31
m ARMOUR RESEARCH FOUNDATION OF ILLINOI
m
ARMOUR RESEARCH FOUNDATION OF ILLINOI
DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
DISCLAIMER
Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.
ARF 1167-9
- - -- - - - -- - - I LEGAL N O T I C E
TUB r e p r t sms pramred as an act-t of Government sanaored wrr: Neltber &a U ~ M sutoa, nar tbe CommIs8loa. nor MY WraoD ecung on beball or Ibe commlsslon:
A. bankes MY wa.rnty or rep;esentn~on.ixpreaafd or ImPlled,vlIh raspect u, he accu- racy, sompla~ncna. or uselvloesa or Ihe Idormnuon conwaed L. thla repon. or tbnt as
prlvnlaly ovmd rubto; o r 0. Assumca MY LInblllUes M I h resmct rn the uso of. or lor * c ~ read-
1 urn Y _ mrmation. . w a r n t m. or tn me repon
(Quarterly'Repost No.. 3)
I
;
.FEASIBILITY STUDY OF A NEW MASS FLOW SYSTEM
As used In Ihs Ibovo, "par- n s W on behall of lk CommJanlaa.' tnslvdea any am- ployee or oonwnoDr of Ihe Commlsalan, or employea or sucb conwnstor. 8 tba axtent tbnt auob cmp~oyoo or emu-tor of tba Commlasioa. or amployea of such conwacu,r preprca. dlamrmnatns, or pmvidea *csosa 8. m y lnlormnuoa wa - t u, U s employmeat or eonu-t wltb Ihe Commtaatoa, or U a employment M Ih avcb comwoclor.
Contract No. ATQll-11-578 Project Agreement No. 5
-- - ARMOUR RESEARCH F~O.UTDATTON
. ,
of Illinois ~ n s t i t u t e of ~ e c h n o l o ~ ~
Technology Center . Chicago. 16, Il8inois.
U. S. Atomic, Energy Commission Chicago Operations Office
9800 South Cass Argonne, Illinois
Attn: Steven1 V. White, Director Research .Contracts Divf s5on
(Covering the period f rom December 1, 11960. to February 28, 1961)
'i A R M O U R R E S E A R C H F O U N D A T I O N O F I L L I N O I S . I N S T I T U T E O F T E C H N O L O G Y
FEASIBILITY STUDY OF* A NEW MASS FLOW SYSTEM
I. INTRODUCTION
.- A number of mass flow devices a r e described in patent and periodi-
cal..l.iterature. However, existing. devices a re . limited.. to spec.i.fic applications, . . . .
. no general purpose unit being presently available. . . There are. a.. number of
desirable characteristics in mass flow measurement systems, i. e. , the ___I -
ability to measure homogeneous flow, slurries, highly corrosive fluids and
.. multiphase. fluids. .In addition,, considerations. such a s pressure drop, abili-
ty;. .to. measure.. external to. the flow, ruggedness. and reliability: a r e also
important. A mass flow measurement technique capable in principle of- '
meeting, the above requirement has,been devised, and is the basis of the -- present expe.rimenta1 investigation, Badger Meter Manufacturing Company,
Milwaukee,, isc cons in, is. a sub -contractor in this: work. and.. the evaluation ... .
i s being performed on a joint basis.
r'/ In the systemrbeing investigated, the fluid ---- i s made to pass through an ------------I_" _ _ _ _
.S-shaped tube wherein.measurements. of the angdar.:momentum and.density -----.I-.- _^.* ..-- --
( yield mass flow directly. The S-tube assembly i s pivoted and t r ies to ro- - I
1 tate due to. the angular momentumof the fluid. A torque motor and. torsion I ; spring maintain the displacement at essentially zero, the restoring, force
i 6
a being a. measure of angular momentum. Density is. measured, by the absorp- d 1 , tion of nuclear radiation passing, througha window in. the S-tube. A
'----.,,---
k. scintillation. counter i s u s e d a s t h e radiation detector, a technique of radia - tion. chopping,being used:..to cancel variations. in.detector sensitivity.
. .Work during the report .interval has. consis.ted. of . -.-------.-..- design. and. con- ....
struction to. complete,models of the experimental mass gauge. Assembly '-------c-'-
A R M O U R R E . S E A R C H F O U N D A T I O N O F . I L L I N O I S I N S T I T U T E O F T E C H . N O L O G Y
of the units has essentially been completed, and testing of the flow system
will then begin.
