This article reviews the scientific and engineering principles and practices involved in the mathematical modeling of flow and heat transfer phenomena in industrial-scale glass melting, delivery, and forming processes. The approach taken is to highlight the characteristic features of flow and heat transfer in each of the three processes, summarize the relevant transport and constitutive equations and boundary conditions, and illustrate practical applications of mathematical models. The article also describes modeling approaches used for auxiliary processes and phenomena associated with melting, delivery, and forming operations. Thus, modeling of batch melting, electric heating of glass melt, convection due to bubbling, combustion, turbulence, and viscoelasticity are discussed. Unlike melting and delivery processes, which share many similarities across the various glass industry segments, forming tends to be segment specific. So, the article focuses on one forming process (container) and, through it, emphasizes the key technical attributes of forming models. A selection of results is provided to bring out modeling capabilities and limitations. The article also provides a historical perspective on the development of advanced mathematical models and their industrial applications. Finally, key areas needing research and development are identified to further enhance the practical utility of mathematical models for the glassmaking processes.
Drilling riser systems are subjected to hydrodynamic loads from vessel motions, waves, steady currents and vortex-induced motions. This necessitates a proper structural analysis during the design phase using techniques such as finite element analysis (FEA). Common approaches within the FEA packages approximate the individual components including BOP/LMRP (Blow-Out Preventer/Lower Marine Riser Package), subsea tree and wellhead using 2D or 3D beam/pipe elements with approximated effective mass and damping coefficients. Predicted system response can be very sensitive to the mass, hydrodynamic added mass and drag of the large LMRP/BOP/Tree components above the wellhead. In the past, gross conservative estimates on the hydrodynamic coefficients were made and despite this, design criteria were generally met. With the advent of large sixth-generation BOP stacks with the possibility of additional capping stacks, such approximations are no longer acceptable. Therefore, the possibility of relying on the more detailed capability of computational fluid-structure interaction (FSI) analysis for a better calculation of these coefficients is investigated. In this paper, we describe a detailed model developed for a 38:1 scaled down BOP and discuss the subsequent predictions of the hydrodynamic coefficients. The model output is compared against the data from the concurrent tests conducted in an experimental tow tank. The comparison demonstrates that computational FSI can be an effective and accurate tool for calculating the hydrodynamic coefficients of complex structures like BOPs.
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