A two-dimensional model for predicting the rate of radiation heat transfer for the interior of an industrial furnace is described. The model is two-dimensional due to the assumptions of the heat source as an infinite radiating plane and the heat sink as rows of parallel tubes that are both infinite in length and in number. A refractory back wall, located behind the tube rows, is also included in some of the model configurations. The optical properties for the heat source, heat sink, and refractory back wall are simplified by assuming the "black-body" case: all are treated as perfect absorbers and emitters of radiation. This assumption allows three different solution techniques-a graphical, crossed-string, and numerical method-to be used in solving for the radiant transfer rate. The numerical method, an innovative Monte Carlo technique, is the one employed in this study. Hottel used a graphical technique to solve the furnace model for a two row configuration in which the tubes are arranged on equilateral triangular centers. His results, along with those produced by the crossed-string method, are used in this work to validate the numerical technique. Having been validated, the numerical method was then employed to extend Hottel's work by adding more tube rows to the original equilateral triangular configuration and by generalizing the results to isosceles arrangements. Findings of this investigation are summarized in a table that lists the direct view factors for a ten tube row configuration arranged in an equilateral triangular array. Values from this table can be used to solve the transfer rate problem for twenty different cases by assuming a nonconducting refractory back wall. Results for twelve cases are represented graphically in this document The results are used to demonstrate the importance of a refractory back wall on overall radiation absorption. Examinations of the two row and five row cases for an isosceles triangular array indicate that the tabular values can be applied to any isosceles arrangement if the ratio of row separation distance to tube center-to-center distance is 0.7 or greater. / Graduation date: 1995

Herein we present the development of a fluorescence-enhanced, frequency-domain radiative transport reconstruction system designed for small animal optical tomography. The system includes a time-dependent data acquisition instrument, a radiative transport based forward model for prediction of time-dependent propagation of photons in small, non-diffuse volumes, and an algorithm which utilizes the forward model to reconstruct fluorescent yields from air/tissue boundary measurements. The major components of the instrumentation include a charge coupled device camera, an image intensifier, signal generators, and an optical switch. Time-dependent data were obtained in the frequency-domain using homodyne techniques on phantoms with 0.2% to 3% intralipid solutions. Through collaboration with Transpire, Inc., a fluorescence-enhanced, frequency-domain, radiative transport equation (RTE) solver was developed. This solver incorporates the discrete ordinates, source iteration with diffusion synthetic acceleration, and linear discontinuous finite element differencing schemes, to predict accurately the fluence of excitation and emission photons in diffuse and transport limited systems. Additional techniques such as the first scattered distributed source method and integral transport theory are used to model the numerical apertures of fiber optic sources and detectors. The accuracy of the RTE solver was validated against diffusion and Monte Carlo predictions and experimental data. The comparisons were favorable in both the diffusion and transport limits, with average errors of the RTE predictions, as compared to experimental data, typically being less than 8% in amplitude and 7% in phase. These average errors are similar to those of the Monte Carlo and diffusion predictions. Synthetic data from a virtual mouse were used to demonstrate the feasibility of using the RTE solver for reconstructing fluorescent heterogeneities in small, non-diffuse volumes. The current version of the RTE solver limits the reconstruction to one iteration and the reconstruction of marginally diffuse, frequency-domain experimental data using RTE was not successful. Multiple iterations using a diffusion solver successfully reconstructed the fluorescent heterogeneities, indicating that, when available, multiple iterations of the RTE based solver should also reconstruct the heterogeneities.

