Digitare l'equazione qui. • Chemical species • Chemical reactions + − ↔ + + − + − + − ↔ ∗ + − ∗ + − ↔ + + − + − + ↔ + + − + − + ↔ ∗ + − ∗ + ↔ + + − + − A selfconsistent unstructured solver for weakly ionized gases R. Pepe 1 , G. Colonna 2 , A. Bonfiglioli 1 , A. D’Angola 1 , R. Paciorri 3 1 Scuola di Ingegneria SI, Università degli Studi della Basilicata, via dell’Ateneo Lucano 10 - 85100, Potenza, Italy 2 Istituto di Metodologie Inorganiche dei Plasmi, CNR, via Amendola 122/D – 70126, Bari, Italy 3 Dipartimento di Meccanica e Aeronautica, Università di Roma La Sapienza, via Eudossiana 18 – 00184, Roma, Italy • Conservation equations Multispecies inviscid flow with finite rate chemistry are considered. The contribution of the magnetic field is neglected and a simple model for the internal ohmic source is considered [2] . + ∙ = (1.1) + ∙ + = (1.2) + ∙ [( + )] = ∙ (1.3) • Laplace equation The electric field ( = − ) is computed solving the Laplace equation for the electrical potential. 2 =0 (2) • Ohm law The current density is computed using the Ohm law. For an argon mixture , the electrical conductivity is computed using the semi-analytic model of Chapman and Cowling [3-4] . = E (3) • Circuit Ohm law: The electric field is generated by two electrodes connected in series to a power supply by an external circuit with a resistence [5] . = ( ) − ( ) (4) The electric current flowing in the circuit is computed integrating the current density on the electrodes surface. = ∫ ∙ (5) A selfconsistent unstructured solver for weakly ionized gases modeling inviscid multi-species conservation equations coupled with a reduced state-to-state kinetics model is presented. Mathematical model have been implemented in EulFS [1] , a CFD unstructured solver using Residual Distribution Schemes, to discretize convective fluxes and chemical source terms. A simple model which couples the weakly ionized gas with an electric field controlled by considering a power supply and an external circuit resistence Rc is considered. Preliminary results will be shown for an argon plasma considering a 2D geometrical configuration. References: [1] Bonfiglioli Int. J. Comput. Fluid Dyn. vol. 14, pp. 21-39, 2000. [2] Giordano. AIAA Paper 2002-2165, 2002) [3] Bisiek, Boyd and Poggie AIAA Paper 2010-4487, 2010. [4]Cambel Plasma Physics and Magnetofluid-Mechanics, McGraw–Hill, New York, 1963. [5] Colonna and Capitelli J. Thermophys Heat Transfer. vol. 22, pp. 414-423, 2008. [6] Bacri and Gomes J. Appl. Phys. vol. 11, pp. 2185-2197, 1978. [7] Vlcek J. Appl. Phys. vol. 22, pp. 623-631, 1989. Abstract Governing equations Chemical model [5-7] Preliminary results • Unstructured mesh: The computational domain is tessellated into triangles (2D) or tetrahedra (3D). • Fluctuation splitting approach: Numerical schemes used is 2° order accurate in space. • Dual time stepping: Unsteady calculations are achieved using a dual time stepping scheme, which is 2° order accurate in time. • Coupling between the fluid code and Laplace solver: At each time step, the boundary conditions for the Laplace equation are updated according to the circuit Ohm law. The electric conductivity depends upon the flow conditions. Numerical method Electron-atom Atom-atom Neutral atoms (ground) ∗ Neutral atoms (metastable 3 P2) + Positive ions − Electrons Neumann Dirichlet ( = + V dis ) Dirichlet (= ) Electric potential = 2 Circuit parameters 4000 V 1000 Ω Initial flow conditions 3000 K 0.1bar u 102 m/s Boundary conditions (Laplace equation) Norm of the Electric field Electric current ( ) Discharge potential ( ) Density ( ≠) Flow speed ( ) ( ≠) Temperature ( = ) Temperature ( ≠)