NUCLEAR SCIENCE AND ENGINEERING: 177, 141–155 (2014)
Examination of Separate-Effect and Integral Phenomena Within a Grid Spacer with Mixing Vanes: Results for the MATiS-H OECD/NEA Benchmark Exercise A. Rashkovan, D. McClure, and D. R. Novog* McMaster University Hamilton, Ontario, Canada Received January 11, 2013 Accepted August 10, 2013 http://dx.doi.org/10.13182/NSE13-4
Abstract – Grid spacers within nuclear fuel assemblies play a critical role in fuel performance and contribute to safety margins by enhancing the margin to the critical heat flux. The Organisation for Economic Co-operation and Development/Nuclear Energy Agency has organized a computational benchmark wherein the prediction of flows and turbulence downstream of a mixing-type grid spacer are examined. Studies performed by McMaster University using STAR-CCMz for the final submission to this MATiS-H blind benchmark exercise related to inter-subchannel mixing and turbulence are presented in this paper. The rationale behind the choice of the computational scheme along with comparisons of the submitted results to the experiments is reported. The goal at the outset of the study was to obtain a reasonably accurate solution with a minimum number of nodes and appropriate turbulence models such that the results would be relevant for engineering applications that include property variations and heat transfer. As such, advanced modeling methods such as large eddy simulation and unsteady Reynolds-averaged Navier-Stokes (URANS) were not included within the scope of the models tested. However, URANS was used to study some specific separate-effect flow features within the grid spacer, and these tests were compared to their steady counterparts. A comprehensive separate-effect study was performed first in order to finalize the computational scheme for the submission. Several partial geometries were studied for steady and unsteady behavior as well as for mesh sensitivity, turbulence, and wall modeling effects. A series of successively more complex simulations, sometimes involving unsteady modeling, was performed up to and including a study of similar 5|5 rod bundle geometry reported in the literature. The final submission results are presented in the paper and are compared with the benchmark data that have recently been released.
I. INTRODUCTION
pressure and temperature gradients, flow, and turbulence generation inside fuel bundles and in safety and licensing applications related to moderator flow and temperature distributions. CFD applications continue to increase in the nuclear safety field. In the light water reactor (LWR) and heavy water reactor communities there are a variety of safety issues where application of CFD is expected to provide insight and assist in closing the issues. Prediction of subchannel flows, even in isothermal conditions, is very challenging. Complicated flow structures, mixing in the gap region, and even unsteady pulsingtype behavior prove challenging for predictive models. This is made more complicated by the presence of grid spacers in
Computational fluid dynamics (CFD) is increasingly being utilized in the design and licensing of nuclear power stations. Internationally, CFD has been used to assess mixing vane spacer designs, examine boron dilution problems, investigate thermal striping–induced aging at a T-junction, and study other localized phenomena. A list of some CFD applications in the nuclear industry can be found elsewhere.1 In Canada, CFD has been applied to primary heat transport system header geometries to study *E-mail:
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LWR assemblies, or end plates in Canada deuterium uranium (CANDU) reactor fuel bundles, which cause rigorous mixing as well as greatly increased local turbulence levels. In many historical studies, subchannel thermalhydraulic codes such as COBRA or ASSERT-PV have been used to predict flow and enthalpy distributions within fuel bundles. However, these subchannel codes are typically formulated using drift-flux approaches and hence have some empiricism related to their two-phase formulations, and they also rely on empirically derived mixing coefficients, hydraulic loss factors, shear stress, and heat transfer relationships to close the system of equations. The advantage of a CFD code for subchannel predictions is that it does not rely to the same extent on geometrically dependent mixing factors and empiricisms; rather, they rely on more generally applicable turbulence models. Hence, CFD results have the potential for wider applicability, notwithstanding their needs for adequate validation and testing.1 The study of CFD code applicability and accuracy has been the topic of a large number of validation exercises as well as international benchmarks. Validation data for nonnuclear-safety–oriented applications is widely available in the open literature [see, e.g., the European Research Community on Flow, Turbulence and Combustion (ERCOFTAC) database]. II. BACKGROUND
