Fluid flow in a diametrally expanded CANDU fuel channel – Part 1: Experimental study

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Fluid flow in a diametrally expanded CANDU fuel channel – Part 1: Experimental study ⁎

M. Bruschewskia,b, , M.H.A. Piroc,d, C. Tropeae, S. Grundmanna a

Institute of Fluid Mechanics, University of Rostock, Rostock, Germany Institute of Gas Turbines and Aerospace Propulsion, Technische Universität Darmstadt, Darmstadt, Germany c Faculty of Energy Systems and Nuclear Sciences, Ontario Tech University, Oshawa, ON, Canada d Fuel and Fuel Channel Safety Branch, Canadian Nuclear Laboratories, Chalk River, ON, Canada e Institute of Fluid Mechanics and Aerodynamics, Technische Universität Darmstadt, Darmstadt, Germany b

A R T I C LE I N FO

A B S T R A C T

Keywords: Fuel channel flow CANDU 3D velocity measurements Magnetic Resonance Velocimetry

The overall aim of this study is to develop and validate experimental and computational capabilities to provide high-resolution isothermal fluid velocity data for nuclear reactor investigations. The current work presents fullfield velocity data in a 1:1 replica of a 37-element CANDU nuclear fuel bundle using the Magnetic Resonance Velocimetry (MRV) measurement technique. The diameter of the pressure tube is 6% larger than at beginning-oflife to simulate the long-term aging process in an actual CANDU nuclear reactor due to diametral creep at end-oflife conditions. In Part 1, the MRV technique is presented with a focus on measurement errors and the estimation of these errors. The three-dimensional, three-component mean velocity field inside the fuel channel, including the subchannel flow between the fuel elements, is provided at a resolution of 0.78 × 0.78 × 0.78 mm3. The MRV data is validated through bulk flow rate calculations and Laser Doppler Velocimetry measurements conducted at selected locations inside the flow system. Overall, the deviations in the full-field MRV data are low except for local differences in regions with high convective acceleration and high velocity. The measurement accuracy can be improved by applying newly developed MRV sequences that are insensitive to these effects. In this specific experiment, it is found that up to 35% of the coolant bypasses the fuel bundle in a 6% diametrally expanded pressure tube containing a single bundle. The data is used as a reference for a companion paper (Part 2), which presents a computational fluid dynamics approach using an implicit large eddy simulation. In conclusion, the presented experimental methodology provides accurate full-field mean velocity data in complex channel geometries. More realistic flow experiments in replicas of entire fuel channels can be investigated in detail with relatively little effort and in a short time.

1. Introduction The conventional measurement techniques used in nuclear reactor safety research, such as hot-wire and laser-optical instruments, can capture some details of the flow field with high accuracy. However, these techniques involve overly complicated experimental work, and they may not be possible under some conditions. As in most nuclear fuel assemblies, the CANDU fuel bundle has extremely narrow sub-channels with no direct optical access from the outside. Matching the refractive index of the fuel element replica with the working fluid requires significant experimental expenses and results in limited fields of view (Ikeda and Hoshi, 2007, Dominguez-Ontiveros et al., 2012, Conner et al., 2013, Chang et al., 2014). Thus, the application of laser optical techniques such as Laser Doppler Velocimetry (LDV) and Particle Image

⁎

Velocimetry (PIV) in models of fuel assemblies is often impracticable. A novel experimental technique that appears to be better suited for rapid measurements in complex flow geometries is Magnetic Resonance Velocimetry (MRV). This technique is based on the medical imaging modality Magnetic Resonance Imaging (MRI), which utilizes the resonant behavior of the quantum-mechanical spin of specific isotopes. An essential feature of MRI is that the recorded signal can be made sensitive to motion and can thus be used to measure flow velocities. Comprehensive reviews on the opportunities and limitations of MRV for fluid mechanics research are provided by Elkins and Alley (2007) and Gladden and Sederman (2013). In brief, MRV can measure the mean velocity field in complex flow systems with relatively minor experimental effort. Since MRV is a fullfield measurement technique, the entire flow structure, including all

Corresponding author at: Institute of Fluid Mechanics, University of Rostock, Rostock, Germany. E-mail address: [email protected] (M. Bruschewski).

https://doi.org/10.1016/j.nucengdes.2019.110371 Received 6 April 2019; Received in revised form 27 September 2019; Accepted 30 September 2019 0029-5493/ © 2019 Elsevier B.V. All rights reserved.

Please cite this article as: M. Bruschewski, et al., Nuclear Engineering and Design, https://doi.org/10.1016/j.nucengdes.2019.110371

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Fig. 1. A 37-element CANDU fuel bundle is shown on the left with salient features identified. The right image shows a 37-element CANDU fuel bundle sitting within a pressure tube, which is housed in a calandria tube (Piro et al., 2016b).

