3D volumetric fluid-structure interaction measurements...

18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016

3D volumetric fluid-structure interaction measurements with non-intrusive optical measurement techniques on an earthquake shake table

Noah A. Weichselbaum 1, Shadman Hussain 1, Morteza Rahimi Abkenar 2, Majid T. Manzari 2, and Philippe M. Bardet1* 1: Department of Mechanical and Aerospace Engineering, The George Washington University, Washington, DC, United States

2: Department of Civil and EnvironmentalEngineering, The George Washington University, Washington, DC, United States * Correspondent author: [email protected]

Keywords: Flying PIV, FSI, PWR

ABSTRACT

Utilization of non-intrusive optical diagnostics in harsh environments allow for obtaining new insights into complex fluid structure interaction (FSI) problems. Here the effects of earthquakes on the core of a nuclear pressurized water reactor (PWR) are studied through optical measurements taken in the moving frame of reference on a large earthquake shake table. The PWR core contains the fissile material in long and slender fuel rods that comprise fuel bundles, and under typical operating conditions is exposed to a constant turbulent axial flow that is used to cool the rods. These fuel bundles are highly non-linear structures, and during an earthquake there is coupling between the external forcing from the seismic activity with the hydrodynamic forces from the surrounding fluid. To gain insights into this fully coupled FSI problem, a refractive index matched (RIM) experimental facility has been constructed to house full height surrogate acrylic fuel bundles. Acrylic (nPMMA=1.491) has a near index match to the working fluid para-cymene (np−cymene= 1.4885) at 20ºC and 589 nm. Through use of a binary mixture of para-cymene with cinnamic aldehyde this index matching is improved to allow for undistorted optical access throughout the facility. Fluid velocity fields are recorded with a custom flying PIV system that is rigidly mounted to the test section on the shake table, hence measurements are taken in the non-inertial reference frame. Simultaneously digital image correlation (DIC) measurements, utilizing a pulsing LED and camera, measure the fuel bundle response. Synchronization of these measurements techniques are achieved with a pulse generator, and timestamps are applied to all data to permit reconstructing the FSI in a post-processing phase. Data is presented with both water and the index matched binary mixture as the working fluid. In water fluid measurements are constrained to the bypass region surrounding the bundle, as the curved interface of the fuel rods would cause errors in the PIV measurement. In the binary mixture fluid measurements are presented in both the bypass region and within the fuel bundle. In both fluids it is found that at a critical Keulegan Carpenter number there is an onset of the shed of vortices from the fuel bundle. This is first of a kind data showing the appearance of these structures, and the significant effects of these structures on the bundle dynamics are presented.


1. Introduction Optical techniques for fluid structure interaction (FSI) measurements can provide fully coupled data with a high order of resolution in both complex geometries and in harsh environments. Here the FSI for a nuclear pressurized water reactor (PWR) fuel bundle in still fluid is studied. The composition of the fuel bundle is a 6×6 array of full height fuel rods (h = 4 m) that are held in this form by 6 spacer grids that constrain the rods with an intricate system of springs and dimples. This test section is mounted on a large 6 degree of freedom (DOF) shake table that is used to apply a base seismic excitation. To measure the structural response to the external forcing, digital image correlation (DIC) is utilized. Simultaneously a custom flying PIV system is used to capture the fluid velocity field in the non-inertial reference frame (Weichselbaum, et al (2015a)). The motivation for this work is to improve knowledge of the FSI that occurs in a PWR core during an earthquake. This is a complex FSI problem due to the non-linear response of the fuel bundles to external forcing. A prototypical fuel bundle in a PWR is composed of a 17×17 array of fuel rods that are zircaloy tubes with pellets of the nuclear material Uranium Oxide stacked inside. These fuel rods are long (h = 4 m) and slender (d = 9.5 mm) and are held together at fixed axial distances by spacer grids. The fuel bundles are only constrained at their vertical extremities by core plates. Hence during seismic events these bundles will vibrate, and concerns arise from the potential for impacts between neighboring bundles or with the core baffle wall. The core of a PWR is comprised of ~200 fuel bundles, with typical spacing between neighboring structures on the order of 2-5 millimeters. Impacts at the spacer grid level can cause irreparable damage to these fuel bundles. This is a twofold problem; 1- if the spacer grid impacts each other and bends guide tubes than control rod insertion is compromised, 2- if the fuel bundles are deformed too severely coolant channel geometry can be adversely affected preventing removal of residual heat from the fuel rods.


