CFD STUDY ON COOLANT MIXING INSIDE VVER-440

FUEL ROD BUNDLE

Tellervo Brandt, Tuukka Lahtinen and Timo Toppila, Fortum Nuclear Services Ltd, Espoo, Finland

Contact: tellervo.brandt@fortum.com, +358 40 5425160, PO Box 100, FI-00048 Fortum

ABSTRACT In this article, we study mixing inside TVEL fuel rod bundles used in VVER-440 -type pressurized water reactors. The computational fluid dynamics (CFD) solver FLUENT 6.3 is utilized. We are interested in the flow conditions under normal operation where the flow is in one phase, the average temperature at the end of active fuel is approximately 315○C and pressure inside the reactor pressure vessel 12 MPa. Our CFD model includes a 30 degree sector of the 2.5 m long fuel rod bundle. In this article the CFD results are presented for both the first and second generation TVEL fuel assemblies, and some ways to further enhance mixing are studied. The CFD results are applied in the calibration of certain parameters of the core performance monitoring system, RESU, used in the Loviisa NPP. In this article, we present comparison between the CFD and RESU results for both the first and second generation TVEL fuel assemblies. We conclude that the changes in the geometry of the fuel assembly that have been made after the year 2000, have only a minor effect on the mixing of the coolant between the subchannels.

1. INTRODUCTION In the Loviisa 1 and 2 nuclear power plants (NPP), the subcooling margin of the hottest subchannel is monitored during normal operation. The temperature of the coolant in the hottest subchannel of the fuel assembly is limited to the saturation temperature. This limit prevents the coolant from reaching bulk boiling and, in addition, prevents excessive crud buildup caused by boiling. Coolant temperature inside the fuel assembly is affected by mixing of the flow inside the fuel rod bundle. However, in traditional isolated subchannel analysis, this mixing cannot be accounted for. In the reactor core performance monitoring system, RESU, used in the Loviisa NPP, mixing between the subchannels is included via parameters which are calibrated against computational fluid dynamics (CFD) results [2]. RESU monitors e.g. the safety margins of the nuclear fuel during normal operation. The parameters of RESU which take into account mixing between the subchannels have been calibrated against the CFD in the year 2000. After this, the orientation of the spacer grids has been changed. Previously all the spacers had the same orientation while in the present fuel assembly every second spacer is rotated by 180 degrees. In addition in the Loviisa NPP, second-generation TVEL fuel assemblies which include burnable poison have been loaded in the reactor. In the present work, we verify that the parameters of RESU are still valid after these changes. In this article, mixing inside TVEL fuel rod bundles is simulated utilizing the CFD solver FLUENT 6.3 [1]. The fluid flow is modeled as a one-phase flow using the Reynolds averaged Navier-Stokes (RANS) equations. CFD studies for coolant mixing in a VVER-440 fuel assembly have previously been reported e.g. in [3-10]. In [3,11], also experimental results for a cold fuel assembly are discussed and CFD results are validated against this data. In the present work, the analysis is repeated for the current geometry of the TVEL 4.0% and for the second generation TVEL 4.4% fuel. In addition, some ways to further enhance coolant mixing are studied. Our main interest is the temperature rise along the length of the active fuel for each subchannel.

2. GEOMETRY In VVER-440 PWR's, the fuel rod bundles are enclosed inside hexagonal shroud tubes. Each bundle includes 126 fuel rods and a central tube. A transversal section of the geometry of a 30○ sector of a bundle which in modeled in our CFD study is depicted in Figure 1. The model includes 15 fuel rods, the central tube and the by-pass channel which is located between the shroud boxes. As described in [3,6,8], the by-pass channel has a major role in the cooling of the flow inside the shroud box. A side view of the CFD model is depicted in Figure 2. In the axial direction, the length of the model is approximately 2.5 m and the active fuel and the 11 spacer grids are included. In this work, we do not model the flow in the head part of the fuel assembly.

Figure 1: CFD model. Black numbers: fuel rods. White numbers: subchannels. Top view.

Figure 2: Axial view of the CFD model.