From 2010 to 2012 the Nuclear Energy Agency (NEA) of the Organisation for Economic Co-operation and Development (OECD) organized a new benchmark to study CFD application to bundle flows and turbulence predictions. This benchmark involved taking experimental data that were hidden from all participants until after the participants had submitted their computational results. Thus, the CFD predictions were ‘‘blind’’ in this respect. The benchmark team released the specifications, geometries, and boundary conditions for these simulations with a proposed submission deadline of May 2012. After submissions, the experimental data were released, and participants were given a chance to present updated results at a closure meeting in September 2012. Flow and heat transfer through vaned spacer grids has been studied both experimentally2–8 and numerically in the past.9–11 Especially interesting are the results of particle image velocimetry studies using the refractive index–matched rod bundle thus allowing detailed velocity measurements in the regions close to the walls.12 Although most cases reported have some proprietary aspects and the exact geometry and flow conditions are not readily available, some of these results were found to be useful in the separate-effect studies performed in this work. In descending order of computational resources needed, turbulent flow modeling strategy goes from direct
numerical simulation (DNS) through large eddy simulation (LES) toward unsteady Reynolds-averaged NavierStokes (URANS) and then steady Reynolds-averaged Navier-Stokes (RANS) equations. DNS is an approach that solves numerically the equations of motion and resolves all turbulence spatial scales and timescales directly, without employing turbulence models. This would have been the method of choice, but it has long been realized that DNS is not feasible for high-Reynoldsnumber turbulent flows because of the extremely large computational resources (fine mesh, small time step, and high-order discretization scheme) required to capture turbulent motions to the smallest dynamically important scale (Kolmogorov microscale). The resources needed for DNS calculations scale with Re3. All other methods are based on the modeling of some or all turbulent motions. A widely used CFD method for engineering calculations is the solution of the RANS equations, coupled with equations to model turbulence. This method has the lowest requirements in terms of computational resources, but its accuracy depends on the geometry and flow conditions as well as the turbulence model capabilities. Moreover, RANS methods cannot resolve time-dependent motions but rather provide a time-averaged representation. URANS methods maintain the turbulence modeling used in RANS but can also resolve some time-dependent largescale motions, if such are present in the flow. URANS requires significantly larger computational resources than RANS and would produce the same solutions as RANS in flows where unsteady effects are not significant. LES solves low-pass filtered dynamic equations, so that motions with a scale smaller than a specified value [subgrid-scale (SGS) motions] are not resolved but are taken into consideration in the solution with the use of an SGS turbulence model. The filter cutoff scale must be within the inertial spectral subrange, which can be quite small in high-Reynolds-number turbulent flows, especially near walls. Thus, the mesh size and time step must be sufficiently small for LES to provide accurate results. A host of hybrid methods, combining LES and/or URANS or otherwise simplifying LES assumptions, have been introduced in an effort to maintain the accuracy of LES at a lower computational cost.13 It has to be noted that using LES for the full rod bundle geometry and including the effects of heat transfer and fluid property variations would be a prohibitively costly task for most engineering studies at this time. To illustrate, LES computations performed on clusters with the number of processors on the order of ten for subchannel geometries of Re (O) 5 104 to 105 without heat transfer require computation time on the order of months.14,15 Because of the much lower computational cost, most of the numerical studies reported on flow through full-sized rod bundle vaned spacer grids were steady RANS simulations of various twoequation models and Reynolds stress models (RSMs). While Holloway et al.10 used Fluent and found that the shear NUCLEAR SCIENCE AND ENGINEERING
