department of physics, faculty of engineering, sari branch ... · study of thermohydraulic...

Study of Thermohydraulic Parameters of the Bushehr’s VVER-1000 Reactor during the

Initial Startup and the First Cycle Using the Coupling of

WIMSD5-B, CITATION-LDI2 and WERL Codes

Yashar Rahmani

Department of Physics, Faculty of Engineering, Sari Branch,

Islamic Azad University, Sari, Iran

Abstract

In this paper, by designing a thermo-neutronic code, the three-dimensional changes of the

thermohydraulic parameters of the Bushehr’s VVER-1000 reactor as well as the temperature

distribution of the fuel elements and coolant in each assembly were studied during the initial startup

and the first cycle. In order to perform the time-dependent cell calculations and obtain the

concentration of fuel elements, the WIMSD5-B code was used. Besides, by utilizing the

CITATION-LDI2 code, the effective multiplication factor and the thermal power distribution of the

reactor were calculated. For considering the real geometry of VVER-1000 fuel rods and also the

effects of the gaseous fission products in calculating of the temperature distribution in the reactor

core, a thermo-hydraulic software (WERL code) was designed using the Enveloped Pin method.

The Dittus-Boelter, Ross-Stoute and Lee-Kesler models were used in the calculations of the heat

transfer coefficient of coolant, gap conductance coefficient and gap pressure, respectively. In

addition, to estimate the concentration of the released gaseous fission products into the gap space,

the Weisman model was used. After calculating the temperature of fuel, clad and coolant in each

axial sub volume of the fuel assemblies (in each time step), the temperature of these elements was

inserted into the input files of the WIMSD5-B code (in each assembly). Thus a sequence of

neutronic and thermohydraulic calculations was formed based on the coupling of WIMSD5-B,

CITATION-LDI2 and WERL codes.

Study of the results demonstrated that the BUSEHR VVER-1000 reactor enjoyed the desirable

thermohydraulical safety thresholds during the initial startup and first cycle.

Finally, it is worth mentioning that the comparison between the results of this modeling and the

final safety analysis report of this reactor made clear that the results presented in this paper are

satisfactorily accurate.

Keywords

VVER-1000, Thermohydraulic analysis, First cycle, WERL code, Ross-stoute ,Weisman

Introduction

During the startup process (from the cold condition), the thermal power of the reactor increases

gradually until it reaches the nominal value (3000 MW). In this regard, the negative reactivity

caused by the control rods and boric acid should be diminished to overcome the temperature

negative feedbacks. Afterwards, to stabilize the reactor’s thermal power in its nominal power (3000

MW), the concentration of boric acid should be gradually decreased during the cycle. In this research, the simplifications common to former researches are avoided in modeling of the

geometry of the fuel assemblies and the reactor core (in the neutronic and thermohydraulic

sections), and the real geometry is taken into account.

Moreover, due to the important effects of the coolant and the fuel temperature feedbacks, the

coupling of neutronic and thermo-hydraulic calculations was utilized.

It is worth noting that a computational program was designed based on the Enveloped Pin method

[13, 18] in thermo-hydraulic calculations. Furthermore, in order to accurately model the effects of

the gaseous fission products on the process of heat transfer from the fuel to the clad, the Ross-

Stoute [14, 18] and Lee-Kesler methods [17] were used in calculating the gap conductance

coefficient and gap pressure, respectively. In addition, the Weisman model [19] was employed to

calculate the amount of the gaseous fission products released into the gap space.

Several researches have been performed in order to time-dependent modeling of nuclear reactor

cores [1,5,6,7,8,9,11,16], which some of them have already been conducted in the field of initial

startup modeling [7,16] and burnup calculations of Bushehr’s VVER-1000 reactor [6]. However,

considering the limited time interval during which these researches were conducted and the fact that

temperature feedbacks, fission gas release and the modeling of real geometry of the reactor core

have not been investigated in these researches, it seems that the calculations performed in this study

are innovative and more accurate comparing to those of the former researches conducted.

The operational conditions of the Bushehr’s VVER-1000 reactor during the initial startup

and the first cycle

The thermo-neutronic parameters of the VVER-1000 reactor were changed during the first cycle. In

this regard, the changes of the reactor’s thermal power and the inlet coolant temperature are shown

in Figures 1 and 2, respectively [3].

