Mathematical Simulation in Glass Technology

This book is one of a series reporting on international research and development activities conducted by the Schott Group companies. With the series, Schott aims to provide an overview of its activities for scientists, engineers and managers from all branches of industry worldwide where glasses and glass ceramics are of interest. Each volume begins with a chapter providing a general idea of the current problems, results and trends related to the subject treated. This volume reports on a large variety of mathematical simulations, covering all production steps of special glass manufacturing: melting, fining, mixing, homogenizing, hot and cold forming, thermal treatment, post-processing. Modern, commercially available software packages have been used and - whenever necessary - modified to satisfy the special requirements and situations in liquid or solid glasses, or the boundary conditions of forming processes.
The CD-ROM shows 27 simulations of different aspects such as surprising details of the pressing and casting process. The mathematical approach often helps understanding the overall and sometimes hidden features of processes and thus is a highly efficient tool for optimization efforts. Complementing and partly replacing experimental investigations, mathematical simulation enables considerable savings in time and money. Several of the results reported here are unique and published for the first time. Today, the methods of mathematical simulation are an integral part of problem solving in glass technology. The book is conceived as a monograph. The individual chapters, however, are written by different Schott experts or Schott's cooperation partners from international research institutes or universities. The scientific and technical background of the methods, as well as selected results and applications are treated in detail.

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This is the first book on mathematical simulation on glass technology, and covers all production steps of special glass manufacturing. The enclosed CD-ROM shows 27 simulations of different aspects, such as surprising details of the pressing and casting process.

