Induced Lorentz Force Research Articles

Experimental and numerical assessment of weld pool behavior and final microstructure in wire feed laser beam welding with electromagnetic stirring

Advantages such as element homogenization and grain refinement can be realized by introducing electromagnetic stirring into laser beam welding. However, the involved weld pool behavior and its direct role on determining the final microstructure have not been revealed quantitatively. In this paper, a 3D transient heat transfer and fluid flow model coupled with element transport and magnetic induction is developed for wire feed laser beam welding with electromagnetic stirring. The magnetohydrodynamics, temperature profile, velocity field, keyhole evolution and element distribution are calculated and analyzed. The model is well tested against the experimental results. It is suggested that a significant electromagnetic stirring can be produced in the weld pool by the induced Lorentz force under suitable electromagnetic parameters, and it shows important influences on the thermal fluid flow and the solidification parameter. The forward and downward flow along the longitudinal plane of the weld pool is enhanced, which can bring the additional filler wire material to the root of the weld pool. The integrated thermal and mechanical impacts of electromagnetic stirring on grain refinement which is confirmed experimentally by electron backscatter diffraction analysis are decoupled using the calculated solidification parameters and a criterion of dendrite fragmentation.

Lattice Boltzmann simulation for melting control through an extra magnetic quadrupole field

Melting widely exists in various industrial applications and melting control through an extra magnetic field is a promising subject. Recent studies mainly focus on the suppression effect of the magnetic induced Lorentz force. However, the influence of magnetic force is less investigated. The present study concentrates on investigating the impact of magnetic force, along with gravity, on the melting process. The magnetic quadrupole field is used to generate magnetic force and the temperature distribution, velocity field and melting front are obtained through lattice Boltzmann method. Results indicate that the magnetic force can enhance the flow and heat transfer during the melting process and it has the potential to be used to control the process. Besides, the gravity accelerates the melting process when the dimensionless magnetic force parameter is less than 20, whereas its effect can be ignored when the parameter is larger than 20.

The numerical analysis on the development of Lorentz force and its directional effect on the suppression of buoyancy-driven flow and heat transfer using OpenFOAM

The development of Lorentz force and its directional effect on the free convection flow and heat transfer in a cube are studied numerically under the influence of a magnetic field using the open source CFD tool kit OpenFOAM. The vertical opposite sidewalls are kept as isothermal while other walls are maintained as insulated. The considered working range of Rayleigh number (Ra) is 104, 106, and 108 at fixed Prandtl number (Pr) of 0.71. The effect of the orientation and intensity of applied magnetic field in the direction normal (Bx) and parallel (By) to the isothermal surface are reported. It is noticed that the distribution of electric potential, the nature of the flow of the electric current and the strength of the Lorentz force varies with the intensity of the magnetic field and its orientation. The hydrodynamic and thermal boundary layers get thinner with the increase in Ra, and the Nusselt number increases in natural convection flow cases. The induced Lorentz force significantly suppress the fluid movement and consequently heat transfer. The damping of fluid motion and convective heat transfer are more in case of Bx magnetic field compared to By field. The detail discussion on the development of Lorentz force and its strength with the direction in the domain is reported. The temperature distribution and iso-surface shows the significance of applied magnetic field on the mode of heat transfer.

Magnetohydrodynamic pressure drop and flow balancing of liquid metal flow in a prototypic fusion blanket manifold

Understanding magnetohydrodynamic (MHD) phenomena associated with the flow of electrically conducting fluids in complex geometry ducts subject to a strong magnetic field is required to effectively design liquid metal (LM) blankets for fusion reactors. Particularly, accurately predicting the 3D MHD pressure drop and flow distribution is important. To investigate these topics, we simulate a LM MHD flow through an electrically non-conducting prototypic manifold for a wide range of flow and geometry parameters using a 3D MHD solver, HyPerComp incompressible MHD solver for arbitrary geometry. The reference manifold geometry consists of a rectangular feeding duct which suddenly expands such that the duct thickness in the magnetic field direction abruptly increases by a factor rexp. Downstream of the sudden expansion, the LM is distributed into several parallel channels. As a first step in qualifying the flow, a magnitude of the curl of the induced Lorentz force was used to distinguish between inviscid, irrotational core flows and boundary and internal shear layers where inertia and/or viscous forces are important. Scaling laws have been obtained which characterize the 3D MHD pressure drop and flow balancing as a function of the flow parameters and the manifold geometry. Associated Hartmann and Reynolds numbers in the computations were ∼103 and ∼101-103, respectively, while rexp was varied from 4 to 12. An accurate model for the pressure drop was developed for the first time for inertial-electromagnetic and viscous-electromagnetic regimes based on 96 computed cases. Analysis shows that flow balance can be improved by lengthening the distance between the manifold inlet and the entrances of the parallel channels by utilizing the effect of flow transitioning to a quasi-two-dimensional state in the expansion region of the manifold.

