Abstract
China initiative Accelerator Driven System (CiADS) combines a linac, spallation target and a Lead-cooled Fast Reactor (LFR) together, which is designed to transmute nuclear waste and accelerate the progress of China’s energy technology research towards the goal of carbon neutrality. A LFR uses helical wire-wrap spacers as positioning components to enhance crossflow mixing in the reactor core. To study the velocity distribution and crossflow characteristics in wire-wrapped rod bundle channels, a 2 : 1 magnified scale 7-pin bundle fuel assembly model was fabricated using polymathic methacrylate. Particle image velocimetry (PIV) and computational fluid dynamics (CFD) simulations were used to investigate the velocity distribution in the 7-pin bundle flow channels at Reynolds number of 1250~5000 in the plane and Reynolds number of 1500 and 2500 in the plane. The deviation between CFD simulation results and PIV experimental data was small, and the Reynolds Average Navier-Stokes model could accurately simulate the flow characteristics of the wire-wrapped fuel rod bundle channels. The maximum crossflow velocity caused by helical wires was about 40% of the axial bulk velocity. The normalized crossflow velocity at the subchannel interface varied approximately sinusoidally with the axial height. As the Reynolds number increased, the velocity distribution trend and the loss rate of axial velocity in flow channels remained essentially constant while the peak value of crossflow velocity increased. The contour images of velocities with different axial heights were obtained from the plane, and their velocity distribution had a certain periodicity. The axial velocity loss rate in each subchannel caused by wire-wrap spacer resistance was between 7.35% and 38.51%, and the axial velocity loss rates in inner subchannels were usually higher than those in edge subchannels.
1. Introduction
A Lead-cooled Fast Reactor (LFR) uses lead or lead-bismuth eutectic (LBE) as the coolant. It is one of the six most promising generation IV nuclear energy systems selected by the Generation IV Forum [1]. Many institutes have been committed to this field, and some research or experimental reactors are being or have been built [2], such as ALFRED [3], MYRRHA [4, 5], SSTAR [6], and PASCAR [7].
In China, the leading research and use of the LFR is the China initiative Accelerator Driven System (CiADS) [8, 9], which combines a linac, spallation target and LFR together. It can transmute long-lived and highly radioactive nuclear waste into short-lived nuclides, reducing the radioactive hazards of nuclear waste and improving the utilization rate of nuclear fuel. It can be used for nuclear waste transmutation technology research and accelerate China’s energy technology research progress towards the goal of carbon neutrality.
The LFR uses coiled wire as a positioning component for fuel rods, which enhances crossflow mixing in the reactor core and flattens the power distribution in the core. LBE operates under high temperatures and is costly. Therefore, the direct use of LBE for the flow characteristics experiment is complex, dangerous, and expensive. Existing LBE experiments [10–12] all employed sophisticated and high temperature resistant loops and instruments. In addition, due to the opacity of LBE, measurements can only be performed using a single-point contact measurement method with low measurement accuracy and a small measurement range. Few LBE experiments conducted velocity distribution measurements in the wire-wrapped rod bundle flow channels.
Researchers typically use polymathic methacrylate (PMMA) to manufacture fuel assemblies with wrapped wires and use refractive index matching (RIM) liquids such as paracymene or sodium iodide solution as working liquids. According to the similarity theory, RIM liquids can simulate the flow characteristics of LBE when the model is scaled correctly, and the Reynolds number is consistent. Particle image velocimetry (PIV) [13] is a noncontact global optical velocimetry method with the advantages of low impact on the flow field, high measurement accuracy, and wide velocimetry range.
