Nikolaos A. Gatsonis

Triple Langmuir Probe Measurements in the Plume of a Pulsed Plasma Thruster

Anexperimentalapparatususingtriplelangmuirprobeswasdesignedtoobtainelectrontemperatureanddensity in theplume of a laboratory-model pulsed plasma thruster (PPT)operating at discharge energy levels of 5, 20, and 40 J. Electron temperature and density were obtained on two planes parallel and perpendicular to the thruster electrodes passing through the thruster’ s centerline. Measurements were obtained for radial distances of 6, 10, 12, 14,16,18,and20cmandforpolaranglesof10,20,30,and45degwithrespectto thecenteroftheTee on ® propellant face.Plumepropertiesshowlargeangularvariationontheperpendiculartotheelectrodesplanebutsmallvariation on the parallel plane cone rming the asymmetry of the PPT plume. Electron density and temperature decrease with increasing radial distance from the Tee on surface. The average maximum temperature is between 2 and 4 eV for all discharge energy levels considered. The average maximum electron density is 1 6 £ 10 20 , 1 6 £ 10 21 , and 1 8 £ 10 21 m i 3 for the 5-, 20-, and 40-J discharge. The time-average electron density increases with increasing discharge energy and is in the range between 10 19 and 2 £ 10 20 m i 3 for 5 J, 3 £ 10 19 and 10 21 m i 3 for 20 J, and 5 £ 10 19 and 1 4 £ 10 21 m i 3 for 40 J. Nomenclature An = area of probe n 1;2;3 ds = probe sheath thickness e

Experimental Investigations and Numerical Modeling of Pulsed Plasma Thruster Plumes

Integration of pulsed plasma thruster (PPT) onboard spacecraft requires the evaluation of potential plume/spacecraft interactions. Important e ndings are summarized of our experimental and modeling plume investigations of rectangular-geometry Tee on ® PPTs. Initial studies of the Lincoln Experimental Satellite 8 /9 PPT plume used time-of-e ight analysis of single langmuir probe data and found two ion populations with approximately 30 and 60 km /s, respectively. A residual gas analyzer identie ed C, F, C xFy, and various thruster materials. Fast ionization gauges detected the presence of slow neutral particles up to 1 ms after the end of the discharge. Subsequent studies used triple langmuir probes and obtained electron temperature and density in the plume of a laboratory PPT operating at 5, 20, and 40 J. Plume properties showed large angular density variation on the perpendicular to the electrodes plane but small variation on the parallel plane. Electron density and temperature were found to decrease with increasing radial distance from the Tee on surface. Time-average temperatures were between 1 and 3 eV. Time-averageelectron density increased with increasing dischargeenergy and are in therange between 10 19 and 2 ££ 10 20 m i 3 for 5 J, 6 ££ 10 20 to 10 21 m i 3 for 20 J, and 2 ££ 10 20 to 1.4 ££ 10 21 m i 3 for 40 J. The PPT plume model is based on a hybrid (particle‐e uid) methodology. Neutrals and ions were modeled with a combination of the direct simulation Monte Carlo and a hybrid-particle-in-cell method. Electrons were modeled as a massless e uid with a momentum equation that includes collisional contributions from ions and neutrals and an energy equation. Simulations of the laboratory PPT operating at discharge energies of 5, 20, and 40 J showed the expansion of the neutral and ion components of the plume during a pulse, the generation of low-energy ions and high-energy neutrals dueto chargeexchange reactions, and the generation ofbacke ow. Numerical predictions showed good quantitative agreements with data.