2. Background

boundary layers, is captured within the discretization limits of the measurement resolution. The velocity data of MRV (i.e., velocity, spatial resolution, and spatial domain) is inherently similar to the data produced by Computational Fluid Dynamics (CFD) analyses applying the Reynolds-averaged Navier-Stokes equations. This feature allows direct three-dimensional three-component (3D3C) comparison of the two data sets, enabling a full-field validation of the numerical solution. Such experimental data is sometimes referred to as “CFD grade data.” The present paper is Part 1 of two companion papers. The overall aim of this combined study is to develop experimental and computational capabilities to provide high-resolution velocity data for nuclear reactor investigations. While the conditions that have been investigated are not directly comparable to what is experienced in-reactor (e.g., differences include isothermal, low temperature, low pressure, single bundle), the primary impetus of the work is to demonstrate progress in developing new experimental capabilities and uncertainty/error estimation. Earlier campaigns include a proof-of-principle with a simplified 8-element fuel bundle (Piro et al., 2016b), which was followed by a second campaign that investigated a single 37-element fuel bundle (to scale, to specification) under isothermal conditions in a normal pressure tube (Piro et al., 2017). This campaign extends the previous work to include a diametrically expanded pressure tube to simulate the effects of flow by-pass, which includes progress in error and uncertainty quantification. The ultimate goal in future campaigns will be to move towards better simulating the environmental conditions pertinent to nuclear reactor safety analyses. This part (i.e., Part 1) focusses on the description of the experimental techniques, results, and validation. The mean velocity field in 3D3C is analyzed throughout the entire flow path inside a model of a CANDU fuel channel. The MRV data is validated through bulk flow rate calculations and LDV measurements conducted at selected locations inside the flow system. The statistical and systematic measurement errors are provided, and the overall accuracy of this experimental method is discussed. Part 2 is presented in the companion paper Piro et al. (2019), which is dedicated to CFD analyses of the same flow system. Numerical work was performed with Large Eddy Simulations (LES) using the CFD toolkit Hydra (Christon, 2017). Moreover, the experimental and numerical results are compared in Part 2, and the benefits of combining CFD-grade experimental data and time-resolved CFD data are discussed. The boundary conditions were carefully chosen to allow reproducible experiments and a straight-forward implementation into the CFD simulations in Part 2. Due to experimental limitations in the current study, the flow conditions – precisely temperature, pressure, and flow rate – were not the same as in-reactor conditions. Instead, this work is intended to provide insight into the effects of flow bypass under simulated conditions while further developing experimental and computational capabilities.

This study describes the third experimental and computational campaign in investigating fluid flow through a CANDU fuel channel. The first investigation was a proof-of-concept that employed a simplified 8-element fuel bundle replica produced with polyamide material using a laser sintering process (Piro et al., 2016b). The second investigation used a 37-element bundle replica sitting in a pressure tube that was geometrically consistent with what is used in industry, specifically the Bruce Nuclear Generating Station (Piro et al., 2017). The third investigation, which is described here, examines fluid flow through a 37-element bundle sitting on the bottom of a pressure tube that is 6% greater in diameter than a standard pressure tube. The replica bundle, fluid material, fluid flow rate, and measurement system were all consistent between the second and third campaigns – the only difference between the second and third campaigns is the pressure tube diameter. Preliminary experimental (Bruschewski et al., 2016a) and computational (Piro et al., 2016a) work on this third campaign were presented at the Organization for Economic and Cooperative Development Nuclear Energy Agency (OECD/NEA) & International Atomic Energy Agency (IAEA) Workshop on Computational Fluid Dynamics for Nuclear Reactor Safety at the Massachusetts Institute of Technology in 2016. In the preliminary work, some issues were observed with the computational mesh concerning insufficient quality and resolution in some regions of the domain. The mesh was entirely recreated to a higher standard, and a new CFD simulation was performed. The numerical results are presented in the companion paper (Piro et al., 2019). In the experimental part, which is shown here, the analysis of the data was refined, and sources of measurement errors were analyzed in more detail. A standard 37-element CANDU fuel bundle is shown on the left in Fig. 1 with salient features identified. In this design, fuel elements are mated together with Zircaloy-4 endplates to maintain spacing between adjacent fuel elements. Spacer pads are located in the mid-length of the bundle to prevent direct contact between fuel elements. Bearing pads are appended to the outer ring of fuel elements to provide spacing from the adjacent pressure tube wall, as shown on the right in Fig. 1, which is intended to provide a pathway for water to travel for cooling purposes. The fuel bundle, pressure tube, and calandria tube collectively constitute the fuel channel. Due to the horizontal configuration of fuel channels in the CANDU design, the fuel bundle sits on the bottom of the pressure tube. Over time, the pressure tube may experience diametral creep due to high internal pressure (i.e., ≈10 MPa), which is accelerated by neutron fluence induced damage mechanisms (Rodgers et al., 2016). As a result of diametral creep, a gap is formed above the fuel bundle. The coolant, following the path of least resistance, flows preferentially above the 2

