EXPERIMENTAL AND NUMERICAL STUDY OF THE BORON ......The experimental study of rapid boron dilution...

International ConferenceNuclear Energy in Central Europe 2000Nuclear Energy in Central Europe 2000Nuclear Energy in Central Europe 2000Nuclear Energy in Central Europe 2000Golf Hotel, Bled, Slovenia, September 11-14, 2000

EXPERIMENTAL AND NUMERICAL STUDY OF THE BORONDILUTION INCIDENT IN VVER–1000 REACTOR

Yu. A. Bezrukov, S. A. Logvinov,EDO “Gidropress”

Ordzhonikidze 21, Podolsk, Moscow region, 142103, [email protected]

O. I. Melikhov, V. I. Melikhov and S. E. YakushElectrogorsk Research and Engineering Centre on NPPs Safety

Bezymyannaya 6, Electrogorsk, 142530, [email protected], [email protected],

[email protected]

ABSTRACT

Results of experimental and numerical study of boron mixing in the VVER-type reactorare presented. The experiments were performed on a 1:5-scale reactor model, the concentra-tion transients caused by propagation of a diluted coolant slug were measured. A numericalmodel was used to reveal the spatial concentration distributions in the reactor during the slugpropagation. Reasonable agreement between the measured and calculated concentrations wasdemonstrated. It was shown that intensive mixing of flows with different boron concentra-tions occured in the reactor downcomer, so that even in the case where the slug is initially bo-ron-free, the boron concentration decrease at the core inlet did not exceed 30-35%.

1 INTRODUCTION

Over the past years, safety analysis of PWRs (VVERs) invariably includes considera-tion of rapid boron dilution incidents in which a slug of coolant with low boron concentrationpenetrates into the reactor core [1]. The slug may be formed in the reactor loops for internal aswell as for external reasons [2]. Restart of coolant circulation causes penetration of low-concentration slug into the reactor flow path and its subsequent propagation through the re-actor core, which may potentially lead to the reactivity accident.

Coolant mixing in the reactor flow path is the process that affects substantially the con-centration of boron reaching the reactor core. Since the flow in the reactor downcomer aftersudden restart of circulation is spatially non-uniform and transient, its detailed study is neces-sary to estimate the mixing characteristics. A number of experimental and theoretical studiesof these processes has been reported recently [3–6]. The most promising approach consists incombining real or reduced-scale experiments with mathematical modelling of the flows in-volved.

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Yu. A. Bezrukov, S. A. Logvinov,… page 2 of 8EXPERIMENTAL AND NUMERICAL STUDY OF THE BORON DILUTION INCIDENT…

Proceedings of the International Conference Nuclear Energy in Central Europe, Bled, Slovenia, Sept. 11-14, 2000

The paper presents the results of experimental and computational studies of boron dilu-tion in the VVER reactor downcomer caused by propagation of a slug with low boron con-centration from one of the reactor loops.

2 EXPERIMENTS

The experimental study of rapid boron dilution was carried out on a test facility basedon a 1:5-scale model of VVER-1000 reactor [5]. The reactor model included the circulationpath from the loop inlets up to the reactor core. A part of one cold leg with the loop seal at thecirculatory pump inlet was reproduced. The simulated leg was manufactured from the 170mm inner diameter pipe. The boron concentration difference was reproduced by the watertemperature difference. Valves were installed at the inlet and outlet of the loop seal for cut-offduring the filling by cold water. The other three loops were reproduced only schematically(by appropriate hydraulic resistances), they were connected to the common collector enablingreversal flow in the idle loops to be modelled. The flow rates through the main loop and thereversal loops were controlled with the relative accuracy within 2%. The core model included151 simulators of fuel assemblies having the same hydraulic resistance as the actual ones.

Coolant with the initial boron concentration was modelled by hot water, while the di-luted slug was represented by a volume of cold water. The measurements of local tempera-tures were carried out by the thermocouple array at the entrance to the core model. Total of 92thermocouples were installed, of which 80 were located as an array at the core inlet, while 12thermocouples were located at the exit of reactor downcomer. The location of thermocouplesin the array is shown in Fig. 1.

