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This study attempts to characterize the variation of pressure loss and the evolution of vortex structures in the steady three-dimensional flow around a 180° sharp bend under a transverse magnetic field. This study is conducted with the Reynolds number, 100 ≤ R e ≤ 400 , and Hartmann number, 0 ≤ H a ≤ 2000. This range of Re and Ha captures both complex three-dimensional structures and the inception of quasi-two-dimensional flows. Numerical simulations display how the pressure loss across the bend region (Δ p 0 ) and the vortex structures undergo four regimes by increasing Ha for fixed Re. These regimes are referred to as regimes I–IV. N 1 c , N 2 c , and N 3 c , the critical values of interaction number Nc for the first appearance of regimes II–IV, are recognized at values 0.8, 3.2, and 40, respectively. In regime I (N ≤ 0.8), Δ p 0 increases slightly and the magnetohydrodynamic flow promotes the recirculating bubble. In regime II (0.8 < N ≤ 3.2), as Δ p 0 decreases, the scope of the recirculating bubble reaches its peak. In regime III (3.2 < N ≤ 40), Δ p 0 grows, while the shrinkage of the recirculating bubble is triggered. Simultaneously, the flow tends to be two-dimensional [J. Sommeria and R. Moreau, "Why, how, and when, MHD turbulence becomes two-dimensional," J. Fluid Mech. 118, 507 (1982)]. In regime IV (40 < N), Δ p 0 is linearly dependent on Ha/Re. The non-monotonic behavior of the recirculating bubble length is caused by the redistribution of momentum at low Ha and by the predominant effect of the Lorentz force at large Ha. The law of how to distinguish the three-dimensional (3D) flow and quasi-two-dimensional (Q2D) flow is discovered by assessing the recirculating bubble length in the center plane. [ABSTRACT FROM AUTHOR]

The work aims to study the convection and diffusion of metallic fluid and the tritium in a cavity under the external magnetic field. The solver based on the finite volume method and the consistent and conservative scheme is developed to solve the Navier–Stokes equation considering the Lorentz force, concentration, and thermal buoyancy. The coupling effects of the magnetic field, the internal volumetric heat source, and the concentration difference between the left and right walls of the cavity are investigated. It is found that both the rotation direction and strength of the main circulation flow are controlled by the concentration buoyancy and the thermal buoyancy only regulates the global flow in the cavity. A larger concentration difference or a stronger internal heat source can lead to unstable flow. However, the stronger magnetic field suppresses the main circulation flow and small secondary vortices. The power law scaling of the Sherwood number vs the ratio of the Rayleigh number of the concentration to the Hartman number based on the force balance agrees with the numerical simulation. Four types of flow modes (large-amplitude low-frequency, large-amplitude high-frequency, small-amplitude low-frequency, and stable modes) are observed under the coupled multi-physics fields of the magnetic field, concentration difference, and heat source. The correlation function describing the influence of magnetic field and concentration strength on mass transfer is concluded. [ABSTRACT FROM AUTHOR]

The flow of liquid metal over a backward-facing step (BFS) exhibits unique flow characteristics due to the influence of strong magnetic field. In this study, direct numerical simulation of the BFS flow under a strong magnetic field is conducted based on a quasi-two-dimensional model (with a large interaction number, N ≫ 1 , and a large Hartmann number, H a ≫ 1). The Reynolds number (Re), Hartmann number (Ha), and expansion ratio (ER) are investigated within the ranges of [ 100 − 80 000 ] , [ 100 − 40 000 ] , and [ 1.67 − 5 ] , respectively. Three typical flow regimes are defined based on the evolution of the free shear layer vortices and the separation state of the boundary layer. Furthermore, a comprehensive flow regime map is presented for different ER, revealing a positive correlation between the critical Reynolds number (R e c 1 ) and Ha at the onset of instability. Specifically, R e c 1 is proportional to H a 0.5 , H a 0.54 , and H a 0.56 for ER = 5, 2.5, and 1.67, respectively. Moreover, the maximum relative thickness of the free shear layer at H a c 1 appears in the range of approximately 0.7 – 0.78 L r for ER = 5, while for ER = 2.5, it appears in the range of approximately 0.80 – 0.85 L r , indicating that the instability position of the free shear layer occurs earlier for large ER. Our numerical investigation also demonstrates that an increase in the transverse magnetic field compresses the free shear layer and delays the process of vortex pairing, thereby suppressing the oscillatory behavior of the shear layer. [ABSTRACT FROM AUTHOR]

