Enhancements of Tow-Steering Design Techniques: Design of Rectangular Panel Under Combined Loads

An extension to existing design tools that utilize tow-steering is presented which is used to investigate the use of elastic tailoring for a flat panel with a central hole under combined loads of compression and shear. The elastic tailoring is characterized by tow-steering within individual lamina as well as a novel approach based on selective reinforcement, which attempts to minimize compliance through the use of Cellular Automata design concepts. The selective reinforcement designs lack any consideration of manufacturing constraints, so a new tow-steered path definition was developed to translate the prototype selective reinforcement designs into manufacturable plies. The minimum weight design of a flat panel under combined loading was based on a model provided by NASA-Langley personnel and analyzed by STAGS within the OLGA design environment. Baseline designs using traditional straight fiber plies were generated, as well as tow-steered designs which incorporated parallel, tow-drop, and overlap plies within the laminate. These results indicated that the overlap method provided the best improvement with regards to weight and performance as compared to traditional constant stiffness monocoque panels, though the laminates did not measure up to similar designs from the literature using sandwich and isogrid constructions. Further design studies were conducted using various numbers of the selective reinforcement plies at the core and outer surface of the laminate. None of these configurations exhibited notable advantages with regard to weight or buckling performance. This was due to the fact that the minimization of the compliance tended to direct the major stresses toward the center of the panel, which decreased the ability of the structure to withstand loads leading to instability

Numerical analysis of the spectrum of the Dirac operator in four-dimensional SU(2) gauge fields

Two numerical algorithms for the computation of eigenvalues of Dirac operators in lattice gauge theories are described: one is an accelerated conjugate gradient method, the other one a standard Lanczos method. Results obtained by Cullum's and Willoughby's variant of the Lanczos method (whose convergence behaviour is closely linked with the local spectral density) are presented for euclidean Wilson fermions in quenched and unquenched SU(2) gauge fields. Complete spectra are determined on lattices up to $8^3 \cdot 12$, and we derive numerical values for fermionic determinants and results for spectral densities.Comment: 6 pages, uuencoded tar-compressed ps-file, contribution to the Proceedings of the International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow'95, talk also given at the DESY Workshop 199

Resolving Exceptional Configurations

In lattice QCD with Wilson fermions, exceptional configurations arise in the quenched approximation at small quark mass. The origin of these large previously uncontrolled lattice artifacts is identified. A simple well-defined procedure (MQA) is presented which removes the artifacts while preserving the correct continuum limit.Comment: Talk presented by E. Eichten at Lattice 97, Edinburgh(UK), July97. 6 pages, LaTeX, 1 table, 5 figure