Current-mode triple and quadruple Langmuir probe methods with applications to flowing pulsed plasmas

A current-mode method for triple and quadruple Langmuir probes was developed and implemented in flowing, pulsed, collisionless plasmas. The current-mode method involves biasing all probe electrodes, and requires the measurement of probe currents providing the electron temperature, the electron density, and the ratio of ion speed to most probable thermal speed. The current-mode theory is developed for a single species, two-temperature, collisionless plasma. The current collection model for a probe aligned with the flow and radius to Debye length ratios of 5/spl les/r/sub p///spl lambda//sub D//spl les/100 accounts for finite-sheath effects while for r/sub p///spl lambda//sub D/>100, current collection is based on the thin-sheath assumption. The ion current to the perpendicular probe assumes a thin-sheath and is given as a function of the ion speed ratio. The numerical procedure for the solution of the nonlinear current-mode equations, as well sensitivity and uncertainty analysis are presented. The plasma source used in the experiments is a laboratory Teflon pulsed plasma thruster, operating at discharge energies of 5, 20, and 40 J, with a pulse duration of 10-15 /spl mu/s, ablating 20-50 /spl mu/g/pulse. Current-mode triple and quadruple probe measurements obtained at various locations in the plume of the plasma source are presented. Extensive comparisons between double probe and current-mode probe measurements validate the new method.

Coupled Controls-Computational Fluids Approach for the Estimation of the Concentration From a Moving Gaseous Source in a 2-D Domain With a Lyapunov-Guided Sensing Aerial Vehicle

The estimation of the gas concentration (process state) associated with an emitting stationary or moving source using a sensing aerial vehicle (SAV) is considered. The dispersion from such a gas source into the ambient atmosphere is representative of accidental or deliberate release of chemicals, or release of gases from the biological systems. Estimation of the concentration field provides a superior ability for source localization, assessment of possible adverse impacts, and eventual containment. The abstract and finite-dimensional approximation framework present couples theoretical estimation and control with computational fluid dynamics methods. The gas dispersion (process) model is based on the 2-D advection-diffusion equation with variable eddy diffusivities and ambient winds. The state estimator is a modified Luenberger observer with a collocated filter gain that is parameterized by the position of the SAV. The process-state (concentration) estimator is based on a 2-D adaptive, multigrid, multistep finite-volume method. The grid is adapted with local refinement and coarsening during the process-state estimation, to improve accuracy and efficiency. The 2-D motion dynamics of the SAV is incorporated into the spatial process and the SAVs guidance is directly linked to the performance of the state estimator. The computational model and the state estimator are coupled in the sense that grid refinement is affected by the SAV repositioning, and the guidance laws of the SAV are affected by grid refinement. Extensive numerical simulations serve to demonstrate the effectiveness of the coupled approach.

Investigation of rarefied supersonic flows into rectangular nanochannels using a three-dimensional direct simulation Monte Carlo method

The rarefied flow of nitrogen with speed ratio (mean speed over most probable speed) of S=2,5,10, pressure of 10.132 kPa into rectangular nanochannels with height of 100, 500, and 1000 nm is investigated using a three-dimensional, unstructured, direct simulation Monte Carlo method. The parametric computational investigation considers rarefaction effects with Knudsen number Kn=0.481,0.962,4.81, geometric effects with nanochannel aspect ratios of (L/H) from AR=1,10,100, and back-pressure effects with imposed pressures from 0 to 200 kPa. The computational domain features a buffer region upstream of the inlet and the nanochannel walls are assumed to be diffusively reflecting at the free stream temperature of 273 K. The flow analysis is based on the phase space distributions while macroscopic flow variables sampled in cells along the centerline are used to corroborate the microscopic analysis. The phase-space distributions show the formation of a disturbance region ahead of the inlet due to slow particles back...

An unstructured direct simulation Monte Carlo methodology with Kinetic-Moment inflow and outflow boundary conditions