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Fig. 2. An end view comparison of a 37-element CANDU fuel bundle sitting in a standard pressure tube (left) and a 6% crept pressure tube (right).

distribution of the hydrogen protons in the volume. Water is typically used as a flow medium. As a result, voxels that contain water have a high intensity while surrounding voxels contain only noise, hence a low intensity. Usually, a sufficiently high signal-to-noise ratio is adequate to distinguish the water volume from the noise floor. The phase angle of the complex image (∠ {S }) can be encoded such that it represents velocity. Encoding is accomplished via bipolar magnetic field gradients (Caprihan and Fukushima, 1990). The phase angle of spins that travel along these gradients is varied linearly according to their velocity. The phase shift depends on the velocity sensitivity VENC, which is defined before the measurement. After the measurement, the velocity is obtained as:

bundle (Bruschewski et al., 2016a, Piro et al., 2016a). Hence, coolant bypasses the inner regions of the bundle, which in turn increases the local temperatures. This phenomenon is commonly referred to as “flow bypass.” Fig. 2 illustrates the difference between the cross-section of a bundle sitting in a normal and a diametrally crept pressure tube. The drawing on the right in Fig. 2 highlights the crescent-shape gap on the top of the fuel channel that gives rise to flow bypass. All pressure tubes in operating CANDU reactors experience some diametral creep over sufficient time, albeit to varying degrees depending on channel position (DeAbreu et al., 2018). The design end-oflife limit of pressure tube diametral creep is 6% in some nuclear stations. As long as sufficient bundle cooling can be demonstrated, higher diametral creep can be accepted as an end-of-life limit without the reactor being de-rated. This limit is currently considered conservative (Holt, 2008). Therefore, there is a direct financial incentive for industry to understand this phenomenon better to provide a technical and objective basis for justifying a larger end-of-life limit for diametral creep. The present work serves two purposes:

u = ∠ {S }

VENC π

(1)

Performing these measurements in all three directions yields the 3D3C mean velocity field. In contrast to point-wise measurement techniques such as LDV, the data in each voxel contains a mixed signal of all spatial frequencies. As a result, the three-component velocity values are time-averaged over the entire acquisition process, which is typically in the order of seconds and minutes. Therefore, transient turbulent effects cannot be measured with standard MRV techniques. Compared to conventional experimental techniques in fluid mechanics, MRV is fast concerning the amount of acquired data. The measurements do not require optical access or any tracers in the fluid. Furthermore, the requirements on the flow models are relatively minor, mainly because no particular optical property is needed. MRV models are often manufactured with rapid prototyping techniques. The limits of MRV are very different from conventional experimental techniques. All structures must be made of materials that do not interfere with the static magnetic field in terms of magnetic susceptibility. Typically, polymer materials are used, which may pose restrictions on the operating temperatures and pressures in the flow circuit. In addition, standard MRI systems are not built for the high temperatures that are typically experienced in thermohydraulic loops. Usually, the sensitive electronic components of the MRI systems are maintained at about 20 °C and specific humidity. In summary, MRV is best suited for stationary single-phase flows at room temperature.

A. to quantify the effects of flow bypass under simulated and reduced conditions from what is experienced in-reactor to aid engineering and fitness-for-service analyses of CANDU fuel channels, and B. to further develop state-of-the-art experimental and computational fluid dynamic capabilities as an intermediate step to support future nuclear reactor performance and safety analyses, which are expected to capture in-reactor conditions more accurately. 3. Experimental setup With MRI (and MRV), the flow model is placed inside a strong external magnetic field of the MRI system. The magnetic interactions between the nuclear spins of the working fluid and their environment form the basis of any magnetic resonance imaging technique. A detailed description of the underlying physics can be found in Brown et al. (2014). The MRV data represents the spatial distribution of the magnetic resonance signal in the Field Of View (FOV). As a particular feature, the data is sampled in the spatial-frequency domain, which describes the sinusoidal components of the image in the three directions. The threedimensional image is obtained after a Fourier Transform. The higher the sampled spatial frequencies, the higher is the resolution in the reconstructed image. The three-dimensional pixels are commonly referred to as “voxels.” The voxel values of the complex image (S) can be encoded in various ways. Most commonly, the image intensity represents the

3.1. MRV measurements The experimental setup, used for the MRV measurements, is visualized in Fig. 3. The experimental setup is a 1:1 scale model of a single 37-element CANDU fuel bundle, made from Polyamide in a laser sintering process (fuel bundle and diffuser) and perspex (pressure tube 3

