John R. Torczynski

The Gaseous Electronics Conference radio‐frequency reference cell: A defined parallel‐plate radio‐frequency system for experimental and theoretical studies of plasma‐processing discharges

A “reference cell” for generating radio-frequency (rf) glow discharges in gases at a frequency of 13.56 MHz is described. The reference cell provides an experimental platform for comparing plasma measurements carried out in a common reactor geometry by different experimental groups, thereby enhancing the transfer of knowledge and insight gained in rf discharge studies. The results of performing ostensibly identical measurements on six of these cells in five different laboratories are analyzed and discussed. Measurements were made of plasma voltage and current characteristics for discharges in pure argon at specified values of applied voltages, gas pressures, and gas flow rates. Data are presented on relevant electrical quantities derived from Fourier analysis of the voltage and current wave forms. Amplitudes, phase shifts, self-bias voltages, and power dissipation were measured. Each of the cells was characterized in terms of its measured internal reactive components. Comparing results from different cells provides an indication of the degree of precision needed to define the electrical configuration and operating parameters in order to achieve identical performance at various laboratories. The results show, for example, that the external circuit, including the reactive components of the rf power source, can significantly influence the discharge. Results obtained in reference cells with identical rf power sources demonstrate that considerable progress has been made in developing a phenomenological understanding of the conditions needed to obtain reproducible discharge conditions in independent reference cells.

Gamma-densitometry tomography of gas holdup spatial distribution in industrial-scale bubble columns

Gamma-densitometry tomography (GDT) experiments have been performed to measure gas holdup spatial variations in two bubble columns: a 0.19 m inside diameter Lucite column and a 0.48 m inside diameter stainless steel vessel. Two-phase air/water flows were examined. Horizontal scans at one vertical position in each column were made for several air flow rates. An axisymmetric tomographic reconstruction algorithm based on the Abel transform has been used to calculate the time-averaged gas holdup radial variation. Integration of these profiles over the column cross section has yielded area-averaged holdup results, which have been compared with volume-averaged gas holdups determined from differential pressure measurements and from the rise in the air/water interface during gas flow. The results agree reasonably well.

Validation of Electrical-Impedance Tomography for Measurements of Material Distribution in Two-Phase Flows

A series of studies is presented in which an electrical-impedance tomography (EXT) system is validated for two-phase flow measurements. The EIT system, developed at Sandia National Laboratories, is described along with the computer algorithm used for reconstructing phase volume fraction profiles. The algorithm is first tested using numerical data and experimental phantom measurements, with good results. The EIT system is then applied to solid-liquid and gas-liquid flows, and results are compared to an established gamma-densitometry tomography (GDT) system. In the solid-liquid flows, the average solid volume fractions measured by EIT are in good agreement with nominal values; in the gas-liquid flows, average gas volume fractions and radial gas volume fraction profiles from GDT and EIT are also in good agreement.

An improved Reynolds-equation model for gas damping of microbeam motion

An improved gas-damping model for the out-of-plane motion of a near-substrate microbeam is developed based on the Reynolds equation (RE). A boundary condition for the RE is developed that relates the pressure at the beam edge to the beam motion. The coefficients in this boundary condition are determined from Navier-Stokes slip-jump (NSSJ) simulations for small slip lengths (relative to the gap height) and from direct simulation Monte Carlo (DSMC) molecular gas dynamics simulations for larger slip lengths. This boundary condition significantly improves the accuracy of the RE when the microbeam width is only slightly greater than the gap height between the microbeam and the substrate. The improved RE model is applied to microbeams fabricated using the SUMMiT V process.

Accuracy and efficiency of the sophisticated direct simulation Monte Carlo algorithm for simulating noncontinuum gas flows

The accuracy of a recently proposed direct simulation Monte Carlo (DSMC) algorithm, termed “sophisticated DSMC,” is investigated by comparing simulation results to analytical solutions of the Boltzmann equation for one-dimensional Fourier–Couette flow. An argon-like hard-sphere gas at 273.15 K and 266.644 Pa is confined between two parallel, fully accommodating walls 1 mm apart that have unequal temperatures and unequal tangential velocities. The simulations are performed using a one-dimensional implementation. In harmony with previous work, the accuracy metrics studied are the ratios of the DSMC-calculated transport properties and Sonine polynomial coefficients to their corresponding infinite-approximation Chapman–Enskog theoretical values. The sophisticated DSMC algorithm is shown to reproduce the theoretical results to high precision. The efficiency of the sophisticated DSMC algorithm relative to the original algorithm is demonstrated for a two-dimensional “real-world” application.

