Robert Rhodes

Multiplexed Laser Induced Fluorescence and Non-Equilibrium Processes in Arcjets.

Abstract : For the past five years there has been an ongoing experimental and analytical program at the University of Tennessee Space Institute (UTSI) to improve our understanding of arcjet physics. A computational model that assumed local thermodynamic equilibrium was first used to simulate arcjet thrusters operating on ammonia, hydrogen, and argon. The UTSI arcjet code was later extended to include a two temperature, finite rate kinetic model for hydrogen plasma. Recently, this code has been used to simulate a radiation-cooled arcjet (MARC thruster) experiment and a water-cooled arcjet (TT1 thruster) experiment performed at The Universitat Stuttgart Institut fur Raumfahrtsysteme. The results of these simulations are presented along with a review of UTSI arcjet computation code development. A two-beam multiplexed laser induced fluorescence (LIF) technique was developed at UTSI to provide detailed measurements of arcjet flows near the nozzle exit plane. Comparison of detailed flowfield measurements with predictions of the computation model were used to provide insight into the physical models used in the arcjet code. The method was first demonstrated using a small, 300 W, water-cooled arcjet operated with argon propellant. The method was then applied to a 1 kW arcjet operated with hydrogen and nitrogen propellant mixtures using the Balmer alpha line of hydrogen. Recently, the method has been extended to use an excited state line in nitrogen. The results of this most recent research are presented. (MM)

Modeling arcjet space thrusters

The UTSI arcjet model is used to compare the performance of a hydrogen and an ammonia arcjet in the same configuration and at the same electrical power. The predicted specific impulse is 50 percent higher for the hydrogen propellant. Numerical studies made of the effect of transport properties on the performance of a hydrogen arcjet indicate that diffusive transport is very significant even in the supersonic part of the flow, and that relatively small changes in transport properties can have a significant effect on performance. These studies also show that nonequilibrium recombination chemistry can have a large effect on the transport coefficients. This leads to the conclusion that finite rate chemical calculations are necessary if accurate arcjet performance is to be calculated.

Numerical modeling of an arcjet thruster

A numerical model of an arcjet thruster was developed and the results of calculations using this model are compared to the experimental data from a 30 kW arcjet using ammonia as a propellant. The model contains equations for the conservation of mass, radial, axial, and azimuthal momentum, energy, and the radial component of the magnetic field and provides a solution for three components of velocity, temperature, and the axial and radial current as a function of position in an axisymmetric flowfield. The model predicts 12 percent more specific impulse than the experiment when the mass flow and power input are constrained to the experimental values. A major conclusion of this study is that improved procedures for calculating transport properties are necessary if the accuracy of the model is to be improved.

Hyperbolic Algorithm for Coupled Plasma/Electromagnetic Fields Including Conduction and Displacement Currents

A numerical procedure that applies to both the magnetic diffusion and wave propagation regimes of a general plasma/electromagnetic system is presented. The method solves the full Maxwell equations, with or without displacement current, in combination with the Navier–Stokes equations. The combined system is placed in a fully coupled conservation form and embedded in a dual-time formulation that enables classical hyperbolic solution algorithms to be effective across the wave and diffusion limits of the Maxwell equations. The dual-time formulation introducesapseudotimewithanartificialspeedoflightthatincludesdivergenceconstraintsthataredriventozeroby means of a Lagrange multiplier technique. The validity of the algorithm is first established by verifying results obtained with the hyperbolic procedure for the diffusion form of the telegraph equation against analytical solutions. Additional verification for the electromagnetic equations is obtained by comparison with magnetic diffusion simulationsobtainedfromtheMACH2code.Representative numericalcalculationsarepresentedforboththewave and magnetic diffusion limits to illustrate the importance of a solution technique that handles all regimes, from insulators to conductors.

Analysis of Magnetohydrodynamic Generator Power Generation

The three-dimensional current and fluid flow characteristics of diagonally connected magnetohydrodynamics generators are studied by means of numerical solutions. The formulation solves the Navier-Stokes equations in conjunction with the magnetic diffusion equation and a two-equation turbulence model on a hybrid unstructured grid. The current is obtained from Amperes law, and a generalized Ohms law is used to include the Hall effect. A flux-split upwind discretization is used for the convective terms along with a nonconservative correction that drives the divergence of the magnetic field to zero. Physical difficulties with boundary conditions are removed by extending the computational domain into the far field to encompass the plasma channel, the conducting and dielectric walls, and the surrounding air. The fluid flow and magnetic field solvers can be updated in loosely or closely coupled fashion depending on the magnetic Reynolds number. Results are shown for supersonic flow generators with both constant and diverging area channels. Properties are based on equilibrium table lookup for combustion gas products with potassium seedant.