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Fig. 3. Schematic of the experimental setup used for the MRV measurements. The bundle model is made from Perspex and Polyamide through a laser sintering process. From Bruschewski et al. (2016a).

measurements. Due to the large FOV (≈550 mm in length and ≈110 mm in diameter), the measurement volume was divided into five separate and overlapping FOVs. Each FOV comprised of a 160 × 180 × 320 data matrix with a spatial resolution of 0.78 mm in each direction. Each FOV was measured twice with a constant flow rate (flow-on scan), to improve the measurement uncertainty of the MRVdata. One flow off scan (i.e., a measurement with the same parameters yet without flow) was carried out for each FOV. Apparent flow velocities within the flow-off scan originate from systematic errors (i.e., induced eddy currents) and are subtracted from the flow-on scans to improve the accuracy of the measurement. Data acquisition for each FOV (two flow-on & one flow-off scan) took 47 min, adding up to a total data acquisition time of just less than 4 h. The values of the imaging parameters were optimized to gain maximum signal-to-noise ratio and reduce motion-related acquisition errors. The final parameter values are given in Table 1. Measurement errors pertinent to this experimental campaign are described in the

replica). Endplates position the 37 elements of the fuel bundle with spacer pads between the single fuel elements and appendages. The fuel bundle was manufactured in two parts and mated together to a total length of 495 mm. The machine used for laser sintering is a Formiga P100 (EOS, Munich, Germany). The average surface roughness of the sintered parts is between 10 and 25 µm depending on the built direction. The effects and experimental uncertainties related to surface roughness are discussed in Section 5. The fuel bundle replica is connected to a flow supply system via Polyvinyl Chloride (PVC) hoses. The flow enters the system from the left through a diffuser section. Grids inside the diffuser prevent flow separation. A nozzle at the end of the system reduces the diameter of the fuel channel to the diameter of the return hose. The measurement region covers nearly the entire fuel channel containing one bundle. The pressure tube inner diameter is increased by 6% to 110 mm (compared to the 103.4 mm as-received inner diameter, which was considered by Piro et al., 2017) to simulate the geometry of a crept pressure tube at end-of-life. The fuel bundle remains the same size as the second campaign. A cross-section of the pressure tube and fuel bundle is visualized in Fig. 3 (top left). Due to the fuel bundle sitting on the bottom of the expanded pressure tube, a flow bypass region is created in the upper part of the pressure tube (shaded red in Fig. 3), with a maximum height of approximately 8 mm. The working fluid is de-ionized water with a copper sulfate contrast agent at a concentration of 1 g/L. The contrast agent enhances the signal intensity, which accelerates the measurements; however, it does not noticeably alter the fluid properties of the water. The water temperature was held constant at 20.5 °C. A continuous volumetric flow rate of 60 L/min was set using the flow supply system. This flow rate is much lower than what is typically experienced in-reactor, which is usually about 1200 L/min. Instead of targeting entirely realistic flow rates, this work intends to gain confidence in the experimental approach using a relatively simple experiment. MRV measurements were carried out using a MAGNETOM Prisma MRI system (Siemens Healthcare, Erlangen, Germany) at the Medical Center Freiburg in Freiburg, Germany. A velocity-encoded gradientecho FLASH (fast low angle shot) sequence was chosen for the

Table 1 Imaging and flow parameters.

4

Imaging parameters

Value

Echo time (TE) Repetition time (for all flow encodings) Flip angle of excitation Receiver bandwidth along one-dimensional readout Velocity sensitivity (VENC) Matrix size per FOV (x,y,z) Isotropic resolution (Δx = Δy = Δz) Number of averages per FOV (NSA) Total acquisition time

5.35 ms 33.20 ms 15° 445 Hz/pixel 0.40 m/s 160, 180, 320 0.78 mm 2 + Flow Off 235 min

Flow parameters

Value

Fluid material Reynolds number based on channel diameter Volumetric flow rate Water temperature Hydrostatic pressure

Light water (H2O) 11550 60 L/min 20.5 °C 1 atm

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following paragraphs.

δu (r ) ≈

3.2. Measurement uncertainty

1 2 NSA

Var {u1 (ROI ) − u2 (ROI )}

(2)

where u1(ROI) and u2(ROI) are vectors containing the velocity values of all voxels in the region of interest (ROI) from two acquisitions. NSA is the number of signal averages, and Var is the variance operator. The factor 2 arises from the subtraction of the two statistically independent images. For each velocity component, the variance is calculated over the three-dimensional ROI which contains millions of data points. The estimated measurement uncertainty represents, therefore, a global value. Note that the local measurement uncertainty can be lower or higher depending on local variations in the signal-to-noise ratio. 3.3. Systematic measurement errors

