Calculations of Coolant Flow in a VVER-440 Fuel Bundle with the Code ANSYS CFX 10.0 Sándor Tóth, Dr. Attila Aszódi Budapest University of Technology and Economics, Institute of Nuclear Techniques Muegyetem rkp. 9, 1111 Budapest, Hungary
[email protected],
[email protected]
2. NUMERICAL MODEL DESCRIPTION
ABSTRACT
A fuel assembly of the VVER-440 type reactor consists of three parts: assembly leg, fuel bundle, and assembly head. A bundle contains 126 fuel rods arranged in a triangular configuration, the first grid, the 10 spacer grids at every 240 mm, and the central tube of the in-core neutron detectors. Considering the symmetries we studied a 60 degrees segment of the 2,420 mm long active part of a fuel pin bundle. Due to the complexity and the extent of the geometry first a 60 degrees segment of the 240 mm long part of the bundle (base geometry) was modelled. The model includes 24 fuel pins, part of the central tube, one of the spacer grids and the inner wall of the shroud (see Fig. 1.) The outer diameter of the rods is 9.1 mm, the rod pitch is 12.2 mm. The inner space of the shroud is 142 mm. The wall thickness of the shroud was neglected and the wall was modelled as thin surface. This simplification is appropriate, because the thickness of the shroud is about 2 mm and the thermal conductivity of the shroud material is relatively good.
From the aspect of planning the power upgrading of nuclear reactors - including the VVER-440 type reactor – it is essential to get to know the flow field in the fuel assembly. For this purpose we have developed models of the fuel assembly of the VVER-440 reactor using the ANSYS CFX 10.0 CFD code. At first a 240 mm long part of a 60 degrees segment of the fuel pin bundle was modelled. Implementing this model a sensitivity study on the appropriate meshing was performed. Based on the development of the above described model, further models were built: a 960 mm long part of a 60degree-segment and a full length part (2420 mm) of the fuel pin bundle segment. Calculations were run using the full length model to investigate a fuel assembly. In the calculations constant coolant properties and several turbulence models were applied. The impacts of choosing different turbulence models were in detail studied. For the investigated fuel assembly calculation was performed using the COBRA subchannel code too [2]. The results of the CFX and the COBRA calculations were compared. The results of the above-mentioned investigations are presented in this paper. 1. INTRODUCTION The power upgrading of the VVER-440 type reactors is being planned in several countries in Europe. Detailed knowledge of the coolant flow in the fuel assemblies is very important both for planning and licensing. Due to the evolution of commercial CFD codes and the growth of the computer capacities, it seems that modelling the thermohydraulic processes in fuel assemblies using CFD codes has become a real alternative. Therefore, development of a complex fuel assembly CFD model is under way in the Institute of Nuclear Techniques (NTI), Budapest University of Technology and Economics. For the model development the ANSYS CFX 10.0 code was used. The code uses the finite volume method to solve the conservation equations of mass, momentum, energy and turbulence quantities. Previously a 240 mm long 60-degree-segment model of a fuel bundle and a fuel assembly head was developed at NTI [1]. Applying the fuel bundle model the flow field, the heat transfer and the coolant mixing processes were investigated in detail. Using the head model the coolant mixing in the fuel assembly head was analyzed. Continuing this work we have developed further models of 240 mm long fuel bundle. Based on the development of the 240 mm fuel bundle model, a 960 mm long and a full active length part (2420 mm) of the fuel pin bundle were developed. Applying the former models calculations were performed using constant coolant properties and several turbulence models. Our main aim is to develop a model that is suitable to carry out accurate calculations, particularly to analyze the flow and heat transfer process in the fuel bundle of VVER-440 type reactors.
