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<p>The high electrolytic currents in aluminum reduction cells can provoke magnetohydrodynamic wave instabilities in the liquid-liquid cryolite-Al interface. Most critical for the safe operation of aluminum smelters is the metal pad roll (MPR) instability, which can set the interface into self-growing rotational wave motions. Such interface instabilities are commonly averted by keeping the poorly conducting cryolite layer sufficiently thick, but at the detriment of the energy efficiency. Mohammad et al. (in: Eskin (ed) Light Metals 2022. The Minerals, Metals &amp; Materials Series, Springer, Cham, 2022; JOM 74:1908–1915, 2022) have recently demonstrated that the cryolite layer can be markedly reduced when adding an oscillating component to the electrolytic current, inhibiting exponential growth of the MPR instability. We dedicate this paper to the investigation of the underlying physics behind this new suppression technique. We analyze the MPR stability using a simplified mechanical model, which reduces the mathematical problem to a set of two coupled Mathieu’s differential equations. The state of stability is calculated both numerically using Floquet theory and analytically by applying the complexification-averaging method. Our analysis reveals that observed stability patterns can essentially be attributed to a simultaneous occurrence of parametric resonance and anti-resonance. We identify ideal system parameters and show ways to verify the rather exotic phenomenon of parametric anti-resonance in MPR experiments.</p>

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Suppression of magnetohydrodynamic interfacial wave instabilities by means of parametric anti-resonance

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月27日

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  • Gerrit Maik Horstmann,
  • Julia Kuhn,
  • Fadi Dohnal

摘要

The high electrolytic currents in aluminum reduction cells can provoke magnetohydrodynamic wave instabilities in the liquid-liquid cryolite-Al interface. Most critical for the safe operation of aluminum smelters is the metal pad roll (MPR) instability, which can set the interface into self-growing rotational wave motions. Such interface instabilities are commonly averted by keeping the poorly conducting cryolite layer sufficiently thick, but at the detriment of the energy efficiency. Mohammad et al. (in: Eskin (ed) Light Metals 2022. The Minerals, Metals & Materials Series, Springer, Cham, 2022; JOM 74:1908–1915, 2022) have recently demonstrated that the cryolite layer can be markedly reduced when adding an oscillating component to the electrolytic current, inhibiting exponential growth of the MPR instability. We dedicate this paper to the investigation of the underlying physics behind this new suppression technique. We analyze the MPR stability using a simplified mechanical model, which reduces the mathematical problem to a set of two coupled Mathieu’s differential equations. The state of stability is calculated both numerically using Floquet theory and analytically by applying the complexification-averaging method. Our analysis reveals that observed stability patterns can essentially be attributed to a simultaneous occurrence of parametric resonance and anti-resonance. We identify ideal system parameters and show ways to verify the rather exotic phenomenon of parametric anti-resonance in MPR experiments.