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stress transport (SST) k-v model with all-yz wall treatment resulted in the closest match with experiment compared with the RSM and realizable k-e models, Conner et al.11 used STAR-CD and found that the RNG k-e model with high-yz grid was better than its counterparts. In9 used the standard ke model incorporated in CFX and reported good agreement with experimental results on flow through a spacer grid with split vanes. No single model has been universally recommended in the literature for the flow through spacer grids with mixing vanes. Hence, a large number of separateeffect studies have been performed prior to simulating the MATiS-H benchmark experiment. Participants in the OECD/NEA benchmark were required to submit their solutions along with the details of the computational scheme. Of particular importance in the present work was the size of the computational mesh used in these simulations. The approach taken was to develop the most accurate solution possible with a reasonable mesh size and computational time such that the approach is suitable for use in engineering design calculations (where flow and heat transfer must be considered). That is to say, for most situations involving complex flows, heat transfer, and potentially time-dependent boundary conditions in a full nuclear rod bundle, it is still necessary to use a somewhat limited number of mesh points such that solutions can be obtained on computational clusters possessing on the order of ten processors within a matter of days. Furthermore, RANS approaches can be used to study the flow field characteristics such that subsequent analyses using LES may focus on the most salient features. Section III describes the separate-effect studies performed in order to select the best possible modeling features for the OECD/NEA blind benchmark. III. SUPPORTING STUDIES AND RESULTS
III.A. Separate-Effect Study Before performing simulations of the experiments reported on flow through spacers with mixing vanes,7,8 a number of separate-effect studies were done, as will be presented in this section. Figure 1 presents schematically the geometry of the spacer grid with the mixing vanes used in these studies. These geometries were used to study the fine detail and flow characteristics within the spacer grid region. Although the vane geometry is different from the blind benchmark, the experimental conditions and the measurement technique are similar to those supplied in the OECD/ NEA documentation. The detailed geometry description and the experimental setup can be found elsewhere.16 The results reported here were calculated using STAR-CCMz software, and all the coefficients of the models used, e.g., turbulent Prandtl numbers and other constants, remained at their default values (no attempt at tuning was performed). The verification studies mainly included mesh sensitivity simulations using transient and NUCLEAR SCIENCE AND ENGINEERING
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Fig. 1. Half of the 5|5 rod bundle used in Refs. 7 and 8.
steady-state modeling with different turbulence models and wall treatments. In particular, a large number of grid topologies and turbulence models including realizable k-e (Ref. 17), k-v (Ref. 18), SST k-v (Ref. 19), and RSM with linear pressure strain20 as well as URANS simulations have been examined. The focus of this study was on two-equation steady RANS models in accordance with the goal of minimizing simulation time. In all the studies, the flow was developed upstream of the grid region using coarse-mesh topologies. The procedure of flow development was chosen because of inadequate specification of the inlet conditions supplied by the benchmark. The partial information supplied could not be interpolated reliably enough to be used as an inlet condition attached upstream of the grid. It was found that approximately 40 Dh (hydraulic diameters) were needed for the flow development using the steady realizable k-e model with high-yz wall mesh. The geometry in such a grid spacer is very complex, as shown in Fig. 1. First, there are a large number of rods in the array with complex turbulent interactions between each of the subchannels and inter-rod gaps. Second, the rods are held in place by small centralizing buttons with approximately two buttons on each quadrant of a rod, one button at the upstream end of the grid and the other near the downstream end. Third, as flow exits the grid there are vanes at the downstream end to promote inter-subchannel mixing, enhance heat transfer, and augment the critical heat flux. Prior to simulating the vaned grid, simulations were performed with a number of simplified geometries; see Fig. 2 for the overall sequence of the separate-effect examination. Each separate-effect geometry was selected to study specific aspects of the flow field that may occur in the full geometry. For example, flow around the centralizing buttons located on the grid plates themselves was simulated with a geometry presented in Fig. 3. Finally, integrated tests against reported experimental results7,8 were performed, and then ultimately the configuration used for the benchmark was selected.