Surface waves of liquid metal film flow under the influence of spanwise magnetic field

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.

Magnetic-field-assisted fabrication of micro-convex domes using long pulse laser

Surfaces with mimic micro-convex domes offer superior functions such as superhydrophobicity, self-cleaning, anti-wear and drag reduction. In this paper, magnetic-filed-assisted laser surface texturing (LST) using long pulse laser was employed to create micro-convex domes on 304L stainless steel. Spherical cap shaped domes with ripples around the bottom were fabricated through LST. The effects of laser power and magnetic flux density on surface morphologies of the created convex domes were investigated. It was found that the height and diameter of the created convex dome increased with the increment of the laser power without magnetic field. Moreover, the height of the created convex dome grew up gradually with the increase of magnetic flux density due to the induced Lorentz force. The height of the convex dome was increased by as much as 14.5% as compared to LST without the applied magnetic field at a laser power of 54 W. However, the applied magnetic field had no evident effect on the diameter of the created convex dome.

Maximum electromagnetic drag configurations for a translating conducting cylinder with distant magnetic dipoles

We report a semianalytic and numerical investigation of the maximal induced Lorentz force on an electrically conducting cylinder in translation along its axis that is caused by the presence of multiple distant magnetic dipoles. The problem is motivated by Lorentz force velocimetry, where induction creates a drag force on a magnet system placed next to a conducting flow. The magnetic field should maximize this drag force, which is usually quite small. Our approach is based on a long-wave theory developed for a single distant magnetic dipole. We determine the optimal orientations of the dipole moments providing the strongest Lorentz force for different dipole configurations using numerical optimization methods. Different constraints are considered for dipoles arranged on a concentric circle in a plane perpendicular to the cylinder axis. In this case, the quadratic form for the force in terms of the dipole moments can be obtained analytically, and it resembles the expression of the energy in a classical spin model. When all dipoles are equal and their positions on the circle are not constrained, the maximal force results when all dipoles are gathered in one point with all dipole moments pointing in radial direction. When the dipoles are equal and have equidistant spacing on the circle, we find that the optimal orientations of the dipole moments approach a limiting distribution. It differs from the so-called Halbach distribution that provides a uniform magnetic field in the cross section of the cylinder. The corresponding force is about 10% larger than that for the Halbach distribution but 60% smaller than for the unconstrained dipole positions. With the so-called spherical constraint for a classical spin model, the maximal force can be found from the eigenvalues of the coefficient matrix. It is typically 10% larger than the maximal force for equal dipoles because the constraint is weaker. We also study equal and evenly spaced dipoles along one or two lines parallel to the cylinder axis. The patterns of optimal magnetic moment orientations are fairly similar for different dipole numbers when the inter-dipole distance is within a certain interval. This behavior can be explained by reference to the magnetic field distribution of a single distant dipole on the cylinder axis.

Boundary normal pressure-based electrical conductivity reconstruction for magneto-acoustic tomography with magnetic induction**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474166 and 11604156), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20161013), the Postdoctoral Science Foundation of China (Grant No. 2016M591874), and the Priority Academic Program Development of Jiangsu Provincial Higher Education Institutions, China.

As a kind of multi-physics imaging approach integrating the advantages of electrical impedance tomography and ultrasound imaging with the improved spatial resolution and image contrast, magneto-acoustic tomography with magnetic induction (MAT-MI) is demonstrated to have the capability of electrical impedance contrast imaging for biological tissues with conductivity differences. By being detected with a strong directional transducer, abrupt pressure change is proved to be generated by the gradient of the induced Lorentz force along the force direction at conductivity boundary. A simplified boundary normal pressure (BNP)-based conductivity reconstruction algorithm is proposed and the formula for conductivity distribution inside the object with the clear physical meaning of pressure derivative, is derived. Numerical simulations of acoustic pressure and conductivity reconstruction are conducted based on a 2-layer eccentric cylindrical phantom model using Hilbert transform. The reconstructed two-dimensional conductivity images accord well with the model, thus successfully making up the deficiency of only imaging conductivity boundary in traditional MAT-MI. The proposed method is also demonstrated to have a spatial resolution of one wavelength. This study provides a new method of reconstructing accurate electrical conductivity and suggests the potential applications of MAT-MI in imaging biological tissues with conductivity difference.

