Mathematical dynamic modeling and thermal-hydraulic analysis of HANARO

Int. Comm. HeatMass Transfer, Vol. 28, No. 5, pp. 651-660, 2001 Copyright © 2001 Elsevier Science Ltd Printed in the USA. All rights reserved 0735-1933/01/S-see front matter

Pergamon

PII: S0735-1933(01)00269-X

MATHEMATICAL DYNAMIC MODELING AND THERMAL-HYDRAULIC ANALYSIS OF HANARO

GeeY. Hart Korea Atomic Energy Research Institute 150 Dukjin-dong, Yusong-gu Taejon 305-353, KOREA

(Communicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT This paper describes the development of a dynamic model of HANARO (High-Flux Advanced Neutron Application Reactor), an open tank in pool type research reactor. The reliable dynamic model of the reactor and its cooling systems is developed to perform the thermal-hydraulic analysis for transients. The developed dynamic model is properly implemented in the transient simulation code, H-SIM, which is compiled and executed on a personal computer (PC) using the DESIRE simulation language. The H-SIM is intended for simulating ettieiently the operational characteristics and the thermal-hydraulic behavior of HANARO for many transients. The simulation for HANARO transients shows a proper thermal-hydraulic behavior trend for the power step change. Results from the H-SIM with reference calculations are found in general to be very encouraging and the dynamic model is judged to be versatile to fulfill its intended purpose. © 2001 Elsevier Science Ltd

Introduction

In recent years, a general interest in the evaluation of the research reactor performance and operational characteristics by the International Atomic Energy Agency (IAEA) has been generated. This interest is directed towards developing simulation program for PC use and is concentrated on thermalhydraulic calculations for research reactor transients. Furthermore, high capability of widely available computers makes feasible the development of simulation codes for transient analysis of research reactors. In view of the growing interest in the research reactor transient analysis, adequate mathematical dynamic models of HANARO and its cooling systems are developed to perform the thermal-hydraulic analysis for transients with reasonable accuracy. 651

652

G.Y. Han

Vol. 28, No. 5

Secondary Cooling Water '%-7

Reactor Pool Isolation Pr,mary

Common Return Line Bypass Line

._~ss

J

8 y p ~

T--[

Control Valve

Purification System P

FIG. 1 Schematic diagram of the HANARO primary coolant system

HANARO [1] is a light water cooled, heavy water reflected, and open-chimney-in-pool type research reactor of 30 MWth. The primary coolant system consists of a forced convection upward flow of the light water reactor coolant enters the inlet plenum located inside the reactor lower supporting structure, flows upward through the flow tubes in the core where either the fuel assemblies or test facilities are located and exits from the chimney via outlet suction nozzles attached on the lower part of the chimney structure. About 10% of the total reactor coolant flow returning from the heat exchangers flows into the bottom of the pool, and slowly rises in the pool outside the reactor and the chimney structure. Then it is drawn into the chimney and flows downward to the chimney bottom where both this bypass flow and the flow from the core are violently mixed and sucked to the reactor coolant system pumps via the chimney outlet nozzles. Two pumps and two heat exchangers are employed to circulate the coolant and to remove the heat in the primary coolant system as depicted in Figure 1.

The purpose of this work is to develop a reliable mathematical dynamic model and the thermalhydraulic simulation code suitable for HANAR0. The reactor and its cooling systems are nodalized to represent the components as correctly as possible and to attain the simplified dynamic models. The dynamic models consist of two-point kinetics model for reactor power calculation at both the core and

Vol. 28, No. 5

THERMAL-HYDRAULIC ANALYSIS OF HANARO

653

the reflector, fuel and coolant temperature feedback model. The lumped parameter models [2] are used for heat transfer calculations for the primary coolant system. The simulation program, H-SIM organizing the differential equations for all the processes involved, is set up for simulating the thermalhydraulic behavior of the HANARO system using the DESIRE [3] simulation language on a PC. The HSIM is extensively used for the evaluation of thermal-hydraulic performance under transient conditions. The transient simulations performed with the H-SIM are very encouraging and versatile. The dynamic models developed are adequate and efficient in providing the analytical tool needed in the transient analysis. However, the H=SIM will be continuously modified for achieving more accurate simulations.