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Fig. 2. Modeling approach scheme.
flow around a single button. Hexahedral computational cells with prism boundary layers was employed throughout the study. A small computational domain allowed the study of a large number of mesh possibilities, turbulence models, and steady versus unsteady behavior. Instabilities may be similar to those appearing in flow over a cylinder with a vortex-shedding effect. These effects are present from relatively low–Reynolds number flows and persist for very high values of Reynolds number, although with varying properties. This vortex-shedding phenomenon is well studied in the unconstrained flow around circular cylinders, but little research is available on cylinders of small length within a confined space. These simulations demonstrated nonsteady flow downstream of the button. Although the geometry of the buttons was that of a cylinder confined between the convex surface of the rod and the flat walls of the grid, the resulting frequency of vortex shedding predicted by STAR-CCMz turned out to be on the same order as that expected in the classical situation, *80 Hz instead of 60 Hz, using a transient SST k-v model. For most configurations of mesh and turbulence selection, instabilities were observed in the steady-state solutions. Subsequent URANS simulations for these cases demonstrated clear vortex-shedding phenomena as expected. It has to be mentioned that the steady flow solution for the steady realizable k-e model converged, and switching to transient simulation did not cause significant instabilities. On the other hand, while steady solution of the SST k-v model appears to be unstable and not converged, its transient counterpart showed a solid basis for the vortexshedding phenomena for a number of time steps and meshes checked, giving the same, i.e., verified, shedding frequency. Figure 4 presents a snapshot of the spacer grid wall shear stress for the unsteady calculations. III.A.2. Infinite Lattice Geometry Sensitivity Study
Fig. 3. Geometry for studying flow over the centralizing buttons.
III.A.1. Centralizing Button Instability The first investigations focused on the flow disturbance caused by the centralizing buttons within the grid spacer. The reason for simulating this region separately is because of the possible instabilities of the flow over the buttons, which resemble a cylinder in cross-flow conditions. A subregion of the 5|5 region that involved one gap and two subchannels was selected for study. The mesh utilized to simulate the geometry contained approximately 100 000 nodes and was used to simulate
The next separate-effect study focused on the flow characteristics in the immediate vicinity of the vane tips. While the buttons may give rise to nonsteady flow characteristics, the subsequent flow interacts with the mixing vanes and may redistribute the downstream flow such that more steady behavior is observed. The geometry chosen for simulating flow around the vanes was that of two subchannels from an infinite bundle lattice (i.e., the effects of channel walls and finite bundle dimensions are not considered here). Translational periodicity conditions on the external gaps at the edges of the two subchannels were used to model an infinite lattice, as shown in Fig. 5. Although no finite-bundle effects in the lateral direction could be incorporated in the geometry presented in Fig. 5 (i.e., the side-wall effects in the actual bundle were not included), the domain was quite small and still represented the main features of the flow over the vaned section. The selection of this subdomain for studying the fine features of the flow allowed the examination of a very NUCLEAR SCIENCE AND ENGINEERING
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Fig. 4. Snapshot of wall shear stress in unsteady simulations: SST k-v.
large number of mesh topologies and a large number of turbulence models and solution parameters. The geometry of the vanes was made as close to the published Korea Atomic Energy Research Institute (KAERI) experiment geometry.7,8 It has to be mentioned that no information concerning the way the rods were centralized in the mentioned KAERI work is provided in Refs. 7 and 8, and the vane geometry was not given in detail. Buttons were assumed to be used as in the case of the benchmark setup; this allowed the study of the combined effects of multiple centralizing buttons and mixing vanes. While resolving the flow instability could eventually result in a more accurate flow field, such effects may need a large computational effort because of the presence of a large number of buttons and the mixing vanes. Furthermore, it was unclear whether the interaction of the instabilities
between subchannels and through the mixing vanes would destroy the coherent structures and make the downstream flow behave with pseudosteady characteristics. As an alternative to the fine-mesh approach, it was considered that a coarse mesh inside the grid and around the buttons would filter out the unsteady behavior. However, such filtering would inevitably reduce the amount of turbulence in the simulated flow field and hence distort the simulations. To study this phenomenon, two cases were considered: (a) The domain was finely meshed with all the boundary layer cells suited for the low-yz wall modeling, and (b) the exact same meshing was used downstream of the grid, but the domain upstream of the mixing vanes was meshed coarsely including the walls where high-yz mesh was applied. It was found that the coarsely meshed grid region did effectively filter out the unsteady features.