This work is dedicated to understand the magnetohydrodynamic (MHD) flow around two identical tandem circular cylinders confined in a duct under external axial magnetic field. The influences of magnetic field (represented by the Hartmann number Ha), inlet velocity of conducting fluid (represented by the Reynolds number Re), and the gap ratio (L/d, the ratio of the distance between the centers of two cylinders to the diameter of the circular cylinder) on the flow regimes, vortex shedding frequency, pressure coefficients, drag coefficients, and pressure drop are investigated. The simulations are conducted in the parameter ranges 2 ≤ L / d ≤ 8 , 180 ≤ R e ≤ 1440 , and 101 ≤ H a ≤ 1818 , respectively. Four flow modes are observed, namely, no vortex shedding, single body, reattachment regime, and vortex shedding (VS) modes, with various H a / R e 2 and L/d values. For L / d > 5 , the flow field presents the VS flow model, a vortex street with synchronous periodic shedding appears behind the two cylinders, and the vortex shedding frequency matches well with that of the single one. The pressure coefficient shows different tendencies because of the arrangement of two circular cylinders. It can be found that the mean drag coefficients for the upstream circular cylinder and the downstream circular cylinder vary with R e / H a 0.8 . For R e = 361 , H a = 504 and R e = 722 , H a = 1212 , the flow field remains almost unchanged, which implies the balance between inertial force and Lorentz force because the inertial force would promote the flow, while the electromagnetic force leads to the reverse effect. Furthermore, the effects of magnetic field and inlet velocity of metal fluid on pressure drop Δ P between inlet and outlet can be fitted as a linear relation Δ P ∼ ReHa. [ABSTRACT FROM AUTHOR]

Abstract: The consistent and conservative scheme developed on a rectangular collocated mesh [M.-J. Ni, R. Munipalli, N.B. Morley, P. Huang, M.A. Abdou, A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I: on a rectangular collocated grid system, Journal of Computational Physics 227 (2007) 174–204] and on an arbitrary collocated mesh [M.-J. Ni, R. Munipalli, P. Huang, N.B. Morley, M.A. Abdou, A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part II: on an arbitrary collocated mesh, Journal of Computational Physics 227 (2007) 205–228] has been extended and specially designed for calculation of the Lorentz force on a staggered grid system (Part III) by solving the electrical potential equation for magnetohydrodynamics (MHD) at a low magnetic Reynolds number. In a staggered mesh, pressure (p) and electrical potential (φ) are located in the cell center, while velocities and current fluxes are located on the cell faces of a main control volume. The scheme numerically meets the physical conservation laws, charge conservation law and momentum conservation law. Physically, the Lorentz force conserves the momentum when the magnetic field is constant or spatial coordinate independent. The calculation of current density fluxes on cell faces is conducted using a scheme consistent with the discretization for solution of the electrical potential Poisson equation, which can ensure the calculated current density conserves the charge. A divergence formula of the Lorentz force is used to calculate the Lorentz force at the cell center of a main control volume, which can numerically conserve the momentum at constant or spatial coordinate independent magnetic field. The calculated cell-center Lorentz forces are then interpolated to the cell faces, which are used to obtain the corresponding velocity fluxes by solving the momentum equations. The “conservative” is an important property of the scheme, which can guarantee computational accuracy of MHD flows at high Hartmann number with a strongly non-uniform mesh employed to resolve the Hartmann layers and side layers. 2D fully developed MHD flows with analytical solutions available have been conducted to validate the scheme at a staggered mesh. 3D MHD flows, with the experimental data available, at a constant magnetic field in a rectangular duct with sudden expansion and at a varying magnetic field in a rectangular duct are conducted on a staggered mesh to verify the computational accuracy of the scheme. It is expected that the scheme for the Lorentz force can be employed together with a fully conservative scheme for the convective term and the pressure term [Y. Morinishi, T.S. Lund, O.V. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, Journal of Computational Physics 143 (1998) 90–124] for direct simulation of MHD turbulence and MHD instability with good accuracy at a staggered mesh. [Copyright &y& Elsevier]

