Thermoelectric Magnetohydrodynamics Research Articles

On the formation of gradient-distributed dendrites in a single crystal nickel-based superalloy directionally solidified under transverse static magnetic field

Directional solidification (DS) of alloys under static magnetic field has attracted extensive attention due to the development of thermoelectric magnetohydrodynamics (TEMHD). Assessing the influence of static magnetic field on solidification microstructures in single crystal (SX) superalloys is of great significance for both the development of SX superalloys and the understanding of external field-assisted solidification. In this contribution, under different transverse static magnetic fields, the evolution of dendritic structure in a SX nickel-based superalloy directionally solidified over a range of solidification velocities is systematically investigated. The results show that applying a transverse static magnetic field (TSMF) during DS does not disrupt the crystal orientation of SX superalloys. The distribution of dendrites or local primary dendrite arm spacings within the cross section of SX superalloys shows a gradient variation in the direction perpendicular to the TSMF. Additionally, the formation of gradient-distributed dendritic structure is closely related to the applied TSMF intensity and solidification velocity. It is easier to form a gradient-distributed dendritic microstructure at low solidification velocities and high magnetic fields. Based on the experiments and simulations, the formation of gradient-distributed dendritic microstructure is supposed to attribute to the variation of interdendritic constitutional undercooling created by the change of solute concentration in interdendritic region, which is induced by the TEMHD. The SX superalloy with a gradient distribution of dendrites may have potential applications due to its gradient properties. Meanwhile, these findings also provide a new method for preparing alloys with gradient microstructures.

Modulating Meltpool Dynamics and Microstructure using Thermoelectric Magnetohydrodynamics in Additive Manufacturing

Meltpool modulation in Selective Laser Remelting Additive Manufacturing via an oscillating magnetic field generates Thermoelectric Magnetohydrodynamics (TEMHD) flow. Numerical predictions show that the resulting microstructure can be significantly altered. A multi-scale numerical model captures the meso-scale melt pool dynamics coupled to microscale solidification showing the microstructure evolution and solute redistribution. The results highlight the complex interaction of the various physical phenomena and also show the method’s potential to disrupt the epitaxial growth defect. The model predictions are supported by preliminary experimental results that demonstrate the dependency of the melt pool depth on magnetic field orientation. The results highlight how a time-dependent field has the potential to provide an independent control mechanism to tailor microstructures.

Structured large-pore foams improve thermal performance of LiMIT-style liquid lithium PFC

As magnetically confined fusion devices improve, the conditions at the walls become increasingly intense. Plasma facing components (PFCs) must withstand these extreme heat and particle loads without damage or degradation. Liquid lithium PFCs are known to be quite resilient, and the presence of lithium also serves to improve plasma properties. The liquid metal infused trench (LiMIT) concept is an open surface liquid lithium PFC design that has been tested extensively at the University of Illinois and in fusion devices around the world. LiMIT utilizes thermoelectric magnetohydrodynamics (TEMHD) to passively drive liquid lithium flow. This work demonstrates an extension of the LiMIT trench geometry to three dimensions. Additively manufactured large pore metallic foams maintain TEMHD drive while drastically improving heat flux handling and resistance to lithium dryout, a phenomenon where locally high TEMHD forces depresses the lithium level and exposes underlying solid structure. COMSOL multiphysics modeling of the system yields insight into the forces at play in dryout development, and shows the 3D structures can eliminate dryout. Low heat proof-of-concept experimental testing of the system matches computational results, and high heat flux electron beam tests more than double the proven operational range of a LiMIT-style PFC, to 6.8 MW m−2, with no indications of dryout or impending damage.

Thermoelectric Magnetohydrodynamic Model for Laser-Based Metal Additive Manufacturing

Magnetic fields are recently being applied to metal additive manufacturing to control the molten pool dynamics and dendritic morphology. To study the molten pool dynamics under an external magnetic field, a thermoelectric magnetohydrodynamic (TEMHD) model is developed by incorporating the electrodynamic model with the Seebeck effect into the multiphysics thermal-fluid flow model. The Seebeck effect in the molten pool is analyzed with the simulation of stationary laser melting on a bare plate. Furthermore, different external magnetic fields are assigned in the TEMHD simulations with the stationary laser melting and the results show that the Lorentz force can damp the keyhole fluctuations. Finally, the laser scanning simulations on a bare plate under external magnetic fields indicate that the Lorentz force can smooth the fluid flow fields in the molten pool and increase the ratio of equiaxed grains in the solidification front.