Fig. 5. Infinite sub-bundle geometry. NUCLEAR SCIENCE AND ENGINEERING
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The same infinite bundle geometry was calculated without the buttons while the whole domain including the spacer grid was meshed finely with low-yz wall boundary layer. A steady converged solution was obtained with both the realizable k-e model and the SST k-v model. It can be concluded that in the limit of the models used, the global unsteadiness of the solution can be attributed to the centralizing buttons. However, it must be recognized that the trade-off of such filtering is to dampen the turbulence in the region, and hence, it was expected that the predicted turbulence levels would be less than those in the real bundle. The infinite bundle geometry discussed above allowed numerous mesh refinement studies to be performed. Because many dominant flow features are related to the rod, button, vane, and grid plate, wall modeling in the interior of the spacer and in the vane region is expected to be important. Hence, in the present simulation the all-yz approach available in STARCCMz was adopted. This approach allowed both highyz meshes and low-yz meshes in the computational domain, and the treatment was in accordance with the mesh resolution. Hence, it was possible to use coarse wall mesh in the vicinity of the walls prior to the vanes (and near the centralizing buttons) and finely meshed walls at the vanes and downstream. Special care was taken in avoiding having yz values in the buffer region (7 v yz v 30). In the presented studies of mesh convergence, the core mesh was changed (0.25, 0.5, and 1.0 mm) while the boundary layer resolution was kept the same in order to focus on the core mesh effects. The conditions of yz on the order of either unity or 30 to 100 were met for all the simulations, thus allowing the proper use of the all-yz approach. Representative results are shown in Fig. 6.
It can be seen from Fig. 6 that a core mesh of 0.5 mm is capable of resolving the main flow features. The same conclusion can be drawn from Fig. 7, which shows streamwise vorticity profiles along with the grid for the infinite bundle with the benchmark geometry split vanes. Because of the high importance of the mesh sensitivity studies, they were repeated for the entire rod bundle geometry. The translational boundary conditions were used only for the verification studies. It is of course important for transient calculations to take special care with the influence of these conditions on the final solution as they constrain the flow structures to be totally periodic at all times. For the steady RANS simulations, no impact on the solution was predicted. III.B. Validation Study Against Experimental Results Preliminary comparisons with the published experimental studies from the same facility, i.e., full 5|5 bundle, though with a slightly different geometry7,8 from that in the benchmark, have been obtained. It has to be noted that because the exact geometry of the mixing vanes in these studies is not cited, nor is the nature of the centralizing buttons, sensitivity studies were performed for the vanes’ cutout size and shape. It was found that while the results immediately downstream of the cutouts are sensitive to the shape of the vane cutouts, other regions appeared to be almost unaffected in the limit of the models used in the present studies. Figure 8 presents the results of the steady simulations using the realizable k-e model and the RSM with a linear pressure strain model with all-yz wall treatment. It can be
Fig. 6. Mesh sensitivity studies for an infinite bundle. NUCLEAR SCIENCE AND ENGINEERING
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Fig. 7. Mesh convergence. Vorticity contours: (a) 1.0-mm core mesh, (b) 0.5-mm core mesh, and (c) 0.25-mm core mesh.
