Magnetic Field Gradient Optimization for Electronic Anti-Fouling Effect in Heat Exchanger

Transcription

1 J Eect Eng Techno Vo. 9, No. 6: , 14 ISSN(Pint) ISSN(Onine) Magnetic Fied Gadient Optimiation fo Eectonic Anti-Fouing Effect in Heat Exchange Yong Han* and Shu-tao Wang Abstact A new method fo optimiing the magnetic fied gadient in the exciting coi of eectonic anti-fouing (EAF) system is pesented based on changing exciting coi sie. In the poposed method, two optimiation expessions ae deduced based on biot-savat aw. The optimiation expessions, which can descibe the distibution of the magnetic fied gadient in the coi, ae the function of coi adius and coi ength. These optimiation expessions can be used to obtain an accuate coi sie if the magnetic fied gadient on a cetain point on the coi s axis of symmety is needed to be the imum vaue. Compaing with the expeimenta esuts and the computation esuts using Finite Eement Method simuation to the magnetic fied gadient on the coi s axis of symmety, the computation esuts obtained by the optimiation expession in this atice can fit the expeimenta esuts and the Finite Eement Method esuts vey we. This new method can optimie the EAF system s anti-fouing pefomance based on impoving the magnetic fied gadient distibution in the exciting coi. Keywods: Eectonic anti-fouing system, Exciting coi, Magnetic fied gadient, Optimiation 1. Intoduction The scae pobem is a big pobem to the devices which have the heat exchange pocess when they wok, such as cooing towe and boie. The scae pobem oots on using had wate. Chemicas wee used to pevent scae buidup at fist [1-]. But using chemicas can bing many pobems such as envionmenta contamination. Then the eectomagnetic anti-fouing method was eseached and used as a substitute. The eectonic anti-fouing (EAF) system is a vey usefu eectomagnetic fied wate teatment system to the scae pobem. The stuctue diagam of EAF system is shown as Fig. 1. When EAF system woks, EAF Conto Unit wi oad a high fequency atenate signa to the exciting coi which is winded on the tube. The atenate signa takes a cetain powe, and the induced eectomagnetic fied geneated by exciting coi teats the minea soution. But the antifouing mechanism of EAF system is sti not a cea as yet. So it is scace of theoetica diection to make a good use of EAF system. Tombac E et a [3, 4] studied the effect of a weak magnetic fied on hematite so in stationay and fowing systems. They found that when the fow diection was vetica to the magnetic fied diection vecto, the custe of eectoyte patice was fomed in the soution. But the Coesponding Autho: Detp. of Measuement Technoogy and Instumentation Key Laboatoy of Hebei Povince, Schoo of Eectica Engineeing, Yanshan Univesity. Qinhuangdao, China. (wangshutao@ysu.edu.cn) * Detp. of Measuement Technoogy and Instumentation Key Laboatoy of Hebei Povince, Schoo of Eectica Engineeing, Yanshan Univesity. Qinhuangdao, China. (hanyong_hit@163.com) Received: Januay 8, 14; Accepted: Api 1, 14 custe of eectoyte patice wasn t obseved in the soution which was paced in the static magnetic fied. They beieved that the custe of eectoyte patice phenomenon was caused by the oent foce. Accoding to the Tombac E s standpoint, thee ae Ca +, CO - 3, Mg +, SO - - 4, HCO 3 and some othe eectoyte patice in the had wate, EAF system can make magnetic fied in its exciting coi, theefoe a kinds of eectoyte patice can be infuenced by oent foce when the had wate is fowing thow the coi. The oent foce is a vey impotant eason fo magnetic fied anti-fouing but not the ony eason. The magnetic fied gadient (MFG) is anothe impotant eason fo magnetic fied anti-fouing. Accoding to the gadient magnetic sepaation theoy, diamagnetism eectoyte patice o paamagnetism eectoyte patice wi be acted on by gadient magnetic foce when they ae in gadient magnetic fied. The gadient magnetic foce can be expessed as [5, 6]: = Whee c is an envionment constant, K m is magnetic susceptibiity, H is magnetic fied intensity, /d is the Fig. 1. Stuctue sketch of the EAF system. (1) 191