Contenu

Overview.- 1.1 Introduction.- 1.2 Systematics and Boundary Conditions of This Book.- 1.3 Some Important 3D Continuum Equations.- References.- 2. Melting and Fining.- 2.1 Modeling of the Melting Process in Industrial Glass Furnaces.- 2.1.1 Application of Process Simulation Models for Glass Furnaces.- 2.1.2 Modeling of Heat Transfer and Convection Flows in Glass-Melting Tanks.- 2.1.3 Sand-Grain Dissolution, Behavior of Gas Bubbles in Glass Melts, and Glass-Quality Index.- 2.1.4 Models for Evaporation and Superstructure Refractory Attack by Vapors.- 2.1.5 Dynamic Modeling.- 2.1.6 Concluding Remarks.- 2.2 Mathematical Modeling of Batch Melting in Glass Tanks.- 2.2.1 Motivation and Requirements on Batch Modeling.- 2.2.2 Survey of Batch Melting.- 2.2.3 Theoretical Basis of Batch Modeling.- 2.2.4 Key Values and Non-Dimensional Numbers.- 2.2.5 Batch Models.- 2.3 High-Frequency Melting of Glass in Crucibles.- 2.3.1 Basics of Electrodynamics.- 2.3.2 Mathematical Formulation of the Simulation Model.- 2.3.3 Simulation Results.- 2.3.4 Conclusion and Outlook.- 2.4 Model-Based Glass Melter Control.- 2.4.1 Model Concepts.- 2.4.2 Model-Predictive Control.- 2.4.3 Extensions of the MPC Technology.- 2.4.4 Application of MPC in the Glass Industry.- References.- 3. Homogenizing and Conditioning.- 3.1 The Intensity of Mixing Processes.- 3.1.1 Description and Quantification of Mixing Processes.- 3.1.2 Flows and Particle Paths in Stirrers.- 3.1.3 Statistics of Residence Time and Dispersion.- 3.1.4 Deformation of Infinitesimal Test Bodies Along Particle Paths.- 3.1.5 Deformation Statistics.- 3.1.6 Example: a Simple Paddle Stirrer.- 3.1.7 Outlook.- 3.2 Instabilities and Stabilization of Glass Pipe Flows.- 3.2.1 Stationary Temperature and Pressure Profiles in the Pipe.- 3.2.2 A Stability Phenomenon.- 3.2.3 Appendix: Derivation of Several Equations.- 3.3 Shape Optimization of Flanges.- 3.3.1 General Shape Optimization: Continuously Varying Thicknesses and Contours.- 3.3.2 Finite-Dimensional Shape Optimization: the 3-Ring/Spoke Flange.- References.- 4. Shaping at Low Viscosities.- 4.1 Heat Transfer Between Glass and Mold During Hot Forming.- 4.1.1 Heat Transfer Coefficient Between Glass and Mold.- 4.1.2 Physics and Mathematics of the Heat Transfer.- 4.1.3 Sample Computations.- 4.1.4 Radiative Contributions to the Heat Transfer.- 4.1.5 Laboratory Experiments.- 4.2 Remote Spectral Temperature Profile Sensing.- 4.2.1 Thermal Radiation in Hot Glass.- 4.2.2 The Inverse Problem of Spectral Temperature Sensing.- 4.2.3 Sample Computations.- 4.2.4 Laboratory Experiment.- 4.2.5 Spectral Imaging of Hot Glass.- 4.3 Heat Transfer During Casting Experiments.- 4.3.1 Experimental Set-Up.- 4.3.2 Comparison Between "Exact" Modeling and Measurement.- 4.3.3 Alternative Modeling Using the Active Thermal Conductivity.- 4.4 Thin-Layer Flows of Glass.- 4.4.1 Example of a Thin-Layer Model.- 4.4.2 Simplified Energy Balance.- 4.4.3 Validation of the Model.- 4.4.4 Fiber- and Tube-Drawing Models.- 4.4.5 More Comprehensive Thin-Layer Flow Models.- 4.5 Pressing of Drinking-Glass Stems.- 4.5.1 Model 1: Finite-Element Modeling.- 4.5.2 Model 2: Analytical Modeling.- 4.5.3 Comparison of Model 1 and Model.- 4.6 The Use of Remeshing Methods in Pressing Simulations.- 4.6.1 Some Technical Aspects of the Method.- 4.6.2 Example: Pressing of a Tumbler.- 4.6.3 Example: Pressing of an "Axisymmetric TV Screen".- 4.7 Chill Ripples in Pressing and Casting Processes.- 4.7.1 A Simple Casting Process.- 4.7.2 A Model for Kluge's Experimental Set-Up.- References.- 5. Reshaping at High Viscosities.- 5.1 Temperature-Dependent Elasticity in Reshaping Simulations.- 5.1.1 Model.- 5.1.2 Simulation Results.- 5.2 Sagging and Pressing of Glass Sheets.- 5.2.1 Model and Boundary Conditions.- 5.2.2 Results of the Model Computations.- 5.3 Calibration of Glass Tubes.- 5.3.1 Model Description.- 5.3.2 Results of the Model Computations.- 6. Thermal Treatment.- 6.1 Verification of Relaxation Models.- 6.1.1 Mathematical Models.- 6.1.2 Experiments in the Lehr.- 6.1.3 Simulation.- 6.1.4 Measuring Stress and Compaction.- 6.1.5 Results.- 6.2 Stresses and Crack Growth in Continuously Formed Slabs.- 6.2.1 Cooling a Continuous Strip.- 6.2.2 Crack Growth.- 6.2.3 Modified Temperature Program in Order to Avoid Cracking.- 6.2.4 Cutting the Strip into Slabs.- 6.3 Thermal Tempering of Drinking Glasses.- 6.3.1 Principles of Thermal Tempering.- 6.3.2 Results for Spatially Inhomogeneous Quenching.- 6.3.3 Realization of a Quenching Process.- 7. Post-Processing by Laser Cutting.- 7.1 Rough Estimation of Process Parameters.- 7.1.1 Stress Levels.- 7.1.2 Laser-Beam Profiling.- 7.1.3 Selection of Laser.- 7.2 Numerical Analysis of Cutting Processes.- 7.2.1 Calculation of Temperature Distributions.- 7.2.2 Calculation of Stress Distributions.- 7.2.3 Condition for Cut Elongation.- 7.2.4 Calculation of Stress Intensities for Laser Cutting.- 7.3 Practical Realization.- 7.4 Appendix: Fundamentals of Fracture Mechanics.- 7.4.1 Fracture Mechanics for Brittle Solids.- 7.4.2 FEA Calculation of Stress-Intensity Factors.- 7.4.3 Prediction of the Crack Path.- 8. Glass Products Under Mechanical and Thermal Loads.- 8.1 Strength Optimization of Airbag Igniters.- 8.1.1 FEA for Axial-Symmetric Models.- 8.1.2 FEA of 3D Models.- 8.1.3 Pull-Out Tests.- 8.1.4 Push-Out Tests.- 8.1.5 Pressure Tests.- 8.1.6 Appendix: Statistical Procedure.- 8.2 Stiffness and Weight Optimization of a Reticle Stage for Optical Lithography.- 8.2.1 equirements for a (9 × 9)? Reticle Stage.- 8.2.2 esign of a Prototype.- 8.2.3 EM Optimization Without Additional Masses.- 8.2.4 EM Analysis With Additional Masses.- References.- 9. Simulation and Test of the Spinning Process Applied to Platinum Metals.- 9.1 Necessity to Shape Materials.- 9.2 Qualitative Description of the Spinning Proce…