Fig. 8. Normalized lateral velocity plots at different distances from the vane tips (1 Dh, 2 Dh, 4 Dh, and 8 Dh). NUCLEAR SCIENCE AND ENGINEERING
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concluded that the main flow features are captured with the STAR-CCMz simulations (although some discrepancies exist that may be attributed to fine differences in the actual experiment to those assumed in the present studies). It can be concluded that the realizable k-e model used in the present study outperforms the RSM simulation results for the grid topology and experimental conditions studied. The streamwise vorticity contours presented in Fig. 9 also point out the general ability of both models to predict the main flow features both qualitatively and quantitatively. Nevertheless, it has to be pointed out that the comparison is somewhat advantageous for the RSM at z 5 1 Dh and for the realizable k-e model at 4 Dh downstream of the mixing vane tips. The difference is more pronounced between the modeled and the experimental results when comparing the normal Reynolds stresses of the two models with the measured values7,8—for example, see Fig. 10. Turbulent stresses for the realizable k-e model were recalculated based on the Boussinesq approximation: LUi LUj 2 {rui uj ~mt z { rkdij : 3 Lxj Lxi As can be seen in Fig. 10, the root-mean-square (rms) velocity values tend to be underpredicted by both turbulence models tested. The realizable k-e model generally predicts higher values of the normal Reynolds stresses as compared with the RSM and thus appears to be closer to the experimentally observed maximum values of both lateral and spanwise components. It has to be noted that all the trends were qualitatively the same
for the final submissions of RANS models by a number of participants in the blind benchmark.16 IV. BENCHMARK GEOMETRY SIMULATIONS AND RESULTS
IV.A. Outlet Plenum Inclusion Sensitivity One of the concerns among the participants of the benchmark study was the relatively short downstream distance from the measuring plane to the outlet plenum. In this region the geometry changes from that in the measurement plane, first in that the rod diameters decrease in the axial direction and second in that the flow passes into a large three-dimensional T-junction with three 120deg-separated outlets as shown in Fig. 11. At issue were any flow changes that may cause some deviation of the flow parameters in the measurement plane from those expected with no outlet plenum. It was understood that if the predictions showed sensitivity to outlet geometry, the final submission would necessarily require the simulation of all aspects of the geometry, which would lead to a very significant increase in the CPU requirements. To verify the possible impact of the outlet plenum on the velocity at the measurement plane, the plenum was simulated using the realizable k-e model. To accommodate such a large volume, the core mesh resolution was reduced to 1 mm in the immediate vicinity of the outlet plane and gradually increased to *2 cm far from the plane. The boundary layer mesh on the plenum walls utilized the high-yz treatment and the boundary layer mesh set at appropriate values. Figure 12 presents the
Fig. 9. Streamwise vorticity comparison for the realizable k-e model and the RSM. NUCLEAR SCIENCE AND ENGINEERING
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Fig. 10. Velocity rms values as predicted by the realizable k-e model and the RSM.
streamwise vorticity contours for both the with-plenum case and the without-plenum case at z 5 1 Dh. As can be seen in Fig. 12, there is no appreciable influence on the flow field due to the presence of the outlet plenum. This was later verified by the additional measurements provided by KAERI prior to the final submission deadline. Thus, it was decided to submit the results with finer mesh resolution but without plenum in the computational domain. The outlet boundary condition was set at constant pressure at approximately 12 Dh downstream of the mixing vane tips, i.e., 2 Dh downstream of the farthest downstream measuring plane required for submission.
Fig. 11. Outlet plenum geometry calculation domain. NUCLEAR SCIENCE AND ENGINEERING
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IV.B. Symmetric and Rotationally Periodic Boundary Condition Sensitivity Finally, some tests were performed to further reduce the computational effort of the final submission. As can be seen in Fig. 13, the geometry of the split vanes has a plane of rotational periodicity, so half of the real rod bundle can
Fig. 12. Outlet plenum impact on the simulated results: streamwise vorticity.
