Showing papers on "Transport phenomena published in 1999"

Stability, Instability, and "Backwards'' Transport in Accretion Disks"

Abstract: The stratification of entropy and the stratification of angular momentum are closely analogous. Of particular interest is the behavior of disks in which angular momentum transport is controlled by convection, and heat transport by dynamical turbulence. In both instances we argue that the transport must proceed ``backwards'' relative to the sense one would expect from a simple enhanced diffusion approach. Reversed angular momentum transport has already been seen in numerical simulations; contra-gradient thermal diffusion should be amenable to numerical verification as well. These arguments also bear on the observed nonlinear local stability of isolated Keplerian disks. We also describe a diffusive instability that is the entropy analogue to the magnetorotational instability. It affects thermally stratified layers when Coulomb conduction and a weak magnetic field are present. The criterion for convective instability goes from one of upwardly decreasing entropy to one of upwardly decreasing temperature. The maximum growth rate is of order the inverse sound crossing time, independent of the thermal conductivity. The indifference of the growth rate to the conduction coefficient, its simple dynamical scaling, and the replacement in the stability criterion of a conserved quantity (entropy) gradient by a free energy (temperature) gradient are properties similar to those exhibited by the magnetorotational instability.

Modeling macro- and microstructures of gas-metal-arc welded HSLA-100 steel

Abstract: Fluid flow and heat transfer during gas-metal-arc welding (GMAW) of HSLA-100 steel were studied using a transient, three-dimensional, turbulent heat transfer and fluid flow model. The temperature and velocity fields, cooling rates, and shape and size of the fusion and heat-affected zones (HAZs) were calculated. A continuous-cooling-transformation (CCT) diagram was computed to aid in the understanding of the observed weld metal microstructure. The computed results demonstrate that the dissipation of heat and momentum in the weld pool is significantly aided by turbulence, thus suggesting that previous modeling results based on laminar flow need to be re-examined. A comparison of the calculated fusion and HAZ geometries with their corresponding measured values showed good agreement. Furthermore, “finger” penetration, a unique geometric characteristic of gas-metal-arc weld pools, could be satisfactorily predicted from the model. The ability to predict these geometric variables and the agreement between the calculated and the measured cooling rates indicate the appropriateness of using a turbulence model for accurate calculations. The microstructure of the weld metal consisted mainly of acicular ferrite with small amounts of bainite. At high heat inputs, small amounts of allotriomorphic and Widmanstatten ferrite were also observed. The observed microstructures are consistent with those expected from the computed CCT diagram and the cooling rates. The results presented here demonstrate significant promise for understanding both macro-and microstructures of steel welds from the combination of the fundamental principles from both transport phenomena and phase transformation theory.

Statistical Thermodynamics and Microscale Thermophysics

Abstract: Many of the exciting new developments in microscale engineering are based on the application of traditional principles of statistical thermodynamics. This book offers a modern view of thermodynamics, interweaving classical and statistical thermodynamic principles and applying them to current engineering systems. It begins with coverage of microscale energy storage mechanisms from a quantum mechanics perspective and develops the fundamentals of classical and statistical thermodynamics. Next, applications of equilibrium statistical thermodynamics to solid, liquid, and gas phase systems are discussed. The remainder of the book discusses nonequilibrium thermodynamics of transport phenomena and introduces nonequilibrium effects and noncontinuum behaviour at the microscale. Although the text emphasizes mathematical development, it includes many examples and exercises illustrating how the theoretical concepts are applied to systems of scientific and engineering interest. It offers a fresh view of statistical thermodynamics for advanced undergraduate and graduate students as well as practitioners in mechanical, chemical, and materials engineering.

The Intermediate Finite Element Method: Fluid Flow and Heat Transfer Applications

Abstract: 1.Introduction 2.Basic Equations of Fluid Dynamics 3.Fundamental Concepts 4.Higher Order Elements 5.Numerical Integration 6.Non-Linearity 7.Time Dependence 8.Steady-State Convective Transport 9.Time Dependent Convection-Diffusion 10.Applications to Viscous Incompressible Fluid Flow 11.Mesh Generation 12.Further Applications Appendices

Advances in the flow and rheology of non-Newtonian fluids

Abstract: Part A. 1. Bio and Food Rheology. 2. Complex Flows. 3. Computational Methods. 4. Constitutive Equations & Viscoelastic Fluids. Part B. 5. Electrorheological Fluids. 6. Industrial Flows. 7. Polymer Processing & Rheology. 8. Polymeric Fibers and Jets. 9. Flow in Porous Media. 10. Suspensions. 11. Transport Phenomena.