Abstract: A conservative formulation of the Lorentz force is given here for magnetohydrodynamic (MHD) flows at a low magnetic Reynolds number with the current density calculated based on Ohm’s law and the electrical potential formula. This conservative formula shows that the total momentum contributed from the Lorentz force is conservative when the applied magnetic field is constant. For the case with a non-constant applied magnetic field, the Lorentz force has been divided into two parts: a strong globally conservative part and a weak locally conservative part. The conservative formula has been employed to develop a conservative scheme for the calculation of the Lorentz force on an unstructured collocated mesh. Only the current density fluxes on the cell faces, which are calculated using a consistent scheme with good conservation, are needed for the calculation of the Lorentz force. Meanwhile, a conservative interpolation technique is designed to get the current density at the cell center from the current density fluxes on the cell faces. This conservative interpolation can keep the current density at the cell center conservative, which can be used to calculate the Lorentz force at the cell center with good accuracy. The Lorentz force calculated from the conservative current at the cell center is equivalent to the Lorentz force from the conservative formula when the applied magnetic field is constant, which can conserve the total momentum. We will further prove that the simple interpolation scheme used in the Part I [M.-J. Ni, R. Munipalli, N.B. Morley, P.Y. Huang, M. Abdou, A current density conservative scheme for MHD flows at a low magnetic Reynolds number. Part I. On a rectangular collocated grid system, Journal of Computational Physics, in press, doi:10.1016/j.jcp.2007.07.025] of this series of papers is conservative on a rectangular grid and can keep the total momentum conservative in a rectangular grid. [Copyright &y& Elsevier]

We report a liquid metal droplet impacting onto a cold substrate under the influence of vertical magnetic field numerically. During the impacting dynamics, the spreading and the solidification of the droplet are seriously influenced by the magnetohydrodynamic effects. The numerical methodology is implemented by coupling the volume of fluid method and the implicit enthalpy approach, the former is used to track the liquid/solid–gas interface, while the latter is employed to simulate the solidification process. At first, the numerical method is validated against a series of benchmark problems. Then, by varying the impacting velocities, the thermal contact resistance and the magnetic strengths, the variations of the maximum spreading diameter against different dimensionless parameters are reported. An interpolation scheme between the impacting effect, the thermal effect, and the magnetohydrodynamic effect is proposed to predict the maximum spreading factor, and very good agreement is observed compared to our numerical results. After that, we identify different impacting behaviors in different parameter regimes. For non-isothermal cases, we find that the solidification makes the droplet transit from full rebound to adhesion on the cold substrate, and the participation of the magnetic field promotes the pinch off phenomena during the retraction of the liquid drop. Mechanisms for the transitions between different impacting regimes are discussed, and the comparisons with the available experimental results and analytical solutions are also delivered. At last, we identify that the thickness growth of the solidified splat can be predicted by solving the simple one-dimensional Stefan problem, implying that the thermal dynamics is dominating over the hydrodynamic or the magnetohydrodynamic effects during the melting process of the spreading droplet. Our work therefore provides a general framework to model and study more complex configurations, such as the droplet impacting problems in the metallurgical industry and Tokamak devices, in which environment the droplet dynamics significantly depend on the non-isothermal magnetohydrodynamic effects. [ABSTRACT FROM AUTHOR]

