We consider the flow of an electrically conducting fluid in a duct in the presence of a constant magnetic field perpendicular to the flow. The technologically relevant approximation of small magnetic Reynolds number is adopted. The focus of investigation is on the nonlinear mechanism of transition consisting of transient growth and subsequent breakdown of finite amplitude perturbations. Numerical analysis demonstrates that the strongest growth is experienced by perturbations localized in the sidewall boundary layers parallel to the imposed magnetic field. This result and the direct numerical simulations of the transition process indicate that the commonly accepted picture of the transition in MHD duct based on the numerical and theoretical analysis of the flow in the Hartmann channel is misleading. The flow may become turbulent within the sidewall layers long before the Hartmann layers on the walls perpendicular to the magnetic field are able to sustain nonlinear transition.
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ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels
August 1–5, 2010
Montreal, Quebec, Canada
Conference Sponsors:
- Fluids Engineering Division
ISBN:
978-0-7918-4948-4
PROCEEDINGS PAPER
Optimal Growth and Transition to Turbulence in Magnetohydrodynamic Duct Flow
Dmitry Krasnov,
Dmitry Krasnov
Ilmenau University of Technology, Ilmenau, Germany
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Oleg Zikanov,
Oleg Zikanov
University of Michigan - Dearborn, Dearborn, MI
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Maurice Rossi,
Maurice Rossi
Universite Pierre et Marie Curie, Paris, France
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Thomas Boeck
Thomas Boeck
Ilmenau University of Technology, Ilmenau, Germany
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Dmitry Krasnov
Ilmenau University of Technology, Ilmenau, Germany
Oleg Zikanov
University of Michigan - Dearborn, Dearborn, MI
Maurice Rossi
Universite Pierre et Marie Curie, Paris, France
Thomas Boeck
Ilmenau University of Technology, Ilmenau, Germany
Paper No:
FEDSM-ICNMM2010-30219, pp. 1153-1159; 7 pages
Published Online:
March 1, 2011
Citation
Krasnov, D, Zikanov, O, Rossi, M, & Boeck, T. "Optimal Growth and Transition to Turbulence in Magnetohydrodynamic Duct Flow." Proceedings of the ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting: Volume 1, Symposia – Parts A, B, and C. Montreal, Quebec, Canada. August 1–5, 2010. pp. 1153-1159. ASME. https://doi.org/10.1115/FEDSM-ICNMM2010-30219
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