Central Tube
Outer Wall of Fuel Rods
Shroud
Spacer Grid
Fig. 1. The 240 mm long base geometry
1
The 10 mm high spacer grid is located in the centre of the model. The wall thickness of the spacer grid is 0.5 mm at the connection of the two component plates, otherwise it is 0.25 mm (Fig. 2.). In this case the thin surface approach was not used to avoid the inaccuracy. The narrow gaps between the two component plates are neglected. Due to the complexity and the dimensions of the geometry a hybrid mesh (Fig. 3.) was created using the ANSYS ICEM meshing software. The hybrid mesh consists of tetrahedral, hexahedral and prismatic volume elements. In the vicinity of the spacer grid unstructured tetrahedral mesh was applied. Inflation elements were used close to the wall to resolve the strong gradients in the boundary layer. To reduce the required computer capacity under and above the tetrahedral region prismatic elements were used, which were generated by extruding the flat elements on the bound of the tetrahedral zone. Using this method it was needless to use interfaces (in CFX it is called GGI – General Grid Interface) between tetrahedral and prism regions. The height of the prism mesh layers is grown exponentially near the tetrahedral regions. In the remaining domain there are same height prism layers (see Fig. 4.). We have performed a sensitivity study on the appropriate meshing. Four different meshes were produced: H1, H2, H3 and H4. The tetrahedral regions of models H1 and H2 are the same but the resolution of the prism mesh is different. In case of H2 the depth of the same height prism layers is half of the height used in H1. The prism mesh of models H2, H3 and H4 is identical, but the resolution of the tetrahedral grid near the spacer grid is different (see Fig. 5.). In the case of models H1, H2 and H3 four layers, in case of the model H4 three inflation layers were defined. We paid attention to the value of the y+ in order to be in the domain of the used wall function (for Scalable wall function 20 ≤ y+ ≤ 100, for automatic wall treatment y+ ≤ 200 [3]). The average y+ on the rod surfaces and the total number of the cells of the different meshes are presented in Table I.
Fig. 2. The model of the spacer grid
Outlet pout=0 Pa B
Wall q’’=840 kW/m2
A
Symmetry
Inlet vin=3.18 m/s Tin=265 °C iturb=10%, µt/µ=100 Fig. 4. Surface grid at the upper part of the symmetry plain Fig. 3. The grid of the base model
2
H1, H2
H3
different mass flow average quantities. The mass flow averages of temperature, velocity and turbulent viscosity were investigated on a plain parallel to the outlet and located 20 mm below the outlet. The results for the four different meshes are shown in TABLE I. The average temperature and velocity values agree well but the eddy viscosity is slightly different in the case of the model H4. In the case of the models H1 and H2 the pressure drop is the same along the length of the models. (The tetrahedral region of the models H1 and H2 is same, but the height of the prism mesh of model H2 is half compared to model H1). It can be seen that the pressure drop of the meshes H3 and H4 is less than the pressure drop calculated using models H1 and H2. Consequently, in terms of the outlet average temperature and velocity the resolutions of meshes H1, H2, H3 and H4 are acceptable, but considering pressure drop meshes H3 and H4 are not fine enough. Therefore the pressure distribution calculated using models H3, H4 can be only qualitatively correct. It can be seen that the pressure drop is very sensitive to the resolution of the tetrahedral mesh near the spacer grid. The effect of the resolution of the prism mesh on the pressure drop is negligible and axial resolution of the mesh H2 is acceptable. Based on the development of 240 mm long model further models of 60 degrees section and both 960 mm long and a full length part (2420 mm) of the fuel pin bundle were developed (Fig. 7.). In this phase of our work the mesh H4 was used to build the full length model since the geometry is very large and unfortunately our available computer capacity was limited. Three INTEL XEON 3000 processors and 6 Gbytes RAMs were reachable to complete the computations. (In the case of using mesh H2 the number of required cells exceeds the 21 millions.) This limit enforced us to use the mesh H4 in spite of its known deficiency. Since the meshes were generated using a mesh mirror technology the application of interfaces can be avoided. Both models consist of 24 fuel pins, the shroud and the central tube for SPN (Self Powered Neutron) detectors. The 960 mm long model includes 4 spacer grids and the full length model includes 10 spacer grids. The total number of cells for the 960 mm long model is 2,770,396. The full length model contains 6,946,090 elements. Applying the 960 mm and the full length model calculations were performed using several boundary conditions. In the case of the full length model these boundary conditions and the results are presented in the next chapters.
H4
Fig. 5. Surface grids at location “A” (see Fig. 3.)
