ORNL-2605 by Jon Morrow

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HELP 0mJ-2605

Contract No, W-7405-eng-26 Reactor Projects Division

GAS COOLED, MOLTEN SALT HEAT EXCHANGER

- DESIGN STUDY

R. E. MacPherson

Date Issued

Oak Ridge National Laboratory Oak Ridge, Tennessee operated by Union Carbide Corporation f o r the U. S. Atomic Energy Commission

3 4 4 5 b 0363239 7

- 2 -

CONTENTS Page No, J

Abstr&ct.~.ooo..D...o.i,.....o.o.v.. Introduction ,. ,. , summary Design Considerations e 1. Heat Exchanger Configuration , , 2. Finned Tubing , 3 . Tubing Size , e 4. General.. + . * . + . * . . a . Discussion 1, Countercurrent, Cross Flow Heat Exchangers e 2. Countercurrent Flow Heat Exchanger Conclusions, Method of Calculation , ., Nomenclature e e Bibliography

.. .. .... ... ... 5 6 ....... ... ... .. . 8 .... ... 8 . . . . . . . . . . . . . . 12 .... ... .... . . . 14 .. . ,..* .16 . . . . . . . . . . . . . . . . . . . . 16 . . .16 . . . . . 24 . . . . . . . . . . . . . . . . ..24 ... .. . . . . 31 . ... ... . . . . 38 . . . . . . . . . . . . . . 40 e

- 3 LIST OF FIGURES Page No. Fig. 1

- Annular Heat Exchanger Geometry . . . . . . . . . . . .

.Design Study Heat Exchanger Geometry. . . . . . . . . . 3 .Annular Heat Exchanger Design Parameters. . . . . . . . 4 .Tubing Size Optimization. . . . . . . . . . . . . . . .

Fig. 2

Fig.

Fig. 5

Fig. 6

for a Four-Pass Heat Exchanger Using H e l i u m at 300 psig with an 8500F I n l e t Temperature

...................... ......................

Fig. 9

f o r a Four-Pass Heat Exchanger Using H e l i u m a t 300 psig with a 700째F I n l e t Temperature

- Design Parameters

for a Four-Pass Heat Exchanger Using Hydrogen a t 300 psig with an 8 5 0 0 ~I n l e t Temperature

......................

Fig.10

- Design Parameters

......................

- Design Parameters for a Three-Pass Heat Exchanger Using Helium a t 150 psig with an 8509 I n l e t Temperature

Fig. 8

- Design Parameters f o r a Three-Pass Heat Exchanger Using H e l i u m a t 300 psig Gith an 850OF I n l e t Temperature

Fig,, 7

- Design Parameters

......................

- Design Par

t e r s f o r a Four-Pass Heat Exchanger Using Steam at 300 psig with an 850OF Inlet

.......

................

Function of Total Blower Power Investment r

Cost per Heat Exchanger Figel?

- S a l t Volume i n Return Bends of

Serpentine Fuel Tubes f o r a Four-Pass Heat Exchanger.

.........

-4ABSTRACT

One of the major problems i n the economic evaluation of the application of forced circvlation,<gas cooling t o high temperature, molten salt power

reactor systems i s the definition of the required heat transfer equipment, i t s s i z e ana operating cost. A design study of the.salt-to-gas heat exchangers f o r such a gas-cooled system has recently been completed, and the results are.repoPted. Helium, hydrogen and steam are considered as coolants.

The effects of

varying heat exchanger tubing size, coolant inlet temperature, coolant pres-

sure level, allowable salt pressure.drop and uranium enrichment of the molten s a l t a r e demonstrated. The relationship between heat exchanger dimensions, f u e l inventory and blower power requirements i s presented i n graphical form for the most pertinent cases. Comparisons are made of annual operating costs and heat exchanger overall s i z e as a function,of coolant type and operating conditions, Hydrogen isrshown t o be the most effective of the coolants considered, with steam and.helium being roughly comparable. Assuming other conditions t o be equal, helium can be made competitive with hydrogen by operating with

a 50

60$ higher helium temperature gradient through the heat exchanger. O p t i m u m heat exchanger geometries based on gas blower power costs and enriched f u e l inventory charges require a t o t a l blower power investment of approximately 0.5% of the plant gross e l e c t r i c a l output. However, substantial reductions i n heat exchanger s i z e can be realized by going t o higher blower power investment levels.