Fig. 1 (a) Rendering of experimental facility with fuel bundle located in middle and PIV measurement region

defined (b) Experimental facility mounted on the George Washington University shake table.

During normal operating conditions a turbulent axial flow cools the fuel rods. However, during a seismic event, ground waves from earthquakes have the potential to cause power outages prior to the ground motion impacting the reactor itself. The reactor will be under a loss of outside power condition and can be in station blackout. In this last accident scenario the fuel bundles would be in small velocity to still water environment when the external forcing is applied. Hence the need for the study of fuel bundle response in still fluid. Past experimental work in this environment has focused primarily on the structural response, commonly using linear variable displacement transducers (LVDT) to measure fuel bundle displacements. One of these experiments utilized pluck tests to evaluate the damping (Lu and Seel (2006)) on prototypical fuel bundles, where it was found that the damping varied exponentially with increasing the initial displacement of the mid-height spacer grid in still water. Experiments have also been conducted on 6 prototypical fuel bundles in a row on a large shake table. Tests were facilitated in air and in still fluid to characterize the added mass effect which is the mass of the fluid entrained by the rods during fuel bundle displacement (Viallet, et al (2003)). In this experiment again only the structure was characterized; LVDTs measured the bundle displacements, resistive force sensors the impacts between spacer grids, and accelerometers monitored the shake table. More recently work has been done to measure the FSI coupling where a single fuel bundle is externally


forced with a hydraulic jack that is rigidly connected to a single spacer grid (Ricciardi and Boccaccio (2014)). The experiments done there were in the presence of axial flow, and they measured the structural displacements again with LVDTs and measured the coupled fluid velocity field in the bypass around the fuel bundle with LDV. Here we are presenting the first work of the FSI coupling in still fluid with a RIM facility, where instead of LVDTs the non-intrusive optical method utilizing DIC tracks the structural response of the fuel bundle and simultaneously time resolved PIV provides full field fluid velocity measurements. 2. Experimental Facility To gain insights into the FSI occurring inside of a reactor core during seismic forcing, it is desired to have the ability to attain fluid velocity fields both around and inside of the fuel bundle. To attain the latter, a refractive index matched (RIM) facility is needed to avoid distortions from the curved rod interfaces that would be detrimental to the optical measurements. Thus a surrogate fuel bundle composed of acrylic rods is utilized here that can be index matched with a binary mixture of P-cymene and Cinnamic Aldehyde (Fort et al. (2015)). Pure P-cymene and acrylic have been used previously as index matched fluids (Haam et al. (2000), Haam and Brodkey (2000), and Hassan and Dominguez-Ontiveros (2008)). However, to match refractive indices accurately with pure P-cymene the working temperature of the fluid needs to be well below room temperature. This was not possible with our closed flow loop facility due to the volume of fluid that is ~3.5 m3, hence the ability to index match with the binary mixture near room temperature was very attractive. The geometry and material properties for the surrogate fuel bundle and a prototypical one can be seen in Table 1 along with the index matching properties for the working fluids.

Table 1. Scaling Parameters and Refractive Index Matching for Surrogate Fuel Bundle


Details of the scaling of this experimental facility that ensure the surrogate fuel bundle has similar dynamic responses as a prototypical one can be found in Weichselbaum et al. (2015b) The surrogate fuel bundle that is a 6×6 array of solid acrylic rods is mounted inside of a primary acrylic rectangular acrylic channel with a 154×124 mm2 cross section, Fig. 2. In the direction of forcing there is a 19 mm spacing, Fig. 2(a), to ensure the bundle oscillations don’t impact the inner channel wall, in the non-forcing direction there is a 5 mm spacing. Six spacer grids are used to hold the acrylic rods in place, where the top and bottom spacer grids are rigidly fixed to the acrylic channel, Fig. 2(b). The remaining 4 intermediate spacer grids are free to deflect. The displacement of these grids are tracked with a multi-camera DIC system that is presented in Section 3. Fig. 2(a) also shows the location of the PIV planes within the bundle cross section, where a horizontal and vertical light sheet intersect. The vertical light sheet, shown in red, is aligned with the center of the second rod from the front of the test section, and this is the location that results will be presented for in Section 4 at an elevation in the middle of the fuel bundle that is ~4 m above ground level.

