Magnetohydrodynamic modeling for an OVD reactor setup

We consider the preconditioned Krylov subspace method for linear systems arising from the finite volume discretization method of steady-state variable-coefficient conservative space-fractional diffusion equations. We propose to use a scaled-circulant preconditioner to deal with such Toeplitz-like discretization matrices. We show that the difference between the scaled-circulant preconditioner and the coefficient matrix is equal to the sum of a small-norm matrix and a low-rank matrix. Numerical tests are conducted to show the effectiveness of the proposed method for one- and two-dimensional steady-state space-fractional diffusion equations and demonstrate that the preconditioned Krylov subspace method converges very quickly.

A unified analytical solution of the steady-state atmospheric diffusion equation

An alternative general solution of the steady-state heat diffusion equation

A potential and stream function analysis of two-dimensional steady-state convective diffusion equations involving Laplace fields

Measurements of effective sizes and diffusivities of nano-colloids and micro-particles

Often in reactor dynamics, higher eigenfunctions of the multigroup diffusion equation must be determined. An algorithm to calculate higher eigenfunctions (modes) of the [lambda]-eigenvalue problem corresponding to the steady-state two-group neutron diffusion equation is presented. The method is based on a special type of subspace iteration for large sparse nonsymmetric eigenvalue problems. Having been tested using an International Atomic Energy Agency benchmark problem and also applied to a VVER-1000 pressurized water reactor assembly, the algorithm was found to work very effectively and reliably. In its application, the algorithm presented is not restricted to the [lambda]-eigenvalue problem only but is also generally applicable to large sparse nonsymmetric eigenvalue problems even with multiple and complex eigenvalues.

An experimental study of heat transfer and particle deposition during the outside vapor deposition process

A theoretical model of reaction/diffusion within conducting polymer microelectrodes is discussed. The model is based on the steady-state diffusion equation containing a nonlinear term related to the Michaelis-Menten kinetic of the enzymatic reaction. An analytical expression pertaining to the concentration of substrate and current is obtained using homotopy perturbation method for all values of diffusion and the saturation parameter. The substrate concentration profile and current response can be used in a large range of concentrations including the non-linear contributions. These approximate analytical results were found to be in good agreement with the previously reported limiting case results.

A diffuse interface–lattice Boltzmann model for conjugate heat transfer with imperfect interface

Because of its low thermal conductivity, high thermal expansion and high oxygen ion conductivity yttria-stabilized zirconia (YSZ) is the material of choice for high temperature electrolyte applications. Current coating fabrication methods have their drawbacks, however. Air plasma spray (APS) is a relatively low-cost process and is suitable for large and relatively complex shapes. it is difficult to produce uniform, relatively thin coatings with this process, however, and the coatings do not exhibit the columnar microstructure that is needed for reliable, long-term performance. The electron-beam physical vapor deposition (EB-PVD) process does produce the desirable microstructure, however, the capital cost of these systems is very high and the line-of-sight nature of the process limits coating uniformity and the ability to coat large and complex shapes. The chemical vapor deposition (CVD) process also produces the desirable columnar microstructure and--under proper conditions--can produce uniform coatings over complex shapes. CVD has been used for many materials but is relatively undeveloped for oxides, in general, and for zirconia, in particular. The overall goal of this project--a joint effort of the University of Louisville and Oak Ridge National Laboratory (ORNL)--is to develop the YSZ CVD process for high temperature electrolyte applications. This report describes the modeling effort at the University of Louisville, which supports the experimental work at ORNL. Early work on CVD of zirconia and yttria used metal chlorides, which react with water vapor to form solid oxide. Because of this rapid gas-phase reaction the water generally is formed in-situ using the reverse water-gas-shift reaction or a microwave plasma. Even with these arrangements gas-phase nucleation and powder formation are problems when using these precursors. Recent efforts on CVD of zirconia and YSZ have focused on use of metal-organic precursors (MOCVD). These are more stable in the gas-phase and can produce dense, crystalline films. With metal-organic CVD, consistent controlled delivery of the precursor vapor is sometimes a problem. Direct vaporization and vapor-phase metering is difficult due to marginal thermal stability of these compounds and changes in vaporization rate over time. A number of special precursor delivery systems have been designed to address these challenges. The direct liquid injection (DLI) method has several advantages for precursor delivery. Liquid metering provides accurate, stable control of precursor delivery rate. With a suitable solvent, a wide variety of precursor compounds can be used, including solids and other compounds not suitable for vapor delivery. Composite or multi-metal coatings require only one precursor source consisting of multiple precursors dissolved in the correct proportion in a single solution. Many uses of DLI-MOCVD involve deposition of thin films for electronic applications. In these applications, the substrate temperature is low and the deposition rate is relatively slow (< 1 {micro}m/hr). Under these conditions the deposition rate is kinetics-limited, i.e. controlled by the rate of reaction of adsorbed species on the substrate surface, and is strongly influenced by temperature. Thermal barrier applications require relatively thick films (50 to 100 {micro}m) and higher deposition rates. At the higher temperatures the deposition rate is ''transport-limited'', i.e. control by the transport rate of precursor to the surface. The purpose of this study is to investigate the deposition of zirconia under transport-limited conditions and to accurately model the deposition rate. Ultimately this model will be used to design a DLI-MOCVD reactor for coating of large, complex shapes.