Effect of external applied steady magnetic field on the morphology of laser welding joint of 4-mm 2024 aluminum alloy

Additional external steady magnetic fields were applied to investigate the influence of a steady magnetic field aligned perpendicular to the welding direction during laser beam welding of 2024 aluminum alloy. The flow pattern in the molten pool and the weld seam geometry were significantly changed by the induced Lorentz force distribution in the liquid metal. It revealed that the application of a steady magnetic field to laser beam welding was helpful to the suppression of the characteristic wineglass-shape and the depth-to-width ratio because of the Marangoni convection. The microstructures and component distributions at various laser power and magnetic field intensity were analyzed too. It was indicated that the suppression of the Marangoni convection by Lorentz force was beneficial to accumulation of component and grain coarsening near the fusion line.

Numerical investigation of the transport phenomena occurring in the growth of SiC by the induction heating TSSG method

A numerical simulation study was carried out to examine the transport phenomena occurring during the Top-Seeded Solution Growth (TSSG) process of SiC. The simulation model includes the contributions of radiative and conductive heat transfer in the furnace, mass transfer and fluid flow in the melt, and the induced electric and magnetic fields. Results show that the induced Lorentz force is dominant in the melt compared with that of buoyancy. At the relatively low coil frequencies, the effect of the Lorentz force on the melt flow is significant, and the corresponding flow patterns loose their axisymmetry and become almost fully disturbed. However, at the relatively higher frequency values, the flow is steady and the flow patterns remain axisymmetric.

On the spreading of impacting drops under the influence of a vertical magnetic field

A theoretical model is developed to predict the maximum spreading of liquid metal drops when impacting onto dry surfaces under the influence of a vertical magnetic field. This model, which is constructed based on the energy conversion principle, agrees very well with the numerical results, covering a wide range of impact speeds, contact angles and magnetic strengths. When there is no magnetic field, we found that the maximum spreading factor can be predicted well by an interpolating scheme between the viscous and capillary effects, as proposed by Laan et al. (Phys. Rev. Appl., vol. 2 (4), 2014, 044018). However, when gradually increasing the magnetic field strength, the induced Lorentz forces are dominant over the viscous and capillary forces, taking the spreading behaviour into the ‘Joule regime’, where the Joule dissipation is significant. For most situations of practical interest, namely when the strength of the magnetic field is less than 3 T, all three energy conversion routes are important. Therefore, we determine the correct scaling behaviours for the magnetic influence by first equating the loss of kinetic energy to the Joule dissipation in the Joule regime, then by interpolating it with the viscous dissipation and the capillary effects, which allows for a universal rescaling. By plotting the numerical results against the theoretical model, all the results can be rescaled onto a single curve regardless of the materials of the liquid metals or the contact angles of the surfaces, proving that our theoretical model is correct in predicting the maximum spreading factor by constructing a balanced formula between kinetic energy, capillary energy, viscous dissipation energy and Joule dissipation energy.

Transducer influence on magnetoacoustic tomography with magnetic induction based on 3D equivalent source analysis for tissues

As a noninvasive imaging modality based on the coupling of magnetic and acoustic fields, magnetoacoustic tomography with magnetic induction (MAT-MI) has been demonstrated to have the capability of imaging the variation of conductivity distribution inside the object. However, the image resolution is still limited by the parameters of the receiver. Based on the theory of acoustic dipole, 3D equivalent source analysis was used to simulate transducer detected pressures and waveforms for MAT-MI. The influence of transducer was studied both theoretically and experimentally for a cylindrical model. It is demonstrated that large-radius transducer with strong reception pattern can detect the acoustic signals transmitted along its normal direction with sharp pressure peaks, reflecting the divergence of the induced Lorentz force. By considering the effect of acoustic attenuation and the accuracy of image reconstruction, the acoustic pressure with acceptable peak pressure ratio and improved SNR can be detected when the scanning distance is 5-10 times the radius of the object. Wide bandwidth transducer should also be selected to reduce the boundary width of borderline stripes and improve the spatial resolution of reconstructed images. The favorable results confirm the influence of transducer on MAT-MI and also provide the fundamentals for transducer selection in further study to improve the accuracy of electrical impedance reconstruction.