The fuel rods are held by spacer grids whose geometry in the computational model is depicted in Figure 3. In the actual bundle, the geometry of the spacer follows a 60○ symmetry, where as in the CFD model, only a 30○ sector is modeled. Thus, there are two different 30○ sectors in the CFD model. Due to the geometry of the spacer grid, the form of the spacer within a subchannel is either the shape of an o or the shape of a y. In the case where the all the spacer grids have the same orientation, there are two types of subchannels in the spacer grid region of the fuel rod bundle. In this case, either the spacer grid geometry on the right-hand side or the left-hand side of Figure 3 is used in the computational model. When every second spacer grid is rotated by 180○, every second spacer is of the type depicted on the left-hand side of Figure 3 and every second of type on the right-hand side. This also means that y and o shaped spacer grid regions follow each other in each subchannel.

Figure 3: 30 degree sectors of the spacer grids.

3. NUMERICAL METHODS AND CFD MODELS The computational grids used in this study are structured grids consisting mostly of hexahedral grid cells. The simulations are performed as one phase, steady state Reynolds averaged Navier-Stokes (RANS) simulations. The pressure-based solver is used with the PISO pressure-correction method. Second-order spatial discretization is applied to the convective and diffusive terms of the conservation equations of momentum, energy and passive scalar. For turbulence modeling, we use the standard the Launder-Spalding k-ε model available in FLUENT 6.3. The model is applied with wall functions. Some comparisons were made with the other two-equation models available in FLUENT 6.3. However, they all predicted almost identical results [9,10]. Also the Reynolds Stress Model (RSM) available in FLUENT has been studied for this application, but the model turned out to be very sensitive to the structure of the computational grid [9,10]. In the computational model, symmetry boundary conditions are applied in the transversal direction. At the model inflow, the axial velocity is set to approx 3.3 m/s, and at the outflow, the reference pressure is fixed. The heat fluxes are prescribed on the rod walls. They represent a fuel assembly in the beginning of its cycle, located in the middle part of the reactor core. The heat fluxes are obtained using the computational codes HEXBU-3D and ELSI-1440 described in

[12,13]. The flow conditions correspond to the conditions under normal operation. The flow is in one phase, the inlet temperature is 264○C, the mass flow through an entire bundle is 24.0 kg/s and the pressure inside the reactor pressure vessel is 12 MPa. In this case, the Reynolds number is 1.3·105. The FLUENT's default values are used for turbulent Prandtl and Schmidt numbers, i.e. 0.85 and 0.7, respectively. The resolution of the computational grids used in the present work varied between 4 100 000 and 6 300 000 grid cells. The resolution on the rod walls is y+<300 and on the spacer grid walls y+<380. The computational grid is depicted in Figure 1 and Figure 4.

Figure 4: Computational grid. Top view (left). Side view (right).

4. TVEL 4.0% FUEL ASSEMBLY For TVEL 4.0% fuel assembly, three computational models were made. In two of the models, all the spacer grids had the same orientation. In one model the geometry on the left-hand side of Figure 3 was used for all the spacer grids and in another one, the geometry on the right-hand side was used. In the third model, every second spacer grid was rotated 180○ and the two spacer grid geometries followed each other. This corresponds to the fuel assembly currently used in the Loviisa NPP. In the present work, a first-year bundle located in the middle of the core was studied. This bundle has a symmetric power distribution. In Figure 6 and Figure 6, we depict the axial velocity field 1 cm and 12 cm above the spacer grid, respectively. The effect of the spacer on the velocity field vanishes quite fast which is also visible in Figure 7 where the axial velocity component is plotted in the center of two adjacent subchannels (for labeling of the subchannels, see Figure 1). This figure is from the case where every second spacer is rotated. We clearly see the velocity maxima in the middle of o-shaped spacers. In the middle of y-shaped spacers, the axial velocity is zero.

Figure 5: Axial velocity field 1 cm above the spacer grid.

Figure 6: Axial velocity field 12 cm above the spacer grid.