Liniengetriebene Winde werden durch Impulsübertrag von Photonen auf ein Plasma bei Absorption oder Streuung in zahlreichen Spektrallinien beschleunigt. Dieser Prozess ist besonders effizient für ultraviolette Strahlung und Plasmatemperaturen zwischen 10^4 K und 10^5 K. Zu den astronomischen Objekten mit liniengetriebenen Winden gehören Sterne der Spektraltypen O, B und A, Wolf-Rayet-Sterne sowie Akkretionsscheiben verschiedenster Größenordnung, von Scheiben um junge Sterne und in kataklysmischen Veränderlichen bis zu Quasarscheiben. Es ist bislang nicht möglich, das vollständige Windproblem numerisch zu lösen, also die Hydrodynamik, den Strahlungstransport und das statistische Gleichgewicht dieser Strömungen gleichzeitig zu behandeln. Die Betonung liegt in dieser Arbeit auf der Windhydrodynamik, mit starken Vereinfachungen in den beiden anderen Gebieten. <br /> Wegen persönlicher Beteiligung betrachte ich drei Themen im Detail. <br /> 1. Windinstabilität durch Dopplerde-shadowing des Gases. Die Instabilität bewirkt, dass Windgas in dichte Schalen komprimiert wird, die von starken Stoßfronten begrenzt sind. Schnelle Wolken entstehen im Raum zwischen den Schalen und stoßen mit diesen zusammen. Dies erzeugt Röntgenflashes, die die beobachtete Röntgenstrahlung heißer Sterne erklären können. <br /> 2. Wind runway durch radiative Wellen. Der runaway zeigt, warum beobachtete liniengetriebene Winde schnelle, kritische Lösungen anstelle von Brisenlösungen (oder shallow solutions) annehmen. Unter bestimmten Bedingungen stabilisiert der Wind sich auf masseüberladenen Lösungen, mit einem breiten, abbremsenden Bereich und Knicken im Geschwindigkeitsfeld. <br /> 3. Magnetische Winde von Akkretionsscheiben um Sterne oder in aktiven Galaxienzentren. Die Linienbeschleunigung wird hier durch die Zentrifugalkraft entlang korotierender poloidaler Magnetfelder und die Lorentzkraft aufgrund von Gradienten im toroidalen Feld unterstützt. Ein Wirbelblatt, das am inneren Scheibenrand beginnt, kann zu stark erhöhten Massenverlustraten führen. / Line driven winds are accelerated by the momentum transfer from photons to a plasma, by absorption and scattering in numerous spectral lines. Line driving is most efficient for ultraviolet radiation, and at plasma temperatures from 10^4 K to 10^5 K. Astronomical objects which show line driven winds include stars of spectral type O, B, and A, Wolf-Rayet stars, and accretion disks over a wide range of scales, from disks in young stellar objects and cataclysmic variables to quasar disks. It is not yet possible to solve the full wind problem numerically, and treat the combined hydrodynamics, radiative transfer, and statistical equilibrium of these flows. The emphasis in the present writing is on wind hydrodynamics, with severe simplifications in the other two areas. <br /> I consider three topics in some detail, for reasons of personal involvement. <br /> 1. Wind instability, as caused by Doppler de-shadowing of gas parcels. The instability causes the wind gas to be compressed into dense shells enclosed by strong shocks. Fast clouds occur in the space between shells, and collide with the latter. This leads to X-ray flashes which may explain the observed X-ray emission from hot stars. <br /> 2. Wind runaway, as caused by a new type of radiative waves. The runaway may explain why observed line driven winds adopt fast, critical solutions instead of shallow (or breeze) solutions. Under certain conditions the wind settles on overloaded solutions, which show a broad deceleration region and kinks in their velocity law. <br /> 3. Magnetized winds, as launched from accretion disks around stars or in active galactic nuclei. Line driving is assisted by centrifugal forces along co-rotating poloidal magnetic field lines, and by Lorentz forces due to toroidal field gradients. A vortex sheet starting at the inner disk rim can lead to highly enhanced mass loss rates.

In partial fulfillment of the requirements for the "Habilitation a Diriger des Recherches" at Pierre et Marie Curie University in Paris

In this study we investigate the flow of a Boussinesq fluid contained in a rotating, differentially heated spherical shell. Previous work, on the spherical shell of Boussinesq fluid, differentially heated the shell by prescribing temperature on the inner boundary of the shell, setting the temperature deviation from the reference temperature to vary proportionally with -cos 20, from the equator to the pole. We change the model to include an energy balance equation at the earth's surface, which incorporates latitudinal solar radiation distribution and ice-albedo feedback mechanism with moving ice boundary. For the fluid velocity, on the inner boundary, two conditions are considered: stress-free and no-slip. However, the model under consideration contains only simple representations of a small number of climate variables and thus is not a climate model per se but rather a tool to aid in understanding how changes in these variables may affect our planet's climate. The solution of the model is followed as the differential heating is changed, using the pseudo arc-length continuation method, which is a reliable method that can successfully follow a solution curve even at a turning point. Our main result is in regards to hysteresis phenomenon that is associated with transition from one to multiple convective cells, in a dfferentially heated, co-rotating spherical shell. In particular, we find that hysteresis can be observed without transition from one to multiple convective cells. Another important observation is that the transition to multiple convective cells is significantly suppressed altogether, in the case of stress-free boundary conditions on the fluid velocity. Also, the results of this study will be related to our present-day climate. / UOIT

