Y Wu

H H Li

G S Duan

X Zhao
email: zhaox@mail.neu.edu.cn

Effects of Magnetic Field Intensity on Carbon Diffusion Behavior in Pure Iron in α-Fe temperature region

Keywords: Magnetic field intensity, Carbon diffusion, Pure iron

Effects of magnetic field intensity on carbon diffusion behavior in pure iron in the α-Fe temperature region were investigated by means of microstructure observation and EPMA analysis. A high purity iron was carburized in α-Fe temperature region applying with different magnetic field intensity. The carbon diffusion coefficient was calculated according to the Fick's second law. It is found that the magnetic field intensity can significantly affect the carbon diffusion behavior in pure iron in the direction parallel to the magnetic field direction in the α-Fe temperature region, and the average carbon diffusion distance and the average carbon diffusion coefficient of specimens decrease gradually with the enhancement of the magnetic field intensity. The application of a magnetic field is likely to change the diffusivity of carbon owing to the change in the fraction of carbon atoms at octahedral and tetrahedral sites. The greater the magnetic field intensity, the stronger of the inhibiting of magnetic field on carbon diffusion.

Introduction

With the rapid development of superconducting technique, the high magnetic field heat treatment technology has risen gradually in the materials science research. Studies on the effects of magnetic fields on solid/solid phase transformation behaviors and microstructures have become popular in the last several years [1][2][3][4][5][6]. During the phase transformation, the atomic diffusion processes are considered as the main driving force for the distribution of solutes and significantly influence the transformation rate. Youdelis et al [7] reported that a 3T magnetic field retarded the diffusion of copper in aluminium. Nakajima et al [8] observed no magnetic effects on the diffusion of nickel in titanium. Pokoev et al [9][10] measured the diffusivity of nickel in α-Fe and Fe-1.94%Si alloy and the magnetic effect on diffusivity were not monotonic as a function of applied magnetic field.

The carbon diffusion is a very important process in diffusional transformations in steels, and most changes in microstructure of steels occur by diffusion. Accordingly, it is of particular importance to study the effect of magnetic field annealing on carbon diffusion behavior in iron. So far, a few reports have been made on the effects of a magnetic field on carbon diffusion in steels. In 2005, Nakamichi et al [11] studied the effects of magnetic field and magnetic field gradient on the diffusion of carbon in γ-Fe and found that the carbon diffusion in γ-Fe was retarded by the application of a 6 T magnetic field. The diffusion of carbon in γ-Fe could be enhanced in a magnetic field gradient when carbon atoms moved towards the direction with a higher magnetic field strength, but be retarded when the opposite magnetic field gradient was applied. In 2006, Ohtsuka [12] studied the influence of 10T magnetic field on carbon diffusion in steel.

The results showed that the high magnetic field retarded the carbon diffusion along the magnetic field direction at 1073K, but had unnoticeable effect at 1203K. In 2011, Fujii and Tsurekawa [13] studied the carbon diffusion in iron under magnetic fields using a diffusion couple made by pure Fe and Fe-0.87C alloy. The results showed that the diffusivity of carbon in α-Fe decreased under a magnetic field, while it increased by twice under a magnetic field gradient of 45 T/m. The above studies have great importance on elucidating the mechanism and the influence rule of high magnetic field on carbon diffusion in Fe-C alloy. However, till now, the study about the magnetic field intensity on carbon diffusion is rarely mentioned. So in this work, we further studied the effect of magnetic field intensity on carbon diffusion behavior in pure iron in the α-Fe temperature region using cementation process. Then the carbon diffusion coefficient was calculated according to the Fick's second law.

Experimental

The material used in this study was high purity iron (99.99%) ingot. The specimens with a dimension of 10mm8mm7mm were cut from the ingot. Specimens were buried in an air-proof melting pot filled up with cementation agent (C: Na 2 C 2 O 4 : Na 2 CO 3 =55:30:15), and respectively subjected to isothermal annealing at 1023K for 4h with a heating rate of 5 o C /min, and then cooled in the furnace. The experimental apparatus is based on a superconducting magnet (JMTD-12 T100, JASTEC, Japan). A magnetic field with different intensity (0 T, 0.1 T, 0.4 T, 0.7 T, 1 T, 6 T, and 12 T) was applied during the whole heating, isothermal holding and cooling processes. During the magnetic field annealing, the specimens were fixed at the center of the applied field, with their long sides (10 mm) parallel to the magnetic field direction (H).

After the heat treatment, the specimens were mechanically polished and then etched with 4% nital. The microstructural observation was performed with an OLYMPUS/ GX71 optical microscope equipped with the analysis software. The metallographic observation surface was the 10mm8mm section of the specimen which was parallel to the magnetic field direction (H).To study the field effect on the carbon diffusion distance, the area percentage of pearlite was examined: The measurement starts from the specimen surface along the carbon diffusion direction (Jc) with a step size of 2μm (The measuring width perpendicular to Jc is 200μm). When the measured area percentage of the pearlite is less than 1%, the distance between this point and the specimen surface is defined as "the carbon diffusion distance". The average carbon diffusion distance of each specimen was calculated from more than 20 measurement data.

The carbon penetration profiles from the surface to iron were measured by Field Emission Electron Probe Micro analyzer of JXA-8530F. The carbon diffusivities in iron under the magnetic field were measured from the carbon penetration profiles. The carbon diffusion coefficients in iron were determined according to Fick's second law, given by

2 2 D c c t x      (1)
Where C is the concentration of atoms, t is the diffusion time, D is the diffusion coefficient, x is the diffusion length.

Results and discussion

Fig. 1 shows the microstructures of the specimens annealed at 1023K for 4h with different magnetic field intensity with the carbon diffusion direction parallel to the magnetic field direction. As the Fig. 1 shows, the black area in the left part of each picture is the carbon diffusion layer of the specimen, they are some phase transition product formed in the cooling process-pearlite (black regions) and Widmanstaten structure ferrite like needle and plate (gray regions), the gray area in the right part of each picture is the ferrite grains where carbon atoms haven't spread to. When the magnetic field intensity is less than 1T, the carbon diffusion layers of annealed specimens all have relatively flat interface and homogeneous thickness, when the magnetic field intensity is higher than 1T, the carbon diffusion layers of annealed specimens begin to have undulating interface and obviously thinner thickness, when the magnetic field is 12T, the carbon diffusion layer disappeared basically. For the case of a pair of semi-infinite solids such as the diffusion couples used in this study, a solution to the diffusion equation is generally given by the error-function solution which can be expressed as following equation:

( , ) 1 1 1 2 xt S erf x Dt C C            (2)
Where erf stands for the error function, D is the carbon diffusion coefficient, t is the annealing time for diffusion, and x is the penetration distance of carbon in iron. From Equation (2), the inverse error function of carbon concentration is proportional to diffusion distance, and the values of erf -1 [1 -C(x,t)/Cs] could be plotted against the penetration distance of carbon atoms as shown in Fig. 2, then D was estimated by the slope of the fitted lines.

Fig. 3 shows the average carbon diffusion distance and the average carbon diffusion coefficient of the specimens carburized with different magnetic field intensity at 1023K, respectively. It is seen that both the carbon diffusion distance and the carbon diffusion coefficient of the specimens decrease gradually with the increase of the magnetic field intensity, especially when the magnetic field intensity is higher than 1T, the carbon diffusion distance decreases remarkably with further increase of the magnetic field intensity. And on the whole, the carbon diffusion distance and the carbon diffusion coefficient of field annealed specimens are all shorter than that of the non-field annealed specimen, which indicates that the magnetic field annealing obviously restrains the carbon diffusion in pure iron in the α-Fe temperature region when the magnetic field direction parallel to the carbon diffusion direction, and this effect increased with further enhancement of the magnetic field intensity.

From the viewpoint of site occupancy of carbon in iron, the carbon atoms in α-Fe are predominantly located in the octahedral sites of the bcc lattice; thermodynamic calculations have revealed that the percentage of the tetrahedral-site occupancy is not more than 0.1% in α-Fe. When a magnetic field is applied, a <100> direction is extended because of a positive value of the volume magnetostriction constant for the <100>directions in α-Fe. Thus, the octahedral sites would be energetically more favorable for carbon atoms in α-Fe under a magnetic field than the tetrahedral sites. Although the fraction of carbon atoms at the tetrahedral sites is extremely small in the α-Fe temperature region, the overall diffusion coefficient is significantly affected by the carbon atoms in the tetrahedral sites because the diffusion coefficient of carbon at tetrahedral sites is ~1000× larger than at octahedral sites [13]. Thus the application of a magnetic field is likely to change the diffusivity of carbon owing to the change in the fraction of carbon atoms at two distinct interstitial sites. The greater the magnetic field intensity, the stronger of the inhibiting of magnetic field on carbon diffusion.

Therefore, the carbon diffusion in pure iron in the α-Fe temperature region is retarded by the applied magnetic field, and this effect increases with the enhancement of magnetic field intensity.

Conclusions

Effects of magnetic field intensity on carbon diffusion behavior in pure iron in the α-Fe temperature region were investigated. The results showed that the magnetic field intensity can significantly affect the carbon diffusion behavior in pure iron in the α-Fe temperature region along the direction parallel to the magnetic field direction, the average carbon diffusion distance and the average carbon diffusion coefficient of specimens decrease gradually with the enhancement of the magnetic field intensity. The application of a high magnetic field is likely to change the diffusivity of carbon owing to the change in the fraction of carbon atoms at two distinct interstitial sites. The greater the magnetic field intensity, the stronger of the inhibiting of magnetic field on carbon diffusion.

Fig. 1 :Fig. 3 :Fig. 2 :

 132 Fig. 1: Microstructures of specimens carburized at 1023K with different magnetic field intensity. (a) 0 T; (b) 0.1 T; (c) 0.4 T; (d) 0.7 T; (e) 1T; (f) 6T; (g) 12T

Acknowledgment

This work is supported by the National Natural Science Foundations of China (Grant Nos. 50801010, 51271052, 50971034) and the "111" Project (Grant No. B07015).The authors would like to express appreciation to the High Magnetic Field Laboratory of Northeastern University for providing the facilities.


H K Bui

G Berthiau
email: gerard.berthiau@univ-nantes.fr

D Trichet

G Wasselynck

Inductive thermography nondestructive testing applied to carbon composite materials: multiphysics and multiscale modeling

Keywords: CFRP composite, NDT, induction thermography, multiphysics and multiscale Modeling

This paper present a high potential NDT technique based on electromagnetic induction and thermography method called induction thermography or eddy-current thermography applied to laminated CFRP composites. Accurate assessment of the performance of this technique requires the development and use of a specific multiphysics and multiscale computation code in which mesoscopic model is used in macroscopic scale simulations. Simulation results show that short time heating is advantageous.