Adaptive fast nonsingular terminal sliding mode control of Lorentz-augmented spacecraft relative motion

An electrostatically charged spacecraft is subject to Lorentz force as it moves through the planetary magnetic field. The induced Lorentz force could be used as propellantless electromagnetic propulsion for orbital maneuvers. Such vehicle is referred to as Lorentz spacecraft. By modeling the Earth’s magnetic field as a tilted dipole that corotates with Earth, a nonlinear dynamical model is developed to characterize the orbital motion of a Lorentz spacecraft relative to an arbitrary Earth orbit. A fast nonsingular terminal sliding mode control law is then proposed, based on which an adaptive controller is designed for Lorentz-augmented spacecraft relative motion to deal with the uncertain parameters and perturbations. Due to the constraint that the direction of Lorentz force is naturally perpendicular to the local magnetic field and the vehicle’s velocity relative to the magnetic field, which does not necessarily coincide with the direction of the required control force, thus, the Lorentz force works as auxiliary propulsion to reduce the fuel consumption in most cases. Then, a fuel-optimal distribution law of Lorentz force and traditional chemical propulsion is proposed. Furthermore, the stability of the closed-loop control system is proved via a Lyapunov-based approach. Numerical simulations substantiate the feasibility and validity of the proposed controller for Lorentz-augmented relative orbital control.

Transducer selection and application in magnetoacoustic tomography with magnetic induction

As an acoustic receiver, transducer plays a vital role in signal acquisition and image reconstruction for magnetoacoustic tomography with magnetic induction (MAT-MI). In order to optimize signal acquisition, the expressions of acoustic pressure detection and waveform collection are theoretically studied based on the radiation theory of acoustic dipole and the reception pattern of transducer. Pressure distributions are simulated for a cylindrical phantom model using a planar piston transducer with different radii and bandwidths. The proposed theory is also verified by the experimental measurements of acoustic waveform detection for an aluminum foil cylinder. It is proved that acoustic pressure with sharp and clear boundary peaks can be detected by the large-radius transducer with wide bandwidth, reflecting the differential of the induced Lorentz force accurately, which is helpful for precise conductivity reconstruction. To detect acoustic pressure with acceptable pressure amplitude, peak pressure ratio, amplitude ratio, and improved signal to noise ratio, the scanning radius of 5–10 times the radius of the object should be selected to improve the accuracy of image reconstruction. This study provides a theoretical and experimental basis for transducer selection and application in MAT-MI to obtain reconstructed images with improved resolution and definition.

Lifetime of Ionic Vacancy Created in Redox Electrode Reaction Measured by Cyclotron MHD Electrode.

The lifetimes of ionic vacancies created in ferricyanide-ferrocyanide redox reaction have been first measured by means of cyclotron magnetohydrodynamic electrode, which is composed of coaxial cylinders partly exposed as electrodes and placed vertically in an electrolytic solution under a vertical magnetic field, so that induced Lorentz force makes ionic vacancies circulate together with the solution along the circumferences. At low magnetic fields, due to low velocities, ionic vacancies once created become extinct on the way of returning, whereas at high magnetic fields, in enhanced velocities, they can come back to their initial birthplaces. Detecting the difference between these two states, we can measure the lifetime of ionic vacancy. As a result, the lifetimes of ionic vacancies created in the oxidation and reduction are the same, and the intrinsic lifetime is 1.25 s, and the formation time of nanobubble from the collision of ionic vacancies is 6.5 ms.

Reconciling Magnetically Induced Vertigo and Nystagmus.