δr (r ) ≈ u (r ) The systematic errors in MRV include acquisition errors and discretization errors. As an example of discretization errors, all voxels at boundaries of different materials, e.g., water and channel wall, contain a mixed signal of both regions. This error is known as the partial volume effect. A higher resolution in voxel size decreases this effect because it better resolves the boundaries. On the other hand, decreasing voxel size also increases the measurement uncertainty because a lower number of spins is measured per voxel, which affects the signal-to-noise ratio. In this respect, a compromise is necessary, which is typically determined through experience and available scanner time. In the analysis of the flow bypass effect, the flow area is divided into two regions, representing the flow through the bundle and the bypass region. The border between these two regions is discretized by voxels and is therefore subject to errors. The maximum local error equals ± 0.5 voxel lengths, which corresponds to the case where the border lies precisely between two adjacent voxels. The uncertainty of whether these voxels belong to one of the two regions affects the flow quantification in these regions. Therefore, the flow rate calculations are carried out for an interval. The uncertainty in the fuel bundle diameter caused by discretization errors yields:

Dbundle = 103.4 mm ± Δx

(4)

Analog to VENC, the parameter AENC represent the sensitivity of the sequence to fluid acceleration, whereby a low value means high sensitivity. Note that the parameter VENC is a design parameter of the sequence, which is usually set as small as possible to achieve better precision. The parameter AENC is a spurious effect. It is emphasized that the actual error can be higher than the estimate in Eq. (4) because the acceleration depends on the actual fluid motion and not on the measured velocity values, which already include this error. So this estimate might not be the most conservative. Between spatial encoding and signal detection, the moving spins change their locations. With conventional MRV techniques as applied in this study, the different coordinates are encoded at different times in the sequence. As a result, the reconstructed signal is not consistent. For example, the reconstructed position of the spins may appear at a location in the fluid that the spins have never physically occupied. The underlying physics of this measurement error is discussed in more detail in Bruschewski et al. (2019). The determining time scale to estimate the degree of this error is the time delay between the individual encoding instances. As a conservative estimate, the misregistration effects are calculated based on the echo time (TE) of the sequence, which is always longer than any specific encoding interval. Thus, an estimate of the local relative misregistration (in numbers of voxels) is given by:

In MRV, the measurement uncertainty is related to the signal-tonoise ratio in the image. A prominent source of noise is the thermal motion of charge carriers in the sample and receiver chain (den Dekker and Sijbers, 2014). In the case that the acquisition is repeated (e.g. to average the signal) the most robust estimate is to calculate the measurement uncertainty from the variance between two individual images (Bruschewski et al., 2016b):

σu =

VENC u (r ) ∇u (r ) AENC u (r )

TE Δx

(5)

In this equation, values higher than one indicate that the acquired spins move further than one voxel length during one echo time. 4. Results 4.1. Flow field measurements The MRV data provides information on velocity and signal intensity. All voxels that are outside of the water volume correspond to signals with relatively weak intensity. These voxels can be removed by a threshold value of the signal intensity. The remaining geometry represents the fluid domain. As a demonstration of the imaging accuracy, the reconstructed geometry is compared to the design geometry of the fuel bundle (CAD, computer-aided design) in Fig. 4. The determined geometry is noisy, but the main features of the fuel bundle are correctly reproduced. An accurate description of the inlet conditions is important to allow a direct comparison to the CFD calculations in Part 2 of this study. The diffuser-nozzle system used in the experiment was designed to produce a flat velocity profile at z = −50 mm. The velocity profiles between the inlet and the leading edge of the bundle are shown in Fig. 5. Measurements directly at the inlet are not available. Nevertheless, it can be seen that the velocity field approaches a flat profile upstream of the leading edge. A flat inlet profile seems to be an appropriate assumption. Fig. 6 shows the axial velocity distribution for various axial positions inside the fuel channel. The other two velocity components (not shown) are close to zero almost everywhere in the flow field. Flow bypass, which is characteristic for this fuel bundle configuration, is visible in this figure. As an inherent feature of MRV, the velocity data is measured on a uniformly spaced Cartesian grid, which allows for a straightforward implementation of the partial derivatives of the velocity vectors. Similar to the results from a CFD simulation, it is possible to infer additional information from the vector field as a post-processing calculation, such as streamlines. Fig. 7 shows an example of streamline visualization. Again, it is seen that the flow bypass region redirects a relatively large amount of flow rate.