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Figure 7: Axial profile of axial velocity component in the middle of two adjacent subchannels. Every second spacer grid is rotated by 180○. In Figure 8, we depict the temperature distribution at the end of active fuel. The location of the hottest subchannel is affected by the power profiles of the fuel rods, the distance from the by-pass channel and by the shape of the spacer grids. To study the effect of these three factors, the same simulation was repeated with all the three models mentioned in the beginning of this section. In the case where all the spacers have the same orientation and the geometry on the right-hand side of Figure 3 is used, the hottest subchannel is number 16. (For labeling of the subchannels, see Figure 1.) There the mass-flow-weighted average temperature over the subchannel cross-sectional area is 316○C at the end of active fuel. This subchannel has a direct contact with the cold subchannels next to the by-pass channel but on the other hand, it has y shaped spacer grid regions. In the present work, it turned out that the y-shaped spacers generally result to a higher temperature at the end of active fuel. When the same simulation is performed with the spacers having the shape depicted on the left-hand side of Figure 3, the hottest subchannel is the number 17 (318○C) which now has y shaped spacers. This subchannel is not directly cooled by the by-pass channel, and thus the obtained temperature rise is larger than with the other computational model. We can thus conclude that the shape of the spacer has a major effect on the location of the hottest subchannel.

Finally, the simulation was performed for the case where every second spacer is rotated which corresponds to the current TVEL-40 fuel assembly. In this case, the two types of spacer grid geometries follow each other, and the choice of the spacer grid geometry does not increase uncertainty of the CFD results. As expected, the situation is between the two cases discussed above. Here, the hottest subchannel is the number 17 (317○C).

Figure 8: Temperature field at the end of active fuel. All the spacer grids have the same orientation.

Mixing in the fuel rod bundle was studied by injecting a passive scalar into the flow field in the inlet of the subchannel shown in Figure 9. There the concentration in this subchannel is 1. The concentration of the scalar at the end of active fuel is depicted in Figure 10. Note that the scale is different in the two figures. We can see that the scalar is mainly spread to the neighboring subchannels, and at the fuel exit, about 30% of the scalar is still in its original subchannel. This result is the same regardless of the orientation of the spacer grids.

Figure 9: Concentration of a passive scalar at the inlet of the model.

Figure 10: Concentration of a passive scalar at the end of active fuel.

5. SECOND-GENERATION TVEL 4.4% FUEL ASSEMBLY In the TVEL 4.4% fuel rod bundle, there are six rods which include gadolinium as burnable poison. In Figure 1, the rod number 5 is the gadolinium rod. In addition when compared to the TVEL 4.0% fuel assembly, there are some changes in the position and the height of the spacer grids. However, according to our CFD studies, the main changes in the flow and temperature fields are caused by the gadolinium and the changes in the power profiles of the fuel rods. In the present work a bundle located in the middle of the core having a symmetric power distribution was studied. The bundle is in the same position in the core as the one studied for the TVEL 4.0% assembly in the previous section. The simulation was repeated both in the beginning and in the end of the cycle. In this case, every second spacer grid was rotated as in the actual second-generation fuel assembly. Temperature field at the end of active fuel for a bundle in the beginning of its cycle is depicted in Figure 11 and for the same bundle in the end of its cycle in Figure 12. The rod number 5 which includes gadolinium has a lower heat flux in the beginning of the cycle. This is clearly visible in the low temperature in subchannels 11, 16 and 17. For the labeling of the subchannels, see Figure 1. As the burn-up of the gadolinium increases, the heat flux of the rod 5 increases and the temperature distribution changes. In the end of the cycle, the location of the hottest subchannel is similar to a fuel with no burnable poison.

Figure 11: Temperature (in Celsius) at the end of active fuel. Beginning of cycle.

Figure 12: Temperature (in Celsius) at the end of active fuel. End of cycle.

In the beginning of the cycle, the hottest subchannels for the studied bundle are the subchannels 3, 19 and 21 having the mass-flow-weighted average temperature of 317○C at the end of active fuel. When compared to the TVEL 4.0% fuel assembly, the location of the hottest subchannel is changed, but the temperature is almost the same. In the end of the cycle, the hottest subchannels are the subchannels 17, 19 and 21 which is similar to the TVEL 4.0% fuel assembly. Now, the maximum mass-flow-weighted average temperature over the subchannel cross-sectional area is approx 315○C at the end of active fuel. In Figure 13, axial distribution of the temperature in the middle of two adjacent subchannels 17 and 18 is plotted for a bundle in the beginning of its cycle. Here, every second spacer is rotated by 180○, and the y- and o-shaped spacer grid regions follow each other. Subchannel 17 is located next to the gadolinium rod and we see a clear difference in the temperature to subchannel 18.

