ORNL-TM-2405.txt

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ORNL-TM-2405
Confrdct No. W-7405-eng-26

INSTRUMENTATION AND CONTROLS DIVISION

DYNAMIC ANALYSIS OF A SALT
SUPERCRITICAL WATER HEAT EXCHANGER
~ AND THROTTLE USED WITH MSBR

Francis H. Clark ~ O. W. Burke

—— LEGAL N€ v
rop an sccount of Government lponsored
 prepared 82 of g
i the Commission, por aAny w:uuon. . behs fosis o o oo ue
| grates, nol s .nywarl‘u\ty or represe muod o e s o |
S A. ‘::;eeteneu. or uaefinlnesse‘.;‘od epsienst qsgclosedm o s |
| rm;omormuon’ : - u&e £, or for damages pesulting
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: r o mumi
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contrsc ormation YT
. ¢ provides acces® o m{ fflh such contractor:
B “"“'”m::;:mmn. or his employmes . '

 JANUARY 1969

" OAK RIDGE NATIONAL LABORATORY

QOck Ridge, Tennessee
- - operated by I
“UNION CARBIDE CORPORATION
| . for the -
MIC ENERGY COMMISSION

 

 

 
 

 

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- CONTENTS

Abstract

Introduction

Steam Generator Design ér'\d Model

Parfiql .Differenfial »eq-nfions of the Sy.sfem'

Réducti’on to Ordinary Differen'fia' Equafions_and Linearization
Parameters of the Problem

A Posifive -Fe;edbcck. ProBIem

Limitations of the Model

Boundaries and Controls

- Results of Simulation

Page

12
16

18

22

23

 
 

 

 
  
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- DYNAMIC ANALYSIS OF A SALT-SUPERCRITICAL
WATER HEAT EXCHANGER AND THROTTLE USED WITH MSBR
Froncrs H. Clark O. W. Burke

 

ABSTRACT

A linearized, coarse space mesh model of a salt-supercritical water
heat exchanger and the downstream throttle was simulated on analog
computers. The effects on certain output quantities of changes in

~ certain input quantities were noted. The output quantities were heat-
exchanger water outlet temperature and pressure, salt outlet temperature,
and enthalpy output. The input quantities were heat-exchanger water
inlet temperature and pressure, salt inlet temperature, salt velocity, and
throttle setfing. Chonges were studied only around design steody state.

Sufficuent lnput-outpui' data were acquired to permit a greatly sim-
plified representation of these componentis for further system studies in
~ the neighborhood of design steady state. A tentative scheme of heat
exchanger=-throttle conirol was devised to hold water outlet temperature
within a 1°F range, and water outlet pressure wnthm a few pounds of
design while enthalpy output follows demand.

~ INTRODUCTION

To design a control system suitable for an electrical power generation system

with a Molten-Salt Breeder Reactor as a thermal source or simply to determine the

control requirements of the reactor alone in such a system, it is essential to under-

‘sfond fhe d*mmic responses ‘ro.F; I'h'e ”moior_ 'system.components. It is economicol and
' 'therefore customary to momfom a consfont inlet femperofure and pressure to i'he B

- hlgh pressure rurblne .cmd to vory mqss flow‘w:th Iood The turbme mlet .temper-
- oi'ure ond pressure ond the heot rofe are, .fi foct the uorlobles. in the power

| ) 'generohon section whlch are mosf closely controlled the temperature and pressure

-
 

 

 

to be near constant,and the heat rate to follow the load. The steam generafor*

and turbine are the components at which these vqriab.es are sensed and where the
control loops make their actiofi felt. The dynamic behavior of the steam generatof-
throttle complex is therefore crucial to determining control requirer.nents-in'.more
remote parts of the system. We have, consequently, simulated and studied these
components. The study was carried out on thé Oak Ridge National Luborfitory
analog computing equipment, consisfing of one EAl 221R and two EAIl 16-31R

computers.

STEAM GENERAfOR DESIGN AND .MODEL.
The steam generator design which was studied may be described roughly as’
follows. It is a vertical U-shaped heat exchanger, total Iéngth about 70 feet.
It is a one shell pass (salt) and one tube pass (water) unit. There are 349 parallel
water tubes. The tubes are of Hastelloy N, OD 0.50 in., thickness 0.077 in. The
shell ID is 18.25 in. The mass flow rate of water is 6;33 x 10° Ib/hr, énd of salt is
3.66 x 10° Ib/hr. The entrance and exit temperatures of the salt were, respectively,

1125°F and 850°F, and of the water, 700°F and 1000°F. The inlet and outlet

 

*Although this is a supercritical system which, strictly, does not have a liqufd,
a boiling, and a steam section, we shall nonetheless use such terminology to describe
the high density, the rapidly changing density, and the low density regions and shall

refer to the component as a steam generator.
 

ok

© of

1]

o m ok )