Introduction Since the early phases of design evaluation on a molten salt power reactor system, it has been desired t o investigate the problems associatea with the use of gas as t h e primary coolant. A s a step i n t h i s direction, a design study has been carried out t o define the salt-to-gas primary heat exchanger which would be required i n such a system. The study concerns a reactor having a thermal output of 640 megawatts (legenerated i n blanket and removed through blanket cooling system) and a gross e l e c t r i c a l output of 275 megawatts. Consideration has been given t o the use of helium, hydrogen and steam as coolants.

ference design was based on the following:

4 primary

heat exchangers

1/2" Inconel tubing (0.050" w a l l )

Circumferential Inconel f i n s Helium coolant 623 lb/sec

Inlet

850'F

Outlet

1025OF

Pressure 300 psig Cross flow Molten Salt (Fuel 130) 1768 lb/sec Inlet

1210OF

Outlet 1075OF Four pass serpentine flow

as t o the desirabili Power Reactor.

The re-

- 6 -

s-rgr

A design study lias been completed covering the application of gas as the

prima-ry coolant i n a molten 'salt power reactgr system.

The use of helium,

hydrogen and steam was investigated along with the effect of gas pressure level, gas inlet Lempemture level and tubing size. The basic heat exchanger geometry studied was a cross, countercurrent

flow arrangement with the molten salt (Mixture 130 62 mol % LiF, 37 mol $ B ~ F1 ~ mol , 9 UF41 making,fo-ur-se&ntine passes ac:osB the gas stream (see Fig, 2 ) . One-half inch Inconel tubing with circumferential Inconel f i n s was use6 i n a l l the f i n a l heat exchanger calculations. Consideration was given i n t h e i n i t i a l phase of the study t o other tube sizes, and the standard s i z e chosen i s f e l t t o approach the optimum, Eea-t exchanger optimization has been based on three c r i t e r i a : first, fuel. inventory i n heat exchaager tubes, return bends and headers; second, gas blower power requirements; and t h i r d , minimum heat exchanger container dimensions. Fdel inventory was evaluated a t $1355/ft 3/year and e l e c t r i c a l pover a t 9 mi~s/kwh. Results of t h e study (Figs. 1 2 and 14) have shown that, at a given heat exchanger gas i n l e t temperature with the out&et temperature fixed, the use of hydrogen results i n a smaller u n i t with a bower f u e l inventory and power requirenent than e i t h e r helium or,steam, Hovever, Yae hazards of large scale hydrogen usage must be balanced against these obvious advantages,

The optimum

helium and steam heat exchanger a r e approximately the stme i n dollars invested

i n f u e l and pmer but d i f f e r geonetrbcally i n that t h e steam u n i t i s l a r g e r i n dtamter and shorter i n length, Since a greater prexgmn i s attached t o diameter i n the construction of the reqv..ired heat exchanger contsime!nt pressure vessel, the s t e m unit i s judged s l i g h t l y i n f e r i o r t o the I?e!-ium u n t t dimensionally.

Hovever, there &re imporkant incentives f o r t h e use of steam cooling.

The

original cost of the steam inventory i s negligib2e and the contaimmxt problem becomes o f minor importance, In addi-t%on, stand&rd and. well de components can be used th%ou@out a steam system, On t h i s basi clude6 t h a t the application of steam t o t'ae gas cooling cycle would have economic adwntages over helium. Changing the coolant pressure bevel f o r a given heat exchanger configuration and. heat load affects the coolant pumping power approxLmate2,y as the inverse

- 7 -

square o the pressure r a t i o ( i r e e , doubling pressure reduces pumping power t o one-fourth)

Changing the coolant pressure level while maintaining a reasori-

ably constant blower power input affects primarily t h e required face area of' t h e heat exchanger with consequent changes i n container size.

Increasing the allowable salt side pressure drop increases the heat exchanger container diameter while reducing i t s length. Optimization of t h i s variable was not undertaken i n the present design study. Decreasing salt enrichment by a factor of f i v e results i n a reduction of yearly heat exchanger costs by factors of 2.5-4 i n the cases of primary

interest e The results of a companion study on longitudinal, countercurrent flow

of coolant over circumferentially finned straight tubing showed t h i s arrangement t o be somewhat l e s s a t t r a c t i v e than the comparable crossflow case. Although the heat exchanger container diameters were approximately the same, the required container lengths were 30 4% greater. The use of such a straight

tube geometry leads t o thermal s t r e s s problems associated with discrete tube plugging or flow variations from tube t o tube.