Introduction

Carbon Fiber Reinforced Polymer (CFRP) Composite is widely used in the aeronautic industry due to their high strength and light weight. For example, the composite ratio in the A320 of Airbus is about 20% of the total mass and has risen to 25% in the A380 and over 50% in the A350-XWB. However, the large-scale development of these materials still requires improvement in the processes during the whole life cycle of the material (forming, assembly, quality control and recycling). Technological obstacles to be overcome are mainly related to production rate issues, process control or evaluation of material health. At various stages of their life cycle, Non Destructive Testing (NDT) methods are often used to control the integrity state of the materials. The objectives of NDT techniques are to detect and characterize defects in the material. They play a vital role in the quality control and risk management. The main requirements for NDT techniques are: the ability to detect and discriminate the defects of various kinds, accurate evaluation of defects, fast and reliable inspection, the inspection capability for complex structures. Due to their complex natures (heterogeneity, strong anisotropy and multilayer) the detection of mesoscopic defects in CFRP composites still present problems which call for new improvement in actual NDT methods. In the following, the principle of a new NDT technique called induction thermography is firstly presented. The development of the numerical simulation tool must deal with some modeling constraint associated to laminated CFRP composites and most encountered defects in these materials. The latter is then briefly explained. Our original multiphysics and multi-scale modeling approach is next presented. Simulation results are discussed.

Induction thermography technique

The Fig. 1 shows the set-up of an induction thermography test bench. By induction heating principle, the workpiece is heated due to Joule effect of eddy-current. The inductor can be of arbitrary form. In this figure, a U-shaped inductor is shown. The temperature exposed to the surface of the workpiece is then measured with an infrared thermal camera. The presence of hidden or open defects can [1]:

disturb the induced currents flow and generate intensified currents areas.

inhibit the heat diffusion in the composite. The zone of intensified eddy-currents is correlated with hotter regions appearing around the defect whereas the presence of low thermal conductivity region in the material leads to the delayed heat flow. This double detection mechanism may enable a high defect detection capability for eddy-current thermography method. Generally, these disturbances lead to unusual distributions and temporal evolution of the temperature on the surface of the material. The latter is then processed and analyzed to detect and characterize the defects. The use of infrared camera allows for a large zone inspection in a single test. The performance of induction thermography technique depends on the used devices, of several process parameters (heating time, inductor shape, electromagnetic source frequency) and thermal signal processing methods so-called temperature contrasts [START_REF] Maldague | Theory and practice of infrared technology for nondestructive testing[END_REF].

Laminated CFRP composite

This material consists of stacks of several unidirectional plies as shown in the Fig. 2. (a). Each ply is characterized by a single fiber orientation whereas the composite material is characterized by its stacking sequence (i.e. the sequence of ply orientations).

(a) Micrographic section (b) A delamination defect between two plies (c) Fiber rupture defect. Fig. 2. Laminated CFRP composite and some encountered defects.

During the manufacturing process or operation time, several defects can occur in the CFRP. They can reduce the mechanical strength and increase the failure risk. Delamination, fiber rupture and porosity are the most commonly encountered defect types. Delamination occurs at the interface between unidirectional plies (Fig. 2. (b)). They can be induced by matrix/reinforcement disbonds that reach the interface between two plies. Fiber ruptures can occur in tension or compression when the plies are solicited in the direction of the fibers (Fig. 2. (c)). Porosity level can be expressed by the ratio of void volume to total volume of the composite. These defects are considered in mesoscopic scale, i.e. the scale of an elementary ply.

Multiphysics and multiscale modeling

CFRP material has a complex multiscale structure. The characteristic size of the microscopic scale is about 7 μm or the diameter of a carbon fiber whereas that of the mesoscopic scale is the thickness of a ply which is about 150 μm. The macroscopic scale consists of the entire laminate. Its size could be in order of some meters. Due to the large scale factor, a multiscale approach is used to simulate the CFRP behavior. Two principal steps are given as follows:

-The mesoscopic scale behavior is obtained using our original microscopic percolation model which gives a homogenized equivalent tensor of electrical conductivities of an unidirectional ply [3][4]. -The macroscopic scale behavior is modeled by means of a 3D multilayer finite element model. Homogenization model gives three components of the electrical conductivity of a unidirectional composite ply: σ||, σ⊥ and σz which are respectively the homogenized electric conductivity in the fiber axis, perpendicular to the fiber axis and in normal direction of ply surface (z-axis). In 3D multilayer finite element model, because a composite ply is very thin and highly anisotropic, if the laminate is meshed, it may lead to some numerical issues due to the distortion of the mesh and the strong anisotropy of constitutive law. In this case, orthogonal hexahedral finite elements are used thank to their stability and accuracy. Moreover, induction thermography simulation model involves a coupled electromagnetic and thermal problem. The following weak electromagnetic 𝑨 -𝜓 and nodal thermal formulations (1), ( 2) and ( 3) are used to calculate the temperature distribution in the laminate [5][6]:

∫ (𝒄𝒖𝒓𝒍𝒘 𝑒 1 𝜇 𝒄𝒖𝒓𝒍𝑨 + [𝝈]𝒘 𝑒 𝑗𝜔(𝑨 + 𝒈𝒓𝒂𝒅𝜓)) Ω 𝑑Ω -∫ 𝒘 𝑒 (𝒏 ∧ 1 𝜇 𝒄𝒖𝒓𝒍𝑨) 𝛤 = ∫ 𝒘 𝑒 𝑱 𝑠 𝑑Ω Ω (1)

∫ (𝑗𝜔[𝝈]𝒈𝒓𝒂𝒅𝑤 𝑛 (𝑨 + 𝒈𝒓𝒂𝒅𝜓))

Ω 𝑐 𝑑Ω = 0

(2)

∫ (𝜌𝐶 𝑝 𝜕𝑇 𝜕𝑡 -𝑑𝑖𝑣[𝝀]𝒈𝒓𝒂𝒅𝑇) 𝑤 𝑛 Ω 𝑐 𝑑Ω = ∫ 𝑃𝑤 𝑛 Ω 𝑐 𝑑Ω (3)
where 𝑨 and 𝜓 are respectively the magnetic vector potential and the primitive in time of electric scalar potential, 𝑱 𝑠 the source current density, 𝑃 the electromagnetic induced power density, 𝑇 the temperature, 𝐶 𝑝 the specific heat, 𝜌 the specific mass of the material, [𝝈] and [𝝀] respectively the tensors of electrical and thermal conductivity. The edge shape function and nodal shape function are denoted by 𝒘 𝑒 and 𝑤 𝑛 respectively. The electrical conductivity tensor [𝝈] of the ply i having a fiber orientation (with respect to the common 𝑂𝑥𝑦 coordinates which lie in the plan of the ply) takes the form:

[ 𝜎 𝑥𝑥 𝜎 𝑥𝑦 0 𝜎 𝑦𝑥 𝜎 𝑦𝑦 0 0 0 𝜎 𝑧 ] = [ 𝜎 ‖ 𝑐𝑜𝑠 2 + 𝜎 ┴ 𝑠𝑖𝑛 2 (𝜎 ‖ -𝜎 ┴ )𝑐𝑜𝑠 𝑠𝑖𝑛 0 (𝜎 ‖ -𝜎 ┴ )𝑐𝑜𝑠 𝑠𝑖𝑛 𝜎 ‖ 𝑠𝑖𝑛 2 + 𝜎 ┴ 𝑐𝑜𝑠 2 0 0 0 𝜎 𝑧 ] (4)
It is noted that the thermal conductivity tensor [𝝀] takes the same form as the electric one. Three orthogonal components of thermal conductivity are studied in [START_REF] Ageorges | [END_REF]. In thermal problem, only the composite domain (Ω ) is considered. In its boundary (denoted by ), the Newman type boundary condition: -[𝝀]𝜕𝑇 𝜕𝒏 = (𝑇 𝛤 𝑐 -𝑇 ) is applied. In this equation, 𝒏 is normal vector of and 𝑇 the room temperature. The exchange coefficient includes both the natural convection and radiation boundary conditions [8].

Case study

The piece to be inspected an 8 plies composite plate with the lay-up sequence [135°/90°/45°/0°] S . The dimension of the plate is 0.2m × 0.2m × 1mm in which the thickness of a ply is 136μm. Two defect types are introduced in a 0° ply of the piece as shown in the Fig. 3. The thickness of the defects is of 68μm or a haft of the ply one.

Electromagnetic simulation results

The Fig. 4 shows the distribution of electric field E and eddy-current J in the laminate in the case without defect. As can be seen, these distributions are very heterogeneous depending strongly on the lay-up sequence of the material. Hence, the precise description of induced fields in the laminated composite cannot be simulated using homogenous macroscopic model. This shows the accuracy of the presented multi-scale modeling approach.

(a) Amplitude of E (b) Amplitude of J. Fig. 4. Distribution of induced fields in the laminated composite. A quarter of the plate (x > 0, y > 0) is shown.

Defect detection by absolute contrast image

Absolute contrast (C a ) technique consists of subtraction between thermal images measured on defective piece and healthy one [START_REF] Maldague | Theory and practice of infrared technology for nondestructive testing[END_REF]. The non-null contrast areas on the resulting images allow for detection of defects. The defects can be detected in transmission mode and reflection mode as well. In the reflection mode, the temperature on the surface in the inductor side of the laminate is measured whereas in the transmission mode the temperature is measured in the opposite (d) Piece with fiber rupture defect. Opposite side. Fig. 5. Absolute contrast image obtained on the inductor side surface of the laminate and its opposite side. Some image of the C a is shown in the Fig. 5. In these cases, the piece is heated during 1s and the images are calculated at instant when the induction generator is turned off.

Advantage of short time heating

The heating duration t h is a parameter to be optimized. Simulations with various heating duration are carried out with the same excitation conditions. The temporal evolution of the absolute contrast on the middle point of the detected defective areas (Fig. 5) is calculated and compared with the maximum temperature (T max ) measured in each case. The Fig. 6 shows the C a /T max curves for various heating durations which are respectively of 0.25s, 0.5s and 1s. (c) Case of fiber rupture defect. Inductor side.

(d) Case of fiber rupture defect. Opposite side. Fig. 6. Time evolution of absolute contrast relative to the maximal temperature measured on the piece with defect.