2 Magnetic Fied Gadient Optimiation fo Eectonic Anti-Fouing Effect in Heat Exchange gadient of magnetic fied. In the had wate, it is known that Ca + and Mg + ae diamagnetism, but CO - - 3, HCO 3 - and SO 4 ae paamagnetism accoding to Van Veck s theoy [7, 8]. Theefoe the diection of gadient magnetic foce acting on Ca + and Mg + is opposite with the diection of gadient magnetic foce acting on CO - - 3, HCO 3 and SO - 4. Theefoe the negative ions and positive ions ae fomed into custes espectivey, and the custes in the soution can become many seeds of the scae cysta. Then the scae cysta can gow up in the had wate soution instead of gowing on the wate tube wa. Some eseaches found that the anti-fouing effect caused by gadient magnetic fied was much bette than the antifouing effect caused by unifom magnetic fied [9, 1]. Theefoe the anti-fouing pefomance of EAF system can be optimied by making a biggest magnetic fied gadient in the exciting coi. The magnetic fied in the coi is not unifom, and the atio of coi adius to coi ength can infuence the magnetic fied gadient in the exciting coi. On the same coss section which is vetica with the axis of symmety of the coi, magnetic fied gadient is amost the same. In addition, the axia component of the magnetic fied is much bigge than the adia component of the magnetic fied, and the tangentia component of the magnetic fied is eo. Theefoe in the pesent study the axia magnetic fied gadient on the axis of symmety of exciting coi wi be optimied by changing the atio of coi adius to coi ength.. Optimiation Method Modeing In this pape the exciting coi is singe aye fo a tighty wound. The coss pofie schematic diagam of the coi is shown as Fig.. In Fig., is the coi ength, is coi adius, is the distance between a cetain point on the coi s axis of symmety and the centa point of the coi. The computationa fomua of the magnetic fied intensity on the coi s axis of symmety is as [11]: = = () + () () () () whee H is the axia magnetic fied intensity, B is the axia magnetic induction intensity, μ is vacuum pemeabiity, I is the exciting eectic cuent, n is the numbe of tuns pe unit ength of the coi. Then the H s deivative with espect to is as: = [ () ] [ () ] (3) It can be known fom Eq. (3) that /d is the function of, and. When =, /d is. Theefoe the magnetic fied gadient on the midpoint of the coi s axis of symmety is aways. It aso can be known fom Eq. (3) that /d s imum vaue can be cacuated ony when is a cetain constant. In the pesent atice we set that <. If the atio of coi adius to coi ength is wanted when magnetic fied gadient on a cetain constant is imum vaue, the optimiation expession shoud be deduced unde two conditions: when the coi ength is a constant o coi adius is a constant..1 When the coi ength is a constant When the coi ength is a constant, assume =, then Eq. (3) can be changed into: = [ ( ) ] [ ( ) ] (4) Eq. (4) is the function of α, assume () = =,, =, then s deivative with espect to α is as: d() d = 1 [ + (1+) ] 3 [ () ] 1 [ + (1) ] [ () ] () [ () () ] [ () ] (5) = (6) Then we can obtain the atio of coi adius to coi ength by soving Eq. (6) when /d is imum vaue.. When the coi adius is a constant When the coi adius is a constant, assume =, then Eq. (3) can be changed into: = [( ) ] [( ) ] (7) Fig.. Coss-section diagam of singe aye fo a tighty wound soenoid. Eq. (4) is the function of β, assume () =, = =, then s deivative with espect to β is as:, 19