An approach for simulating the transport of spherical particles in a rarefied gas flow via the direct simulation Monte Carlo method

An approach is presented for computing the force on and heat transfer to a spherical particle from a rarefied flow of a monatomic gas that is computed using the direct simulation Monte Carlo (DSMC) method. The particle concentration is taken to be dilute, and the gas flow around the particle (but not necessarily throughout the flow domain) is taken to be free-molecular. Green’s functions for the force and heat transfer are determined analytically, are verified by demonstrating that they yield certain well-known results, and are implemented numerically within a DSMC code. Simulations are performed for the case of gas confined between two parallel plates at different temperatures for broad ranges of pressures and particle velocities. The simulation results agree closely with analytical results, where applicable. A simple approximate expression relating the thermophoretic force to the gas-phase heat flux is developed, and the drag and thermophoretic forces are found to be almost decoupled for a wide range of...

Direct simulation Monte Carlo convergence behavior of the hard-sphere-gas thermal conductivity for Fourier heat flow

The convergence behavior of the direct simulation Monte Carlo (DSMC) method is systematically investigated for near-continuum, one-dimensional Fourier flow. An argon-like, hard-sphere gas is confined between two parallel, fully accommodating, motionless walls of unequal temperature. The simulations are performed using four variations based on Bird’s DSMC algorithm that differ in the ordering of the move, collide, and sample operations. The primary convergence metric studied is the ratio of the DSMC-calculated bulk thermal conductivity to the infinite-approximation Chapman-Enskog (CE) theoretical value, although temperature and heat flux are also considered. Ensemble, temporal, and spatial averaging are used to reduce statistical errors to levels that are small compared to the discretization errors from the time step (Δt), the cell size (Δx), and the number of computational particles per cell (Nc). The errors from these three parameters are determined using over 700 individual cases selected from the range...

Normal solutions of the Boltzmann equation for highly nonequilibrium Fourier flow and Couette flow

The state of a single-species monatomic gas from near-equilibrium to highly nonequilibrium conditions is investigated using analytical and numerical methods. Normal solutions of the Boltzmann equation for Fourier flow (uniform heat flux) and Couette flow (uniform shear stress) are found in terms of the heat-flux and shear-stress Knudsen numbers. Analytical solutions are found for inverse-power-law molecules from hard sphere through Maxwell at small Knudsen numbers using Chapman-Enskog (CE) theory and for Maxwell molecules at finite Knudsen numbers using a moment-hierarchy (MH) method. Corresponding numerical solutions are obtained using the direct simulation Monte Carlo (DSMC) method of Bird. The thermal conductivity, the viscosity, and the Sonine-polynomial coefficients of the velocity distribution function from DSMC agree with CE results at small Knudsen numbers and with MH results at finite Knudsen numbers. Subtle differences between inverse-power-law, variable-soft-sphere, and variable-hard-sphere rep...

A kinetic-theory approach for computing chemical-reaction rates in upper-atmosphere hypersonic flows

Recently proposed molecular-level chemistry models that predict equilibrium and nonequilibrium reaction rates using only kinetic theory and fundamental molecular properties (i.e., no macroscopic reaction-rate information) are investigated for chemical reactions occurring in upper-atmosphere hypersonic flows. The new models are in good agreement with the measured Arrhenius rates for near-equilibrium conditions and with both measured rates and other theoretical models for far-from-equilibrium conditions. Additionally, the new models are applied to representative combustion and ionization reactions and are in good agreement with available measurements and theoretical models. Thus, molecular-level chemistry modeling provides an accurate method for predicting equilibrium and nonequilibrium chemical-reaction rates in gases.

An Experimental Assembly for Precise Measurement of Thermal Accommodation Coefficients.

An experimental apparatus has been developed to determine thermal accommodation coefficients for a variety of gas-surface combinations. Results are obtained primarily through measurement of the pressure dependence of the conductive heat flux between parallel plates separated by a gas-filled gap. Measured heat-flux data are used in a formula based on Direct Simulation Monte Carlo (DSMC) simulations to determine the coefficients. The assembly also features a complementary capability for measuring the variation in gas density between the plates using electron-beam fluorescence. Surface materials examined include 304 stainless steel, gold, aluminum, platinum, silicon, silicon nitride, and polysilicon. Effects of gas composition, surface roughness, and surface contamination have been investigated with this system; the behavior of gas mixtures has also been explored. Without special cleaning procedures, thermal accommodation coefficients for most materials and surface finishes were determined to be near 0.95, 0.85, and 0.45 for argon, nitrogen, and helium, respectively. Surface cleaning by in situ argon-plasma treatment reduced coefficient values by up to 0.10 for helium and by ∼0.05 for nitrogen and argon. Results for both single-species and gas-mixture experiments compare favorably to DSMC simulations.