As can be seen, the defect detection is more efficient with brief heating time. However, it is also necessary to increase the temperature of the piece to deal with high noise level problem. The use of high excitation current or high frequency induction heating device is therefore recommended.

Fig. 1 .

 1 Fig. 1. Configuration of an induction thermography test bench.

  (a) with fiber rupture defect. (b) with delamination defect. Fig. 3. Case study configuration. Inductor dimensions: h c = 30mm, w c = 40mm. A vertical rectangular inductor (coil) is used in this study. It is placed right above the piece and centered on it. The excitation current intensity is of 100A RMS at 1MHz.

  . Fig. 3 (b)). The choice of working mode depends on the accessibility of the infrared thermal camera. (a) Piece with delamination defect. Inductor side. (c) Piece with fiber rupture defect. Inductor side. (b) Piece with delamination defect. Opposite side.

  (a) Case of delamination defect. Inductor side. (b) Case of delamination defect. Opposite side.


Licheng Dong

Yunbo Zhong

Zhe Shen

Tianxiang Zheng

Huai Wang

Effect of static magnetic field on preparation of manganese oxides by hydrothermal process

Keywords: MnOOH, Mn 3 O 4, static magnetic field, nanowires, polyhedral products

The influence of magnetic field on the preparation of nanomaterials has been the subject of interest to researchers for a long time. In our experiment, manganese oxides were prepared through hydrothermal synthesis at different temperature under static magnetic field. Then the products were analyzed with SEM and TEM. It can be found that, the shape of product was changed by the magnetic field. The manganese oxides prefer to form nanowires in zero magnetic fields. However, when the magnetic flux density reached 6T, the shape of the product we have got was polyhedral. And the microstructure of product is characterized by means of the X-ray diffraction patterns. It can be found that, MnOOH was prepared in zero magnetic fields. Increasing the magnetic field intensity, the product was composed of Mn 3 O 4 . Magnetic field changed the hydrothermal reaction in thermodynamic aspect, which made the hydrothermal reaction turn to generate the product with higher susceptibility.

Introduction

Over the past few years, manganese oxides of various oxidation states and different structures have been attracting considerable research interest due to their promising application potentials in catalysis [1], ion exchange [2], molecular adsorption [3], magnetic field [4], secondary batteries [5], and supercapacitors [6][7][8]. Manganese oxyhydroxides, MnOOH, are of considerable importance in many technological applications, e.g., electrochemical reaction, battery and electrochromic. Mn 3 O 4 is a potentially interesting electrode material for electrolytic supercapacitors because of its low cost, environmental compatibility, and intrinsically high capacity. [9] On the basis of the above application potentials, various methods have been developed to synthesis manganese oxides with desired shape in order to obtain ideal functions for their unique applications. A high external magnetic field could be obtained easily with the development of superconducting technology. Magnetic fields have been recently introduced as an efficient tool to influence morphology and magnetic property of magnetic materials. A lot of researchers have already reported that static magnetic field can modulate the growth and final morphology of materials. Wang [10] found that single-crystalline nanowires of Fe 3 O 4 were formed under 0.35T magnetic field, while square and hexagonal particles were formed under zero magnetic fields. On the other hand, the magnetic field can affect the chemical reaction. Wang [11] obtained γ-Fe 2 O 3 nanotubes under 12T magnetic field, while the assynthesized samples were a single phase of α-Fe 2 O 3 . Due to the effect of static magnetic field, manganese oxides/oxyhydroxides were prepared by low-temperature hydrothermal synthesis under high magnetic field. In this communication, we report the preparation of manganese oxides/oxyhydroxides by a hydrothermal process in a static magnetic field, and the effect of the static magnetic field and temperature on the morphology and magnetic property of nanoparticles was studied.

Experiment and Characterization

The chemical reagents used in the work were manganese (Ⅱ) chloride tetrahydrate (MnCl 2 •4H 2 O, CAS No.:13446-34-9) and sodium hydroxide (NaOH, CAS No.:1310-73-2).All chemicals were analytical grade and purchased from Sinopharm Chemical Reagent Co.Ltd. In a typical process, 0.004 mol of MnCl 2 •4H 2 O was put into distilled water at room temperature to form an aqueous solution.20ml alkaline solution of 3M NaOH was slowly dripped into the above solution to precipitate Mn 2+ ions during constant magnetic stirring, and then a brown suspension solution was formed. The suspension solution was transferred to a stainless steel Teflon-lined autoclave (15ml effective volume) with a filling 80% volume of the autoclave for hydrothermal treatment. The autoclave was sealed and maintained at 120℃ for 4h with and without magnetic field. Finally, they were cooled down to room temperature. The products were filtered and washed with distilled water and absolute ethanol for few times, and then dried in an oven at 60℃ for 8h. A schematic diagram of the apparatus used in this experiment is shown in Fig. 1. The autoclave was put in the center of the magnetic field. The magnetic field (up to 6T) was applied parallel to the longitudinal direction and the temperature in the furnace chamber could be adjusted automatically by the temperature controlling apparatus. The morphologies of as-prepared samples were observed by a transmission electron microscopy(TEM)and highresolution transmission electron microscopy(HRTEM) (JEOL JEM-2010F, Japan).The crystal structures were characterized by X-ray diffraction(XRD; Rigaku D/MAX-2200,Tokyo, Japan) with Cu Kα radiation (60kV and 40mA). The magnetic properties were also measured using a vibrating sample magnetometer (VSM, LakeShore 7407, America) at room temperature.

Results and Discussion

Figure 1 shows the XRD patterns of the samples synthesized by hydrothermal process in various magnetic flux densities (MFD). Figure 1 demonstrates that the samples directly extracted were monoclinic MnOOH with lattice constants a=5.3Å, b=5.278Å, and c=5.307Å (JCPDS 41-1379) in zero magnetic fields. Increasing MFD to 0.6T, some diffraction peaks appeared which can be indexed to the tetragonal Mn 3 O 4 with lattice constants a=b=5.762Å and c=9.470Å (JCPDS 24-0734). In addition, the diffraction peaks of Mn 3 O 4 increased while the diffraction peaks of MnOOH decreased with the increase of MFD. When the MFD reached 6T, all diffraction peaks can be indexed to Mn 3 O 4 , accompanied by the disappearance of MnOOH. However, considerable changes in the morphology of the particles could be found when an static magnetic field was applied. In addition to nanowires, some cubic particles were observed in the samples when a 0.6T magnetic field was applied. Moreover, when the magnetic flux density reached 1T and 2T, more and more cubic particles were obtained. Furthmore, a large number of cubic particles formed, accompanied by the disappearance of the nanowires when the strength reached 6T.The results clearly show that the static magnetic field could be responsible for the formation of cubic particles. The former results indicate that the magnetic field affected the phase of samples intensively, because the only difference in preparation method between the samples is the MFD. From a thermodynamic perspective, magnetic field, like temperature, is an independent variable that changes the free energy, and makes the chemical reaction turn to generate Mn 3 O 4 , which may be a major reason. The formation reactions can be expressed by following equations (Equation ( 1) is for formation of MnOOH and Equation ( 2) is for formation of Mn 3 O 4 ).

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • ★ ★ ★ ★ 6T 4T 2T 1T 0.6T 0T • • • • • • • • • • • • • • • • ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ •-Mn 3 O 4 ★-MnOOH
2 22 11 M n 2 O H O M n O O H H O 42        1 1 T G 1 6 1 .4 k J / m o l    2 2 3 4 2 11 M n 2 O H O M n O H O 63        2 2 T G 1 4 4 .5 k J / m o l   
When a static magnetic field is applied, the resulting free-energy changes are classified into two terms [10]: the thermal Gibbs free energy, △G T , and the magnetic Gibbs free energy, △G M . Therefore, if a static magnetic field is imposed during the preparation of manganese oxides/ oxyhydroxides, a new equilibrium, (△G T +△G M ), will be reached [START_REF] David R Lide | Handbook of Chemistry and Physics[END_REF].△G T1 is the thermal Gibbs free energy for formation of MnOOH, and △G T2 is the thermal Gibbs free energy for formation of Mn 3 O 4 .△G T1 is lower than △G T2 at 120℃, which indicates that the product of the decomposition for MnCl 2 was MnOOH without a static magnetic field. However, a new equilibrium △G, (△G T +△G M ), will be reached, when a static magnetic field is applied. The magnetic Gibbs free energy, △G M , can be expressed as Equation (3).

B (T) (1) (2)
Fig. 4: Gibbs free energy △G in various magnetic field intensities

Conclusion

It is observed that a static magnetic field can significantly influence the phase and magnetic property of the samples synthesized by low-temperature hydrothermal method. Single-crystalline nanowires(diameter 20 nm and length about 1um) of MnOOH were obtained under zero magnetic fields. However, some cubic particles of Mn 3 O4 were formed when a 1T magnetic field was applied. What's more, the yield of Mn 3 O 4 increased with the increase of MFD. VSM results confirm that all of the samples were superparamagnetic, and the magnetism of the samples was increased with the enhancement of the magnetic field intensity. All results showed that a static magnetic field could destroy the stability of the chemical reaction, and make the chemical reaction turn to generate the products with higher magnetism. It is excited that the process could be a promising technique to synthesize other materials, and the related work is still under investigation.

Fig. 1 :

 1 Fig. 1: Schematic map of the apparatus for hydrothermal process in a superconducting magnet.

Fig. 2 :

 2 Fig.2: XRD pattern of the samples prepared in various magnetic field intensities Fig 3 displays SEM images of the samples prepared under static magnetic fields, which clearly reveal the effect of magnetic field on the nucleation and growth process of manganese oxides/ oxyhydroxides. It can be found that the products consisted of a large quantity of nanowires (diameter 20 nm and length about 1um) without magnetic field.

Fig. 3 :

 3 Fig.3: SEM images of the samples obtained in various magnetic field intensities (a) 0T, (b) 0.6T, (c)1T,(d) 2T, (e) 4T, (f) 6T

  Fig 4 shows Gibbs free energy △G in various magnetic field intensities, which indicates that the magnetic field makes the hydrothermal reaction turn to generate Mn 3

Acknowledgment

The authors would like to thank National Science Foundation of China (No.50974085, No.51034010), Key Project supported by Science and Technology Commission of Shanghai Municipality (No.13JC1402500), Development Foundation for Talents in Shanghai, China (No.2009046), National High-tech R&D Program of China (No. 2009AA03Z109). Financial Supported by Natural Science Foundation of Jiangsu Province, China (No. BK2011501), Financial Supported by Innovation Fund for Technology Based Firms, China (12C26213202452).


