ABSTRACT The International Standard Problem, ISP 43, was defined by the OECD/NEA and the US NRC for the validation of threedimensional Computational Fluid Dynamics (CFD) software. The underlying experiment was performed in the 2×4 Loop Facility of the University of Maryland, College Park, U.S.A (UMCP). The test facility is a scaled-down model of the Three Mile Island TMI-2 reactor with detailed reconstruction of the reactor pressure vessel (RPV). The ISP 43 experiments focussed on rapid boron dilution transients in the RPV cold leg and downcomer. The simulations of the ISP 43 were performed with the CFX-TASCflow software. Numerical errors were monitored by comparing results obtained with different higher order discretisation schemes. Uncertainties related to physical modelling, like buoyancy effects and reactor core models, were also investigated. The simulation results show good agreement with data and prove that CFD methods can be usefully applied to this class of nuclear reactor problems

Martina Scheuerer

CiteSeerX

 
Proceedings of ASME International: 
Downloaded FromFluids Engineering Summer Conference 
July 14-18, 2002 Montreal, Canada 
FEDSM2002-31407 
 
SIMULATION OF OECD/NEA INTERNATIONAL STANDARD PROBLEM NO. 43 ON 
BORON MIXING TRANSIENTS IN A PRESSURIZED WATER REACTOR 
 
  
 Martina Scheuerer 
Gesellschaft für Anlagen- und 
Reaktorsicherheit, Germany 
Martina.Scheuerer@grs.de  
 
 
Proceedings of ASME FEDSM02 
ASME 2002 Fluids Engineering Division Summer Meeting 
Montreal, Quebec, Canada, July 14-18, 2002 
 
FEDSM2002-31407  
 
 
ABSTRACT 
The International Standard Problem, ISP 43, was defined by 
the OECD/NEA and the US NRC for the validation of three-
dimensional Computational Fluid Dynamics (CFD) software. 
The underlying experiment was performed in the 2×4 Loop 
Facility of the University of Maryland, College Park, U.S.A 
(UMCP). The test facility is a scaled-down model of the Three 
Mile Island TMI-2 reactor with detailed reconstruction of the 
reactor pressure vessel (RPV). The ISP 43 experiments focussed 
on rapid boron dilution transients in the RPV cold leg and 
downcomer. The simulations of the ISP 43 were performed with 
the CFX-TASCflow software. Numerical errors were monitored 
by comparing results obtained with different higher order 
discretisation schemes. Uncertainties related to physical 
modelling, like buoyancy effects and reactor core models, were 
also investigated. The simulation results show good agreement 
with data and prove that CFD methods can be usefully applied 
to this class of nuclear reactor problems. 
 
INTRODUCTION 
Boric acid is used as a soluble neutron absorber in the 
primary system of pressurized water reactors. Under normal 
operating conditions, the concentration of boric acid in the core 
is controlled by the chemical and volume control system. How-
ever, during small break loss of coolant accidents boiling and 
condensation can occur and de-borated water collects in the 
steam generator tubes and the pump suction lines, see encircled 
area in Fig. 1. If the de-borated water is transported into the 
reactor core, a heterogeneous distribution of boric acid may 
cause an excursion of reactivity and damage to the reactor core. 
Therefore, it is important to know to which extent fluid-mixing 1
 
: https://proceedings.asmedigitalcollection.asme.org on 06/29/2019 Terms of Uprocesses can mitigate or even prevent inhomogeneous boron 
mixing incidents.  
CFD methods are an effective tool to calculate three-di-
mensional mixing phenomena. Because of the rapid 
development of computer hardware and software, it has now 
become feasible to simulate transient, three-dimensional flows 
and the transport of de-borated water in pressurized water 
reactors. However, the applied numerical methods and turbulen-
ce models require experimental validation based on detailed 
flow and temperature fields. The ISP 43 was specifically 
designed and performed to provide such data for validating and 
assessing CFD software.  
 
NOMENCLATURE 
CFD Computational fluid dynamics 
CL Cold leg 
DC Downcomer 
HL Hot leg 
ISP International standard problem 
RCP Reactor coolant pump 
RPV Reactor pressure vessel 
SG Steam generator 
TMI-2 Three Mile Island, Power Plant Unit 2 
UMCP University of Maryland, College Park 
 
ISP 43 EXPERIMENTS 
The UMCP 2×4 Loop Facility is a scaled model of the 
Babcock & Wilcox TMI-2 reactor with a detailed reconstruction 
of the RPV. The test facility shown in Fig. 1 consists of two 
reactor cooling systems with two hot legs (HL), four cold legs 1 Copyright © #### by ASME 
 Copyright © 2002 by ASME 
se: http://www.asme.org/about-asme/terms-of-use
 