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Fig. 13. Partial geometry for split-vaned grid and swirlvaned grid.
be simulated. The swirl-vaned grid has quarter-bundle symmetry. Figure 14 presents comparisons of the fullgeometry and partial-geometry simulation results. While the comparison of the partial to full geometries for both the swirl-vaned case and the split-vaned case was of acceptable quality, as seen in Fig. 14, it was nevertheless decided to submit the results of the full-geometry runs because of their higher relevance to the real rod bundle problem where nonsymmetric velocity and temperature fields are expected and the partial-geometry simulation would not be appropriate.
IV.C. Final Submission Comparison with OECD/NEA–KAERI Experimental Data While the OECD/NEA organizers indicated that comparisons would be performed at four different streamwise locations and three spanwise-positioned lines, only
the results at 1 Dh and 4 Dh were considered for the final comparison at one spanwise-located line.16 The results at z 5 1 Dh and z 5 4 Dh for split-vaned grids and swirl-vaned grids are presented in Figs. 15 and 16, respectively. It can be generally concluded that the results for the split vanes fit better to the experiments than those of the swirl vanes. The average velocity profiles are overall more extreme; i.e., the maxima and minima of the profiles are overpredicted and underpredicted, respectively. The rms values are generally underpredicted near the vanes and are comparable with the measured values’ magnitudes at the far downstream location of 4 Dh. Figures 15a and 16a present additional results of split vanes for the coarser grid, 1.0-mm core mesh instead of the submitted 0.5-mm core mesh with the same boundary layer. In the case of the 1.0-mm core mesh, the computational cell number is approximately five times less than that for the submitted 0.5-mm mesh: 13 million cells instead of 60 million cells. This means that the computational time could be cut by a factor of *5. Usual calculations with 60 million cells for both split and swirl grids took *30 h of clock time per case on a computer system containing 32 processors (2-GHz x86-64 CPU) with 64 Gbytes of memory, running under Linux (Centos 5.5, kernel version 2.6.18). It is seen that using a coarser grid did not generally affect the average velocity values predicted. On the other hand, the rms values, especially close to the grid, were significantly underpredicted with the coarser mesh. In some of the cases, the average velocities were even better predicted with a coarser grid (e.g., U velocity at 4 Dh—see Fig. 15a, topleft graph), but it was by no means justified to use it as it did not satisfy the mesh convergence criteria. To obtain a more complete picture of the comparison of the rms velocity values, Fig. 17 presents the Urms maps as measured at a distance of 1 Dh from the vane tips of the split-type grid along with its submitted counterpart. The black dashed line represents the line along which the results were submitted—see the bottom-left graph in Fig. 15a.
Fig. 14. Vorticity contours for partial geometries at 1 Dh: (a) swirl quarter model, (b) swirl full geometry, (c) split half geometry, and (d) split full geometry. Subchannels presented are as shown in Fig. 13. NUCLEAR SCIENCE AND ENGINEERING
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Fig. 15. (a) Split-vane results and (b) swirl-vane results at 1 Dh: red circles 5 measured; blue line 5 submitted results; black dashed line 5 calculations with coarse core mesh (color online).
As was expected from the comparison presented in Fig. 10 with measured velocity rms values,7,8 while the locations of the minima and maxima were predicted correctly in most cases, the absolute values were underpredicted by the steady RANS model used. This may in part have been due to the approach adopted to filter the NUCLEAR SCIENCE AND ENGINEERING
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unsteady behavior caused by the centralizing buttons within the assembly. Figure 18 presents comparisons of the calculated and measured contours of streamwise vorticity. Measured values close to the rods are absent because of the experimental difficulties. It can be seen that although
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Fig. 16. (a) Split-vane results and (b) swirl-vane results at 4 Dh: red circles 5 measured; blue line 5 submitted results; black dashed line 5 calculations with coarse core mesh.
some discrepancies are present, both qualitatively and quantitatively the simulation succeeded in capturing this flow field variable. One of the important criteria for the effectiveness of the mixing-vane grid is its ability to maintain high values
of vorticity as far downstream as possible. This can be further related to the heat transfer enhancement. Participants were asked to submit the streamwise vorticity (vz) integral (circulation, C) over one subchannel area (as shown in Fig. 13) at four downstream locations: NUCLEAR SCIENCE AND ENGINEERING
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Fig. 17. Urms values at 1 Dh for the split-type grid.