8 -

ger Conf igdration e r a l heat exchanger configurations i l l u s t r a t e d i n Figures 1 2 were given detailed consideration.

The first, which was ultimately cted as the l e a s t desirable of the two, was basically an annular tubing arrangement with the salt flox sttraight through and the helium -countercurrent f l o v around disc and donut baffles. The anry imposed no r e s t r i c t i o n on t h e number of helium p s s e s

e bundle since the helium could be in%roduc:e2 and cola1 esse bo%k t o o r from the ceater of the tube bmue he outside of the bmC!e, Base6 on correlations preace 1, a three-pass arrwgement was chosen as giving a satisfactory approach t o pure countercurrent heat transfer ( i e e Q 9ess e n t i a l l y no correction factor t o be applied t o the l o g mean temperature difference based on the hot and cold stream inlet and outlet temperature under consideration).

A t t h e same t i n e , 8 s w i l l be shown later, keeping

the numbe;P of passes t o a minimm restil-ts i n the most compct he8t ex-

chcmger geometry. Qne disadvantage of t h i s arrangement i s that, since straight tubes are used running fromthe salt i d e t t o the salt outlet header, plugging 05 one tube could lead t o a serious d i f f e r e n t i a l t h e m expasion

condition,

To a l e s s e r extent, flow d i s p a r i t i e s between. sepamte

tubes could cause thermal stresses t o be imposed on the tubing and f l o w fluctua-kions i n individual tubes could lead -to s t r a i n cycling of

tubing m t e r i a l , Since t h i s condition could be relieved somewhat by a simple geonetrical armgement such as a r i g h t m&e bend in %he tubing a% o r near e i t h e r the apper o r l o ~ f e rheader, it cannot be considered as a major stumbling block t o the use of t h i s geometry. The primary obstacle appeered during the course of the study.

O p t i m heat exchanger geometries

from a f u e l inventory an6 overall s i z e stand,point proved. t o have internal

M m e t e r s which resulted i n high gas velocities as shorn in Fig, 3 . The head losses associated with changes i n coolant flow direction and vel o c i t y i n t h i s geometry are hard t o evaluate precisely, but it m s estimated t h a t 2 3 velocity heads would be l o s t per pass, Since t'mese losses approach i n magnitude t h e losses associated with f l o w across the

-9-

UNCLASSIFIED ORNL-LR-DWG 3 2 5 5 6

Fig. 1. Annular Heat Exchanger Geometry.

-1 0-

UNCLASSIFIED ORNL-LR-DWG 31210

FINNED TUBE MATRIX

Fig. 2. Design Study Heat Exchanger Geometry.

-11-

Fig. 3. Annular Heat Exchanger Design Parameters.

- 12 heat transfer surfaces, they were f e l t t o be prohibitive, bundle was therefore rejected as a suitable geometry.

The annular

second heat exchanger geometry considered was a more n t having serpentine salt tubes with the gas flowing through t h e heat transfer matrix, In t h i s case, it was sary t o provide a four pass arsangement t o provide c al t h e m expansion i n the tubing while avoi diff which would be required i f only three passes ing t h e four pass arrangement allows the salt inlet

entional

* .,

ight

close together, an arrangement which stands t h the amount of piping required t o connect &he he

All f i n a l optimization studies were done on the basis of the serpent i n e salt tube arrangement. A study was also made of the required heat exchanger geometry and o-gemting costs f o r the case of countercurrent flow of helium over c i r cunferentially finned tubing.