A condensed multigroup formulation is developed which maintains direct consistency with the continuous energy or fine-group structure, exhibiting the accuracy of the detailed energy spectrum within the coarse-group calculation. Two methods are then developed which seek to invert the condensation process turning the standard one-way condensation (from fine-group to coarse-group) into the first step of a two-way iterative process. The first method is based on the previously published Generalized Energy Condensation, which established a framework for obtaining the fine-group flux by preserving the flux energy spectrum in orthogonal energy expansion functions, but did not maintain a consistent coarse-group formulation. It is demonstrated that with a consistent extension of the GEC, a cross section recondensation scheme can be used to correct for the spectral core environment error. A more practical and efficient new method is also developed, termed the "Subgroup Decomposition (SGD) Method," which eliminates the need for expansion functions altogether, and allows the fine-group flux to be decomposed from a consistent coarse-group flux with minimal additional computation or memory requirements. In addition, a new whole-core BWR benchmark problem is generated based on operating reactor parameters in 2D and 3D, and a set of 1D benchmark problems is developed for a BWR, PWR, and VHTR core.

Thermal radiation is of significant importance in a broad range of engineering applications including high-temperature and large-scale systems. Although the governing equations of thermal radiation have been known for many years, the complexities inherent in the phenomenon, such as the multidimensionality and integro-differential nature of these equations, have made it difficult to obtain an accurate, efficient, and robust computational method. Developing the finite volume radiation method in the 1990s was a significant progress but not a panacea for computational radiation. The major drawback of this method, which is common among all methods that solve for directional intensities, is its slow convergence rate in many situations which increases the solution cost dramatically. These situations include large optical thicknesses, strongly reflecting boundaries, and any other factor that causes strong directional coupling like complex geometries. Several acceleration schemes have been developed in the heat transfer and neutron transport communities to expedite the convergence and reduce the solution cost, but none of them led to a general and reliable method. Among these available schemes, the two most promising ones, the multiplicative scheme and coupled ordinates method, suffer from failing on fine grids and being very complicated for complex scattering phase functions, respectively. In this research, a new computational method, called the QL method, has been introduced. The main idea of this method is using the phase weight concept to relate the directional and average intensities and re-arranging the Radiative Transfer Equation to find a new expression for the radiant heat flux. This results in an elliptic-type equation for the average intensity at each control volume which conserves the radiant energy in all directions in the control volume. This formulation gives the QL method a great advantage to solve for the average intensity while including the directional effects. Since the directional effects are included and the radiant energy is conserved in each control volume, this method is expected to be accurate and have a good convergence rate in all conditions. The phase weight distribution required by the QL method can be provided by a method like the finite volume method or discrete ordinates method. The QL method is applied to several 1D and 2D test cases including isotropic and anisotropic scattering, black and partially reflecting boundaries, and emitting absorbing problems; and its accuracy, convergence rate, and solution cost are studied. The method has been found to be very stable and efficient, regardless of grid size and optical thickness. This method establishes very accurate predictions on the tested coarse grids and its results approach the exact solution with grid refinement.