(3)

Acquisition errors encompass all image distortions that are related to the signal acquisition process before image reconstruction. For example, distortions in the magnetic field lead to clearly visible distortions in the image. Other examples of acquisition errors are chemical shift effects and susceptibility effects, which are related to the measured materials. These sources of error can be effectively avoided in welldesigned MRV experiments. The acquisition errors that are most important for MRV measurements are the errors that are directly related to the fluid motion. The velocity acquisition neglects all higher orders of motion. This assumption is never valid in actual flow as the fluid particles change their velocity as they travel through the flow domain. This effect is known as convective acceleration (u (r ) ∇u (r ) with r being the threedimensional position). The spurious effect of acceleration can be estimated directly from the measured velocity field. The local relative velocity deviation yields: 5

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Fig. 4. Comparison of the CAD design of the CANDU fuel bundle geometry (left) with the reconstructed geometry from the MRV measurement (right). From Bruschewski et al. (2016a).

Skovlunde, Denmark). Titanium dioxide was used for seeding purposes, which is a requirement for LDV but not MRV. Two positions were evaluated: one position (pos 1) was in the bypass region; the other position (pos 2) was in the center of the first sub-channel below the bypass region. It was not possible to measure the inside regions of the fuel bundle with LDV due to the limited optical access to the subchannel flow – only on the very top subchannel. For noise reduction, the MRV data is averaged over 3 × 3 grid points in the transversal plane, which corresponds to a rectangular area with 2.34 mm edge length. The LDV data is measured on a single line with an approximately circular measurement area with diameter 0.98 mm. The results in Fig. 10 confirm that the MRV data compares well with the LDV data for most of the axial positions. However, some deviations are visible at the leading edge of the fuel bundle. The location of these deviations agrees well with the differences observed in the flow rate calculation in Fig. 8. Note that these errors can also be a result of a possible mispositioning between the LDV traversing system and the MRV measurement grid. To sum up the current findings, the MRV data compares well with the reference data (flow meter and LDV). However, there are some deviations, particularly at the edges of the fuel bundle that need to be considered in the flow field analysis. The cause of these deviations is analyzed next.

4.2. Uncertainty and error analysis As a quantitative measure of the overall accuracy, the volumetric flow rate is calculated from the MRV velocity data for all streamwise positions. The calculation is accomplished by integrating the axial velocity from all voxels that contain water at each axial position. Fig. 8 shows the comparison of the calculated flow rate from MRV across the axial direction and the actual flow rate from the flowmeter. Most of the values are within the uncertainty limits of the flow rate sensor. However, at the edges of the bundle and the middle appendages, the calculated flow rate deviates more noticeably. The source of these errors will be discussed in this section. Fig. 9 shows the calculated area based on the MRV data compared to the known geometry from CAD. It can be seen that the area from MRV is slightly larger than the original design. The manufacturing process (i.e., laser sintering) has a much lower manufacturing tolerance than the deviations observed in Fig. 9. The differences between measurement and CAD must, therefore, come from discretization errors, i.e., partial volume errors. Note that the voxels at the boundaries contain a relatively low velocity. The contribution of this effect to the observed flow rate deviation is therefore expected to be relatively small. Fig. 10 shows a line-wise comparison of the MRV data to an LDV measurement under the same experimental conditions. The LDV data was obtained using a FlowExplorer system (Dantec Dynamics,

Fig. 5. Vertical (left) and horizontal (right) velocity profiles upstream of the bundle compared to the bulk velocity (Ub). The velocity profiles are averaged over the specified intervals to remove noise. 6

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Fig. 6. Contour plots of the axial velocity component at various axial positions. From Bruschewski et al. (2016a).

degree of error must appear in the flow rate calculation. It is particularly noteworthy that the actual flow rate deviations (Fig. 8) and the estimated error have a similar magnitude and the same characteristic trend in this region. The highest flow rate deviations occur in the flow region with the highest convective acceleration.

4.2.1. Measurement uncertainty Using Eq. (2), the three components of the measurement uncertainty are estimated as σu = [0.0104, 0.0098, 0.0102] m/s everywhere in the flow field. The relative uncertainty of the axial velocity is shown on the top right image in Fig. 11. Except for the boundary layers, the uncertainty is approximately 3% inside the subchannels of the fuel bundle and between 7% and 10% in the regions upstream to the bundle. The uncertainty represents the statistical deviations of the velocity data and explains the noisy velocity values in the velocity field shown in the top left image in Fig. 11. The statistical variations may also explain the noisy velocity data in Fig. 10 The volumetric flow rate calculation in Fig. 8 is an averaging process. The statistical deviations in the flow rate results are, therefore, significantly lower than the statistical variations of the individual velocity values. For this reason, the flow rate variations in Fig. 8 must arise from systematic errors. Two types of systematic errors are presented in detail, acceleration errors, and the effect of misregistration.