~ treated as an mcompressnble flu:d

~ water pressures used were 3800 Psl and 3600 psi respectively.” Further details

related to the design of this eomponent are given inref 1, p. 46 ff, case A,

The system modeled has been _v’astly simplified from the design system. 1t is |

believed, however, that the properties essential to the study of steady sllal'e control

have been presew_ed.
 The model is a single, water tubular channel surrounded by a salt annular

channel. ' The cross-sectional area of each channel is taken equal to the total

crosssectional areas of flow of water and salt, respectively, in the design system.
 Heat transfer coefficients were computed to be consistent with the steady state, local

heat fransfer and temperature profiles. The water-film heat transfer coefficient was

taken to vary as lh_e 0.6 power of the water velocity,and the corresponding salt-
film coefficient as :the 0.8 powef of the salt veloeity

Compress:blllfy effecfs in fhe ‘water were dealt wrfh explicrlly The salt was

£

 

*The reference desugn glves 3766 psi as the inlet water pressure, ancl 3600 psi as

fhe outlet._ The sfahc desngn, however, neglected |mportan’r compress:bllnty effects

and fmled to achleve a system enfhalpy balcmce-.‘ Both theSe effeots, whnch are,

- in fact, probably not separai'e ute allowed for if one mcreases the mlel' pressure to

o 3800 psi.
 

 

4
" Figure 1 is a schematic representation of the modeled system.

ORNL DWG. 68-13413
l Salt Inlet

 

 

 

| | M N
Salt Outlet 4—0-— ¥ Y
. Water Inlet ==————————— —p- Water Qutlet Throttle
e —

 

 

Fig. 1. - Model of Heat Exchanger.
Station 0 is the water inlet (salt outlet) end of the steam génerator._ Station M

is the water outlet, salt inlet end. Station N is the throttle. MN is the pipe section

connecting the steam generator to throttle.

PARTIAL DIFFERENTIAL EQUATIONS OF THE SYSTEM

The following set of partial differential equations was taken to describe the

system:
-atfi +§—R— =0 . .(1)
24 - BB - o
WCom = -0 QT e0-0 R @
pscps%%=(a_9)_a(:+)23+pscps XVBAXG ' (5)
R=pV
; s =ph (7)
: CP=Rem ®)
T=Teh - ©)
where | o | - .
p = water density (Ib/ft%),
V= water \‘/_e|oci'ty (Ft/sec),.'positive for motion from low to high X,
P = water pressure (psi), |
K = unit conversion fac.torj (slugs per Ib) x (sq in. per sq ft),
C = friction coeffiéient i.n .\’A-rqter tfibe, . |
o = temperature in Hastelloy N wall (°F),
s T = temperature in water (-°F),;‘ '
) 0 ;témfiefature in salt (;F) o -
(HA) = heat fransfer coeffucnent (BTU/sec-°F), faken as
12 for metal to woter and 23 for salt to metal,
dv = dlfferenhal volume in system |
| p";n = metal density (Ib/fl'a)
= pg = sali' denscfy (lb/fta)
‘Cprrll = specific heat at consfant pressure for mefal
Cp§ = _specl_fic heat at cgns_fgnt_ pressure for salt,
*)j ' W = salt velocity (ff/ sec), po;.i_fivé’ for m_dfiofi from high to_lquX.

Equations (T), (2), and (3) aré the co'nServatic;:nr equations in water for

u | mass, momentum, and energy, respectively. Equations (4) and (5) are energy

T S\ AR T Rt T ke e b e+ oA .
 

conservation equations in the metal and the salt; (6) and (7) are definitions of
R and S; (8) and (9) are two different aspects of the equation of state.

~ At the throttle, which terminates the system at the downstream end, we

write! A
LG3S |
~ R= TFeT’ ! (10)
where
AT | | |
== throttle flow area as fraction of steady state,

T/ = number of de._grees. above some reference temperature (reference
about 750°F),

m, b = empirical coefficients.
Equation (10) is, of course, a boundary condition.

Representation of the friction term in (2) as CV? is a simplification. The
~ kinetic energy and the potential energy, both of which are small compared with
fhe. enthalpy, have been omitted from the X derivative operand in Eq. (5). | In
Eq. (5) the kinetic and potential energy terms are again omitted from the space
aerivative. The space derivative of the kinetic energy term in (5) is zero by
reasor;t of the assumption that the salt is incomp;'essible. Neglect of the potential
energy terms is equivalent to an assumption that the system is horizontal. Both

terms are small in any event.
al

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]

no

- “where -

All variables are known at all valves of X at t =0, - Further, at all values
of +,P(0), T(0), 6(M) are arb.ifi;ary funcfio.ns of time (0 repréfients water inlet

location and M represents w:::!"er'outlet or salt inlet as in Fig. 1).