Fig. 6. Cross sectional grid at location “B” (see Fig. 3.) TABLE I. Comparison of different meshes
Mesh H1 H2 H3 H4
Total Number of Cells 2,239,500 2,091,180 1,233,690 685,899
y+ave Tave vave ν t ave [1] [°C] [m/s] [Pas] 35.36 271 3.22 0.0118 35.37 271.01 3.22 0.0119 35.69 271.01 3.23 0.0119 60.16 271.05 3.22 0.0113
∆p [Pa] 3,835.9 3,835.1 3,551.3 3,348.4
In order to compare the meshes calculations were carried out using models H1, H2, H3, and H4. The boundary conditions were the following: velocity inlet, pressure outlet, walls and symmetries (see Fig.3.). 3.18 m/s normal velocity, 265 °C temperature, 10% turbulence intensity and 100 [1] viscosity ratio (µt/µ) were defined as an inlet boundary condition. At the outlet 0 Pa average static pressure was set. The wall of the shroud and the spacer grid are modeled as no slip adiabatic walls. At the wall of the rods no slip boundary condition with an 840 kW/m2 constants heat flux was defined. It is obvious that the used heat flux differs from the real operating conditions (the average heat flux is about 560 kW/m2, but the maximal heat flux in the core is near to this 840 kW/m2 value), the primary aim was the comparison of different meshes. In all cases the roughness of the walls was ignored. On the symmetry planes symmetry boundary condition was defined. The calculations were carried out using the k-Omega twoequation turbulence model, which is applicable to simulate a complex geometry. The results were compared by analyzing 3
3. BOUNDARY CONDITIONS
Outlet pout=0 Pa
In this phase we investigated a fuel assembly of the Paks Nuclear Power Plant that was in operation in Unit 3 during the fifteenth cycle. The boundary conditions of the calculations are based on measurements and burn up calculations [2]. According to the calculations in terms of the thermal power of fuel pins this assembly has a symmetry of 60 degrees so it was sufficient to study a 60-degree segment of the fuel assembly. The types of the boundary conditions were in accordance with the conditions of the 240 mm long model. At the lower end of the model inlet boundary condition was used. The mass flow rate of the incoming flow is 3.74 kg/s and the inlet temperature of the fluid is 265.03 °C. The turbulence boundary conditions are not known accurately, 10% turbulence intensity and 100 [1] viscosity ratio was assumed in the calculations. At the upper end of the bundle outlet condition of 0 Pa average static pressure was defined. The wall of the shroud and the walls of the spacer grids were handled as no slip adiabatic walls. In these calculations the roughness of the walls was not taken into account and smooth walls were defined. Necessarily on the symmetry plans symmetry boundary conditions were used. In the core the thermal flux changes both in radial and axial directions, therefore the wall heat flux of the pins changes as well. The effect of the axial heat flux distributions was investigated. The axial distribution of the heat flux was modeled using a polynomial of sixth-degree. This polynomial was multiplied by the power of the pins in order to obtain the heat flux distribution of the rods in the axial direction:
Wall q’’= q’’(Z)
q& p ' ' ( z ) = q& p ⋅ p( z )
(1)
When the heat flux distribution is integrated on the surface of fuel pin the power of pin is obtained:
Symmetry
q& p = ∫ q& p ' ' ( z )dA = A
H 2π
∫ ∫ q&
p
' ' ( z )rdϕdz
(2)
0 0
The pin powers used are shown in Fig. 8. and the heat flux distribution of pin No. 126 is presented in Fig. 9. The constant properties of water coolant were specified on 124 bar pressure and 287 °C temperature. For turbulence modeling the k-Omega, Shear Stress Transport (SST) two equation turbulence models with automatic near-wall treatment and SSG Reynolds stress model with Scalable wall function were used [3]. The computations were performed in steady state mode.
Inlet min=3.74 kg/s Tin=265.03 °C iturb=10%, µt/µ=100 Fig. 7. The 960 mm long and the full length fuel bundle model
Fig. 8. Thermal powers of the pins [kW] ([2]) 4
800
700
2
Heat Flux [kW/m ]
600
500
400
300
200
100
0 0
0.5
1
1.5
2
2.5
Height [m]
Fig. 9. Axial heat flux distribution of pin No. 126.
