外文原文-通过有限元分析高梯度磁选机的磁场

Magnetic fi eld analysis of high gradient magnetic separator via fi nite element analysis S.K. Baik, D.W. Ha, R.K. Ko, J.M. Kwon Korea Electrotechnology Research Institute, Seongju-dong 28-1, Changwon, Republic of Korea a r t i c l ei n f o Article history: Received 21 March 2011 Received in revised form 24 April 2012 Accepted 26 April 2012 Available online 7 May 2012 Keywords: HGMS Matrix Magnetic particles Wastewater FEM a b s t r a c t High Gradient Magnetic Separator (HGMS) uses matrix to make high magnetic fi eld gradient so that ferro- or para-magnetic particles can be attracted to them by high magnetic force. The magnetic force generated by the fi eld gradient is several thousand times larger than that by the magnetic fl ux density alone. So the HGMS shows excellent performance compared with other magnetic separators. These matrices are usually composed of stainless wires having high magnetization characteristics. This paper deals with superconducting HGMS which is aimed for purifying wastewater by using stainless steel matrix. Background magnetic fi eld up to 6 T is generated by a superconducting solenoid and the stainless steel matrices are arranged inside of the solenoid. In order to calculate magnetic forces exerting on mag- netic particles in wastewater, it is important to calculate magnetic fi eld and magnetic fi eld gradient those are proportional to the magnetic force acting on the particle. So we presents magnetic fi eld distribution analysis result and estimates how many times of magnetic force will act on a particle when the matrix are arranged or not. Magnetic fi eld is calculated in 3 dimensions by using Finite Element Method (FEM) and also compared with results obtained from 2 dimensional analysis. ? 2012 Elsevier B.V. All rights reserved. 1. Introduction Paper factories use a large amount of water and same amount of wastewater is generated. Koreas paper industry is worlds 11th production; however, Korea is water shortage nation. So, it is important to save water resources and to purify the wastewater. The existing water treatment facilities like precipitation process need large-scale equipment and wide space to purify the wastewa- ter of paper factory. High Gradient Magnetic Separation (HGMS) system has the merits to purify wastewater rapidly and to occupy small space. The wastewater of paper factory contains many kinds of organic components such as pulp, fi broid materials, colorant, cohesion agent and other suspended solid in high concentration. Because organic components do not have magnetism, it is neces- sary to attach ferromagnetic particles to them, which is called magnetic seeding. The formation of magnetic fl ock with ferromag- netic particles and organic components can purify the wastewater of paper factory by HGMS. If the wastewater can be utilized again for paper manufacturing process after purifi ed by HGMS, it is pos- sible to save energy and solve water shortage problem. The word, High Gradient, means that magnitude of magnetic fl ux density varies so sharply in a space where magnetic separation happens. The density of the magnetic energy wmin a linear isotro- pic medium is given by: wm 1 2 H ! ? B ! 1 where H and B are, respectively, the magnitudes of the magnetic fi eld and the magnetic fl ux density (magnetic induction). It transpires from Eq. (1) that the magnetic energy Umpof a mag- netisable particle of volume Vp placed in the magnetic fi eld is: Ump 1 2lpVpH 2 2 while the magnetic energy of a fl uid of the same volume is given by Umf 1 2lfVpH 2 3 In Eqs. (2) and (3),lpandlfare magnetic permeabilities of the particle and the fl uid, respectively. The energy increment U of the system (particle + fl uid) is given, to fi rst order, as the difference be- tween the energies given by Eqs. (2) and (3). For weakly magnetic particles this is a good approximation 1. Thus: U 1 2 lf?lpVpH24 In general, a force can be expressed as F ! m ?rU, whereris the operator of the gradient. Taking into account thatlj=l0(1 + kj), where kjis the volume magnetic susceptibility of material j and 0921-4534/$ - see front matter ? 2012 Elsevier B.V. All rights reserved. /10.1016/j.physc.2012.04.036 Corresponding author. E-mail address: skbaikkeri.re.kr (S.K. Baik). Physica C 480 (2012) 111117 Contents lists available at SciVerse ScienceDirect Physica C journal homepage: /locate/physc l0is the magnetic permeability of vacuum, the magnetic force can be written (in SI units): Fm ! 1 2l0kp ? kfVprH25 In practical situations the magnetic fl ux density B is frequently used, rather than the magnetic fi eld strength H, and Eq. (5) can then be expressed as: Fm ! 