* REDUCTION TO ORDINARY DIFF.ERENTIAL B
EQUATIONS AND LINEARIZATION .
The analog_. computer cén _de'_(_:’l COnfinquusly with only one inde'peride'nf variable.
Hence, fb.sc'alve parfial diffe_lic.a.r.l'rial_ e;quations,'we .must cppl'ya ‘mlesh or aifferencing
scheme tb all but one of the indepefident variables-- in our case,. to the Xvariable. |

After differenbing, the equations are

 

 

 

 

 

o= RatR) ' (le)
n-1,n - | : |
R |
n-1 _ 1 = 7 = = _
ot - 1 n=-1 n-1 Rn n *K (P P )} Cn n-1 (2_0)
3% LA |
“n _ ] T O T T Y. k,12 —_— -
ot {.-Sn_-;l vrj-]" V_Sn_VnJ *- v _(— Tk) (3a)
n-1 S T 'k
g R, (HA)k g
o m—;c:_‘_Tk“';“k) + ol kc (gk ) @
@, (AR e
n-1_ k, 23 u S
= (k k)+__._(§ . n_,I) L (5a)
~ snps . en o o |

Msn = salf mass bétwéen n :drid n=1,
 

 

8

' Mn-1k = total mass between k and k~1,

R=2n ¥, e
Sk - 7
) e
TeTG,R) N 6o
G,
"N = 1+bT'

k=n ifn odd and n-1if n is even.

Each time-dependent variable has the symbol " —" above it.

T oof +f a)

where

Tn(t) = the variable at time t

. fn = the variable at time t=0
r ) .

fn(t) = increment in the variable since t =0

We shall neglect all terms involving products of increments. Our set of linearized

equations thus becomes
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1 )

 

 

 

3p L
n _ 1 .
2t L , (Rn-l - Rn)
n=1,n '
3R |
n-1 1
ot el n {Rn-l,ovn-l fvn-l,ORn-].-,'Rn,O'vn -Vn,ORn
KO ]-P )} -2C V. 1,0 Vet
BSn 1 | , -
¥ T {Sn-l,(}vn-l *Va-1,0°n-1 " %n,0" .‘Vn,osn}
12,0 @ );(“k,o “Tko M
v % - k v oV k
k | k
o (HA)k 120 1 gy (HA)k 23,0 (o _.)
3t M, C Yt C k™%
mk “pm | mk ~“pm -

 

 

g79,0 M, 1

V, +

M'kC Y k M C

L (HA)k 23,0

 

sk

“'mk pm--wa_w

 

skr

(°'k 0-5%,0 e('"'A)k 23

- = —— ( ,?9 )
| i.-at | Mskcps Qi(k Mkc aW L
0 (o -+ —nu0 "ol 0
* 6" e_ )+ —W W

W

w

(1b)

(2b)

(3b)

(4b)

(5b)
 

 

10

- (6b)

n,Opn-

anpn,()vn-l-V

S _pn,Ohn 'hh,Opn

p_( (@ W e

!

e > W e

F

(7b)

T/A

"N NO{PNO (T/A>

-bTN}_ ) o (10b)

Additionally, we compute a fractional changé in the flow of enthalpy from a

‘region bounded by nodes r and s as

SV -S V . -SV +S V

 

AHN _ s's 5050 rr "r07r0
() = sy | (12)

r,s 5,0'5,0 °r,0°r,0

Linearized, this equation becomes 7
N 55,0% 7 Vs0% %0V Vi 0%
H /r,s S OVs,O - Sr,O Vr,O_

 

(12b)

Figure 2 is an analog computer diagram of the system described by Egs.
"(1b) through (10b) and (12b). The subscripts r and s in (12b) are, respectively, 3
and 7 in Fig. 2. The subscrip't‘ n runs through the values
| | o h=3,4‘."..'N

N = 8 (throttle).
 

11
ORNL DWG. 13414
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12

' There are a few optional connections in Fig. 2 beyond those indicated by the
above équafions. These optional connections are feedback control loops which
were developed in the study and which will be dealt with in the section entitled

Boundaries and Conirols, p. 22.

PARAMETERS OF THE PROBLEM
Initially, the system was cut into eight spatial nodes whose location in ‘thé
laboratory reference frame was held fixed. With so few nodes it would have been |
better to permit at least some of them, those associated‘with the "boiling" region,
to float. The problem was already of such complexity, however, that we could

not possibly meet the equipment demands of such an approach,and the nodes were

| assigned fixed coordinates.

Steady state design values of the system variables are given in Table 1.
Table 2 giv.es the derived paramefers and constants at various nodes. Table 3 gives
the sets of parameters used to represent the equation of state of water. Other
parameters used in the study include

Crosssectional area of water flow = 0,2277 f#

Cross-sectional area of salt flow = 1,34 f#

b = 0.00065 (°F~")°

1+ bT0 2 |

a
m ET')o Po
—T—_I_—EFO——- = 772,22
W0 = 6.1 ft/sec.

