modeling multiphase materials processes

[...]... flow phenomena in metallurgical processes In this chapter, the modeling of gas–liquid two-phase flows is classified into two broad categories Some basic physical situations of relevance in multiphase metallurgical processes are then introduced Finally, the nature of individual multiphase flows in real processes is discussed 1.2 Classification of Models 1.2.1 Physical Modeling Modeling can generally be classified... conditions would be similarly different In addition, M Iguchi and O.J Ilegbusi, Modeling Multiphase Materials Processes: Gas-Liquid Systems, DOI 10.1007/978-1-4419-7479-2 1, c Springer Science+Business Media, LLC 2011 1 2 1 Introduction any presumption regarding the true situation cannot be readily verified through experimentation on real processes In light of the above, we rely on model experiments and theory... 1.3 General Strategy for Modeling Two-Phase Phenomena 3 A variety of examples of the second and third categories are given in this book, and the key features of physical modeling are examined 1.2.2 Mathematical Modeling Mathematical modeling involves the use of a set of algebraic or differential equations to describe the fluid flow and associated heat and mass transfer in the real processes [1, 4, 6] The... calculation techniques, mathematical modeling is now widely applied in engineering and science practice The techniques of mathematical modeling and their applications to metallurgical processes are given in detail in Chaps 9 and 10 Additional information on mathematical modeling principles is also available in other texts [1, 4, 6] In physical as well as mathematical modeling of transport phenomena, it... steelmaking processes, such as converters, ladles, RH degassing processes, and other metals refining processes In order to enhance the efficiency of these processes, precise information on the behavior of rising bubbles in a molten metal bath and resultant molten metal flow induced by the bubbles is required Since it is difficult to study bubble and liquid flow characteristics using actual processes, many... Springer, New York 4 Szekely J, Ilegbusi OJ (1989) The physical and mathematical modeling of tundish operations Springer, Berlin 5 Sahai Y, St Pierre GR (1992) Advances in transport processes in metallurgical systems Elsevier, Amsterdam, pp 260–263 6 Ilegbusi OJ, Iguchi M, Wahnshiedler W (1999) Mathematical and physical modeling in materials processing operations Chapman & Hall/CRC, Boca Raton 7 Perry RH,... bath at high temperatures are very difficult At present, the mean velocity can be measured under limited conditions by using reaction probes [13–16] and Karman M Iguchi and O.J Ilegbusi, Modeling Multiphase Materials Processes: Gas-Liquid Systems, DOI 10.1007/978-1-4419-7479-2 2, c Springer Science+Business Media, LLC 2011 19 20 2 Turbulence Structure of Two-Phase Jets vortex probes [17, 18] even if... experience and insight into the phenomena, the fundamental procedure in mathematical modeling is common to a certain extent even if the processes differ from one another The same is true in physical modeling 4 1 Introduction 1.4 Basic Physical Situations of Relevance in Gas–Liquid Processes 1.4.1 Gas–Liquid Two-Phase Flows in Cylindrical Bath 1.4.1.1 Bubbling and Jetting Two types of bubble dispersion patterns... 329 9.5 Numerical Solution 331 Reference 332 10 Numerical Modeling of Multiphase Flows in Materials Processing 10.1 Overview 10.2 Control Volume-Based Finite Difference Method 10.2.1 Continuum Mixture... and pipelines are usually poorly wetted by molten metal The variety of multiphase flows encountered in metallurgical processes [1–6] include; gas–liquid, liquid–liquid, gas–solid, solid–liquid, and gas–liquid–solid systems This book focuses on gas–liquid two-phase flows, being the most popular and relevant to current metallurgical processes Due to their complexity, the exact equations governing gas–liquid .