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Figure 13: Axial temperature profiles in the middle of two subchannels. Begininng of cycle.

In Figure 14, the corresponding temperature profiles are depicted in the end of the cycle. As the differences in the heat fluxes between the rods decrease, also the temperatures in the adjacent subchannels become almost identical. We can see small differences between the temperatures in the two adjacent subchannels. This is caused by the different shapes of the spacer grids. When the subchannel 17 has a y-shaped spacer grid region, the subchannel 18 has an o-shaped one and vice versa. As we saw in the previous section, the temperature tends to rise more in the subchannels with the y-shaped spacer grid regions.

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Figure 14: Axial temperature profiles in the middle of two subchannels. End of cycle.

6. SOME WAYS TO ENHANCE COOLANT MIXING As we saw in the previous sections, the hottest subchannels are typically located on the second column from the shroud box. To enhance mixing in this area, we included guiding vanes on the edges of the spacer grids of our TVEL 4.0% computational model. The vanes are depicted on the edge of the 30 degree model (1/12 of the spacer) in Figure 15. The height of a guiding vane is 5 mm and it is set to the angle of 20○ with respect to the vertical plane. We studied two types of geometries. In the first one, we had all the three guiding vanes shown in the left-hand side of Figure 15, and in the second one, the middle vane was removed as in the figure on the right-hand side. This means that in the whole spacer grid, there are six or four guiding vanes on each side of the hexagonal grid.

Figure 15: Geometry of the 30 degree sector of the spacer grid with six (left) and four (right) guiding vanes on the outer edge. The axial velocity field from the case with no guiding vanes was already plotted in Figure 6. The axial velocity fields from the cases with six and four guiding vanes are depicted in Figure 16, Figure 17, respectively. These plots are from the end of active fuel which is approx 43 cm above the 10th spacer grid. Vanes affect the axial velocity only in the subchannels closest to the shroud box. However, their effect remains in the flow field for a longer axial length than that of the spacer grid. With four guiding vanes, the velocity profile is clearly more distorted than with six guiding vanes. Including a guiding vane in all the subchannels on the boundary actually restrains the rotation of the flow and thus diminishes mixing of the coolant.

Figure 16: Axial velocity field. Six guiding vanes on each edge on the spacer grid.

Figure 17: Axial velocity field. Four guiding vanes on each edge on the spacer grid.

Spreading of a passive scalar from the same subchannel as used in the previous section (see Figure 10), is depicted in Figure 18, Figure 19 for six and four and four vanes, respectively. In the case with six vanes, 20% of the scalar remains in its original subchannel at the fuel exit while with four vanes, this concentration is only 8%.

Figure 18: Concentration of a passive scalar at the end of active fuel. Geometry with six guiding vanes.

Figure 19: Concentration of a passive scalar at the end of active fuel. Geometry with four guiding vanes.

The enhanced mixing is also visible in Figure 20 and Figure 21 where we have the temperature field at the end of active fuel. With six guiding vanes, the maximum mass-averaged temperature in the hottest subchannel is reduced by 2○C and with four guiding vanes by 7○C.

Figure 20: Temperature at the end of active fuel. Geometry with six guiding vanes.

Figure 21: Temperature at the end of active fuel. Geometry with four guiding vanes.

7. COMPARISON TO THE RESU RESULTS The parameters which take into account the mixing between the subchannels in the RESU reactor core performance monitoring system, were previously calibrated against CFD results in the year 2000. To assure that the parameters are valid also for the new geometry of the TVEL 4.0% fuel assembly and for the second-generation fuel TVEL 4.4%, a comparison between the RESU results and the present CFD results were made. To compare the RESU and CFD results, the difference in the mass-flow-weighted average temperature at the end of active fuel between the two results was evaluated for each subchannel. This quantity is depicted in Figure 22 for the current TVEL 4.0% fuel assembly. The largest difference occurs in the subchannel next to the central tube. This is caused by the modeling of the flow inside the central tube in the CFD model. In the TVEL 4.0% fuel bundle, the next largest difference is in the subchannel 16, 1.4○C, and otherwise, the difference between the two codes is less than 1○C. On average, the temperature is higher in the CFD than in the RESU results. However, since the power of the fuel bundles and the mass flow are the same in both simulations and energy is conserved, the average temperature over the entire bundle should also be the same in both simulations. The obtained average difference is probably caused by small differences in the material properties of the codes, and the CFD results are slightly biased. In Figure 23 and Figure 24 the comparison between the RESU and CFD results are presented for the TVEL 4.4% fuel in the beginning and in the end of the cycle, respectively. For the TVEL 4.4% fuel rod bundle, the difference between the RESU and CFD results is even smaller than for the TVEL 4.0% fuel. We can thus conclude that the mixing parameters of RESU do not require re-calibration for the second-generation fuel. In addition, to the bundles located in the middle of the core and having a symmetric power distribution, some bundles located near the edge of the core were studied. In these cases with non-symmetric power distribution, the hottest 30○ sector was simulated with the CFD model. An example of this type of study is given in Figure 25. Again we see that the difference between the two codes is fairly small.