Huai Wang

Yunbo Zhong

Qiang Li

Yipeng Fang

Zuosheng Lei

Evolution of the droplet in ESR process under a transverse static magnetic field

Keywords: Electroslag remelting, Visualization experiment, Refinement of droplets, Static magnetic field, Electromagnetic vibration

To visualize the electroslag remelting(ESR) process, a transparent experimental model was built. Thanks to the transparent model, it's convenient to record the evolution of the droplets at the tip of the consumable electrode with and without magnetic field clearly by the high-speed camera. The visualized process of formation and detachment of the droplet under different conditions are given. The results showed that there are some obvious differences can be found when an external transverse static magnetic field of 0.7 Tesla is superimposed comparing with no magnetic field. The neck of the droplet became stronger than that without magnetic field and then something seeming like an inflated secondary droplet appeared in the middle of the neck, but shortly afterwards, the secondary droplet and the liquid neck were smashed into a lot of smaller droplets. The separation of the numerous small droplets increases the interface of the metal and slag tremendously which means the removal efficiency of the inclusions can be improved. The mechanism how the transverse static magnetic field affects the evolution of the droplets was discussed.

Introduction

Nonmetallic inclusions remained in the alloy steel ingots or high-temperature alloy ingots will destroy the matrix's continuity, then will increase the risk of inducing micro cracks under stress, which will reduce the mechanical properties and service life of the products made by these ingots. ESR process is an efficient way to remove impurities and inclusions in the above ingots [1].

The area size of the interface between the metal and slag is an important factor to impact the purification efficiency during the ESR process. And the droplet evolution behavior at the end of the consumable electrode is one of the key points to influence the contact area of metal/slag. So it is necessary to research the droplet evolution behavior. To improve the droplet evolution, the process named of Magnetic Control ESR(MC-ESR) [2,3] was taken into account as shown in Fig. 1. Here, a transverse static magnetic field of 0.7 Tesla was adopted during the ESR process.

It is clear that the industry ESR process is operated under the bad working conditions with strong current and high temperature. So most researches of the ESR process were concentrated on physical simulations and numerical simulations. J. Campbell [4] using Pb, Zn, Al and Cu as the consumable electrodes and molten LiCl-KCl as the slag to simulate the ESR process. The droplet evolution pictures were given but very ambiguous. Ice(the comsumable electrode) and vegetable oil(the slag) were utilized by O. A. Troyanskyy [START_REF] Troyanskyy | Proceedings of the International Workshop on Metal-Slag Interaction[END_REF] to study the mechanism of droplet transfer. A. Kharicha et al. [START_REF] Kharicha | International Symposium on Liquid Metal Processing and Casting[END_REF] established a 3D magneto-hydrodynamic model to simulate the dripping process of droplets. They found that superimposing a transverse magnetic field can make the droplets become smaller, however the numerical model was under the condition with the DC current. Wang et al. [START_REF] Wang | [END_REF] developed a 3D mathematical Fig. 1: Schematic of magnetic controlled MC-ESR. model, and they found that the momentum and heat were brought to the metal pool by the droplets. In this paper, a transparent experimental model which is similar with J. Campbell's [4] was built to visualize the ESR process.

Experiment

The experiments were done using the transparent model apparatus as shown in Fig. 2. Quartz glass tube with internal diameter of 31 mm was used as the mold. Zinc bar with diameter of 15mm was selected as the consumable electrode. Molten ZnCl 2 was chosen as the molten slag for its fine transparency and electrical conductivity. To observe the droplet evolution process elaborately, a high-speed camera was utilized to record the whole process happening at the end of the consumable electrode with the record frequency of 200 frames per second.

Water cooling system of the bottom electrode was kept constant in each experiment, and the operational parameters were listed in Tab. 1. The depth of the molten slag was about 70 mm. The consumable electrode was immersed into the molten slag for about 10 mm. The feed rate of the consumable electrode was manual controlled to maintain the intensity of remelting current constant. The experiments were done with and without a transverse static magnetic field of 0.7 Tesla generated by an electromagnet.

Results and discussion

Fig. 3 shows the representative decomposed video on the descending process of the droplet without magnetic field. To demonstrate the droplet evolution process better, the time when the droplet detaches from the consumable electrode is set as T second and the time intervals of the continuous pictures are the same. From Fig. 3, it can be found that the droplet connects with the end of the consumable electrode by a slender neck, and then the neck becomes thinner and thinner until it is snapped under the action of the detaching force(electromagnetic pinch force and gravity). When the big droplet separates from the droplet neck, the slender neck quickly rises up to the tip of the consumable electrode and there is a small droplet form from the liquid neck under the action of the surface tension and gravity. In the meantime, the big detached droplet sinks quickly in molten slag with the shape of a saucer. Here the big droplet is called as 'main droplet' in that sometimes one or two small droplets may form and sink after the 'main droplet' and the small droplet is called as 'satellite droplet' for distinction.

Fig. 3: The droplet evolution process under the condition without the external magnetic field.

Fig. 4: The droplet evolution process under the condition with a transverse static magnetic field of 0.7 Tesla.

When a transverse static magnetic field of 0.7 Tesla were superimposed during the ESR process, the droplet evolution was changed a lot as shown in Fig. 4. Comparing with the situation without the external magnetic field, the liquid neck connecting with the consumable electrode and the main droplet becomes stronger and then something seeming like an inflated secondary droplet appeared in the middle of the neck, but soon after, the secondary droplet and the liquid neck were smashed into a lot of smaller droplets, and then the small satellite droplets sink slowly in the molten slag.

It is well known that the electromagnetic vibration(EMV) [2,[START_REF] Vivès | Tsukihashi[END_REF] can be generated by simultaneously superimposing an alternative current and a static magnetic field whose action direction is perpendicular to the former in the molten metal. The mechanism of the phenomenon described above under the condition with a transverse static magnetic field of 0.7 Tesla can be explained as following: The alternative remelting current shuttles along the consumable electrode and the molten slag in a vertical direction. When a transverse static magnetic field is superimposed during the ESR process, the EMV will be generated. During the ESR process, the alternative current will mainly flow through the droplet neck to minimize the electric resistance for the high electrical resistivity of the slag. So a tremendous EMV will be generated and act on the liquid droplet neck. The violent EMV can change the shape of the liquid droplet neck from a column into a flat strip. That's why the droplet neck under the condition with the magnetic field looks like stronger than that without the magnetic field.

As the forceful EMV and gravity act on the flat strip, the middle of the strip becomes thinner and the border begins to expand outward, so something like an inflated bulge appearing in the middle of the strip is not a secondary droplet actually. The periodic reverse force make the center area of the strip become so thin that a hole appears and quickly grows bigger. Then, the alternative current will focus on flowing through the frail margin area of the liquid strip, eventually the effect of the EMV becomes so huge that the whole liquid droplet neck is smashed into a lot of satellite droplets.

To verify the smashing effect of the EMV acting on the droplet neck was not an accidental phenomena, the zinc bar consumable electrode was replaced by the lead bar during the physical simulation experiments. The droplet evolution processes without and with a transverse static magnetic field of 0.7 Tesla are shown in Fig. 5 Apparently, the phenomenon of the liquid droplet neck being smashed into many smaller droplets indicates that the interface between the metal and the slag is increased largely. So the inclusions and impurities removal efficiency will be expected to be improved.

Conclusions

In this paper, physical simulations of the ESR process have been done with the aid of the transparent model apparatus. The visualized results showed that superimposing a transverse magnetic field will influence the ESR process remarkably. The mechanism how the transverse static magnetic field affects the evolution of the droplets was discussed. Main results obtained in this study are following: (1) The visualized process of formation and detachment of the droplet under different conditions are given; (2) Applying a transverse static magnetic field of 0.7 Tesla during ESR process, the liquid droplet neck can be smashed into a lot of smaller droplets; (3)The technique of the MC-ESR can increase the contact area of metal/slag enormously which indicates that the removal efficiency of nonmetallic inclusions can be improved significantly.

Fig. 2 :

 2 Fig. 2: Schematic of the transparent model apparatus.

  (a) and (b) respectively. It is clear that the liquid lead droplet neck is also smashed into lots of samll droplets under the power of the EMV as shown in Fig. 5(b), and which shows the universality of the smashing effect. (a) Without the external magnetic field. (b) With a transverse static magnetic field of 0.7 Tesla. Fig. 5: The droplet evolution process with the consumable electrode of lead bar.

Acknowledgment

The authors gratefully acknowledged the financial support of Nature Science Foundation of China (Key Project No. 51034010), Science and Technology Commission of Shanghai Municipality (Key Project No. 3JC1402500), Natural Science Foundation of Jiangsu Province (BK2011501) and Innovation Fund for Technology Based Firms (12C26213202452);


Zuo-Sheng Lei

Song-Bao Wang

Yong-Chao Shi

Jia-Hong Guo

Coarsening Research of 2D Ferro-Foam under Magnetic Gravity Compensation

Keywords: coarsening, ferro-foam, magnetic gravity compensation

Coarsening process, concerning the bubble growth rules, was studied in the 2D ferro-foam system under both normal gravity and magnetic gravity compensation conditions. Here, the 2D ferro-foam was produced by continuously blowing bubbles into the ferro-fluid filled in a closed Hele-Shaw cell. Afterwards, we placed the prepared ferro-foam in center of the Helmholtz-Maxwell coils, which can generate a uniform magnetic gradient field acting on the ferro-fluid, so as to compensate the gravity. The evolutionary dynamics of coarsening was recorded in four hours by a digital camera using the time-lapse function, and the coarsening data was extracted from the Image-Pro Plus program. The results show that on both conditions, the law of coarsening confirms with the Von Neumann's, while the magnetic gravity compensation was applied, the dynamics process was suppressed according to the external magnetic field.