Mathematical Dynamic Models Reactor Dynamic Model

~2utcm~Kmm~ HANARO is regarded as two-point representing the core and reflector. Thus, two-point kinetics models with 6=delayed neutron groups and 9-photoneutron groups are developed to correctly represent the effect of the photoneutron generation in a large heavy water reflector [4,5]. The normalized neutron power in the core region is described as dNc(t)_ ptot(t)-13 dt

A

No(t)+

_

C, (t)- o--~- (1- %){No (t)- N, (t)}

(I)

The delayed neutron precursor equation for the i-th group is given by

dC~(t) =X {No(t)- C, (t)}, dt c'

i = 1,2,...,6

(2)

The normalized neutron power in the reflector region is

dN,(t) dt

J T

,d, D,(t)+

~L~__ ~ A

A

0_ ,. X)qo(t)_ N, 0))_ yd N,(,)I A

j

(3)

The photoneutron precursor equation for the j-th group is expressed as

dDj(t) dt

-7"d~ {No(t)-DJ (t)}'

j = 1,2,...,9

(4)

where No is the neutron power in core region, NriS the neutron power in reflector region, Pt~ is the total reactivity, A is the neutron generation time, 13is the delayed neutron total yield fraction,

13,is the iqh

delayed neutron yield fraction, 7~, is the i-th delayed neutron decay constant, co is the fraction of steady state neutron power of core to that of reflector, Ci is the delayed neutron precursor of i-th group, ~(1 -

654

G.Y. Han

Vol. 28, No. 5

~ ) is the coupling coefficient from core to reflector, Td is the photoneutron total yield fraction, T4 is the j-th photoneutron yield fraction, Dj is the photoneutron precursor ofj-th group, t~(1 - z~) is the coupling coefficient from reflector to core, and ~,ajis the j-th photoneutron decay constant.

Xmoa.I~am~ Xenon dynamics is described by the typical point equations. The net rate of formation of iodine and xenon concentrations is represented by dI(t) _ Xt {No(t)- I(t)} dt

(5)

dX(t)_kx +k e {,/~Nc(t)+~ii(t)}_{~.x +~.~No(t)} X(t) dt yx+yl

(6)

where ).~ is the decay constant of ~3sI, Lx is the decay constant of ~3SXe, %, is the effective decay constant of ~3sXe, YIis the yield fraction of ~35I,and ~'xis the yield fraction of J3SXe.

1~aahdlg~a~ The reactivity feedback due to the coolant and fuel temperature variations and the xenon buildup are expressed as pf =otf{Tf(t)-Tfo }

(7)

Pe =c%{Tc(t)-Too }

(8)

p~ : ct x {X(t)-X 0 }

(9)

where a is the reactivity coefficient and T©, Too and Xo are the fuel, coolant temperatures and xenon level at the initial state, respectively. The total reactivity inserted in the core is the sum of the control rod and the above reactivity feedback from fuel and coolant temperature variations, and xenon load.

To simplify the heat transfer model, the spatial variation of temperature in each component is ignored by using the average value and the transport time delay between the reactor and the heat exchanger is treated by the mixing volume model [6].

The reactor thermal power of HANARO is produced both in the core and reflector. The core power, Qo, and the reflector power, Q. are be represented by

Vol. 28, No. 5

THERMAL-HYDRAULIC ANALYSIS OF HANARO

655

Qc = Nt "Qt "rlc

(10)

Qr =Nt "Qt .(l-rlc)

(II)

where Qt is totalthermal power, Nt is the thermal power including decay heat, and Ho is the fraction of power produced in core. The totalthermal power is the sum of Qo and Qr.

Core The energy balance for the fuel allowing for the energy transported by the coolant is given by MfCf ~ : ~ q f O c fit

-UfAf

(r, ~T~~

(12)

The temperature of the coolant passing through the reactor channels, To, can be obtained by M~C~ ~

= (1-'qf)O c +UfAf (Tf -Te)-2W¢Ce(T¢ -'It)

(13)

where Ivlfis the fuel mass, Cf is the specific heat of fuel, Tf is the fuel temperature, To is the mean value of inlet and outlet temperature, TIfis the fraction of fission energy absorbed in fuel, Ur is the heat transfer area in fuel, and At is the heat transfer area in fuel.

Chaam~ The core flow rate Wo and the bypass flow rate Wb are mixed in the ehirrmey and divided into primary flow rate Wp] and Wv2.The mixing temperature in the chimney, Tin,can be calculated from MmCc dTm(t)=W e Ce (2Tc -Tt)+WbCcTw -(Wp] +Wp2)CcTm dt

(14)

Reactor Pool and Intermediate Pinin~ v

For the inlet temperature in the heat exchanger primary side, the temperature increases a little due to the heat produced by the reactor coolant pump, Qp dThk / Mhk C~ - - ~ =Qp, +WpkC~[Tu~ --Thk)

(15)

where k = 1 or 2 for the corresponding coolant loop, respectively.