Figure 1. The reactor’s thermal power versus time

during the initial startup and the first cycle.

Figure 2. The reactor’s inlet coolant temperature versus time

during the initial startup and the first cycle.

Furthermore, the critical concentration of boric acid and the entrance height of the control rods in

the group No. 10 were changed during the first cycle.

Figures 3 and 4 illustrate the time-dependent changes of these parameters respectively [3].

Figure 3. The critical concentration of boric acid

versus time during the initial startup and the first cycle.

Figure 4. The entrance height of the control rods (group No. 10)

versus time during the first cycle.

Figure 5, also shows the arrangement of the Bushehr’s VVER-1000 reactor core in the first cycle

[2].

Figure 5. The arrangement of the fuel assemblies in the core of

Bushehr’s VVER-1000 reactor in the first operational cycle.

Methods In order to estimate the time-dependent changes of the thermo-neutronic parameters of Bushehr’s

VVER-1000 reactor during the initial startup and the first cycle, the coupling of neutronic and

thermo-hydraulic calculations was used. To do this, the physical group constants of the fuel

assemblies and reflectors were calculated using the WIMSD5-B code [15].

Furthermore, to obtain the time-dependent changes in the fuel composition and calculate the rate of

burnup in each fuel assembly, the computational capabilities of the WIMSD5-B code were utilized

[15]. By inserting the physical group constants obtained from the WIMSD5-B code into the input

file of the CITATION-LDI2 code [4] and defining the geometry of the reactor core, the effective

multiplication factor and the three-dimensional distribution of the reactor’s thermal power were

calculated.

In this study, a thermo-hydraulic computational program (WERL code) was used for calculating the

temperature distribution of the Bushehr’s VVER-1000 reactor core based on the thermal power

distribution obtained from the CITATION-LDI2 code.

By using the results of the thermo-hydraulic calculations, the temperature and density of the fuel,

clad and coolant elements (in each fuel assembly) were applied to the neutronic calculations and

thus, a continuous sequence of neutronic and thermo-hydraulic calculations was created.

In the following paragraphs, the methods of calculations in each of the neutronic and thermo-

hydraulic sections will be explained in detail.

Neutronic calculations

Use of the WIMSD5-B code in the cell calculations of the VVER-1000 reactor core

Calculation of the physical group constants of the fuel assemblies and reflectors was performed

using the WIMSD-B code (with ENDF-BVII library). In this code, the neutron transport equation

was solved in the real geometry of each fuel assembly using the Discrete SN method [15].

To insert the real geometry of each fuel assembly into the WIMSD5-B code, 36 radial arrays were

employed to position the fuel rods.

Moreover, to define the complement space of the fuel rods in each assembly, their interior space

was divided into 54 annuluses.

In the cellular calculations of radial reflectors such as downcomer, core barrel, core baffle, water

holes and pressure vessel, the entire geometry of Bushehr’s VVER-1000 reactor core was modeled

using the WIMSD5-B code. In this regard, the materials of each fuel assembly were homogenized

at first. Then the hexagonal geometries of the assemblies were transformed into circular form so

that the fuel assemblies could be considered as a cylindrical rod in modeling the entire reactor core

(by WIMSD5-B code). In order to determine the position of the 163 fuel assemblies and the 138

water holes, 28 and 23 arrays were used, respectively. Besides, 8 and 4 radial annuluses were

employed to define the complement spaces of the fuel assemblies and the radial reflectors in the

reactor core respectively.

To obtain the time-dependent changes of the fuel composition and calculate the rate of burnup in

each fuel assembly, the computational capabilities of WIMSD5-B code were utilized. For this

purpose, the thermal power of each fuel assembly and duration of each time step were defined in the

input file of the WIMSD5-B code.

Use of CITATION-LDI2 code in calculating the neutronic parameters of the VVER-1000

reactor core

After entering the physical group constants of each fuel assembly (obtained from the WIMSD5-B

code) into the input file of the CITATION-LDI2 code and defining a three-dimensional geometry

for the reactor core in the latter code, the neutron-diffusion equation was solved three-dimensionally

by using finite-difference method [4]. Thus, the effective multiplication factor and the reactor’s

thermal-power distribution were calculated three-dimensionally at each time step. Since the reactor

core has a symmetric arrangement in the first cycle, the meshing carried out in the CITATION-

LDI2 code was intended for one -sixth of the reactor core. In line with this, the reactor core is

divided into 10 axial sub volumes, and the radial sector is composed of 7938 triangular meshes.