Figure 1 Thermocouple array used in the experiments. N1 is the inlet of the activeloop, N2–N4 are passive loops. Points P1–P4 are used for comparison with the numericalcalculations



Quick-response thermocouples with the response time constant of about 0.01 s wereconnected to the data acquisition system manufactured by NATIONAL INSTRUMENTS.The following parameters were measured in the tests:

� Initial temperature of hot and cold water� Water temperature at the lower part of downcomer� Water temperature at the core inlet� Flowrate at the model inlet� Reversal flow rate in the non-operating loops

Before the experiment the test facility was filled with water heated up to 40–80C, thetemperature uniformity was achieved by maintaining circulation while heating the water. Thecirculation was then stopped, and the loop seal was filled with cold water. The test started byopening the loop seal cut-off valves and switching on the circulation pump in the active loop.

At the initial stage of the experiments effects of heat exchange between the water andthe model were studied. The tests were carried out for the flowrates between 180 and650 m3/h, the hot water temperatures maxT were in the range of 40–80°C and the cold watertemperatures minT between 15 and 25°C. The time dependences of the relative temperatures

)/()( minmaxmin TTTT −−=θ obtained for the same flowrates were compared. It was shown thatthe results of measurements practically did not depend on the temperature differences used,which means that heat exchange between the water and the metal structures does not influ-ence the measurements. Also, good reproducibility of the results was confirmed.

In the main experiments transient characteristics of the temperature field at the core in-let were obtained in the range of total flowrate Q between 270 and 770 m3/h. Comparison ofthe results obtained shows that, although the time necessary for the diluted slug to reach thecore inlet is inversely proportional to the flowrate, the levels of concentrations are practicallyindependent of Q. In all experiments (performed with and without recirculation in the passiveloops) no penetration of pure coolant into the core zone occurred, which shows that the mix-ing processes in the flow path are intensive enough, and the initially deborated coolant rapidlymixes up with the high-concentration coolant. The relative temperature did not fall below70% of its normal level during all the process.

The experiments have also shown that the dilution may be affected by the time offlowrate increase after the circulation pump restart. Comparison of temperature time historiesfor the characteristic times of 2 s and 14 s shows that in the case of more rapid flowrate in-crease the dilution of coolant by the low-concentration slug proceeds more rapidly, and thedrop in concentration is more pronounced. Thus, the pump restart transient may be an impor-tant feature which has to be considered in the possible incident scenario.

3 NUMERICAL MODEL

Transient turbulent flows of incompressible liquid in the reactor downcomer are mod-elled on the basis of three-dimensional Reynolds-averaged Navier-Stokes equations approxi-mated by the finite-element method [7]; the solver is implemented in the code BOR3D. Ge-ometry-fitted unstructured grids with hexahedral cells are used providing the flexibility neces-sary to reproduce the complex geometry of the reactor downcomer. The concentration field iscalculated from the convection-diffusion equation solved together with the main system ofgoverning equations:



0=∂

∂+∂∂+

∂∂

zW

yV

xU (1)

zU

zyU

yxU

xxP

zUW

yUV

xUU

tU

∂∂

∂∂+

∂∂

∂∂+

∂∂

∂∂+

∂∂−=

∂∂+

∂∂+

∂∂+

∂∂ ννν

ρ1 (2)

zV

zyV

yxV

xyP

zVW

yVV

xVU

tV

∂∂

∂∂+

∂∂

∂∂+

∂∂

∂∂+

∂∂−=

∂∂+

∂∂+

∂∂+

∂∂ ννν

ρ1 (3)

zW

zyW

yxW

xzP

zWW

yWV

xWU

tW

∂∂

∂∂+

∂∂

∂∂+

∂∂

∂∂+

∂∂−=

∂∂+

∂∂+

∂∂+

∂∂ ννν

ρ1 (4)

zCD

zyCD

yxCD

xzCW

yCV

xCU

tC

∂∂

∂∂+

∂∂

∂∂+

∂∂

∂∂=

∂∂+

∂∂+

∂∂+

∂∂ (5)