Highlights • Behaviors of a deformed electrically conducting droplet falling through a non-uniform horizontal magnetic field is investigated numerically. • Falling behaviors of the droplet, such as the deformation, the falling velocity and the energy conversion, are related to the sign of the MF gradient. • Internal flows inside the droplet significantly reduce the current density, and hence the droplet falls faster if the non-uniform MF is stronger. Abstract A single electrically conducting droplet falling through a non-uniform horizontal magnetic field is numerically investigated. Its dynamic behaviors, such as the decrease in the falling velocity, the deformation of the shape, and the flow fields inside the droplet are discussed. Within the numerical framework, the Volume-of-Fluid interface tracking method coupling with an adaptive mesh refinement technique is utilized, while a consistent and conservative scheme is applied for the calculation of the induced electromagnetic field. Basically, it is found that if the droplet keeps spherical shape during the translating, the magnetohydrodynamic effects are identical whether the nonuniform magnetic field is linearly increased or linearly decreased along the falling direction of the droplet, and the numerical results are in good agreement with the analytical solutions. However, in most of the cases that the droplet deformations can not be ignored, their shapes evolve into two categories: being prolate or oblate depended on the direction of the magnetic field gradient. Besides, the aspect ratio of the droplet and the deceleration of its falling velocity are also related to three factors: the initial velocity of the droplet, the gradient and the global strength of the magnetic fields. In addition, we find the internal flows inside the droplet to be rather important in affecting the droplet motion, which is not reported before. Moreover, sometimes we observe the shape of the droplet to oscillate after exiting the non-uniform magnetic field, complying with an oscillatory mode 2. After that, we consider other circumstance by adjusting the inclination between the magnetic field and the gravitational direction, finding the trajectory of the droplet to deviate from the rectilinear path, and the evolutions of the vortex structures at the tail of the droplet are presented when the inclined angle is varied. [ABSTRACT FROM AUTHOR]

Highlights • Both 3D and Q2D numerical simulations are conducted to study the magneto-convection. • The physical mechanism of heat transfer enhancement with lower magnetic fields has been analyzed in detail. • The results confirm that the damping velocity and kinetic energy of main convection are scaled as Gr / Ha. • The average Nusselt number can be correlated as a function of Ha / Gr 3 / 4 . Abstract Both three-dimensional (3D) and quasi-two-dimensional (Q2D) numerical simulations are conducted to study the natural convection in an electrically insulated cavity with imposed horizontal magnetic fields (MF) normal to the main circulation, where two opposite vertical walls are kept at different temperatures and the other four are thermally insulated. We mainly focus on flows at Hartmann (Ha ⩽ 10 4 ) and Grashof (Gr ⩽ 4 × 10 7 ) numbers. It is found that, with lower MF, the strengthening of the main convection, which is due to the suppression of the secondary flow along the MF lines by the Lorentz forces, results in the enhancement of heat transfer. Once the Q2D is achieved, the convection and the heat transfer would be damped by the further increase of MF. Our numerical results have confirmed that the damping velocity and kinetic energy of main convection are scaled as Gr / Ha (see Ref. Tagawa et al. (2002)). At the same time, the computed average Nusselt number (Nu) agrees well with the experimental results of Okada and Ozoe (1992), which can be correlated as a function of Ha / Gr 3 / 4 rather than Ha / Gr 1 / 3 . [ABSTRACT FROM AUTHOR]

Through performing numerical simulations, the three-dimensional thermally driven flows, namely the Rayleigh-Benard convection (RBC hereafter) flows, have been studied under the influence of magnetic field in the confined rectangular enclosure full of liquid metal. To validate our numerical methodologies, some of our numerical solutions are compared with the available experimental results that good agreements are found between them. Besides, the correlations between the Nusselt number ( Nu hereafter) and the Rayleigh number ( Ra hereafter) are also in accordance with the experimental results, whereas the Hartmann number ( Ha hereafter) keeps constant. Nevertheless, in the present study, a new correlation law between Nu and varied Ha is established when Ra is fixed, this formula is more helpful when particularly considering the influence of the magnetic field. Regarding the horizontal magnetic field, it is found that the evolution of Nu versus magnetic intensity can be divided into three stages: when Ha is small, Nu increases with Ha because the three-dimensional RBC flow transits to transient-two dimensional pattern; when Ha is moderate, Nu increases with Ha because the transient-two dimensional flow is more stable that the dynamic motion of vortex cells is disappeared gradually; when Ha continues to increase, Nu still increases with Ha due to the growth in number of the convective cells. It should be noted that such transient process of the flow field can be hardly observed in the experiments, because the liquid metal is opaque, however, we are able to present the evolutions of the temperature fields as well as the flow structures with the help of numerical techniques. [ABSTRACT FROM AUTHOR]