Thermo-hydraulic calculations

During the first cycle, a fraction of the gaseous fission products (including xenon and krypton) is

released into the gaseous space of the gap between the fuel and the clad. Considering the fact that

the gap’s gaseous space is filled with helium in the beginning, therefore, due to the lower thermal

conductivity of krypton and xenon gases compared to helium, the release of these gaseous fission

products into the gap leads to a decrease in the rate of heat transfer from the fuel to the clad.

Therefore, for considering the real geometry of fuel rods and also the effects of the gaseous fission

products in calculating of the temperature distribution in the reactor core, a thermo-hydraulic

software (WERL code) was designed using the Enveloped Pin method [13,18]. The Dittus-

Boelter[18], Ross-Stoute [14,18] and Lee-Kesler [17] models were used in the calculations of the

heat transfer coefficient of coolant, gap conductance coefficient and gap pressure, respectively.

Calculation of fuel elements and coolant temperatures:

Now, in this part and in order to complete the computational cycle, the temperature distribution in

fuel elements should be calculated, which the clad's outer surface temperature, could be calculated

as follows:

(1) )(

)(2)( tT

thR

qtT

aveout cool

coolCo

clad +′

=π

The internal surface temperature of the clad will be obtained through the following correlation [18]:

(2) )()

2

)ln(

2

1()( tT

K

R

R

hRqtT cool

clad

ci

Co

coolCo

clad in++′=

ππ

For the calculation of the outer surface temperature of fuel, the following correlation will be applied

[18]:

(3) )()

4

)ln(

2

1

2

1()( tT

K

R

R

hRhRqtT cool

clad

ci

Co

coolCogapgap

fuelout+++′=

πππ

The central temperature of fuel will be calculated as follows [18]:

(4)

)(]

1)(

)ln(

1[4

)(2

2

tT

R

R

R

R

K

qtT

outin fuel

fi

fo

fi

fo

f

fuel +

−

−′

=π

Where ciR , coR , fiR foR are the inner and outer radius of clad and fuel respectively.

fk and cladk are the thermal conductivity coefficient of fuel and clad, and

coolh is the heat transfer

coefficient of coolant.

By using control volumes for each fuel, clad and coolant elements, the average temperatures of

these items will be calculated at different times as follows:

(5) )()( )()(

_

)()1(

n

iclad

n

outfuelfoigap

n

ifuel

n

ifuel

fuel TTAhPt

TTm −−=

∆

−+

(6)

)(

)()(

)()(

_

)()(

_

)()1(

n

icool

n

outcladcoicool

n

iclad

n

outfuelfoigap

n

iclad

n

icladclad

TTAh

TTAht

TTm

−−

−−=∆

−+

(7)

50,....,1

)()()( )()(

_

)()(

)()1(

=

−+−=∆

−+

i

TTAhhhmt

hhm n

icool

n

outcladcoicool

n

icool

n

iinpcool

n

icool

n

icool

icool&

Where, fuelm , cladm and coolm are the mass of fuel, clad and coolant respectively. Furthermore,

foA and coA are the area’s of the outer surface of fuel and clad.

Therefore by using the finite difference method in solving equations No. 5, 6 and 7 and also

solving correlations No. 1 up to 4 in each time steps, we will be able to calculate the temperatures at

different surfaces of fuel, clad and the coolant, which are needed in the chained calculations. For

completion of this computational cycle and performing precise calculations, the estimation of

probable two phase condition in calculations of the coolant's heat transfer coefficient has been

considered [18].In the stage of temperature calculations of coolant, after calculating enthalpy of

each axial sub-volume, the mass quality of fluid is calculated by using thermodynamic tables

considered in the structure of the program and through following formula:

(8)

ffgg

ffi

ihh

hhX

−

−=

It's clear that other thermodynamic parameters of coolant can also be calculated via this method.

Also along the accomplishment of abovementioned temperature calculations, in order to calculate

gap conductance coefficient (in gaseous space between fuel and clad), the ROSS-STOUTE gap

model [18] has been used, which the manner of applying it, is expressed in a computational cycle

existent in the papers written by authors in reference [13,14].