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TVEL 4,0 % TPL, A14 @ BOCFLUENT: A14_rot sektori p1Tin = 264 degC, G=7608 kg/s, SG=1.071

Figure 22: Comparison between RESU and CFD results. TVEL 4.0%. Symmetric power distribution.

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RESU Tout (degC)FLUENT Tout (degC)abs. dev. (degC)

TVEL 4,4 % TPL, A14 @ BOCFLUENT: A14_rot sektori p3Tin = 264 degC, G=7608 kg/s, SG=1.071

Figure 23: Comparison between RESU and CFD, TVEL 4.4% beginning of cycle.

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RESU Tout (degC)FLUENT Tout (degC)abs. dev. (degC)

TVEL 4,4 % TPL, A14 @ 200 fpdFLUENT: A14_rot sektori p3Tin = 264 degC, G=7608 kg/s, SG=1.071

Figure 24: Comparison between RESU and CFD, TVEL 4.4% end of cycle.

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291 293 303 303 300 299 297 296 294 292 283 281

290 292 301 301 299 298 296 294 284 282

289 290 300 300 298 296 285 282

288 289 299 298 286 284

287 289 288 285

288 287

140

144 128

151 129 118

158 135 120 111

166 141 124 112 105

176 149 130 116 106 101

189 157 137 122 110 100 100

167 145 129 116 104 97

183 153 136 123 110 99 99

164 143 130 117 104 97

181 151 136 127 111 100 99

163 143 134 121 104 97

180 151 137 0 112 100 100

162 143 134 122 105 98

181 151 137 128 111 100 101

164 143 131 118 105 99

182 153 137 124 111 101 102

166 145 130 118 106 100

187 156 138 124 112 104 103

174 148 132 119 109 105

165 142 126 115 109

157 136 123 115

151 132 122

145 131

142

287 RESU Tout (degC)

142 lhr ave (W/cm)

296.2294.02.2

299.4299.5−0.1

301.2301.4−0.2

302.4302.7−0.3

305.6305.9−0.3

307.5308.2−0.7

292.0292.7−0.7

299.9300.2−0.3

300.7301.0−0.3

303.1303.3−0.2

304.7305.1−0.4

306.9307.5−0.6

294.6294.7−0.1

301.2301.4−0.2

302.5302.7−0.2

305.7306.0−0.3

307.6308.3−0.7

292.1292.00.1

303.3303.5−0.2

305.0305.3−0.3

307.2307.5−0.3

294.8294.30.5

306.2306.5−0.3

308.2308.8−0.6

292.5293.1−0.6

307.8309.0−1.2

295.7296.3−0.6

294.4294.6−0.2

0 137 151 180

134 143 163

136 151 181

143 164

153 183

167

189

294.4294.6−0.2

RESU Tout (degC)FLUENT Tout (degC)abs. dev. (degC)

TVEL 4,0 % TPL, A18 @ BOCFLUENT: A18_rot sektori m3Tin = 264 degC, G=7608 kg/s, SG=1.071

Figure 25: Comparison between RESU and CFD. TVEL 4.0%. A bundle located near the edge of the core.