11. TECHNICAL DISCUSSION
A. Source Procurement
Experimental measurements described in previous reports have
shown that x-ray sources made f rom promethium-147 represent the best
available isotope for use in the density gauge. Promethium-147 emits a
0. 223 mev beta and has a 2.6 year half life. The Isotopes Division a t
Oak Ridge has perfected a technique for making pressed pellets of P m 0 2 3'
having. a density of approximately 6.0 gramslcc . The Pm203 available
has an approximate activity of 300 curies per gram of total r a r e earth
oxide. These values, have.:been.used. to. calculate the. size .. . of . source. that .is
. .required..-to give a detector counting, r.ate,of one million counts per second.
. . In.,the design.. to. be utilized,. a specific target material .is not used I . . . .
,.,in conjunction.with. the.. beta. .. source. . Instead,: .the x-ray output represents , . . .
, . k- shell fluorescence radiation. fyom the promethium and. the.. bremsstrahlung
L. ., continuum. Fpr a source of this. design, optimum. thickness. i s approxi-
L mately 600 mg/cm , so that the thickness should be one millimeter. For - a source-detector distance of 10 cm and a detector diameter of 3 cm, a
. source of approximat,ely 3. mm in. diameter:.is required,. to achieve the ,de - sired detector counting, rate. The calculation includes the approximate
3.. 2. cm. of . plastic..and, 3.4 c m of water that represents the sample and
sample. holder. . A 3 mm diameter., by one. mm:.thick. source represents a
%,beta activity of ,1.2. 7 curies.
' , rn The P m . .2 . .3 0 . will . . be sealed .in. an. aluminum. cylinder with. a 1 5., mil
. . thick.window at one end. For. the energy.being considered,, the window will
. :p A R M O U R R ' E S E A R C . H F O U N D A T I O N O F I L L I N O I S I N S T I T U T E O F T E C H N O L O G Y
,absorb abovt.five percent of :the radiation. The. source holder i s internally
1y threaded,. and:. is fastened. to the .threaded. section on, the end. of the. vibrating
. . , reed,. solder being: used. to seal the threaded joint. Two. sources. of, this.' type U
. .
. .. have . . been. orde.redfrom Oak 'Ridge, and. delivery .is. expected, by, ;the end. of
April.
0peration.of . . . the density gauge in .the. x-ray region.has. sugges.ted. a
possible modification of the vibrating reed system. The advantage of
physically moving, the source instead- of the shield is. obvious for energies
above 100 kev. However, for x-rays insthe 40 kev region, the mass of
absorber required to give the necessary radiation attenuation could be made
comparable tobethe mass of the source assembly. In such a system, the
.x-ray source. would..be fixed. and an absorber mounted.on.the end-of the
. . ~ b r a t i n g , . . reed.. would. modulate the . radiation. . beam. This. technique would
pr,obably .simplify. handling, and. mounting of the. sources.
Because of .the delay in. delivery of ,the promethium sources, reed
assemblies loaded with cobalt-60 will be used for the initial check out of
the system. Nuclear ?Chicago. i s making. the sources ,, and delivery is ex-
pected March 20th. Although. the absorption. of cobalt radiation. will be
- much:,ies , s. . . . than, the. optimvm. value,. i t will permit evaluation. of, the. vibrating . .
, reed. system and. the deqsity servo system.
B. Construction and Testing of Equipment
. . Two. expe.rimenta1 models of the mass gauge: have e.ssentiallybeen I
completed. One unit . will . be used.for. flow rate testing and..the o,ther for
..testing of ,.the. density.measuring system. Testing, of .the unit for flow
conditions i s expected to begin the week. of March 13th. Final assembly
, of the unit for density measurement i s awaiting the delivery of the servo
A R M O U R R E S E A R C H F O U N D A T I O N O F I L L I N O I S I N S T I T U T E O F T E C H N O L O G Y .
motor, which i s expected about March 15th. The electronics for the density
portion of, the unit .is. now: being, construc,ted,, and. should. be comple,ted.. by the
t ime that ,the experimental unit .is. available.
C. Flow System
In the appended report deacribirig, work- at Badger, flow element
.. design..features. are . discussed, as well as pose.ible. e r rors . in. such.a. system.
For a.20. to. 1, range-in.flow rate,. a.400 to.. 1 range in torquemust be coyered,
.-- and. the problem.-.in . measur.ing,.torque to 0.0 5% a r e considered. In. addition,
possible sources of e r r o r in..the fl0.w element a r e discussed, together. with .:
means fop minimizing, the effects of such e r rors .
111. SUMMARY
Construction of two experimental mass gauge units has essential-
ly been comple.ted, and. testing.. of the flow and.density characteristics .is
. expected. to. begin.during. the next month. The delay in obtaining promethium
sources. has. necessitated. initial testing of the. density gauge using cobalt-60.