Here (x,y,z) are the Cartesian coordinates, (U,V,W) are the velocity components, P is the pres-sure, ρ is the density. The relative boron concentration c is defined in terms of absolute con-centration C as

%100minmax

min ⋅−

−=CC

CCc (6)

where maxC and minC are the maximum and minimum boron concentrations respectively, C isthe local concentration. The value of relative concentration %100=c corresponds to the high(normal) boron contents in the coolant, while 0=c corresponds to the undiluted slug. Theequation for the relative concentration coincides with that for the absolute concentration C.The pressure field is found from the elliptic equation

02

2

2

2

2

2

=∂∂+

∂∂+

∂∂

zP

yP

xP (7)

The k-ε turbulence model is used to calculate the turbulent quantities and obtain the turbulentviscosity ν and diffusivity D. The turbulence kinetic energy k and dissipation rate ε are de-termined from the equations

εσν

σν

σν −+

∂∂

∂∂+

∂∂

∂∂+

∂∂

∂∂=

∂∂+

∂∂+

∂∂+

∂∂ G

zk

zyk

yxk

xzkW

ykV

xkU

tk

kkk

(8)

( )εεεσνε

σνε

σνεεεε

εεε21 CGC

kzzyyxxzW

yV

xU

t−+

∂∂

∂∂+

∂∂

∂∂+

∂∂

∂∂=

∂∂+

∂∂+

∂∂+

∂∂ (9)

,2222222

��

�

�

��

�

�

��

��

�

∂∂+

∂∂+�

�

��

�

∂∂+

∂∂+��

�

��

�

∂∂+

∂∂+

��

�

�

��

��

�

∂∂+��

�

��

�

∂∂+�

�

��

�

∂∂=

yW

zV

xW

zU

xV

yU

zW

yV

xUG ν

ScDkC ν

εν µ == ,

2

(10)



The standard set of constants was used in the calculations: ,09.0=µC ,44.11 =C ,93.12 =C,0.1=kσ ,3.1=εσ Sc = 0.7.

The initial and boundary conditions corresponded to the scenario of sudden restart ofone of the circulation pumps with allowance for the backflow in the other three loops. Initiallythe coolant was at rest and contained high boron concentration:

100 ===== c,WVU:t (11)

The no-slip boundary conditions were posed on all solid surfaces of the reactor (bound-ary ΓΓΓΓ), the concentration flux on these was also set to zero:

0n

0n

,0 =∂∂=

∂∂=

ΓΓΓ

PCU (12)

The velocities of inflow at the active loop inlet and of outflows at the passive loop inlets arespecified according to the experimental data, the exponential approximations are used:

��

��

��

�

�−−=

00 exp1)(

ttQtQ α (13)

In the calculations presented below the maximum flowrate through the active loop was takenequal 650max =Q m3/h, the time constant providing the best fit is t0 = 3.5 s. The passive loopflowrates were all taken with the proportionality constant of α = 0.1. In Fig. 2 the experimen-tal flowrates through the active (a) and passive (b) loops are shown together with their expo-nential approximations (13).

0 5 10 15t

0

200

400

600

800

QN1 (experim.)

(a)

Approximation

0 5 10 15t

0

20

40

60

80

Q

N4

N3

N2

Approximation

(b)

Figure 2 Experimental flowrates through the active (a) and passive (b) loops andtheir exponential approximations



4 RESULTS

The numerical calculations were performed on a grid containing 5600 nodes and 4800elements. The vertical cross-section and top view of the grid are presented in Fig. 3. Thecoolant with low concentration of boron is supplied during the first 2.5 s, after which the rela-tive concentration in the active loop is set to unity. In Fig. 4 the relative concentration distri-butions obtained in the calculations of the flow following the restart of the pump in the activeloop are shown. The left picture corresponds to the instant t = 1.5 s. The slug may be seen tospread sideways from the inlet. Some fraction of the coolant with low concentration is cap-tured by the reversal flow and removed from the downcomer through the passive loops, whilethe remaining low-concentration coolant moves downward to reach the core. The right pictureshows the concentration distribution at the instant t = 3.0 s. By this time the inflowing coolantin the active loop contains high (normal) boron concentration.