 
Dow(CL) with the main coolant pumps (RCP), and two steam 
generators (SG). Figure 2 shows the RPV and the location of  
thermocouples in the downcomer (DC). The instrumentation is 
concentrated in the DC area to allow a detailed comparison with 
CFD results. Gavrilas et al. [1] give a detailed description of the 
test facility. 
The ISP 43 consists of Test Cases A and B, see Gavrilas and 
Kiger [2]. In both experiments density differences between de-
borated pure water and borated water are emulated by tem-
perature differences. The reactor system is initially filled with 
stagnant hot water and cold water is injected into cold leg A1 by 
actuating the RCP. Three-dimensional mixing effects in the cold 
leg, and in the downcomer lead then to temporal and spatial 
variations of the cold water (or boron) concentration at the 
reactor core entrance.  
In Test Case A, a continuous flow of cold water is injected 
into cold leg A1 from an external tank. This effectively simula-
tes a ‘water front’ rather than a slug passing through the system. 
In Test Case B, a finite amount of cold water is injected in-
to the bottom of the steam generator A and the cold water slug is 
then set into motion by pump A. 
 
CFD METHOD 
The calculations of the ISP 43 test cases are performed with 
the CFX-TASCflow software of AEA Technology, assuming 
transient, turbulent flow of an incompressible fluid. The mathe-
matical model consists of the three-dimensional, ensemble-
averaged conservation equations for mass, momentum and ener-
gy. The turbulent transport terms in the conservation equations 
of the momentum and energy equations is calculated using an 
 
Figure 1: UMCP 2x4 Loop Facility  
2 
 
nloaded From: https://proceedings.asmedigitalcollection.asme.org on 06/29/2019 Terms of Useeddy diffusivity approach in combination with the k-ε two-
equation turbulence model see Launder and Spalding [3]. 
The numerical solution method of CFX-TASCflow is based 
on a conservative, control volume-based finite-element method 
with co-located variable storage. The numerical grid consists of 
non-orthogonal, hexahedral elements. 
In the current calculations, temporally and spatially second-
order accurate discretisation methods are used. The temporal 
discretisation method is an implicit backward Euler method 
using quadratic interpolation functions. The spatial discretisa-
tion schemes for the convective terms in the model differential 
equations are based on Raithby’s [4] linear profile skew upwind 
methods combined with the Physical Advection Correction 
(PAC) method. Tri- and bi-linear form functions are used to ap-
proximate the diffusive flux terms and source or sink terms 
involving gradients of dependent variables with second order 
truncation error. 
The coupled non-linear algebraic equation system arising 
from discretisation is linearized with a substitution or Picard 
scheme. CFX-TASCflow uses a pressure-based solution method, 
and the equations for the pressure and velocity fields are solved 
in a coupled manner. The resulting large coefficient matrix is 
solved with an iterative algebraic multi-grid method. This 
solution technique provides robust and rapid convergence and 
has a linear operation count, see [5].  
 
 
Figure 2: Thermocouple Position 2 Copyright © #### by ASME 
Copyright © 2002 by ASME 
: http://www.asme.org/about-asme/terms-of-use
Down 
COMPUTATIONS 
The computational geometry is based on a three-dimen-
sional CAD surface model in IGES format. The model is im-
ported into the CFX-Hexa grid generation software, with which 
a block-structured grid with 470.000 hexahedral flux elements 
is generated. Figure 3 shows the surface grid of the reactor 
system including the cold legs, the lower plenum and the inner 
downcomer wall. The outlet is placed at hot leg A. 
The calculations were performed on Compaq/DEC Alpha 
Server 8200 with 1 GB RAM. The test cases require approxi-
mately 150 h calculation time each. 
 
Test Case A  
In Test Case A, the RPV is initially filled with warm (i.e. 
borated) water at a temperature of T = 72 oC. Within 5 s the 
temperature of the injected water front decreases from 72 oC to 
12 oC. The mass flow rate reaches its maximum value of 7.2 
kg/s after 27 s. Values for the velocity and length scale of the 
turbulence at the inlet cross section are derived from existing 
data. At the outlet, the average static pressure is described. The 
core is simulated as a porous medium with a prescribed pressure 
loss of 1500 Pa for steady-state conditions. The no-slip 
boundary condition in combination with logarithmic wall 
functions are applied on all inner walls of the reactor systems. 
The outer walls are assumed adiabatic. 
As a first step in the calulation of the ‘blind’ Test Case A, 
the robustness and potential of CFX-TASCflow to predict 
 
