Validation of CFD analysis for rod bundle flow test with vaned spacer grids

Annals of Nuclear Energy 109 (2017) 370–379

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Validation of CFD analysis for rod bundle flow test with vaned spacer grids Xi Chen ⇑, Sijia Du, Yu Zhang, Hongxing Yu, Songwei Li, Huanhuan Peng, Wei Wang, Wei Zeng Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China, No. 328, Section 1, Changshun Avenue, Shuangliu Sub-district, Chengdu, Sichuan, 610213, China

a r t i c l e

i n f o

Article history: Received 2 December 2016 Received in revised form 22 May 2017 Accepted 24 May 2017

a b s t r a c t Spacer grids with mixing vanes are generally used in fuel assemblies of Pressurized Water Reactor (PWR), which is because that mixing vanes could enhance the lateral turbulent mixing in subchannels. Thus, heat exchangements are more efficient, and the value of departure from nucleate boiling (DNB) is greatly increased. This paper presents the CFD simulation and validation of the turbulent mixing induced by spacer grid with mixing vanes in rod bundles. Experiment data used for validation came from 5
5 rod bundle test with Laser Doppler anemometry (LDA) technology, which is organized by Science and Technology on Reactor System Design Technology Laboratory. A 5
5 rod bundle with two spacer grids were used. Mean axial velocities and turbulent intensities (Wrms) were measured in the test as well as the pressure drop of spacer grids. This simulation employed the ANSYS code CFX 14.5. RANS models such as K-epsilon, RNG K-epsilon, Shear-Stress Transport (SST) K-omega and BSL Reynolds-stress turbulence model were chosen for validation. Validation results showed that RANS models were nearly adequate for prediction of mean velocities, while K-epsilon and RNG K-epsilon are more accurate under low Re condition, and Shear-Stress Transport (SST) K-omega and BSL RSM have better performance under high Re condition; as to turbulent intensities, all RANS models underestimate them; as to the pressure drop comparison results, RANS models predict well under high Re condition, especially for RNG K-epsilon, but there are large deviations under low Re condition. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Fuel assemblies of PWR are constituted of rod bundles arranged in regular square configuration by spacer grids. Spacers promote two main effects: hold the rod bundles and strengthen local heat transfer adjacent to the wall downstream the grids. Actually turbulent mixing is composed of two kinds of flows: swirling flow inside the subchannel and cross flow between subchannels. Swirling flow could induce mixing between hot water near the rod and cold water in the center of the subchannel, and may accelerate deviation of the bubbles from the rod surface. Besides, crossing flow help to mixing water between hot subchannels and cold subchannels, which impact relatively large flow area. As a result, how to accurately capture and how to predict the complicated mixing phenomenon are of great concernments. Thermal-hydraulic design and performance strongly depend on experiments and numerical investigations. Following the rapid development and quick growth in computational technology at the end of 20th century, numerical simula⇑ Corresponding author. E-mail address: [email protected] (X. Chen). http://dx.doi.org/10.1016/j.anucene.2017.05.055 0306-4549/Ó 2017 Elsevier Ltd. All rights reserved.

tions of turbulent flow with the use of computational fluid dynamics (CFD) have been applied nowadays as an analysis method for nuclear engineering, especially for single phase calculation. Given direct numerical simulation (DNS) being not optional for high Reynolds number flows and large eddy simulation (LES) having many restrictions for complex geometries, usage of Reynolds-Averaged Navier-Stokes (RANS) is considered fit for widespread engineering applications. Among those studies performed including CFD methods of rod bundles with spacer grids, the most significant are: Imaizumi and Ichioka (1995) demonstrated the utilization of single subchannel CFD methodologies coupled with experimental results from LDV and pressure loss measurements on the development of fuel designs for PWR; Karoutas et al. (1995) performed a 3-D flow analysis for the design of spacers by CFD and experimental methods; Chen et al. (2009) made comparisons for the design of spacers by CFD and experimental methods, and those were mostly consistent with each other; Chen et al. (2010) provided mesh division technology for spacer grids simulation; Liu and Ferng (2010) used CFD to simulate thermal–hydraulic characteristics; Navarro and Santos, 2011 made a series of four subchannels CFD simulations to analyze 5
5 rod bundle with spacer grids.