4. RESULTS AND DISCUSSION approximately 1,520-1,570 Pa using k-Omega and SST model and 1,350-1,400 Pa computed by SSG turbulence model. In the case of applying k-Omega and SST model the total pressure drop is 48-49,000 Pa, using SSG model this value is about 46,000 Pa. It must be mentioned that the mesh sensibility study showed that using the mesh H4 the pressure drop is underestimated so the results are only qualitatively reasonable. Further investigation of the pressure drop in the bundle with more accurate mesh is needed. Fig. 11. shows the mass flow average temperature along the height of the fuel bundle. At first the bulk temperature increases quickly therefore the heat flux rises rapidly too. In the middle of the model the variation of the temperature is nearly linear to the length because the heat flux changes just slightly. At the end of the bundle the temperature rises slowly because the heat flux decreases fast. In case of using kOmega, SST and SSG Reynolds stress turbulence models the results are similar. The outlet bulk temperature is 304.96 °C therefore the average increase in the coolant temperature is 39.93 °C. The increase in the coolant temperature calculated from the heat balance is 40.07 °C. The 0.35% difference can be attributed to the error of the polynomial approximation of the heat fluxes (Because of the error of the polynomial approximation the pin powers are slightly lower than the values in Fig. 8.) and to numerical error.
The pressure drop of fuel assemblies significantly influences the pressure loss of a core, therefore the required coolant pump power. Hence it is important to know accurately the pressure drop and pressure distribution of the fuel assemblies. The mesh sensitivity study proved that the mesh H4 is not fine enough to calculate the pressure drop accurately. But this examination showed as well that the axial distribution of the average pressure is qualitatively the same in case of all meshes so these results are presented too. Fig. 10. shows the calculated average static pressure at different height levels calculated using k-Omega, SST and SSG Reynolds Stress turbulence models. The average pressure distributions shown in Fig 10. contain the three elements of the pressure loss [4]: the loss caused by the spacer grids, by gravity and by the friction on the fuel rods and on the shroud. The effect of the ten spacer grids on the static pressure is clearly visible in Fig. 10. Through the spacer grids pressure drops first and than rapidly increases. The explanation of this behaviour is that the flow velocity rises in the spacer grids because of the contraction and it causes a decrease in the static pressure. Behind the spacer grids the velocity decreases rapidly and the static pressure increases to a value which is less than it was in front of the spacer grids, because spacer grids cause a friction loss and a separation loss. The pressure loss of one spacer grid is
5
Spacer Grid 1
50,000
k-Omega Model SST Model SSG Model
Average Static Pressure [Pa]
40,000
30,000
20,000
10,000
0 0
0.5
1
1.5
2
2.5
Height [m]
Fig.10. The pressure loss in the flow direction 330 Spacer Grid 1
320
Temperature [°C]
310
300
290
280
270
Cladding Average Temperature - k-Omega; SST Model Cladding Average Temperature - SSG Model Coolant Bulk Temperature - k-Omega; SST; SSG Model
260
250 0
0.5
1
1.5
2
Height [m]
Fig. 11. The bulk temperature and average cladding temperature in the flow direction
6
2.5
0.08
k-Omega Model Spacer Grid 1
0.07
SST Model
Average Turbulence Kinetic Energy [m2/s2]
SSG Model 0.06
0.05
0.04
0.03
0.02
0.01
0 0
0.5
1
1.5
2
2.5
Height [m]
Fig. 12. The average kinetic energy as a function of height 35,000
Average Heat Transfer Coefficient [W/(m2K)]
30,000
25,000
20,000
Spacer Grid 1 15,000
10,000
k-Omega; SST Model SSG Model Dittus-Boelter Correlation Dittus-Boelter Correlation + 25%
5,000
Dittus-Boelter Correlation - 25% 0 0
0.5
1
1.5
2
2.5
Height [m]
Fig. 13. The heat transfer coefficient as a function of height
Calculated by k-Omega and SST turbulence model the results are nearly the same. In Fig. 11. it can be seen that the cladding average wall temperature decreases at the spacer grid. When the coolant flows into the holes of the spacer grid the velocity and the turbulence kinetic energy grow rapidly (see Fig. 12.), therefore the conditions of heat transfer improve (see heat transfer coefficient in Fig. 13.) and the temperature of the cladding decreases suddenly.