Inductively coupled plasma (ICP) generators involve complex interactions between electromagnetic, thermal, and chemical processes, making direct diagnostics difficult. To clarify these coupling mechanisms, a two-dimensional axisymmetric model of an argon ICP torch operating at kilopascal pressure was developed using COMSOL Multiphysics under both local thermodynamic equilibrium (LTE) and nonequilibrium (NLTE) assumptions. A two-dimensional axisymmetric magnetohydrodynamic (MHD) model was established, incorporating electromagnetic induction, convective–radiative heat transfer, and a seven-reaction argon plasma chemistry mechanism. The LTE model assumes a uniform temperature for all species, while the NLTE model independently solves for the electron temperature (&lt;i&gt;T&lt;sub&gt;e&lt;/sub&gt;&lt;/i&gt;) and gas temperature (&lt;i&gt;T&lt;sub&gt;g&lt;/sub&gt;&lt;/i&gt;), thereby accounting for incomplete energy exchange between electrons and heavy particles.At a discharge power of 1000 W and working pressure of 10 kPa, the LTE model predicts a peak temperature of approximately 8200 K, concentrated around the induction coils. In contrast, the NLTE model yields a maximum gas temperature of about 5990 K, with the hot zone shifted downstream. The NLTE model reveals a clear two-temperature structure: &lt;i&gt;T&lt;sub&gt;e&lt;/sub&gt;&lt;/i&gt; peaks near the coil wall (~0.93 eV) while &lt;i&gt;T&lt;sub&gt;g&lt;/sub&gt;&lt;/i&gt; reaches its maximum downstream, indicating a pronounced thermal non equilibrium state where electrons are preferentially heated by the induced field. The calculated skin depth (~11.3 mm) coincides with the region of strongest electromagnetic energy deposition.Species analysis shows that the plasma core is dominated by ground-state argon (Ar) (&gt;99%), while excited argon (Ar&lt;sup&gt;*&lt;/sup&gt;) and argon ions (Ar&lt;sup&gt;+&lt;/sup&gt;) increase notably near the coil region, confirming that excitation and ionization processes are localized within the skin layer. Furthermore, comparison between 5 kPa and 10 kPa cases demonstrates that as pressure decreases, the difference between &lt;i&gt;T&lt;sub&gt;e&lt;/sub&gt;&lt;/i&gt; and &lt;i&gt;T&lt;sub&gt;g&lt;/sub&gt;&lt;/i&gt; widens, reflecting enhanced thermal non-equilibrium due to reduced collisional coupling.Overall, the results highlight that LTE and NLTE assumptions lead to markedly different predictions of temperature and energy coupling at kilopascal pressures. The NLTE model captures delayed energy transfer and spatial temperature decoupling more realistically, providing new insights into the electromagnetic– thermal–flow interactions of ICP discharges and offering a modeling reference for ICPbased high-enthalpy plasma wind tunnel design and related aerospace applications.