X. Chen et al. / Annals of Nuclear Energy 109 (2017) 370–379

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Nomenclature w wi wrms N d k

mean velocity, m/s instantaneous velocity, m/s root mean square of fluctuating velocity, m/s number of samples confidence bound turbulent kinetic energy

Subscripts i number mean average magnitude rms root mean square

Dimensionless Numbers Re Reynolds number

In order to acquire the best practice guidance (BPG) of singlephase CFD analysis, benchmark activities were conducted, such as OECD/NEA KAREI MATiS-H test that was carried out by Chang et al. (2012). In the test, a fill-length 5
5 rod bundle, fitted with a spacer grid of PWR fuel assemblies, was measured. CFD study employed the CD-Adapco code Star-CCM+ by Cinosi et al. (2014). Various RANS models were chosen to predict velocity profiles. This paper proceeds as follows. We describe the experimental facilities, and the details of the benchmark. Then, we compare the simulated and experimental results. Finally, we draw the conclusions towards the BPG of rod bundle simulation for single-phase CFD.

2. Experiment description 2.1. Test facility The schematic of test facility consists of a 5
5 rod bundle array which is shown in Fig. 1. An electromagnetic flow meter is installed on the large-size line to measure the flow rate through the test section. A heat exchanger is also installed to control temperature in the main loop. The mock-up of test section is presented as Fig. 2 which is shown by Xiong et al. (2016). Water flows into the test section from the elbow which turns the horizontal flow vertical. Downstream of the inlet elbow a circle-to-square adapter is utilized to adapt the channel shape. In order to minimize the effect of elbow and adapter, a honeycomb flow straightener, 50 mm in length and 3.2 mm in pitch, is installed upstream of the rod bundle. The bottom supporter of rod bundle is a 5 mm-thick stainless steel plate drilled with circular or oval holes which distribute the flow more

Fig. 2. Vertical cross section of test section.

Fig. 1. Schematic of test facility.

uniformly across the rod bundle. Two visualization windows are set respectively upstream and downstream of the first spacer grid. Both windows are 65 mm x 120 mm in size. Details of test section is shown in Fig. 3. Rod bundle scale is 5
5 arrayed in squares with a 65.0 mm wide housing. Each rod diameter is 9.5 mm with a bundle pitch of 12.6 mm. In the 1250 mm long rod bundle two spacer grids with mixing vanes are installed. The first spacer grid is installed 410 mm above the bottom supporter. The distance between the first and second spacer grids is 300 mm. Two visualization windows are set respectively upstream and downstream of the first spacer grid. Both windows are 65 mm
120 mm in size. Dantec Fiber Flow 3D Laser Doppler Anemometry (LDA) is utilized to measure the flow field. Fig. 4 presents details of spacer with vanes. Besides, springs and dimples are located into the strap. Flow distributions downstream the grid are generally determined by mixing vanes, and how to simulate grid precisely and economically will be discussed later.

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X. Chen et al. / Annals of Nuclear Energy 109 (2017) 370–379

Fig. 5. Upstream mean velocity distributions.

2.2. Benchmark details We use the Dantec FiberFlow 3D Laser Doppler Anemometry to measure the axial velocities. For each point, we have at least 5000 samples or the sampling time is longer than 60 s. Based on the instantaneous velocity, axial mean velocity w comes from the following formula:

w¼

Fig. 3. Details of test section including spacer grids.

P 1 Ni¼1 wi Dti PN N i¼1 Dt i

where N is the number of samples, wi is instantaneous velocity, and Dti is the transit time of sample point going through measuring volume. Turbulent intensities are derived from root mean square of fluctuating velocity wi0 as follows vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uPN 02 u i¼1 Dt i wi wrms ¼ t P N i¼1 Dt i

i w0i ¼ wi  w Fig. 6 shows the distributions of sampled velocity. As the sampling number is limited, we need to evaluate the measuring uncertainty. 95% confidence bound of mean velocity can be defined as follows

dmean ¼ 1:96

wrms pffiffiffiffi w N

As to root mean square (RMS) of fluctuating velocity, it’s 95% confidence bound can be calculated by the formula

1 drms ¼ pffiffiffiffiffiffiffi 2N Table 1 shows the operating conditions of the test. Temperature of the test is 25 °C, and working pressure is 1 atm. There are two velocities measured in the test, which are 1.0 m/s and 3.0 m/s. Reynolds number (Re) are 14,600 and 34,800, so the flow should be in the turbulent region. Definition of Re is presented as follows Fig. 4. Details of spacer grid with vanes.

Upstream velocity distributions are displayed in Fig. 5. We can see that velocities are almost uniform radially, and measurement points are labeled in Fig. 7.

Re ¼

qwD l

where q is density, D is hydraulic diameter, w is velocity magnitude and l is dynamic viscosity. Figs. 7 and 8 show the placements of measuring points for both windows. The top surface of bottom supporter is defined as Z = 0. For window A, axial velocities on four horizontal planes are mea-

X. Chen et al. / Annals of Nuclear Energy 109 (2017) 370–379

Fig. 6. Distributions of sampled velocity.