4.2.3. Misregistration The effect of misregistration was evaluated with Eq. (5) and the results are shown in the bottom right image in Fig. 11. The estimated misregistration exceeds 2.5 voxels in the selected field of view, which means that fluid particles can move up to 2 mm downstream during the encoding process. Misregistration is only a minor issue if the velocity stays approximately the same in the streamwise direction. However, in regions with strong convective acceleration; hence, at the edges of the fuel bundle, the misregistration effect is most pronounced. Presumably, this is another reason for the local flow rate deviations in Fig. 8. Other effects that contribute to the observed flow rate deviations are partial volume effects and masking errors. For example, the boundary layer at the leading edge of the fuel bundle is presumably smaller than one voxel length. Thus, any wall-adjacent voxel that contains flow but is masked by mistake contributes strongly to an underestimation of the flow rate. In summary, the presented MRV measurements provide accurate results but suffer from some measurement errors in certain areas that

4.2.2. Acceleration error The velocity deviation due to acceleration is estimated with Eq. (4). The results are shown in the bottom left image in Fig. 11. It can be seen that the acceleration error is generally low, except for the region at the leading edge of the fuel bundle. The velocity deviations are between 5 and 8% in this region. Because this effect is a systematic error, a similar 7

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Fig. 7. Three-dimensional axial velocity distribution and streamlines at the inlet of the fuel bundle. The CAD design of the CANDU fuel bundle geometry is shown in gray. From Bruschewski et al. (2016a).

are inherent to the MRV acquisition. These errors are predictable. It is shown that the estimated degree of error and its location in the flow field is consistent with the actual deviations. 4.3. Flow rate distribution in the fuel channel After the validation of the measurement results, the effect of flow bypass is examined in detail. As a quantitative measure, the flow bypass effect is characterized by the relative amount of flow rate in the bypass region:

Qbypass Qtotal Fig. 8. Volumetric flow rate calculated from the MRV velocity data compared to the actual flowrate as measured by the flow meter during the measurement. For better orientation, the geometry of the fuel assembly is shown in the graph.

=

Qbypass Qbundle + Qbypass

(6)

The associated flow regions are defined similarly to Fig. 3: the flow area of the fuel bundle (subscript: bundle) is a 103.4 mm diameter circular area minus the cross-sectional area of all 37 fuel elements. Possible discretization errors are considered, see Eq. (3). The flow area in the bypass region (subscript: bypass) is defined as the crescentshaped gap between the fuel bundle and the 110 mm diameter pressure tube. The evaluation of Eq. (6) with the MRV data is depicted in the top graph in Fig. 12. In addition to the calculated values, an error interval that contains velocity uncertainty (i.e., Eq. (2)) and discretization errors (i.e., Eq. (3)) is provided. It is noteworthy that the overall error is mainly contributed to discretization errors. The velocity uncertainty has a relatively small impact since this kind of error is reduced in the flow rate calculation, as explained before. It can be seen that near the upstream end plate, the relative flow rate through the bypass region is approximately 25% ± 2%. This value increases downstream as a more considerable amount of fluid is redistributed through the bypass region. It appears that the relative flow rate stabilizes at around 35 ± 3% near the downstream endplate. This value is significantly larger than the relative area of the bypass region of approximately 25%. As another method of quantifying the effect of flow bypass, the bulk

Fig. 9. Flow area measured by MRV compared to the target flow area from the original design (CAD). For better orientation, the geometry of the fuel assembly is shown in the graph.

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Fig. 10. Comparison of axial velocity measurements by MRV and LDV. The measurement positions in the transversal plane are defined on the right. The MRV data is averaged over 3 × 3 grid points in the transversal plane. For better orientation, the geometry of the fuel assembly is shown in the graph.

flow velocities are evaluated in the bypass region and the fuel bundle region:

Ubypass Ubundle

=

Qbypass Abundle Qbundle Abypass

region upstream of the fuel bundle contains a relatively high percentage of boundary layer flow. Therefore, less flow rate is transported through this region as compared to the projected bundle region. As the flow approaches the fuel bundle, the flow rate is redirected towards the bypass region. Similar to the axial development of the relative flow rate in Fig. 12 (top), the values increase until they converge to an almost constant value near the downstream endplate. At this streamwise position, the flow rate per unit area is approximately 90 ± 5% higher in the bypass region than in the sub-channels of the fuel bundle. Three spikes are observed near z = 0 mm, 250 mm and 500 mm that correspond to the upstream end plate, middle appendages, and

(7)

A value of one means that the flow rate per unit area is distributed equally in the bundle region and bypass region. A value higher than one means that the bulk flow velocity is increased in the bypass region. The bottom graph in Fig. 12 shows the evaluation of Eq. (7). Values smaller than one are seen upstream of the fuel bundle. These numbers are correct since the projection of the bypass region onto the flow

Fig. 11. Two-dimensional view of the axial velocity at the entrance of the fuel bundle (top left). Evaluation of the measurement uncertainty using Eq. (2) (top right). Assessment of the acceleration error (bottom left) and misregistration effect (bottom right) using Eqs. (4) and (5), respectively. From Bruschewski et al. (2016a). 9