Although absorption of cobalt radiation in.. the sample T s ' l e s s than. optimum, . 8
4'
i t will permit evaluation of the vibrating reed system and the density gauge. "-
servo. system. After testing. of the experimental units .is completed,, '.it
should be possible to predict the manner in which the mass gauge will meet
.the de sircid accuracy and stability requirements.
Respectfully submitted, I
ARMOUR RESEARCH FOUNDATION of Blinois Institute of ~ e c h n o l o g ~
A. m. y G. M. Burgwa d, Group Leader
C. A. Stone, Supervisor sics Research Nucl oa r Phyoico Sectiuxi
A R M O U R R E S E A R C H F O U N D A T I O N O F I L L I N O I S I N S T I T U T E O F T E C H N O L O G Y
FEASIBILITY STUDY OF A
NEW MASS FLOW SYSTEM
Q u a r t e r l y Report
( N o . 9 , Period from December 1 , 1960 - February 28 , 1961)
Prepare.d f o r Submittal t o :
I l l i n o i s I n s t i t u t e o f Technology Technology Center Chicago, I l l i n o i s
Contract No. AT (11-1 ) -578 P r o j e c t Agreement No. 5
Armour - Badger Subcontract
BADGER METER MANUFACTURING COMPANY 4545 WEST BROWN BEER ROAD MILWAUKEE 2 3 , WISCONSIN
C O N T E N T S
S e c t i o n :
& I .
Page :
D e s c r i p t i o n of t h e -Experimental Mass Flow Meter . . . O . . . . . . . O 0 1
Flow Element Design F e a t u r e s . . . . . . . . 1
Flow Element S c a l i n g . . . . . . . . . . . . 5
Dens i ty Element- Design F e a t u r e s . . . . ., . . 8
Dens i ty Element S c a l i n g . . . . . . . . . 12
Source S i z e . . . . . . . . . . . . . 12
C a l i b r a t e d Wedge Dimensions. . . . . . . . . . 12 M u l t i p l i c a t i o n , Square. Root, E x t r a c t i o n , and I n t e g r a t i o n . . . . . . . . . 16
P o s s i b l e -Sources o f , Plow 'Element E r r o r , . . . . . . , . . . . . . . . 17
.E r ro r Due t o P r e s s u r e Drop a long t h e .S- tube , . . . . . . . . . . . . . . . . . 17 Errop Due t o V a r i a t i o n s i n E f f e c t i v e Bend R a d i i , . . . . . . . . . . . . . . . . . 19
E r r o r Due ' t o Unequal Coupling C r o s s . S e c t i o n Areas. . . . . . . . . . . . . 19
Figure :
F I G U R E S -
Page :
-Flow Element with. S ide Housing:Removed . 1
l+".'s-tube Flowmeter , . . . . . , . . . , . . . ., 2
Torque Readout and Transmi t t e r of Flowmeter Element . . . . . . . . . . . . . . . 3
.Flow. Element I n l e t and Q u t l e t .Conf-iguration . . . . . . . .. . . . . 4
Yar. ia t ion of Sp r ing Windup wi th Torque . . . . . ' 5
~Var i a t . i on of Torque and :Spring :Windupwith . ,Flow:Rate . . a . ' 7
S e c t i o n .Showing. Flow :Densi ty Measurement . . 9
V i b r a t i n g Reed-Radia t ion Chopper wi th Window Removed a . . . . 110 :Vibrating.Reed.Radfatiom Chopper wi th Window i n P l ace . . . . . . . . . . . . I0
I s o t o p e Capsule V i b r a t i n g Behind t h e Window . . . 10
. - . . Dens i ty Servo Showing .Reed' and
Rotary , Wedge . . . . . . . . . . . . . . . . . . . 11
Dens . i t l :Readout and Transmitter o f . D e n s i t y Servo . ., 411
K2C03 S o l u t i o n Composit ion E f f e a t s . . . . . . . . 1 5
!Servo f o r Square Root: Extractioan a n d . I n t e g r a t i o n . . . . . . . . . . . . . . . 16
B a l l and Disc I n t e g r a t o r far Read~ut of Mass Flow Quantity . . . . . . . . . . . , 16
- 1 - March 9, 1961
I . DESCRIPTION OF THE EXPERIMENTAL MASS FLOW METER MODEL.
A. Flow Element D e s i g n a t u r e s . The i so l a t ed S-shaped s ec t i on of conduit shown i n Figure 1
and 2 generates a torque about its a x i s of suspension when flow passes through it. This torque has t he same s ign regard less of the d i r ec t i on of flow, s o the flow element is b id i r ec t i ona l . For a known densi ty , torque is d i r e c t l y proport ional t o the square of mass flow r a t e . Therefore, a measurement of t he square roo t of t h i s torque and of dens i ty provide a measurement of mass flow rate.