The finned tubing geometry was not optiimized so the results may not represent the best t h a t can be done with t h i s heat

exchanger type, However, they are satisfactory as a rou remainder of the study. 2,

e-in with the

Finned Tubing Several design restrictions imposed a t the .time t h e he stu&j was undertaken made it desirable t o select a Timed tubing for consideratio@.t h a t was less than the optimum from a heat t

Inconel tubing was chosen since data on the thermal. eo a more l i k e l y material of fabrication, are currently zmg?e&

f i n s fabricated of Inconel were chosen t o avoid completely any nbterials incompatability i n view of the extended l i f e power reactor heat exchanges, The use of nickel f i n s W Q U ~ t in a more compact heat exchanger, Copper core f i sement over nickel but would introduce the require f i n s t o the tubing i n order t o protect -&hecogper a of attack by the coolant o r by impurities therein. the Introduction of the brazing requirement is cons

- 13. primarily from a materials compatability standpoint. On the basis of information received from the GPiscom-Russell Corporation'') a bond efficiency of loo$ was assigned to the mechanical bond between the Inconel fins and tubes. The use of longitudinally finned tubing with the coolant in pure countercurrent flow WBS not investigated, since literature references ( 2 9 3 )

indicate a continuous longitudinal fin to have poor heat transfer characteristics. The use of a split longitudinal fin OF pin fins mlght result in a competitive heat exchanger; however, these choices were not investigated since it was felt that simple mechanical bonding of such fins to the 'cubing could not be guaranteed to give the r of stpuktural reliability, The circumferentially finned tubing configuration chosen was experimentally evaluated by Kays and. Londd4). The tubing dimensions listed below were scaled up from the eqerimental tube as indicated, Experimental Tube Tube O.D,, in.

Design Study Tube 0.500

0.420

0 .bo

Tube I.D., in. 0 861

1.024

0.019 8 72 fins/inch

0.023

parallel to flow, in.

0.800

perpendicular to flow, in.

Fin O,D,, in, Fin thickness, in. Fin pitch

7.32 fins/inch

Tube pitch

952

1,160

975 S

at the University Experimental Tube

Tube 0, D., in. Tube I. De, in. Fin 0 , D o 9 in, Fin thickness, in. Fin pitch.

649

-_ 102% eo255 5.85 fins/inch

Design Study Tube 0 500

0.400 1.ooo 0.0197 '7.60 fins/inch

TL ,ng Size The majority of the design study was based on 1/2 inch tubing with a .C5C inch w a l l thickness.

Figure

4 presents

t h e pertinent information

leading t o the choice of t h i s tubing size. It can be demonstrated that the optimum salt inventory f o r a given

set of design conditiâ&#x20AC;&#x2122;ona occurs when the unit i s sized so t h a t %he salt pressure drop through the heat exchanger i s at the maximum allowable value. This maximum i s 36 psi, since 10% of the available 40 psi which has been customarily assigned t o the heat exchanges has been u t i l i z e d

by entrance and e f i t effects. Furthemore, based on the assumption t h a t the amount of power t o be u t i l i z e d i n coolant circulation would be between 0.5 and 10% of the plant gross e l e c t r i c a l output as extremes, it i s possible t o define the range of tube lengths and number of tubes which meet design requirements for a given tube size. On t h i s basis, the l i n e s representing the length vs number of tubes a t maxilinun salt pressure dro-g f o r 3/4 inch, l/2 inch and 3/8 inch tubing wi-bh 0,050 inch w a l l were established.

The location of t h e l i n e s re-

presenting blower power investments of 0.5% and 1% of the plant gross e l e c t r i c a l output demonstrate t h a t there i s a f a i r l y narrow range of length-number of tubes combinations which will s a t i s f y the design requirements. Three-fourths inch tubing was judged t o be undesirable because of time exeessive length requirement, although the number of tubm required, f o r the heat exchanger was very a t t r a c t i v e , Three-eighths inch tubing was judged somewhat unsatisfactory f o r the opposi$e reason,

Al-bhough

the tube length was satisfactory, the nmiber of tubes required was judged excessive.

One-half inch tubing seemed t o represent a reasonable

approach t o optimum, although 7/16 inch tubing might be presumed e q W l y satisf actory. It should be pointed out t h a t increasing the wall thickness of the

negligible effect om the calculations,

- 0,065

inch would have a The t o t a l resistance

heat exchanger tubing from 0,050 t o 0.060

wall t o heat transfer normally approximated 10% of t h e overall resistance.