8. CONCLUSIONS In this paper, we have studied the turbulent flow inside the TVEL fuel rod bundles used in the Loviisa NPP. The main focus of the paper was the temperature change of the coolant along the length of the active fuel. The CFD models were made for the present TVEL 4.0% and TVEL 4.4% fuel assemblies. It turned out that the rotation of every second spacer grid has some effect on the coolant temperature. It mainly evens out the temperature differences between the subchannels. However, the effect on e.g. mixing of a passive scalar was rather small. In the second-generation fuel assembly, the power profiles of the fuel rods differ from the TVEL 4.0% fuel assembly especially in the beginning of the cycle. As can be expected, this affects the position of the hottest subchannels. In the end of the cycle, the situation is similar as with the TVEL 4.0% fuel. In addition, a possibility to enhance mixing of the coolant by including guiding vanes on the edges of the spacer was studied. Based on the temperature fields and spreading of a passive scalar, we propose that including four guiding vanes on each edge of the current spacer grids would reduce the temperature of the hottest subchannels of the bundle. Finally, the CFD results were compared to the results of the RESU core performance monitoring system. The aim of the present work was to assure that the parameters that take into account the mixing between the subchannels are still valid for the present geometry of the TVEL 4.0% fuel and for the second-generation TVEL 4.4% fuel. We can conclude that rotation of the spacers or the changes in the power profiles have only a minor effect on the mixing between the subchannels. Thus, the parameters of RESU do not require a new calibration.

REFERENCES [1] FLUENT 6.3 Documentation, User’s guide, Fluent inc, 2007. [2] Antila, M. and Kuusisto, J., Core design and operating experience using new fuel types at uprated power in Loviisa NPP, In 14th AER Symposium on VVER Reactor Physics and Reactor Safety, Espoo, Finland & Baltic Sea Cruise to Stockholm, September 13-17, 2004. [3] Lestinen V. and Gango, P., Experimental and numerical studies of the flow field characterictics of VVER-440 fuel assembly, In 9th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-9), San Francisco, USA, October 3-9, 1999. San Francisco, CA, USA 1999. [4] Rautaheimo, P., Salminen, E, Siikonen, T. and Hyvärinen, J., Turbulent mixing between VVER-440 fuel bundle subchannels: a CFD study, In 9th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-9), San Francisco, USA, October 3-9, 1999. San Francisco, CA, USA 1999.

[5] Aszodi, A. and Legradi, G., Detailed analysis of coolant mixing in VVER-440 fuel assemblies with the code CFX-5.5, In The 10th International Topical Meeting on Nuclear reactor Thermal Hydraulics (NURETH-10), Seoul, Korea, October 5-9 2003. [6] Lestinen V. and T. Toppila, CFD studies on coolant flow conditions inside a VVER-440 fuel assembly, In 3rd Finnish-Hungarian Seminar on VVER-440 Fuel Operational Experience and Prospect for Development, Vantaa, Finland, 19. - 20. October 2004. [7] Toth S. and Aszodi A., Analysis of mixing processes in VVER-440 rod bundle with RANS method, In AER, Yalta, Crimea, Ukraine, 24.-29. September 2007. [8] Toppila, T. and Lestinen, V., Simulation of coolant flow inside the VVER-440 fuel assembly and assembly top nozzle using CFD methods, In Safety Assurance of NPP with WWER, Fsue Edo Gidropress, 29. May - 1. July 2007 [9] Brandt, T. and Toppila T., CFD study on mixing in VVER-440 fuel rod bundle with guiding vanes in spacer grids, In Proceedings of the 17th International Conference on Nuclear Engineering (ICONE17) , Brussels, Belgium, July 12-16, 2009 [10] Brandt, T. and Toppila T., Ways to enhance mixing inside VVER-440 fuel rod bundle, In Workshop on Nuclear Fuel Assembly Modelling and Experiments (NuFAME), KTH, Sweden, July 9-10 2009 [11] Lestinen, V., Experimental and numerical studies of the flow field characteristics of VVER-440 fuel assembly, Master´s thesis, Department of Energy Technology, Lappeenranta University of Technology, 1999. [12] Kaloinen, E., New version of the HEXBU-3D code, In II Symposium of AER, Paks, 21-26 September 1992. [13] Kuusisto, J., Antila M. and Siltanen, P., Comparison of ELSI-1440 calculations with measured pinwise power distributions in the Armenian-1 experimental core, In IV Symposium of AER, Sozopol, Bulgaria, 10-14 October 1994.