Computational fluid dynamics by boundary–domain integral method

Abstract: A boundary-domain integral method for the solution of general transport phenomena incompressible fluid motion given by the Navier-Stokes equation set is presented. Velocity-vorticity formulation of the conservations is employed. Different integral representations for conservation field functions based on different fundamental solutions are developed. Special attention is given to the use of subdomain technique and Krylov subspace iterative solvers. The computed solutions of several benchmark problems agree well with available experimental and other computational results.

Progress in direct numerical simulation of turbulent heat transfer

Abstract: With high performance computers, reliable numerical methods and efficient post-processing environment, direct numerical simulation (DNS) offers valuable numerical experiments for turbulent heat transfer research. In particular, one can extensively study the turbulence dynamics and transport mechanism by visualizing any physical variable in space and time. It is also possible to establish detailed database of various turbulence statistics of turbulent transport phenomena, while systematically changing important flow and scalar field parameters. The present paper illustrates these novelties of DNS by introducing several examples in r ecent studies. Future directions of DNS for turbulence and heat transfer research are also discussed. In the following, with introductory remarks on computational requirement for respectable DNS, progress in numerical techniques is first reviewed. Then, an effort to reveal the effect of Prandtl number on turbulent heat transfer is sketched with an emphasis on the new techniques developed for making DNS over a wide range of Prandtl number possible. Both methods of saving grid points and Lagrangian particle tracking are found very useful in the future work on turbulent heat and mass transfer. The complex buoyancy effects on turbulent transport are discussed in a series of DNSs of horizontal and vertical channel flows. It is found that the buoyancy effect appears much differently depending upon the directional alignment of the buoyant force and the mean flow. In the vertical flow, the buoyancy effect results in an increased or decreased Reynolds number effect, which appears through a change in the Reynolds stress distribution and hence in the shear production rate of turbulent kinetic energy near the wall. In the horizontal flow, however, it causes substantial alternation in the turbulence structures and transport mechanism so that the resultant heat transfer coefficient would behave in a much more complex manner. The thermal plumes and internal gravity waves characteristic of these flows play an important role in the interaction with the quasi-coherent structures of wall turbulence. DNSs of the channel flow under active turbulence and heat transfer control are discussed finally. In these simulations, an array of micro deformation actuators on a wall surface or intelligent micro particles are tested as control schemes. It is shown that these sophisticated devices possibly bring about notable friction drag reduction and heat transfer enhancement. A perspective view is given that DNS will be even more useful in evaluating future turbulence control methodologies based on new algorithms such as optimum control theory and neural networks. These simulations have been triggered by the rapid development of microelectromechanical systems (MEMS) technology, but hopefully future DNSs will lead further development of MEMS-based controller units integrating micro sensors, micro actuators and IC.

Theory of Transport Phenomena in High-T c Cuprates

Abstract: In this paper we point out that the anomalous transport phenomena in high- T c cuprates are comprehensively understood on the basis of Fermi liquid theory by taking account of a strong anti-ferromagnetic spin fluctuation. We assume phenomenologically the spectrum of magnetic excitation from experiment and calculate the self-energy on the basis of the one loop approximation. We show that the T -linear term of damping rate, the momentum dependence of lifetime and the transformation of Fermi surface are important to explain the anomalous transport phenomena such as resistivity, Hall coefficient and c -axis resistivity. In particular, the strong spin fluctuation leads to the transformation of Fermi surface which leads to a form more appropriate to nesting. This effect plays an important role. At last we show that our theory is applicable to not only the normal state but also the pseudogap state.