0 0 0

0 0

0 0 0

..-w -m .-E tC

0 0

0" .-

[r:

w m

5z i

3 I-

.-cn LL

- 16 4, General The reactor core heat load of 574 thermal megawatts was a r b i t r a r i l y divided among four primary heat exchangers of 143.5 megawatts capacity each, Coolant blower efficiency was taken as 80%~S a l t and helium physical properties were evaluated a t t h e i r mean temperature i n the heat exchanger. The pressure drop distribution i n the coolant c i r c u i t was a r b i t r a r i l y assigned as follows: Heat Exchanger Steam Generator

6% 3%

Ducts 10% Fin efficiencies were taken from correlations presented by Gardner ( 8 ) The s a l t pressure drop was taken as 40 psi t o t a l , with lO$ assigned t o

entrance and exit effects and 9 6 assigned t o heat exchanger tube f r i c t i o n losses, Coolant blower power cost was evaluated a t 9 mills/kwh, and a load factor of 8% was assigned t o the power plant. Enriched f u e l was assigned a yearly cost of $1335/ft 3 based on t h e following factors: Barren salt

$1278/ft 3

1) Capitalized a t 14%

u-235

per year

$179

$17/gm 1) .48 Mol $ UF4 i n f u e l 2) Rental a t &$/annum

$1156 $1335

Sn calculating coolant gas pressure drop across the tube bundle, the head l o s s due t o flow acceleration caused by temperature and pressure change was neglected, Due t o the low pressure drop and coolant temperat u r e rise, the error resulting from t h i s assumption i s w e l l within the limits of error of the overall calculation, Discussion 1. Countercurrent, Cross Flow Heat Exchangers Figures 5 t o 10 present heat exchanger design study results f o r a given coolant, coolant pressure level, coolant i n l e t temperature and number of cross flow passes. Lines of constant baffle spacing, tube bank "depth" and salt volume i n the tubing are given i n each case on

-1 7-

-1 8-

-1 9I 0 L

0 rr)

.-cn In

c 0

I v) In

PI a,

-r I-

a, a,

S u)

-20-

E Q)

I-

c 0 Q)

I v)

U a

L 0 L

2 2 Q)

-21

an 0

I 3 0 L

-22-

ea I

I-

--a C

B c

L. 9)

D -c

v X

c U

a I v) v)

0 a

I 3 0 L

U L

22 L v)

a a

.I5 S

- 23 %

a basic plot of blower power investment versus the number of tubes, The active length of eaeh he&% exchanger tube is the product of the baffle spacing times the number of passes. A l l heat exchangers falling along a line of constart tube baak "depth" between the number of tubes at which the fuel Reynolds Number is 3000 (3500 tubes) and the number of tubes at which %he fuel pressure drop is 36 psi are satisfactory f o r the transfer of 143.5 megawatts from the salt to the coolant under the conditions specified. However, those Paraits represented by the intersection 0% a line of constant tube bank "depth" with the line of I'na;ximurafie1 pressare drop represent the optirmun heat exchaagers from a. Pael inventory staarndpoint.

Since tube bank "depth" is given in number of tube rows, the value &st be an integer, normally in the range of two to fifteen. Study of the figures w i l l make clear that for a given blower power investment them is one "best" heat exchanger geometry. As blower power is increased, the required number of tubes decreases until the optimum geometry f o r that tube bank "depth" is reached at the intersection wfth the m x i m salt pressure drop line. If this point is inside the horfzon%al projection of the line representing the next higher tube bank TPdepth"2 a much larger heat exchanger will also opemte at this same @QWW level, arad further power increases require heat exchaagers repsesentecl by points along the higher "depth" line, If the point previously referred to is not insiae the horizontal projection of the next higher tube bank. '*depth",there is a a g e of power vdues wbich cannot be used ho suitable heat W g e r configuration e%eists in this mnge %he vdues on the abscissa (Total Blower Power $ of Plant Gross Fdeetrical Output) represent %he proporkion of 275 megawatts which is four primary changer 0

four heat exc is tion assignable to one heat exchanger is 15$ of the abscissa value, Design study results are presented for the follossing cases:

- 24 Coolant

I n l e t Temp. OF

C ircui t Pressure,psi

Number of Passes

850

300

Eelim

850 850

150

Helium

700

300

Eyarogen

850 850

300

4 3 3 4 4

300

Helium Eelim

Stem

Pig, Hoe

6 7

8 9 10

Comtercurrent flow heat exchanger re 11 presents the results of the study on pure longitudinal urrent flow over ciscumferentially finned tubes.