3 Yong Han and Shu-tao Wang () () = [() ] [() ] () [() ] [() ] (8) = (9) Then we can obtain the atio of coi adius to coi ength by soving Eq. (9) when /d is imum vaue. 3. Resut Simuation Veification and Discussion 3.1 Simuation veification fo Eq. (6) We set =.m, eectic cuent density of the coi is 15 A/m 3, n=5/m, and is.m,.5m and.8m. In ode to veifying the coectness of Eq. (6), fist we use Eq. (6) to cacuate the imum vaue of /d and atio of coi adius to coi ength when /d is imum vaue. Then we use Finite Eement Method to cacuate the vaue of /d when the atio of coi adius to coi ength is diffeent, and find the imum vaue of /d and find the atio of coi adius to coi ength when /d is imum. The Finite Eement cacuation is done by using Ansys 1. softwae, which has powefu computing capabiity based on the FEM (finite eement method). It can do an accuate cacuation of eddy cuent, inductance, magnetic fied intensity and so on [1]. PLANE53 eement is used in buiding the mode. PLANE53 is defined by 8 nodes and has up to 4 degees of feedom (DOF) pe node. These DOFs ae vi. the -component of the magnetic vecto potentia (AZ), the time-integated eectic scaa potentia (VOLT), the eectic cuent (CURR), and the eectomotive foce (emf) [1]. When using Eq. (6), the cacuating esut is shown as Tabe 1. Tabe 1. MFG imum and the coesponding atio of to when =.m,.5m and.8m. d =.m =.5m =.8m Tabe. MFG imum with diffeent atio of to when =.m d d When using Finite Eement Method, the cacuating esut is shown as Tabes - Tabe 4, and the fitting cuves of the esuts is shown as Figs. 3 - Fig. 5. It can be seen fom Tabe 1 and Figs (3-5) that the Tabe 3. MFG imum with diffeent atio of to when =.5m d d Tabe 4. MFG imum with diffeent atio of to when =.8m d d Magnetic fied gadient imum(a/m ) / Fig. 3. Fitting cuve of MFG imum with diffeent atio of to when =.m Magnetic fied gadient imum(a/m ) MFG imum MFG imum cuve MFG imum MFG imum cuve / Fig. 4. Fitting cuve of MFG imum with diffeent atio of to when =.5m 193

4 Magnetic Fied Gadient Optimiation fo Eectonic Anti-Fouing Effect in Heat Exchange Fig. 5. Fitting cuve of MFG imum with diffeent atio of to when =.8m Tabe 5. MFG imum and the coesponding atio of to when =.m,.5m and.8m. d =.m =.5m =.8m Tabe 6. MFG imum with diffeent atio of to when =.m d d Tabe 7. MFG imum with diffeent atio of to when =.5m d d Tabe 8. MFG imum with diffeent atio of to when =.8m d d Magnetic fied gadient imum(a/m ).5 x MFG imum MFG imum cuve / Fig. 6. Fitting cuve of MFG imum with diffeent atio of to when =.m Fig. 7. Fitting cuve of MFG imum with diffeent atio of to when =.5m Magnetic fied gadient imum(a/m ) Magnetic fied gadient imum(a/m ) Magnetic fied gadient imum(a/m ) / MFG imun MFG imun cuve MFG imum MFG imum cuve / MFG imum MFG imum cuve / Fig. 8. Fitting cuve of MFG imum with diffeent atio of to when =.8m esuts cacuated by Eq. (6) can fit we with finite eement cacuation esuts. Theefoe the coectness of Eq. (6) is veified. 3. Simuation veification fo Eq. (9) We set =.1m, eectic cuent density of the coi is 194

5 Yong Han and Shu-tao Wang 15 A/m 3, n=5/m, and is.m,.5m and.8m. In ode to veifying the coectness of Eq. (6), fist we use Eq. (9) to cacuate the imum vaue of /d and atio of coi adius to coi ength when /d is imum vaue. Then we use Finite Eement Method to cacuate the vaue of /d when the atio of coi adius to coi ength is diffeent, and find the imum vaue of /d and find the atio of coi adius to coi ength when /d is imum. When using Eq. (9), the cacuating esut is shown as Tabe 5. When using Finite Eement Method, the cacuating esut is shown as Tabe 6 - Tabe 8, and the fitting cuves of the esuts is shown as Fig. 6 - Fig. 8. It can be seen fom Tabe 5 and Figs (6-8) that the esuts cacuated by Eq. (9) can fit we with finite eement cacuation esuts. Theefoe the coectness of Eq. (9) is veified. 