Plasma flows in a 100-kWe-class, steady-state, self-field magnetoplasmadynamic (MPD) thruster were simulated by a plasma flow solver coupled with an electrode sheath model, which enables us to evaluate electrode fall voltages quantitatively. In this paper, influences of the coupling with the electrode sheath model on discharge pattern are discussed as well as dependences of thruster performances on the propellant mass flow rate and the discharge current. By the coupling, it is shown that a thrust is not significantly affected while a discharge voltage is increased attributed to a cathode fall voltage comparable with a potential fall just in the bulk plasma. The thrust and discharge voltage evaluated with the electrode sheath roughly agree with existing experimental results. For an argon mass flow rate of 2.0 g/s and a discharge current of 8 kA, the average cathode fall voltage was estimated to be 7.1 V, which is comparable with the average bulk fall voltage (7.1 V). Thus, it can be said that energy consumption within the cathode sheath is a significant loss factor of the MPD thruster.
NomenclatureB = magnetic flux density B = magnetic flux density vector D = diffusion coeffcient E = energy density, electric field e = elementary charge e = unit vector F EM = electromagnetic thrust Ī = unit tensor J d = discharge current j = current density j = current density vector k B 2 ṁ = propellant mass flow rate n = number density p = (static) pressure q = heat flux r = radius, radial coordinate s = distance from wall T = temperature t = time U = internal energy density, diffusion velocity U = diffusion velocity vector u = velocity vector V = voltage z = axial coordinate α = electrode coefficient β = Hall parameter Г = particle flux δE = energy relaxation from electron to heavy particle λ = thermal conductivity µ 0 = space permeability ρ = mass density σ = electrical conductivity τ = viscous stress tensor ϕ = work function Subscripts //