The case f o r

heaim a t 300 psig with an i n l e t temperature of 8 5 0 " ~i s considered. In t h i s figure, the length represents the t o t a l active length of tbe finned tubing and the pitch represents the tube spacing i n , a "delta" armgement, @Qll@lUSiOXlS

Figure 1 2 presents optimization curves f o r t h e various coolaats a d ogemting conditions i n t h e fsm of yearly cost o f f u e l inventory

blower p w e r for one heat exchanger versus heat sxchmger ~ ~ ~ ~ k ben&h a ~ c ? d.imeter. Although an eCOnOmi@ Q l p t i m m i s found for each case presented, it must be realized tb-t the cost of heat axchanger

i a ~ e r n p

fabrication and t h e effects of heat exchaager size on overall p l a t cons%metioilcosts have not been considexed i n this presentatfm, By a53aa3 percentage increases i n yearly operating costs above the optimum

v'due shmm i n Fig, 12, sizable PedUCtfQnS i n heat axchmger length a r e realized.

Determination of how far o m should go i n t h i s d i m c t i

m i i d be one necessaq step i n an overall plant

~ C O X X I L ~analysis. ~

Far a given set sf operating conditions, hydrogen -groves t o be the mo~ata t t r a c t i v e coolm%. If it i s desired to avoid the hazards o f hyamgen usage, reauction of the helium inlet tempmture

~%5s~a

tc 700째F (mintaining the outlet tempemtme of 1025째F constant) gives a tmit smaller and cheaper t o ogemte than i s t h e case f o r hyarogen a t the higher i n l e t temperature level. Use o f a coolant inlet temperature "&fch is lower than the freezing point of the Nifiure l3Q ( 8 5 0 " ~com-

-25-

! -

-26-

UNCLASSIFIED

.._

ORNL-LR-DWG. 32585 _ _

Fig. 12. Heat Exchanger Container Dimensions us a Function of Annual Operating Cost per Heat Exchanger.

..s

- 27 -

plicate8 the c i r c u i t coiltrol system somewtmt,

I-

bo accommodate a salt

flow failure, some provision would have t o be ma.& f o r diversion of the

coolant stream around the heat exchanger t o avoid freezing t h e salt i n

the tubing. The use of steam ab? a coolant gas appears competitive with helium

since the containment problem i s minor and the gas replacement costs &re negligible, The ogtimm steam heat exchanger is shorter but somewhat larger i n diameter than i s t h e caae f o r helium.

There i s ess e n t i d l y n~ difference i n operating cost, Another strong incentive for t h e use of steam i s the existence of a well developed technology and the a v a i l a b i l i t y of commercial components suited to such a system. A l s o presented i n Figure 12 i s the container dimensions f o r a

pure countercurrent flow heat exchanger using helium with an 8 5 0 ~

fadlet, temperature in l o n g i t u d i w flow over a. "delta" array of" circumf e r e n t i d l y finned tubing. Ignoring any particular admatage t h i s arrangerneht m i g h t possess which i s outside the scope of the present study,,

this case does not appear as a t t r a c t i v e as the comparable crossflow case. The eontaine~diameter i s somewhat larger and the required container length i s longer thrsu&out the opemting cost m g e of' primary interest,. I n addition, t h i s geometry does not possess the freedom f o r differential. t h e m expasion t h a t i s inherent i n the four pass s e r p n t i n e salt tube!. It should be noted that the curves of Figares 12 and13 are not

continuous as drawn (except for the c 12). Since each point on the cum@represents a tube bank. "depth" i n tube rows (one less o r one greater t its neighbor) heat exchangers im salt inventsees only occur

. I

Increasing the allowable salt side pressure drop mwns t h a t the length sf the salt flow path @an be increased. Since % U s increases the I

available heat transfer surface per tube, the number of tubes can be reduced. Figure 14 shows that the end result 02 %his change is a heat

-28-

03 3 0 J

4 EI-

YJ 9

v) v)

a (3

2 K

2g d

-29-

Fig. 14. Effect of Varying Allowable Salt Pressure Drop and Uranium Enrichment on Annual Operating Cost per Heat Exchanger.

exchanger container larger i n diameter and shorter i n length than i s the case with a smaller salt side pressure drop,

There i s a p m c t i c a l l i m i t

t o how far the design should be carried i n t h i s direction.