The average temperature of the cladding, the average kinetic energy and the average heat transfer coefficient as functions of the height are shown in Figures 11., 12., and 13. The average heat transfer coefficient was calculated as:
α=
q&w ' ' Tw − Tave
(3) 7
Behind the spacer grid, the temperature of the cladding rises again first, because the average turbulence kinetic energy (Fig. 12.) decays. Therefore, the conditions of the heat transfer become worse and the heat transfer coefficient decreases. Further from the spacer gird due to the effect of the production the turbulence kinetic energy rises, therefore heat transfer coefficient increases and the temperature of the fuel rods rises only slightly or decreases. This process returns in the case of all spacer grids. The maximum of the average cladding temperature is located after the 8th spacer grid at level of 1.9 m. In case of using SSG Reynolds stress model the processes are similar but there is a great difference near the region of the spacer grid. When the coolant streams into the holes of the spacer grid the turbulence kinetic energy decays first and then it increases slightly. The turbulence kinetic energy does not increase such as in the case of SST or k-Omega model, therefore the decrease of the cladding temperature is less. The value of the turbulence kinetic energy is approximately half of the calculated by omega-models everywhere therefore the heat transfer coefficient is smaller and the cladding temperature is 2-3 °C higher. The heat transfer coefficient calculated by Dittus-Boelter approach (4) [6] is 27,570 ± 6,900 W/(m2K). (The accuracy of the correlation is ± 25%)
Nu D = 0.023 ⋅ ReD
0.8
⋅ Pr 0.4
The heat transfer coefficient computed by k-Omega and SST model agrees with this value, but in SSG model it is lower. At the end of the model a decrease of the heat transfer coefficient can be seen. The reason of this decrease is the rapidly falling heat flux of the fuel rods. The outlet temperature distribution of the coolant calculated by SST turbulence model is presented in Fig. 14. On the left the temperature distribution at the outlet plane is shown, and on the right this field is represented as a surface, where the height of the surface is proportional to the value of the temperature. It can be seen that the temperature is relatively uniform; the regions near the shroud and near the central tube are exceptions. Lower temperature regions develop in these locations because no heat enters from the direction of the adiabatic walls in the model. The temperature close to the shroud would have been even lower if the by-pass flow had been investigated too. Higher temperature region develops on the right-middle part of the outlet plane, because the power of the fuel pins is higher at this section of the model. The temperature has local maximums at the surfaces of the fuel roads in the boundary layer. The difference between the cladding temperature and the bulk temperature of the coolant is much less than in the middle height regions of the model. The explanation of the small difference is the low value of the pin heat fluxes at this level.
(4)
Fig. 14. The outlet temperature field calculated by SST model
Peaked Velocity Distribution Uniform Velocity Distribution Spacer Grid Fig. 15. The outlet w - velocity field using SST model 8
Mass flow averaged outlet temperatures of the different subchannels calculated by k-Omega, SST and SSG Reynolds Stress models are presented in Fig. 17. and the numbering of subchannels is shown in Fig 16. The lower temperature subchannels – as stated above – are next to the shroud and next to the central tube. The outlet temperature of these is lower by 10-20 °C than the temperature of the other subchannels. The difference between the outlet temperatures of other subchannels is less than 5-7 °C. In the most cases the outlet temperatures of subchannels estimated by k-Omega, SST and SSG Reynolds Stress models differ by about 0.3-0.6 °C. The maximal difference is 1.3 °C. The maximal outlet temperature of subchannels calculated by k-Omega model is 313.41 °C, by SST model is 313.27 °C and by SSG is 313.45 °C (in the all cases for the subchannel 44). Fig. 15. shows the w-component (axial component) of the outlet velocity computed by SST model. On the left the w-velocity distribution on the outlet plane is shown, and on the right the profile of the w-velocity is presented. It is visible that the spacer grids strongly affect the velocity distribution. In the subchannels that involve the small holes of spacer grids the w-velocity distribution is peaked (case ‘A’). In the other subchannels w-velocity profile is more uniform (case ‘B’). The area averaged outlet w-velocities by different subchannels are shown in Fig. 18. It can be seen that in the case ‘A’ the average velocity is higher by 10-15
percent than in the case ‘B’. Due to the higher velocity the mass flux and the turbulence kinetic energy are higher in these subchannels, therefore the conditions of the convective heat transfer are better. Discrepancies of the subchannels’ velocities calculated by the three different turbulence models are 0.01-0.02 m/s. The maximal difference is 0.033 m/s.