Fig. 2 (a) Schematic of fuel bundle location inside primary acrylic channel (b) Mounting of surrogate fuel bundle


Fig. 2 also shows the direction of forcing from the shake table that applies 1D sinusoidal forcing in the x-direction. Results presented range in acceleration from 0.01 – 0.2 g where all optics mounted to the shake table have been tested up to accelerations of 0.4 g. 3. Instrumentation To measure the FSI coupling careful timing and synchronization of all measurement techniques has to be utilized to allow for data reconstruction. Data is recorded from three separate systems here; 1- DAQ module recording from 5 accelerometers at 2048 Hz, 2- DIC cameras recording at 256 fps, and 3- PIV cameras recording at 512 fps. For the DIC system, a pair of high powered pulsing LED’s and USB 3.0 cameras are used to track the movement of each of the 4 spacer grids that are free to deflect (Weichselbaum et al. (2015c)). 4 DIC systems are used to track the in plane displacements, while one additional system tracks the out of place displacements of spacer grid 2. Images are recorded from each camera at 256 fps with a resolution of 1280 x 256 pixels are recorded to a single computer. This computer is equipped with eight 1 TB hard drives in RAID 0 configuration for parallel writing along with dedicated USB 3.0 PCIe cards for optimum data transfer performance. With this setup data can be recorded from all 5 cameras for up to 4.5 hours. A cross correlation algorithm is then utilized to determine the displacements of the spacer girds to an accuracy of 4 µm. Fluid velocity measurements are attained with a custom flying PIV system is utilized (Weichselbaum et al. (2015a)). The working fluid is seeded with 30 micrometer neutrally buoyant hollow glass spheres, and the laser used to illuminate these particles is a dual cavity Nd:YLF laser capable of delivering up to 60 mJ per pulse at 1 kHz and has a repetition rate adjustable from 0 to 20 kHz with a fixed wavelength (λ = 527 nm). To deliver the laser light in a harsh environment, on a vibrating shake table, high powered multi-mode step index fiber optics are utilized. The laser is located 10 m away from the measurement region on a vibration isolation table. The cavities of the laser are first separated with a polarizing beam splitter, Fig. 3(a), then each cavity is further separated into at least 3 beams to allow for launching of 6 fiber optics. Each of the 6 fiber launch are paired to result in 3 flying PIV systems, where one beam is sent into a 100 µm fiber for the vertical light sheet and one beam into a 600 µm fiber for the horizontal light sheet. The two intersecting light sheets, Fig. 2(a), have a dual purpose; 1- from the horizontal light sheet the location of the vertical light sheet can be ascertained with a high level of accuracy


that is important for alignment with the center of rod 2, 2- allows for monitoring of beam vibrations in the vertical light sheet from the shake table forcing. A full description of this system and its attributes can be found in Weichselbaum et al. (2015a), in brief the output of the fiber optics is re-collimated, spread into a light sheet, and focused in the test section with a 5 lens element cage system. Normal to the vertical light sheet is a high speed CMOS camera that records straight to hard drive, at a resolution of 4 Mpixel at 560 fps this camera can record for up to 15 minutes continuous. Both the cage system and the camera for the vertical light sheet are mounted on remote controlled linear stages that allow for accurate alignment of light sheet within the test section and for focusing of the camera.