The transport time delay occurs in the intermediate piping from the reactor to the heat exchanger. Assuming no heat loss in the pipe transportation system, the heat transfer equations used in modeling the components of the primary coolant system such as the hot leg, cold leg, common return line, and

656

G.Y. Han

Vol. 28, No. 5

bypass line are given by Muk C~ ~dT.~

= Wpk C e

(T~ -To,)

(16)

MaC c ~dTa = Wp,C~ (2Tin - Th; )+ Wp2C~ (2T~2 - Th2)- (Wp~+ Wp2)CcTd

(17)

dTb M~,Cc --~-= WcCc (Ta -Tb)

(18)

dT~

(19)

M+Co -di- = W Co

Reflector Coolant Svstem There is a large amount of heavy water reflector surrounding the core and the heat produced in the reflector tank, Q~, contributes to increasing the secondary outlet temperature, T,o, through the reflector heat exchanger. The temperature at the reflector tank is MrcCr dTrc d'-'~--=Or-2WrCr

(Trc-Tn)

(20)

In the intermediate piping of the reflector, the inlet and outlet temperatures are MnCr -dTn ~ - =WrCr(2T _T~o_Tn )

(21)

M reCr --~dTr°-- WrCr (2 T~ -Tn -Tro)

(22)

HP,at.F.xdmam The plate type heat exchanger used in the primary coolant system is modeled into 3 parts such as primary coolant, plate metal, and secondary coolant. By the application of energy balance for each side, the following relations are obtained for the primary coolant heat exchangers dTpp, MppkCc dt =2WpkCc(Thk-TpPk)-UppkAI~k (TPpk-Tptk)

(23)

dT~,, dT~,

M~ Cc----~ = Up,kAp,k (Tptk - Tp~k)- 2Wsp Ce (T~ - Ts,)

(25)

Vol. 28, No. 5

THERMAL-HYDRAULIC ANALYSIS OF HANARO

657

By applying the same principle used for the primary coolant heat exchanger, the energy balance equations for the reflector heat exchanger are MrpC r y

= 2WrCr(T

(26)

M C t---~-= dT~ U~Arp (T~p-T~)-U.A~, (T. -T~)

(27)

M,~C~ dd-~-= U . A . (T~ - T . ) - 2W,~C~(T~ -T,i )

(28)

Secondary Coolant Svstem Since all the heat transferred from primary and reflector coolant systems through heat exchangers is assumed to be completely removed in the secondary coolant system, the secondary inlet temperature, T,i, is assumed constant regardless of the reactor power. The secondary outlet temperature, T,o, is determined by T~o = W~I T~l + W,paT~o2 + W~rT=o W,

(29)

Results and Discussion

The transient calculations in the test case are considered to simulate the HANARO performances following a step increase of the thermal power from 90% to 100% of full power with a constant coolant flow. Figures 2 through 5 show the comparisons of the transient response of HANARO induced by the power step change during a response time of 30 seconds. All plotted values indicate transient responses from the initial steady state values.

When a step change in the demand power is inserted at 90% to 100% of full power, the reactor gives out an instantaneous increase in the first core power output accompanied by a slow increase in the reflector. The core power reaches a high power level rapidly, until inherent feedback characteristics take over without any control action, and then brings the core power level down to a new steady state level. Figure 2 illustrates the transient responses of the normalized neutron power and the reactor thermal power produced in the core and reflector regions during 30 seconds of power change.

658

G.Y. Han

Vol. 28, No. 5

30.0 ~0.99

: i

o

7

.., i i

! i

i i

..c

i !

~ 0.97

25.0 20.0

:~ 0.95 :

o~ 15.0 Q_

~ :~ 0.93 t . . . .

i "

i

N(c~re, E 10.0

-- ~" - N(reflector)i . . . . . .

b-

0.- ..... 0

i ............ 5

i ....

10

15

20

i

......

5.0 0.0

. . . .

25

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

•

:II:

30

- Q(core) - - - Q(reflector)

i !.

7 :i 2 ::::ill::~::::!:lll 10 15 20

i

Time, sec

....... :

•

! 25

30

Time, sec

(a)

(b)

FIG. 2 Transient response of power level in the core and reflector regions for power step change (a) normalized neutron power; (b) reactor thermal power The change in temperature of the primary coolant causes a significant reactivity change of the reactor through the temperature coefficient at once. The temperature coefficients for the reactivity feedback effect depend on the instantaneous state of the fuel and depend primarily on the coolant. Figure 3 represents the variations of the reactivity inserted by the control rod and the total reactivity for the power step change case.