An experimental reactor to study the intrinsic kinetics of catalytic partial oxidation of methane in the presence of heat-transport limitations

Abstract: The catalytic partial oxidation (CPO) of methane with oxygen was studied at atmospheric pressure in a continuous-flow reactor containing a single Pt metal gauze. Experiments were performed at catalyst temperatures and residence times in the range of 950–1200 K and 0.02–0.2 ms, respectively. Heat-transport limitations are taken into account explicitly, by measuring the catalyst temperature directly by means of a surface thermocouple. The experimental results indicated that the conversions of methane and oxygen were determined by transport phenomena; however, the CO selectivity appeared to be influenced significantly by the kinetics of the catalytic reactions. Hydrogen was found only at temperatures above 1273 K. In order to be able to derive intrinsic kinetic information from the experimental data, a reactor model consisting of two rows of parallel flat plates in series was developed, taking into account the relevant transport phenomena. This flat-plate reactor model was validated by comparing the model results to 3D fluent simulations of simultaneous heat and mass transfer in case of a simple surface reaction on the gauze catalyst. A series-parallel CPO reaction mechanism allowed simulation of the observed conversions and selectivities at different space-times. More detailed elementary-step reaction mechanisms can be developed, using both the experimental data and the flat-plate reactor model.

Modeling of fluid flow and heat transfer in a hydrothermal crystal growth system: Use of fluid-superposed porous layer theory

Abstract: Hydrothermal synthesis, which uses aqueous solvents under high pressure and relatively low temperature, is an important technique for difficult to grow crystalline materials. It is a replica of crystal growth under geological conditions. A hydrothermal growth system usually consists of finely divided particles of the nutrient, predetermined volume of a solvent and a suitably oriented crystal seed under very high pressures, generally several thousand bar. The nutrient dissolves at a higher temperature in the lower region, moves to the upper region due to buoyancy-induced convective flows, and deposits on the seed due to lower solubility if the seed region is maintained at a lower temperature. The system can be modeled as a composite fluid and porous layer using the Darcy-Brinkman-Forchheimer flow model in the porous bed. Since the growth process is very slow, the process is considered quasi-steady and the effect of dissolution and growth is neglected. This first study on transport phenomena in a hydrothermal system therefore focuses on the flow and temperature fields without the presence of the seed and mass transfer. A three-dimensional algorithm is used to simulate the flow and heat transfer in a typical autoclave system. An axisymmetric flow pattern at low Grashof numbers becomesmore » three-dimensional at high Grashof numbers. A reduction in the porous bed height for fixed heated and cooled regions can result in oscillatory flows. These results, for the first time, depict the possible flow patterns in a hydrothermal system, that can have far reaching consequences on the growth process and crystal quality.« less

Role of collisionless heat flux in magnetospheric convection

Abstract: A fluid model of magnetospheric convection appropriate for the inner magnetosphere, including the effects of heat flux in collisionless plasma, is presented. The plasma is assumed to be isotropic, with the flow speed much less than the thermal speed, and parallel electric fields and loss cone effects are neglected; the effects of slow time variations of the magnetic field are included. The classical transport coefficients are considered and, except for the collisionless heat flux, shown to be negligible in plasma in the inner magnetosphere. Beginning with three-dimensional two-fluid equations, we derive two-dimensional equations for transport of mass and energy mapped to the magnetospheric equator. The equation of mass transport, derived from the mass conservation equations, is equivalent to those obtained in previous studies [e.g., Peymirat and Fontaine, 1994]. The equation of energy transport contains the effects of collisionless heat conduction that represents the transport of energy in the rest frame of the species and has hitherto been neglected in magnetospheric fluid and MHD models. The energy transport equation is shown to be equivalent to that of Peymirat and Fontaine [1994] if the heat flux is neglected. The two equations are coupled first-order partial differential equations; they can be uncoupled by taking linear combinations. The uncoupled equations show that the effect of the collisionless heat flux is to spread information across the fluid drift paths in a manner quite different from that of fluid flow neglecting heat flux.

Transport phenomena at a critical point: Thermal conduction in the Creutz cellular automaton

Abstract: The nature of energy transport around a critical point is studied in the Creutz cellular automaton. The Fourier heat law is confirmed to hold in this model by a direct measurement of heat flow under a temperature gradient. The thermal conductivity is carefully investigated near the critical point by the use of the Kubo formula. As a result, the thermal conductivity is found to take a finite value at the critical point, contrary to some previous works. Equal-time correlation of the heat flow is also analyzed by a mean-field type approximation to investigate the temperature dependence of thermal conductivity. A variant of the Creutz cellular automaton called the Q2R is also investigated and similar results are obtained.