When the

diametef of the contaiment vessel becomes too large f o r the eorrespnd-

ing length, a change t o a s i x salt pass geometry should be investigated, The present study was not carried t h i s far, but the basic equations

l i s t e d i n Table 6 a r e applicable f o r t h i s purpose, igure 14 a l s o i l l u s t r a t e s the effect of lowering u r a i m enrich.a factor of five. I n the area of interest, t h i s reduces annual ng charges f o r blower power and f u e l inventory t o 25 a t the higher enrichtnent

- b$ of

results of t h i s study can be used t o predict the heat exchanger requim&ents f o r increased o r decreased reactor power levels for the specific cases and opemting conditions considered, Tbe length of the heat exchanger i s a direct function of heat load and a direct r a t i o can therefore be applied t o t h i s dimension, provided t h e change is not so great 8s t o disproportionate the length-diameter relationship of the heat, exchanger containero

- 31 Method of Calculation Case 640 thermal megawatts 576 megawatts ;in reactor core 64 megawatts in blanket 275 electrical megawatts 4 primary:core circuit heat exchangers Helium coolant 300 psig,coolant pressure 8 5 0 ' ~ coolant iflet,temperature 4 serpentine salt passes 1/2 inch Inconel, 0.050 inch wall thickness Tubing "delta" array, modified 1.19 inch tube sgacing perpendicular to flow 0.952 inch r o w spacing pamllelto flow Fins Inconel, mechanically bonded, circumferentially wound 1.024 inch outside diameter 0,023 inch thick 7.32 fins/inch

- -

Operating Conditions Salt Inlet Temp. '' Outlet Temp. H

Mean Temp.

Flow

1210O F

1075"F 135O F

Temp.

1143째F 1768 lb/sec 850째F io25 OF 175"F 937째F 300 PSQ3 4,89 x 108 lBTU/hr 203.5"F

Physical Properties Salt at 1143'F heat capacity

0.57 BTU/lb"F

viscosity thermal conductivity density Prandtl Number Helium at 937째F heat capacity viscosity thermal conductivity density specific volume P m d t l Number Inconel at 1000QF thermal conductivity

22.76 lb/ft hr 3.5 BTU/hr ft"F 122.7 lb/ft3

3 706 1.248 BTU/lb째F

0.0865 lb/ft hr 0.175 lBTU/hr ftQF 0.084 lb/ft3 ll.9 ft3/lb 0.616

140.4 W / h r ft째F

Salt Pressure Drop

f = .31& S

(Re)se25 (Re)s = De s = O

AiPs

4 wS 7LDeNPS

0,0578 (L) = 36 psi (N)1*75 (De)4*75

De = 0.0333 ft

(L)

.Bo1 x 10-4 (N)l*75

Helium Pressure Drop h

= 10.41 x 106

- 0.768 f t22 f i n area/ft tube 0.109 f t tube area/ft tube 2

0,877 f t t o t a l area/ft tube

0.877 L N f t 2 A = 0,0476 L M ft A =

1 = .952 D f t . 12

2.8

1 =1 U h C

+ t f i A , +$A, kI%

s As

- 34 -

q =

1,837 x loe3

(y -)

*2'6

q = 4,89 x 1 0 '

178.5 (L) N + 2.645 x 10''

*286

(L)N = 5.032 x 10

+ 1.85

+ 7.246 x lo3 + ,5068

x 10-7 N1.28

d*28

BTU/hr

Listed below are the basic equations arrived at by the above method. These equations were used to establish the grid of Figure 5. This grid presents all heat exchanger configurations in the range of probable interest which meet the design conditions. 1) Salt Pressure Drop

at design AP of 36 psi for De = 0.0333 ft. S

(L) = 0.601 x i o-4 (N>l*75

E]""

2) Coolant Pressure Drop = 4.608 x 10'-

~! , I(

3) Heat Transfer (L)N = 5.032 x 103 ($286

+ 7.246

lo3 + ,5068

By assumption of the number of passes, baffle spacing, L, and tube bank depth, D, the heat transfer equation can be solved for a corresponding number of tubes, Substitution of these values in the coolant pressure drop equation gives a corresponding pressure drop which can be converted to blower power consumption as follows: $ of circuit pressure drop assigned to ht. ex. 60$ Volumetric flow rate through blower 6950 ft3/sec Number of heat exchanger <circuits 4