Fig. 16. Numbering of subchannels and pins
315 k-Omega Model SST Model SSG Model
Outlet Temperature of Subchannels [°C]
310
305
300
295
290
285 1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
Number of Subchannels
Fig. 17. The outlet average temperatures of the subchannels
9
37
39
41
43
45
47
49
3.5
k-Omega Model SST Model SSG Model
3.4
Outlet Velocity of Subchannels [m/s]
3.3 3.2 3.1 3 2.9 2.8 2.7 2.6 2.5 1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
49
Number of Subchannels
Fig. 18. The outlet average w-velocities of the subchannels
5. COMPARISON WITH COBRA The COBRA code is a widely used subchannel code for reload pattern design calculations. The code solves the conservation equations of mass, momentum and energy by applying a one dimensional finite difference scheme. The interaction between adjacent subchannels is modeled by convective and turbulent cross-flows. The calculation of the turbulent cross flow is based on the use of the so called mixing scalars. The main aim of the comparison of the CFX and the COBRA results is to verify the accuracy of the mixing scalars of COBRA model, which are applied for VVER-440 fuel assemblies in Paks NPP. Hence, calculation was performed for the studied fuel assembly. The same boundary conditions (inlet mass flow, inlet temperature, outlet pressure, pin power) were applied in both CFX and COBRA models [2]. The thermal powers of pins nodes were calculated from the heat flux (eq. 1):
q& p , n =
z nt 2π
∫ ∫ q&
p
' ' ( z )rdϕdz
The outlet average temperatures of subchannels calculated by CFX (SST model) and by COBRA code are presented in Fig. 19. It can be seen that there are some differences between CFX and COBRA results. In the results of the COBRA calculation, the maximal outlet temperature is 311.9 °C (subchannel 41), in the case of the CFX calculation this temperature is 313.27 °C (subchannel 44), and thus the difference is 1.37 °C. It can be realized that the outlet temperatures of subchannels adjacent to the central tube or to the shroud (adjacent to adiabatic walls) are higher in the COBRA results than in the CFX results. Most of the other subchannel temperatures calculated by CFX are greater than temperatures calculated by COBRA. The highest difference between the two calculations (3.59 °C) occurs in subchannel 1. In Fig. 20. the outlet mass flows of subchannels are shown. The differences are about ±4%, the maximal difference is 12.5% (subchannel 1) These results may indicate that the mixing scalar of the COBRA model is too large. Therefore, the code may overestimate the mixing between the subchannels. For further investigations more detailed model (finer mesh, consideration of temperature dependence of coolant properties) is needed.
(5)
z nb 0
In the case of COBRA calculations the temperature dependence of the coolant properties was taken into account properly. In the CFX calculations, constant coolant properties were used.