Fig. 7. Cross-section measurements for window A.

Table 1 Operating conditions of the test. Property

Magnitude

Temperature Pressure Mean axial velocity Mean Re

25 °C 1 atm 1.0 m/s, 3.0 m/s 14600, 34800

sured upstream the first spacer grid. On each plane, points are measured along four lines, which are located at X = 13.6 mm, 26.2 mm, 38.8 mm, 51.4 mm. For window B, axial velocities on three horizontal planes are measured downstream the first spacer grid. On each plane, points are measured along twelve lines shown in Fig. 8. Fig. 9 compares the measured axial velocities with Chang’s data. We can see that measured axial velocity at the plane of Z = 205 mm is very close to the Chang’s fully developed data in the center of sub-channels with the y-axis of 1.0 pitch to 2.5 pitch. As to the large deviation for near-wall region, it perhaps comes from the wall boundary effects. Z = 0 is define at the top surface of bottom supporter that is the same shown in Fig. 3. So the experimental data is verified by other test results, and the experimental results are accurate.

Fig. 8. Cross-section measurements for window B.

Fig. 9. Comparison of axial velocities with Chang’s data.

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X. Chen et al. / Annals of Nuclear Energy 109 (2017) 370–379

of spring geometry on downstream flow is presented in Fig. 11, which is a sensitivity to the geometry of the spring. All the velocities plotted are normalized to the bulk velocity, and the horizontal axis is normalized by the pitch between rods. Both of them predicted well against experiments results. Thus, when we focus on the flow, we use simplified spring to cut down the mesh amount. Table 2 shows the pressure drop results for different springs. We easily draw the conclusion that when we want pressure drop result, we should use the real spring. Above sensitivity study showed that geometry of spring structure made a great importance for pressure drop calculation while has little impact on downstream mixing flow. Thus mixing flow comparison was based on simplified springs, and pressure drop comparison was based on real springs. 3.3. Mesh generation and sensitivity study

Fig. 10. Computational domain.

3. Simulation exercise 3.1. Computational domain Fig.10 shows the computational domain. Whole length of the model is 1171 mm, while the upstream part is 508 mm long. As there are too many test results, we chose some typical ones on three planes that contain two planes downstream the first grid and one plane upstream the first grid. On the cross-section of each plane, measurements on only one line are compared at X = 26.2 mm. 3.2. Geometrical features Geometry of springs inside the spacer grid is complex and has influences on downstream flow and pressure distributions, so it’s necessary to study how to simulate the spring correctly and economically. The interior of spring is hollow for real geometry. On one hand, we could use the real spring that will bring too many mesh. On the other hand, we could use the simplified spring that has inner gap filled, which brings better quality of mesh. The effect

ICEM 14.5 was adopted to generate mesh. In order to reduce the numerical errors brought by the interface value transfer according to the former method, this paper put forward a new means: hybrid mesh generation. Firstly, tetra mesh was generated in the complex spacer region with Octree method. Secondly, mesh quality was enhanced by smoothing tetra cell. Thirdly, based on the surface mesh (shell) of the interface, the shell was swept along the axial direction to build the structured mesh for the bare bundle region. The simulation results indicate that physical values were consistent through interface which was considered more accurate numerically. The local cut-open view is demonstrated in Fig. 12. Aiming to define proper mesh size, mesh dependency test for strap grid was performed based on one spacer grid. As shown in Fig. 13, three meshes were generated applying different mesh refinements on global size. Besides, pressure drop calculated downstream the grid by Blasius correlation was shown in the figure to validate our calculation. We chose mesh 2, and number of meshed of spacer grid are 15 million, while meshes of rod bundle between two grids are about 2 million. Average y + is about 30. Final mesh size (mesh2) was selected in the Table 3. 3.4. Numerical method The analysis was performed using commercial CFD code CFX 14.5. Uniform inlet velocity and temperature magnitudes were

1.60

1.40

W/Wbulk

1.20

Exp

1.00

SST-real spring SST-simplified spring 0.80

0.60

0.40 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Y/Pitch Fig. 11. Normalized axial velocity at Plane 2(Z = 554 mm) for different springs.

