1. Introduction

The steel production in an integrated mill requires complex operation units and demands a large amount of energy. In the operation units comprising the transformation of the liquid steel

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

into slabs, several aspects of the product quality are assured [1–6]. The security and stability of the operations as well as the productivity with lower defects are the main concern and have driven the new development on this step. Of special interest is to fit the dimensions of the slabs suitable for further hot working processes free of internal and superficial defects. The strict control of these steps is the primary effort to high-quality steel slab. A general schematic overview of the continuous casting facilities including the metal transfer steps is presented in Figure 1. The initial step is the metal transfer from the ladle to the tundish filling the vessel and establishing the synchronised mass flows. The tundish distributor is used to control the feeding rate of the oscillating mould of the continuous casting step using the submerse tune and flowing valve control. The heat transfer and the flowing phenomena within the oscillating mould are key phenomena to attain the adequate microstructure of the solidified steel and keep the safety of the process with the formation of the solidification skin, which plays the major role on the cooling zones for final solidification of centre of the slab.

reached, where the cooling is performed only by radiation. At the end of the vein, the slab is cut and discharged on a rolled table. Due to process complexity, which involves heat transfer coupled with phase transformation and fluid flow, the prediction of process parameters and their optimization is usually performed by using empirical procedures. However, the development of efficient numerical techniques and the availability of fast and low-cost computers has bust recently the simulation of real operational conditions [8–13]. To date, it is possible to investigate virtually the manufacturing of several kinds of steels aiming low cost and high material efficiency. Several works in the literature have been reported to analyse the metal behaviour within the oscillating mould of the caster machine due to its importance on the productivity and on the product final quality [4–15]. The oscillating mould is an important component of the caster machine and has strong influence on surface defects and on the temperature distribution inside the mould [2–8]. The heat transfer analysis during solidification is traditionally performed by analytical and numerical methods. Although analytical methods are more elegant, they require a series of assumptions that usually lead to a considerable simplification of the physical phenomena producing unrealistic or limited solutions. Considering numerical methods, four techniques are commonly used: finite differences [7–11], finite elements [12–15], finite volumes [16] and boundary elements [17]. These methods are able to solve the energy, the mass, species and momentum equations. In order to improve scientific calculation performance, continuous changes have been arisen in computational platform paradigm. In the past, the scientific simulation was normally performed in shared memory large computers or in common sequential computers [18]. The fast rate of development in processor technology and the commercial availability of inexpensive powerful personal computers have created a perfect scenario to build up cluster of personal computers as an alternative to the larger and more expensive ones [19]. As consequence of low price, easy maintenance and powerful processors, these so-called Beowulf clusters are becoming popular among scientific computational groups. This architecture offers collective memory to solve scientific complex problems [17, 21]. Although the rise of distributed computer platforms was only an alternative for high-cost supercomputer solutions, they changed profoundly the rule of code development, which now needs to encompass distributed machines [18, 19]. Distributed platforms are suitable for problems in which domain can be split up into small subdomains containing common boundaries. Most CFD codes demand high amount of memory, which is normally available in distributed memory architecture [17, 18]. However, for accuracy and consistency reasons, a parallel implementation needs to interchange information with subdomain boundaries. This synchronisation scheme leads to an increase in the data transfer time due to the existence of a synchronisation elapsed time [17–21]. The communication among computers is carried out by using libraries of Message Passing Interface (MPI) [25]. The library Message Passing Interface (MPI) has largely been used in its freeware version called MPICH [17–21]. In this context, this work newly presents a multidomain parallel numerical model able to simulate the continuous casting of steel. The main objective is to demonstrate the validity of the model and point out the improvement in calculation speedup by developing a code based on multidomain parallel MPI compared to a serial and to a simple MPI parallel code. All the computer codes used in this study are homemade ones, which were

Numerical Study of Turbulent Flows and Heat Transfer in Coupled Industrial-Scale Tundish of a Continuous…

http://dx.doi.org/10.5772/intechopen.75935

291

developed and tested by the authors.