Many researchers have studied the flow characteristics of wire-wrapped fuel assemblies using PIV. In 2017, Nguyen et al. [14] used PMMA as the model material and paracymene as the RIM liquid. PIV experiments were conducted on the 61-pin wire-wrapped fuel assembly (the diameters of the rod and the wire were 15.9 mm and 3.0 mm, respectively), and the flow field data in the inner subchannel was measured when the Reynolds number was about 19000. The data of the turbulent flow field near the wall were analyzed by two-point velocity crosscorrelation and the proper orthogonal decomposition method, revealing the main structure of the turbulent flow. In 2018, Goth et al. [15] performed PIV experimental measurements on the flow field distribution of multiple inner subchannels in a 61-pin wire-wrapped fuel assembly with a Reynolds number of 19000. The global average velocity of the flow field, the root mean square (RMS) of the fluctuating velocity, and the Reynolds stress were measured. The data of this experiment could be used to benchmark the calculation results of the Reynolds Average Navier-Stokes (RANS) model and large eddy simulation. In 2020, Song et al. [16] used epoxy resin as the model material and fennel oil as the RIM liquid to carry out PIV experiments on the 19-pin wire-wrapped fuel assembly with a rod diameter of 20.0 mm, and the ratio of / was 1.2. They measured the velocity distribution of the flow field in inner and edge subchannels with Reynolds numbers ranging from 15000 to 17000. PIV experimental results were qualitatively compared with CFD results to verify the accuracy of CFD calculations. In 2021, Fan [17] used PMMA as the model material and 62.932 wt% sodium iodide solution as the RIM liquid to study the flow characteristics in the and planes of the 19-pin wire-wrapped fuel assembly. The diameter of fuel rods and wires was 12.995 mm and 2.005 mm (/ was 1.154), and the wire pitch length (H) was 144 mm. The study was carried out on the Visual Hydraulic ExperimentaL Platform (VHELP) and found that the trend of axial velocity distribution did not change with increasing Reynolds number and the velocity values increased proportionally. A small crossflow can be observed near the winding wire.
Few of the above studies photographed the flow in the cross-section ( plane) of a fuel assembly model. When performing experimental shooting in the plane, the distance from the cross-section to the nearest air-model boundary is usually 300~400 mm. Compared to the plane (depth of 50~100 mm), the difference is very significant. Thus, it brings higher requirements for the photography equipment and matching degree and transparency of the RIM liquids. At the same time, the existing PIV experimental studies always use small-diameter wires, so the narrow flow channel is not conducive to the fine measurement of flow and brings extra difficulty to the photography shooting in the plane. This paper carried out the PIV research on a 7-pin wire-wrapped fuel assembly with a 2 : 1 expansion ratio. The crossflow in the cross-section was photographed and data processed. The velocity distribution of the axial flow in subchannels was photographed, and the flow near the wire-wrap spacer was finely measured.
2. Experimental Methods
The schematic diagram of the VHELP [18] is shown in Figure 1. The primary loop of the experimental platform is driven by a KSB main pump (pump 1). The working liquid flows through pump 1 to the heat exchanger, water tank 2, filter, and flowmeters and then reaches the test section. After flowing through the outlet of the test section and reaching water tank 3, the working liquid returns to pump 1. The secondary loop, which includes water tank1, the water chiller, and pump 2, is connected to the primary loop through the heat exchanger. Pump 3 was used to pump working liquid into the primary loop.
The test section was a 7-pin wire-wrapped fuel assembly made of PMMA. The actual average fuel rod and wrapping wire diameters were 25.915 mm and 4.066 mm, respectively (), and the H was 288.000 mm. The overall length of the model fuel rod was 1008 mm (3.5 H). Meanwhile, the actual clad outer diameter of the CiADS LFR fuel assembly is 13.1 mm, and the wire diameter is 2.0 mm [19]; so, the test section is an expansion of the CiADS LFR fuel assembly with the ratio of 2 : 1. The wire-wrap spacers and the fuel rods were manufactured through a self-designed gear synchronous positioning device.
The principle of PIV is shown in Figure 2. A proper amount of tracer particles with a similar density of the RIM liquid are sown into the liquid. Then, the tracer particles are irradiated with the double-pulse laser. Under the control of the synchronizer, the double-pulse laser emits twice at a concise time interval . The laser is diffused into a sheet light source with a thickness of 1 ~ 2 mm through the light guide arm and lens group. The sheet light source illuminates the tracer particles in the flow field, and at the same time, a charge-coupled device (CCD) camera takes a pair of particle images through the control of the synchronizer. The Insight 4G software calculates the displacement of the particles during the time interval through the crosscorrelation algorithm [20], and then the velocity of the particles can be calculated. In a PIV experiment, it is necessary to select the tracer particles whose density is close to that of the liquid to ensure the flow followability of the tracer particles. Because the PIV method has the characteristics of noncontact, it is recognized as one of the flow field velocity measurement methods with the highest accuracy.