Development of a Multi-field Two-fluid Approach for Simulation of Boiling Flows

Safe and reliable operation of nuclear power plants is the basic requirement for the utilization of nuclear energy since accidents can release radioactivity and with that cause irreversible damage to human beings. Reliability and safety of nuclear reactors are highly dependent on the stability of thermal hydraulic processes occurring in them. Nucleate boiling occurs in Pressurized Water Reactors (PWRs) and Boiling Water Reactors (BWRs) as well as in their passive safety systems during an accident. Passive safety systems are solely driven by thermal gradients and gravitational force removing residual heat from the reactor core independent of any external power supply in the case of accidents. Instability of flow boiling in these passive circuits can cause flow oscillations. These oscillations may induce insufficient local cooling and mechanical loads, which threatens the reactors’ safety. Analysis of boiling two-phase flow and associated heat and mass transfer requires an accurate modeling of flow regime transitions and prediction of boiling parameters such as void fraction, steam bubble sizes, heat transfer coefficient, etc. Flow boiling has been intensively investigated through experiments, one-dimensional codes, and Computational Fluid Dynamics (CFD) methods. Costly hardware and no accessibility to all locations in complex geometries restrict the experimental investigation of flow boiling. Since one-dimensional codes such as ATHLET, RELAP and TRACE are ”lumped parameter” codes, they are unable to simulate complex flow boiling transition patterns. In the last decades, with the development of supercomputers, CFD has been considered as a useful tool to model heat and mass transfer occurring in flow boiling regimes. In many industrial applications and system designs, CFD codes and particularly the Eulerian-Eulerian (E-E) two-fluid model are quickly replacing the experimental and analytical methods. However, the application of this approach for flow boiling modelling poses a challenge for the development of bubble dynamics and wall boiling models to predict heat and mass transfer at the heating wall as well as phase-change mechanism. Many empirical and mechanistic models have been proposed for bubble dynamics modelling. Nevertheless, the validity of these models for only a narrow range of operating conditions and their uncertainties limit their applicability and consequently presently necessitate us to calibrate them for a given boundary condition via calibration factors. For that reason, the first aim of this thesis is the development of a bubble dynamics model for subcooled boiling flow, which needs no calibration factor to predict the bubble growth and detachment. This mechanistic model is formulated based on the force balance approach, physics of a single nucleated bubble and several well-developed models to cover the whole bubble life cycle including formation, growth and departure. This model considers dynamic inclination angle and contact angles between the bubble and the heating wall as well as the contribution of microlayer evaporation, thermal diffusion and condensation around the bubble cap. Validation against four experimental flow boiling data sets was conducted with no case-dependent recalibration and yielded good agreement. The second goal is the implementation of the developed bubble dynamics model in the E-E two-fluid model as a sub-model to improve the accuracy of boiling flow simulation and reduce the case dependency. This implementation requires an extension of the nucleation site activation and wall heat-partitioning models. The bubble dynamics and heat-partitioning models were coupled with the Population Balance Model (PBM) to handle bubble interactions and predict the Bubble Size Distribution (BSD). In addition, the contribution of bubble sliding to wall heat transfer, which has been rarely considered in other modelling approaches, is considered. Validation for model implementation in the E-E two-fluid model was made with ten experimental cases including R12 and R134a flow boiling in a pipe and an annulus. These test cases cover a wide range of operating parameters such as wall heat flux, fluid velocity, subcooling temperature and pressure. The validated parameters were the bubble diameter, void fraction, bubble velocity, Interfacial Area Density (IAD), bubble passing frequency, liquid and wall temperatures. Two-phase flow morphologies for an upward flow in a vertical heating pipe may change from bubbly to slug, plug, and annular flow. Since these flow patterns have a great impact on the heat and mass transfer rates, an accurate prediction of them is critical. The aim of this thesis is the implementation of the developed bubble dynamics and heat-partitioning models in the recently developed GENeralized TwO-Phase flow (GENTOP) framework for the modelling of these flow patterns transition as well. An adopted wall heat-partitioning model for high void fractions is presented and for a generic test case, flow boiling regimes of water in a vertical heating pipe were modelled using ANSYS CFX 18.2. Moreover, the impacts of wall superheat, subcooling temperature and fluid velocity on the flow boiling transition patterns and the effects of these patterns on the wall heat transfer coefficient were evaluated.:Nomenclature xi 1 Introduction 1 1.1 Background and motivation . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 State-of-the-art in modelling of subcooled flow boiling 11 2.1 Physics of boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Bubble growth modelling . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 CFD simulation of boiling flows . . . . . . . . . . . . . . . . . . . . . 21 2.3.1 The Eulerian-Eulerian two-fluid model . . . . . . . . . . . . . 21 2.3.2 The Population Balance Model (PBM) . . . . . . . . . . . . . 22 2.3.3 Governing equations of the two-fluid model . . . . . . . . . . 25 2.3.4 Closure models for adiabatic bubbly flow . . . . . . . . . . . . 28 2.3.5 Phase transfer models . . . . . . . . . . . . . . . . . . . . . . 37 2.3.6 The Rensselaer Polytechnic Institute (RPI) wall boiling model 37 2.4 Flow boiling transition patterns in vertical pipes . . . . . . . . . . . . 42 2.5 The GENeralized TwO-Phase flow (GENTOP) concept . . . . . . . . . 45 2.5.1 Treatment of the continuous gas . . . . . . . . . . . . . . . . 46 2.5.2 The Algebraic Interfacial Area Density (AIAD) model . . . . . 46 2.6 Interfacial transfers of continuous gas . . . . . . . . . . . . . . . . . 47 2.6.1 Drag and lift forces . . . . . . . . . . . . . . . . . . . . . . . . 48 2.6.2 Cluster and surface tension forces . . . . . . . . . . . . . . . . 49 2.6.3 Complete coalescence . . . . . . . . . . . . . . . . . . . . . . 50 2.6.4 Entrainment modelling . . . . . . . . . . . . . . . . . . . . . . 51 2.6.5 Turbulence modelling . . . . . . . . . . . . . . . . . . . . . . 51 2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3 An improved bubble dynamics model for flow boiling 55 3.1 Modelling of the bubble formation . . . . . . . . . . . . . . . . . . . 55 3.1.1 Bubble growth rate . . . . . . . . . . . . . . . . . . . . . . . . 57 3.1.2 Force balance . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 ix 3.1.3 Detachment criteria . . . . . . . . . . . . . . . . . . . . . . . 63 3.1.4 Wall heat flux model . . . . . . . . . . . . . . . . . . . . . . . 69 3.1.5 Heat transfer in the heating wall . . . . . . . . . . . . . . . . 70 3.2 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.2.1 Discretization dependency study . . . . . . . . . . . . . . . . 72 3.2.2 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.2.3 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . 79 3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4 An improved wall heat-partitioning model 85 4.1 The cavity group activation model . . . . . . . . . . . . . . . . . . . . 85 4.1.1 Bubble sliding length and influence area . . . . . . . . . . . . 88 4.1.2 Model implementation in the Eulerian-Eulerian framework . . 89 4.2 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.2.1 DEBORA experiments . . . . . . . . . . . . . . . . . . . . . . 90 4.2.2 Subcooled flow boiling of R134a in an annulus . . . . . . . . 102 4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5 Modelling of flow boiling patterns in vertical pipes 115 5.1 Adopted wall heat-partitioning model for high void fractions . . . . . 115 5.2 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5.2.1 Effect of wall superheat on the flow boiling transition patterns 118 5.2.2 Effect of flow morphologies on the wall heat transfer coefficient124 5.2.3 Comparison of GENTOP and Eulerian-Eulerian two-fluid models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.2.4 Effect of subcooling on the flow boiling transition patterns . . 129 5.2.5 Effect of inlet fluid velocity on the flow boiling transition patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6 Conclusions and outlook 133 6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 References 137 Declaration 15