Magnetic Effects on Microstructure and Solute Plume Dynamics of Directionally Solidifying Ga-In Alloy

The effects of applying a 0.2-T transverse magnetic field on a solidifying Ga-25 wt%In alloy have been investigated through a joint experimental and numerical study. The magnetic field introduced significant changes to both the microstructure and the dynamics of escaping high-concentration Ga plumes. Plume migration across the interface was quantified and correlated to simulations to demonstrate that thermoelectric magnetohydrodynamics (TEMHD) is the underlying mechanism. TEMHD introduced macrosegregation within the dendritic structure, leading to the formation of a stable “chimney” channel by increasing the solutal buoyancy in the flow direction. The resulting pressure difference across the solidification front introduced a secondary hydrodynamic phenomenon that subsequently caused solute plume migration.

Revealing the mechanisms by which magneto-hydrodynamics disrupts solidification microstructures

A key technique for controlling solidification microstructures is magneto-hydrodynamics (MHD), resulting from imposing a magnetic field to solidifying metals and alloys. Applications range from bulk stirring to flow control and turbulence damping via the induced Lorentz force. Over the past two decades the Lorentz force caused by the interaction of thermoelectric currents and a magnetic field, a MHD phenomenon known as Thermoelectric Magnetohydrodynamics (TEMHD), was also shown to drive inter-dendritic flow altering microstructural evolution. In this contribution, high-speed synchrotron X-ray tomography and high-performance computational simulation are coupled to reveal the evolution, dynamics and mechanisms of solidification within a magnetic field, resolving the complex interplay and competing flow effects arising from Lorentz forces of different origins. The study enabled us to reveal the mechanisms disrupting the traditional columnar dendritic solidification microstructure, ranging from an Archimedes screw-like structure, to one with a highly refined dendritic primary array. We also demonstrate that alloy composition can be tailored to increase or decrease the influence of MHD depending on the Seebeck coefficient and relative density of the primary phase and interdendritic liquid. This work paves the way towards novel computational and experimental methods of exploiting and optimising the application of MHD in solidification processes, together with the calculated design of novel alloys that utilise these forces.

Study of thermoelectric magnetohydrodynamic convection on solute redistribution during laser additive manufacturing

Melt pools formed in laser additive manufacturing (AM) are subject to large thermal gradients, resulting in the formation of thermoelectric currents due to the Seebeck effect. When in the presence of an external magnetic field, a Lorentz force is formed which drives fluid flow in the melt pool. This Thermoelectric Magnetohydrodynamics (TEMHD) phenomenon, can have a significant impact on the melt pool morphology and can alter the microstructural evolution of the solidification process. By coupling steady-state mesoscopic melt pool calculations to a microscopic solidification model, predictions of the resulting microstructure for multiple deposited layers have been obtained. The results indicate that the magnetic field can have a transformative effect on the microstructure and solute redistribution. This study highlights the theoretical potential for using magnetic fields as an additional control system to tailor AM microstructures.

Thermoelectric magnetohydrodynamic control of melt pool dynamics and microstructure evolution in additive manufacturing.

Large thermal gradients in the melt pool from rapid heating followed by rapid cooling in metal additive manufacturing generate large thermoelectric currents. Applying an external magnetic field to the process introduces fluid flow through thermoelectric magnetohydrodynamics. Convective transport of heat and mass can then modify the melt pool dynamics and alter microstructural evolution. As a novel technique, this shows great promise in controlling the process to improve quality and mitigate defect formation. However, there is very little knowledge within the scientific community on the fundamental principles of this physical phenomenon to support practical implementation. To address this multi-physics problem that couples the key phenomena of melting/solidification, electromagnetism, hydrodynamics, heat and mass transport, the lattice Boltzmann method for fluid dynamics was combined with a purpose-built code addressing solidification modelling and electromagnetics. The theoretical study presented here investigates the hydrodynamic mechanisms introduced by the magnetic field. The resulting steady-state solutions of modified melt pool shapes and thermal fields are then used to predict the microstructure evolution using a cellular automata-based grain growth model. The results clearly demonstrate that the hydrodynamic mechanisms and, therefore, microstructure characteristics are strongly dependent on magnetic field orientation. This article is part of the theme issue 'Patterns in soft and biological matters'.