 
-

. Table 1. Steady State Design Value of Variables

 

- - | o o . Heat
‘Water ~ Water  Water Water Water Salt Mean Metal Transfer

Node - Pressure  Temperature  Density Enthalpy  Velocity  Temperature  Temperature per Node
~ (psi) | (°F) (Ib/f) ~ (Btu/1b) (ft/sec) (°F) (°F) (Btu/sed

1380 - 700 34,13 769.2  22.63 80 s -
2  -§797"'f 768,9.' o R.6 ;7§7.7 24.01 g2 782 . 5012.5
3w 778 mss @2 M w4 W1 sns
4  ;_3771 _'5'::7377_ 1600 988.35  48.26 9425 826 285175

5 :.__374of ) ,773;7 o4 1150.5 80.95 1011 883 28517.5 |
6 W.'3688.j ~887;9 fu?.ss : 1285.75 105.35 1068 .5_' 974 . 23786.4
7 _“'3&00-"-'1600 | 5.03 1421 153.52_ ' 1125 . | 'hjogzgsl‘  23786.4

8 325 997 . 491 1416, . 160.48 . — -

 

€l
 

Table 2. Nodal Constants and Derived Pdrameters

 

 

 

Nodal Heat Transfer Coefficient Metal Salt

| Nocrle Friction Metal to Salt to Specific E Density =~ Specific Density
Node Length- Coefficient Water Metal Heat = - Heat o
() (Ib/ft4) Btu/°F-sec)  (Btu/°F-sec) (Btu/°F-Ib) (Ib/f¥) ~ (Btu/°F-Ib} (Ib/f)
2 2.9  8.64 34,29 31,33 0.112 548 0.3 124
3 290 7.3 34,29 31.33 |
4 145  9.05  160.2 122.4 0.113 548 0.36 124
5 450 3.5 160.2  122.4 |
6 1450  2.36 138. 1 126.5 0.115 548 0.36 124
7 1450 231 1381 126.5

g 150 '0.049

7

 

 
[ U " - " "o . - At c

" Table 3. Parameters Representing Equation of State by Nodes | - )

e () (8), (@ D

h

 

@ @ @, c"*\

3 el T | 0.0046 - -0.218  -0.032  2.63
4 13® 23 03 s.624 —
5 831 5263 125 .41

6 8.3 5.3 125 29.41

61

7 8.3 5263 . 125 29.41

8. 8333 523 125  29.4]

 
 

 

 

16

A POSITIVE FEEDBACK PROBLEM

Consider the equation |

___dfg:r D _ o) | (13)

If £(X, 1) represents a quantity having a net motion in the space coordinate frame,

 

 

 

then |
dX
diX,t) _ afX, 1) . f  af(X,1) (130)
dt : ot dt ;X 7
where
Xf = X coordinate of f. Then, writing
de '
V=, (14)
we have
(XY, afiXt) _ |
ot +V aX - g(f). . (]3b)
For the purposes of a numerical integration in X,we shall define
o |
h =ah ,+bh , | | (15)

and
hn-l =h (Xn-l) '
no h (xn)

:= mean value of h on the interval (Xn_l, Xn) .
"

"

W

17 -

We will assume both a positive and b non-negative (as they are in any reason-

able rule that occurs to us). Further, for definiteness, let us assume that

Xn > Xn_l,and that V>0; that is, that motion is from low to high values of X.

Let us also assume that the boundary condition on f is applied at high values of X,
so that, in @ marching numerical integration, the value at Xn will be known and the .

value at Xn-l will be solved for..- Let us now integrate Eq. (135) over X to yield

     

 

of a0 . | o

(x =X _ T 1 9, =V M -f (1) Qe

, Bfn_] :. : N | Ty

(Xn»- Xn-l) T =V-Fn---l(t) +-{(xn -Xn-_-l)g n(t)-_ | (16a)
VR =X 'Xn_-l_)b ot +

We have, for siniplicity,' assumed that Vis not a funétion of X. Note that
the terms in the brackets in (16a) are all known at the time one is solving for fn-l .
Hence, the équatibn is of the form
dg?) 7 ?\F(t)"'G(t) o o o | (17)

a0 (e)

. Condition (18) is the'condi_fi-qh. of positive feedback, which implies_instability |
- of F unless G s&a‘fisfies some r.igoropscbndifiqn. For example, if j 
AF(t) + G(f) < T o (19a)

o:>0' '
 

 

18
ast - =, M a constant, then F(t) approaches a limit. Or if

AF(t) + G(t)

=0 <0 . (19b)

for F() #0as t »; fhén F(t) is bounded and approaching zero or is constant.

If either (19a) or (19b) is satisfied, it implie‘s, of course, that G(t) contains
implicitly some.negafive feedback that compensates for the explicit positive feed-
back AF(Y) in (17) and (18).

Note that the positive feedback in (17) and (18) was due entirely to two
circumstances:

1. That a in (15) was taken positive.

2. That the direction of integration was upsfream.;. that is, tht the
boundary condition was applied at the high-value end of X,while the velocity V
was positive.

It is clear that when these two conditions for positive feedback are met,an.d if
' there is an overall implicit negative feedback contained in G by reason of fhé
satisfaction of (19a) or (19b), one must be careful in what one does with G not to
desfroy the sometimes delicate balance. This problem and these considerations

will be found to be \}ery relevant to the problem at hand.

LIMITATIONS OF THE MODEL
In checking out fhe problem on the analog computer. it was foufid that there
were instabilities generated in the first two nodes. We have not made a complete
analysis of these instabilities, but we did arrive at a partial understundihg of them,

at least.
i

.

