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Research Papers: Flows in Complex Systems

Modified Shallow Water Equations With Application for Horizontal Centrifugal Casting of Rolls

[+] Author and Article Information
Abdellah Kharicha

Department of Metallurgy,
University of Leoben,
Franz Josef-Strasse 18,
Leoben 8700, Austria
e-mail: abdellah.kharicha@unileoben.ac.at

Jan Bohacek

Department of Metallurgy,
University of Leoben,
Franz Josef-Strasse 18,
Leoben 8700, Austria
e-mail: jan.bohacek@unileoben.ac.at

Andreas Ludwig

Professor
Department of Metallurgy,
University of Leoben,
Franz Josef-Strasse 18,
Leoben 8700, Austria
e-mail: andreas.ludwig@unileoben.ac.at

Menghuai Wu

Laboratory for Advanced Simulation
of Solidification and Melting
Department of Metallurgy,
University of Leoben,
Franz Josef-Strasse 18,
Leoben 8700, Austria
e-mail: menghuai.wu@unileoben.ac.at

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 24, 2014; final manuscript received May 28, 2015; published online July 21, 2015. Assoc. Editor: Samuel Paolucci.

J. Fluids Eng 137(11), 111105 (Jul 21, 2015) Paper No: FE-14-1091; doi: 10.1115/1.4030760 History: Received February 24, 2014

A numerical model based on the shallow water equations (SWE) was proposed to simulate the two-dimensional (2D) average flow dynamics of the liquid metal spreading inside a horizontally rotating mold. The SWE were modified to account for the forces, such as the centrifugal force, Coriolis force, shear force with the mold wall, and gravity. In addition, inherent vibrations caused by a poor roundness of the mold and the mold deformation due to temperature gradients were applied explicitly by perturbing the gravity and the axis bending, respectively. Several cases were studied with the following initial conditions: a constant average height of the liquid metal (5, 10, 20, 30, and 40 mm) patched as a flat or a perturbed surface. The angular frequency Ω of the mold (∅1150–3200) was 71.2 (or 30) rad/s. Results showed various wave patterns propagating on the free surface. In early stages, a single longitudinal wave moved around the circumference. As the time proceeded, it slowly diminished and waves traveled mainly in the axial direction. It was found that the mean amplitude of the oscillations grows with the increasing liquid height.