With regard to the important point that at the beginning of the calculations, gap pressure is 2 MPa,

therefore, we could not use the complete gas model in the pressure calculations, and in order to

solve such a deficiency, we used the Lee-Kesler model [17].

One of the outstanding points that should be mentioned here is the impact of pressure parameter

changes on radius changes in fuel and clad.

Pressure increasing causes formation of stress on the fuel and clad surfaces which, with regard to

the elasticity characteristic present in fuel and clad, such a stress will develop strain in fuel and clad

surfaces, thus causing change in their radius. Of course, in addition to the radius changes caused

due to the elasticity phenomenon, reference should be also made to the radius changes caused as a

result of thermal expansion in fuel and clad, which play a key role in the gap thickness changes in

these calculations. In this study the effects of the both phenomena have been considered in

calculating the gap thickness.

In addition, to estimate the concentration of the released gaseous fission products into the gap

space, the Weisman model was used.

After calculating the temperature of the fuel, clad and coolant in each axial sub volume of the fuel

assemblies (in each time step), the temperature of these elements was inserted into the input files of

the WIMSD-B code (in each assembly). Thus a sequence of thermo-neutronic calculations was

formed based on the coupling of WIMSD5-B, CITATION-LDI2 and WERL codes. Figure 6

provides a schematic description of the applied computational flowchart.

Figure 6. Schematic description of the applied computational flowchart.

Calculation of the concentration of gaseous fission products released into the gap space

A fraction of the gaseous fission products such as xenon isotopes and krypton, which are produced

in the fuel pellet, is released into the gap space through the knockout and recoil processes[12]. Since

they leave important effects on the heat transfer process and also on the neutronic calculations of

the reactor, here their releasing process was modeled using the Weisman method[19].

To this end, the concentration of the gaseous fission products of each fuel assembly was calculated

using the WIMSD5-B code (in each time step). Then the concentration of the fission products

released into the gap space was calculated using the correlations 1-5 [19].

))exp(1(

)])exp(1)[1

((

2

2

2

1

1tKC

tKK

KtCC

i

ii

ret

prorel

∆−−×+

+∆×−−−

−∆×=

− (9)

iii reltotret CCC −= (10)

1−−=

iii rettotpro CCC (11)

)84.166.6916

exp(1 +−

=T

K (12)

)44.11894

exp(10944.6 5

2T

K−

××=−

(13)

Where itotC, iproC

, irelC and iretC

are the concentrations of the total, produced, released and trapped

gases (in moles) in the i th time step, respectively. In addition, t∆ is the length of the time step (in

seconds), and T denotes the fuel average temperature (in Kelvin). Since the gaseous spaces of the

gap and the upper capsule are interconnected, the released fission gases are distributed in the entire

space of this gaseous space. From neutronic point of view, a fraction of the gaseous space,

including the upper capsule and central hole, is almost enumerated as inactive space. Therefore,

when the modeling of the fission gases release is taken into account, the negative reactivity caused

by these gases will be lower than the case where this process is not taken into account. Moreover,

because of the high absorption of neutron by these gases, once the gaseous fission products are

entered into the central hole of a pellet, the fission rate in the central section is decreased and as a

result, the central temperature of the fuel is reduced.

To take into account the effects of the released fission gases on the calculation of the temperature

distribution in the reactor core, first the pressure changes caused by these gases were calculated

using the Lee-Kesler model. Next, after calculating the mole fraction of each of the released

gaseous fission products, this parameter was applied to the calculation of the gap conductance

coefficient (based on the Ross-Stoute model).

Calculation of the critical boric acid concentration during the cycle

In order to increase the precision of the calculations, the cycle length was divided into small time

steps. Therefore, the concentration of boric acid had to be calculated in each time step.

Employing the conventional iterative methods requires a great deal of time to be spent on the

related calculations; therefore, the critical boric acid concentration was directly calculated using the

following correlation [10]:

)1(1092.1 0

3 fCBB −×××=−ρ

(14)

In this correlation, which is employed to estimate the negative radioactivity caused by boric acid,

Bρ is the amount of negative radioactivity caused by boric acid with a concentration of BC (ppm)

and 0f is the thermal utilization coefficient in the absence of boron. The effective multiplication

factor of the reactor in each time step was calculated using the CITATION-LDI2 code and

subsequently the amount of the reactivity in each time step was also calculated. Therefore, by

replacing the amount of the excess reactivity with the Bρ parameter, the corresponding critical

boric acid concentration was calculated.