In this paper, a 610035 synchronizer, 630094 CCD camera (29MP) of TSI Incorporated, and the 532 nm double-pulse laser of Beamtech Optronics Co., Ltd. were selected to carry out the PIV experiment. The control and PIV processing software was Insight 4G. The working liquid was 62.932 wt% sodium iodide solution with a density of 1.876 g/cm3, and the tracer particles were silver-coated hollow glass beads with a density of 1.7 g/cm3, which was close to the density of sodium iodide solution and had good flow followability.
3. CFD Settings
In this paper, the simplified strategy of 0.1 mm indentation was adopted for the wires. The boundary layer was set to 4 layers. Figure 3 shows the meshing in STAR CCM+ and local details of the mesh near the wire-wrap spacers. Taking the static pressure in the edge subchannel with the Reynolds number of 2500 as the example, the grid independence analysis of the base size of 2.1 mm~1.3 mm was carried out, and the results are shown in Figure 4. It can be seen that with the refinement of the grid, the results tend to be consistent gradually. Considering the calculation accuracy and cost comprehensively, a grid with a base size of 1.5 mm was selected. Combined with the analysis of existing research literature [21–23], the SST - model has better applicability to the wire-wrapped bundles, so the SST - turbulence model was selected. The calculations were performed by ANSYS Fluent software, which has a rich set of turbulence models and wall functions. The residual of continuity in all the CFD simulation was 10-8, and the inlet and outlet of the calculated area were velocity inlet and pressure outlet, respectively.
4. Results and Discussions
In this paper, the PIV experiment shooting of a 7-pin wire-wrapped fuel assembly with a 2 : 1 expansion ratio was carried out in the and the planes, respectively. The shooting positions and names of the plane are shown in Figure 5. In the plane, planes with heights of 972 mm and 936 mm in -axis were selected for shooting, and the starting point of the -axis was the starting point of wires on fuel rods. The schematic diagram of shooting in the plane is shown in Figure 6.
4.1. Plane
The bulk Reynolds number is calculated by where , , and are density, flow velocity, and dynamic viscosity of the liquid, respectively. And is the hydraulic diameter of the fuel assembly. In the 7-pin wire-wrapped fuel assembly with the hexagonal inner wall, hydraulic diameter is calculated by where , , , , and are cross-section area and wetted perimeter of the fuel assembly, the side length of the hexagonal inner wall, and the diameter of the rod and the wire, respectively.
Figures 7 and 8 show the velocity distribution contour images of U of PIV and CFD results at 1GAP in the plane (, , and are the velocity components on the , , and axis, respectively). The results show that when the Reynolds number is 2500 (the bulk velocity is 0.308 m/s), there is a crossflow with a maximum velocity of about 0.12 m/s in the local area near the wire, which is about 39.0% of the bulk velocity. The comparison of the velocity contour images of the -axis velocity component shows that the CFD calculation results in the downstream of the wire are slightly higher. The PIV experiment shows that the flow velocity in the downstream of the wire is about 0.44~0.48 m/s, while the CFD result is 0.48-0.52 m/s. Overall, the difference between the CFD calculation results and the PIV data is about 8.33%, which proves that the RANS simulation results are in good agreement with the experimental data and can accurately simulate the flow characteristics inside the wire-wrapped fuel assembly.
Figures 9 and 10 show the distribution of velocity contour images of PIV and CFD at 2GAP, and the Reynolds numbers are 2500 and 3750, respectively. It can be seen from the contour images that there is a crossflow along the spiral direction of the wire downstream, the maximum crossflow velocity is 0.12 m/s and 0.18 m/s, respectively, and the ratio to the axial bulk velocity is 39.0%. It can be concluded that the maximum crossflow velocity is proportional to the bulk velocity, and the ratio is about 40%, which is close to the existing experimental results of the 19-pin wire-wrapped fuel assembly [17].
To quantitatively compare the results of PIV and CFD, the root mean square of crossflow velocity and are introduced to evaluate the effect value of the velocity. and are calculated by
In this paper, all velocity components of the same -axis coordinate are selected to calculate or . Figures 11 and 12 show the comparison results of PIV and CFD.
