An Analysis of the Axial-disk Vgms Characteristics

An analysis of the axial-disk VOlldS characteriatice on condition that the magnetic aystem is optimal has been performed. Phe aim of the present work is to find the optimal geosetrg of the axial-disk volume-gradient magnetic separators (VGHS) , prooeeding from the given design charaoteristios, and to calculate the operating efficiency of these VGBdS, as well as to estimate their power of separation of ore eomponenta with close magnetic auaceptibility values. We consider two typea of 0ptimil;ation prooedure. The first one is to aohieve the maximel productivit per separator length unit (@ux'PL ) and the second one, to obtain tSe maximal productiviig per superconductor volume unit Cmar(P/ \Js ?33. The axial-disk VGMS setup is presented in Figel. The magnetic field bCI Pig.1 A se*up of the axial-disk VGBlCS in separation sons f: ia generated by coil aet 11, The axial magnetic field components of the neighbowing coils are directed opposite to each other.!Che VOEI(S of such a pe is characterised by the internal coll rad&us , the dlmensiozeas paraaeter~ d = &z /a, : /i= d /a, ; J% 2/&, the separator length L and teohnological clearance parameter S_ = 1 P / ~ ~ ~ where R is the tank radius, %he c~culation method ia based on the analyaia of particle motion i n the separation Bone /I/. The analysia is carried out with in the pulp Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19841162 Cl-794 JOURNAL DE PHYSIQUE particle nonintexaction approximation. Phe calculation is performed with due regard to the dependence of the magnetic system design current density maximal value on the system geometry.Both the wet and dry rseparetdon processes stre considered. 'Phe mathematical problem statament is a# fo1lows.At the fixed , & a n d h ( h is the superconducting material space factor of the magnetic eyertern) it is required to find suchd , /5 and Yvaluea,which maximise either the PI, value for the optimioation method of the first type or the P/VsGp one for that of the second type,provided the followLng conditions are fulfilled: J,< = J;c (a) , (1 B = p a . hrr7c.x.A. 3, ( 2 ) where (I) defines the dependence of the superconducti material critical currants on the magnetic field induction 8 ,eq. (8 implies the linear relation between the ma etic field and the design current density in the magnetic system, %M is the maximal magnetic fkeld intensity value on the magnetic system surface at the unit design current density. Let us aasme dependence (1) to be linear: YK= J , ( I B/B,). (1') Then F(1L ) ? . ~ ~ ? 2 P, ( g m ) = ,s ("")'. +tam) (l+ui*, (3) p ( a m ) = M Z ( h . 3 0 ) : S + I a m ) . J 3 ( C L ~ I ) . ( ~ + K ) $ ~ ) where n= 1 d s yzP , . %"&or the dry separation, whereas n= 2 S= 9 / .w.&) for ;he we* oneellen $ is the specific magnetic &P eept i iw;Q-the pulp viscosity;&,the characteristic particle t(=,t.,;),.8~,h,/~ ,T(R,) , the extraction geometrical factor / I / , and SUBsize ; As is seen from eqa (3) and (41, the P,, and P/vS,,, values can be represented within the acauracy up to the comeant factor depending on the pulp properties S ap the inLtial design, data a, , E , A and3, in the form of rU(r + K)J, where U depends only ono(,p and y,ht us introduce Q=/tr,. )r + a, -34s r then K= GI (hwx/a,),Qdepenb only on magnetic separator deai& chemacteristice whereas h m d /ar is a function of o( , fi and r only, since h m . x ia proportional to CLI .!thus, the magnetic system optmation problem within the linear dependence approximation for superconducting material critical properties (eq. (I l) ) is reduced to that of searching for the al and rparameter~,whLch maximise either P. or P / v s a p at faed d/lmereiore, d , , 4 , , PI, and P/v ,up ,as well aa other possible V W oharacteristica,appear to be uoambiguou~ Iunotiona of the universal design factor Q . Piga 2-4 preeent the main aalculation results, ice. the characterfatics of the optimal axial-disk VGMS veraus the universal design Q factor.Phe Q variation range correspond to th actual separator de@ign&.!Phe calculation. according to r n o $ ~ / \ / ~ ~ p 7 for the dry separation procees are not preeented,sinoe suoh a separator cannot be