Numerical Simulation of Plasma Flow in a Self-field MPD Thruster Coupled with Electrode Sheath

Abstract

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 //

1D and quasi-2D numerical models of the cathode temperature in steady-state magnetoplasmadynamic thrusters

“…As a result, MPD thrusters can significantly reduce the mass of a spacecraft at launch. Thus, they are a primary candidate for unmanned and manned travel and cargo spacecraft on interplanetary missions [1][2][3][4]. MPD thrusters can typically be categorized as pulsed, steadystate, self-field, or applied-field.…”

“…The MPD thruster life is known to currently be limited by cathode erosion, which can occur owing to the interaction between the cathode and the plasma region inside the thrusters, especially the plasma sheath. That is, heat transfer in the plasma sheath region can be in either direction depending on the operating characteristics [2][3][4]. Hence, many numerical models have been developed to predict the cathode temperature profile in an MPD thruster before its malfunction [1,2,4,6].…”

“…That is, heat transfer in the plasma sheath region can be in either direction depending on the operating characteristics [2][3][4]. Hence, many numerical models have been developed to predict the cathode temperature profile in an MPD thruster before its malfunction [1,2,4,6]. Many experiments have shown that the steady-state temperature of an MPD thruster is about 3000-3500 K at the cathode tip and 500-1500 K at the cathode base depending on the experimental setup [1,2,4].…”

“…Hence, many numerical models have been developed to predict the cathode temperature profile in an MPD thruster before its malfunction [1,2,4,6]. Many experiments have shown that the steady-state temperature of an MPD thruster is about 3000-3500 K at the cathode tip and 500-1500 K at the cathode base depending on the experimental setup [1,2,4]. Some numerical models have been developed of the cathode in MPD thrusters that include the transient condition until the system reaches a steady-state condition, and they have confirmed that the cathode tip temperature is around 3000-3500 K [2][3][4].…”

“…Many experiments have shown that the steady-state temperature of an MPD thruster is about 3000-3500 K at the cathode tip and 500-1500 K at the cathode base depending on the experimental setup [1,2,4]. Some numerical models have been developed of the cathode in MPD thrusters that include the transient condition until the system reaches a steady-state condition, and they have confirmed that the cathode tip temperature is around 3000-3500 K [2][3][4]. The cathode voltage drop, which consumes a great deal of power, has similarly been shown in experiments and numerical models to have an approximate value of -6 to -9 V [2][3][4].…”