19

'First, we note that the explicit poSifive feedback of (17) and (18) is present.

- [Boundary condition (10b) is epplied at high X,and V is positive; hence, both

conditions for this kind of feedback are met. ] There is a negative feedback due

to friction which, in all nodes except one and two, overcomes the positive feed-

back. Other terms which contribute to the implicit negative feedback are less .

tightly coupled to the flow integrato;sf" It is believed that the spatial nodes form

such a coarse mesh that this implicit feedback does not arrive with the gain and

phase necessary to insure sfabil'irf)} o

The f:rst two nodes, as can be seen in Tables 1 and 2, comprise about 10‘% of

the length and heat tronsfer capcblhty of the system. They further are confined

to fhe 'water" section, that is; the'region where 'the ‘water density is high _and is

changmg reasonably slowly. The 'bo:lmg region: Iaes beyond them.

~ In order to nd the sysfem of the msfabllll'y, the first two nodes were arbl‘l'rarlly

| excluded and the water enh_'ence_ boundary was placed at node three. Such-drastic

action was taken only with great reluctance. In extenuation it is argued

- o,

2.

thaf only ab'oUt IO% of :fhe System is excluded-'

-thaf from the v:ewpomt of dynemlcs the wclter reg:on, whlch was

- | _:excluded has fhe leasf changeeble charactenshc on account of |fs near

-mcompresublhty P
- *fhat the mstablhfy excluded was almost surely mtroduced by the numerical
- scheme employed qqdr-yeqld n'ot _therefore be o :physma'l 7|nstab|l|ty;

" that correction of the'?ins'}abi‘l'ity would probably require numerical methods

which imply far more computing equipment than the amount available.
| . )
 

 

20

-In any event, the first important limiiufion of the model is the truncation
of the water section. |

As indicated in earlier secfiofis, the actual system is a bundle of 349 parallel
water tubes. The system as modeled is a single .water tube. Parallél channel systems,
by reason of interactions and -oscillations possible between channels, are almost
always subject to certain kinds of instabilities which simply do not exist in a one-
?:hannel system. The restriction to one channel was dictated by the limited amount
of computing machinery available. The second important limitation is, therefore,
the single water channel. |

Reference to Table 1 will show that from node 3 to node 7 the water density
changed by a factor of about 6. Clearly, that indicates too broad a range of
physical variation to be treated at all adequcfely.with only five nodes. Agdin |
equipment limitations dictated the restriction.. A faithful spatial representation
would have demanded many additional nodes. The third important limitation is
the coarseness of the spatial mesh. |

.We have already described the procedures by which the problem was linearized
and higher order terms neglected. In view of the lineariz&fioq one should place
no faith in the validity of the description of any system disturbance whi_ch lta:ads to
a change of more than 10% in any system variable. Small changes about design
point are sufficient to permit studies related to désign of a steady state .c:ontrol
system. In this the linearized model is sufficient. It is insufficient, however, to

study an automatic control system as it makes large changes in load derhand, for

»
[}l

»

o -

21

‘example. . Essentially all instabilities which will be of interest in a real system

are non-linear. So are olrl accident events. The linearized model fs of little help
in the study of such n'on:-li-rieqr'_ evenfs..

I.t would have been poss.ible'wii'h' available equipmefif to have simulated some
of the non-linear aspects of fhe's‘ystém. This was not done for the following
reasonss |

1. It was believed, and subsequent experience showed it to be so, that the
problem would place véry_ s-e_vjé:r.e.démar.zds upon mdchifié performance. Linear com~
ponents are génerally less fréuslesbme' in operation than non-l#néa’r. 'Hence, lineari-
zé-fion ificreases the sficc'ess pr§babi|ity of the problem. |

2, ‘The very coarse spoce mesh demcnded that dync:mlc chfinges be restricted

to fcurly small changes from steady state. For any large amphtude spahal effecfs

would be badly dlstorted on fhe coarse space mesh This ampllfude llmltcmon, in

', eFfect conflnes the problem to the regnon of lmearlty in time.

3. Not all non-linear effects could be handled with the __equiprhent available.
- The fourth major limifation of the model is, therefore, the neglect of non-
line’ar effects.

lt is ewdent in each of these :mportanf resmchons on the model thaf fhe

. hmlted amount of compuhng equrpment avullcble causes. the resmchon on the model.,
:Thls ought not to be surpr:smg The dynamlc behavuor ofa once-fhrough bonler is

'known to be tremendously comphcafed

Such sysfems have been successfully studled on hybr:d compufers, buf not on

machines of lesser capcblllty, digital or analog. Hence, to al'fempt the study
 

 

22

on an analog machine, or on anything less than a hybrid, was to insure that
something less then a full study be made.

As has been previously indicafed this abbreviated mode! should answer some
important questions about control in the neighborhood of design steady state.
It should not be adequate to handle questions of control following large load

changes, of non-linear stability, or of accidents.