Introduction

Foam coarsening process, which involves the transport of gas between bubbles of different sizes, leading to the area change of polyhedral bubbles with time, has posed significant issues for both fundamental research and practical applications [1][2][3] . At present, the study of foam coarsening dynamics is mainly divided into two aspects [4][START_REF] Weaire | proceedings of the Materials Science Forum[END_REF][START_REF] Glazier | [END_REF] : the coarsening dynamics involves in the continuous evolution of the bubble structure, so the analysis of the topological dynamics acts as the first primary research content; on the other hand, in the process of gas transport, how to quantitatively describe the area change of polyhedral bubbles is another major research. But on the normal earth conditions, foam coarsening is frequently coupled to foam drainage, which is mainly driven by gravity, and the coupling is not easy to account for [7] . Meanwhile, gravity also plays an important role in the formation of foam and its subsequent evolutionary dynamics. So microgravity conditions are therefore ideal to study the coarsening process. However, the opportunities of experiments in space are rare and their waiting time is often very long. For this reason, Magnetic Gravity Compensation [8,9] , as a replacement way to achieve reduced or even micro gravity condition by imposing a magnetic volume force directly anti-parallel to the gravity, makes it possible to perform ground-based experiments under simulated reduced or microgravity in a long term with reasonable cost. In this paper, we develop an apparatus made of two pairs of Helmholtz-Maxwell coils, which can generate a uniform magnetic gradient field for ferro-fluid filled in a closed Hele-Shaw cell, so as to produce a uniform magnetic volume force to compensate the gravity. First, we analyze the distribution of magnetic field and the gravity level of ferro-fluid experimentally. The numerical simulation was shown in our previous work [START_REF] Zuo-Sheng | The 7th International Conference on Electromagnetic Processing of Materials[END_REF][START_REF] Yong-Chao | proceedings of the Advanced Materials Research[END_REF] . Whereafter, the coarsening process of 2D ferro-foam was recorded on both normal gravity and magnetic gravity compensation conditions respectively.

Experiment apparatus

Here, the magnetic gravity compensation was realized by combining the two pairs of Helmholtz-Maxwell coils and ferro-fluid. The specifications of the coil system is illustrated in Table 1. The configuration of the Helmholtz-Maxwell coil system is shown in Fig 1.

Table 1 The configuration of the magnetic compensation apparatus is illustrated in Fig. 1. The outer pair is Helmholtz coil, which consists of two identical circular magnetic coils that are placed symmetrically one on each side of the experimental area along a common axis, and separated by a distance h equals to the radius R of the coil. While the space of inner pair satisfies h = 3 R, thus form a Maxwell coil. Once the appropriate current was putted into the coil separately, we can get a uniform magnetic gradient field ( B  ) in the centre area of the coil system. As shown in Fig. 2, we measure the average gradient of magnetic field along vertical direction in the centre area of the coil system, the results indicate that field distribution is linear along the vertical direction, and uniform in the centre area. Subsequently, by calculating the gravity compensation level of magnetic fluid, we found that a uniform gravity compensation region existing in the centre of the external coils. The gravity level was defined by the ratio of effective gravitational acceleration (g eff = g + F m /ρ) and normal acceleration(g eff /g). And the gravity could be totally compensated while the current in Maxwell coil reached a specific value(93A). Details of the effective gravity in ferrofluid was shown in Fig. 3. Fig. 2: The average gradient of center magnetic field Fig. 3: The effective gravity level of ferro-fluid Afterwards, the Hele-Shaw cell, with internal dimensions 60×100×1mm, was placed perpendicular to the external field in centre area of the coil system. The ferro-fluid, which is a colloidal suspension of nanoscale ferromagnetic grains, is filled into the cell. And 2D ferro-foam was generated by blowing gas into the cell continuously. Then, by keeping track of the coarsening dynamics process in two dimensional foam for four hours, we analyse two fundamental dynamics mechanism, which refers to the topological evolution and bubble growth rules. First, there is the neighbor-switching process shown in Fig. 4 (a)(b) and Fig. 5 (a)(b), which we shall call a T1 process. It can be pictured as taking place as an edge shrinks to zero, to be replaced by another one in such a way that the connections to vertices are rearranged. This, incidentally, justifies the statement that only vertices with z = 3 (in 2D) are topologically stable. Secondly, faces (2D cells) may vanish-the T2 process of Fig. 4(c)(d) and Fig. 5 (c)(d). We confine this to the vanishing of a three-sided cell as shown. (A cell with more than three sides can vanish through a series of T1 processes to make it three-sided, followed by a T2 process.) Fig. 6: Generalized von Neumann's laws in ferro-foam (a):normal gravity; (b):magnetic gravity compensation Meanwhile, as shown in Fig. 6, on both normal gravity and magnetic gravity compensation conditions, the 2D bubble growth rule conforms well to the Von Neumann's Law [START_REF] Neumann | Metal interfaces[END_REF] : Where  is the surface tension coefficient,  is a constant referring to permeability of the gas in bubbles.

  6 3 n dA = n dt    (1)
The Von Neumann's Law assumed that the gas was incompressible, so the rate of area transfer across a wall between two bubbles is simply proportional to the product of the wall area and the pressure difference between the bubbles. As we can see in Fig. 6, the slope of bubble growth curves was decreased from 0.039 to 0.011 while the magnetic gravity compensation was applied. It indicates that the gas transmission between neighbouring bubbles was restrained under magnetic gravity compensation, this is due to the properties of liquid membrane was changed with the external magnetic field, as a consequence of making the foam itself more stable [START_REF] Elias | Foams and Emulsions[END_REF][START_REF] Sudo | [END_REF] .

Conclusions

By measuring the distribution of magnetic field in Helmholtz-Maxwell coil system and the gravity level of ferro-fluid in external magnetic field, we realized the simulated micro-gravity in normal earth conditions in a long term with reasonable cost. Meanwhile, the coarsening process was proceeded in 2D ferro-foam under both normal gravity and magnetic gravity compensation. The results show that the 2D bubble growth rule conforms well to the Von Neumann's Law on both conditions. But the gas transmission between neighbouring bubbles was restrained under the latter situation.

Fig. 1 :

 1 Fig.1: Helmholtz-Maxwell coil system

Fig. 4 :Fig. 5 :

 45 Fig.4: Structural evolution of ferro-fluid in normal gravity condition

  Where R is the radius of each coil, N is the number of turns per coil, H is the height of each coil.

			Specifications of the coil system
		Helmholtz Coils		Maxwell Coils
	R H [mm]	N H	H H [mm]	R M [mm]	N M	H M [mm]
	210	140	210	100	140	173.2

Acknowledgment

This project financially supported by National Science Foundation of China (No.51274137 and NO.11372174).


V Fireteanu

E Rousset

E Chauvin

N Chouard

Simultaneous Induction Heating and Electromagnetic Stirring of a Molten Glass Bath

Keywords: molten glass, induction heating, electromagnetic stirring, finite element models, travelling magnetic field, rotating field, helicoidal field, fluid dynamics computation

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

The electromagnetic stirring generated by Lorentz forces in electro-conductive bodies like molten glasses in the presence of AC magnetic fields is not independent on the heat generation by the Joule effect of induced currents [1], [2]. All solutions studied in this paper, able to ensure first of all an intense electromagnetic stirring in cold crucible induction furnaces, are characterized by the same value of the power induced in the molten glass bath. Results issued from three-dimension (3D) models for electromagnetic field and for molten glass flow concern for the same geometry and physical properties of the molten glass bath in Table 1, and:

(a) an one-phase inductor of a reference furnace for molten glass induction heating; (b) an eight-phase inductor of travelling magnetic field type for induction heating and electromagnetic stirring; (c) a thirty-two-phase inductor of rotating magnetic field type; (d) a thirty-two-phase inductor of helicoidal magnetic field type.

Electromagnetic and fluid dynamic models applied to the reference one-phase induction cold crucible furnace.

The reference furnace is an induction cold crucible furnace for nuclear waste immobilization in glass [START_REF] Brun | WM2009 Conference[END_REF], [START_REF] Naline | WM2010 Conference[END_REF]. The conversion of the electric energy into heat in this device is the result of the Joule effect of the induced currents in the molten glass placed in the AC magnetic field generated by the inductor. The FLUX3D-EM model of the reference furnace takes into account the active components -the one-phase reference inductor and the molten glass charge, Fig. 1, solid conductor regions, which are surrounded by an infinitely extended non-conductive and non-magnetic region. The surface impedance model of the inductor is considered in the computation of the electromagnetic field. The steady state AC magnetic problem for the frequency 285 kHz considers the intensity of the inductor current for which the power in the molten glass has the reference value 150 kW. The current density in the inductor turns and in the molten glass region and the arrows representation of Lorentz forces are presented in Fig. 2 and3. The FLUENT-CFD model of the viscous molten glass flow considers the Lorentz force volume density imported from the EM model/problem. The calculation is made upon the following assumptions: the flow is laminar, the molten glass is incompressible and the flow is isothermal. Main results feature the arrows of the velocity in the vertical xOz plane, Fig. 4, and the flow streamlines in Fig. 5. The molten glass flow, Fig. 4 and 5, is the result of the radial bath compression, which is maximal in the middle. In connection with the molten glass stirring effect of the electromagnetic field, the values of the maximum Lorentz force volume density in the molten glass is only 3.354 N/m 3 , Fig. 3, and the maximum of the velocity is only 0.54 mm/s, Fig. 5. With such a small value of the velocity, the electromagnetic stirring of the molten glass bath in the reference furnace is completely negligible.

Conclusions

The calculations establish that the simultaneous direct induction heating a strong electromagnetic stirring of a viscous molten glass bath is workable by using inductors that generate high magnitude Lorentz forces with multi-phase AC magnetic field. The inductors, intended for travelling, rotating or helical field, operate at relatively low frequency and have important pole pitches. Thus an efficient stirring featuring a velocity above 200 mm/s in a significant volume of the molten glass associated with a reasonable heating of the bath is achieved. Such significant electromagnetic stirring able to generate important and well oriented driving effects in the molten glass may be promising for the nuclear waste vitrification technology, which require important mass and heat transfer in order to incorporate and melt solid particles.

Fig. 1 .

 1 Fig. 1. The EM computation domain Fig. 2. Current density [A/m 2 ] in the inductor and molten glass regions

Fig. 3 .

 3 Fig. 3. Arrows of Lorentz force Fig. 4. Velocity vectors of Fig. 5. Volume streamlines coloured volume density [N/m 3 ] the molten glass [mm/s] by local velocity [mm/s] Induction heating and electromagnetic stirring with an inductor of travelling field type.The studied travelling field inductor consists in eight co-axial circular turns, Litz type/filiform conductor made, around the molten glass bath, Fig.6. The eight currents of frequency 2 kHz are evaluated so that the power induced in the molten glass has roughly the value 150 kW in order to have the same heating as in the reference furnace. To generate an one-pole travelling field, the phase-shift between two successive currents of the inductor is 180/8 = 22.5 degrees.

Fig. 8 .