In the present paper, some preliminary experimental studies have been conducted to show the flow pattern of liquid metal flow using visualization method. For the convenience of experiments in lab, Ga 67 In 20.5 Sn 12.5 in liquid state at room temperature is used. A test section made by stainless steel is inserted in a traverse magnetic field with strength ( B 0 ) varies from 0 to 1.28 T. The inclined angle of stainless steel plate in test section is about 9°. Visualization results obtained by high-speed camera (Phantom M/LC 310) shown that GaInSn liquid flow on inclined stainless steel plate behaved unstable liquid column flow pattern in the low flow rate, while behaved large area spreading flow pattern with small waves on the free surface in the large flow rate. However, in the magnetic field, under the action of electromagnetic force, the flow patterns of GaInSn liquid have some significant changes on the spreading width and surface structure of free surface. Some detailed analyses on these changes have been also showed in the present paper. Plans for future work are also presented. [ABSTRACT FROM AUTHOR]

• The path and trajectory of a millimetre-sized air bubble in a liquid metal are numerically examined by varying the strength of the transverse magnetic field. • It is shown that the spiralling motion of an air bubble observed without magnetic field transforms into a purely zigzagging motion under an applied transverse magnetic field. • It is found that the twisted double-threaded vortices observed in a spiralling bubble appear to rotate perpendicularly to the applied magnetic field, making the bubble shift its trajectory from spiralling to zigzagging. • The present study demonstrates the mechanism to control the trajectory of an air bubble under the application of a magnetic field. We investigate the dynamics of a millimetre-sized air bubble rising in a liquid due to buoyancy under the influence of a magnetic field applied in a direction transverse to the bubble motion by conducting three-dimensional numerical simulations. The path and trajectory of the air bubble are examined by varying the strength of the transverse magnetic field. In the absence of a magnetic field, it is well known that under certain conditions a tiny air bubble undergoes spiralling motion due to its shape deformation and vortex shedding in the wake region. It is shown here that the spiralling motion of an air bubble observed without magnetic field transforms into a purely zigzagging motion under an applied transverse magnetic field. To understand the mechanism, we analyse the evolution of the wake vortices and forces experienced by the bubble in the presence of a transverse magnetic field. It is found that the twisted double-threaded vortices observed in a spiralling bubble in the absence of a magnetic field appear to rotate perpendicularly to the applied magnetic field across the vertical axis, thereby making the bubble shift its trajectory from spiralling to zigzagging. By calculating the lift and drag forces acting on the bubble, it is shown that how these forces acting on the bubble contribute to the vortex shedding patterns. Thus, the present study demonstrates the mechanism to control the trajectory of an air bubble under the application of a magnetic field. [ABSTRACT FROM AUTHOR]

Considering the existence of a horizontal magnetic field, we experimentally investigate the process of a liquid metal drop with high surface tension impacting a film of the same liquid. High-speed photography is adopted here to capture the dynamics of the interaction between the drop and the liquid film. We observe three typical outcomes after drop impact on the film, namely, symmetric crown, asymmetric crown, and prompt splashing, among which the asymmetric crown is first discovered by the present experiments. Moreover, the experimental variables, such as the drop size, impact velocity, initial film thickness, and intensity of the magnetic field, are included to study the three outcomes in detail. For crown formation, the external horizontal magnetic field changes the shape of the crown from symmetric to asymmetric during the crown expansion process, while for prompt splashing, the external horizontal magnetic field promotes splashing from the liquid layer where the drop and the liquid film meet and reduces the critical Weber number where prompt splashing occurs. Therefore, the present experimental results conclusively prove that the external horizontal magnetic field affects the process of liquid metal drop impact on a liquid metal film. Finally, by selecting a typical case, we carried out the direct numerical simulation to calculate the distribution of the magnetic-field-induced Lorentz force inside the droplet after impact, which helps us fully understand the phenomena observed. [ABSTRACT FROM AUTHOR]