The synchronised control of the cooling rate along the mould, bender, speed, and radiation regions is the key for a successful operation of the entire system. In order to improve the process safety, control and productivity comprehensive mathematical models have been developed separately for the tundish and continuous casting processes [1, 4]. Progress in computational simulation has provided tools to help to comprehend the processes. Consequently, several investigations of the parameters which affect the performance under safety operation conditions were driven [3–7]. The tundish operation is carried out in order to assure the compositional and thermal homogeneity of the liquid with low level of impurities and inclusions. The caster machine is designed to promote continuous solidification of liquid metal fed by a tundish through a submerse valve. In the mould region, a strong heat flux is imposed, and a thick solid shell is formed. Water cooling is continuously applied until a secondary region is

Figure 1. Schematic view of coupling of ladle feeding, tundish and continuous casting process and facilities.

into slabs, several aspects of the product quality are assured [1–6]. The security and stability of the operations as well as the productivity with lower defects are the main concern and have driven the new development on this step. Of special interest is to fit the dimensions of the slabs suitable for further hot working processes free of internal and superficial defects. The strict control of these steps is the primary effort to high-quality steel slab. A general schematic overview of the continuous casting facilities including the metal transfer steps is presented in Figure 1. The initial step is the metal transfer from the ladle to the tundish filling the vessel and establishing the synchronised mass flows. The tundish distributor is used to control the feeding rate of the oscillating mould of the continuous casting step using the submerse tune and flowing valve control. The heat transfer and the flowing phenomena within the oscillating mould are key phenomena to attain the adequate microstructure of the solidified steel and keep the safety of the process with the formation of the solidification skin, which plays the

The synchronised control of the cooling rate along the mould, bender, speed, and radiation regions is the key for a successful operation of the entire system. In order to improve the process safety, control and productivity comprehensive mathematical models have been developed separately for the tundish and continuous casting processes [1, 4]. Progress in computational simulation has provided tools to help to comprehend the processes. Consequently, several investigations of the parameters which affect the performance under safety operation conditions were driven [3–7]. The tundish operation is carried out in order to assure the compositional and thermal homogeneity of the liquid with low level of impurities and inclusions. The caster machine is designed to promote continuous solidification of liquid metal fed by a tundish through a submerse valve. In the mould region, a strong heat flux is imposed, and a thick solid shell is formed. Water cooling is continuously applied until a secondary region is

Figure 1. Schematic view of coupling of ladle feeding, tundish and continuous casting process and facilities.

major role on the cooling zones for final solidification of centre of the slab.

290 Numerical Simulations in Engineering and Science

reached, where the cooling is performed only by radiation. At the end of the vein, the slab is cut and discharged on a rolled table. Due to process complexity, which involves heat transfer coupled with phase transformation and fluid flow, the prediction of process parameters and their optimization is usually performed by using empirical procedures. However, the development of efficient numerical techniques and the availability of fast and low-cost computers has bust recently the simulation of real operational conditions [8–13]. To date, it is possible to investigate virtually the manufacturing of several kinds of steels aiming low cost and high material efficiency. Several works in the literature have been reported to analyse the metal behaviour within the oscillating mould of the caster machine due to its importance on the productivity and on the product final quality [4–15]. The oscillating mould is an important component of the caster machine and has strong influence on surface defects and on the temperature distribution inside the mould [2–8]. The heat transfer analysis during solidification is traditionally performed by analytical and numerical methods. Although analytical methods are more elegant, they require a series of assumptions that usually lead to a considerable simplification of the physical phenomena producing unrealistic or limited solutions. Considering numerical methods, four techniques are commonly used: finite differences [7–11], finite elements [12–15], finite volumes [16] and boundary elements [17]. These methods are able to solve the energy, the mass, species and momentum equations. In order to improve scientific calculation performance, continuous changes have been arisen in computational platform paradigm. In the past, the scientific simulation was normally performed in shared memory large computers or in common sequential computers [18]. The fast rate of development in processor technology and the commercial availability of inexpensive powerful personal computers have created a perfect scenario to build up cluster of personal computers as an alternative to the larger and more expensive ones [19]. As consequence of low price, easy maintenance and powerful processors, these so-called Beowulf clusters are becoming popular among scientific computational groups. This architecture offers collective memory to solve scientific complex problems [17, 21]. Although the rise of distributed computer platforms was only an alternative for high-cost supercomputer solutions, they changed profoundly the rule of code development, which now needs to encompass distributed machines [18, 19]. Distributed platforms are suitable for problems in which domain can be split up into small subdomains containing common boundaries. Most CFD codes demand high amount of memory, which is normally available in distributed memory architecture [17, 18]. However, for accuracy and consistency reasons, a parallel implementation needs to interchange information with subdomain boundaries. This synchronisation scheme leads to an increase in the data transfer time due to the existence of a synchronisation elapsed time [17–21]. The communication among computers is carried out by using libraries of Message Passing Interface (MPI) [25]. The library Message Passing Interface (MPI) has largely been used in its freeware version called MPICH [17–21]. In this context, this work newly presents a multidomain parallel numerical model able to simulate the continuous casting of steel. The main objective is to demonstrate the validity of the model and point out the improvement in calculation speedup by developing a code based on multidomain parallel MPI compared to a serial and to a simple MPI parallel code. All the computer codes used in this study are homemade ones, which were developed and tested by the authors.