Fig. 3 (a) Optics design to launch 6 fiber optics from a single dual cavity laser (b) Intersecting light sheets delivered

to test section with high powered pulsing LED in background

To synchronize all of these measurement techniques a pulse generator is utilized from Berkley Nucleonics to trigger the USB 3.0 cameras and high powered pulsing LED’s for the DIC system, as well as the laser and high speed CMOS cameras for the PIV measurements (Weichselbaum et al. (2015c)). Additionally the pulse generator sends a 10 MHz clock out signal to discipline the master clock which is a SecureSync system from Spectracom. The system has the ability to synchronize its clock with GPS satellite and can output time and frequency information in various forms based on the options selected. In this setup, the time is sent to the computers recording data from the DAQ module, from the DIC cameras, and the PIV cameras via a military standard IRIG B protocol. Each computer has a dedicated PCIe based TSync card, also from Spectracom, to accept the time signal. This ensures that all the computers are referenced to the same time which is what allows for reconstructing the FSI coupling in a post processing phase.


4. Results To demonstrate the way in which the data from all three systems, defined in Section 3, are reconstructed, a single figure is shown in Fig. 4 with data from each measurement technique aligned by the time stamp embedded in each respective computer. In still water the first mode frequency of the bundle is found to be at 1.2 Hz, the amplitude of displacement at the center of the bundle will be largest at this mode, hence characterization of the coupled structure and fluid response here are of particular interest. In Fig. 4 a shaking test (ST) is reported with a fixed amplitude of 5 mm and a fixed frequency of 1.2 Hz for 30 cycles. This test runs for 27.7 seconds resulting in 7,090 frames with a field of view of 41.9×31.0 mm.

Fig. 4 Time histories of shake table acceleration, spacer grid 2 displacement, and vertical fluid velocity with water as

working fluid

It can be observed here that the fuel bundle oscillations that are reported for spacer grid 2 that is nearest the center of the bundle, lag the shake table oscillations by 333o for this particular case. PIV measurements here are from the vertical light sheet between the inner channel wall and the first rod in the positive x-direction, Fig. 2(a). Here two components of velocity are extracted W and U that correspond to z and x respectively, Fig. 2(b). PIV data is processed in DaVis version 8.2 where to accommodate for the moving boundary that is the rod wall, an algorithmic mask is utilized to automatically define the moving boundary (x = 11 mm in Fig. 5(a)) and the PIV interrogation domain. PIV processing consists of a four pass scheme, with interrogation


windows starting at 48×48 pixels and the final deformable window 24×24 pixels with 50% overlap. A sample vorticity contour derived from the full vector field can be seen in Fig. 5. A time history of a point at the center of the bypass, similar to what is shown in Fig. 5, for W is plotted in Fig. 4. This time series of W starts and stops with the bundle oscillations and takes approximately 10 cycles to reach a steady state for this vertical pulsatile flow.

Fig. 5 (a) Vorticity contour with ST at 7.5 and 1.4 Hz, (b) Vorticity contour with ST at10 and 1.4 Hz

With a ST at 5 mm and 1.2 Hz observations of the vorticity field only portrayed a viscous sublayer that changed signs with the direction of the pulsatile flow, this is similar to what is shown in Fig. 5(a). However, at larger ST amplitudes, Fig. 5(b) at 10 mm and 1.4 Hz, a periodic shedding of vortices is found to develop from the rod wall. These vortices have a consistent axial spacing that can be better observed in Fig. 6 where phase averaged vorticity contours are shown. Here the 0o phase angle is the neutral position of the bundle as it is moving in the positive x-direction, hence 90o is when the bypass is widest and 270o when it narrowest. This behavior is consistent at other frequencies, and is found that the onset of the shedding of vortices can be predicted by defining a critical Keulegan Carpenter (KC) number and β parameter.


Fig. 6 Phase averaged vorticity contours with ST at 10 mm and 1.4 Hz

The KC and β parameter (Eq. 1 and 2 respectively) were defined by Sarpkaya (1985) for a single cylinder oscillating sinusoidally in an unconfined viscous fluid, where um is the velocity of the cylinder, T the period of oscillation, and D the cylinder diameter. 𝐾𝐶 = %&'

( (1)

𝛽 = *+,- (2)

Sarpkaya found that coefficient of drag decreases linearly with increasing KC number until the critical KC number is met. At this point the coefficient of drag reaches a minimum value, after which it increases with a non-linear relationship with KC number. Here, although our geometry is much more complex and we are in a confined environment, we find that our data follow a similar trend. For an increasing β we find a decreasing KC value. Critical KC values for ST frequencies of 1.0, 1.2, 1.4, and 1.6 Hz in still water are shown in Fig. 7 with the colored data point. It can be observed here that the fuel bundle maximum displacement amplitude follows a


linear trend with the ST amplitude up to the critical KC value, after which the bundle displacement amplitude diverges for all cases.