It has long been known that dizziness and vertigo can sometimes be experienced in and around the high-strength magnetic fields of magnetic resonance imaging (MRI) scanners. Three early mechanistic proposals by which magnetic fields may induce vertigo via stimulation of the vestibular system were dependent on head movement, time-varying magnetic fields, and magnetic field spatial gradients, respectively (1, 2). Although these factors might have a role to play, it has recently become clear from both human and animal studies that they are not necessary to achieve strong magnetic vestibular stimulation: see review by Ward et al. (3). For example, a person lying still in a strong homogenous magnetic field in darkness will experience robust, persistent nystagmus that is dependent on an intact vestibular system (4). The mechanism that was proposed (4) to account for this submits that magnetic fields interact with spontaneous ionic current flowing in labyrinthine endolymph to induce Lorentz forces strong enough to deflect semicircular canal cupulae (4, 5). With this mechanism, a stationary head in a magnetic field will receive vestibular input analogous to a constant angular acceleration, and a person being moved into a magnetic field (such as during patient entry into an MRI scanner) will receive an input akin to a ramp angular acceleration (6, 7). In addition to nystagmus, most individuals will also perceive apparent body rotation when exposed to a 7 T static magnetic field in darkness (4, 8). However, there are inconsistencies between this perception and the induced nystagmus that question whether the two are caused by the same mechanism. The purpose of this article is to discuss these apparent discordances and to put forward arguments that allow for a common mechanism. The article condenses arguments made previously (8) and extends them in light of more recent observations (9).

Momentum partition between constituents of exotic atoms during laser-induced tunneling ionization

The tunneling ionization of exotic atoms such as muonic hydrogen, muonium and positronium in a strong laser field of circular polarization is investigated taking into account the impact of the motion of the center of mass on the the tunneling ionization dynamics. The momentum partition between the ionization products is deduced. The effect of the center of mass motion for the momentum distribution of the ionization components is determined. The effect scales with the ratio of the electron (muon) to the atomic core masses and is nonnegligible for exotic atoms, while being insignificant for common atoms. It is shown that the electron (muon) momentum shift during the under-the-barrier motion due to the magnetically induced Lorentz force has a significant impact on the momentum distribution of the atomic core and depends on the ratio of the electron to the atomic core masses.

Pseudospectral method for optimal propellantless rendezvous using geomagnetic Lorentz force

A charged spacecraft is subject to the Lorentz force when it orbits a central body with a magnetic field. The induced Lorentz force provides a new mean of propellantless electromagnetic propulsion for orbital control. Modeling the Earth magnetic field as a tilted dipole that co-rotates with the Earth, this paper develops a nonlinear dynamical model that describes the relative motion of the Lorentz spacecraft about an arbitrary reference orbit. Based on the proposed dynamical model, feasibility of Lorentz-propelled rendezvous with no restrictions on the initial states is investigated. The rendezvous problem is then formulated as an optimal control problem, and solved with the Gauss pseudospectral method (GPM). Numerical simulations substantiate the validity of proposed model and method, and results show that the propellantless rendezvous is achieved at both fixed and free final time.

The effects of natural, forced and thermoelectric magnetohydrodynamic convection during the solidification of thin sample alloys

Using a fully coupled transient 3-dimensional numerical model, the effects of convection on the microstructural evolution of a thin sample of Ga-In25%wt. was predicted. The effects of natural convection, forced convection and thermoelectric magnetohydrodynamics were investigated numerically. A comparison of the numerical results is made to experimental results for natural convection and forced convection. In the case of natural convection, density variations within the liquid cause plumes of solute to be ejected into the bulk. When forced convection is applied observed effects include the suppression of solute plumes, preferential secondary arm growth and an increase in primary arm spacing. These effects were observed both numerically and experimentally. By applying an external magnetic field inter-dendritic flow is generated by thermoelectrically induced Lorentz forces, while bulk flow experiences an electromagnetic damping force. The former causes preferential secondary growth, while the latter slows the formation of solute plumes. This work highlights that the application of external forces can be a valuable tool for tailoring the microstructure and ultimately the macroscopic material properties.

Impact of Coil Geometry on Magnetohydrodynamic Flow in Liquid Aluminium and Its Relevance to Inclusion Separation by Electromagnetophoresis

AbstractMagnetohydrodynamic (MHD) flow will be produced in liquid aluminium by gradients in the Lorentz forces created by the interactions of induced currents and the time-varying magnetic field of an induction coil. The magnitude of the velocity field is driven by the curl of the Lorentz forces. Practical coils are “Short” and produce magnetic fields having both lower flux densities and Lorentz forces than very “Long” or infinite coils. Unlike infinite coils, the magnetic fields of “Short” coils contain both axial and radial components, which vary with position and thereby produce powerful MHD mixing. When such a coil is used with the objective of achieving non-conductive particle migration in a liquid metal by electromagnetophoresis, the obtained mixing effects can be highly detrimental. In the present study different coil geometries and induced Lorentz forces with resulting MHD mixing are modelled (COMSOL® 4.4), and the obtained Lorentz forces compared to analytical results.