Thermal radiation is of significant importance in a broad range of engineering applications including high-temperature and large-scale systems. Although the governing equations of thermal radiation have been known for many years, the complexities inherent in the phenomenon, such as the multidimensionality and integro-differential nature of these equations, have made it difficult to obtain an accurate, efficient, and robust computational method. Developing the finite volume radiation method in the 1990s was a significant progress but not a panacea for computational radiation. The major drawback of this method, which is common among all methods that solve for directional intensities, is its slow convergence rate in many situations which increases the solution cost dramatically. These situations include large optical thicknesses, strongly reflecting boundaries, and any other factor that causes strong directional coupling like complex geometries. Several acceleration schemes have been developed in the heat transfer and neutron transport communities to expedite the convergence and reduce the solution cost, but none of them led to a general and reliable method. Among these available schemes, the two most promising ones, the multiplicative scheme and coupled ordinates method, suffer from failing on fine grids and being very complicated for complex scattering phase functions, respectively. In this research, a new computational method, called the QL method, has been introduced. The main idea of this method is using the phase weight concept to relate the directional and average intensities and re-arranging the Radiative Transfer Equation to find a new expression for the radiant heat flux. This results in an elliptic-type equation for the average intensity at each control volume which conserves the radiant energy in all directions in the control volume. This formulation gives the QL method a great advantage to solve for the average intensity while including the directional effects. Since the directional effects are included and the radiant energy is conserved in each control volume, this method is expected to be accurate and have a good convergence rate in all conditions. The phase weight distribution required by the QL method can be provided by a method like the finite volume method or discrete ordinates method. The QL method is applied to several 1D and 2D test cases including isotropic and anisotropic scattering, black and partially reflecting boundaries, and emitting absorbing problems; and its accuracy, convergence rate, and solution cost are studied. The method has been found to be very stable and efficient, regardless of grid size and optical thickness. This method establishes very accurate predictions on the tested coarse grids and its results approach the exact solution with grid refinement.

The bidirectional reflectance distribution function (BRDF) that describes the scattered energy distribution is the most fundamental radiative property to calculate other properties. Although recent progress in surface metrology allows topography measurement in an atomic level, most studies still assume statistical distributions of roughness because of difficulty in roughness modeling. If the BRDF of rough silicon wafers is modeled with assumptions, predicted radiative properties may be inaccurate because non-Gaussian and anisotropic roughness of some wafers cannot be approximated with known statistics. Therefore, this thesis focuses on development of BRDF modeling that accounts for anisotropic roughness to accurately predict radiative properties of rough silicon surfaces with thin-film coatings. Monte Carlo ray-tracing methods are developed to consider multiple scattering and the change of polarization states and to satisfy physical laws such as the reciprocity principle. Silicon surface topographic data measured with an atomic force microscope are incorporated into the ray-tracing algorithms to model anisotropic roughness statistics. For validation, BRDF and emittance predictions are compared with measurements using an optical scatterometer and an integrating sphere. Good agreement between prediction and measurement demonstrates that the incorporation of topography measurement into BRDF modeling is essential for accurate property prediction. Roughness effects on the BRDF are so strong that BRDFs also reveal anisotropic features regardless of the presence of coating. Anisotropic roughness increases multiple scattering although first-order scattering is dominant, and thus enhances emittance noticeably. Silicon dioxide coating changes the magnitude of BRDF and emittance and reduces the anisotropic roughness effect on emittance enhancement. The research in this thesis advances the method to predict radiative properties by incorporating anisotropic rough statistics into BRDF modeling.

In this thesis, the parallel performance of the finite element-spherical harmonics (FE-PN) method implemented in the general-purpose radiation transport code EVENT is studied both analytically and empirically. EVENT solves the coupled set of space-angle discretized FE-PN equations using a parallel block-Jacobi domain decomposition method. As part of the analytical study, the thesis presents complexity results for EVENT when solving for a 3D criticality benchmark radiation transport problem in parallel. The empirical analysis is concerned with the impact of the main algorithmic factors affecting performance. Firstly, EVENT supports two solution strategies, namely MOD (Moments Over Domains) and DOM (Domains Over Moments), to solve the transport equation in parallel. The two strategies differ in the way they solve the multi-level space-angle coupled systems of equations. The thesis presents empirical evidence of which of the two solution strategies is more efficient. Secondly, different preconditioners are used in the Preconditioned Conjugate Gradient (PCG) inside EVENT. Performance of EVENT is compared when using three preconditioners, namely diagonal, SSOR(Symmetric Successive Over-Relaxation) and ILU. The other two factors, angular and spatial resolutions of the problem affect both the performance and precision of EVENT. The thesis presents comparative results on EVENTs performance as these two resolutions are increased. From the empirical performance study of EVENT, a bottleneck is identified that limits the improvement in performance as number of processors used by EVENT is increased. In some experiments, it is observed that uneven assignment of computational load among processors causes a significant portion of the total time being spent in synchronization among processors. The thesis presents two indicators that identify when such inefficiency occur; and in such a case, a load rebalancing strategy is applied that computes a new partition of the problem so that each partition corresponds to equal amount of computational load.