Results:

In this paper, the time dependent or axial changes of the thermal power, mass quality, gap

conductance coefficient of fuel, heat transfer coefficient of coolant, gap pressure & thickness and

the temperature distribution of fuel elements and coolant of Bushehr’s VVER-1000 reactor core has

been studied during the initial startup and first cycle.

In figures 7 to 11 the time dependent changes of fuel, clad and coolant temperatures of fuel

assemblies in the Bushehr’s VVER-1000 reactor has been shown.

Of course due to one-twelfth symmetry of the Bushehr’s reactor core in the first cycle, the results

were presented only for a symmetric section of the core.

250

350

450

550

650

750

850

950

1050

1150

1250

1350

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

Time (Day)

Internal temperature of fuel pellet

(oC)

FA 82

FA 83

FA 84

FA 85

FA 86

FA 87

FA 88

FA 97

FA 98

FA 99

FA 100

FA 101

FA 102

FA 112

FA 113

FA 114

FA 115

FA 126

FA 127

Figure7. Time dependent changes of the internal surface temperature

of fuel pellet in each assembly during the first cycle (in the middle of the core)

250

275

300

325

350

375

400

425

450

475

500

525

550

575

600

625

650

675

700

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

Time (Day)

External surface temperature

of fuel pellet(oC)

FA 82

FA 83

FA 84

FA 85

FA 86

FA 87

FA 88

FA 97

FA 98

FA 99

FA 100

FA 101

FA 102

FA 112

FA 113

FA 114

FA 115

FA 126

FA 127

Figure8. Time dependent changes of the external surface temperature

of fuel pellet in each assembly during the first cycle (in the middle of the core)

280

290

300

310

320

330

340

350

360

370

380

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

Time (Day)

Internal surface temperature

of clad (oC)

FA 82

FA 83FA 84

FA 85FA 86

FA 87FA 88

FA 97FA 98

FA 99

FA 100FA 101

FA 102FA 112

FA 113FA 114

FA 115FA 126

FA 127

Figure 9. Time dependent changes of the internal surface temperature

of clad in each assembly during the first cycle (in the middle of the core)

280

285

290

295

300

305

310

315

320

325

330

335

340

345

350

355

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300Time (Day)

External surface temperature

of clad(oC)

FA 82

FA 83FA 84

FA 85FA 86

FA 87FA 88

FA 97FA 98

FA 99

FA 100FA 101

FA 102FA 112

FA 113FA 114

FA 115FA 126

FA 127

Figure10. Time dependent changes of the external surface temperature

of clad in each assembly during the first cycle (in the middle of the core)

280

285

290

295

300

305

310

315

320

325

330

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

Time (Day)

Coolant outlet temperature (oC)

FA 82

FA 83

FA 84

FA 85

FA 86

FA 87

FA 88

FA 97

FA 98

FA 99

FA 100

FA 101

FA 102

FA 112

FA 113

FA 114

FA 115

FA 126

FA 127

Figure 11. Time dependent changes of the outlet coolant temperature

in each assembly during the first cycle.

Figures 12 to 16 describe the time dependent changes of produced thermal power, mass quality, gap

conductance coefficient, gap pressure and thickness in each assembly of Bushehr’s VVER-1000

reactor.

0

2

4

6

8

10

12

14

16

18

20

22

24

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

Time (Day)

Fuel assemblies power (MW)

FA 82

FA 83FA 84FA 85FA 86

FA 87FA 88

FA 97FA 98

FA 99FA 100FA 101FA 102

FA 112FA 113

FA 114FA 115

FA 126FA 127

Figure 12. Time dependent changes of the reactor’s thermal power

in each assembly during the first cycle.

