4 Integration and testing of SUBCHANFLOW in the NURESIM platform
4.2 Testing of the SUBCHANFLOW integration in the NURESIM platform
To demonstrate the functionality of SCF inside the NURESIM platform, different problems related to mini-cores consisting of PWR fuel assemblies were selected to be simulated with SCF using both the fluid centered and rod centered sub-channel approach since the neutronic nodalization at pin level (rod centered) differs from the traditional sub-channel nodalization. The need for having two types of meshes derive from the spatial discretization implemented in the N and TH and the treatment of feed- backs inside the platform. The first step was to verify the need to have two meshes instead of one (rod and coolant centered). If SCF is able to obtain accurate results while implementing rod centered sub- channels in a reasonable amount of time, then there is no need to have two different meshes. Although some studies were performed in the past [Espiel01], it was still uncertain the advantages or disad- vantages of this type of modeling. For this purely TH study four different pin clusters were modeled (3x3 rods and eleven axial levels). All of them contained the same number of fuel rods (eight heated rods and one instrumentation rod), same operating conditions, thermo-physical properties and power distribution (as seen in Table 4 and Fig 12).
Table 4. Normalized axial power distribution for the (3x3) pin cluster model.
Axial level 0 1 2 3 4 5 6 7 8 9 10
power 0.5 0.6 0.7 0.8 0.9 1.0 0.9 0.8 0.7 0.6 0.5
Fig 12. Normalized radial power distribution for the (3x3) pin cluster model (top view). 0.95 0.95 0.95
0.95 0.00 0.95 0.95 0.95 0.95
The only difference between the models is the number of sub-channels in the pin cluster and their spa- tial arrangement, as seen in Fig. 13.
Fig. 13. Study of different sub-channel discretizations implemented in four models.
After running the stand alone steady state SCF simulation with a cross flow friction factor of 0.7 it was noted that rod and coolant temperatures did not suffered drastic deviations on the temperature profile between each other, leading to a maximum fuel rod centre line temperature (TCL) difference of T = 0.99 K (between 1st model and 4th model). Selected parameters which support the predictions with these models are shown in Appendix C, Fig. 73 and Fig. 74. The biggest difference however appears when revising the convergence of each solution. It can be noted that the coolant centered sub-channel model (3rd) converges faster than the other models; after nineteen iterations compared to twenty-four for the 1st model, thirty-two for the 2nd model (rod centered discretization) and thirty-nine for the 4th model. The flow error (defined in Chapter 3.2.1) predicted by SCF vs. iteration number for these four models is shown in Fig. 14.
In addition, a mini-core consisting of a 3x3 FAs is simulated with SCF using two different sub- channel radial discretizations for the TH domain: one is rod centered and the other is coolant centered. Recall that feedbacks inside SALOME are exchanged between the N field and the TH field by mesh superposition. In this approach, the values of each field are stored in a one dimensional array of size 6480 for a coolant centered discretization (this value is obtained by multiplying the number of sub- channels in one plane with the number of axial levels, e.g. (18x18) x 20 = 6480). In this array, the 6480 values of the power distributions, moderator temperature/density, or fuel temperature are stored. But the neutronic mesh will have 17x17 cells in one radial plane, which differs from the 18x18 sub- channels in one radial plane of the TH domain. Hence any mesh superposition of the N and TH mesh- es will fail since there are more TH meshing elements than N ones.
Difficulties are found when filling out the Doppler temperature field in SALOME since now the TH mesh (18x18 = 324 values in one plane) is filled out with the number of rods (17x17 = 289 values in one plane) corresponding to the Doppler temperature. The fields are initialized to zero, which means that the field corresponding to the Doppler will have the “real” temperature for the first 289 values of the array, but the remaining thirty five values will have a temperature equal to zero Kelvin. These dif- ferences are reflected while exchanging the parameters, when the N code encounters very strong tem- perature discontinuities in radial and axial directions, leading to more iterations for convergence and non physical results (e.g. neighboring nodes with temperature differences of hundreds of degrees).
To avoid this, two types of meshes for the TH were developed for pin base simulations: one mesh used for the exchange of the moderator density or temperature (fluid mesh), and the other one for the ex- change of the Doppler temperature (structural mesh). To study in detail the differences that provide both meshes, a square mini-core composed of nine FAs with a 17x17 rods configuration was investi- gated with SCF. Geometrical specifications were taken from the OECD/NEA and US NRC PWR MOX/UO2 (simplify the terminology as PWR MOX/UO2) core transient benchmark [Downar06]. For this specific case a MOX type of FA and eight UO2 type FAs were implemented with a power distri- bution related to the enrichment and position of the fuel pins (no CRs were modeled and the MOX FA is surrounded by the UO2 FAs). Fig. 15 shows the normalized radial power distribution used in one quarter of the two FAs modelled (lower right corner of the assembly). The normalized axial power distribution for both types of assemblies followed a cosine shape with a maximum (unity) at half core.
Fig. 15. Normalized radial power map for 1/4 of a PBP FA: MOX FA (left), UO2 FA (right).
The only difference between the two mentioned models was the number of sub-channels, the neigh- boring sub-channels, distance between edge sub-channels and gap widths. All other parameters were kept constant and equal for both types of meshes, e.g. thermo physical properties, power distribution, operating conditions, geometry, convergence criteria and TH correlations. The meshes generated by SCF inside SALOME are shown in Fig. 16. Specifically, Fig. 16 ((a) and (b), coolant centered) and ((c) and (d), rod centered) illustrate clearly the difference between the two types of radial discretizations.
Fig. 16. Coolant centered mesh isometric view (a) and top view (b), and rod centered mesh isometric view (c) and top view (d).
Bundle or averaged parameters predicted by SCF for the two types of meshes were the same. Differ- ences were encountered comparing the channel and fuel rod parameters predicted by SCF using the coolant and rod centered approach. For example, with the coolant centered approach SCF underesti- mated the TCL by a maximum of ~7.0 K. On the other hand, SCF needed a simulation time (ttotal) of ttotal
Several mechanisms influence the differences encountered between both solutions, the ones discussed hereafter. Even though the gap width (S in the right hand side of eq. (3.2)) influences the heat gener- ation for each sub-channel the temperature difference between consecutive iterations during a conver- gence loop might be assumed to be small enough to significantly increase the energy for coolant cen- tered sub-channels, especially at the end of the calculation, when the flow error is reduced as seen in Fig. 14. In rod centered sub-channels this difference is bigger due to the radial discretization, where strong temperature gradients are encountered leading to more iterations for convergence. Only the direct energy release to the coolant and the energy calculated through the linear heat rate are affected through the heated perimeter, which differs between coolant centered and rod centered individual sub- channels, especially when dealing with highly heterogeneous media (presence of CR, instrumentation tubes, etc.). A similar analysis is applied to the momentum balance in the axial direction, where mix- ing is influenced partly by the axial effective velocity between consecutive iterations, as in eq. (3.4). Finally, the momentum balance in the lateral direction is sensitive not only to the gap width, but also to the distance between neighboring sub-channels as shown in the first term on the right hand side of eq. (3.5), where the effect is enlarged especially in sub-channels located at the edges.
Based on these investigations it can be stated that the coolant centered sub-channel model converges faster than the rod centered sub-channels model. In addition, the coolant centered mesh underestimates the local Doppler temperatures. In conclusion, the analysis of mini-cores based on rod centered discretizations does not exhibit strong influence on the final result, especially when modeling relative- ly homogeneous cores. Consequently the rod centre sub-channels discretizations will be used in the frame of this dissertation.