AN ANALYSIS OF THE AXIAL-DISK VGMS CHARACTERISTICS

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Submitted on 1 Jan 1984

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AN ANALYSIS OF THE AXIAL-DISK VGMS CHARACTERISTICS

P. Cheremnykh, V. Fyodorov, A. Piskunov

To cite this version:

P. Cheremnykh, V. Fyodorov, A. Piskunov. AN ANALYSIS OF THE AXIAL-DISK VGMS CHARACTERISTICS. Journal de Physique Colloques, 1984, 45 (C1), pp.C1-793-C1-796.

�10.1051/jphyscol:19841162�. �jpa-00223636�

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AN ANALYSIS OF THE AXIAL-DISK VGMS CHARACTERISTICS

P.A. Cheremnykh, V.K. Fyodorov and A.N. Piskunov

I. V. Kurchntov I n s t i t u t e of Atomic Energy, Moscow, U.S.S.R.

Rgsumg

-

Une a n a l y s e d e s c a r a c t g r i s t i q u e s des VGMS a x i a u x 2 d i s q u e s dans l e c a s d ' u n systsme magngtique o p t i m a l a B t B f a i t e . Abstract

-

^Ananalysis of the axial-disk VOlldS characteriatice on condition that the magnetic aystem is optimal has been per- formed.

Phe aim of the present work is to find the optimal geosetrg of the ax- ial-disk volume-gradient magnetic separators (VGHS)

,

prooeeding from the given design charaoteristios, and to calculate the operating ef- ficiency of these VGBdS, as well as to estimate their power of separa- tion 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 supercon- ductor volume unit Cmar(P/ \Js

?33.

The axial-disk VGMS setup is presented in Figel. The magnetic field

bCI

Pig.1

-

^Ase*up of the axial-disk VGBlCS

i n 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 ~ c u l a t i o n method ia based on the analyaia of particle motion i n the separation Bone /I/. The analysia i s carried out with in the pulp

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19841162

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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 ge- ometry.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 Y- valuea,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 co- nditions are fulfilled:

J,<

=

^J;c

(a) ,

⁽¹

B

^{= p a .}hrr7c.x.A.

3,

( 2 )

where (I) defines the dependence of the superconducti material cri- tical currants on the magnetic field induction 8 ,eq.

(8

implies the linear relation between the ma etic field and the design current de- nsity in the magnetic system,

%M

is the maximal magnetic fkeld in- tensity value on the magnetic system surface at the unit design curr- ent density.

Let us aasme dependence (1) to be linear:

Y K =

J , - ( I

-

^B/B,). ^{( 1 ' )}

Then

F(1-

L ) ? . ~ ~ ?

²

P,

^{( g m )}

=

^,s

("")'.

+tam) ( l + u i * , (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 d r y separation, whereas n= ² S= 9

&P

/

.w.&)

for ;he we* oneellen $ is the specific magnetic eept i iw;Q-the pulp viscosity;&,the characteristic particle t(=,t.,;),.8~,h,/~

,T(R,) ,

the extraction geometrical factor / I / ,

and

SUB-

size ; As is seen from eqa (3) ^and(41, the

P,,

and P/vS,,, values can be re- presented 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 r U ( 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 / a r is a fu-

nction of o(

, fi

and

r

only, since h m . x ia proportional to CLI .!thus, the magnetic system o p t m a t i o n problem within the linear dependen- ce approximation for superconducting material critical properties (eq. (I l ) ) is reduced to that of searching for the al and rparame- ter~,whLch maximise either

P.

or P / v s a p at f a e d d/lmereiore,

d ,

,4

, , PI,

and P / v ^,up,as well aa other possible V W oharacteri-

stica,appear to be uoambiguou~ Iunotiona of the universal design factor Q

.

Piga 2-4 preeent the main aalculation results, ice. the characterfa- tics 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 separati- on procees are not preeented,sinoe suoh a separator cannot be actual- ly'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, e s t a t e the design current density value (A-$/(l +t4jn

,

the magaetio

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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.

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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 ra- tio of the~dvalues for the wet separation aPd of t h e q values for the

dT

one of the ore components,which is required for the extracti- on to e at the levels of 90 and IO%,reapectively,

?he main conclusions from figs 2-4 w e as follows.!Che optimal magne- tic system geometries obtained within the maxP, method are practical- ly the same for the wet and dry separations, &

-

^$

^, ^fi

⁺â^$ând^jr- Î

when the magnetic system sizes are increased that,the

P,

value approaches the constant quantity for the wet sepa- (a, -m, ~ e , Q +

-

⁾^.At

rafion,wherms

PL

rises proportionally to a , for the dry one.The wet pyocess separators calculated according to rnay

h

(Fig.3) have pro- ductivity appr-tely two times as high per length unit and materi- al 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 li- near dependence approximation for the superconducting material criti- cal currents allow us to determine the optimal geometry and other cha- racteristics 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 J K

(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 characteria- tics to that with the line- dependence J K = Y ~ ( I - B / B ~ ) ,which is a tangent to the

JK(8)

curve at the point where the latter cuts the lo- ad 1ine~i.e. 3K4bK)s J , ( I - B K / 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 in- to account the fol1owing.A certain optimal magnetic system geometry with the respective critical current value &corresponds to each straight 1-e 3~=3~.(1- B/u, having a point of trangency d t h the gi- ven 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 in- tersection 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 optimi- sation procedure% of maximization of both the productivity per separa- tor length unit and that per superconducting material volume unit are employed for the d r y ^aj?dwet separation procesaes,It ha.8 been provea that the considered characteristics appear to be unambiguous functi- ons of the universal design

Q

factor.!Che use of these functions ma- kes 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,, C h e r q k h , P,A.

-

^DokLady^Aka-

demii DTauk, @ (1983) 868,

AN ANALYSIS OF THE AXIAL-DISK VGMS CHARACTERISTICS

HAL Id: jpa-00223636

https://hal.archives-ouvertes.fr/jpa-00223636