Publications

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Noncontinuum gas-phase heat transfer in two microscale geometries is investigated using two computational methods. The motivation is microscale thermal actuation produced by heating-induced expansion of a near-substrate microbeam in air. The first geometry involves a 1-μm microgap filled with gas and bounded by parallel solid slabs. The second geometry involves a heated I-shaped microbeam 2 μm from the adjacent substrate, with gas in between. Two computational methods are applied. The Navier-Stokes slip-jump (NSSJ) method uses continuum heat transfer in the gas, with temperature jumps at boundaries to treat noncontinuum effects. The Direct Simulation Monte Carlo (DSMC) method uses computational molecules to simulate noncontinuum gas behavior accurately. For the microgap, the heat-flux values from both methods are in good agreement for all pressures and accommodation coefficients. For the microbeam, there is comparably good agreement except for cases with low pressures and near-unity accommodation coefficients. The causes of this discrepancy are discussed. Copyright © 2005 by ASME.

Modeling microscale heat transfer with the computational-heat-transfer code Calore is discussed. Microscale heat transfer problems differ from their macroscopic counterparts in that conductive heat transfer in both solid and gaseous materials may have important noncontinuum effects. In a solid material, three noncontinuum effects are considered: ballistic transport of phonons across a thin film, scattering of phonons from surface roughness at a gas-solid interface, and scattering of phonons from grain boundaries within the solid material. These processes are modeled for polycrystalline silicon, and the thermal-conductivity values predicted by these models are compared to experimental data. In a gaseous material, two noncontinuum effects are considered: ballistic transport of gas molecules across a thin gap and accommodation of gas molecules to solid conditions when reflecting from a solid surface. These processes are modeled for arbitrary gases by allowing the gas and solid temperatures across a gas-solid interface to differ: a finite heat transfer coefficient (contact conductance) is imposed at the gas-solid interface so that the temperature difference is proportional to the normal heat flux. In this approach, the behavior of gas in the bulk is not changed from behavior observed under macroscopic conditions. These models are implemented in Calore as user subroutines. The user subroutines reside within Sandia's Source Forge server, where they undergo version control and regression testing and are available to analysts needing these capabilities. A Calore simulation is presented that exercises these models for a heated microbeam separated from an ambient-temperature substrate by a thin gas-filled gap. Failure to use the noncontinuum heat transfer models for the solid and the gas causes the maximum temperature of the microbeam to be significantly underpredicted.

Abstract not provided.

Abstract not provided.

For gas flows in microfluidic configurations, the Knudsen layer close to the wall can comprise a substantial part of the entire flowfield and has a major effect on quantities such as the mass flow rate through micro devices. The Knudsen layer itself is characterized by a highly nonlinear relationship between the viscous stress and the strain rate of the gas, so even if the Navier-Stokes equations can be used to describe the core gas flow they are certainly inappropriate for the Knudsen layer itself. In this paper we propose a "wall-function" model for the stress/strain rate relations in the Knudsen layer. The constitutive structure of the Knudsen layer has been derived from results from kinetic theory for isothermal shear flow over a planar surface. We investigate the ability of this simplified model to predict Knudsen-layer effects in a variety of configurations. We further propose a semi-empirical Knudsen-number correction to this wall function, based on high-accuracy DSMC results, to extend the predictive capabilities of the model to greater degrees of rarefaction. © 2005 American Institute of Physics.

The Knudsen layer is an important rarefaction phenomenon in gas flows in and around microdevices. Its accurate and efficient modeling is of critical importance in the design of such systems and in predicting their performance. In this paper we investigate the potential that higher-order continuum equations may have to model the Knudsen layer, and compare their predictions to high-accuracy DSMC (direct simulation Monte Carlo) data, as well as a standard result from kinetic theory. We find that, for a benchmark case, the most common higher-order continuum equation sets (Grad's 13 moment, Burnett, and super-Burnett equations) cannot capture the Knudsen layer. Variants of these equation families have, however, been proposed and some of them can qualitatively describe the Knudsen layer structure. To make quantitative comparisons, we obtain additional boundary conditions (needed for unique solutions to the higher-order equations) from kinetic theory. However, we find the quantitative agreement with kinetic theory and DSMC data is only slight. © 2005 American Institute of Physics.