-0.45

-0.425

-0.4

-0.375

-0.35

-0.325

-0.3

-0.275

-0.25

-0.225

-0.2

-0.175

-0.15

-0.125

-0.1

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

Time (Day)

Mass quality

FA-82

FA-83FA-84

FA-85

FA-86

FA-87FA-88

FA-97

FA-98

FA-99FA-100

FA-101

FA-102FA-112

FA-113

FA-114

FA-115FA-126

FA-127

Figure 13. Time dependent changes of coolant’s mass quality

in each assembly during the first cycle

2500

2750

3000

3250

3500

3750

4000

4250

4500

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

Time (Day)

Gap conductance coefficient

(W/m^2k)

FA 82FA 83FA 84FA 85FA 86FA 87FA 88FA 97FA 98FA 99FA 100FA 101FA 102FA 112FA 113 FA 114FA 115FA 126FA 127

Figure 14. Time dependent changes of the gap conductance coefficient in each assembly during the

first cycle (in the middle of the core)

1.95

2

2.05

2.1

2.15

2.2

2.25

2.3

2.35

2.4

2.45

2.5

2.55

2.6

2.65

2.7

2.75

0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300

Time (Day)

Gap pressure (MPa)

FA-82

FA-112

FA-83

FA-84

FA-97

FA-85

FA-98

FA-86

FA-99

FA-87

FA-100

FA-113

FA-88

FA-101

FA-126

FA-102

FA-115

FA-127

FA-114

Figure 15. Time dependent changes of the gap pressure in each assembly during the first cycle

0.000575

0.0006

0.000625

0.00065

0.000675

0.0007

0.000725

0.00075

0.000775

0.0008

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

Time (Day)

Gap thickness (m)

FA-82

FA-83

FA-84

FA-85

FA-86

FA-87

FA-88

FA-97

FA-98

FA-99

FA-100

FA-101

FA-102

FA-112

FA-113

FA-114

FA-115

FA-126

FA-127

Figure 16. Time dependent changes of the gap thickness in each assembly during the first cycle (in

the middle of the core)

In figures 17 to 24, the axial variations of mass quality, heat transfer coefficient and temperature of

coolant as well as the central temperature of fuel has been shown in the end of both startup

process(Day=100) and first cycle(Day=289.71).

Day=100

-0.4

-0.375

-0.35

-0.325

-0.3

-0.275

-0.25

-0.225

-0.2

-0.175

-0.15

-0.125

-0.1

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75

Core's axial length (m)

Mass quality

FA 82FA 112FA 83FA 84FA 97

FA 85FA 98FA 86FA 99FA 87FA 100FA 113FA 88FA 101

FA 114FA 126FA 102FA 115FA 127

Figure17. The changes of mass quality of coolant

in the axial direction of the core (in the end of initial startup)

Day=100

25000

25250

25500

25750

26000

26250

26500

26750

27000

27250

27500

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75


Hcool(W/m^2oC)


FA 87FA 100FA 113FA 88FA 101FA 114FA 126FA 102FA 115FA 127

Figure18. The changes of heat transfer coefficient of coolant


Day=100

285

290

295

300

305

310

315

320

325

330

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75


Coolant temperature(oC)

FA 82FA 112FA 83FA 84FA 97FA 85FA 98FA 86FA 99FA 87FA 100FA 113FA 88FA 101FA 114FA 126FA 102FA 115FA 127

Figure19. The changes of coolant temperature


Day=100

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75


Fuel inside temperature

(oC)

FA 82

FA 112

FA 83

FA 84

FA 97

FA 85

FA 98

FA 86

FA 99

FA 87

FA 100

FA 113

Figure 20. The changes of central temperature of fuel


Day=289.71

-0.375

-0.35

-0.325

-0.3

-0.275

-0.25

-0.225

-0.2

-0.175

-0.15

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75

core's axial length (m)

Mass quality


Figure 21. The changes of mass quality of coolant

in the axial direction of the core ( in end of first cycle )

Day=289.71

25000

25250

25500

25750

26000

26250

26500

26750

27000

27250

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75

Time (Day)

Hcool(W/m^2oC)

FA 82FA 112FA 83FA 84FA 97


FA 114FA 126FA 102FA 115FA 127

Figure 22. The changes of heat transfer coefficient of coolant

in the axial direction of the core (in end of first cycle)

Day=289.71

290

295

300

305

310

315

320

325

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75

Time (Day)

Coolant temperature

(oC)


FA 87FA 100FA 113FA 88FA 101FA 114FA 126FA 102FA 115FA 127

Figure 23. The changes of coolant’s temperature


Day=289.71

400

500

600

700

800

900

1000

1100

1200

1300

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75Time (Day)

Fuel inside temperature

(oC)


Figure 24. The changes of central temperature of fuel


Figures 25 and 26 compare the calculated results of maximum power peaking factor and the

reactor’s radial power peaking factor distribution with the data presented in the safety analysis

report of Bushehr’s VVER-1000 reactor (Atomenergoproekt, 2003b).