, ~

:+s8; APM

trical Output

2,85 x

1.341

e e l o ~ ~ ,

-2 10 =

- 277 megawatts

Total Blower Power Percent = Plant Gross Electrical Output

Power Investment

- 36 The salt pressure drop equation was used t o define the number of tubes a t which salt pressure drop is a maximum f o r a given baffle spacing, Lo and number of passes. The salt Reynolds Number equation (Re)s = 10.41 x 106

N defines the m a x i m number of tubes which can be used without going below a given Reynolds number, In all cases, 3000 was taken as the Ihini

this

eynolds number, FOP the 1/2" tubing under consideration s the m a x i m number usable. f o r the various cases presented i n Figures12,

13 and 14 were based on the parameter values taken from t h e i r respective grids a t the intersection of the l i n e s of constant tube bank "depth" with the l i n e of maximum s a l t pressure-drop. T h i s defines power investment, D, L, M and N f o r each case as w e l l as the f u e l volume i n the tubes. Bend f u e l volume was obtained from Figure 15 and header volume was calculated on the basis of a cone with a base diameter of 16.5 inches and a length determined by 0.1 M feet.

-37-

Fig. 15. Exchanger.

Salt Volume in Return Bends of Serpentine Fuel Tubes for a Four-Pass Heat

- 38 Nomenclature A

AT% -

f i n plus tube heat transfer area/pass, f t2 2 coolant f r e e flow area, f t 2 salt flow area, f t t o t a l heat transfer area (A R), f t2 hean tube wall area, f t 2

salt side heat transfer area, f t2

coolant specific heat, E?TU/lb째F tube bank "depth", i n tube rows arranged perpendicular t o direction of flow

salt side equivalent diameter, f t

coolant Fanning (small) f r i c t i o n f a c t o r - salt f r i c t i o n factor gravitational constant, ft/sec 2

% S

coolant mass velocity, lb/sec f t 2

l i -

coolant heat transfer coefficient, BTU/hr ft2"F salt heat transfer coefficient, BTU/hr f t2 OF

Colburn j-factor

[q(Pr) h

2 Inconel thermal conductivity, BTUihr f t ')?/in

salt thermal conductivity, BTU/hr ft2"F/ft tube bank depth/pass, f t baffle spacing (pass width), f t t o t a l tube length (L.R), f t number of tubes i n a row perpendicular t o coolant flow

(M = M/D)

- t o t a l number of tubes coolant pressure drop/pass, lb/f t 2 t o t a l coolant pressure drop salt pressure drops l b / i n 2

(me . R),

koolant Pmndtl Number

t o t a l heat load, BTU/hr - tube bank hydraulic radius, f t

4rh=4A 1 A C

(7)

lb/ft2

R number of crossflow passes (Re)c- coolant Reynolds Number (Re)s- salt R e y n o l d s Number t - tube w a l l thickness, inches mean temperature difference, O F &LM- log overall heat transfer coefficient, IJTU/hr ft2 O F u coolant specific volume, ftâ&#x20AC;&#x2122;3/~, salt velocity, ft/sec fin height, inches coolant flow rate, lb/sec salt flow rate, lb/sec fin thickness/2, inches fin efficiency (8) coolant viscosity, lb/ft sec salt viscosity, lb/ft sec salt density, lb/ft 3

- 40 Bibliography 1. Personal communication of writer with representatives of GriscomRussell Corporation during a visit to the Oak Ridge NationaJ Labopatopy. 2, McAdams, W. H., Heat Transmission, 3rd Edition, p. 269 3. Norris, R. H. and Spofford, W. A., ASME, Advance Paper, New York (December, 1941). 4, Kays, W. M. and London, A. L., Compact Heat Exchangers, The ;National Press, 1955, p. 114. 5. Knudsen, J. G. and Katz, D. L., Heat Transfer and Pressure Drop in Anmuli, Chem. Eng. Prog. 46, 490 500 (1950). 6. Op.Cit., Compact Heat Exchangers, p. 21. 7. Ibid, p. 3. 8. Gardner, K. A., Efficiency of Extended Surfaces, Trans. ASME, 67,

621.- 631-(1945). 9. Amos, J. C., MacPherson, R. E., Senn, R. L., Preliminary Report of Fused Salt Mixture 130 Heat Transfer Coefficient Test, ORNL, CF Memo 58-4-23,April 2, 1958.

- 41 -

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- 43 -

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OR1TG- 260 5 Reactors Power TID-4500 (14th ed,

-49-

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