C The flow range is equal t o the square roo t of torque range, s o a 20: l flow range r equ i r e s a 400:l range i n the torque measure- ment. This f a c t together with an accuracy requirement of t he order 0% 0.05 % on torque measurement means tha t a very s e n s i t i v e measure- ment technique must be used. A n u l l balanced servo was se lec ted which has exce l l en t threshold, l i n e a r i t y , and dynamic c h a r a c t e r i s t i c s , a s described i n the following.
FLOW ELEMENT WITH SIDE BQUSTNG RWOVED FIGWE 1
1% -SO TUBE FLOWMETER FIGURE 2
Torque due t o the passage of flow through t he S-tube is re- s i s t e d by a c o i l sp r ing wound up by a torque motor. The torque motor is driven by an ampl i f i e r which rece ives its input from a synchro whose r o t o r is connected t o the S-tube a x i s as shown i n Figure 1 and 2. This closed servo loop cons t ra ins the S-tube t o its n u l l pos i t ion , and provides a l i n e a r r e l a t i o n s h i p between torque and t he angular pos i t ion of the torque motor s h a f t . The angular pos i t ion of the torque motor s h a f t is read by means of t he two d i a l s shown i n Figure 3. These d i a l s provide a coarse and f i n e readout. The coarse d i a l r o t a t e s one f u l l t u rn f o r maximum flow r a t e while the f i n e d i a l r o t a t e s t en turns . Hence the torque read- out is i n t e r m s of percent maximum torque. A t en t u rn potent io- meter is geared t o t he f i n e d i a l f o r transmission of a vol tage proport ional t o torque.
Torque Readout and Transmitter of Flowmeter Element, FIGURE 3
The e n t i r e spring-S -tube -synchro assembly is immersed i n a
f sealed o i l bath t o cancel t he e f f e c t s of l i n e xmtp re s su re , and pressure l o s se s along t he S-tube. The enclosure shown i n Figure 1 is closed by a mating o i l t i g h t s i d e cover shown i n Figure 4. The i n l e t and o u t l e t conduits are on opposi te s i d e s of the flow-element a s indica ted i n Figure 4. The S-tube is connected t o these conduits by means of f l e x i b l e couplings, the c h a r a c t e r i s t i c s of which m u s t be se lec ted with care. (Paragraph 11.)
3.5 .- Torque Ft.-lbs.
'3 .0
F t . l b s Slope: 1.53
I .
. . . . I..
I I 1 0.5 1.0 - 1.5 : . , ? 2.0 ' : ' 2*,5 ' , 3 .0
Motor R a t o r . - S p r i a g Angle Revolu t ions ,
VARIATION OF SPRING , w Z ~ - U P WITH TORQUE . .
B , Plow Element -Sca l ing .
Tho t o r q u s equa.tion210T the Plow e le~oer l l is a s fo l lows: 2 1 w - 2 1 f Q - w2
T=PA- A - 40 ..a - -
f' - 4 0 . 7 ( 3 ~ ~
where 1 : E f f e c t i v e l e v e r a r m W : Mass -Plow. Rate A : Conduit c r o s s s e c t i o n a r e a Q : Volume Plow:Rate. p : Dens i ty
A s shown i n F igu re 5 , t h e c o i l s p r i n g r a t e is 1,53 f t . l b s . / r e v . F igu re 6 is a p l o t of f low r a t e v e r s u s to rque and d i a l r ead ing . From t h i s cu rve , t h e f low range is nominally 40 t o 980 pounds pe r minute. The minimum f low r a t e a t a given accuracy is l i m i t e d by f r i c t i o n i n t h e S- tube.support ' bea r ings . The maximum f low ra te is l i m i t e d by i n t e r l e a v e c l e a r a n c e s of t h e coil . s p r i n g and t h e maximum cont inuous to rque r a t i n g of to rque motor.