1 l0 kp? kfVpBrB6 where kpis the volume susceptibility of the particle; kfis the vol- ume susceptibility of the fl uid. As shown in Eq. (6) the magnetic force on a weakly magnetic particle is proportional to the magnitude of magnetic fl ux density and the gradient. So we can get higher magnetic separation perfor- mance by increasing the magnetic fi eld and the gradient. The mag- netic fi eld can be increased by using a stronger magnet having Table 1 Typical values of BrB for selected magnetic separators. BB (T2/m) Suspended magnet Nd drum magnetic separator Nd roll magnetic separator HGMS with steel wool matrix 0.05803005 ? 104 Fig. 1. Schematic diagram of the HGMS system in KERI for water purifi cation. Fig. 2. Photo of the HGMS system in KERI. 112S.K. Baik et al./Physica C 480 (2012) 111117 more ampere-turns and the fi eld gradient can be increased by changing magnetic polarities and using steel wool matrix. Table 1 shows typical values of BB for selected magnetic separators. HGMS shows the distinguished magnitude of BB because of steel wool matrix. In this paper we fi rstly analyzed magnetic fi eld distribution of a superconducting solenoid that is utilized for a HGMS system in Korea Electrotechnology Research Institute (KERI) and then ar- ranged stainless matrix fi lter within the solenoid in order to calcu- late magnetic fi eld gradient. 2. HGMS System in KERI For treatment of wastewater we developed a HGMS system for experiments in laboratory. Fig. 1 shows the schematic diagram of the developed HGMS system, where wastewater passes through a superconducting (SC) magnet which is conduction-cooled by Gif- fordMcMahon (GM) cryocooler. Fig. 2 shows the HGMS system being assembled in KERI and Fig. 3 shows stainless steel matrix fi l- ters which generate high magnetic fi eld gradient to attract mag- netic particles. Stainless steel, SUS430, matrix fi lter was used as magnetic fi lter for magnetic separation. There are several kinds of stainless steel fi lter according to the shape. For example, mesh type and sponge type of stainless steel is able to be used for mag- netic fi lter. In our system, mesh type stainless steel fi lters were adopted with an automatic fi lter movable system. Based on the SC coil dimensions given in Table 2, magnetic fl ux density distribution was calculated to generate 6 T at the center of the coil. The calculation was done by using Z-axis symmetric mod- el with a 2 dimensional fi nite element analysis tool. We were able to fi nd turn number of the SC coil in order to generate 6 T at the center with 82.7 A operating current, which is 15,535 turns. The maximum fl ux density is 6.37 T located along the inner diameter of the SC coil at Z = 0. Fig. 4 shows the distribution of the magni- tude of fl ux density, BMOD, and Fig. 5 shows the magnitude and the Z-component, BZ, along R-coordinate from the center. Fig. 3. Photo of stainless matrix fi lter for HGMS system. Table 2 Specifi cation of superconducting (SC) magnet for the HGMS system in KERI. Contents Specifi cation Height of magnet600 mm Inductance22 H Central magnetic fi eld6.0 T Operating current82.7 A Warm bore diameter100 mm Height of SC coil210 mm Inner diameter of SC coil135 mm Outer diameter of SC coil205 mm SC wireNbTi Cooling methodConduction by GM cooler Fig. 4. Distribution of magnitude of magnetic fl ux density by exciting SC coil with 82.7 A operating current. Fig. 5. Distribution of magnitude (BMOD) and Z-component (BZ) of fl ux density along R coordinate from the center of SC coil. S.K. Baik et al./Physica C 480 (2012) 111117113 3. Magnetic fi eld and the gradient calculation from 2D analysis In order to calculate the infl uence of stainless steel matrix inser- tion into the SC coil, the stainless steel matrix was modeled by cir- cles with 1 mm diameter arranged within the SC coil as shown in Fig. 6. Each circle is spaced 5 mm distance radially and composes one layer with 8 circles at the same Z-coordinate. Because this analysis was also done in Z-axis rotational symmetry condition, each small circle with 1 mm diameter composes a large circle cen- tered on the Z-axis. Although this circular shaped matrix fi lament model is different from the actual shape shown in Fig. 3, it is pos- sible to see magnetic fi eld variation around stainless steel matrix. And by using this axis-symmetry model it is possible to make very tiny meshes around the matrix fi lament as shown in Fig. 6. One wire cross-section of 1 mm diameter is made of 10 meshes. When 4 meshes were made for one wire, it was not suffi cient to get fl at top of magnetic fi eld distribution inside of the wire 3. The matrix fi lter is composed of stainless steel, SUS430, which has the BH curve shown in Fig. 7. This BH curve is calculated by Eq. (7) based on measured magnetization data from Physical Property Measurement System (PPMS) 4. B ! l0H ! M ! 