2-D moving mesh modeling of lithium dryout in open surface liquid metal flow applications

Liquid lithium displays increasing promise as a replacement for solid plasma facing components (PFCs) in fusion device applications. The Liquid Metal Infused Trench (LiMIT) system, developed at the University of Illinois (UIUC), has demonstrated how thermoelectric magnetohydrodynamics (TEMHD) can be harnessed to drive liquid lithium flow in an open surface PFC. However, in the highest heat flux applications, large local acceleration is created via TEMHD, and the sudden increase in velocity can cause the liquid level to expose the underlying solid, eliminating the protective benefits of the lithium. In order to study potential mitigation strategies, a 2-D COMSOL Multiphysics model was developed using the moving mesh module to capture free surface flow. The model depicts the development of the dryout phenomenon for 2 test cases – slow (1 cm/s) and medium (10 cm/s) flow in 5 mm deep trenches – including the liquid level reduction under the high heat flux and the pileup of slower flow both upstream and downstream of the heat stripe. The effectiveness of trench shaping dryout mitigation strategies is examined. For the slow flow case, it is shown that a 1.8 mm ledge placed under the heat stripe will stop dryout, and for the medium flow case, a 2.7 mm ledge is required to mitigate the effect. This model can be used to identify strategies for increasing the viable heat load for open surface liquid lithium PFCs.

Multi-physics simulation of dendritic growth in magnetic field assisted solidification

Magnetic field assisted casting and welding attracted research attentions in the recent decades because it has been observed that the inter-dendritic flow of liquid metals can be controlled by the imposed external magnetic field. However, the underlying mechanism of dendritic growth under a magnetic field is still not fully understood because of the limitations in in-situ experimental methods. To elucidate the mechanism, a new multi-physics model is proposed in this work to simulate the dendritic growth under the influence of an external magnetic field with the consideration of the natural convection. In this model, the physics of solute transport, phase transition via phase field method, natural convection and thermoelectric magnetohydrodynamics via lattice Boltzmann method are tightly coupled. Simulation reveals that intense thermoelectromagnetic convection occurs in the vicinity of the solid-liquid interface, and vortices are generated between dendritic arms. It is shown that the thermoelectromagnetic convection has a major influence on dendritic morphology. The simulation results help explain the experimental observation of curved solidification front and tilted primary trunks. The simulation model is validated by comparing the microstructure morphology and composition distribution with experimental results.

Thermoelectric magnetohydrodynamic effects on the crystal growth rate of undercooled Ni dendrites.

In the undercooled solidification of pure metals, the dendrite tip velocity has been shown experimentally to have a strong dependence on the intensity of an external magnetic field, exhibiting several maxima and minima. In the experiments conducted in China, the undercooled solidification dynamics of pure Ni was studied using the glass fluxing method. Visual recordings of the progress of solidification are compared at different static fields up to 6 T. The introduction of microscopic convective transport through thermoelectric magnetohydrodynamics is a promising explanation for the observed changes of tip velocities. To address this problem, a purpose-built numerical code was used to solve the coupled equations representing the magnetohydrodynamic, thermal and solidification mechanisms. The underlying phenomena can be attributed to two competing flow fields, which were generated by orthogonal components of the magnetic field, parallel and transverse to the direction of growth. Their effects are either intensified or damped out with increasing magnetic field intensity, leading to the observed behaviour of the tip velocity. The results obtained reflect well the experimental findings.This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

Measurements and modelling of dendritic growth velocities of pure Fe with thermoelectric magnetohydrodynamics convection

Dendritic growth velocities of pure Fe under static magnetic fields of intensity ranging from B=0T to B=6T were measured using a high speed camera. The data measured at undercoolings up to ΔT=190K show a depression followed by a recovery of the growth velocities as the magnetic field intensity increased from a low range, B=1–3T to a high range, B=4–6T. These magnetic field effects are similar to those previously observed for pure Ni and can be attributed to competing thermoelectric magnetohydrodynamic (TEMHD) convection patterns in the local liquid. The experimental measurements for the two metals were modelled using a three-dimensional dendritic growth theory taking into account convection to estimate the effective flow velocities in the tip growth direction. The calculated effective flow velocities identify two undercooling dependences and a distinct type of magnetic field intensity dependence in common for the two metals. In comparison, the calculated effective flow velocities for pure Fe are generally smaller in magnitude. This difference between the two metals can be related to their differences in material-dependent properties as is revealed by a simple model proposed for a transverse TEMHD flow.

The effects of Thermoelectric Magnetohydrodynamics in directional solidification under a transverse magnetic field

The mechanism of macrosegregation and modification to dendrite size and spacing from a transverse magnetic field has been modelled through direct numerical simulation. The primary driver for this mechanism was identified as a strong Lorentz force formed in the interdendritic region, which leads to a large scale flow circulation. The microstructure evolution is modified by convective transport of solute and the predicted morphological features compare favourably to experimental data in the literature. The numerical results also give an insight into the magnitude of flow velocities within the interdendritic region.