-The s.ynchr-o uszed t o d e t e c t S- tube r o t a t i o n has a s e n s i t i v i t y of 200 m i l l i v o l t s per degree . The a m p l i f i e r whfch d r i v e s t h e
I- - t o rque motor de l i . ve r s maximum power t o t h e to rque motor (4.59 f o o t pounds) a t an i n p u t vo l t age of BOO m i . l l i v o l t s . Therefore , %;he g r e a t e s t angu la r d e f l e c t i o n descri.bed by the S-tube a t maximum s t a t i c f low r a t e is 30 minutes of a m . Each f l e x i b l e coupPing - is 3 i nches from t h e S- tube c e n t e r , s o maximum coup l ing e l o n g a t i o n .E is given by:
where R: 3''
8: 30 miqukes o r 8 degree
A t ,4 maximum f low r a t e , coupl ing e l o n g a t i o n 5,s:
0.262/4 o r 0.0655?v,
The squa re r e l a t i o n s h i p between a m p l i f i e r ou tpu t v o l t a g e and t o ~ q u e c o n s t i t u t e s a v a r i a b l e g a i n which can cause s e r v o i n - s t a b i l i t y problems a t h igh f low rates. A t maximum f low ra te , t h i s g a i n e q u a l s 0.0425 f o o t pounds of to rque pe r volt of a m p l i f i e r o u t p u t . A t minimum flow r a t e , t h i s g a i n drops t o 0.821 f t . l b / v o l t , lower by a f a c t o r of two. T o t a l loop g a i n must be z d j u s t e d f o r a c lo sed loop damping f a c t o r 3 g r e a t e r than 0.5 a t h igh f low rates. The dynamic c h a r a c t e r i s t i c s of ma%o~-spr ing-S- tube combination are y e t t o be eva lua t ed . I t is expected that t h e v i scous drag of t h e o i l w i l l provide s u f f i c i e n t damping f o r a c c e p t a b l e t r a n s i e n t response . However, f o r purposes of e v a l u a t i o n , 8 BC tachometer w i l l be geared t o t h e t o rque motor s h a f t t o p rov ide h igh l e v e l ra te feedback. Adjustment of t h e g a i n of t h i s feedback channel a l l o w s a s e l e c t i o n o f t r e s p o n s e from underdamped t o h e a v i l y overdamped, -and response t i m e s from milniseconds t o 20 - 38 seconds.
C IA 4 C 'OR( _ AN- -.PRI 1 ' 3P Gal.. L A WITH FLOW RATZ
E/\Y 120. 1002 in FIGURE 6 Q = 108.1 gpm
%w = 904 ppm 108 ,, 835
90 . '751
when Q : gal/min of H20 a t 6 8 O ~ 80 .. 668
T = 5.62 w2 '7!3 584 when .W .: Ibs/min,
I
I I I
10 ., 8 3 . 5 I 5 41.7 I
0 I 1 I I t I , I
I
. 02 .05 0 . 2 0:5 2 f 5 I 1
. ooa i
'Torque : F t . l b s 4.59
Motor Rotor - Spring Angle : Degrees & Percent Max. -
C . Dens i ty Element Design F e a t u r e s . -. -
A s ske tched i n F igu re 7 , t h e measurement of d e n s i t y is accomplished by means of comparing r a d i a t i o n from a s t a n d a r d sou rce wi th t h a t from ano the r source a f t e r i ts r a y s a r e absorbed by t r a v e r s a l a c r o s s t h e S-tube and through the r o t a r y wedge. The wedge is pos i t i oned by a c lo sed s e r v o d r i v e i n such a way t h a t r a d i a t i o n l e v e l s r each ing t h e d e t e c t o r from each sou rce are equa l . For t h i s c o n d i t i o n , t h e angu la r p o s i t i o n of t h e wedge is p r o p o r t i o n a l t o t h e d e n s i t y of t h e subs t ance w i t h i n t h e S- tube c e n t e r . The same d e t e c t o r is used t o measure r a d i a t i o n from bo th s o u r c e s , s o time must be sha red between them. I n
.a
o t h e r words, t h e dua l r a d i a t i o n beams must be chopped s o t h a t one r eaches t h e d e t e c t o r whi le t h e o t h e r is a t t e n u a t e d and
- v i c e v e r s a . The technique f o r accomplishing t h i s is p i c t u r e d i n F i g u r e s 8, 9 , and 10. A s shown on F igu re 8, a s t r o n g l y f e r r o - magnetic s t a i n l e s s steel reed is clamped between mounting b locks and caused t o v i b r a t e by means of A . C o e x c i t e d e lec t romagnets . The capsu le a t t h e f r e e t i p of t h e r eed c a r r i e s a charge of r a d i o - a c t i v e material. This capsu le is surrounded by a l e a d s h i e l d excep t f o r a r a d i a t i o n a p e r t u r e o r i e n t e d as shown i n F igu re 9. A s t h e r eed v i b r a t e s , r a d i a t i o n from t h e capsu le is a l t e r n a t e l y t r a n s m i t t e d and a t t e n u a t e d by t h e s h i e l d . F igu re 1 0 p i c t u r e s t h e v i b r a t i o n of t h e capsu le w i th in t h e s h i e l d looking through t h e a p e r t u r e .