BOUNDARIES AND CONTROLS
We have already indicai‘ed that l'h»e specification of the water pr'es;ure‘and
temperdfure at boundary 0, in Fig. ],v and the salt ‘i'emperali'ure at Boundory M
are left available to the user as boundary conditions. We have notéd fHat R, P, and

T are connected by Equation (10b) at the eighth node, and this relation serves as

 

a boundary condition on vR. In this relation( AT ), the %hroflle setfipg, can
be varied as an additional control at the di#posal of the user. The final available
control is "W", the change in the salt velocity. |

All of the above controls canat the user's option, be set to a vulué selected
by the user. (With a linearized modzl, of course, change of any system variqble by
more than 10% from design steady state would probably be unjustified.) Provision
has also been made to operate some of these controls, at fhey user's option, with a
feedback error signal. After some experimenfation with thé system it was déterrriined

that the following feedback signals should be optionally incorporated for investigation.
23

Feedback Signal

 

Variable Changed )

 

 

 

 

 

- | ) - | Heat Output " Thrbfile Setting
; Ovutlet Water Temperature ' Salt Velocity
Salt Ye'lodfy “Inlet Saltv'l;'emperature
Outlet Water Pi'gss't.:u_"e' - ~ Inlet Water Pressure
Table 4 fderfiifies the 'c.fillpli:fiér symbol in Fi‘gl.“2‘cor.rés;t>.onding to each o-f- the
’a:bove vfirfablés. | | ER - N
Table 4. -Vq.r___i:ql;_lzej '-C"odihg-cjm Cir:cuit _Diagram_ -
~—Variable ~AmpTifier Code No.
'Heat Outppt' 48,
Ou—flét Water Temperature 18,
; Salt Velocity ' -005
: Outlet Water Pressure | 40,
Tl;rottle -Se'tting‘" 19,
Inlet Salt Temperature 20
.‘.lfiléthfer-Pressure - | 513
Inlet _Watér-Témperat_uref_ : - 063 ce
o . Wa_tel; Mass Flow Rate ” B/ 7'
© RESULTS OF SIMULATION
O . | | Five vdriables'ha;le -b'eeri res_efiréd to beE driven byfeedback signals if de%iféa.

- They are inlet water temperature Ty | (063), inlet water pressure P3 (513), inlet
 

 

 

24

salt temper&ture 87 (204), salt velocity W (005), and fracfionql-thro.ttle setting
AT/A (192), It can be seen in Fig. 2 that each of the abové variables _is‘cm
integrator output. Each of these integrators is provided with first-order Igg circuitry.
All of them excepf (063), the inlet water temperature,are provided with an o‘pfion to
switch them out of the first-order-lag urbitrary‘ input circuitry into an er-ror-signal-.
feedbackcircuifry. These feedbacks will be dealt with shortlyf Not shown in
Fig. 2 but available with minor patching_chunges is the ccnpcbflity of chfifiging each
of these variables by an arbritrary amount in step fashion. -

fhe variables which we wish to oBserve mosf carefully witH a view to their con-
trol ére outlet water temperature Ty (18,), outlet water pressure .F"y' (40;), heat
output -AH/H (48), salt velocity W (003), and water mass flow rate (75).

A séf of eight diagnostic runs was performed. Each run started from design
steady state, and in each run a single variable was changed in a first-order qu or
a step. Table 5 summarizes what was done in each of these runs. Figures 3 through
10 are time fraces of fhesé runs showing the effects on important variables. From
these results rough gain-lag information can be estimated by examining steady states
before and after excitation. This information is summarized in Table 6. Use of
such information will permit a much abbrevicted- description of- the steam genéquor
for incorporation in a system analysis.

Attension is next fixed on feedback control schemes. No attempt was made to find
anything like optimum control. There would be no point to such an attempt at this

stage of design. Accordingly, only simple integrating feedbacks were used.
25

- Table 5. Summary of Diagnostic Runs

 

 

Run No. Variable Changed ' Naturer,of Change Fig. No.
27 Throttle Increased Setting 5% on 1 sec 3
) (AT /A) flrsi"-order:lag
28 Inlet Water Increased 5 psi 4
Pressure, Py on I-sec first-order lag
29 Inlet Water Increased 5 psi in step | 5
Pressure, Pj3 | . ;
30 Inlet Water : . '.In'c,:reased 5°F on l-sec first- 6
Temperature, T3 order lag |
31 Inlet Water | | _Decre_céed 5°F in'ste_p : 7
. Temperature, T3 | | |
32 Inlet Salt " Increased 5°F in step B
Temperature, 67 |
33 Inlet Salt Increased 5°F on 1-sec first-  9
| Temperature, 67 order lag
34 " Salt Velocity, ‘W Increased 109 (0.61 ft/sec) 10

on l-sec first-order lag

 
 

Table 6, Gains and Lags from Diagnostic Runs

 

Water Outlet Salt Outlet Change in Heat Water Outlet . Water Outlet

Inlet Run  Temperature, T;  Temperature, 63 Rate, AH/H Pressure, Py Mass Flow Rate, Ry

 

Quantity Gain Lag (sec) Gain Llag(sec) Gain Lag(sec) Gain Lag (sec) ‘Gain  Lag (sec)

Inlet - 29 0.1°F/psi <0.1 -0.6°F/psi 8  +0.26 %/psi <0.1 1psi/psi <0.1 0.04 %/psi I<O.l
Water | ' | | I
Pressure, P3

o

Throttle 27 3.4°F/4 4  -1.2°F/4% 1 0.524/% “lApsi/g 10 104/ <0.1

AT/A

Inlet 30 1.6°F/°F 4 _'0.92°F/°F 10.5 -0.244/°F 2 -1.4 psi/°F 6 -0.16%/6F' 1]
Water : .