Influence of asymmetries in the magnetic draping pattern at Titan on the emission of energetic neutral atoms

Chemical vapor deposition (CVD) is a widely used manufacturing process for obtaining thin films of materials like silicon, silicon carbide, graphene, and gallium nitride that are employed in the fabrication of electronic and optical devices. Gallium nitride (GaN) thin films are attractive materials for manufacturing optoelectronic device applications due to their wide band gap and superb optoelectronic performance. The reliability and durability of the devices depend on the quality of the thin films. The metal-organic chemical vapor deposition (MOCVD) process, which uses compounds that contain metals and organic ligands as precursors in a CVD reactor, is a common technique used to fabricate high-quality GaN thin films. The deposition rate and uniformity of thin films are critical to a successful and useful process. These are determined by the thermal transport processes and chemical reactions occurring in the reactor, and are manipulated by controlling the operating conditions and the reactor geometrical configuration. In this study, the epitaxial growth of GaN thin films on sapphire (Al2O3) substrates is carried out in two commercial MOCVD systems: a vertical rotating disk MOCVD reactor and a close-coupled showerhead MOCVD reactor. The surface morphology and crystal quality of GaN thin films have been examined using atomic force microscopy (AFM) and scanning electron microscope (SEM). This paper focuses on the composition of the precursor and the carrier gases since earlier studies have shown the importance of precursor composition. The results show that the flow rate of trimethylgallium (TMG), which is the main ingredient in the process, has a significant effect on the deposition rate and uniformity of the films. Also, the carrier gas plays an important role in deposition rate and uniformity. Using hydrogen as a carrier gas enhances the quality of the thin film but a lower deposition rate occurs on the wafer surface. On the other hand, a high flow rate of pure nitrogen gas improves the growth rate of the film. However, it decreases the uniformity of the film and promotes carbon contamination on the wafer surface. Thus, the use of an appropriate mixture of hydrogen and nitrogen as the carrier gas can improve the deposition rate and quality of GaN thin films.

This paper investigates the simulation, response surface modeling, and optimization of the metalorganic chemical vapor deposition (MOCVD) process for the deposition of gallium nitride (GaN). Trimethylgallium (TMGa) and ammonia (NH3) are the precursors carried by hydrogen into the rotating-disk reactor. The deposition rate of GaN film and its uniformity form the focus of this study. Computational fluid dynamics (CFD) model simulates the deposition of the GaN film. CFD model is employed to identify two design variables, inlet velocity and inlet precursor concentration ratio, which significantly affect the deposition rate and uniformity of GaN film. Compromise response surface method (CRSM) is used to generate response surfaces for average deposition rate and uniformity. These response surfaces are used to generate the Pareto front for the conflicting objectives of optimal rate of average deposition and uniformity. Pareto front captures the trade-off between deposition rate and uniformity of the GaN film. It is observed that for the whole range of design variables, there are numerous options to get stable uniformity levels than deposition rate. The optimal inlet velocity and precursor concentration for different objective functions considered tend to be near the upper bounds.

A two-dimensional and stationary magnetohydrodynamic model of a plasma spray torch operated with argon is developed to predict the plasma properties in a steady operating mode. The model couples a submodel of a refractory cathode and its non-equilibrium boundary layer to a submodel of the plasma in local thermodynamic equilibrium in a self-consistent manner. The Navier–Stokes equations for a laminar and compressible flow are solved in terms of low and high Mach number numerical approaches. The results show that the Mach number can reach values close to one. Simulations are performed for electric currents of 600 A and 800 A, and gas flow rates of 40, 60, and 80 NLPM. The plasma parameters obtained by the two approaches differ, and the differences become more pronounced for higher currents and gas flow rates. The arc voltage, the electric power, and the thermal efficiency from both the low and high Mach number models of the plasma agree well with experimental findings for a current of 600 A and a flow rate of 40 NLPM. For higher currents and gas flow rates, the results of the low and high Mach number models gradually differ and underline the greater appropriateness of the high Mach number model.