Figure 3 Grid used in the calculations. Left: cross-section, right: top view

To compare the predictions with the experimental results, the temporal dependencies ofthe relative concentrations were obtained in four points at the elevation of 0.328 m, whichcorresponds to the height of the thermocouple array used in the experiments. The location ofthe points P1–P4 is shown in Fig. 1. In Fig. 5 a–d the calculated dependencies are presentedtogether with the measured thermocouple readings. The profiles of the concentration are fea-tured by quite rapid concentration decrease caused by propagation of the slug front, followedby slow concentration recovery. It can be seen that the numerical results agree quite reasona-bly with the measurements. In particular, the time corresponding to the minimum of concen-tration is reproduced adequately. The lowest concentrations obtained numerically are within20% of the experimental ones. The numerical solutions, however, exhibit faster concentrationrecovery than it is obtained in the tests.

5 CONCLUSIONS

Results of experimental and numerical study of boron dilution in the 1:5-scale model ofVVER-1000 reactor are presented. Mixing of coolant with the low-concentration slug in thereaction downcomer is shown to decrease substantially hazards of reactivity accident: even inthe case where the slug initially contains coolant with zero boron concentration, the drop inthe boron concentration at the core inlet does not exceed 30% of the normal level. The nu-merical results are in good agreement with the experimental data.



Figure 4 Boron concentration distributions in the reactor downcomer.Left: t = 1.5 s, right: t = 3.0 s

0 4 8 12 16t,[s]

0.5

0.6

0.7

0.8

0.9

1

c,[-]

0 4 8 12 16t,[s]

0.5

0.6

0.7

0.8

0.9

1

c,[-]

0 4 8 12 16t,[s]

0.5

0.6

0.7

0.8

0.9

1

c,[-]

0 4 8 12 16t,[s]

0.5

0.6

0.7

0.8

0.9

1

c,[-]

(a) (b)

(c) (d)

Figure 5 Temporal dependencies of the relative boron concentration at the pointsP1 (a), P2 (b), P3 (c) and P4 (d). Solid lines: experiments, dashed lines: calculations



6 NOMENCLATURE

21,, CCCµ constants in the turbulence modelC absolute concentrationc relative concentrationD diffusion coefficientk turbulence kinetic energyP pressureQ mass flowrateSc Schmidt number, ν/DT temperaturet timeU, V, W velocity componentsε dissipation rateν viscosityθ relative temperatureρ mass density

kσ , εσ constants in the turbulence model

7 REFERENCES

[1] J. Hyvarinen. The inherent boron dilution mechanism in pressurized water reactors. Nu-clear Engineering & Design, 1993, v. 145, pp. 227-240.

[2] B. I. Nigmatulin, C. N. Din, R. Kh. Khasanov. On the study of the class of reactivityincidents cause by boron dilution in VVER-type reactors. Report EREC L1121/95,Electrogorsk, 1995.

[3] B. Hemstrom, N. G. Andersson. Physical modelling of a rapid boron dilution tran-sient. – I. Reynolds number sensitivity study for the Ringhals case. Report No. US 95:5.Vattenfall Utveckling AB, 1995.

[4] P. Gango. Numerical boron mixing studies for Loviisa nuclear power plant. NuclearEngineering and Design, 1997, v. 177, pp. 239 – 254.

[5] Yu. A. Bezrukov, S. A. Logvinov. Experimental study of the fast boron dilution at theVVER-1000 core inlet. First Workshop on EUBORA Project, Vantaa, Finland, 21-23Oct. 1998.

[6] L. I. Zaichik, B. I. Nigmatulin, A. P. Skibin, R. Kh. Khasanov, S. M. Petukhov. Un-steady one-dimensional model for analysis of non-uniformity of boron acid dilution inthe first loop of the pressurised water reactor. Atomic Energy, 1997, V. 83, pp. 305–307.

[7] S. Turek. Efficient Solvers for Incompressible Flow Problems An Algorithmic andComputational Approach. Lecture Notes in Computational Science and Engineering,V. 6. Springer Verlag, 1999, 352 pp.

EXPERIMENTAL AND NUMERICAL STUDY OF THE BORON ......The experimental study of rapid boron dilution...

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