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Fig. 12. Evaluation of the flow bypass effect. The top graph shows the relative flow rate through the bypass region corresponding to the total flow rate. The bottom chart shows the ratio of bulk flow velocities (flow rate per unit area). The error interval includes velocity uncertainty, Eq. (2) and partial volume effects, Eq. (3). For better orientation, the geometry of the fuel assembly is shown in the graphs.

downstream end plate, respectively. These spikes likely result from experimental errors, including partial volume effects and flow-related measurement errors as discussed in the previous section. 5. Discussion

•

The results strongly suggest that flow bypass is significant in a pressure tube that has a diameter 6% higher than as-received. These analyses applied a flow rate, temperature, and hydrostatic pressure that are all much less than what is experienced in-reactor. Another point worth making is that only a single bundle was investigated in this experiment, while there are 12–13 bundles per channel in a commercial plant. As previously mentioned, the diametral profile of the pressure tube in the axial direction is parabolic and often asymmetric at end-oflife (DeAbreu et al., 2018). Therefore, one must keep in mind that the results shown here are not directly transferable to commercial operation. The purpose of this study is rather to demonstrate the usefullness and efficiency of MRV for such type of problem as a demonstration problem. More realistic experiments in replicas of entire fuel channels with realistic diametral profiles are possible. The following effects need to be considered in designing such an investigation.

•

•

• Experimental setup: All presented experiments were conducted on a

clinical MRI system, which posed restrictions on the size and weight of the experimental equipment that ultimately limited the maximum Reynolds number attainable. Flexible hoses were used to connect

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the fuel channel model with a transportable pump unit. More realistic experiments with replicas from entire fuel channels (i.e., 12 bundles instead of one) require significantly more space, more powerful pumps, and heavy-duty piping. Recently, a new MRI laboratory was set up at the University of Rostock, which allows such experiments. Fabrication of fuel bundle replicas: At higher Reynolds numbers, the effect of surface roughness on the redistribution of the flow becomes more critical. The laser-sintered parts investigated in this study may not have a sufficiently smooth surface to be representative of real fuel bundles. There are other techniques for additive manufacturing that should be considered to achieve a more consistent surface roughness to a real bundle. Achievable pressures and temperatures: In this experiment, the pressures and temperatures of the system were limited by technical restrictions. It might be possible to find suitable MRI-compatible materials that can withstand more realistic conditions. However, future MRV experiments will still largely be limited to single-phase isothermal flows. Flow-related measurement errors: With higher velocity magnitude, the effect of flow misregistration becomes more pronounced. The standard MRV methods might be too inaccurate for such flow measurements. There are MRV methods that were specially developed for velocities larger than 1 m/s, such as SYNC SPI (Bruschewski et al., 2019). Note that these measurements take much longer than standard MRV examinations. Measurement precision: The measurement resolution in the MRV

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References

experiments should be increased to decrease partial volume effects. This measure will improve the accuracy of the results, in particular, the prediction of the flow redistribution.

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Compared to the experiments in this study, the experimental expenses, including the setup and the measurement time, will be significantly higher in more realistic fuel bundle experiments. It can be expected that such measurement will take days, compared to the 4-hour measurement demonstrated here. Excluding the investment costs of the MRI system, the overall costs will be still significantly lower than similar mean flow measurements using laser-optical measurement techniques. 6. Conclusion In this study, the 3D3C velocity distribution in a single 37-element CANDU fuel bundle replica residing in a 6% diametrally expanded pressure tube replica was analyzed under isothermal conditions. The MRV measurements showed that up to 35% of the fluid bypasses the bundle under these conditions. With regards to measurement accuracy, it was verified that the results are close to the actual flow behavior in the investigated fuel bundle replica. The data of this study is used for the validation of a CFD simulation conducted in Part 2 (Piro et al., 2019). The investigated model in this study represents a simplified case of a CANDU fuel channel at end-of-life conditions. More realistic tests could be performed using the same experimental methodology as in this study. These studies would require higher experimental expenses and longer measurement time. The overall expenses, however, would be relatively low given the amount of experimental data. In conclusion, this study demonstrates how the local mean velocities and flow distribution through a specific fuel channel configuration can be obtained with MRV. The experimental data is useful to validate numerical flow simulations and to assess the accuracy of nuclear reactor safety codes. Acknowledgments M. Bruschewski thanks Daniel Freudenhammer and Florian Wassermann (both formerly Technische Universtät Darmstadt) for providing their expertise and support for the experimental work. M.H.A. Piro thanks T. Nitheanandan (formerly CNL), M. Griffiths (formerly CNL), J. Spencer (CNL) for valuable technical discussions. This research was undertaken, in part, thanks to funding from the Canada Research Chairs program (950-231328) of the Natural Sciences and Engineering Research Council of Canada.

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