3.3 Expeimentation Veification fo Eqs. (6) and Eq. (9) In the pesent study the vaidity of Eqs. (6) and Eq. (9) was aso veified expeimentay. We made the cois with diffeent sie accoding to the Finite Eement modes which wee buit in the section A and section B of pat III above. The exciting coi was made up by coppe wie, and the esistivity of the coppe wie was (Ωᆞm) when ambient tempeatue was 5. The diamete of the coppe wie was.m. The exciting eectic cuent was 1.5 A. The magnetic fied gadient on the axis of exciting was measued with a weak magnetic fied gadient mete (poduced by Beijing Zhong Hui Tian Cheng technoogy co., LTD). The weak magnetic fied gadient mete s highest esoution was.1µt, and its ecoding sensitivity and egistation accuacy wee.4 µt/cm and ±.5% espectivey. The expeimenta setup is shown in Fig. 9. Tabe 9. The expeiment esuts of stage 1 d was measued unde diffeent coi adius, and the coesponding coi adius was found out when the magnetic fied gadient on the axis point of was imum. At ast the imum magnetic fied gadient vaue was ecoded. Then we changed the axis points of =.5m and =.8m and epeated the expeimenta steps above Stage =.m =.5m =.8m (m) Tabe 1. The expeiment esuts of stage d =.m =.5m =.8m (m) Fist we et the adius of exciting coi as a constant: =.1m, and we changed the coi s ength fom.1m to.1m. The magnetic fied gadient on the axis point of =.m was measued unde diffeent coi ength, and the coesponding coi ength was found out when the magnetic fied gadient on the axis point of was imum. At ast the imum magnetic fied gadient vaue was ecoded. Then we changed the axis points of =.5m and =.8m and epeated the expeimenta steps above. The unit of imum magnetic fied gadient vaue measued by weak magnetic fied gadient mete was tansfomed fom µt /cm into A/m accoding to Eq. (1). B=µ H (1) Fig. 9. Schematic diagam of expeimenta setup The expeiment was divided into two stages Stage 1 Fist we et the ength of exciting coi as a constant: =.m, and we changed the coi s adius fom.1m to.1m. The magnetic fied gadient on the axis point of =.m ( is the distance fom the media point of axis) whee B is magnetic induction intensity (the SI unit is T ) and H is magnetic fied intensity (the SI unit is A/m). μ is vacuum pemeabiity. The expeimenta esuts ae shown in Tabes 9 and Tabe 1. It can be seen fom Tabes 9 and Tabe 1 that expeiment esuts can fit we with the esuts cacuated by Eqs. (6) and Eq. (9) which ae shown in Tabes 1 and Tabe Discussion 1) Accoding to Eq. (1), the magnetic fied gadient is invesey popotiona to magnetic fied intensity when is a constant. The magnetic fied gadient is bigge when the magnetic fied intensity is smae. The magnetic 195

6 Magnetic Fied Gadient Optimiation fo Eectonic Anti-Fouing Effect in Heat Exchange fied intensity is popotiona to the exciting cuent. In the pesent pape we obtain a mathematica method to optimie the magnetic fied gadient in exciting coi. It means that a sma exciting cuent can obtain a big magnetic fied gadient, which means a good anti-fouing effect. ) The method to optimie the magnetic fied gadient in exciting coi in the pesent pape can be used to make a good anti-fouing effect in the wanted aea in the wate tube o the heat exchange. It is hepfu fo some aea in the wate cicuation system which is had to cea. 3) In this pape the exciting coi is singe aye fo a tighty wound. This kind of coi is widespead used in many fied. Theefoe the optimiation method can be used in some fied that the magnetic fied gadient in the coi is needed to be contoed accuatey. 