Figure 3: Numerical Grid  
3
 
loaded From: https://proceedings.asmedigitalcollection.asme.org on 06/29/2019 Terms of Utransient, three-dimensional, turbulent flows in the ISP 43 
reactor geometry are tested using robust numerical discretisa-
tion schemes with first order accuracy. In addition, variable den-
sity and buoyancy effects are neglected. In the second step, 
solution errors are reduced by applying second-order accurate 
temporal and spatial discretisation methods. The final calculati-
ons are run with variable density and buoyancy models switched 
on. 
The accuracy of the CFD results are assessed based on the 
transient circumferentially averaged temperature distribution on 
level 4 of the DC, see Fig. 2. Level 4 is the lowest DC level, at 
which temperature measurements were made. The temperature 
distribution at this location is an important indicator for the 
mixing of the de-borated cold water and the borated hot water in 
the RPV.  
 
Table 1: Comparison of Average Temperatures at Level 4 
Tavg, 
oC Time 24 s 28 s 32 s 36 s 
Experiment 56.98  41.04 25.19 21.96 
51.82  49.64 21.95  18.17 1st Order 
9.0 % 20.9 % 12.9 % 17.3 % 
51.31  48.23  24.11 18.66  2nd Order 
9.9 % 17.5 % 4.2 % 15.0 % 
52.63  35.75  26.92  22.32  Buoyancy 
7.6 % 12.9 % 6.9 % 1.6 % 
 
The experimental circumferentially averaged temperatures, 
Tavg, are compared with the calculated results 24, 28, 32, and 36 
s into the simulation. The third row shows the averaged tempe-
ratures calculated with first order accurate schemes. The ma-
ximum difference to the experiment is 20.9 %. The differences 
to the data are reduced to a maximum of 12.9 % by application 
of second order accurate schemes and by using variable density 
and buoyancy models, as shown in rows four and five of Table 
1, respectively. 
 
Test Case B 
In Test Case B, a cold-water slug is injected into the water-
filled system. This experiment is closer to the reality of a de-
boration incident than Test Case A. Initially the coolant in the 
primary system is at a temperature of 69 oC. The minimum tem-
perature of the de-borated slug is 15 oC. The transient mass flow 
rate and temperature distribution at the inlet of CL A1 is shown 
in Fig. 4. The pressure drop across the reactor core is set to 
2000 Pa. 
Calculations are performed with the optimised numerical 
and physical models of Test Case A. Figure 5 shows the tem-
perature distribution in the DC, 20 s after start of the transient. 
It displays three-dimensional effects due to the non-symmetrical 
injection of the de-borated water plug. At the entrance of the 
DC, cold water flows both in the downward and in the circum-
ferential direction. Increased temperatures appear where the DC 3 Copyright © #### by ASME 
 Copyright © 2002 by ASME 
se: http://www.asme.org/about-asme/terms-of-use
Dowwidth increases. These are caused by local recirculation due to 
the geometric discontinuity. After 20 s cold water has already 
reached the lower plenum where strong recirculation zones 
develop. The circumferential, local temperature distribution on 
level 4 is shown in Fig. 6. In the experiment and in the simula-
tion the flow separates and cold water flows down on the left 
and right side of the inlet region. After 30 s, the injected water 
has almost recovered its initial temperature of 69 oC, see Fig. 7. 
On level 4, the temperature is still lower than at the inlet. There 
is strong mixing in the lower part of the vessel. The 
corresponding circumferential temperature on level 4 is shown 
in Fig. 8. The strong temperature gradients have disappeared and 
the fluid is well mixed. After 40 s, the DC has filled up with hot 
water see Fig. 9. Only in the core region, at the outlet, some 
colder water remains. The detailed comparison on level 4 in Fig. 
10 shows good agreement between measurements and data. 
 
CONCLUSIONS AND OUTLOOK 
The paper describes numerical simulations of boron mixing 
transients in a pressurised water reactor. The test cases are the 
ISP 43 experiments conducted at University of Maryland 
College Park. The simulations were performed with the CFX-
TASCflow software, employing three-dimensional, averaged 
conservation equations for mass, momentum and energy in 
combination with a two-equation turbulence models. 
The transient calculations described in this paper were 
conducted with a grid consisting of 470,000 hexahedral 
0
1
2
3
4
5
6
7
8
9
10
0 50 100 150 200
time (s)
flo
w
 r
at
e 
(l/
s)
0
10
20
30
40
50
60
70
tem
perature (deg. C
)
 