10
315 CFX (SST Model) COBRA
Outlet Temperature of Subchannels [°C]
310
305
300
295
290
285 1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
49
39
41
43
45
47
49
Number of Subchannels
Fig. 19. The outlet average temperatures of the subchannels 0.18
Outlet Mass Flow of Subchannels [kg/s]
0.16 CFX (SST Model)
0.14
COBRA
0.12
0.1
0.08
0.06
0.04
0.02
0 1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
Number of Subchannels
Fig. 20. The outlet mass flows of the subchannels
11
35
37
6. CONCLUSIONS [3] ANSYS, 2005, “ANSYS CFX-Solver, Release 10.0: Theory”
In this paper velocity, pressure and temperature distributions in a VVER-440 fuel bundle were studied. The investigations were carried out using the ANSYS CFX 10.0 commercial CFD code. Because of the complexity and the dimensions of the fuel bundle, first a 240 mm long 60degree segment model was built. Four different meshes were generated to study the adequacy of the mesh resolution. Calculations were run using different meshes with identical boundary conditions. The results of the calculations were compared to check mass flow averaged quantities. These investigations showed that the model with about 686,000 volume elements can give a good prediction for the outlet average temperature and velocity. The results also show that in terms of pressure drop this mesh is not fine enough near the spacer grids. Using the previously mentioned model a 2,420 mm long fuel bundle model was developed. The model contains 6,946,090 elements. Using this model we have investigated a fuel assembly of the Paks NPP. The boundary conditions of the calculations are based on measurements and burn up calculations. The computations were performed using the kOmega, the SST and the SSG Reynolds Stress turbulence model. The results of the three calculations were compared. The distribution of average coolant temperature was equal in the three cases. The average pressure distributions are qualitatively the same, but the average heat transfer coefficient and the average cladding temperature distribution are slightly different. The comparison with analytic calculation shows that the SST and the k-Omega model are in better agreement to heat transfer coefficient than the SSG Reynolds stress model. Outlet velocity distribution and subchannel average outlet velocity demonstrated that there was a 10-15 percent difference in mass flux among the subchannels. The temperature distribution at the outlet is more uniform except for the near adiabatic wall regions (with 10-20 ºC lower temperature). Applying the same boundary conditions calculation was carried out by COBRA subchannel code. Comparison of results of the two calculations indicates that the mixing scalar of the COBRA model could be too large. Therefore, the subchannel code may overestimate the mixing between the subchannels. For further investigations a more detailed model in needed so in the future our main aim is to develop a fuel bundle model that is suitable to calculate the thermalhydraulic processes in a fuel bundle more precisely. Therefore first the mesh of the whole length model will be refined and a sensibility study is going to be performed. The effect of changing of material properties and by-pass flow both on the flow and on the heat transfer will be investigated, too.
[4] Rautaheimo, P., Salminen, E., Siikonen, T., and Hyvärinen, J., 1999, “Turbulent Mixing Between VVER440 Fuel Bundle Subchannels: a CFD Study”, Proc. 9th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, San Francisco [5] Lestinen, V., and Gango, P., 1999, “Experimental and Numerical Studies of the Flow Field Characteristics of VVER-440 Fuel Assembly”, Proc. 9th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, San Francisco [6] Incropera, F. P., and DeWitt D. P., 2002, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, New York, 5th Edition NOMENCLATURE
A H iturb min pout p(z ) Pr Nu D q& p q& p ,n q& p ' ' ( z ) q& w ' ' ReD Tave Tin Tw y+ y + ave vave vin z nt , z nb
α ∆p ν t ave µ µt
REFERENCES [1] Aszódi, A., and Légrádi, G., 2002, “Detailed CFD Analysis of Coolant Mixing in VVER-440 Fuel Assemblies With the Code CFX 5.5”, Proc. Technical Meeting on Use of CFD Codes for Safety Assessment of Reactor Systems, Pisa, Italy [2] Szécsényi, Zs. and Beliczai, B., 2006, Personal communication from Paks NPP, Paks, Hungary 12
surface of active part of fuel pin height of active part of pin turbulence intensity inlet mass flow rate outlet pressure polynomial of sixth-degree Prandtl number Nusselt number thermal power of the ‘p’ pin thermal power of the ‘p’ pin’s ‘n’th node in COBRA model heat flux distribution of the ‘p’ pin average heat flux Reynolds number mass flow averaged temperature of coolant inlet temperature average temperature of claddings dimensionless distance from the wall average dimensionless distance from the wall mass flow averaged velocity inlet velocity axial position of top and bottom of “n”th element in COBRA model average heat transfer coefficient pressure drop mass flow averaged eddy viscosity dynamic viscosity turbulent dynamic viscosity
