommendations