Numerical Study of an Electron-Beam-Confined Faraday Accelerator

Abstract

The numerical solution of a magnetoplasmadynamics accelerator intended for supersonic airbreathing propulsion systems is presented. The numerical method solves the Favre-averaged Navier-Stokes equations closed by the Wilcox k! model, including the nitrogen vibrational energy and a finite rate chemical solver accounting for electron-beam ionization, electron attachment, and dissociative recombination. The fluid-flow equations are solved in conjunction with the electric-field-potential equation. Because of the recombination time of the electrons with the charged particles being in the order of microseconds, the interaction region is more or less confined to the area when e-beam ionization is applied. In this manner, a Faraday-type configuration can be obtained by using only one electrode pair. The impact of the length of the interaction region and the strength of the magnetic field on the efficiency are assessed. It is observed that the efficiency obtained numerically is as much as 40% less than the theoretical predictions for the highest magnetic field considered of 4 T. This is attributed to 1) the current concentration near the electrodes' edges causing a significant voltage drop and 2) unsteady behavior in the center of the channel due to the interaction between finite rate chemistry and electromagnetism. Nonetheless, an efficiency within 25% of the theoretical predictions can be obtained at high magnetic field by decreasing the width of the interaction region to one-tenth of its height. NomenclatureA = Avogadro's number, 6:02257 10 23 B = magnetic field vector b = constant function of and K C = charge, C C P = specific heat at constant pressure c = mass fraction E = electric field vector E = total energy e = charge of one electron, 1:60207 10 19 C e = internal energy e v = nitrogen vibrational energy e 0 v = nitrogen vibrational energy at equilibrium h = enthalpy j = current vector K = work interaction parameter, E y =v x B z k = turbulence kinetic energy L = length of the interaction region M = Mach number M = molecular weight m = atom or molecule mass N = number density P = pressure P k = turbulence kinetic energy production term Pr = Prandtl number q = flow speed q b = energy deposited to the flow from the electron beams R = gas constant Sc = Schmidt number St = Stuart number, eff B 2 L=q s = sign of a species ( 1 for negative ions and electrons and 1 for positive ions) T = temperature v = velocity vector W = chemical source term X = matrix needed to compute the effective conductivity = ratio of the specific heats ij = Kronecker delta = efficiency v = nitrogen characteristic vibration temperature = thermal conductivity e = electron thermal diffusion = viscosity, mobility = mass diffusion coefficient = ratio between the Joule heating and the work = density = electrical conductivitỹ = tensor conductivity eff = effective electrical conductivity taking into account ion slip k = user-defined constant for the Wilcox k! model ! = user-defined constant for the Wilcox k! model vt = vibration-translation relaxation t...

Generalized Ohm’s law and potential equation in computational weakly-ionized plasmadynamics

“…While not necessarily a common occurrence in weakly-ionized flowfields, such a high Hall parameter combined with a strong conductivity gradient has been observed in Faraday generators and accelerators using e-beam-ionized airflow as the working fluid (see Ref. [11] for instance).…”

“…The EHD interaction (or ion wind) is suspected to be one of the mechanisms responsible for the high success of plasma actuators in preventing or delaying boundary layer separation [3], in enhancing jet mixing [4], in keeping the flow attached on turbine blades [5], or in controlling the vortices above a delta wing [6]. On the other hand, the MHD interaction could be useful in controlling the inlet flowfield [7,8], in suppressing boundary-layer separation [9], in imparting momentum to a gas [10,11], or in generating electrical power aboard a flight vehicle through a MHD generator [12,13].…”

“…doi:10.1016/j.jcp.2010. 11.012 A computational study of plasmas generally requires the coupled solution of the Navier-Stokes equations to obtain the bulk flow properties and of the Maxwell equations to obtain the electric and magnetic field distributions. However, when a plasma is weakly-ionized (that is, when the fraction of the gas molecules that are ionized are in the range 10 À8 -10 À4 ) and when the applied magnetic field does not vary in time, it can be shown that the sole solution of the electric field potential provides a reasonable approximation to the electromagnetic fields.…”

Electron Losses in Hypersonic Flows

“…The physical model consists of the Navier-Stokes equations for the neutral species and the drift-diffusion model for the charged species. The vibrational temperature of nitrogen and the electron temperature are obtained through separate transport equations as outlined in [28,14]. The gas is assumed thermally perfect but calorically non-perfect with the enthalpies for each species determined from the NASA Glenn high-temperature polynomials [29].…”

Sheath governing equations in computational weakly-ionized plasmadynamics

“…Such a low conductivity near the cathode results in a large voltage drop for a desired current, and this in turn leads to a large amount of power dissipated within the sheath in form of heat. Because of this, accurately modeling sheaths is generally deemed essential to assess adequately the performance of plasma-based devices such as MHD generators and accelerators [1,2], or plasma actuators [3][4][5].…”