The spreading characteristics of a liquid metal droplet impacting onto a flat solid surface under the influence of a horizontal magnetic field are investigated numerically. The simulated parameters are selected based on our previous experiment but over a wider range of magnetic field (0-5 T). The time evolution of the droplet shape is shown in detail and exhibits an elliptical spreading pattern, namely the droplet is stretched in the direction perpendicular to the magnet lines, which agrees well with the experimental results. To clarify the mechanism underlying the elliptical spreading pattern as well as the asymmetrical rim bulges appeared at the later stage of spreading, the current line distribution and the resultant Lorentz force at two representative times are analyzed quantitatively. The effect of the magnetic field intensity and the initial impact velocity on the anisotropic spreading of droplets is demonstrated by the maximum spreading radius and the time required to reach this maximum extent in two orthogonal directions. Finally, an energy conversion analysis of the overall spreading process is presented and the dissipation of the initial kinetic energy of droplets by Joule heat explains the inhibition effect of the horizontal magnetic field on the average spreading radius. [ABSTRACT FROM AUTHOR]

Highlights • Establish experimental facility to study liquid lithium film flow in magnetic field. • Liquid lithium film fully covers the stainless steel pre-wetted by lithium before. • Very significant MHD effect in lithium film flow under horizontal magnetic field. Abstract An experimental facility has been established at the University of Chinese Academy of Sciences (UCAS) to study the liquid lithium film flow under the influence of the spanwise magnetic field. The test section, which is placed in an electromagnet with maximum intensity of 2T, could generate the lithium film with a width of 60 mm. The test section has been inclined to the horizontal plane at an angle of 6° to produce gravity to drive the liquid lithium film flowing. By using the experimental facility, the lithium film flow is able to fully cover the test section by pre-wetting the stainless steel surface. Afterwards, the experiments are carried out under different flow rates and different magnetic intensities. The results show that the magnetic field strongly influences the film flow, not only to hold the flow back but even to limit it at the upstream of the test section, regardless of different flow rates. Moreover, when the magnetic field is strong enough, the liquid lithium will accumulate at the inlet of the test section, and they will not flow downstream due to the strong MHD effect. [ABSTRACT FROM AUTHOR]

The present paper focuses on the investigation of the surface wave of liquid GaInSn film which flows along a non-electric conductivity surface in the presence of a spanwise magnetic field. Using the high-speed camera with frame rate 1000 1/s, we experimentally observed the time-varying surface waves at different Reynolds number and Hartmann number. Furthermore, we also extracted the gray value from two fixed lines in photos to show the wave information quantitatively along the streamwise direction and spanwise direction. Experimental results show that the present spanwise direction magnetic field plays an important role in the regularization of film surface waves, namely when gradually increasing the strength of magnetic field, the random surface waves can be firstly damped along the direction of magnetic field and then strongly inhibited due to the induced Lorentz force. The decreasing of wave velocity also indicates that the spanwise magnetic field has a stabilizing effect on the film flow. [ABSTRACT FROM AUTHOR]

The spreading characteristics of a liquid GaInSn alloy droplet on a glass surface with the action of a horizontal magnetic field have been experimentally investigated in the present paper. With changing the impact velocity from 0.1 m/s to 1.2 m/s and increasing the magnetic field from 0 T to 1.6 T, we focus on studying the influence of the horizontal magnetic field on the spreading characteristics of a liquid metal droplet using the shadow-graph method. The elliptical spreading pattern of a liquid metal droplet induced by the horizontal magnetic field was discovered by experiments. By introducing a numerical method in getting the distribution of current lines and the Lorentz force inside the droplet, we give a detailed explanation on the mechanism of elliptical spreading. Furthermore, some quantitative results on a maximum spreading factor and time at moment of maximum spreading varied with the Hartmann number and Weber number are shown to give us a comprehensive understanding of the elliptical spreading. With the increasing of the magnetic field, the maximum spreading factor in the front view is reduced while that in the side view is increased, which reveals a larger deformation happened during the spreading process. While with the increasing of impact velocity, the spreading factor increased. Finally, we present a non-dimensional parameter to get scaling laws for the averaged maximum spreading factor and the aspect ratio of the maximum spreading factor; results show that the predict data can agree with experimental data in a certain degree. [ABSTRACT FROM AUTHOR]