- The d e n s i t y element u s e s two such reed assembl ies o r i e n t e d wi th r e s p e c t . t o each o t h e r as i n d i c a t e d i n .Figure 7 . The s c i n t i l l a t i o n c r y s t a l de t ec , t o r is one inch i n d iameter by two inches i n t h i ckness . Rather than be ing mounted h o r i z o n t a l l y as i n - F igu re 7, i t has been mounted v e r t i c a . 1 1 ~ and i n s e r t e d i n t h e
.! - '
p l a s t i c window. Radia t ion from t h e r e f e r e n c e sou rce s t r i k e s t he c r y s t a l r a d i a l l y . Rad ia t ion from t h e measuring s o u r c e , a f t e r p a s s i n g through t h e wedge and3S-tube s t r i k e s t h e c r y s t a l
.. a x i a l l y . .
The ou tpu t of t h e p h o t o m u l t i p l i e r tube which is o p t i c a l l y coupled t o t h e s c i n t i l l a t i o n c r y s t a l is a ne t ,AC e r r o r v o l t a g e p r o p o r t i o n a l t o t h e d i f f e r e n c e between r a d i a t i o n i n t e n s i t i e s f.rom t h e r e e d s , This vo l t age is ampl i f i ed and used t o d r i v e t h e d e n s i t y s e r v o motor. This motor r o t a t e s t h e ' c a l i b r a t e d wedge and d e n s i t y r eadou t d i a l s p i c t u r e d i n F i g u r e s ll and 12. A t null, t h e p o s i t i o n of t h e wedge and r eadou t d i a l s are p r o p o r t i o n a l t o d e n s i t y . The, d i a l s are geared t o g e t h e r through a 10: 1 r a t i o , wi th one r o t a t i o n of t h e c o a r s e d i a l cor responding t o one r o t a t i o n of t h e c a l i b r a t e d wedge,
Vibrating b e d R a d i a t i o n Chamr Vibrating R e e d Rad%at.iom CIzapper vxtlxitb w i ~ d w ramaved wikh wWfdow i n glace
FI&UBE 8 FXCUBE 9
Isotope CagetuXe Vibeating behlltd the window
FLfSlBB 10
Density Servo Showing Reed and Rotary Wedge FIGURE 11
Densi teadout and Transmitter of Density Servo FIGURE 12
D . . Density .Element Scal ing. -
.. The d i s t ance between the measuring source and the c r y s t a l is about 15 cent imeters . A t t h i s d i s t a n c e , the c r y s t a l d e t e c t i o n e f f i c i e n c y is 0.06 %. . .
A counting r a t e g r e a t e r than lo6 counts per second is requi red t o provide adequate s t a t i s t i c a l accuracy. Considering t h a t t h e r e a r e two gamma quanta per d i s i n t e g r a t i o n f o r Cobalt-60, and one d u r i e r e p r e s e n t s the d i s i n t e g r a t i o n of 3.7 (101°) atoms per second, - a t an a i r d i s t ance of 15 cm. we r e q u i r e
+06 2 ( .0006)~3-;7)-ii-j10) = 0,0225 c u r i e s
The ac%ual conf igura t ion of the r a d i a t i o n path is given below:
Source. 1
I n order t o a l low f o r a d d i t i o n a l absorb$ion .wi th in the wedge, p l a s t i c and o i l , and wi th in t h e flow stream i t s e l f , a BOO m i l l i - c l i r ie source.was chosen f o r the . f i r s t - e x p e r i m e n t a l model. The ,
energ ies qf the Cobalt-60 gammas a r e too h i g h . t s provide o p t i - mum sens ' i ' t iv i ty f on. the flow s e c t i o n dimensions of the model. Therefore, Promethium 147 b e t a exc i t ed x-ray sources with gamma energy around 40 kev a r e a l s o t o be prepared a t Oak'Ridge f o r an a d d i t i o n a l p a i r of reeds .
I
0.815 0.485 0.875 0.625 1.33 0.625 - -
-FOP the Cobalt-60 reeds, . t h e seed s h i e l d w i l X a t t e n u a t e one r a d i a t i o n beam by a f a c t o r of t h r e e while ' the o t h e r is exposed.