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X. Chen et al. / Annals of Nuclear Energy 109 (2017) 370–379 Table 2 Pressure drop for different springs. Turbulence Model

Geometry

CFD/Pa

Exp./Pa

SST

Simplified spring Real spring

8523.3 9299.4

9674.3

Table 3 Mesh size of the simulation. Property

Magnitude

Max global size/mm Min global size/mm Max grid size/mm Min grid size/mm Max axial size/mm Min axial size/mm Growth ratio

0.8 0.5 0.7 0.4 5.0 1.0 1.05

Table 4 Configuration of the simulation. Property

Magnitude

Inlet velocity/m/s Temperature/°C Pressure /atm Turbulence Model

1.0, 3.0 25 1 k-epsilon RNG k-epsilon SST BSL RSM

4. Comparison of simulated and experimental results Fig. 12. Cut-open view of hybrid mesh.

4.1. Velocity profiles

applied at the inlet plane, and of 0 Pa was defined for mean static pressure at the outlet. Adiabatic condition was used, and no-slip conditions were used for the fuel rods, spacer geometry, and walls of the flow housing. The exact quantities were listed in Table 4. Four turbulence models are applied in the simulation, such as kepsilon, RNG k-epsilon, K-x based Shear-Stress-Transport (SST), and BSL Reynolds Stress Model. K-epsilon model is the most widely used one, and RNG k-epsilon seems more advanced where the geometry has a strong curvature change. SST model is considered accurate for separation flow, while RSM model solves more equations for anisotropy simulation, but it cost more computational source. A residual RMS target value of 106 was defined for discretization accuracy evaluation. HP workstation with sixteen parallelized Xeon 3.47 GHz CPUs was used for the simulations.

Figs. 14 and 15 show the normalized axial velocity downstream the spacer grid for different turbulence models with the inlet velocity of 1.0 m/s. It is notable that at the near-grid region (Plane 2), all the various numerical methods produce very similar results except for those near-wall region due to wall boundary effects, and the agreement with the measurement is nonetheless good, but at the far away region, the agreements seem not very well. Quantitative differences are presented in Tables 5and 6. The mean deviations come from mean value of all deviations between calculation and test result for each point that could demonstrate local comparisons generally. We can see that at the low Re condition, k-epsilon and RNG k-epsilon predict better than SST and BSL RSM. The reason is probably that k-epsilon type of turbulence model deals well with the near-wall region, especially important for low Re condition condition.

average stac pressure/Pa

12000

9000

3 million

6000

15 million 31 million Blasius 3000

0 -0.2

0

0.2

0.4

0.6

axial altude/m Fig. 13. Mean static pressure with different meshes along axial direction.

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X. Chen et al. / Annals of Nuclear Energy 109 (2017) 370–379 1.60

1.40

W/Wbulk

1.20

Exp ke

1.00

RNGke SST 0.80

BSL-RSM 0.60

0.40 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Y/Pitch Fig. 14. Normalized axial velocity at Plane 2(Z = 554 mm) for different turbulence models with the inlet velocity of 1.0 m/s.

1.60

1.40

W/Wbulk

1.20

Exp ke

1.00

RNGke SST 0.80

BSL-RSM 0.60

0.40 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Y/Pitch Fig. 15. Normalized axial velocity at Plane 3(Z = 614 mm) for different turbulence models with the inlet velocity of 1.0 m/s.

Table 5 Mean deviation of normalized axial velocity between exp. and simulations for Fig. 14.

Table 6 Mean deviation of normalized axial velocity between exp. and simulations for Fig. 15.

Turbulence Model

Mean deviation/%

Turbulence Model

Mean deviation/%

k-epsilon RNG k-epsilon SST BSL RSM

10.89 10.76 13.49 13.20

k-epsilon RNG k-epsilon SST BSL RSM

7.87 7.90 8.02 8.23

Figs. 16 and 17 show the normalized axial velocity downstream the spacer grid for different turbulence models with the inlet velocity of 3.0 m/s. Same as the low Re condition, near-grid region predict good except for those near-wall region, but at the far away region, the agreements seem not very well. Quantitative differ-

ences are presented in Tables 7 and 8. We can see that at the high Re condition, SST and BSL RSM predict better than k-epsilon and RNG k-epsilon, which is maybe because that SST and BSL RSM simulate separate flow better and it turns out very important in high Re condition.

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X. Chen et al. / Annals of Nuclear Energy 109 (2017) 370–379 1.60

1.40

W/Wbulk

1.20

Exp ke

1.00

RNGke SST 0.80

BSL-RSM 0.60

0.40 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Y/Pitch Fig. 16. Normalized axial velocity at Plane 2(Z = 554 mm) for different turbulence models with the inlet velocity of 3.0 m/s.

1.60

1.40

W/Wbulk

1.20

Exp ke

1.00

RNGke SST 0.80

BSL-RSM 0.60

0.40 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Y/Pitch Fig. 17. Normalized axial velocity at Plane 3(Z = 614 mm) for different turbulence models with the inlet velocity of 3.0 m/s.

