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

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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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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