L E
$t C r y s t a l T T
W E D G E
"
- f
A D
e c
S T H
A I R
S T ,I
B O P L I L A L A
2. C a l i b r a t e d .Wedge Dimensions,
By p l a c i n g t h e wedge i n t h e measuring b e a m ' r a t h e r than the r e f e r e n c e beam, t h e wedge t h i c k n e s s v a r i a t i o n need r e p r e s e n t o n l y t h e v a r i a t i o n s i n f low d e n s i t y r a t h e r than t h e t o t a l f low d e n s i t y . The PPuids t o be used i n our tests are v a r i o u s s o l u t i o n s of potassium carbona te i n water having d e n s i t i e s va ry ing , f rom u n i t y t o 1.54, The wedge has been cons t ruc t ed f o r u se wi th f low d e n s i t y v a r i a t i o n s between 0.9 and 1.6. The.. S-tube c e n t e r is s q u a r e i n c r o s s s e c t i o n w i t h a s i d e dimension of 3.378 cm,,
-
For aluminum e = 2 ~ 7 and
A x = 06885 c m o r 0.317 inches .
The wedge wps cons t ruc t ed as shown i n F igu re 13, vary ing i n t h i c k n e s s from 06125 t o 00485 inches . This wedge is r o t a t e d by t h e density s e r v o immediately i n f r o n t of t h e measuring sou rce a p e r t u r e , a s shown i n F igu re 11. .Zero on t h e d e n s i t y r eadou t d i a l corresponds t o about P = 0.95 and 80 corresponds t o about P = 1.55. P r e c i s e c a l i b r a t i o n of t h e readout w i l l be done wi th a set of p r e - . .
c i s i o n a b s o r b e r s , r
The a d d i t i o n of K&O3 t o t h e water changes t h e a b s o r b t i o n I - I c o e f f i c i e n t a s a f u n c t i o n of d e n s i t y , .F igu re . 14 is a p l o t of
t h i s composit ion e f f e c t and shows a 3.13 % change 54 % change i n . P
I!! i
r r c AAuW" la 360' -- BADGER METER MFG CO. LB5---5/
7 7 0 ~ FLOM &?PA~u&A/~uT .Ip - - DIU
$? / Z L
FIGURE 13 ---- , s ~ ~ R _ f l z2t=G~ - .LO U QIDCElro
.L-- -N I APPII~VK-
K 2 C o ~ by w e i g t
\ / 54 % change
Solut ion /
3.13 % change
D e n s i t y : gm/cm?
K2C03 COMPOSITION EFFECTS
FIGURE 14
E . Mul t ip l ica t ion , Square Root Extrac t ion , and In tegra t ion .
A s given i n the torque equat ion, s ec t i on I -B , mass flow r a t e W is propor t ional t o F ~ where T is torquc and p is densi ty . The torque motor d r ive on the flow element provides a pot vol tage
I propor t ional t o T and the dens i ty servo provides a pot posi t ioned by P and excited by T. The wiper vol tage of t h i s pot is pro- po r t i ona l t o T P . The servo loop shown i n Figure 15 e x t r a c t s the square roo t of t h i s voltage using a p a i r of high accuracy v e r n i s t a t s i n a conventional analog roo t ex t rac t ion . The s h a f t pos i t ion of the servo d r ive motor is propor t ional t o mass flow rate. I f t h i s s h a f t is used t o t r a n s l a t e the ca r r i age of a b a l l and d i s c i n t eg ra to r shown i n Figure 16, the i n t eg ra to r w i l l read mass quan t i ty d i r e c t l y .
I I . POSS ][BEE, . ... SOURCES -.-- . . OF ----- .FLOW ' ELEMENT. ERROR
A'. E r r o r due t o P r e s s u r e Drop.APong t h e S- tube.
Due t o p r e s s u r e l o s s around t h e two 90° bends i n t h e S - tube , shorn i n F igu re 1'7, t h e p r e s s u r e a t t h e i n l e t P1 does n o t e q u a l -the p r e s s u r e P2 a t t h e o u t l e t . It w a s t h e r e f o r e considered t h a t ''an e r r o r tor'que may e x i s t equa l t o :
where A : I . E f f e c t i v e a r e a over which t h e t o . t a l p r e s s u r e d i f f e r e n t i a l a c t s .
R : E f f e c t i v e bend r a d i u s .
However, P i and P2 are conversan t wi th t h e o i l b a t h s u r - rounding t h e S- tube through f l e x i b l e coupl ings C 1 and C2. Therefore a p r e s s u r e P3 e x i s t s i n the o i l ba th e q u a l t o
which is t h e a r i t h m e t i c average of P i and P2. POP our purposes , t h e c a s t i n g which forms t h e o u t e r c o n t a i n e r f o r t h e o i l b a t h is r i g i d , and t h e o i l is v i r t u a l l y incompress ible (0 .1 % volume re- duc t ion a t 100 p s i . )
Equat ion (2 ) ho lds r e g a r d l e s s of t h e magnitude of P3 i f t h e r a d i a l e las t ic p r o p e r t i e s of C 1 and C2 are t h e same and f l e x i b l e r e l a t i v e t o t h e c o m p r e s s i b i l i t y of the o i l and expansion of t h e housing under p r e s s w e , Therefore:
The f o r c e due t o P1 is PIA. It is r e s i s t e d by a f o r c e P3A. The f o r c e due t o P2 is P2As r e s i s t e d b y t h e same coun te r f o r c e P3A.