Non-local model analysis of heat pulse propagation and simulation of experiments in W7-AS

Abstract: A new model equation which includes the non-local effect in the heat flux is introduced to study the transient transport phenomena. A non-local heat flux, which is expressed in terms of the integral equation, is superimposed on the conventional form of the heat flux. This model is applied to describe the experimental results from the power switching [U. Stroth et al. : Plasma Phys. Control. Fusion 38 (1996) 1087] and the power modulation experiments [L. Giannone et al. : Nucl. Fusion 32 (1992) 1985] in the W7-AS stellarator. A small fraction of non-local component in the heat flux is found to be very effective in modifying the response against an external modulation. The transient feature of the transport property, which are observed in the response of heat pulse propagation, are qualitatively reproduced by the transport simulations based on this model. A possibility is discussed to estimate the correlation length of the non-local effect experimentally by use of the results of transport simulations.

Finite-Element Method for Contaminant Transport in Unsaturated Soils

Abstract: A numerical model to simulate miscible contaminant transport through unsaturated soils is presented. To account for the influence of multiple nonequilibrium sources on the contaminant transport, six governing phenomena of the miscible contaminant transport (i.e., convection, mechanical dispersion, molecular diffusion, adsorption, degradation, and immobile water effect) are integrated into the present model. The pollutant volumetric concentration in mobile water is taken as primary unknown, whereas the pollutant concentration in immobile water and the solid particles of soils are treated as state variables at the element integration points. Based on a splitting of the generalized convective operator from the diffusive operator, a modified version of the characteristic Galerkin method is developed to discretize the equations governing the contaminant transport phenomena. A fully explicit algorithm is then derived for the numerical solution of the finite-element equations in time domain. The numerical examples illustrate the performance and the capability of the presented model and algorithms.

Transport phenomena in sublimation growth of SiC bulk crystals

Abstract: Sublimation growth of SiC bulk crystals in the atmosphere of concentrated multi-component vapor is studied using a specially developed model of transport processes coupled with heterogeneous reactions at the source and the seed surfaces. The convective and multi-component diffusion mechanisms of the gas phase transport, dependence of the pressure level inside the growth chamber on the growth conditions, and kinetic jumps of the species partial pressures at the Knudsen layers on the reactive surfaces are taken into account in the model. The latter effect is described by introduction of novel boundary conditions representing extension of the Hertz–Knudsen relationship for the case of multi-component vapor. The results of calculations are shown to be in a good agreement with the available experimental data.

A finite cell method for simulating the mass transport process in porous media

Abstract: This paper presents a new numerical method, the finite cell method (FCM), for simulating complex biological and chemical transport phenomena in porous media. It has the same advantages as the random walk method (RW): there is no advection-dispersion equation to be solved, it is unnecessary to calculate the concentration distribution in each time step, and there is no numerical dispersion for the case of high Peclet number. The concept of FCM, however, is different from the RWM in several aspects. The minimum unit in the FCM is a cell that has a certain volume and carries variable mass, while in the RWM the minimum unit is a particle that has no volume but carries a certain mass. In the FCM we use multiple sets of cells to represent different phases in a porous medium. A mobile or an immobile cell may carry multiple biological and/or chemical components. Mass exchanges may occur not only between cells but also within cells. These mass exchanges can be described by different rules: equilibrium or nonequilibrium, linear or nonlinear. In this paper, a one-dimensional FCM code is developed and used to simulate the solute transport with nonequilibrium adsorption, colloid transport with kinetic deposition and release, and colloid facilitated transport with kinetic mass exchanges. The FCM solutions have been compared with available analytical solutions and the solutions obtained by the finite difference method (FDM). Results show that both FCM and FDM solutions match analytical solutions quite well when the concentration front is flat. When the concentration front is sharp, however, the FDM solutions become inaccurate because of numerical dispersion, but the FCM can still produce very accurate peak and tailing concentrations. From the example of colloid-facilitated transport, we can see how a complex chemical and biological transport procedure in porous media can be simulated directly by the FCM without solving any advection-dispersion equation.

