Publications

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The effect of particle diameter on downward co-current gas-liquid flow through a fixed bed of particles confined within a cylindrical column is investigated. Several hydrodynamic regimes that depend strongly on the properties of the gas stream, the liquid stream, and the packed particle bed are known to exist within these systems. This experimental study focuses on characterizing the effect of wall confinement on these hydrodynamic regimes as the diameter d of the spherical particles becomes comparable to the column diameter D (or D/d becomes order-unity). The packed bed consists of polished, solid, spherical, monodisperse particles (beads) with mean diameter in the range of 0.64-2.54 cm. These diameters yield D/d values between 15 and 3.75, so this range overlaps and extends the previously investigated range for two-phase flow. Measurements of the pressure drop across the bed and across the pulses are obtained for varying gas and liquid flow rates. Copyright © 2005 by ASME.

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.

A previously-developed experimental facility has been used to determine gas-surface thermal accommodation coefficients from the pressure dependence of the heat flux between parallel plates of similar material but different surface finish. Heat flux between the plates is inferred from measurements of temperature drop between the plate surface and an adjacent temperature-controlled water bath. Thermal accommodation measurements were determined from the pressure dependence of the heat flux for a fixed plate separation. Measurements of argon and nitrogen in contact with standard machined (lathed) or polished 304 stainless steel plates are indistinguishable within experimental uncertainty. Thus, the accommodation coefficient of 304 stainless steel with nitrogen and argon is estimated to be 0.80 {+-} 0.02 and 0.87 {+-} 0.02, respectively, independent of the surface roughness within the range likely to be encountered in engineering practice. Measurements of the accommodation of helium showed a slight variation with 304 stainless steel surface roughness: 0.36 {+-} 0.02 for a standard machine finish and 0.40 {+-} 0.02 for a polished finish. Planned tests with carbon-nanotube-coated plates will be performed when 304 stainless-steel blanks have been successfully coated.

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.

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Several mixture models are evaluated for their suitability in predicting the equivalent permittivity of dielectric particles in a dielectric medium for intermediate solid volume fractions (0.4 to 0.6). Predictions of the Maxwell, Rayleigh, Bottcher and Bruggeman models are compared to computational simulations of several arrangements of solid particles in a gas and to the experimentally determined permittivity of a static particle bed. The experiment uses spherical glass beads in air, so air and glass permittivity values (1 and 7, respectively) are used with all of the models and simulations. The experimental system used to measure the permittivity of the static particle bed and its calibration are described. The Rayleigh model is found to be suitable for predicting permittivity over the entire range of solid volume fractions (0-0.6).

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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.

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.

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An experimental program was conducted to study a proposed approach for oil reintroduction in the Strategic Petroleum Reserve (SPR). The goal was to assess whether useful oil is rendered unusable through formation of a stable oil-brine emulsion during reintroduction of degassed oil into the brine layer in storage caverns. An earlier report (O'Hern et al., 2003) documented the first stage of the program, in which simulant liquids were used to characterize the buoyant plume that is produced when a jet of crude oil is injected downward into brine. This report documents the final two test series. In the first, the plume hydrodynamics experiments were completed using SPR oil, brine, and sludge. In the second, oil reinjection into brine was run for approximately 6 hours, and sampling of oil, sludge, and brine was performed over the next 3 months so that the long-term effects of oil-sludge mixing could be assessed. For both series, the experiment consisted of a large transparent vessel that is a scale model of the proposed oil-injection process at the SPR. For the plume hydrodynamics experiments, an oil layer was floated on top of a brine layer in the first test series and on top of a sludge layer residing above the brine in the second test series. The oil was injected downward through a tube into the brine at a prescribed depth below the oil-brine or sludge-brine interface. Flow rates were determined by scaling to match the ratio of buoyancy to momentum between the experiment and the SPR. Initially, the momentum of the flow produces a downward jet of oil below the tube end. Subsequently, the oil breaks up into droplets due to shear forces, buoyancy dominates the flow, and a plume of oil droplets rises to the interface. The interface was deflected upward by the impinging oil-brine plume. Videos of this flow were recorded for scaled flow rates that bracket the equivalent pumping rates in an SPR cavern during injection of degassed oil. Image-processing analyses were performed to quantify the penetration depth and width of the oil jet. The measured penetration depths were shallow, as predicted by penetration-depth models, in agreement with the assumption that the flow is buoyancy-dominated, rather than momentum-dominated. The turbulent penetration depth model overpredicted the measured values. Both the oil-brine and oil-sludge-brine systems produced plumes with hydrodynamic characteristics similar to the simulant liquids previously examined, except that the penetration depth was 5-10% longer for the crude oil. An unexpected observation was that centimeter-size oil 'bubbles' (thin oil shells completely filled with brine) were produced in large quantities during oil injection. The mixing experiments also used layers of oil, sludge, and brine from the SPR. Oil was injected at a scaled flow rate corresponding to the nominal SPR oil injection rates. Injection was performed for about 6 hours and was stopped when it was evident that brine was being ingested by the oil withdrawal pump. Sampling probes located throughout the oil, sludge, and brine layers were used to withdraw samples before, during, and after the run. The data show that strong mixing caused the water content in the oil layer to increase sharply during oil injection but that the water content in the oil dropped back to less than 0.5% within 16 hours after injection was terminated. On the other hand, the sediment content in the oil indicated that the sludge and oil appeared to be well mixed. The sediment settled slowly but the oil had not returned to the baseline, as-received, sediment values after approximately 2200 hours (3 months). Ash content analysis indicated that the sediment measured during oil analysis was primarily organic.

