Michail A. Gallis

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...

Direct Simulation Monte Carlo: The Quest for Speed.

In the 50 years since its invention, the acceptance and applicability of the DSMC method have increased significantly. Extensive verification and validation efforts have led to its greater acceptance, whereas the increase in computer speed has been the main factor behind its greater applicability. As the performance of a single processor reaches its limit, massively parallel computing is expected to play an even stronger role in its future development.

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...

Thermophoresis in Rarefied Gas Flows

Numerical calculations are presented for the thermophoretic force acting on a free-molecular, motionless, spherical particle suspended in a rarefied gas flow between parallel plates of unequal temperature. The rarefied gas flow is calculated with the direct simulation Monte Carlo (DSMC) method, which provides a time-averaged approximation to the local molecular velocity distribution at discrete locations between the plates. A force Greens function is used to calculate the thermophoretic force directly from the DSMC simulations for the molecular velocity distribution, with the under-lying assumption that the particle does not influence the molecular velocity distribution. Perfect accommodation of energy and momentum is assumed at all solid/gas boundaries. Earlier work for monatomic gases (helium and argon) is reviewed, and new calculations for a diatomic gas (nitrogen) are presented. Gas heat flux and particle thermophoretic forces for argon, helium, and nitrogen are given for a 0.01 m spacing between plates held at 263 and 283 K over a pressure range from 0.1 to 1000 mTorr (0.01333- 133.3 Pa). A simple, approximate expression is introduced that can be used to correlate the thermophoretic force calculations accurately over a wide range of pressures, corresponding to a wide range of Knudsen numbers (ratio of the gas mean free path to the interplate separation).

Icarus: A 2-D Direct Simulation Monte Carlo (DSMC) Code for Multi-Processor Computers

Icarus is a 2D Direct Simulation Monte Carlo (DSMC) code which has been optimized for the parallel computing environment. The code is based on the DSMC method of Bird[11.1] and models from free-molecular to continuum flowfields in either cartesian (x, y) or axisymmetric (z, r) coordinates. Computational particles, representing a given number of molecules or atoms, are tracked as they have collisions with other particles or surfaces. Multiple species, internal energy modes (rotation and vibration), chemistry, and ion transport are modeled. A new trace species methodology for collisions and chemistry is used to obtain statistics for small species concentrations. Gas phase chemistry is modeled using steric factors derived from Arrhenius reaction rates or in a manner similar to continuum modeling. Surface chemistry is modeled with surface reaction probabilities; an optional site density, energy dependent, coverage model is included. Electrons are modeled by either a local charge neutrality assumption or as discrete simulational particles. Ion chemistry is modeled with electron impact chemistry rates and charge exchange reactions. Coulomb collision cross-sections are used instead of Variable Hard Sphere values for ion-ion interactions. The electro-static fields can either be: externally input, a Langmuir-Tonks model or from a Greens Function (Boundary Element) based Poison Solver. Icarus has been used for subsonic to hypersonic, chemically reacting, and plasma flows. The Icarus software package includes the grid generation, parallel processor decomposition, post-processing, and restart software. The commercial graphics package, Tecplot, is used for graphics display. All of the software packages are written in standard Fortran.

Calculations of the near-wall thermophoretic force in rarefied gas flow

The thermophoretic force on a near-wall, spherical particle in a rarefied, monatomic gas flow is calculated numerically. The rarefied gas flow is calculated with the Direct Simulation Monte Carlo (DSMC) method, which provides the molecular velocity distribution. The force is calculated from the molecular velocity distribution using a force Green’s function. Calculations are performed over a Knudsen-number range from 0.0475 to 4.75 using Maxwell and hard-sphere collision models. Results are presented for the thermophoresis parameter, ξ, a dimensionless quantity proportional to the thermophoretic force. The spatial profiles of ξ show a clear progression from free-molecular conditions (ξ is constant throughout the domain) to near-continuum conditions (ξ is constant in the interior but increases in the Knudsen layers). For near-continuum conditions, the DSMC calculations and Chapman–Enskog theory are in excellent agreement in the interior, suggesting that their velocity distributions are similar in this regio...

Measurement of Gas‐Surface Accommodation

Thermal accommodation coefficients have been determined for a variety of gas‐surface combinations using an experimental apparatus developed to measure both the pressure dependence of the conductive heat flux and the variation of gas density between parallel plates separated by a gas‐filled gap. Effects of gas composition, surface roughness and surface contamination have been examined with this system, and the behavior of gas mixtures has also been explored. Results are discussed in comparison with previous parallel‐plate experimental studies as well as numerical simulations.