Modeling of multilayer drying of polymer films

Abstract: A model was developed to predict the drying behavior of multilayer polymer films on inert substrates. The model considers simultaneous heat and mass transfer controlled by complex thermodynamic and transport properties of polymer solutions. Key components of the model are the incorporation of the free volume theory to predict diffusivities in each polymer layer, the use of heat and mass transfer coefficients to describe complex transport phenomena in the gas phase, the incorporation of exact equilibrium boundary conditions at polymer–polymer interface, and the use of the Flory–Huggins theory to describe both liquid–liquid and vapor–liquid equilibria. The model can be applied to guide processing, product formulation, scale-up, and oven design. As an example, the model is applied to simulate the drying of a two-layer coating of poly vinyl acetate (in toluene) over polystyrene (also in toluene) on a polyester substrate. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1665–1675, 1999

Microscopic theory of vertical-transport phenomena in semiconductor heterostructures: Interplay between two- and three-dimensional hot-carrier relaxation

Abstract: A theoretical analysis of vertical-transport phenomena in semiconductor heterostructures is presented. In particular, the scattering coupling between two- and three-dimensional states in multiple quantum wells is investigated. To this purpose, a fully three-dimensional approach for the description of both localized and extended states in the heterostructure is proposed. Starting from such three-dimensional states, obtained from a self-consistent Schrodinger-Poisson calculation, a Monte Carlo solution of the corresponding Boltzmann transport equation is performed. In contrast to various phenomenological transport models, the present simulation scheme allows a kinetic description, i.e., based on microscopic scattering rates, of vertical transport across a generic heterostructure. Our results provide a rigorous description of hot-carrier relaxation between extended and localized states. This simulation scheme has been applied to finite multiple quantum wells with different geometries and doping profiles. A detailed analysis of the electron current as a function of temperature in quasiequilibrium conditions shows good agreement with experimental results. Moreover, in non-equilibrium conditions (i.e., hot-carrier regime) the scattering coupling between three- and two-dimensional states is found to play a significant role in modifying the carrier mobility as well as the fraction of conducting electrons.

Lattice-based simulations of chain conformations in semi-crystalline polymers with application to flow-induced crystallization

Abstract: Polymer fiber processes, such as high-speed spinning of nylon and PET, are highly complex involving a complicated interplay between an evolving internal molecular microstructure, macroscopic transport phenomena, such as fluid mechanics and heat transfer, and also non-equilibrium thermodynamics and kinetics affecting nucleation and subsequent crystal growth. All of the above processes are important in determining the final product's semi-crystalline morphology which is primarily responsible for its mechanical properties. Our approach to attack this problem is a hierarchical one: A macroscopic (continuum) model is developed based on the Hamiltonian formalism of non-equilibrium thermodynamics for flowing systems [Beris and Edwards, Oxford University Press, Oxford, 1994]. This approach allows us to follow the dynamic evolution of several macroscopic (continuum) variables involving both kinematic and structural parameters. To implement this approach successfully, an accurate modeling of the (extended) free energy (Hamiltonian) of the system under consideration and the dissipation therein is necessary. While the later is, at the moment, phenomenological, we are developing a first principles approach for the former based on a microscopic modeling of chain conformations using a lattice model. Lattice models have been used extensively before for the analysis of chain conformations in both purely amorphous and semi-crystalline polymers. We have reinterpreted some of the earlier lattice models by systematically deriving the relevant statistics of polymer chains and by outlining the a priori approximations in those models which are necessary to arrive at closed-form expressions. Although we do make use of such earlier work, we have also extended it through a computer-aided analysis. This analysis has enabled us to generate from first principles free energy surfaces for a system consisting of polymer chains, represented as multiple self- and mutually-avoiding random walks, on a 2-D fully populated semi-crystalline lattice. It is shown that the numerical results for dense semi-crystalline systems can be fitted with low order polynomials that provide closed-form approximations for the configurational entropy in terms of non-equilibrium structural parameters, such as the orientation and stretching of the polymer chains. Finally, chain statistics for bulk amorphous polymers have been validated against their theoretical predictions.

The role of macroscopic transport phenomena in film microstructure during epitaxial growth

Abstract: A multiscale integration hybrid algorithm is introduced to describe film microstructure in epitaxial growth under conditions where fluid mechanics and transport phenomena in the adjacent fluid phase are important, such as in chemical vapor deposition at relatively high pressures. This algorithm is demonstrated in a stagnation point flow reactor. It is shown that mass transfer limitations delay the transition from the step flow to the two-dimensional nucleation growth mode, as the substrate temperature decreases, and could possibly eliminate kinetic microroughening. Furthermore, the temporal development of morphological features upon changes in operating conditions is determined by the bulk convective flow.