actually'corustmzcted,otherrcSse it should have had infidtely amall coil w i nding thickness (d=L) and, oonsequentlg , an infinite separator length, so as to achieve finite'productivity. Using the f2gures one can determine real separator siaes viad,/5, r, the productivity by employing the (0'9s). ( I -k K )n dependences, estate the design current density value (A-$/(l +t4jn , the magaetio m10' 0 Fig.2 Characteristics of the optimal axial-diek V W calculated for the ciry separation. Ptg.3 Charaoterie%ioe of the optimal axial-disk VOMS calculated for the wet separation. F3.g 4 Characteristics of the optimal a8ial-disk VGMS oalculated for $he wet separation. Cl-796 JOURNAL DE PHYSIQUE field value Bo l ( / ( r + K) ,as well as the ore component separation power of the given separator employing 6= (P(o.9)/q(0.1). !Che Gvalue is the ratio of the~dvalues for the wet separation aPd of theq values for the dT one of the ore components,which is required for the extraction to e at the levels of 90 and IO%,reapectively, ?he main conclusions from figs 2-4 w e as follows.!Che optimal magnetic system geometries obtained within the maxP, method are practically the same for the wet and dry separations, & $ , fi + a $ and jrI when the magnetic system sizes are increased (a, -m, ~ e , Q+ ) .At that,the P, value approaches the constant quantity for the wet separafion,wherms PL rises proportionally to a, for the dry one.The wet pyocess separators calculated according to rnay h (Fig.3) have productivity appr-tely two times as high per length unit and material consumption four times as much as compared with thoae calculated according to ma%(P/' Vsv) (Pig*4)* m e results obtained in cerlculating the axial-disk VGMS within the linear dependence approximation for the superconducting material critical currents allow us to determine the optimal geometry and other characteristics of a separator for any method of optimiliation and any type of aeparation,provLded the separator magnetic system is made of a superconducting material wLth arwtrarg critical propertie8,Xn so doing,one should use two statementa,w~ch are easily proven,First, the load line 0 =pc. hm<a.X . 3 of the optimtrl system outs the Jw (0) curve only at the point where JK (D) has a negative derivative,i.e, d J~/dB/~,&~,Second, the optimal magnetic system for the given g~(f3) relation is identical in its size,productivity and other characteriatics to that with the linedependence J K = Y ~ ( I B / B ~ ) ,which is a tangent to the JK(8) curve at the point where the latter cuts the load 1ine~i.e. 3K4bK)s J,(I-BK/B~ ) and d5/dBlsK=--3~/Bo. %he procedure for detenxking the optimal separator geometry with an arbitrary critical property dependence becomes clear if one takes into account the fol1owing.A certain optimal magnetic system geometry with the respective critical current value &corresponds to each straight 1-e 3~=3~.(1B/u, having a point of trangency d t h the given critical characteristic &.(B) ,Roceeding from figs 2-4,one can construct 9~ as Q function the tangency point abscissa,i.e.obtain the curve 3~ (B) ,The tangent to YK(6) at the point of its intersection with JK(B) exactly defines the O. value associated with the optimal geometry, Thus,the analysis of the axial-disk V N characteristics on condition that the magnefic system is optimal has been carried out,The optimisation procedure% of maximization of both the productivity per separator length unit and that per superconducting material volume unit are employed for the dry aj?d wet separation procesaes,It ha.8 been provea that the considered characteristics appear to be unambiguous functions of the universal design Q factor.!Che use of these functions makes it possible to immediately determine the optimal geometry and the respective curial-diak VOBBS characteristics within the linear !JK(8) approximation,whereas in the case of the nonlinear dependence ~ ~ ( p ) the problem solution is reduced to a simple construation. The authors thank DT.A.Chernoplyokov for the constant attention paid by him to their work,as well as for usef'ul discussions and advice given REFEFGNCE 1 Piskuaov, A,%, rnodorov, V,K,, Cherqkh, P,A. DokLady Akademii DTauk, @ (1983) 868,