Temperature,
T3 |
inlet 33 1.2°F/°F 6  0.6°F/°F 12 0.084/°F 8 -0.4psi/°F 12 -0.24/°F 2
Salt . . | |
Temperature,
67
Salt 34 1.4°F/4 6  0.75°F/% 12 0.1%/4% 8 -0.7psi/% 10 -0.124/% 1.5

Velocity, W

9C

 

 
 

| Fig. 3.
Throttle.

 

PAEATE M WA A

 

27

~ First-Order Change in | |

CONTROLS CORPORATION  SUFFALOL NTW YORK

&

 

| "Fig. 4. Firsf-O'rder Iricrease in
“Inlet Water Pressure. |
 

 

 

Fig. 5. Step Increase in Inlet
Water Pressure. :

28

 

Fig. 6. First-Order Increase in
Inlet Water Temperature. |

Ty
 

BUEFALD, NEW YORK

 

o an 7. Step Decr‘easéji_'_n __l_nl__e_t o

Water Temperature.

29

 

- Fig. 8. - Sl'ép Increase in Inlet
~Salt Temperature. . _
 

 

30

 

 

———re mMwea ERICORBIND CHARTE] nnAMC CONT

 

Fig. 9. First=Order Increase in | Fig. 10. First-Order Increase in
Inlet Salt Temperature. Salt Velocity. .
31

| Tho question to which an o:nswer was sought was whether a scheme .of control

could be found whlch would | |

1.  be generally cons:stenf w:i'h the expected dynomlc response of fhe reactor-
heat exchanger; | - |
| 2 : provide a heat fafo whfo_h o_losely_followe'd load demand;

3. hold water ouflet témpéfdtur_e within a 1°F band of vorioi'ion;

4.  hold water ou’rlref pressose_,Within .o small (bus unspocified) band of
vario‘tion. | |

| To regulote outlet -.wotef pressure;a feedbaok connection from outlet water pressure

to inlet water prossofo was_consfiootod as .shown fn Fig. 11. Run 35 was made |
with I'ho connécfions:and lgoins as shown in Fig. 11. The system was excited by a
109 _incroaso in salt vélo'c'i_ty'on.o__'l--soc.first-order lag. Fi.g.ur'e 12 shows the
f résults' of this >run.r With -othef vo'riaoles ignored the outlet préssuro is very satis-
foctonly held wnthm a range of 2 lb of steody state, and fhese small fluctuations
damped oui' within 12 sec.

Flgure 13 shows the o:rcu:try for sendmo a feedback slgnal .from the heat sote

omphf’ er (482) to the throh‘le m!'egrotor (192) Also shown on thof f' gure is fhe
r’ri.jclrcmh'y for mserhng heot demond by woy of mtegrofor(52) | | |
- Runs 36 37A 37B and 37C were oonducted to fi nd an oppropraofe feedbock
from heot roi'e to throftle in order fo hold the heat rate sfobly ona selected volue.

'_"f—‘[The volue selected is determmed by the outpuf of (52) T"HS OUfPU" was held at
 

 

32

ORNL DWG. 68-13415

LC. OT. 1. 0000

10

Fig. 11. Pressure Feedback
Circuitry. |

Fig. 12_.. Salt Velocity
Change with Pressure Feed-
back (Run 35).

ORNL DWG. 68-13416

 

+100V ~100V

Fig. 13. Circuitry for Heat Rate,
Heat Demand, and Throttle Feedback.
33

zero with FS3 open dunng these runs. 7 In these runs the gain in the feedback

~ lags was s voried as follows.

 

 

Run No. lSetting-Pot 35 | | 'Gain Pot 35, to (19;)
36 0.05 o 10 |
A 0.2 1
¥ 0.05 o
37C 0 S

In each of these runs the systetn was excited \-Nhen in steady state by increasing salt
velocity by 10% on a 1-sec first-order lag. Figures '14, 15, 16, and 17 ore
the time tracer of Runs 36, 37A; 378B, ond 37C .respectiv.ely. Figure -14 shows a
c.ossicol divergentoscillotion cousecl by too much gain. Figur-es 15, 16, 17-.ore_
all fCIiI'IV)‘( comparable showing te_osonohle stoh'iltty over a broad range of gain. The
pressure controller (Fig.' ) Es,sti'l.l in the systefn, but there is a more lively variation
.in outlet pressure with the throttle control also present. Conf:gurotlon 37C (Fig. 16)
was chosen asa sohsfoctory comprom:se between heat rate and pressure control