Figure 25.Comparison of the results of time dependent changes of the maximum

power peaking factor of Bushehr’s VVER-1000 reactor with the data of FSAR .

Figure26.Comparison of the results of the power peaking factor distribution

of the Bushehr’s VVER-1000 reactor with the data of safety FSAR

in the end of the first cycle.

The mole fractions of the released fission gases at the end of the first cycle are shown in Figure 27.

Figure 27. The mole fractions of the released fission gases

at the end of the first operational cycle.

Given that for the first time these calculations have been done in Bushehr reactor, therefore,

experimental data was not available for benchmark. However, with regard to the fact that there was

a graph for gap conductance coefficient changes for the hot fuel pin (versus Burnup changes) during

first cycle in the final safety analysis report of VVER-1000 Reactor of Bushehr NPP, in order to

ensure from the authenticity of the calculations made in this research, we were forced to make the

similar calculations in this regard, and the comparison results were indicative of minor error in this

case, which are outlined in figure28.

Figure 28. A comparison between the gap conductance coefficient resulted by FSAR data [2] with

results obtained through Ross-Stoute calculations (for the hot fuel pin)

Discussion and conclusion

Through study of figures 7 to 16, it is noticed that by increasing the thermal power of Reactor

(during startup process) and subsequently increase in temperature(figures7 to 11), the gap effective

thickness(figure.16) will reduce as a result of thermal expansion, which as a result of this the gap

pressure(figure. 15) will go up. By reference to the equations presented in the Ross-Stoute model

[14, 18] and also study of figure.14, it will be noticed that such changes in these parameters will

increase the gap conductance coefficient. Through observation of such phenomena, it could be

concluded that the VVER-1000 Reactor typically operates under a self-control and inherent safety

status against increase in thermal power and temperature of the Reactor.

Furthermore, with the addition of gaseous fission products into the gap area, the gap pressure will

increase, and as it was noticed in the Ross-Stoute model, will increase the gap conductance

coefficient, and also in its second role as a control feedback, by exerting stress in the fuel and clad

surfaces, will create strain in them (due to the presence of elastic characteristic in fuel and clad). It

should be noted that this phenomenon will reduce the radius increasing caused by thermal

expansion in fuel which, as a control feedback, will prevent extra decrement of the gap thickness.

Because no study has been conducted to calculate the time dependent changes of the

thermohydraulic parameters of Bushehr’s VVER-1000 reactor during initial startup and first cycle,

and no report is given in the final safety analysis report of this reactor (FSAR), there was no

opportunity to compare our results with other studies. However, with regard to the calculations and

modeling which were published by author in references no. [13]&[14] and also the comparison

drawn between the results of the power peaking factor distribution in the end of cycle(figure.26)

and the time dependent changes of maximum power peaking factor(figure. 25) during the initial

startup and first cycle of Bushehr’s VVER-1000 reactor with FSAR data, it can be observed that the

calculations performed in this paper are satisfactorily accurate.

Bearing in mind the particular structure of the fuel rods of Bushehr’s VVER-1000 reactor, making

use of conventional codes (such as COBRA-EN) was not feasible for the thermo-hydraulic

modeling of this reactor.

Furthermore, the previous codes had deficiencies with regard to modeling and estimating the heat

transfer process in the gaseous space of the gap.

To this purpose, a thermo-hydraulic computational program was designed to correct these flaws, so

that it would have the capability of estimating the concentration of the released gaseous fission

products into the gap and applying it to the heat transfer process in this area.

Finally by observing the time dependent changes of fuel elements and coolant temperatures and also

the value of mass quality (figure.13), gap pressure and thickness during the initial startup process

and first cycle, it can be concluded that the Bushehr’s VVER-1000 reactor is completely safe during

this period.

References

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department of physics, faculty of engineering, sari branch ... · study of thermohydraulic...

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