It can be seen from the root mean square velocity distribution diagrams Figures 13 and 14 that in the left half of the flow field, the results of CFD are in good agreement with those of PIV, and the CFD results have a local peak due to the local crossflow velocity near the wire. In the right half of the flow field, due to the slightly higher calculated value of the crossflow velocity downstream of the wire from the CFD results, the scatter points representing the CFD results are higher than those of the PIV results. Comparing the scatter diagrams of different Reynolds numbers, the increase of the Reynolds number will slightly increase the peak value of the scatter points and basically has no effect on the overall trend of the scatter point distribution.
In the plane 2GAP, the value and trend of the root mean square velocity distribution of PIV and CFD results are basically consistent. Due to the deviation of CFD results in the wire downstream, the peak value of scattered points representing CFD results deviates. In this flow channel, as the Reynolds number increases, the trend of the scatter points is also basically unaffected, but the peak value of the scatter points increases accordingly.
4.2. Plane
Figure 15 shows the velocity distribution contour image of the 7-pin wire-wrapped fuel assembly. It can be seen that the velocity distribution contour image is complete and clear. The rod bundle and wires can be clearly distinguished in the flow channels, clearly showing the local flow structure of the wire-wrapped fuel assembly, which can be used for further studies.
When shooting in the plane, once the flow velocity is too high, more tracer particles will escape from the sheet light source within the time interval, which will lead to more error vectors in the crosscorrelation calculation. In this paper, only the Reynolds numbers of 1500 and 2500 were taken in the plane.
Figures 16 and 17, respectively, show contour images of the PIV and CFD results of the plane velocity components and at the -axis height of 972 mm with the Reynolds number of 1500. The contour images of PIV and CFD are very similar. There is a counterclockwise flow with a local high velocity in the edge subchannel of the plane. The direction is consistent with the winding direction of wires, which is consistent with the research results of Wang et al. [24]. When the Reynolds number is 1500, the bulk velocity in the module is 0.192 m/s. The maximum crossflow velocity (0.12 m/s) in the plane is about 62.5% of the bulk velocity. According to the existing research, the pressure distribution in the wrapped wire fuel assembly changes periodically along the spiral direction of the wire [18], and it is speculated that the cross-flow velocity distribution is similar to it. The existing CFD calculation [25] confirmed that there is a periodicity of the crossflow velocity distribution in the wire-wrapped fuel assembly. Figure 18 compares the plane velocity distribution contour images with a height difference of 36 mm (1/8 H). It can be seen that the velocity distribution changes with the precession of the wire, which preliminarily confirms the existence of periodicity.
To accurately quantitatively compare and analyze the velocity distribution results of PIV and CFD in the plane, the shooting positions of the plane were taken as the baselines, the data within ±0.2 mm width along the baseline were extracted from the velocity distribution data of the plane by the MATLAB program, and scatter points were drawn to compare the results. Figure 19 shows the area of extracted data (black line).
It can be seen from Figures 20–23 that the plane PIV results can better capture the velocity distribution characteristics of the crossflow field than the plane. The scatter point distributions of and are basically consistent (including the peak and trend). Comparing the velocity components and at Reynolds numbers of 1500 and 2500, it can be found that the peak values of are higher than by about 42.3% and 60.0%, respectively. The increase of the Reynolds number has basically no effect on the distribution trend of the scatter points but only affects the peak value of them.
4.3. Influence of Wire-Wrap Spacers
As the positioning components of the LFR fuel rods, the wires not only enhance the crossflow mixing but also bring additional flow resistance, resulting in the decrease of the axial flow velocity in each subchannel.
Figure 24 shows the numbering of some subchannels in this paper. In order to measure the influence of wire-wrap spacers on crossflow mixing, at the subchannel interface is defined as the normalized crossflow velocity, namely, where is the average crossflow velocity at the same height at the interface, and is the bulk axial velocity.
Figure 25 shows the distribution of with the normalized axial height under different working conditions at the interface of subchannels 3 and 4 and subchannels 5 and 6. A positive value of means that the crossflow velocity flows from subchannel 3 (5) to subchannel 4 (6). At the two interfaces, changes with the axial height, showing a distribution similar to a sinusoidal curve, and is not affected by the Reynolds number. The maximum absolute value of is close to 0.4, which is consistent with the conclusion obtained in Section 4.1.