Analytic Solutions to Determine Critical Magnetic Fields for Thermoelectric Magnetohydrodynamics in Alloy Solidification

During alloy solidification, it has been observed that the morphology of microstructures can be altered by applying an external DC magnetic field. This structural change can be attributed to solutal convective transport introduced by thermoelectric magnetohydrodynamics (TEMHD) which drives fluid motion within the inter-dendritic region. Complex numerical models with grid resolutions on the microscopic scale have been constructed to solve the equations governing TEMHD. To complement these computationally intensive numerical models, analytic solutions were sought. Specifically, the analytic solutions presented herein are asymptotic solutions derived for TEMHD under low and high magnetic field intensities. Combination of these asymptotic solutions leads to simple formulae for estimating critical magnetic fields which can be readily evaluated in terms of characteristic lengths of materials that have been identified in experiments as key parameters of critical fields. Indeed, the critical magnetic fields predicted with the asymptotic solutions exhibit magnitudes consistent with those applied in current ongoing experiments where significant changes in microstructure have been observed. The capability to predict accurate results indicates that the analytic solutions described herein are valuable precursors not only for detailed numerical simulations but also for experimental design to study critical magnetic fields in alloy solidification.

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.

Vertical flow in the Thermoelectric Liquid Metal Plasma Facing Structures (TELS) facility at Illinois

Flowing liquid metal PFCs may offer a solution to the issues faced by solid divertor materials in tokamak plasmas. The Liquid–Metal Infused Trenches (LiMIT) concept of Illinois Ruzic et al. (2011) is a liquid metal plasma facing structure which employs thermoelectric magnetohydrodynamic (TEMHD) effects to self-propel lithium through a series of trenches. The combination of an incident heat flux and a magnetic field provide the driving mechanism. Tests have yielded experimental lithium velocities under different magnetic fields, which agree well with theoretical predictions Xu et al. (2013). The thermoelectric force is expected to overcome gravity and be able to drive lithium flow along an arbitrary direction and the strong surface tension of liquid lithium is believed to maintain the surface when Li flows in open trenches. This paper discusses the behavior of the LiMIT structure when inclined to an arbitrary angle with respect to the horizontal.

Influence of a Slow Rotating Magnetic Field in Thermoelectric Magnetohydrodynamic Processing of Alloys

The effects of a slow rotating magnetic field on thermoelectric magnetohydrodynamics during alloy solidification were investigated using a micro-scale numerical model. For conventional directional solidifcation it was shown that in general the time-dependent acceleration force on the fluid flow is negligible. Using an undercooled growth model with directional solidification approximations the effect on dendritic morphology is predicted, suggesting thermoelectric induced flows will create a significant increase in secondary branching and preferential growth directions on one side of the primary trunk. The extent of macro-segregation under these conditions was also estimated.

Heat transfer of TEMHD driven lithium flow in stainless steel trenches

The Lithium/Metal Infused Trenches (LiMITs) concept, which utilizes the thermoelectric magnetohydrodynamic (TEMHD) driven flowing liquid lithium to cool the divertor surface, has been successfully demonstrated at the University of Illinois. The IR camera results show that such self-driven flowing liquid lithium in the open surface stainless steel trench structure can withstand heat fluxes of up to 10MW/m2 for 10s without significant evaporation. A clear asymmetric temperature distribution was observed from the IR result and such asymmetry can be affected by the direction of the driven magnetic field. Thermocouples are embedded in different positions to monitor the temperature within the lithium. These direct measurements also reveal that flowing liquid lithium can effectively bring the heat from the direct heating area and the efficiency can be influenced by magnetic field and heating power.

The effect of secondary arm growth on thermoelectric magnetohydrodynamics

Direct numerical simulations of 3D dendritic growth in the presence of moderate-high magnetic fields have shown that significant fluid flow can be driven in the mushy interdendritic region. The onset of secondary branches caused by the heat and mass transport of fluid flow causes thermoelectric microcirculations to form, which act to amplify the Lorentz force. However magnetic damping will dominate when a region lacks thermoelectric currents.

A Numerical Model Coupling Thermoelectricity, Magnetohydrodynamics and Dendritic Growth

The purpose of this paper is to discuss in detail the numerical techniques used to investigate the effects of Thermoelectric Magnetohydrodynamics on dendrtic growth. A numerical model is proposed which couples the growth mechanics, solution to the electric potential, fluid mechanics and the transport of heat and mass. The implementation of the equations, solution techniques and the coupling between each of the various physical phenomena is described. A finite difference sharp interface enthalpy based method is used to solve the evolution of the liquid/solid front. The electric potential becomes the solution to Laplace's equation, with a boundary condition applied to the interface and a sub meshing technique is applied to improve the accuracy. The problem is also inherently 3-dimensional and it can be shown analytically that classical 2-dimensional approximations lead to stagnation of the flow. Therefore a quasi 3-dimensional approximation is used which effectively allows simulations to be carried out in 2-dimensions, which significantly reduces the computational time required.