Fig. 18. Vorticity contours for split vanes: comparison with experiments. (a) 1.0-Dh calculations, (b) 1.0-Dh measurements, (c) 10-Dh calculations, (d) 10-Dh measurements.
Because of the difficulties in measuring the velocity components close to the rod walls, a thin strip was excluded from the vorticity integral required for submission. The comparison of the submitted circulation values with the measured values for both grids is presented in Fig. 19b.
Lv Lu vz ~ { Lx Ly ðð : C~ vz dA subchannel
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Fig. 19. Circulation: (a) comparison with measurements and (b) absolute circulation over the bundle cross section.
As in the case of the average velocity values, the circulation was predicted better for the case of the split vanes. It can also be seen that although the higher circulation values are those for the split-vaned grid rather than for the swirl grid, its decrease with downstream distance is also higher as was predicted numerically. As can be seen from Fig. 19a, the streamwise vorticity integral (circulation) as it was defined in the benchmark specifications behaves in a nonmonotonic manner. The absolute value of the circulation could be suggested as an alternative comparison method and integrated over the entire bundle cross section: ðð C~ jvz jdA : total cross section
The results of the absolute circulation for both grids are presented in Fig. 19b. It shows a monotonic decay with streamwise distance from the mixing vanes for both swirl and split cases toward its asymptotic value of the bare rod bundle. V. CONCLUSIONS
The goal of the present study was twofold: to outline the rationale behind the calculation scheme for the final submission for the rod bundle benchmark and to present a comparison of the submitted results with the measurements of the OECD/NEA co-organized MATiS-H experiments. In general, the approach adopted involved selection of the most simplified models and meshes that could adequately capture the physics such that the lessons learned could be applied in more relevant engineering simulations that may involve heat transfer. First, the methodology for modeling turbulent flow within the grid spacer was discussed. This included the separate-effect studies that were performed on small-scale geometry domains. This allowed the use of fine-mesh
resolution and transient calculation in order to quantify the potential impact of different flow features on the final result. Based on the studies of partial geometries, large mesh sizes were used within the grid itself to filter out potentially unstable behavior caused by the positioning buttons. A fine-mesh structure was adopted in the vane tips and downstream sections. The steady realizable k-e model as incorporated in the commercial CFD STARCCMz software was employed for the final submission. The choice of the model was mainly dictated by the desire to obtain a reasonably accurate solution with a minimal number of nodes and appropriate turbulence models such that the results would be engineering relevant (i.e., capable of adding in heat transfer effects as would be needed in industrial CFD applications). The comparison of the simulations with the experimental results showed very good agreement on the vorticity and axial velocity distributions, while the rms values were significantly underpredicted. The rms results indicated that to some extent the turbulence levels were underestimated, in part because of the filtering applied to the unsteady features around the centralizing buttons. Thus, the mutual conclusion for both geometries is that most of the average velocity profiles show that their local extrema are overpredicted by the model used, perhaps resulting from the underprediction of turbulence levels. Overall, the simulations demonstrated reasonable agreement with the blind benchmark exercise results, in particular when it is recognized that the overall objective of this work was to achieve adequate results with minimal CPU effort. ACKNOWLEDGMENTS The authors would like to acknowledge the direct financial support for this work provided by the Canadian Nuclear Safety Commission and in particular J. Szymansky for his excellent insight. We would also like to acknowledge CD-ADAPCO, NUCLEAR SCIENCE AND ENGINEERING
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developer of STAR-CCMz, for its generous license support and its high-quality and responsive user support.
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NUCLEAR SCIENCE AND ENGINEERING
VOL. 177
JUNE 2014