In order to quantitatively measure the influence of wire resistance on axial velocity, define α as the loss rate of axial velocity, namely, where is the root mean square value of the axial velocity in the subchannel.
Figure 26 shows the α values in the subchannels with the Reynolds number of 2500. Due to the influence of multiple wires in the inner subchannels, their axial velocity loss rates are usually higher than those of the edge subchannels.
Figure 27 shows the axial velocity loss rate line chart in each subchannel under different working conditions. Obviously, in the inner subchannel 6, the axial velocity loss is higher, and α is close to 40%; in the edge subchannel 8, the axial velocity loss rate is the lowest. Axial velocity loss rate has no significant relationship to Reynolds number variation.
Figure 28 shows the precession of wires during the axial height 1.75-2.25 H. There are always different wires in inner subchannels, and it validates the conclusion of Figure 27. However, the α in edge subchannel 5 is higher than those in inner subchannel 7 and 10. It can be explained that during the axial height 1.00-1.75 H, the wire mainly exists in the edge subchannel 5, and the influence does not fade during 1.75-2.25 H.
5. Conclusions
In this paper, the crossflow characteristics in a 7-pin wire-wrapped fuel assembly with a 2 : 1 expansion ratio were studied by PIV and CFD methods, and the experimental results were compared with the CFD calculation results: (1)The CFD calculation results were in good agreement with the experimental results, and the RANS model SST - could accurately simulate the crossflow characteristics in a wire-wrapped fuel bundle. From the comparative analysis of velocity contour images in the plane, the difference between the CFD and PIV results was about 8.33%. Comparing the and scatter diagrams showed that the CFD results were very consistent with the PIV results, and the peak distribution was also consistent with the scatter points trend(2)As the Reynolds number increased, the velocity distribution trend in the flow channel remained basically unchanged, and the peak value of the crossflow velocity increased accordingly. The maximum crossflow velocity caused by the wire-wrap spacer was about 40% of the axial bulk velocity(3)The crossflow velocity distribution at the interface of subchannels caused by wire-wrap spacer was approximately sinusoidal with the variation of axial height and had nothing to do with the Reynolds number. The axial velocity loss rate in each subchannel caused by wire-wrap spacer resistance was between 7.35% and 38.51%. The axial velocity loss rate in inner subchannels was usually higher than those in edge subchannels. However, during the axial height of 1.00-1.75 H, the wire mainly exists in the edge subchannel 5, so the axial velocity loss rate is high than those in the inner subchannels 7 and 10. The axial velocity loss rate was also not related to the Reynolds number(4)In further studies, parameters such as cross-flow velocity distribution and axial velocity loss rate at different axial heights would be compared to analyze whether there is periodicity along the axial height
Abbreviations
| CCD: | Charge-Coupled Device |
| CFD: | Computational Fluid Dynamics |
| CiADS: | China initiative Accelerator Driven System |
| LFR: | Lead-cooled Fast Reactor |
| PIV: | Particle Image Velocimetry |
| PMMA: | Polymethyl Methacrylate |
| RANS: | Reynolds Average Navier-Stokes |
| RIM: | Refractive Index Matching |
| SST: | Shear Stress Transfer |
| VHELP: | Visual Hydraulic ExperimentaL Platform. |
| a: | Side length of the hexagonal inner wall |
| : | Cross-section area |
| : | Hydraulic diameter of the |
| : | Outer diameter |
| : | Wire pitch length |
| : | Wetted perimeter of the fuel assembly |
| : | Pitch of the rod bundle |
| Re: | Reynolds numbers |
| : | Average crossflow velocity at the same height at the interface of subchannels |
| v: | Flow velocity of the liquid |
| , , : | Velocity component of the , , and axis. |
| α: | Axial velocity loss rate |
| ρ: | Density of the liquid |
| μ: | Dynamic viscosity of the liquid. |
| bulk: | Bulk velocity in the test section |
| : | Rod |
| RMS: | Root mean square |
| : | Normalized velocity at the subchannel interface |
| : | Wire. |
Data Availability
Data available on request from the authors. The data that support the findings of this study are available from the corresponding author [author initials] upon reasonable request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (No. 12122512) and the National Key Research and Development Program of China (No. 2020YFB1902100).