 8 Fig. 8. Arrows and streamlines of the velocity field [mm/s] for upward orientation of the traveling field An important change of electromagnetic stirring in a one-pole travelling field it results when reverses the field direction of propagation. As shown in Fig. 9, the effect consists in the displacement of the main stirred part of the molten glass volume from the lower to upper half of the bath.

Fig. 9 .

 9 Fig. 9. Velocity field [mm/s] for downward orientation of the traveling field Induction heating and electromagnetic stirring in rotating magnetic field type. The rotating field inductor, able to generate a two-poles rotating magnetic field, consists in thirty-two identical Litz type conductor regions with axial orientation, Fig. 10, uniformly distributed around the molten glass region. These thirty-two conductors, representing from physical point of view the phases of the inductor, are supplied with currents having the same rms value. To obtain a two-poles rotating magnetic field, the currents in two successive phases are characterized by the phase shift 360/32 = 11.25 degrees. Same supply frequency 2 kHz as previously is considered.

Fig. 10 .

 10 Fig. 10. Rotating field type inductor, 32 phases, Fig. 11. Color map and arrows of the current density without and with magnetic core [A/m 2 ] induced in the molten glass bath Compared to the travelling magnetic field previously studied, a completely different spatial configuration of induced currents, respectively of molten glass induction heating, characterizes the rotating magnetic field. In rotating field the induced currents closes in vertical planes, Fig. 11-right, and the maximum of the power volume density is located in the centre of the upper free surface, Fig. 11-left, and the centre of bath bottom.In rotating magnetic field the vectors of the Lorentz force density, Fig.12, are tangent to circles in horizontal planes.The driving effect of the rotating field decreases in radial direction, from the maximum value on the lateral wall to zero on the bath axis. Consequently, the electromagnetic stirring in rotating field consists in the horizontal glass rotation.

Fig. 12 .

 12 Fig. 12. Lorenz force density [N/m 3 ] in rotating fieldIn case of the rotating field inductor without magnetic core, Fig.10-left, the power 153.5 kW is induced in the molten glass for the current 33.8 kA in the inductor phases. The correspondent maximum value of the Lorentz force density, 955.9 N/m 3 , is incomparable higher than in case of the reference inductor. An inductor including a

Fig. 17 .

 17 Fig. 17. Molten glass motion in helicoidal field -horizontal and vertical components of glass velocity in [m/s] in different horizontal planes and the vertical component of the velocity in a vertical symmetry plane

Table 1

 1

	: Molten glass bath properties
	Volume [m 3 ]	0.14
	Electric conductivity [S/m]	15
	Viscosity [Pas]	1.0
	Density [kg/m 3 ]	2700


Lijun Fan

Yunbo Zhong

Yulai Xu

Zhe Shen

Tianxiang Zheng

Zhongming Ren

Suppressed interdiffusion behavior of Fe/Fe-Si alloy under static magnetic field

Keywords: Fe-Fe50wt.%Si couple, Diffusion, Magnetic field

Effect of static magnetic field on interdiffusion behavior and intermediate phase growth characteristics in Fe-Fe50wt.%Si diffusion couples has been investigated. It was found that both FeSi and solid solution layers formed after annealing at different temperatures with and without magnetic field. Growth of FeSi and solid solution layers obeys parabolic law and is suppressed under magnetic field due to the reduced frequency factor D 0 but not the activation energy Q.

Introduction

Magnetic fields have great effect on recrystallization, grain growth, phase transformation, texture formation and so on during the processing of advanced materials which involves the diffusion of atoms [1][2][3]. Youdelis et al. [4] found that magnetic field which was perpendicular rather than parallel to diffusion direction could retard the diffusion of Cu atoms in Al-AlCu diffusion couple. While Nakajima et al. [5] found that no significant difference between the diffusivities of Ni in Ti perpendicular and parallel to the magnetic field direction. Li et al. [6] found that the thickness of intermediate phases in Mg-Al diffusion couple was reduced under magnetic field at 340-420 °C. However, Liu et al. [7,8] found that the thickness of intermediate phases in Al-Zn and Al-Mg diffusion couples increased in a parabolic law in the alternative magnetic field at 330-430 °C. The 6.5wt.%Si steel has great potential for electrical device and applications [9][10][11]. At present the mass production of 6.5wt.%Si steel sheets by cold rolling is almost impossible, and manufacture even by hot rolling becomes difficult when Si content exceeds 4 wt. % [12]. To solve the problem about the strong brittle characteristic of 6.5wt.%Si steel, methods such as chemical vapor deposition, powder metallurgy and composite electro-deposition have been considered [13]. It is the key point for all these methods to realize and control the interdiffusion process of Fe-Si. Considering the orientation effect by superimposition of magnetic field during diffusion process, it is important to understand how static magnetic field affects diffusion behavior in Fe-Si system. Influence of static magnetic field on growth of intermediate diffusion layer in Fe/Fe-Si diffusion couples has been investigated and the mechanism has also been discussed in this paper.

Experimental procedure

The experimental setup designed and installed, and procedures of preparing and treating the Fe/Fe-Si diffusion couples under magnetic field are shown in Fig. 1. The Fe50wt.%Si alloys were prepared with high-purity Fe (99.9 wt. %) and Si (99.9 wt. %) by vacuum induction melting in a high-purity graphite crucible. The alloys were poured into a pure Fe cylindrical mold with external diameter of 20 mm and inner cuboid dimension of 10 × 10 × L mm (L: length) to cast specimens by pulling up the alundum rod (Fig. 1(a)). The castings were cut into the sliced samples with a thickness of 3 mm vertical to the length direction (Fig. 1(b)). The samples were ground with SiC abrasive papers from No. 400 to 2000 and polished mechanically with the 1.0 μm diamond paste before placed in the furnace. In order to obtain a well combination interface between Fe and Fe50wt.%Si, scanning electron microscope (SEM) equipped with energy dispersive spectroscopy (EDS) was employed to analyze the variation of silicon content at the interface of the diffusion couples. The original diffusion couples are annealed at 1050, 1100 and 1150 ºC for 3, 6, 9, 12 h, respectively, with and without the 0.8 T magnetic field in an Argon atmosphere. The experimental apparatus consists of a static electromagnet and a heating furnace equipped with a temperature controller (Fig. 1(c)).

Results and Discussion

The typical SEM morphologies of Fe-Fe50wt.%Si after annealing at 1150 ºC for 3 h and 1100 ºC for 9 h with and without magnetic field are shown in Fig. 2. It can be clearly seen that the interdiffusion direction is perpendicular to that of magnetic field and the Fe50wt.%Si, FeSi, and Fe layers can be easily identified (Fig. 2(a)). The Fe 2 Si and Fe 3 Si layers were observed after annealing at 1150 ºC for 3 h both with and without magnetic field (Fig. 2(b)).

The thickness of Fe 2 Si and Fe 3 Si layers are respectively about 7 and 3 μm according to the chemical composition variation of SEM-EDS (Fig. 2(c)). However, the Fe 2 Si and Fe 3 Si layers can be hardly observed after annealing at 1050-1150 ºC for more than 3 h. Hence, the FeSi phase is very stable in Fe-Fe50wt.%Si diffusion couple. In addition to the typical FeSi layer (Fig. 2(d)), the solid solution layer according to SEM-EDS mapping analysis is observed in Fig. 2(e). The thickness of FeSi layer increases from about 43 μm after annealing at 1050 ºC for 3 h to 80 μm for 12 h. With the increase of annealing temperature to 1100 and 1150 ºC, the thickness of FeSi phase respectively increases from about 57 and 76 μm to 99 and 119 μm with the increase of annealing time from 3 h to12 h. However, the thickness of FeSi layer under magnetic field perpendicular to diffusion direction dramatically decreases compared with that without magnetic field. For example, the thickness of FeSi phase after annealing at 1100 ºC for 9 h apparently decreases from about 87 μm without magnetic field (Fig. 2(d)) to about 64 μm under the 0.8 T magnetic field (Fig. 2(f)). The thickness variation of the solid diffusion layer exhibits similar tendency to that of FeSi layer. What is more, compared with that perpendicular to diffusion direction, the thickness of FeSi and solid diffusion layers varies very slightly and the difference can be even neglected at 1050-1150 ºC for up to 12 h under the magnetic field parallel to diffusion direction. So the magnetic field exhibits a suppressing effect on interdiffusion behavior of Fe/Fe-Si alloy and no significant difference between the diffusivities in perpendicular and parallel directions. Fig. 3 shows the thickness of FeSi and solid solution layers plotted against the square root of diffusion time according to the equation [8]:

The above results indicate that the magnetic field change in the growth of FeSi and solid solution layers is probably due to the reduced frequency factor D 0 . A theory developed by Youdelis et al. [14] shows that the diffusivity in a magnetic field is reduced by the factor 1/(1+ω ce 2 /υ e 2

), where ω ce and υ e are the cyclotron and collision frequencies respectively of the diffusion transported electrons. Generally, such atom diffusion process is via atom-vacancy jump mechanism, in which the diffusion coefficient D could also be expressed as [15,[START_REF] Porter | Phase Transformations in Metals and Alloys[END_REF]:

[] 2 m v m v Δ S Δ S-Δ H Δ H D = n Z α υ e x p ( + ) e x p ( - ) K K K T K T  ( 3
)
where n is the constant, Z is the coordination number of one atom, υ is the vibration frequency of atoms, α is the jump distance of atoms, and ΔS m , ΔS v , ΔH m , ΔH v are the entropy and enthalpy change for moving an atom to a vacancy and for producing a vacancy, respectively, R is the gas constant and T is the absolute temperature. According to Eq. ( 2) and

(3), it can be deduced that the magnetic field may affect the entropy but not the enthalpy needed during the diffusion process. Hence, the effect of magnetic field on the growth of interdiffusion phase is the thermally activated process rather than the barrier height because the influence is mainly on the frequency factor but not on the activation energy in the Fe-Fe50wt.%Si diffusion couple.

Conclusions

Interdiffusion behavior of Fe-Fe50wt.%Si diffusion couple had been studied. The FeSi, Fe 2 Si and Fe 3 Si have been identified after annealing within 3 h, but the Fe 2 Si and Fe 3 Si disappear when further prolonging the diffusion time up to 12 h both with and without magnetic field. No significant difference between the diffusivities of FeSi and solid solution layers perpendicular and parallel to the magnetic field direction has been detected. Growth of FeSi and solid solution layers obeys the parabolic law with and without magnetic field. Growth of intermediate phase is suppressed under magnetic field due to the reduced frequency factor D 0 but not the activation energy Q.

