Sudarshan K. Loyalka

Poiseuille flow of a rarefied gas in a cylindrical tube: Solution of linearized Boltzmann equation

The existence of a minimum in the cylindrical Poiseuille flow of a rarefied gas has been known since the experiments of Knudsen [Ann. Phys. 4, 75 (1909)]. Previously, the phenomenon has been studied with models of the Boltzmann equation, but results for the Boltzmann equation itself have not been reported. In the present paper, proceeding from recent studies, first the SN numerical algorithm for solving the linearized Boltzmann equation for the cylindircal geometry is outlined. Then, explicit numerical results for a rigid sphere gas and the boundary condition of diffuse specular reflection are obtained. The results show a minimum of the flow rate, and generally, provide a good description of the experimental data.

Mechanics of aerosols in nuclear reactor safety: A review

Abstract Although the estimated public risks from the nuclear reactors are not high, a significant fraction of these arises from the accident sequences that lead to severe core damage. Calculation of release fractions of the core radioactive inventories for such accidents requires an understanding of the evolution of aerosols in primary coolant systems and reactor containment. There have been considerable advances in aerosol mechanics as applied to the safety of nuclear reactors. In this paper, the state-of-the-art in the mechanics of a single aerosol particle is first reviewed and then available work on coagulation of two aerosol particles is discussed. Progress in kinetic theory descriptions and experimental works is described and directions of future work are noted. Next the General Dynamic Equation for the aerosol distribution is considered, and several forms of this for conditions of interest are noted. Methods of solution that are discussed include analytical techniques, similarity transforms, moments methods and numerical techniques. Computer programs that have been developed in the past few years are also discussed, and their capabilities and limitations are noted. Finally, the comparison of computed results with the available experimental data is discussed, and needs for future research are emphasized.

Temperature jump and thermal creep slip: rigid sphere gas

The half‐space problems of temprature jump and thermal creep slip are solved for a rigid sphere gas based on the linearized Boltzmann equation. The SN method is used, and it is shown that accurate results for the jump/slip coefficients and the temperature, density, and velocity can be obtained in relatively short computational times. The previously reported variational results for the jump/slip coefficients are found to be quite good (1%–3% error). It is noted, however, that for rigid sphere molecules the Knudsen layer is somewhat thinner than for the BGK model. The creep slip coefficient is in good agreement with the experimental data of Annis [J. Chem. Phys. 57, 2898 (1972)], but for other quantities experimental data are needed.

A Numerical Method for Solving Integral Equations of Neutron Transport—II

In a recent paper it was pointed out that the weakly singular integral equations of neutron transport can be quite conveniently solved by a method based on subtraction of singularity. This previous paper was devoted entirely to the consideration of simple one-dimensional isotropic-scattering and one-group problems. The present paper constitutes interesting extensions of the previous work in that in addition to a typical two-group anisotropic-scattering albedo problem in the slab geometry, the method is also applied to an isotropic- scattering problem in the x-y geometry. These results are compared with discrete S/sub N/ (ANISN or TWOTRAN-II) results, and for the problems considered here, the proposed method is found to be quite effective. Thus, the method appears to hold considerable potential for future applications. (auth)

Slip coefficients for binary gas mixtures

A full description of rarefied gas flows requires the solution of the Boltzmann equation. In the near continuum regime, however, the preferred approach is to solve the Navier–Stokes equation subject to appropriate slip boundary conditions. For gas mixtures, the slip coefficients that enter into the conditions are dependent upon a host of parameters. Thus, one desires simple algebraic expressions for these coefficients that are also quite accurate. We describe in this article a study of the slip problems associated with the flow of binary gas mixtures. Using some general conservation laws, we first augment some previously reported expressions for the velocity and diffusion slips with an expression for the thermal slip and then we reduce all of the expressions to very convenient forms. Next, we report results of numerical computations for some specific gas mixtures using Lennard-Jones potentials and show previously unknown dependencies of the slips on the mixture properties. The new slip coefficients should...