The Effect of Proficiency and Task Type on the Use of Paraphrase Type in Writing among Iranian EFL University Students

Academic writers use paraphrasing as an important borrowing strategy when integrating source text into their writing. To have a better understanding of L2 university students’ paraphrasing strategies, the present study examines how language proficiency and the type of writing task (summary tasks vs. opinion tasks) affect students’ use of paraphrase type: near copy, minimal revision, moderate revision, and substantial revision. The participants of the study were 127 EFL learners at 3 different levels of proficiency (44 advanced, 42 high intermediate, and 41 low intermediate). They were given a text based on which they were asked to do a writing task. In each proficiency group, half of the participants were asked to summarize the source text (ie., to do a summary task) and the other half were required to write their opinions about the text (i.e., to do an opinion task). The assignment of the tasks to individuals was done randomly. The participants’ use of attempted paraphrases within the summary and opinion tasks was compared. It was found that the advanced group used more attempted paraphrases in their writing. In addition, the participants who did the summary task used more attempted paraphrases than those who did the opinion task. Furthermore, low and high intermediate groups used more near copies than the advanced group. Conversely, the advanced participants used more minimal, moderate, and substantial revisions than the other two groups. However, task type appeared to have no effect on the use of paraphrase type

Wilson Fermions in Lattice Quantum Chromodynamics

We have studied the Wilson fermion matrix in the lattice QCD in the quenched approximation. Having implemented the Lanczos algorithm to study Wilson fermion spectrum on finite volumes we have presented results to confirm the existence of a phase transition accompanied by a massless mode from a phase where parity is restored to a phase where this discrete symmetry is violated in accordance with Aoki's lattice QCD phase diagram. In an effort to set up the most suitable algorithm to investigate hadron spectrum for Wilson fermions, we have also studied different versions of the Lanczos and conjugate gradient algorithms and have found that the block Lanczos algorithm is really superior for inverting large sparse matrices. In particular we have shown that the rate of convergence of the block Lanczos algorithm becomes effectively independent of the details of the fermion matrix such as gauge coupling constant and hopping parameter. The application of the block Lanczos algorithm to investigate scalar and pseudoscalar meson propagators shows that the massless mode associated with the transition from parity-restoring to parity-violating phase in the above phase structure is indeed where the pion becomes massless

On the spectrum of the Wilson-Dirac lattice operator in topologically non-trivial background configurations

We study characteristic features of the eigenvalues of the Wilson-Dirac operator in topologically non-trivial gauge field configurations by examining complete spectra of the fermion matrix. In particular we discuss the role of eigenvectors with real eigenvalues as the lattice equivalents of the continuum zero-modes. We demonstrate, that those properties of the spectrum which correspond to non-trivial topology are stable under adding fluctuations to the gauge fields. The behavior of the spectrum in a fully quantized theory is discussed using QED_2 as an example.Comment: Revised version, to appear in Nuclear Physics B; introductory part rewritten and shortened, references update