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.
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Abbreviations
- D e :
-
Diffusivity (m2 s−1)
- D ε :
-
Energy diffusivity (m2 s−1)
- \(\overrightarrow {E}\) :
-
Electric field vector (V s−1)
- e :
-
Elementary charge (C)
- R ε :
-
Energy loss from all reactions (V m−3 s−1)
- E t :
-
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)
- k j :
-
Rate coefficient of the reaction (m3 s−1)
- L s :
-
Slip length (m)
- n :
-
Normal projection (1)
- n e :
-
Electron density (m−3)
- n ε :
-
Electron energy density (V m−3)
- N i :
-
ith Species number density (m−3)
- n i :
-
Ions density (m−3)
- N n :
-
Total neutral number density (m−3)
- n t :
-
Total density (kg m−3)
- P i :
-
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)
- T e :
-
Electron temperature (V)
- t p :
-
Tangential projection (1)
- u :
-
Tangential velocity (m s−1)
- u w,t :
-
Tangential velocity near to the wall (m s−1)
- \(\overrightarrow {V}\) :
-
Velocity (m s−1)
- W e :
-
Electron source term (m−3 s−1)
- X :
-
Distance according to the x-coordinates (m)
- x j :
-
Mole fraction of the target species for reaction j (1)
- Y :
-
Distance according to the y-coordinates (m)
- Z i :
-
The ith species electrical charge (1)
- α :
-
Shock angle (°)
- α v :
-
Accommodation coefficient (1)
- \(\Delta \varepsilon_{j}\) :
-
Energy loss from reaction j (V)
- ε 0 :
-
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)
- μ e :
-
Electron mobility (m2 V−1 s−1)
- μ ε :
-
Energy mobility (m2 V−1 s−1)
- ρ :
-
Density of the flow (kg m−3)
- σ T :
-
Thermal tangential jump (1)
- \(\overline{\overline{\tau }}\) :
-
Viscous stress tensor (Pa)
- τ n,t :
-
Tangential stress (Pa)
- EEDF:
-
Electron energy distribution function
References
Corke T, Cavalieri D (1997) Controlled experiments on instabilities and transition to turbulence in supersonic boundary layers. In: 28th Fluid dynamics conference, p 1817
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
Moreau E (2007) Airflow control by non-thermal plasma actuators. J Phys D Appl Phys 40(3):605
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):10–17
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):113303
Bletzinger P, Ganguly B, Van Wie D, Garscadden A (2005) Plasmas in high speed aerodynamics. J Phys D Appl Phys 38(4):R33
Ganguly B, Bletzinger P, Garscadden A (1997) Shock wave damping and dispersion in nonequilibrium low pressure argon plasmas. Phys Lett A 230(3–4):218–222
Kuo S, Bivolaru D (2001) Plasma effect on shock waves in a supersonic flow. Phys Plasmas 8(7):3258–3264
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 TN
Mishin G (1997) Experimental investigation of the flight of a sphere in weakly ionized air. AIAA Paper 2298
Lapushkina TA, Erofeev AV, Ponyaev SA, Bobashev SV (2009) Supersonic flow of a nonequilibirum gas-discharge plasma around a body. Tech Phys 54(6):840–848
Gnemmi P, Charon R, Dupéroux JP, George A (2008) Feasibility study for steering a supersonic projectile by plasma actuator. AIAA J 46(6):1307–1317
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):465–537
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 21:106103
Parisse JD, Lago V (2013) Shock modification induced by a DC discharge: numerical and experimental study. Int J Aerodyn 3 (1/2/3)
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):271–278
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):102
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):075201
Bogdanov EA, Demidov VI, Kudryavtsev AA, Saifutdinov AI (2015) Is the negative glow plasma of a direct current glow discharge negatively charged? Phys Plasmas 22:024501
Aoki K, Takata S, Aikawa H, Golse F (2001) A rarefied gas flow caused by a discontinuous wall temperature. Phys Fluids 13(9):2645–2661
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):722
Bogaerts A, Gijbels R (1995) Modeling of metastable argon atoms in a direct-current glow discharge. Phys Rev A 52(5):3743
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):033502
COMSOL Multiphysics documentation. Plasma module users guide
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 1146–1153
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):2081–2100
Mahadevan S, Raja LL (2012) Simulation of direct-current surface plasma discharges in air for supersonic flow control. AIAA J 50(2):325–337
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Hamdoun, S., Liani, B., Oumeziane, A.A. et al. DC Discharge Electronic Non-equilibrium Effects Investigations on a M = 2 Rarefied Supersonic Flow Over a Flat Plate. Plasma Chem Plasma Process 38, 557–571 (2018). https://doi.org/10.1007/s11090-018-9887-1
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DOI: https://doi.org/10.1007/s11090-018-9887-1