Comparative study of finite difference approaches in simulation of magnetohydrodynamic turbulence at low magnetic Reynolds number

Krasnov, Dmitry; Zikanov, Oleg; Boeck, Thomas

doi:10.1016/j.compfluid.2011.06.015

Cited by 79 publications

(77 citation statements)

References 29 publications

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“…The numerical model is based on the explicit projection-type finite difference scheme of second order described as the scheme B in Krasnov et al (2011a). The scheme uses the collocated grid arrangement and follows the principles developed by Morinishi et al (1998) and extended to liquid metal MHD by Ni et al (2007).…”

Section: Physical Model and Numerical Methodsmentioning

confidence: 99%

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Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers

2012

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High-resolution direct numerical simulations are conducted to analyse turbulent states of the flow of an electrically conducting fluid in a duct of square cross-section with electrically insulating walls and imposed transverse magnetic field. The Reynolds number of the flow is 10 5 and the Hartmann number varies from 0 to 400. It is found that there is a broad range of Hartmann numbers in which the flow is neither laminar nor fully turbulent, but has laminar core, Hartmann boundary layers and turbulent zones near the walls parallel to the magnetic field. Analysis of turbulent fluctuations shows that each zone consists of two layers: the boundary layer near the wall characterized by small-scale turbulence and the outer layer dominated by large-scale vortical structures strongly elongated in the direction of the magnetic field. We also find a peculiar scaling of the mean velocity, according to which the reciprocal von Kármán coefficient grows nearly linearly with the distance to the wall.

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Section: Physical Model and Numerical Methodsmentioning

confidence: 99%

“…As a numerical method, we apply the finite difference scheme described by Krasnov, Zikanov & Boeck (2011a). The scheme is based on the conservative discretization of Morinishi et al (1998) extended to the case of MHD flows by Ni et al (2007).…”

Section: Introductionmentioning

confidence: 99%

Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers

2012

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“…For later comparisons with the DNS results, we solve the above model equations (14) to (16) by a finite-difference method on a uniform grid.…”

Section: One-dimensional Approximate Model Of Kamkar and Moffatt (Km82)mentioning

confidence: 99%

Simulation of flux expulsion and associated dynamics in a two-dimensional magnetohydrodynamic channel flow

Bandaru

Pracht²,

Boeck

et al. 2015

Theor. Comput. Fluid Dyn.

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We consider a plane channel flow of an electrically conducting fluid which is driven by a mean pressure gradient in the presence of an applied magnetic field that is streamwise periodic with zero mean. Magnetic flux expulsion and the associated bifurcation in such a configuration is explored using direct numerical simulations (DNS). The structure of the flow and magnetic fields in the Hartmann regime (where the dominant balance is through Lorentz forces) and the Poiseuille regime (where viscous effects play a significant role) are studied and detailed comparisons to the existing one-dimensional model of Kamkar and Moffatt (J. Fluid. Mech., Vol.90, pp [107][108][109][110][111][112][113][114][115][116][117][118][119][120][121][122] 1982) are drawn to evaluate the validity of the model. Comparisons show good agreement of the model with DNS in the Hartmann regime, but significant diferences arising in the Poiseuille regime when non-linear effects become important. The effects of various parameters like the magnetic Reynolds number, imposed field wavenumber etc. on the bifurcation of the flow are studied. Magnetic field line reconnections occuring during the dynamic runaway reveal a specific two-step pattern that leads to the gradual expulsion of flux in the core region.

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“…22 The equations are discretized using a second-order finite difference scheme with a collocated grid arrangement. The formulations proposed by Morinishi et al 26 and Ni et al 28 are incorporated into the code making the numerical scheme highly conservative for mass, momentum, and electric charge.…”

Section: Direct Numerical Simulationsmentioning

confidence: 99%

Interaction of a small permanent magnet with a liquid metal duct flow

Heinicke

Tympel

Pulugundla

et al. 2012

Journal of Applied Physics

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If a permanent magnet is located near a liquid metal flow, the magnet experiences a Lorentz force, which depends on the velocity of the flow. This effect is embodied in a noncontact flow measurement technique called Lorentz force velocimetry (LFV). Although LFV is already under way for global flow measurement in metallurgy, the possibility of using LFV for local velocity measurement has not yet been explored. The present work is devoted to a comprehensive investigation of the Lorentz force acting upon a permanent magnet near a liquid metal flow in a square duct when the size of the magnet is sufficiently small to be influenced by only parts of the fluid flow. We employ a combination of laboratory experiments in the turbulent regime, direct numerical simulations of laminar and turbulent flows using a custom-made code, and Reynolds-averaged Navier-Stokes (RANS) simulations using a commercial code. We address three particular flow regimes, namely the kinematic regime where the back-reaction of the Lorentz force on the flow is negligible, the low-Reynolds number dynamic regime and the high-Reynolds number dynamic regime both being characterized by a significant modification of the flow by the Lorentz force. In all three regimes, the Lorentz force is characterized by a nondimensional electromagnetic drag coefficient CD, which depends on the dimensionless distance between the magnet and the duct h, the dimensionless size of the magnet d, the Reynolds number Re, and the Hartmann number Ha. We demonstrate that in the kinematic regime, CD displays a universal dependence on the distance parameter, expressed by the scaling laws CD ∼ h−2 for h ≪ 1 and CD ∼ h−7 for h ≫ 1. In the dynamic regime at low Re, the magnet acts as a magnetic obstacle and expels streamlines from its immediate vicinity. In the dynamic regime at high Re, we present experimental data on CD(Re) for 500 ≤ Re ≤ 104 and on CD(h) for 0.4 ≤ h ≤ 1 and demonstrate that they are in good agreement with numerical results obtained from RANS simulations for the same range of parameters.

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Comparative study of finite difference approaches in simulation of magnetohydrodynamic turbulence at low magnetic Reynolds number

Cited by 79 publications

References 29 publications

Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers

Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers

Simulation of flux expulsion and associated dynamics in a two-dimensional magnetohydrodynamic channel flow

Interaction of a small permanent magnet with a liquid metal duct flow

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