4. Concusion In this pape a mathematica method to optimie the magnetic fied gadient in exciting coi is pesented fo giving a theoetica basis to the optimiation design of exciting coi of EAF system, and the coectness of the expessions, which ae used to cacuate the magnetic fied gadient imum, is veified by Finite Eement Method and expeimentation. This optimiation method can be used to make a biggest magnetic fied gadient in the cetain aea in the coi and impove the EAF system s antifouing pefomance by cacuating the appopiate atio of coi adius to coi ength. This optimiation method can aso be used in othe coi-using fied which the magnetic fied gadient is needed to be optimied. Acknowedgment This wok was financiay suppoted by the Nationa Natua Science Foundation of China (Gant No ), Nationa Natua Science Foundation of China (Gant No ), the Speciaied Reseach Foundation fo the doctoa pogam of highe education of China (Gant No ) and Natua Science Foundation of Hebei Povince (Gant No.F1434). Refeences [1] F.C. Nachod and J.Schubet, Ion Exchange Technoogy, Academic Pess, New Yok, pp. 1, [] D.L. Owens, Pactica Pincipes of Ion Exchange Wate Teatment, Ta Oaks Pubishing, Litteton, CO, pp. 15, [3] E. Tombac, C. Ma, K. W, Busch, et a, Effect of a Weak Magnetic Fied on Hematite So in Stationay and Fowing systems, Cooid Poym. Sci, vo. 69, pp , [4] A. Jedovsky-Hajdú, E. Tombác, I. Bányai, et a, Caboxyated magnetic nanopatices as MRI contast agents: Reaxation measuements at diffeent fied stengths, Jouna of Magnetism and Magnetic Mateias, Vo. 34, no. 19, pp , Sep. 1. [5] X Wang, J Zhao, Y Hu, et a, Effects of the Loent foce and the gadient magnetic foce on the anodic dissoution of nicke in HNO 3 +NaC soution, Eectochimica Acta, Vo. 117, no., pp , Jan. 14. [6] S K Baik, D W Ha, J M Kwon, et a, Magnetic foce on a magnetic patice within a high gadient magnetic sepaato, Physica C: Supeconductivity, Vo. 484, no. 15, pp , Jan. 13. [7] Smytkowski and Radosaw, Lamo diamagnetism and Van Veck paamagnetism in eativistic quantum theoy: The Godon decomposition appoach, Physica Review A - Atomic, Moecua, and Optica Physics, vo. 65, no. 3 A, pp. 311/1-311/8, Mach.. [8] E. Taik, M. Subka, M. Kupa, et a, Van Veck paamagnetism in ead yttebium niobate and tantaate singe cystas, Jouna of Cysta Gowth, Vo. 318, no. 1, pp , Mach. 11. [9] L.Y. Qi, X.F. Zhang and Y.H. Li, Effects of fequency on CaCO 3 scae by ow fequency high gadient magnetic fied, Jouna of Inne Mongoia Univesity of Science and Technoogy, vo. 7, no. 3, pp , 8. [1] X. F. Zhang, G. Y. Liu, D. Q. Cang, C. Y. Song and T.C. Sun, Mechanism of High-Gadient Magnetic Teatment of Cicuating Cooing Wate, Ion and Stee, vo. 41, no. 9, pp. 8-84, 6. [11] C.S. Li, G.S. Ling, Y. Wang and C.L. Li, The Optimiation of the Unifomity of the Soenoid Magnetic Fied, Jouna of Nationa Univesity of Defense Technoogy, vo. 17, no., pp. 9-93, [1] S. D. Koe, P. Dhanesh, S. V. Kukani and P. P. Date, Numeica modeing of eectomagnetic weding, Intenationa Jouna of Appied Eectomagnetics and Mechanics, vo. 3, no. 1, pp. 1-19, 1. Yong Han. He eceived his B.S. and M.S. degees fom Habin Institute of Technoogy, Habin, China, in 3 and 8, espectivey and the Ph.D. degee in Instument Science and Technoogy aso fom Institute of Technoogy in 13. His eseach inteests ae appied eectomagnetics and eectonic anti-fouing technoogy. 196

7 Yong Han and Shu-tao Wang Shu-tao Wang. He eceived his B.S. and M.S. degees fom Yanshan Univesity, Qinhuangdao, China, in 1999 and, espectivey. He eceived his Ph.D. degee in Instument Science and Technoogy fom Institute of Technoogy, Habin, China, in 6. His eseach inteests ae weak signa detection and pocessing and mechanica faut diagnosis. 197