Trevor Moeller

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)

A strong conservative Riemann solver for the solution of the coupled Maxwell and Navier-Stokes equations

The coupled system of the Navier-Stokes and Maxwell equations are recast into a strong conservative form, which allows the fluid coupling to the Maxwell system to be written in terms of flux divergence rather than explicit source terms. This effectively removes source terms from the Navier-Stokes equations, although retaining an exact coupling to the electromagnetics. While this relieves the stiff source terms and potentially stabilizes the system, it introduces a much more complicated eigenstructure to the governing equations. The flux Jacobian and eigenvectors for this strong conservative system are presented in the current paper for the first time. An approximate Riemann solver based upon these eigenvectors is then introduced and tested. The solver is implemented in a preconditioned, dual-time implicit form. Validations for classic one- and two-dimensional problems are presented, and the performances of the new formulation and the traditional source-coupled formulation are compared.

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.

A Maxwell formulation for the equations of a plasma

In light of the analogy between the structure of electrodynamics and fluid dynamics, the fluid equations of motion may be reformulated as a set of Maxwell equations. This analogy has been explored in the literature for incompressible turbulent flow and compressible flow but has not been widely explored in relation to plasmas. This letter introduces the analogous fluid Maxwell equations and formulates a set of Maxwell equations for a plasma in terms of the species canonical vorticity and its cross product with the species velocity. The form of the source terms is presented and the magnetohydrodynamic (MHD) limit restores the typical variety of MHD waves.

Classical field isomorphisms in two-fluid plasmas

Previous work recognized a new framework for the equations of a multifluid plasma, wherein each species can be described by a set of equations remarkably similar to the Maxwell equations of classical electrodynamics. This paper extends the previous effort to form an exact isomorphism between the multifluid theory and classical electrodynamics. The major benefits of the new formulation are that the explicit coupling between different species is minimized, and theorems and techniques of classical electrodynamics can be immediately applied to the new multifluid formulation. We introduce the exact isomorphism and investigate some of the immediate consequences from classical electrodynamics. To provide a visualization of the isomorphism, previous 1D and 2D numerical simulations are postprocessed and presented to illustrate the generalized fields and source terms.

Advected Upstream Splitting Method for the Coupled Maxwell and Navier–Stokes Equations

A solution procedure for the fully coupled Navier–Stokes and Maxwell equations is described. The approach implements a conservative fluid formulation in which the Lorentz body force and Ohmic heating terms are recast as convective terms. This removes explicit sources from the fluid equations, which have previously introduced severe stiffness and demanded a very delicate numerical treatment. The coupling with the full Maxwell equations enables displacement current effects, charge separation effects, low-conductivity plasma behavior, and electromagnetic wave propagation to be incorporated directly. To circumvent the issue of complicated eigenvectors, an AUSM-type flux splitting scheme is proposed. Validation of the approach is presented for problems of electromagnetic wave propagation in low-conductivity plasma and high-conductivity magnetohydrodynamic problems, which demonstrates a robust, unified hyperbolic method for resolving both the wave and diffusion limits of the electromagnetic behavior in the plasma.

A Strong Conservative Implicit Riemann Solver for Coupled Navier-Stokes and Full Maxwell Equations

The effects of electromagnetic wave propagation, charge separation and higher-frequency effects can play a significant role in a plasma. Although the magnetohydrodynamic (MHD) model is the incumbent approach for describing plasmas of engineering interest, this model is incapable of resolving these features. In this paper, we introduce a split-flux Roe scheme approach for solving the single-fluid plasma model that retains the full Maxwell equations. This model is capable of resolving the missing effects. The approach is implemented in a multidimensional implicit dualtime solver and is validated against one- and two-dimensional problems of magnetohydrodynamics and electromagnetic wave propagation.

A discontinuous wave-in-cell numerical scheme for hyperbolic conservation laws

A new Riemann solver scheme for hyperbolic systems is introduced. The method consists of a discretization of the initial data into an approximate representation by discrete, discontinuous waves. Instead of calculating an intercell flux based on these waves, the discontinuous waves are propagated directly. Since the sum total of all discontinuous waves represents an extension of the linear Riemann problem, the solution is determined straightforwardly. For nonlinear systems, each timestep is considered a separate linear Riemann problem, and the projected waves are weighted to a background grid. This method is strikingly similar to the particle-in-cell approach, except that discontinuous waves are pushed around instead of macroparticles. The method is applied to Maxwells equations and the equations of inviscid gasdynamics. For linear systems, exact solutions can be achieved without dissipation, and exact transmissive boundary condition treatments are trivial to implement. For inviscid gasdynamics, the nonlinear method tended to resolve discontinuities more sharply than the Roe, HLL or HLLC methods while requiring only between 30% and 50% of the execution time under identical conditions. The approach is also extremely robust, as it works for any Courant number. In the limit that the Courant number becomes infinite, the nonlinear solution approaches the linearized solution.

A Strong Conservation Formulation for Finite Volume Plasma Simulations with Displacement and Conduction Current

A solution procedure for the Navier-Stokes equations coupled with the full Maxwell equations is described. The approach implements a strongly conservative fluid formulation in which the Lorentz force and Ohmic heating terms are recast as convective terms. This removes explicit sources from the Navier-Stokes equations, which have previously introduced severe sti ness and demanded a very delicate numerical treatment. The coupling with the full Maxwell equations enables the displacement current to be incorporated directly. To demonstrate the e ectiveness of this technique, a fully explicit finite volume approximate Riemann solver is used to obtain numerical solutions to the Brio and Wu electromagnetic shock problem. Comparisons with the analytical solution show good agreement, and the implementation requires less than an hour of computational time on a single processor machine. Simulations using large and small conductivities confirm that the formulation captures both wave and di usion limits of the magnetic field.

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.