3.45E-02

30E-04 .

344E-02

2.5E-04

3.43E-02

-~. 2.0E-O4

..~ 3 42E-02

1 5E-04

:

i F

< L.)

"~ 3 41E-02

....... ! ..........

!

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

"~ 10E-04

y_

R(CAR) 3 40E-02

5 0E-05

3.3gE-02

00E+O0

5

10

15 Time, sec

(a)

20

25

30

0

5

10

15

20

Time, sec

(b)

FIG. 3 Transient response of reactivity variations for power step change (a) reactivity inserted by control rod; (b) total reactivity

25

30

Vol. 28, No. 5

THERMAL-HYDRAULIC ANALYSIS OF HANARO

659

The fuel temperature increases very fast and then begins to level off, whereas the coolant temperature begins to increase very slowly as indicated in Figure 4(a). The heat flow through the reactor fuel to the coolant rises the coolant temperature. The rising coolant temperature extracts reactivity with negative temperature coefficient. The general temperature change pattern of the fuel element is similar to the pattern of the coolant temperature. Figure 4(b) shows the temperature responses of the chimney path flow and the bypass flow for safety concern inside the pool•

95 0

450 ..............................................

85.0

o

43.0

0

75.0

o

. . . . . . . . . . i ..........................

41.0

•..............................

2

m 65.0

~39.0

........... i ...........................................

E37,0

: T(chimney) ........... i . . . . . . . . . . . . . . . . . . . . . . :: ......... T(bypass)

T(fuel)

E 55.0

p-

.......... T ( c o o l a n t ) ...........................................

45.0 35.0

;.. . . . . ',,..~ 0

?. . . . . . . .

~. . . . . . . . . . . + . . . . . . .... i ....

~

5

15

10

- ~ ....

!.................... ..4. i .... 20

35.0

~ ....

===============================

33.0

25

30

5

10

sec

Time,

15

(a)

20

25

30

sec

Time,

(b)

FIG. 4 Transient response of temperature variations for power step change (a) fuel and coolant; (b) chimney and bypass

490

40.5

39.5

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

470

L+l

(J

o . 38.5

" .............

i ..............

~ ..............................

: ...............

~..........

50 I

37.5

i E 36.5 m

...........

_ =_

T(hx,pr)

+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i i + +

T(~,se) ....... i. . . . . . . . . . . . . : ! .... ~ ....... + .....

35.5 :

:

34.5

: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : O

+ 5

10

+

15 Time,

(a)

4,.o ::

20 sec

L

r,-o

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

-,--Tso

+

......

+i .............

i

+ 25

370 30

================================= 0

5

10

15 Time,

20

25

30

sec

(b) FIG. 5 Transient response of coolant and outlet temperature variations for power step change (a) primary and secondary side in heat exchange; (b) pool, reflector, and secondary coolant system

660

G.Y. Han

Vol. 28, No. 5

Figures 5(a) and (b) indicate the transient responses of coolant temperatures of the primary and secondary sides in the heat exchanges and outlet coolant temperatures in the pool, reflector, and secondary coolant system. The increase in primary coolant temperature causes an increase in secondary temperature since more heat is transferred from the coolant. Results from the H-SIM with reference calculations are found in general to be very encouraging and are judged to be proper to achieve the intended goal of the dynamic model development.

Conclusions

Through the thermal-hydraulic analysis to the power level change, it is concluded that: 1) The transient Wends of the system safety parameters for power change are found to be consistent, 2) The H-SIM code is suitable for evaluating the thermal-hydraulic performance of HANARO, 3) The H-SIM code can be easily coupled with other component dynamic models of HANARO such as the secondary coolant system model for integrated performance analysis.

This work was performed under the Research Agreement No. ROK 9103 between the International Atomic Energy Agency (IAEA) and the Korea Atomic Energy Research Institute (KAERI).

References

1. KAERI, HANARO Safety Analysis Report (SAR), KAERFTR-710/96, Korea Atomic Energy Research Institute (1996). 2. E. E. Lewis, Nuclear Power Reactor Safety, John Wiley & Sons, New York (1977). 3. G. A. Kern, DESIRE/N96T Reference Manual, G. A. and T. M Kern Industrial Consults, Chelan, Washington (1996). 4. D. L. Hetrick, Dynamic of Nuclear Reactors, University of Chicago Press, Chicago (1971). 5. T. W. Nob, et al., Journal of the Korean Nuclear Society 19, 192 (1987). 6. M. A. Schultz, Control of Nuclear Reactors and Power Plants, McGraw-Hill Book Company, Inc., New York (1955).

Received May 10, 2001