Fig. 1

 1 Fig. 1 Experimental apparatus, (a) vacuum induction melting and casting, (b) sliced sample preparation and SEM-EDS analysis of Fe/Fe-Si interface, and (c) diffusion in magnetic field.

Fig. 2

 2 Fig. 2 SEM morphologies, (a) 1150 ºC × 3 h, 0.8 T, (b) enlarged morphology, (c) SEM-EDS of the yellow arrow line, (d) 1100 ºC × 9 h, 0 T, (e) SEM-EDS mapping analysis, (f) 1100 ºC × 9 h, 0.8 T.

Acknowledgments

The authors gratefully acknowledged the financial support of National Natural Science Foundation of China (No.51034010), Science and Technology Commission of Shanghai Municipality (No.13JC1402500), and Natural Science Foundation of Jiangsu Province (No.BK2011501).

(1) where W is the thickness, t is the annealing time and k is the rate constant. So it turned out distinctly that the parabolic law is fulfilled for the growth of diffusion layer. The slope increases with the increase of temperature both with and without magnetic field. The slope significantly decreases with the superimposition of magnetic field after annealing at 1050-1150 ºC. From the temperature dependence of the rate constant, the frequency factor (D 0 ) and the activation energy (Q) for diffusion layer growth with and without magnetic field have been calculated. The growth rate is expressed by the Arrhenius-type of relation [6]:

) RT (2) where D 0 is the frequency factor, Q is the activation energy, R is the gas constant, and T is the absolute temperature. The logarithm of the diffusion coefficient D was plotted versus the reciprocal of absolute temperature T in Fig. 4, D 0 and Q were respectively measured by the intercept and slope of the fitted straight lines (Table 1). The activation energy Q for growth of FeSi and solid solution layers is nearly the same with and without magnetic field. However, the corresponding frequency factor D 0 for growth of FeSi and solution layers dramatically decreases with magnetic field.


T Steinberg
email: steinberg@etp.uni-hannover.de

E Baake

Adaption and verification of numerical models for gas bubble dynamics in electroconductive fluid

Keywords: Electromagnetic Fields, MHD, Two-Phase Flow

This paper describes the investigation of bubble rise dynamics in a special molten metal bubble reactor which is used at Karlsruher Institute of Technology (KIT) to investigate the CO2-free production of hydrogen. The focus of the 2D simulations presented in this paper is the single bubble rise dynamics through the previously mentioned column and its comparison to the rise dynamics with applied AC EM field.

Introduction

The common process to produce hydrogen is the CO2 intensive steam reforming process. Due to this fact it seems to be highly attractive to investigate processes which produce hydrogen with lower or without CO2 emission. One of these processes is the thermal cracking of methane. It takes place in a molten metal bath of a chemical bubble reactor shown in Fig. 1 at ambient temperatures above 600 °C. The chemical bubble reactor is a cylindrical vessel with an heated wire wrapped around it. In Fig. 1 is also shown a possible inductor coil to apply the electromagnetic (EM) field, in order to manipulate the liquid metal flow. Fig. 1: Chemical bubble reactor with liquid tin and bubbly methane flow [START_REF] Tucs | Proceedings of the International Conference on Heating by Electromagnetic Sources[END_REF] Table 1: Material Properties of liquid tin and methane used in simulation [ The goal of this work is to develop and verify numerical models to describe the bubble flow dynamics in molten metal bath and using this models to investigate the impact of applied external EM fields on the process.

The applied fields are used to manipulate the bubbly flow in order to gain maximal efficiency of the hydrogen production process. In previous works calculation results for single bubble rise dynamics in 2D axisymmetric consideration for various characteristic dimensionless numbers in the presence of external DC EM field have been obtained and verified through experimental and simulation data from literature [START_REF] Tucs | Proceedings of the International Conference on Heating by Electromagnetic Sources[END_REF]. Moreover, Jakovics et. al. Have made numerical investigations regarding the same experimental setup applying DC magnetic fields and its impact on the bubble dynamics [START_REF] Jakoivcs | Electromagnetic Processing of Materials[END_REF]. In the first part of this paper the adaption of the investigated numerical model to a new experimental setup compared to the investigations of A. Tucs et al. [START_REF] Tucs | Proceedings of the International Conference on Heating by Electromagnetic Sources[END_REF] is described and the obtained simulation results for a single bubble rise dynamics in 2D are presented. In the second part of the paper, a method for breaking up the bubbles into smaller blebs and its simulation results are discussed. Due to an external AC magnetic field at the bottom of the molten metal vessel, a flow pattern with an opposite flow direction in relation to the bubble rise is created. By reason of the shear forces the bubble split up into several pieces and creates thereby a bigger surface active area for chemical reaction. The increase of the surface by the separation leads to a higher amount of chemical reaction and an increase of the process efficiency.

Set-up of the model

In order to investigate the bubble rise in the chemical bubble reactor, a two-dimensional model is chosen due to calculation time. The model of the reactor is a rectangle with a height of 1.15 m and a filling level of liquid tin of 1 m. The diameter of the column is 0.036 m. Facts of the model are shown in table 2. To gain the residence time resp. the terminal velocity of the bubble in dependence on the bubble diameter a single bubble is initialized at the bottom of the column and its path through the column with focus on the trajectory and velocity is observed. One of the common methods in numerical simulation to simulate two immiscible fluids tracking the volume fraction of each of the fluids to figure out the motion of bubbles, taken into account the change of their shape during the flow through the column is the Volume of Fluid (VoF) method. This method is based on a transport equation which represents the filling level of each cell in the computational domain. After every time step the shape can be approximated using different methods like Simple Line Interface Calculation (SLIC), Piecewise Linear Interface Calculation (PLIC) or the Donor-Acceptor scheme. Due to the fact that the PLIC scheme is the most accurate in the commercial CFD-Code FLUENT, this scheme is used in the geometric reconstruction approach [START_REF] Jakoivcs | Electromagnetic Processing of Materials[END_REF] and is used in the simulations presented in this work.

Results 2D Simulation

The process has been analyzed by simulating the residence time in dependency of the diameter of the bubbles.

For bubbles with a diameter of 2 mm the residence time is around 25 sec. This time is decreased very fast with a bigger diameter e.g. the residence time of a bubble with a diameter of 10 mm is according to this simulation 9 sec. The terminal velocity is shown in fig. 3 and is anti-proportional to the diameter. The results of terminal velocity is between 4 cm/s of a small bubble (2 mm) to ca. 12 cm/s of a big bubble (10 mm). Thus can be seen that a bigger diameter is a disadvantage of the process. The trajectory of the bubbles can be seen in fig. 4 and5. The oscillation of bubbles e.g. shown in fig. 4 are another reason of high residence time in the column. Calculating the Eötvös number, which describes the relative influence of surface tension to body forces and thus is in relation to an oscillating trajectory it turns out that this number is much greater than 1 and it is highly presumable that oscillations appear. In this case there is just a single bubble which is observed during its path through the column, but there would be much more influence on the path of the bubbles and thus more oscillations due to another inlet condition that is creating a bubble plume and due to the interaction of bubbles. The results are in accordance with an independent simulation of the same case using the TwoPhaseEulerFOAM solver of the opensource code OpenFOAM and with results figured out in [START_REF] Jakoivcs | Electromagnetic Processing of Materials[END_REF] However, this results should be compared to the results of the second part of the paper.

Electromagnetic stirring of bubbles

In bubble columns with high gas rate, it happens that bubbles conglomerate and create big bubbles (3-10 mm). These bubbles accelerate due to the increased Archimedes force. This means that the residence time of the bubbles are decreased very much and the efficiency of the process also decreased. A possibility to split up those conglomerated big bubbles is to use the electrical conductivity and apply an AC electromagnetic field, which induces electromagnetic forces, which create a turbulent flow. The advantages of these method are the increase of surface active area of methane bubbles and the decrease of the driving force of the bubbles. Both effects increase efficiency of the process. The disadvantages are besides the energy used for the induction system, the turbulent flow pattern which maybe accelerate the bubbles and decrease their residence time. First of all, this investigation shall show on the one hand if it is possible to split up bubbles due to shear stresses and on the other hand if the bubbles are accelerated or decelerated.

Theory

First of all, the electromagnetic forces are calculated using the commercial software ANSYS. This is done by solving the following

The model of the column was the same as for the hydrodynamical mesh, since the mesh was setup in ANSYS and exported to FLUENT. Using the VoF-method, the forces are solved as sum of volume forces in the following equation

To apply the external AC magnetic field an inductor with three turns was placed at a particular height of the column to induce the forces locally. The electrical parameters are chosen in a way that the penetration depth of the magnetic field fits the size of the radius of the column. With material properties of liquid tin at 600 °C it turns out that a frequency of ca. 250 Hz has to be used. Furthermore, a parameter study according the magnitude of force density to separate the bubble has been done by adjusting the magnitude of inductor current. The resulting forces and their coordinates were exported to a text file and spread onto the cells of the hydrodynamical mesh using a User-Defined function. To ensure that the magnitude of the forces are reduced if the bubble passes by, the forces are adjusted with the factor of volume fraction of primary phase in every time step. Thus they are 0 if the bubble with volume fraction 1 of secondary phase reaches the penetration depth of the electromagnetic field and receive a linear approximated force in the intermediate zone of the two phases. The velocity profile in the region of the inductor creates the velocity profile shown in Fig. 6. The velocity develops values up to 0.23 m/s. Due to the forces created by this velocity bubbles can be split up, which is shown in Fig. 7. In this case a bubble with a diameter of 8 mm is split up into two bubbles which are pushed to the walls. During the further path of the bubbles through the column it is shown that the residence time is slightly increased resp. the velocity is slightly lower compared to the simulation without EM field. The separation was observed at bubble diameter larger than 6 mm, in other cases the bubbles were simply pushed aside. The residence time has been simulated three times and the median was calculated and is shown in fig. 8 and9.

Conclusion

In order to investigate the separation of bubbles a two dimensional case according to an experimental setup has been set up. A study of the rise of single bubbles with different diameters has been performed and the trajectory, the residence time and the terminal velocity have been obtained. In the second part the numerical model was extended by an induction coil which was placed around the bubble column and an electromagnetic investigation of the induced electromagnetic forces has been done. These forces were implemented in the hydrodynamical model and a hydrodynamical calculation with focus on a possible separation was performed. It was shown that shear stresses of induced by an induction coil with 250 A and 250 Hz has been big enough to separate bubbles with a diameter larger than 6 mm. The influence of the induced flow was according to residence time and terminal velocity neglectible. The bubbles were may be accelerated by the upper vortex of the induced flow pattern, but before they were decelerated and had afterwards a smaller diameter and a reduced driving force. Further investigations are planned to verify this method in experiments.