Figure 4: Inlet Temperature and Mass Flow Rate  
4 
 
nloaded From: https://proceedings.asmedigitalcollection.asme.org on 06/29/2019 Terms of Uselements. The results show very satisfactory agreement with 
measured temperatures at different measurement locations. It 
therefore appears that the essential three-dimensional flow 
structures are captured by CFX-TASCflow and that the software 
is well suited to studying boron injection scenarios or geometric 
variations of the reactor. 
Future work will be concerned with quality assurance of 
the results, i.e. further quantification of solution errors by space 
and time wise grid refinement, investigation of the influence of 
uncertainties arising from inlet and outlet boundary conditions, 
from the reactor core model, and from different turbulence and 
near-wall models. This work will necessitate the consequential 
use of parallel computers to restrict and confine the required 
calculation times.  
 
ACKNOWLEDGMENTS 
The author would like to acknowledge the support of the 
German Federal Ministry BMWi under contract INT 9113. She 
would also like to thank Holger Grotjans from CFX Germany 
for help in grid generation and Georg Scheuerer and John Stokes 
of CFX Germany for discussions and suggestions during the 
course of this work.  
 
REFERENCES 
 
[1] Gavrilas, M., Gavelli, F., Garbe, C., Parsely, E., Tafre-
shi, A., 1996, ‘Boron-Mixing Tests in the UMCP 2×4 Loop 
Facility’, Report UMCP-DMNE-NEP-TH001. 
 
[2] Gavrilas, M., Kiger, K., 2000, ‘OECD/CSNI ISP Nr. 43 
Rapid Boron-Dilution Transient Test for Code Verification’, 
NEA/CSNI/R(2000)22. 
 
[3] Launder, B.E., Spalding, D.B., 1974, ‘The Numerical 
Computation of Turbulent Flows’, Comp. Meth. Appl. Mech. 
Eng., Vol. 3, pp. 269 – 289. 
 
[4] Raithby, G. D., 1976, “Skew-Upstream Differencing 
Schemes for Nearly-Steady Problems Involving Fluid Flow”, 
Comp. Meth. Appl. Mech. Eng., Vol. 9, pp. 153 – 164. 
 
[5] Raw, M.J., 1996, ‘Robustness of Coupled Algebraic 
Multigrid for the Navier-Stokes Equations’, AIAA-Paper 96-
0297. 4 Copyright © #### by ASME 
Copyright © 2002 by ASME 
e: http://www.asme.org/about-asme/terms-of-use
Do 
 
Figure 5: 3D Temperature Distribution, Time = 20 s 
 
Figure 7: 3D Temperature Distribution, Time = 30 s  5 
 
 
5 
 
wnloaded From: https://proceedings.asmedigitalcollection.asme.org on 06/29/2019 Terms of Use: http://w10
20
30
40
50
60
70
80
0 30 60 90 120 150 180 210 240 270 300 330 360
Degrees from CLA1 
T
em
pe
ra
tu
re
, C
20s
GRS_20s
Figure 6: Local Temperature on Level 4, Time = 20 s 
10
20
30
40
50
60
70
80
0 30 60 90 120 150 180 210 240 270 300 330 360
Degrees from CLA1 
Te
m
pe
ra
tu
re
, C
30s
GRS_30s
Figure 8: Local Temperature on Level 4, Time = 30 s 
 
Copyright © #### by ASME 
Copyright © 2002 by ASME 
ww.asme.org/about-asme/terms-of-use
Dow 
Figure 9: Temperature Distribution, Time = 40 s  6 
6 
 
nloaded From: https://proceedings.asmedigitalcollection.asme.org on 06/29/2019 Terms of Use: htt10
20
30
40
50
60
70
80
0 30 60 90 120 150 180 210 240 270 300 330 360
Degrees from CLA1 
T
em
pe
ra
tu
re
, C
40s
GRS_40s
Figure 10: Local Temperature on Level 4, time = 40 sCopyright © #### by ASME 
Copyright © 2002 by ASME 
p://www.asme.org/about-asme/terms-of-use


FEDSM2002-31407 SIMULATION OF OECD/NEA INTERNATIONAL STANDARD PROBLEM NO. 43 ON BORON MIXING TRANSIENTS IN A PRESSURIZED WATER REACTOR

http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=F2A133033641D83532D8E857F642C2B1?doi=10.1.1.1077.6750&rep=rep1&type=pdf

FEDSM2002-31407 SIMULATION OF OECD/NEA INTERNATIONAL STANDARD PROBLEM NO. 43 ON BORON MIXING TRANSIENTS IN A PRESSURIZED WATER REACTOR

Abstract

Similar works

Full text

Available Versions

CiteSeerX