Table 7 Mean deviation of normalized axial velocity between exp. and simulations for Fig. 16.

Table 8 Mean deviation of normalized axial velocity between exp. and simulations for Fig. 17.

Turbulence Model

Mean deviation/%

Turbulence Model

Mean deviation/%

k-epsilon RNG k-epsilon SST BSL RSM

10.95 10.99 9.42 9.06

k-epsilon RNG k-epsilon SST BSL RSM

8.05 8.26 6.73 7.26

Fig. 18 show the normalized axial velocity upstream the spacer grid for different turbulence models with the inlet velocity of 1.0 m/s. Different simulation results have similar trends qualitatively, and agree well with the experiment. Table 9 presents the quantitative comparison.

4.2. Turbulent intensities profiles Figs. 19 and 20 show the normalized fluctuating velocity downstream the spacer grid for different turbulence models with the inlet velocity of 1.0 m/s and 3.0 m/s. It is notable that no matter

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X. Chen et al. / Annals of Nuclear Energy 109 (2017) 370–379

Table 9 Mean deviation of normalized axial velocity between exp. and simulations for Fig. 18. Turbulence Model

Mean deviation/%

k-epsilon RNG k-epsilon SST BSL RSM

12.76 13.76 11.61 11.49

wrms

rffiffiffiffiffiffi 2k ¼ 3

4.3. Pressure drop results

at low or high Re condition, all the various numerical methods underestimate turbulent intensities, which is probably because that RANS method has the time-averaged velocity, and fluctuating velocity wrms are approximately derived from turbulent kinetic energy k.

Table 10 presents the pressure drop comparison of exp. and simulations for various turbulence models. Pressure was measured on two planes. One is 63 mm to the bottom of strap, and the other is 234 mm to the top of strap. Pressure drop contains mixing grid and rod bundle. All the RANS models predict well under high Re condition, in which RNG k-epsilon has behaved best and BSL RSM has agreed the worst. However, under low Re condition, none of the RANS make good agreements. Perhaps this is due to that the low–Re flow is in the transition area and turbulence model couldn’t simulate well.

1.40

1.20

W/Wbulk

1.00

Exp

0.80

ke RNGke

0.60

SST BSL-RSM

0.40

0.20

0.00 0.0

0.5

1.0

1.5

2.0

2.5

Y/Pitch Fig. 18. Normalized axial velocity at Plane 1(Z = 319 mm) for different turbulence models with the inlet velocity of 1.0 m/s.

0.25

Wrms/Wbulk

0.20

0.15

Exp ke RNGke

0.10

SST BSL-RSM 0.05

0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Y/Pitch Fig. 19. Normalized axial velocity at Plane 2(Z = 554 mm) for different turbulence models with the inlet velocity of 1.0 m/s.

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X. Chen et al. / Annals of Nuclear Energy 109 (2017) 370–379 0.25

Wrms/Wbulk

0.20

0.15

Exp ke RNGke

0.10

SST BSL-RSM 0.05

0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Y/Pitch Fig. 20. Normalized axial velocity at Plane 2(Z = 554 mm) for different turbulence models with the inlet velocity of 3.0 m/s.

Table 10 Mean deviation of pressure drop between exp. and simulations for various turbulence models. Turbulence Model

CFD/Pa

Exp./Pa

Relative deviation/%

1.0 m/s

k-epsilon RNG k-epsilon SST BSL RSM

1678.2 1648.2 1884.3 1877.1

1212.8

38.3 35.9 55.3 54.7

3.0 m/s

k-epsilon RNG k-epsilon SST BSL RSM

10103.1 9895.7 9299.4 8675.8

9674.3

4.4 2.3 3.9 10.3

5. Conclusions Based on the study of validations in this paper, the following conclusions may be drawn: (1) CFD simulation predicts the axial velocity well for various RANS models. K-epsilon and RNG k-epsilon seems better than SST and BSL RSM under low Re, while it’s the opposite under high Re. More advanced model RSM doesn’t simulate more accurate than ordinary RANS. (2) Because of own limitations, RANS models couldn’t get turbulent intensities precisely. (3) When pressure drop was needed, we’d better use the exact geometry, and RANS models predict well under high Re. (4) In future research, LES may be used to simulate turbulent intensity. Besides, it’s necessary to evaluate the numerical accuracy of lateral velocity in rod bundles including spacer grids.

Acknowledgments This paper includes the results obtained under the research program from Science and Technology on Reactor System Design

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