With pressure ond heot—rate controls m,ottentlon was turned to water outlet
- temperoture. Flgure 18 showe a feedbock pcth connectmg water outlet temperoture
T; (18) tosalt inlet temperature 87 (203) Runs 38A ond 388 were conducted

) wnth the followmg vclues set on the components in Flg. 18*

Rin P2 i CPI3 K GainP29 o (20)
A 01 0009 0 1

38 01 009 1 1
 

 

 

CONTROLE CONPORATION BUEFALD, NLW YORK

AT

 

Fig. 14. Salt Velocity Change : Fig. 15. Salt Velocity Change
with Pressure and Throttle Feedback with Pressire and Throttle Feedback
(Run 36). ~ (Run 37A).
Fey

(Run 37B).

 

Fig. 16. " Salt Velocity Chérige__

with Pressure and Throfl'le Feedback

35

 

. peeiew e waA ERECORITNG.

 

|  Fig. 17, Salt Velocity Chqnge
 with Pressure and Throfl'le Feedchk
~ (Run 37C) | '

 
 

 

 

36

ORNL DWG. 68-13417

 

Fig. 18. Circuitry for Feedback from Water Outlet Temperature to Salt
Inlet Temperature. |

The system was excited from design steady state in each of ffiese runs with |
5% increase in heat demand (see Fig. 13) ins;arted at a ramp rate of 5%/min.

Figures 19 and 20 are the time traces of Runs 38A and 38B respecfivély.-
Figure 19 shows an 8°F vafiation in water outlet temperature, comple'tlellg.( |
 unacceptable. Figure 20 shows a variation a shade over 1°F. This would .be very
nearly acceptable. However, the feedback circuitry does not reflect the very con-
sideréble time delay to the salt inlet temperature 6; that would be calusved by the
'pre;se-nce of the reactor and the p;'imry héat exchanger. (The pressufe and fhroffle |
controls were present in these runs.) |

Run 39A was like 38B except thdt the inlet salt temperature 07 was inserted
through a 10-sec first-order lag. Figufe 21, which is the time frace; is t';scillctory
and diverging. Run 39B is like 39A but with feedback gain reduced to 1/10 its
~value in 39A, Further, the ex&ifafio_n was limited to a 3% heat demand increase.
Figure 22 shows the sysfem now convergent but with an unacceptdble_ oscillofi.;an.

" In order to avoid the oscillation introduced by the tfme lag on 87, it was

determined to control the water outlet terfiperdture by Qorying s<;.1|f velocii'y. This

makes possible a much quiéker response. The salt velocity could then be returned to

. ;o
"y

T

37

 

F|g 19.  Heat Demand Change wuth Wafer Outlel' Temperature to Sult
Inlet Temperoture Feedback (Run.38A).
 

 

. GRIEDNRETHARTE anarm

 

Fig. 20. Heat Demand Change | Fig. 21. Heat Demand Change

with Water Outlet Temperature to Salt with Water Outlet Temperature to Salt

Inlet Temperature Feedback (Run 38B). ~ Inlet Temperature Lagged Feedback
. ' ~ (Run 39A). |
Wy

39

its normal value by the slower fespohding salt inlet femperature.‘ Figure 23 shows
the feedback circuitry uSed In Run 40 thls circuitry, along with the pressure and

throttle controls of F:gs. H and 13 was employed. Flgure 24 is a trace of the run.

 REFERENCES

1. ORNL General Engmeermg and Ccnstruchon Division, Design Study of a

 

Heat Exchange Sys'rem for One MSBR Concept, ORNL-TM-1545 (Sept. 1967)

2. J. Kenneth Sc:hsbury, Steom Turbines and their Cycles, Wlley, New York
- 1950.

3. Steam, lis Generchon and Use, 37th ed., Babcock and Wnlcox Co., New
York, 1955. |

 
 

 

~ ORNL DWG. 68-13418

 

| "Fig.- 23. Two-Stage Water
Outlet Temperature Control Circuitry.

 

 

 

Fig. 22. Heat Demand Change Jpg A rLe JHb

with Water Outlet Temperature to Salt Fig. 24. Heat Demand Change
Inlet Temperature Lagged Feedback with Two-Stage Water Outlet Temper=

(Run 39B). | ature and Control.
wh

— it

13-17.
18.
19-33.

34.
- 35.

37.
38.

40.
41,
42,
43,

45,

47,

48,

L 4.

100.

101,

4]

ORNL-TM-2405

. INTERNAL DISTRIBUTION . -

J. L. Anderson

50.

R. E. MacPherson _

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P. H. Haubenreich - 75. Gale Young -
R. E. Helms 76-77. Central Research Library
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P. R. Kasten =~ - 79-81. - Laboratory Records Department
M. T. Kelley ~ 82, Llaboratory Records, ORNL R, C
T. W. Kerlin =~~~ .~ 83,  ORNL Patent Office
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e i e i
 

 

42

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