Fig. 7 Fixed ST frequency plots with varying ST amplitude and critical KC value in water shown with filled data

point

From all of these tests in water it is found that the vertical pulsatile flow is repeatable for a ST fixed amplitude and forcing frequency. This is due to the initial and boundary conditions for the fuel bundle being tightly controlled in addition to the forcing from the shake table being repeatable. Thus a 3D scanning methodology can be employed where the laser sheet and camera are translated over the course of one experimental campaign and a total of 19 planes are acquired sequentially. The spacing between each plane is 1 mm, which corresponds to scanning between two rod centers (from row 2 to row 3). For each plane a total of 30 cycles are acquired with all the instruments with ST at 10 mm and 1.2 Hz. The results for this can be seen in Fig. 8 where instantaneous velocity profiles for U and W are plotted at varying phase angles in still water. To reconstruct the phased averaged data, the accelerometer and DIC data are first compared to assure that the table and structure behaved with a consistent and repeatable manner. In fact, for the run presented below, it was found that the first investigation plane was not repeatable and was discarded. Once the structural data have been qualified, displacement of spacer grid 2 obtained with DIC is used as a common instant in time to reconstruct the three dimensional velocity over the 30 cycles: each PIV plane is stacked next to the other in y direction.


What can be observed in this figure is that the pulsatile flow has a consistent phase lag across the bypass in the y-direction, and that in the middle of the two rods the W velocity fluctuations are greater than at the edges where the laser plane is aligned with the center of the rods. Additionally for the U component it can be observed now that fluid is injected and ejected from between the rods which wasn’t observable from the vertical PIV plane aligned with the center of rod 2.


Fig. 8 3D Instantaneous U and W Velocity Profiles at Varying Phase Angles in Still Water with ST forcing at 10 mm

and 1.2 Hz

With water as the working fluid PIV measurements were limited to the bypass region around the fuel bundle. With the index matched fluid that is a binary mixture of P-cymene and Cinnamadlehdye, measurements within the fuel bundle become attainable. Fig. 9 presents


vorticity contours at varying phase angles in the index matched fluid similar to the contours presented in Fig. 6 where water was the working fluid. The axially spaced vortices are again apparent, however, due to a difference in density and kinematic viscosity between water and P-cymene, which constitutes the majority of the binary mixture, it can be observed in Fig. 10 that the critical KC value occurs at a much lower ST forcing amplitude.

Fig. 9 Vorticity contours at varying phase angles for index matched fluid with ST at 5 mm and 1.3 Hz


Fig. 10 Fixed ST frequency plots with varying ST amplitude and critical KC value in index matched fluid shown

with filled data point

5. Discussion Non-intrusive optical techniques have been presented for acquiring full coupled FSI data on an earthquake shake table. From these measurements, a vertical pulsatile flow in still fluid that was not expected was found. This pulsatile flow makes sense though if the flow in the bypass is thought of as a pressure driven flow. As the bundle oscillates in the x-direction, a high pressure region will be created at the front of the bundle and a low pressure region in the wake. If the bundle was perfectly rigid this pressure gradient would be constant along the axial height. However, the bundle is not, and at first mode resonance there is a significant difference in bundle displacement from the mid-height of the fuel bundle to the bundle extremities. It is proposed that these differences in pressure gradient in the x-direction result in a pressure gradient in the z-direction that result in the pulsatile flow that is observed. Additionally KC and β parameters were found to be able to predict the onset of the shedding of vortices in this environment that will have a direct impact on fuel bundle dynamics. It is found that in both tests using water and the refractive index matched binary mixture, that similar critical KC and β values for a particular ST frequency predicted the appearance of these vortices.


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