The mathematical and computational aspects of the direct simulation Monte Carlo on unstructured tetrahedral grids (U3DSMC) with a Kinetic-Moment (KM) boundary conditions method are presented. The algorithms for particle injection, particle loading, particle motion, and particle tracking are presented. The KM method applicable to a subsonic or supersonic inflow/outflow boundary, couples kinetic (particle) U3DSMC properties with fluid (moment) properties. The KM method obtains the number density, temperature and mean velocity needed to define the equilibrium, drifting Maxwellian distribution at a boundary. The moment component of KM is based on the local one dimensional inviscid (LODI) boundary conditions method consistent with the 5-moment compressible Euler equations. The kinetic component of KM is based on U3DSMC for interior properties and the equilibrium drifting Maxwellian at the boundary. The KM method is supplemented with a time-averaging procedure, allows for choices in sampling-cell procedures, minimizes fluctuations and accelerates the convergence in subsonic flows. Collision sampling in U3DSMC implements the no-time-counter method and includes elastic and inelastic collisions. The U3DSMC with KM boundary conditions is validated and verified extensively with simulations of subsonic nitrogen flows in a cylindrical tube with imposed inlet pressure and density and imposed outlet pressure. The simulations cover the regime from slip to free-molecular with inlet Knudsen numbers between 0.183 and 18.27 and resulting inlet Mach numbers between 0.037 and 0.027. The pressure and velocity profiles from U3DSMC-KM simulations are compared with analytical solutions obtained from first-order and second-order slip boundary conditions. Mass flow rates from U3DSMC-KM are compared with validated analytical solutions for the entire Knudsen number regime considered. Error and sensitivity analysis is performed and numerical fractional errors are in agreement with theoretical errors. The KM method is shown to be a robust technique allowing efficient computation of subsonic flows. Additional verification of U3DSMC is achieved with simulations of the heat transfer process in a stationary argon gas between two flat plates. The numerical heat flux is in agreement with analytical results that cover the transitional to free molecular regimes. Additional validation of U3DSMC is achieved with simulations of hypersonic rarefied flows of nitrogen over a finite thickness flat pate at 0 and 10 degrees angle of attack. Numerical predictions of the pressure and heat flux to the plate are in agreement with experiments.

Three-Dimensional Magnetohydrodynamic Modeling of Plasma Jets in the North Star Space Experiment

The Active Plasma Experiment (APEX) North Star mission involved the injection of two high-speed plasma jets. The first plasma jet with 30 x 10 - 3 kg of aluminum and kinetic energy of 6 MJ was injected at 360-km altitude nearly perpendicular to the ambient magnetic field. An air cloud was formed prior to the injection by releasing 12 x 10 - 3 kg of air. The jet, the air cloud, and the ambient constitute a partially ionized plasma modeled with a three-dimensional, single-fluid, unsteady, viscous, compressible magnetohydrodynamic formulation. The model equations are discretized with a finite volume implementation, and time integration is carried out with a multistep Runge-Kutta scheme. The simulation shows the deceleration of the jet, the induction of motion into the initially stationary ambient plasma and the formation of three-dimensional magntetohydrodynamic waves. The plasma density shows an enhancement over the ambient similar to Langmuir-probe measurements taken onboard the plasma diagnostics payload located approximately 468 m downstream the injection point. The simulation predicts the formation of a large diamagnetic cavity that almost excludes the ambient induction, in accordance with magnetometer measurements on the diagnostics payload. The numerical predictions of the components of the magnetic induction are also in good agreement with the measurements.

Unstructured 3D PIC simulations of the flow in a retarding potential analyzer

A three-dimensional particle in cell (PIC) code is developed on unstructured tetrahedral grids. Zero-order (Nearest Grid Point) and linear (volume) particle charge weighting and force interpolation schemes are incorporated. A parametric investigation of the numerical heating in unstructured 3D PIC simulations is presented. The PIC methodology is applied to the simulation of the flow inside the segmented microchannel of a directional-Retarding Potential Analyzer. Simulations show the flow characteristics of the ions and electrons and provide estimates of the collected current by the microplate.

UNSTRUCTURED 3D PIC SIMULATIONS OF FIELD EMISSION ARRAY CATHODES FOR MICROPROPULSION APPLICATIONS

A 3D particle in cell/direct simulation Monte Carlo (PIC/DSMC) code is developed using unstructured tetrahedral grids with adaptation. The grid generation methodology, adaptation, charged-particle transport, field solver and particle/force weighting methodologies are reviewed. The numerical code is used to simulate a field emission array cathode operating in an environment induced by a Hall thruster. The electron emission includes cold (0.1 eV) and hot (5 eV) electrons emitted in a 5-eV background plasma. The simulations show the formation of a virtual cathode under certain emission conditions that results in a limitation in the transmitted current through the sheath. The simulations show perturbations in the background electrons and beam/background coupling phenomena. The results are compared favorably with previous computations.

