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


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.


Plasma actuators Glow discharge Supersonic flow COMSOL multiphysics 

List of symbols



Diffusivity (m2 s−1)


Energy diffusivity (m2 s−1)

\(\overrightarrow {E}\)

Electric field vector (V s−1)


Elementary charge (C)


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


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

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

Electrical force density vector (N m−3)


Unit tensor (1)


Stress tensor (Pa)


Rate coefficient of the reaction (m3 s−1)


Slip length (m)


Normal projection (1)


Electron density (m−3)


Electron energy density (V m−3)


ith Species number density (m−3)


Ions density (m−3)


Total neutral number density (m−3)


Total density (kg m−3)


Partial pressure of the ith species (Pa)


Total pressure (Pa)

\(\overrightarrow {q}\)

The heat flux (W m−2)


Temperature of the flow (K)


Time (s)


Electron temperature (V)


Tangential projection (1)


Tangential velocity (m s−1)


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

\(\overrightarrow {V}\)

Velocity (m s−1)


Electron source term (m−3 s−1)


Distance according to the x-coordinates (m)


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


Distance according to the y-coordinates (m)


The ith species electrical charge (1)



Shock angle (°)


Accommodation coefficient (1)

\(\Delta \varepsilon_{j}\)

Energy loss from reaction j (V)


Vacuum permittivity (F m−1)

\(\overline{\varepsilon }\)

Mean electron energy (V)


Electron flux density (m−2 s−1)

\(\varGamma_{\varepsilon }\)

Electron energy flux (V m−2 s−1)


Mean free path (m)


Viscosity (Pa s)


Electron mobility (m2 V−1 s−1)


Energy mobility (m2 V−1 s−1)


Density of the flow (kg m−3)


Thermal tangential jump (1)

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

Viscous stress tensor (Pa)


Tangential stress (Pa)



Electron energy distribution function


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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

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