A direct-numerical-simulation-based second-moment closure for turbulent magnetohydrodynamic flows

Kenjereš, Saša; Hanjalić, K.; Bal, Dharmendra Kumar

doi:10.1063/1.1649335

Cited by 34 publications

(21 citation statements)

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“…Finally, slow, rapid, and electromagnetic parts of the pressure-strain correlation are modeled as are the magnetic turbulent kinetic-energy production, the anisotropy, the mean rate of strain, and the mean vorticity tensors, respectively. This final version of the model is essentially a combination of the Speziale et al 48 second-moment closure with MHD extensions proposed by Kenjereš et al 46 Finally, all model coefficients are given in Table I.…”

Section: ͑A6͒mentioning

confidence: 99%

“…The additional source/sink terms in the u i u j and equations, S ij M and S M , respectively, representing effects of the fluctuating Lorentz force on turbulence, must be included, according to Kenjereš and Hanjalić 42,45 ͑see, also, Hanjalić and Kenjereš 43,44,47 ͒. The redistributive terms ͑⌽ ij ͒, the slow ͑⌽ ij S ͒ and rapid contributions͑⌽ ij R ͒ are modeled using the model of Speziale et al 48 ͑RSM_SSG͒, extended to account for the magnetic effect by an additional rapid term ͑⌽ ij M ͒ proposed by Kenjereš et al 46 In this study, we adopted a new extended variant of the previously proposed MHD Reynolds stress model of Kenjereš et al, 46 where the MHD terms have been added to the linear version of the pressure-strain correlation together with the wall-reflection terms according to Gibson and Launder. 49 The choice of the Speziale et al 48 model is primarily motivated by its ability to reasonably reproduce the near-wall stress anisotropy without introducing any special wall-reflection term.…”

Section: ͑3͒mentioning

confidence: 99%

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Coupled fluid-flow and magnetic-field simulation of the Riga dynamo experiment

et al. 2006

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Magnetic fields of planets, stars, and galaxies result from self-excitation in moving electroconducting fluids, also known as the dynamo effect. This phenomenon was recently experimentally confirmed in the Riga dynamo experiment ͓A. Gailitis et al., Phys. Rev. Lett. 84, 4365 ͑2000͒; A. Gailitis et al., Physics of Plasmas 11, 2838 ͑2004͔͒, consisting of a helical motion of sodium in a long pipe followed by a straight backflow in a surrounding annular passage, which provided adequate conditions for magnetic-field self-excitation. In this paper, a first attempt to simulate computationally the Riga experiment is reported. The velocity and turbulence fields are modeled by a finite-volume Navier-Stokes solver using a Reynolds-averaged-Navier-Stokes turbulence model. The magnetic field is computed by an Adams-Bashforth finite-difference solver. The coupling of the two computational codes, although performed sequentially, provides an improved understanding of the interaction between the fluid velocity and magnetic fields in the saturation regime of the Riga dynamo experiment under realistic working conditions.

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confidence: 99%

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confidence: 99%

Coupled fluid-flow and magnetic-field simulation of the Riga dynamo experiment

et al. 2006

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“…In the RANS approach, the instantaneous fields are decomposed into their time-or ensemble-averaged values and the fluctuations, i.e., U i U i u i , B i B i b i . As a result of this averaging, additional unknown correlations appear, u i u j , b i b j , u i b j , etc., [15][16][17][18][19]. In order to close this system, additional equations for these correlations must be introduced, what constitutes a turbulence closure model.…”

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confidence: 99%

“…In order to close this system, additional equations for these correlations must be introduced, what constitutes a turbulence closure model. The starting point in our analysis is the second-moment (Reynolds stress) u i u j ÿ " model with the newly included additional MHD effects (the source/sink and the redistributive terms are taken into account), [17], which was validated in a range of generic situations for 5 10 3 Re 10 5 and 0 Ha 1000-where Ha B 0 L = p is Hartmann number) showing in all cases good agreement with the available experiments, DNS and large eddy simulations (LES) studies, [17]. For the high Re Riga-dynamo with the specific solid-body-like strong initial swirl, we opted for a simplified model and solved the transport equation for the turbulence kinetic energy k 0:5u i u i instead of for all six turbulent-stress components u i u j .…”

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Numerical Simulation of a Turbulent Magnetic Dynamo

Kenjereš

Hanjalić

2007

Phys. Rev. Lett.