A smooth dissipative particle dynamics method for domains with arbitrary-geometry solid boundaries

A smooth dissipative particle dynamics method with dynamic virtual particle allocation (SDPD-DV) for modeling and simulation of mesoscopic fluids in wall-bounded domains is presented. The physical domain in SDPD-DV may contain external and internal solid boundaries of arbitrary geometries, periodic inlets and outlets, and the fluid region. The SDPD-DV method is realized with fluid particles, boundary particles, and dynamically allocated virtual particles. The internal or external solid boundaries of the domain can be of arbitrary geometry and are discretized with a surface grid. These boundaries are represented by boundary particles with assigned properties. The fluid domain is discretized with fluid particles of constant mass and variable volume. Conservative and dissipative force models due to virtual particles exerted on a fluid particle in the proximity of a solid boundary supplement the original SDPD formulation. The dynamic virtual particle allocation approach provides the density and the forces due to virtual particles. The integration of the SDPD equations is accomplished with a velocity-Verlet algorithm for the momentum and a Runge-Kutta for the entropy equation. The velocity integrator is supplemented by a bounce-forward algorithm in cases where the virtual particle force model is not able to prevent particle penetration. For the incompressible isothermal systems considered in this work, the pressure of a fluid particle is obtained by an artificial compressibility formulation for liquids and the ideal gas law for gases. The self-diffusion coefficient is obtained by an implementation of the generalized Einstein and the Green-Kubo relations. Field properties are obtained by sampling SDPD-DV outputs on a post-processing grid that allows harnessing the particle information on desired spatiotemporal scales. The SDPD-DV method is verified and validated with simulations in bounded and periodic domains that cover the hydrodynamic and mesoscopic regimes for isothermal systems. Verification of the SDPD-DV is achieved with simulations of transient, Poiseuille and Couette isothermal flow of liquid water between plates with heights of 10^-^5 m and 10^-^3 m. The velocity profiles from the SDPD-DV simulations are in very good agreement with analytical estimates and the field density fluctuation near solid boundaries is shown to be below 5%. Verification of SDPD-DV applied to domains with internal curved solid boundaries is accomplished with the simulation of a body-force driven, low-Reynolds number flow of water over a cylinder of radius R=0.02 m. The SDPD-DV field velocity and pressure compare favorably with those obtained by FLUENT. The results from these benchmark tests show that SDPD-DV is effective in reducing the density fluctuations near solid walls, enforces the no-slip condition, and prevents particle penetration. Scale-effects in SDPD-DV are examined with an extensive set of SDPD-DV isothermal simulations of liquid water and gaseous nitrogen in mesoscopic periodic domains. For the simulations of liquid water the mass of the fluid particles is varied between 1.24 and 3.3x10^7 real molecular masses and their corresponding size is between 1.08 and 323 physical length scales. For SDPD-DV simulations of gaseous nitrogen the mass of the fluid particles is varied between 6.37x10^3 and 6.37x10^6 real molecular masses and their corresponding size is between 2.2x10^2 and 2.2x10^3 physical length scales. The equilibrium states are obtained and show that the particle speeds scale inversely with particle mass (or size) and that the translational temperature is scale-free. The self-diffusion coefficient for liquid water is obtained through the mean-square displacement and the velocity auto-correlation methods for the range of fluid particle masses (or sizes) considered. Various analytical expressions for the self-diffusivity of the SDPD fluid are developed in analogy to the real fluid. The numerical results are in very good agreement with the SDPD-fluid analytical expressions. The numerical self-diffusivity is shown to be scale dependent. For fluid particles approaching asymptotically the mass of the real particle the self-diffusivity is shown to approach the experimental value. The Schmidt numbers obtained from the SDPD-DV simulations are within the range expected for liquid water.