Torque about 0 = PlAR - P3AR + B2A.R - P3AR
= AR~Pl-P3+P2-P3) . (4 )
But equa t ion (3 ) s t a t e s t h a t : PI-I?,-P3+P2 = 0
Therefore t h e to rque about 0 is z e r o and equa t ion (1 ) is n o t v a l i d .
LIP A P A - -- FOF # = A l = A2 : Error t0tqUez 2 . A - 0 ' ,
A P 'P p p E2 .+ ,
For A1 #= A2 : Error torque=, - 8-1 '- -2- A P3 . P3
B. E r r o r Doe t o Va,riiptions i n E f f e c t i v e ~ c h d Radii.-
D i f f e r ences i n t h e v e l o c i t y p r o f i l e a c r o s s $h& pqpe a& t h e e n t r a n c e to t h e two 90° bends of t h e S- tube may ,cause d i f f e r e n c e s betw-een t h e mean r a d i i R1 and R2. For a l l f low rates under con- s i d e r a t i o n , f low w i l l be t u rbu len t . A d d i t i o n a l e d d i e s and r e - c i r c u l a t i o n ~ can be expected t o form as t h e f low pas ses over t h e d a s t i c coupl ings and around t h e bends. Accordingly i t is d i f f i - c u l t t o p r e d i c t what t h e e f f e c t i v e f low p r o f i l e a c r o s s any p i p e s e c t i o n . w i l l lo& .Bike. For any one conf igukabion i t would be expected t h a t t h e e f f e c t i v e r a d i i d i f f e r e n c e s would be independent of p r e s s u r e and would vary r e p e a t a b l y w i th f low ra te , i t a t a l l . I n t h i s even t t h e 'flow r a t e ou tpu t s i g n a l of t h e meter would de- p a r t from a < p e r f e e t squa re f u n c t i o n i n a r e p e a t a b l e f a s h i o n and could be compensated. P re s su re d i f f e r e n c e s caused ,by l o s s e s due t o t h i s l o c a l secondary f low produce a to rque r e a c t i o n which is negated e x a c t l y as i n A . above.
C . .. E r r o r Due t o Unequal Couplliang . Gross :Sec t ion . Areas.
Unequal p r e s s u r e s P 1 and P2 w i l l cause unequal areas a t t h e coupl ings as Cl expands and-C2 c o n t a c t s rad ia l1 .y . , A twofold e r r o r is p o s s i b l e as a r e s u l t .
1. An erlpor to rque can a r i s e due t o unequal; p r e s su re -a rea p h d u c t s a c r o s s boundar ies 1 and ..a.
where A 1 = A pa P3
and A 2 = A - p3
2. An e r r o r to rque c a n a l s o a r i s e due t o f o r c e s t r a n s m i t t e d t o t h e S- tube due t o a x i a l s t r e s s i n g of t h e coupl ing i n bo th compression and t ens ion .
Ne i the r of t h e s e e r r o r to rques are compensated by t h e o i l b a t h , These p o s s i b l e e r r o r s can be minimized however, by proper s e l e c t i o n of coup4,ing c h a . r a c t e r i ~ % i c s . The coupl ing must have &he folJowing e las t ic p r o p e r t i e s :
a. Radia l s p r i n g c o n s t a n t s t i f f enough t h a t a B p s i p r e s s u r e w i l l cause on ly n e g l i g i b l e r a d i a l s t r a i n ; b u t f l e x i b l e r e l a t i v e t o t h e s t i f f n e s s of t h e con- t a i n e r c a s t i n g .
b e Ax ia l s p r i n g c o n s t a n t very f l e x i b l e so a s t o minimize 2. above.
The p r e s s u r e drop a long t h e S- tube a t 10 gpm is about 0.02 p s i , a t 100 gpm i t is 2.0 p s i . A f l e x i b l e coupl ing having t h e s e c h a r a c t e r - is t i c s is r e a d i l y a v a i l a b l e .
R e s p e c t f u l l y Submit ted,
Will iam K. Genthe Research Engineer
APPROVED :
chi&$ ~ e s e a r c h d Development Engineer /pr'
Marvin .E. Hartz D i r e c t o r o f . R e s and Engineer ing