Fig. 2 :

 2 Fig. 2: Residence time of single bubbles in respect to their diameter in the bubble column.

Fig. 3 :

 3 Fig. 3: Terminal velocity of single bubbles in respect to their diameter in the bubble column.

Fig 4 :

 4 Fig 4: Trajectory of a bubble with 2 mm diameter in the bubble column.

Fig 5 :

 5 Fig 5: Trajectory of a bubble with 4 mm diameter in the bubble column.

Fig. 6 :Fig. 7 :

 67 Fig. 6: Velocity due to induced electromagnetic forces.

Fig 8 :

 8 Fig 8: Comparison of residence time of bubbles in respect to their diameter with applied and without EM field Fig 9: Comparison of velocity of bubbles in respect to their diameter with applied and without EM field

Table 2 :

 2 Facts of 2D model

	Elements	Shape of Elements	Nodes	Grid type	Symmetry
	26250	Triangles	27156	Structured	planar

Table 2 :

 2 Using the VoF-method a single momentum equation, which depends on the volume fractions of each phase, is solved. Furthermore, a time-dependent solution is chosen for this simulation. Schemes and Time Step settings used in this simulations are shown in the following table: Used Solver setup and numerical schemes.

	Solver

Table 4 :

 4 Electrical Parameters to induce EM force density

	Current [A]	Frequency	Penetration	Number of	Induced	Maximum	Achieved
		[Hz]	depth [mm]	turns	power	force density	velocity of
					density	[N/m]	melt [m/s]
					[W/m]
	250	250	20	3	46.2	0.017	0.23

Acknowledgment

The research is supported by the Helmholtz Association in frame of the Helmholtz-"Alliance LIMTECH".


Zuo-Sheng Lei

Sheng-Yang Song

Chun-Long Xu

Jia-Hong Guo

Natural convection of magnetic fluid inside a cubical enclosure under magnetic gravity compensation

Keywords: natural convection, magnetic fluid, magnetic gravity compensation

The experimental studies on natural convection of magnetic fluid inside a cubical enclosure under magnetic gravity compensation are presented. The bottom wall of the enclosure was uniformly heated by a heating element from a DC power supply while the top wall was cooled by ice water flowing from a container. The cubical enclosure was positioned in the center of the Helmholtz-Maxwell coils, which can provide a uniform gradient magnetic field. The magnetic force applied to the magnetic fluid was large enough to compensate gravitational force of the magnetic fluid, which was the driven force of natural convection. The Nusselt number was calculated by measuring the heat flux on the bottom wall and the temperature of both walls. Heat transfer efficiency of natural convection of magnetic fluid under different effective gravitational accelerations was compared in this study.

Introduction

Experimental and numerical studies have been carried out on natural convection. Enhancements or suppressions of natural convection heat transfer have been long-term research topics investigated by many researchers. The driving force for natural convection is the buoyancy force caused by the density difference between hot and cold regions of the fluid in terrestrial conditions. And controlling natural convection may be difficult as the gravitational acceleration is constant and uniform on the earth. In recent years, another option for flow control has appeared-the magnetic buoyancy force. One of the first works on magnetic convection was carried out by Carruthers and Wolfe [1] . They found that when an insulating paramagnetic fluid such as gaseous oxygen was subjected to combined thermal and magnetic field gradients, a magnetic body force was shown to exist which was analogous to that of gravity. The possibility of magnetic control of thermal convection was discussed for several instances. Braithwaite et al. [2] used a magnetic field both to enhance and suppress buoyancy-driven convection in a solution of gadolinium nitrate, and showed that the effect depended on the relative orientation of magnetic field and temperature gradient. Quantitative treatment of air convection under magnetic fields was initiated by Bai et al. [3] . Huang et al. [4] studied the effect of a static, nonuniform magnetic field on a laterally unbounded nonconducting paramagnetic fluid layer heated from below or above using a linear stability analysis of the Navier-Stokes equations supplemented by Maxwell's equations and the appropriate magnetic body force. Tagawa et al. [5] employed a procedure similar to the Boussinesq approximation and developed model equations for convection resulting from a gradient magnetic field. Ozoe et al. [6] installed a four-poles magnet to apply the cusp-shaped magnetic field to air in the cubic enclosure. A simple model equation was derived for magnetizing force and numerically computed for the system. Bednarz et al. [7][8][9][10] investigated natural convection of paramagnetic fluids in a differentially heated cubic enclosure under magnetic fields. It was shown in their works that by using a strong magnetic field they can enhance, suppress or invert the usual gravitational convection with different combinations of the two main body forces (gravitational and magnetic buoyancy forces) that act together to drive thermo-magnetic convection of paramagnetic fluids.

In this present study, we develop an apparatus made of two pairs of Helmholtz-Maxwell coils, which can generate a uniform magnetic gradient field for ferro-fluid filled inside a cubical enclosure, so as to produce a uniform magnetic volume force to compensate the gravity. Then natural convection of water-based magnetic fluid inside the cubical enclosure under magnetic gravity compensation is studied experimentally.

Experimental apparatus and the working fluid

The experimental setup is presented in Fig. 1, here the magnetic gravity compensation was realized by combining the two pairs of Helmholtz-Maxwell coils and ferro-fluid [START_REF] Zuo-Sheng | The 7th International Conference on Electromagnetic Processing of Materials, Beijing[END_REF] . The specifications of the coil system and the configuration of the Helmholtz-Maxwell coil system is described in our other work [START_REF] Lei | The 8th International Conference on Electromagnetic Processing of Materials[END_REF] . The experimental cell consisted of a cubical enclosure filled with magnetic fluid placed in the centre of the Helmholtz-Maxwell coils, a heater control system, a cooling system, a heat flux meter and a portable data acquisition module connected to a personal computer. The details of experimental cell is shown schematically in Fig. 2. Six separate elements were designed to assemble the final experimental model. Those are: two copper plates (one for the cooling side and the other for the heating side) with one hole in each to place two K-type thermocouples, a quartzose cubic cavity, the cooling chamber is made of stainless steel, the base is made of polytetrafluoroethylene. There were a heat flux sensor and a heater between the heating plate and the base. The heater was connected to a DC power supply (KXN-305D). The cooling copper plate was cooled by water pumped from a container which is full of ice water. The cubic cavity had an internal dimension of 40mm on each side. In the present experiment a water-based magnetic fluid which contains magnetic nanoparticles was used as the working fluid. The major properties of the working fluid are listed in Table 1. When all parts of the experimental setup were assembled, it was possible to fill the enclosure with the working fluid. This was done with a syringe and a thin needle. There was a hole through the cooling copper plate and the cooling chamber. When the enclosure was filled, the hole was sealed by hot glue and the experimental apparatus was placed in the center of the Helmholtz-Maxwell coils. The environmental temperature was kept constant. The electric current to the Helmholtz coils was 130A while the electric current to the Maxwell coils increased from 0A to 93A in order to modulate the gravity level. The heater power was set to 2W at the beginning of every group of experiments. The temperature of heated and cooled side walls were monitored continuously. After about 1 hour, when the system had reached a steady state, the temperatures and the heat flux were recorded. Then the heater power gradually increased by 2W until it reached 20W.

Results and Discussion

Fig. 3: The Nusselt number at different heating power under normal gravity and a uniform magnetic field

In Fig. 3, the natural convection Nusselt numbers are plotted against the heating power. As seen in Fig. 3, the Nusselt number increases with the heating power no matter under normal gravity or under a uniform magnetic field. Because the temperature gradient increases with the heating power, natural convection heat transfer is enhanced. The viscosity of magnetic fluid increases under a uniform magnetic field, so the natural convection heat transfer efficiency under a uniform magnetic field is lower than that under normal gravity consequently. As we can see in Fig. 3, the Nusselt number is less under a uniform magnetic field at the same heating power. In order to figure out the effect of magnetic force to natural convection, we calculate the magnetic Grashof number. The Nusselt numbers are plotted against the magnetic Grashof numbers in Fig. 5. The Nusselt number increases with the magnetic Grashof number under the same effective gravitational acceleration but decreases with the increase of effective gravitational acceleration. The magnetic force acting on the magnetic fluid applied by the gradient magnetic field causes the magnetic acceleration. The magnetic force will suppress natural convection of magnetic fluid when the direction of the magnetic acceleration is contrary to the direction of the gravitational acceleration. The magnetic acceleration increases with the increase of magnetic force, so does the suppression of natural convection.

Fig. 5 The Nusselt number at different magnetic Grashof number under different effective gravitational accelerations

Conclusions

In this paper, natural convection of magnetic fluid under magnetic gravity compensation in a cubical enclosure has been investigated experimentally. The enclosure is placed in the center of the Helmholtz-Maxwell coils. The heat transfer measurements show that, as the magnetic field increases, the effective gravitational acceleration decreases, the Nusselt number decreases, indicating that convection is suppressed.

Fig. 1 :Fig. 2 :

 12 Fig. 1: Experimental setup

Fig. 4 :

 4 Fig.4: The Nusselt number at different heating power under different effective gravitational accelerations Fig.4shows natural convection heat transfer of magnetic fluid under different effective gravitational accelerations. It is clear in the figure that the Nusselt number decreases with the decrease of effective gravitational acceleration. In order to figure out the effect of magnetic force to natural convection, we calculate the magnetic Grashof number. The Nusselt numbers are plotted against the magnetic Grashof numbers in Fig.5. The Nusselt number increases with the magnetic Grashof number under the same effective gravitational acceleration but decreases with the increase of effective gravitational acceleration. The magnetic force acting on the magnetic fluid applied by the gradient magnetic field causes the magnetic acceleration. The magnetic force will suppress natural convection of magnetic fluid when the direction of

Table 1

 1 Important properties of the working fluid at room temperature

	Property	Va lue	Unit
	α(thermal diffusivity)	1.2×10 -7	m 2 /s
	β(thermal expansion coefficient)	5.2×10 -4	1/K
	λ(thermal conductivity)	0.59	W/(m•K)
	ν(kinematic viscosity)	4.24×10 -6	m 2 /s
	ρ(density at room temperature)	1.18×10 3	kg/m 3

Acknowledgment

This project financially supported by National Science Foundation of China (No.51274137 and NO.11372174).