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We present numerical simulations of a turbulent magnetic dynamo mimicking closely the Riga-dynamo experiment at Re 3:5 10 6 and 15 Re m 20. The Reynolds-averaged Navier-Stokes equations for the fluid flow and turbulence field are solved simultaneously with the direct numerical solution of the magnetic field equations. The fully integrated two-way-coupled simulations reproduced all features of the magnetic self-excitation detected by the Riga experiment, with frequencies and amplitudes of the selfgenerated magnetic field in good agreement with the experimental records, and provided full insight into the unsteady magnetic and velocity fields and the mechanisms of the dynamo action. DOI: 10.1103/PhysRevLett.98.104501 PACS numbers: 47.11.ÿj, 47.27.Eÿ, 47.65.ÿd, 91.25.Cw Complex interactions between turbulent flow of electrically conductive fluids and electromagnetic fields play the key role in many physical phenomena in nature and technology. Of particular interest is the conversion of the mechanical energy of a moving electrically conductive medium into the magnetic energy, known as the magnetic dynamo. It is believed that the magnetic dynamo effects are responsible for the creation of magnetic fields in spiral galaxies, stars, and planets (including Earth's magnetic field), e.g., [1]. In order to create the favorable conditions for possible self-excitation of a magnetic field, it is necessary to achieve regimes where stretching of the magnetic field will overcome its resistive damping. This condition is defined by the critical magnetic Reynolds number Re m UL= > 1 (where U and L are typical velocity and length scale, respectively, and is magnetic diffusivity). In order to reach such conditions, one needs relatively large length scales and high velocities -even for the best electrically conductive fluids (e.g., liquid sodium, 1= 0 0:1 m 2 =s), where 0 and are the magnetic permeability and electric conductivity. For such configurations, the hydrodynamical Reynolds number (Re UL= ) will be also very high (Re 10 5 -10 6 ), making the flow highly turbulent. Experimental studies of magnetic fluid dynamos face many practical problems associated with large dimensions of setups and potentially hazardous working fluids (sodium). This explains why it was not until late 1999 when two experimental groups in Riga ([2 -6]) and Karlsruhe ([7-9]) finally and independently succeeded in detecting the self-excitation and subsequent sustenance of a magnetic field for the very first time. Although this is an important step towards understanding and explaining the Earth's magnetic field from the magnetic dynamo effect, both experiments were not designed to actually mimic the Geo-Dynamo (Earth-like) conditions, but rather to provide experimental proof of the magnetic field self-amplification.Despite their remarkable success, the experimental studies provided only the time records of the magnetic field components at particular locations -so information addressing the detailed spatial distribution of the magnetic field and its dynamics...

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“…(1)- (4) is performed by using a finite-volume solver for general (non-orthogonal) structured multi-block geometries, Kenjereš and Hanjalić [20,23,24,27,28], Kenjereš et al [26]. All variables are located in the centres of control volumes (CVs) and the Rhie-Chow interpolation [35] and SIMPLE algorithm are used for coupling between velocity and pressure fields.…”

Section: Methodsmentioning

confidence: 99%

Large eddy simulations of targeted electromagnetic control of buoyancy-driven turbulent flow in a slender enclosure

Kenjereš

2009

Theor. Comput. Fluid Dyn.

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We conducted a large eddy simulation (LES) of a locally applied electromagnetic control of turbulent thermal convection of an electrically conductive fluid (electrolyte solution) inside of a slender enclosure. Generic configurations, consisting of two or three magnets of opposite polarities located below the lower wall, and two oppositely charged electrodes along the side walls, are considered. The neutral situation (pure thermal convection) is selected to be in turbulent regime at Ra = 10 7 , Pr = 7. A magnetically extended Smagorinsky type model for the subgrid turbulent stresses and a simple-gradient diffusion model for the subgrid turbulent heat fluxes are used. Different intensities of applied DC current through electrodes are imposed. The effects of the resulting Lorentz force on flow, turbulence reorganisation and wall-heat transfer are analysed. It is demonstrated that significant flow and turbulence structure reorganisation takes place in the proximity of the lower horizontal wall and in the central parts of the enclosure-even for weak DC current of I = 1 A. Significant turbulence increase, generated by the elevated electromagnetic mixing, produced significant enhancements of the wall-heat transfer-up to 70% for the 2-magnet configuration.

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A direct-numerical-simulation-based second-moment closure for turbulent magnetohydrodynamic flows

Cited by 34 publications

References 21 publications

Coupled fluid-flow and magnetic-field simulation of the Riga dynamo experiment

Coupled fluid-flow and magnetic-field simulation of the Riga dynamo experiment

Numerical Simulation of a Turbulent Magnetic Dynamo

Large eddy simulations of targeted electromagnetic control of buoyancy-driven turbulent flow in a slender enclosure

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