7 Some of lines are indicated in Fig. 8 for analysis of magnetic fi eld distribution at stainless steel mesh fi lters. The diameter of fi l- ter wire was 1 mm and the gap between wires was 5 mm. Fig. 9 shows distribution of magnetic fl ux density magnitude around the fi lter wires those are located along the lines 14 when the magnet generates 6 T of magnetic fi eld at the center (R = 0, Z = 0). Great changes of magnetic fi eld around fi lter wires that are located along lines 1 and 3 are shown. This means that large magnetic fi eld gradient is generated by the stainless mesh fi lters, which increases tremendously magnetic force acting on a particle which passes through the fi lters. These data can be used to choose proper mesh size of fi lter and gap distance of fi lter housing. Fig. 10 shows distribution of magnitude of fl ux density around the fi lter wires those are located along the lines 1040shown in Fig. 8. Large magnetic fi eld gradient is also generated around stain- less steel wire, but there is smaller magnetic fi eld gradient be- tween the wires because distance between them is two times larger than Fig. 3 case. Fig. 11 shows magnifi ed view of magnetic fi eld distribution around the stainless steel wires. Magnetic fi eld near the side sur- faces of the wires is lower than background fi eld but higher near the upper and the bottom surfaces of the wires. Fig. 12 shows the magnitude ofB around the matrix in the area, 0 R 50 mm and 0 Z 10 mm. The maximum gradient is 2201.6 T/m located at R = 30.5 mm and Z = 5 mm. The minimum value is 0.4496 T/m located at R = 26.5 mm and Z = 8 mm. The maximum gradient is 4897 times as large as the minimum gradi- ent. The peak values shown in Fig. 12 are located very close to the matrices. The average gradient obtained from the data shown in Fig. 12 is 72.14 T/m which is 160 times as large as the minimum gradient. Because the minimum gradient is close to the values Fig. 6. Finite element meshes to calculate infl uence of stainless steel matrix insertion. Fig. 7. BH curve of stainless steel matrix. 114S.K. Baik et al./Physica C 480 (2012) 111117 without the matrices, the magnetic force acting on a particle in- creases 160 times in average from Eq. (6) by inserting stainless steel matrix in the background fi eld in this model. The maximum magnitude of BB in this analysis is 14,551 T2/m, which is a little smaller than the typical value of HGMS shown in Table 1 refer- enced from 2. 4. Magnetic fi eld and the gradient calculation from 3D analysis The 2D (2 dimensional) analysis described above assumed that the matrix is composed of circular wires. However, actual matrix has a shape of mesh composed of straight wires. So we did 3D (3 dimensional analysis) through modeling the matrix as a shape of mesh like the actual system. Fig. 13 shows a 3D analysis model showing stainless steel matrices located within the bore of the 6 T superconducting solenoid magnet. Two matrices are modeled Fig. 8. Magnitude of fl ux density around the matrix when the SC solenoid generates 6 T at the center (R = 0, Z = 0). Fig. 9. Magnitude of fl ux density around the fi lter wires those are located along the lines 14 in Fig. 8 when the SC solenoid generates 6 T at the center (R = 0, Z = 0). Fig. 10. Distribution of magnetic fl ux density magnitude around the fi lter wires those are located along the lines 1040in Fig. 8 when the SC solenoid generates 6 T at the center (R = 0, Z = 0). Fig. 11. Magnifi ed view of fl ux density distribution around the fi lter wires when the SC solenoid generates 6 T at the center (R = 0, Z = 0). S.K. Baik et al./Physica C 480 (2012) 111117115 and located 10 mm, 30 mm above the center of the solenoid. The diameter of the matrix is 60 mm and that of the wire is 0.8 mm. The distance between adjacent wires is 5.08 mm and the upper wire has 30? misaligned angle with the lower wire. The same mag- netic property (BH curve) with 2D analysis is applied to the stain- less steel (SUS430) mesh. Symmetric condition is given to the upper half and the lower half of the solenoid, so it is regarded that the same two matrices with the upper half are symmetrically lo- cated 10 mm, 30 mm below the center of the solenoid. Fig. 14 shows distribution of the magnitude of magnetic fl ux density on the surface of the matrices, where the fl ux density is lower around the intersections of the wires. Fig. 15 shows distribu- tion of the magnitude of magnetic fl ux density along straight lines parallel to X-axis with Y coordinate, 2.54 mm (0.5 in.) and Z coordi- nate, 10 mm, 11 mm, 12 mm, 13 mm. If Z = 10, the straight line passes through the lower matrix as shown in Fig. 14. Along this line the magnetic fl ux density varies the most sharply. If the distance from the matrix becomes larger and larger, the fl ux density distri- bution becomes smoother and smoother. 3D analysis result shows Fig. 12. Magnitude ofB around the matrix. Fig. 13. Three dimensional analysis model of 6 T superconducting solenoid and matrices. Fig. 14. Distribution of the magnitude of magnetic fl ux density on the surface of matrices. 116S.K. Baik et al./Physica C 480 (2012) 111117 a little higher peaks of fl ux density distribution than the 2D analy- sis result shown in