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References

Shailesh, P. , Kumar, B. P. , Sundarrajan, S. , and Komariahia, M. , 2012, “Experimental Investigation on Centrifugal Casting of 5500 Alloy: A Taguchi Approach,” Sci. Res. Essays, 7(44), pp. 3797–3808.
Chirita, G. , Stefanuscu, I. , Barbosa, J. , Puga, H. , Soares, D. , and Silva, F. S. , 2009, “On Assessment of Processing Variables in Vertical Centrifugal Casting Technique,” Int. J. Cast Met. Res., 22(5), pp. 382–389. [CrossRef]
Chirita, G. , Stefanuscu, I. , Soares, D. , and Silva, F. S. , 2006, “Centrifugal Versus Gravity Casting Techniques Over Mechanical Properties,” An. Mec. Fractura, 1, pp. 317–322.
Chang, S. R. , Kim, J. M. , and Hong, C. P. , 2001, “Numerical Simulation of Microstructure Evolution of Al Alloys in Centrifugal Casting,” ISIJ Int., 41(7), pp. 738–747. [CrossRef]
Hirt, C. W. , and Nichols, B. D. , 1981, “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” J. Computat. Phys., 39(1), pp. 201–225. [CrossRef]
Keerthiprasad, K. S. , Murali, M. S. , Mukunda, P. G. , and Majumdar, S. , 2010, “Numerical Simulation and Cold Modeling Experiments on Centrifugal Casting,” Metall. Mater. Trans. B, 42(1), pp. 144–155. [CrossRef]
Zagorski, R. , and Sleziona, J. , 2007, “Pouring Mold During Centrifugal Casting Process,” Arch. Mater. Sci. Eng., 28(7), pp. 441–444.
Kaschnitz, E. , 2012, “Numerical Simulation of Centrifugal Casting of Pipes,” IOP Conf. Ser.: Mater. Sci. Eng., 33(1), p. 012031. [CrossRef]
Daming, X. , Limin, J. , and Hengzhi, F. , 2008, “Effects of Centrifugal and Coriolis Forces on the Mold-Filling Behavior of Titanium Melts in Vertically Rotating Molds,” China Foundry, 5(4), pp. 249–257.
Xu, Z. , Song, N. , Tol, R. V. , Luan, Y. , and Li, D. , 2012, “Modelling of Horizontal Centrifugal Casting of Work Roll,” IOP Conf. Ser.: Mater. Sci. Eng., 33(1), p. 012030. [CrossRef]
Fjeld, A. , and Ludwig, A. , 2009, “Flow Patterns and Re-Melting During the Filling of a Large Composite Casting,” Int. J. Cast Met. Res., 22(1–4), pp. 111–114. [CrossRef]
Ludwig, A. , Kharicha, A. , and Wu, M. , 2014, “Modeling of Multiscale and Multiphase Phenomena in Materials Processing,” Metall. Mater. Trans. B, 45(1), pp. 36–43. [CrossRef]
Leveque, R. J. , 2002, Finite Volume Methods for Hyperbolic Systems, Cambridge University Press, New York.
Dellar, P. J. , and Salmon, R. , 2005, “Shallow Water Equations With a Complete Coriolis Force and Topography,” Phys. Fluids, 17(10), pp. 1–23. [CrossRef]
Hirt, C. W. , and Richardson, J. E. , 1999, “The Modeling of Shallow Flows,” Flow Sci. Tech. Notes, 48, pp. 1–14.
Lanser, D. , Blom, J. G. , and Verwer, J. G. , 2001, “Time Integration of the Shallow Water Equations in Spherical Geometry,” Modell. Anal. Simul., 171(1), pp. 373–393.
Audusse, E. , Bouchut, F. , Bristeau, M.-O. , Klein, R. , and Perthame, B. , 2004, “A Fast and Stable Well-Balanced Scheme With Hydrostatic Reconstruction for Shallow Water Flows,” SIAM J. Sci. Comput., 25(6), pp. 2050–2065. [CrossRef]
Martinez, G. , Garnier, M. , and Durand, F. , 1987, “Stirring Phenomena in Centrifugal Casting of Pipes,” Appl. Sci. Res., 44(1–2), pp. 225–239. [CrossRef]
Love, A. E. H. , 1888, “The Small Free Vibrations and Deformations of a Thin Elastic Shell,” Philos. Transl. R. Soc. London, Ser. A, 179, pp. 491–546. [CrossRef]
Donnell, L. H. , 1935, “Stability of Thin-Walled Tubes Under Torsion,” N.A.C.A. Report No. 479.
Li, H. , Lam, K.-Y. , and Ng, T.-Y. , 2005, Rotating Shell Dynamics, Elsevier, London.
Bryan, G. H. , 1890, “On the Beats in the Vibration of Revolving Cylinder or Bell,” Proc. Cambridge Philos. Soc., 7(3), pp. 101–111.
Casulli, V. , 1999, “A Semi-Implicit Finite Difference Method for Non-Hydrostatic, Free-Surface Flows,” Int. J. Numer. Methods Fluids, 30(4), pp. 425–440. [CrossRef]
Osher, S. , and Sethian, J. A. , 1988, “Fronts Propagating With Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations,” J. Comput. Phys., 79(1), pp. 12–49. [CrossRef]

Figures

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Fig. 1

A schematic of the horizontal centrifugal casting of the outer shell of a work roll

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Fig. 2

A schematic of a part of the HSC section

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Fig. 3

A schematic of the computational domain created by unfolding the internal cylindrical surface of the mold into the plane (x, y)

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Fig. 4

Mode shapes of a vibrating cylindrical shell: (a) axial mode shapes and (b) circumferential mode shapes

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Fig. 5

A frequency spectrum of the horizontally accelerating carrying roller perpendicular to the mold axis

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Fig. 6

An instantaneous shape of the free surface at 4 s for N8 and N12, respectively. (a) A constant liquid height h along the axial direction. (b) An influence of the axis bending on the longitudinal wave formed during the early stage of the simulation.

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Fig. 7

A fully developed pattern at 100 s for N8 and N12, respectively. (a) A pattern resembling annular waves and (b) A pattern disrupted by the presence of the axis bending.

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Fig. 8

An evolution of the mean amplitude of the free surface for Ω = 71.2 rad/s

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Fig. 9

An evolution of the mean amplitude of the free surface for Ω = 30 rad/s

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Fig. 10

A verification of the SWE model; a comparison with the hydrostatic free-surface model by Casulli [23]

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Fig. 11

Schematic of vectors

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