Velocity slip and defect: Hard sphere gas

The half‐space problem of rarefied gas flow (the Kramers problem) is considered and use of the SN algorithm is outlined. Accurate numerical results for the velocity slip coefficient and velocity defect are obtained for a hard sphere gas and are compared with previously reported results and experimental data.

Motion of a sphere in a gas: Numerical solution of the linearized Boltzmann equation

An understanding of the motion (translation and rotation) of single particles in a gas is required in disciplines as diverse as environmental sciences, cloud physics, nanophase materials manufacturing, health and medical physics, astrophysics, and aeronautics. In this work an accurate description of a sphere’s motion based on the linearized Boltzmann equation is provided.

Diamond ultraviolet photovoltaic cell obtained by lithium and boron doping

Polycrystalline high quality freestanding 300-μm-thick diamond films were doped by diffusion of B and Li under electric bias in order to fabricate vertical p-n junctions. Circular contacts were obtained by high dose ion implantation of B and Li. The I–V characteristics were rectifying. When illuminated by deuterium lamp, an open circuit voltage was 2.6 eV. The shape of the I–V characteristic under illumination points to the existence of shunt and series resistances. The obtained structure is most probably a p-n junction with bad contacts.

THERMOPHORETIC DEPOSITION IN A CYLINDRICAL TUBE : COMPUTATIONS AND COMPARISON WITH EXPERIMENTS

Abstract Thermophoresis causes particle deposition on nuclear reactor components from gas/vapor streams, both during normal and accident conditions, and it is of interest to develop good computational tools for estimation of such deposition. This paper describes a numerical technique to solve the coupled equations of energy and particle continuity. The numerical technique was verified by comparing the solution of the Graetz energy transport problem obtained by using the present numerical technique with the series solution. Thermophoretic deposition efficiency obtained from the present numerical technique agrees with the analytical solution for short tubes. Deposition efficiencies for the case RePr = 1 and Pr K = 1 are in good agreement with the published theoretical expressions for thermophoretic deposition efficiency. Also, the results from the numerical solution for thermophoretic deposition efficiency compare well with some experimental data published in the literature. Dependence of deposition efficiency η on thermophoretic coefficient K was studied, and it was observed that the dependence is more linear for smaller thermal gradients than for the larger gradients. Further, the computational fluid dynamics program FLUENT® 6.3 was also used to explore calculations of the thermophoretic deposition efficiencies for some cases, and it was noted that results are sensitive to mesh size and that very fine mesh near the surface was needed for accurate results. The results computed are in good agreement with our numerical calculations and experimental data.

Carbon Nanoparticle Generation, Collection, and Characterization Using a Spark Generator and a Thermophoretic Deposition Cell

Abstract Nanoparticles can form during nuclear accidents as well as during normal nuclear reactor operations and can be both radioactive and nonradioactive. It is important to understand particle size characteristics, transport properties, and deposition in order to better predict the behaviors of, and effects due to, these particles in a reactor. Fission products can deposit (adsorb/absorb) on the graphite dust in the core [an amount of carbon dust is present in the Pebble Bed Modular Reactor (PBMR) because of graphite sphere abrasion] and can also be carried by the helium flow (together with some dust). Generating nanoparticles of desired shape, size, and purity for experimental purposes is difficult, and hence, there is a need for new and refined synthesis techniques. Nanoparticle generation using high-voltage electric sparks has become a technique of interest for a wide range of conducting materials, and particles with sizes ranging from a few nanometers up to microns have been generated in this manner in an aerosol state. Our purpose in this paper is to report on the generation, collection, and characterization of carbon nanoparticles. We have used a spark generator and a thermophoretic deposition cell, as well as environmental scanning electron microscopy, transmission electron microscopy, and scanning mobility particle spectrometry. We have explored a number of experimental conditions, and we find that one can generate and effectively collect test particles with a variety of different useful characteristics. We also discuss some computational fluid dynamics simulations of particle deposition in the thermophoretic deposition cell.