A combined experimental/modeling study was conducted to better understand the critical role of gas-surface interactions in rarefied gas flows. An experimental chamber and supporting diagnostics were designed and assembled to allow simultaneous measurements of gas heat flux and inter-plate gas density profiles in an axisymmetric, parallel-plate geometry. Measurements of gas density profiles and heat flux are made under identical conditions, eliminating an important limitation of earlier studies. The use of in situ, electron-beam fluorescence is demonstrated as a means to measure gas density profiles although additional work is required to improve the accuracy of this technique. Heat flux is inferred from temperature-drop measurements using precision thermistors. The system can be operated with a variety of gases (monatomic, diatomic, polyatomic, mixtures) and carefully controlled, well-characterized surfaces of different types (metals, ceramics) and conditions (smooth, rough). The measurements reported here are for 304 stainless steel plates with a standard machined surface coupled with argon, helium, and nitrogen. The resulting heat-flux and gas-density-profile data are analyzed using analytic and computational models to show that a simple Maxwell gas-surface interaction model is adequate to represent all of the observations. Based on this analysis, thermal accommodation coefficients for 304 stainless steel coupled with argon, nitrogen, and helium are determined to be 0.88, 0.80, and 0.38, respectively, with an estimated uncertainty of {+-}0.02.

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. © 2004 IEEE.

The molecular velocity distribution of a gas with heat flow was analyzed using Bird's direct simulation Monte Carlo (DSMC) method. Large numbers of computational molecules represented the gas in DSMC. Chapman-Enskog behavior was obtained for inverse-power-law molecules at continuum nonequilibrium conditions. It was shown that the Sonine-polynomial coefficients differ systematically from their continuum values as the local Knudsen number is increased, at noncontinuum nonequilibrium conditions.

The development of advanced thermal barrier coatings of yttria stabilized zirconia (YSZ) that exhibit lower thermal conductivity through better control of electron beam-physical vapor deposition (EB-PVD) processing is of prime interest to both the aerospace and power industries. Recently, processing technology was developed to create graded TBCs by coupling ion beam assisted deposition (IBAD) with substrate pivoting in the alumina-YSZ system. The Electron Beam-1200 kW (EB-1200) PVD system was used to deposit a variety of TBC coatings with micron layered microstructures and reduced thermal conductivity of 1.5 W/mK. The use of IBAD produced fully stoichiometric coatings at a reduced substrate temperature of 600 °C and a reduced oxygen background pressure of 0.1 Pa. In addition to the process technology, the results of Direct Simulation Monte Carlo plume modeling and spectroscopic characterization of the PVD plumes are presented. © 2003 Elsevier B.V. All rights reserved.

A Micro Electro Mechanical System (MEMS) typically consists of micron-scale parts that move through a gas at atmospheric or reduced pressure. In this situation, the gas-molecule mean free path is comparable to the geometric features of the microsystem, so the gas flow is noncontinuum. When mean-free-path effects cannot be neglected, the Boltzmann equation must be used to describe the gas flow. Solution of the Boltzmann equation is difficult even for the simplest case because of its sevenfold dimensionality (one temporal dimension, three spatial dimensions, and three velocity dimensions) and because of the integral nature of the collision term. The Direct Simulation Monte Carlo (DSMC) method is the method of choice to simulate high-speed noncontinuum flows. However, since DSMC uses computational molecules to represent the gas, the inherent statistical noise must be minimized by sampling large numbers of molecules. Since typical microsystem velocities are low (< 1 m/s) compared to molecular velocities ({approx}400 m/s), the number of molecular samples required to achieve 1% precision can exceed 1010 per cell. The Discrete Velocity Gas (DVG) method, an approach motivated by radiation transport, provides another way to simulate noncontinuum gas flows. Unlike DSMC, the DVG method restricts molecular velocities to have only certain discrete values. The transport of the number density of a velocity state is governed by a discrete Boltzmann equation that has one temporal dimension and three spatial dimensions and a polynomial collision term. Specification and implementation of DVG models are discussed, and DVG models are applied to Couette flow and to Fourier flow. While the DVG results for these benchmark problems are qualitatively correct, the errors in the shear stress and the heat flux can be order-unity even for DVG models with 88 velocity states. It is concluded that the DVG method, as described herein, is not sufficiently accurate to simulate the low-speed gas flows that occur in microsystems.