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.

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.

An experimental program is being conducted to study a proposed approach for oil reintroduction in the Strategic Petroleum Reserve (SPR). The goal is to assess whether useful oil is rendered unusable through formation of a stable oil-brine emulsion during reintroduction of degassed oil into the brine layer in storage caverns. This report documents the first stage of the program, in which simulant liquids are used to characterize the buoyant plume that is produced when a jet of crude oil is injected downward from a tube into brine. The experiment consists of a large transparent vessel that is a scale model of the proposed oil injection process at the SPR. An oil layer is floated on top of a brine layer. Silicon oil (Dow Corning 200{reg_sign} Fluid, 5 cSt) is used as the simulant for crude oil to allow visualization of the flow and to avoid flammability and related concerns. Sodium nitrate solution is used as the simulant for brine because it is not corrosive and it can match the density ratio between brine and crude oil. The oil is injected downward through a tube into the brine at a prescribed depth below the oil-brine interface. Flow rates are determined by scaling to match the ratio of buoyancy to momentum between the experiment and the SPR. Initially, the momentum of the flow produces a downward jet of oil below the tube end. Subsequently, the oil breaks up into droplets due to shear forces, buoyancy dominates the flow, and a plume of oil droplets rises to the interface. The interface is deflected upward by the impinging oil-brine plume. Two different diameter injection tubes were used (1/2-inch and 1-inch OD) to vary the scaling. Use of the 1-inch injection tube also assured that turbulent pipe flow was achieved, which was questionable for lower flow rates in the 1/2-inch tube. In addition, a 1/2-inch J-tube was used to direct the buoyant jet upwards rather than downwards to determine whether flow redirection could substantially reduce the oil-plume size and the oil-droplet residence time in the brine. Reductions of these quantities would inhibit emulsion formation by limiting the contact between the oil and the brine. Videos of this flow were recorded for scaled flow rates that bracket the equivalent pumping rates in an SPR cavern. Image-processing analyses were performed to quantify the penetration depth of the oil jet, the width of the jet, and the deflection of the interface. The measured penetration depths are shallow, as predicted by penetration-depth models, in agreement with the assumption that the flow is buoyancy-dominated, rather than momentum-dominated. The turbulent penetration depth model provided a good estimate of the measured values for the 1-inch injection tube but overpredicted the penetration depth for the 1/2-inch injection tube. Adding a virtual origin term would improve the prediction for the 1/2-inch tube for low to nominal injection flow rates but could not capture the rollover seen at high injection flow rates. As expected, the J-tube yielded a much narrower plume because the flow was directed upward, unlike the downward-oriented straight-tube cases where the plume had to reverse direction, leading to a much wider effective plume area. Larger surface deflections were caused by the narrower plume emitted from the J-tube. Although velocity was not measured in these experiments, the video data showed that the J-tube plume was clearly faster than those emitted from the downward-oriented tubes. These results indicate that oil injection tube modifications could inhibit emulsion formation by reducing the amount of contact (both time and area) between the oil and the brine. Future studies will employ crude oil, saturated brine, and interfacial solids (sludge) from actual SPR caverns.

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An improved model for the gas damping of out-of-plane motion of a microbeam is developed based on the Reynolds equation (RE). A boundary condition for the RE is developed that relates the pressure at the beam perimeter to the beam motion. The two coefficients in this boundary condition are determined from Navier-Stokes (NS) simulations with the slip boundary condition 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 for cases where the beam width is only slightly greater than the gap height.

A novel electrical-impedance tomography (EIT) diagnostic system, including hardware and software, has been developed and used to quantitatively measure material distributions in multiphase flows within electrically-conducting (i.e., industrially relevant or metal) vessels. The EIT system consists of energizing and measuring electronics and seven ring electrodes, which are equally spaced on a thin nonconducting rod that is inserted into the vessel. The vessel wall is grounded and serves as the ground electrode. Voltage-distribution measurements are used to numerically reconstruct the time-averaged impedance distribution within the vessel, from which the material distributions are inferred. Initial proof-of-concept and calibration was completed using a stationary solid-liquid mixture in a steel bench-top standpipe. The EIT system was then deployed in Sandia's pilot-scale slurry bubble-column reactor (SBCR) to measure material distributions of gas-liquid two-phase flows over a range of column pressures and superficial gas flow rates. These two-phase quantitative measurements were validated against an established gamma-densitometry tomography (GDT) diagnostic system, demonstrating agreement to within 0.05 volume fraction for most cases, with a maximum difference of 0.15 volume fraction. Next, the EIT system was combined with the GDT system to measure material distributions of gas-liquid-solid three-phase flows in Sandia's SBCR for two different solids loadings. Accuracy for the three-phase flow measurements is estimated to be within 0.15 volume fraction. The stability of the energizing electronics, the effect of the rod on the surrounding flow field, and the unsteadiness of the liquid temperature all degrade measurement accuracy and need to be explored further. This work demonstrates that EIT may be used to perform quantitative measurements of material distributions in multiphase flows in metal vessels.

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.