Numerical modeling of a radio frequency plasma in argon

An axisymmetric, two-dimensional mathematical model of a radio frequency gas heater is described and compared with experimental data. The model includes mass, axial momentum, radial momentum, and energy conservation equations along with Maxwells equation for the circumferential component of the electric vector potential. Buoyancy along the heater axis and radial Lorentz forces are included in the momentum equations. Ohmic heating and radiation losses are included in the energy equation. The radiation loss terms are divided into an optically thin component that leaves the gas directly and an optically thick component that is modeled as a conduction term. Results from the model agree reasonably well with data obtained from a laboratory-sca le gas heater using a bluff body to stabilize the plasma. Calculated results at increased mass flow and pressure are shown to indicate the models capability in designing larger scale heaters. Nomenclature

Computational Simulations of Power Extraction in MHD Channel

A detailed computational analysis of the flow in, and power extraction from, a combustion-driven, MHD channel is described. The geometrical configuration considered is taken from a companion experiment involving a combustor discharging into a convergingdiverging nozzle that, in turn, feeds an MHD channel. A mixture of jet fuel and aluminum slurry was burned with gaseous oxygen to provide a high-temperature working fluid. Electrical conductivity was provided by seeding the propellants with potassium carbonate powder. The C-D nozzle was designed to deliver a nominally uniform Mach 2 flow to the MHD channel. The computations started from the burned gases at the entrance to the C-D nozzle, and included a full 3-D analysis of both fluids and electromagnetics. In the MHD power extraction tests, an external magnetic field is applied and the two ends of the Hall channel are connected electrically by means of a load resistor. The resulting MHD power generation is then measured experimentally and the detailed electromagnetic and fluid dynamic conditions are predicted computationally as a validation case for the combined fluids/electromagnetic simulation. Overall, the prediction appears to provide reasonable agreement with the measurements while simultaneously providing local details of both magnetic and fluid dynamic phenomena that are beyond the resolution capability of available instrumentation.

Numerical simulation of cableguns using MACH2

A radiation-driven ablation model was developed for the MHD code MACH2 to provide a numerical simulation for cableguns. Ablation from the insulator surface is driven by radiation from an optically thin gray gas in the computational domain adjacent to the insulator surface. Two parameters required for the model-specific opacity and vapor layer transmissivity-were determined from baseline experiments. Using these parameter values, numerical simulations for five additional cablegun configurations were compared with experimental measurements obtained using a two-beam laser interferometer. Equations of state models for copper-Teflon and polyethylene plasmas were calculated for use in these simulations. Comparisons were made for radial profiles of electron density, plume velocity, and plume width. Based on the results obtained in this study, it appears that MACH2 simulations can be used to provide reasonable estimates of cablegun plume properties that are difficult or impossible to obtain experimentally, such as the spatial flow details inside the cavity or the temporal distribution of mass loss.

A Hyperbolic Algorithm for Numerical Solutions of Coupled Plasma/EM Fields Including Both Real and Displacement Currents

A numerical procedure that applies to both the magnetic diffusion (MHD) and wave propagation regimes of a general plasma/electromagnetic system is presented. The method solves the full Maxwell equations, with or without displacement current, in combination with the Navier-Stokes equations. The combined system is placed in fully coupled conservation form and embedded in a dual-time formulation that enables classical hyperbolic solution algorithms to be effective across the wave and diffusion limits of the Maxwell equations. The validity of the algorithm is first established by verifying results obtained with the hyperbolic procedure for the diffusion form of the telegraph equation against analytical solutions. Additional verification for the electromagnetic equations is obtained by comparing with MHD simulations obtained from the MACH2 code. Representative numerical calculations are presented for both the wave and MHD limits to illustrate the importance of a solution technique that handles all regimes from insulators to conductors. The transient operation of a representative, pulsed plasma thruster that contains regions of high density plasma in close proximity with vacuum is presented as a practical application of the method.

Experimental and computer simulation studies of a pulsed plasma accelerator

Summary form only given. The present abstract describes an on-going effort to provide detailed experimental diagnostics and advanced computational simulations of the behavior and performance of high power plasma thrusters for possible applications in nuclear electric propulsion systems. Electromagnetic acceleration of plasmas for propulsion has long been seen as a means to efficient high specific impulse systems. Our approach is to evaluate simulations results from advanced computational codes with data collected from a laboratory prototype thruster that is designed for accurate diagnostics. The thruster is a coaxial electrode design that discharges plasma through a section of vacuum chamber with flat quartz windows that are used for optical diagnostics. High speed photography has documented successful firing of the thruster, a heterodyne laser interferometer has been used to obtain line-of-site electron number densities near the thruster exit, and Rogowski coils have been utilized to monitor thruster current. Tests with an array of B-dot probes positioned to help characterize the thruster current sheet have commenced. The supporting simulations are being obtained from two computer codes, MACH2 and GEMS. MACH2 is a well-established MHD code based upon the ALE formulation. It has been applied to diverse problems, and its capabilities are well recognized. For the present problem, however, it has several limitations: it is a 2-D code; its grid capabilities are limited to quadrilaterals; and its architecture does not lend itself to parallel computation. Of primary importance in the present application is MACH2s restriction to the MHD approximation, disallowing magnetic field propagation by wave processes. Therefore, we are extending the electromagnetics capability of the three-dimensional general equations mesh solver (GEMS) code that has been previously used to simulate a steady-state MHD generator to provide a time accurate simulation capability that incorporates modern computational methods. This extension has focused on identifying methods for solving coupled electromagnetic/fluid dynamic problems in regions where the MHD approximation fails. We have developed a solution algorithm that does not depend upon the MHD approximation, but solves the complete Maxwell equations at resource levels that appear to be similar to those associated with the magnetic induction equation. Comparisons between results from the present tests and those obtained from MACH2 and GEMS are expected to be available for ICOPS