Fluid flows that do not have local equilibrium are characteristic of some of the new frontiers in engineering and technology, for example, high-speed high-altitude aerodynamics and the development of micrometre-sized fluid pumps, turbines and other devices. However, this area of fluid dynamics is poorly understood from both the experimental and simulation perspectives, which hampers the progress of these technologies. This paper reviews some of the recent developments in experimental techniques and modelling methods for non-equilibrium gas flows, examining their advantages and drawbacks. We also present new results from our computational investigations into both hypersonic and microsystem flows using two distinct numerical methodologies: the direct simulation Monte Carlo method and extended hydrodynamics. While the direct simulation approach produces excellent results and is used widely, extended hydrodynamics is not as well developed but is a promising candidate for future more complex simulations. Finally, we discuss some of the other situations where these simulation methods could be usefully applied, and look to the future of numerical tools for non-equilibrium flows.

A general, approximate expression is described that can be used to predict the thermophoretic force on a free-molecular, motionless, spherical particle suspended in a quiescent gas with a temperature gradient. The thermophoretic force is equal to the product of an order-unity coefficient, the gas-phase translational heat flux, the particle cross-sectional area, and the inverse of the mean molecular speed. Numerical simulations are used to test the accuracy of this expression for monatomic gases, polyatomic gases, and mixtures thereof. Both continuum and noncontinuum conditions are examined; in particular, the effects of low pressure, wall proximity, and high heat flux are investigated. The direct simulation Monte Carlo (DSMC) method is used to calculate the local molecular velocity distribution, and the force-Green's-function method is used to calculate the thermophoretic force. The approximate expression is found to predict the calculated thermophoretic force to within 10% for all cases examined.

Abstract not provided.

An approach is presented to compute the force on a spherical particle in a rarefied flow of a monatomic gas. This approach relies on the development of a Green's function that describes the force on a spherical particle in a delta-function molecular velocity distribution function. The gas-surface interaction model in this development allows incomplete accommodation of energy and tangential momentum. The force from an arbitrary molecular velocity distribution is calculated by computing the moment of the force Green's function in the same way that other macroscopic variables are determined. Since the molecular velocity distribution function is directly determined in the DSMC method, the force Green's function approach can be implemented straightforwardly in DSMC codes. A similar approach yields the heat transfer to a spherical particle in a rarefied gas flow. The force Green's function is demonstrated by application to two problems. First, the drag force on a spherical particle at arbitrary temperature and moving at arbitrary velocity through an equilibrium motionless gas is found analytically and numerically. Second, the thermophoretic force on a motionless particle in a motionless gas with a heat flux is found analytically and numerically. Good agreement is observed in both situations.

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 Green's 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.

Abstract not provided.

Abstract not provided.

This paper presents an investigation of a technique for using two-dimensional bodies composed of simple polygons with a body decoupled uniform Cmtesian grid in the Direct Simulation Monte Carlo method (DSMC). The method employs an automated grid pre-processing scheme beginning form a CAD geometry definition file, and is based on polygon triangulation using a trapezoid algorithm. A particle-body intersection time comparison is presented between the Icarus DSMC code using a body-fitted structured grid and using a structured body-decoupled Cartesian grid with both linear and logarithmic search techniques. A comparison of neutral flow over a cylinder is presented using the structured body fitted grid and the Cartesian body de-coupled grid.

A new scheme to simulate elastic collisions in particle simulation codes is presented. The new scheme aims at simulating the collisions in the highly collisional regime, in which particle simulation techniques typically become computationally expensive.The new scheme is based on the concept of a grid-based collision field. According to this scheme, the particles perform a single collision with the background grid during a time step. The properties of the background field are calculated from the moments of the distribution function accumulated on the grid. The collision operator is based on the Langevin equation. Based on comparisons with other methods, it is found that the Langevin method overestimates the collision frequency for dilute gases.