Investigations On Flow And Flow-Induced Vibration Of Candu Fuel Bundles

Excitations induced by three-dimensional unsteady flows of ordinary water coolant through a string of CANDU fuel bundles in a fuel channel are investigated in this thesis. Several comprehensive computational fluid dynamics (CFD) models are developed and solved by means of large eddy simulation (LES), high performance computers and parallel processing scheme. The 12-bundle flow model is the first ever developed concerning flow in a very complex CANDU fuel channel. The lateral fluid flow and flow-induced excitations on every fuel bundle are obtained and analyzed for various combinations of bundle angular positions. The coherent nature of the flow through the multiple bundles inside the fuel channel exhibiting fluid excitations of frequencies spreaded over a wide band in the power spectra is a source of bundle lateral vibration. The flow features of different bundle regime are correlated both in time and frequency domain and they are sensitive to the bundle-to-bundle angular position. This finding directs that, to study the flow and flow-induced excitations and vibrations of a bundle string, it is necessary to include all bundles for fluid-structure interactions. Results from the computational model reveal that the misaligned interface


C ij
Cross stress tensor

Operating experiences
During normal reactor operations, vibration of the fuel bundles induced by flow is observed.
From the inherent design of the CANDU bundle and the fuel channel, the horizontally-laid bundles can have various types of small scale motion inside a pressure tube -rolling, sliding and bending vibration with respect to the designed equilibrium positions. However, it can induce impact or rubbing between the bundle outer surfaces and the pressure tube inner wall. Over a long period of time (almost decades), these bundle motions can cause wear and material loss from the pressure tube wall which is called fretting wear. It would be worth mentioning right at this point that, in reality, the fuel channel system is highly pressurized single phase flow in order to achieve the maximum possible turbulence of the coolant in the bundle subchannels so that heat transfer rate is maximized. Still there might be some minor leakages in the system which could lead to some bubble formation inside, which however, is not desirable.
Under operating conditions, unsteady coolant flow through fuel bundles were known to cause moderate to severe fretting marks on the inside surfaces of the pressure tube between the 4 o'clock and 8 o'clock positions (Judah, 1992;Norsworthy et al., 1994;Norsworthy and Ditschun, 1995). According to a survey of the commercial reactors (Stewart, 1992), fretting marks on the pressure tube inner wall were present in all fuel channels and were the worst near the inlet bundles.

Fuel bundle vibration phenomenon
Flow-induced vibration (FIV) mechanisms which are relevant to nuclear reactor components are: fluidelastic instability, vortex shedding, turbulence-induced excitation and acoustic resonance.
The fluid-elastic instabilities result from coupling between fluid-induced dynamic forces and the motion of structures. Instability occurs when the flow velocity is sufficiently high so that the energy absorbed from the fluid forces exceeds the energy dissipated by damping. The fluid-elastic instability usually leads to excessive vibration. The minimum velocity at which instability occurs is called the critical velocity for fluid-elastic instability. Since, the flexural rigidity of components such as piping and fuel elements is relatively large, the flow velocities are much lower than the critical velocity. The details on the fluid-elastic instability are documented by researchers (Blevins, 1993;Au-Yang, 2001;Paidoussis, 1966Paidoussis, , 2004. Earlier studies, both analytical and experimental, have shown that for fuel bundles, fluid-elastic instability is not a driving factor since the mean flow velocity in the bundle is much less than the critical value, required for instability to occur (Paidoussis, 2004;Zhang and Yu, 2008).
Vibration induced by the vortex shedding is another form of flow-induced structural motion.
A structure (e.g., a cylinder) when subjected to cross-flow, sheds vortices alternatively from one side and then the other which exerts varying pressure distribution on the structure, causes net fluctuating reaction forces. When the natural frequency of the structure, corresponding to lateral structural movement in the direction of the flow, matches the vortex shedding frequency, a phenomenon called lock-in occurs resulting in an amplified vibration.
The flow inside a fuel bundle structure was earlier regarded as parallel flow (Pettigrew, 1993;Blevins, 1993). However, the flow in the inlet endplate subchannels and bundle-tobundle interface regions are practically cross-flow Zhang and Yu, 2011;Bhattacharya et al., 2011a;Bhattacharya et al., 2012).
The fuel bundle vibration may be caused by turbulence. Turbulence-induced excitation generates random pressure fluctuations around the surface of a component. Turbulenceinduced excitation was considered to be the principal vibration excitation mechanism in axial flow since the flow velocity in the fuel bundles falls in the subcritical region.
Therefore, it was believed that turbulence-induced excitations may produce enough bundle vibration to cause wear in the supporting tube. However, Yetisir and Fisher (1997) pointed out that the small scale parallel-flow turbulence alone is not sufficient to produce the required level of bundle vibration and work-rate for the observed fretting marks on the pressure tube surface. Moreover, some recent studies report that the mixed parallel and cross flow through the various bundle subchannels and bundle interfaces can act as a potential source of FIV of fuel bundles (Zhang and Yu, 2011;Bhattacharya et al., 2011a;Bhattacharya et al., 2012).
The acoustic pressure pulsations, originating from the pumps or acoustic noise generated by piping elements such as valves can excite acoustic resonances in a receptive component of the piping system. If the acoustic resonance frequency is close to that of the component, significant vibration may occur. The possible damage due to acoustic pulsations can be reduced to some extent by modifying the system components, as documented by Misra et al., (1994). In this sense, it would be worthwhile to mention that acoustic frequencies exhibit sharp spikes which are easily distinguishable and thus provide scope for necessary modification on the structural design to avoid matching of any such frequencies in order to skip resonance.

Analytical and experimental study
Over the past few decades, research has been conducted in the field of CANDU fuel bundle vibration, emanating from a single element to a complete fuel bundle. However, most of them, during the earlier time, considered fuel bundle vibration as a parallel flow phenomenon. An analytical model was developed for a cluster of cylinders in the axial flow and the fluid coupling terms in the added mass were derived by Chen and Wambsganss (1972) and Chen (1975). In another work by Paidoussis (1982), a thorough study was made on the vibration problem encountered in reactors and reactor peripherals by the axial and the cross flow.
Another aspect of fuel bundle vibration subjected to axial flow is due to the turbulence experienced by the structure. Gorman (1971) modeled the random vibration response of a fuel element in two-phase turbulent coolant flow and came up with a conclusion that higher amplitude vibration is related to the statistical properties of the pressure field surrounding the surface of the fuel element. Paidoussis and Curling (1985) develped an anlytical model for vibration of a cluster of cylinders in parallel turbulent flow. They later carried out an experimental investigation on the characterization of the wall pressure fluctuation (Curling and Paidoussis, 1992). The turbulence, the axial velocity and the wall shear stress variation in subchannels around a CANDU-6 bundle were measured through experiments by D'Arcy and Schenk (1987). Pettigrew (1993), in an experimental investigation on CANDU fuel bundle vibration, reported that the vibration amplitudes increase with the mass flow rates and the recorded RMS values of vibration response was within 10 μm. Yetisir and Fisher (1997) developed an analytical model for a single fuel element subjected to turbulence excitation modeled by random excitation forces applied uniformly on the fuel element. They found that the fuel element vibration due to the flow-induced random turbulent excitation is insufficient by itself to produce the required level of work rate causing the fretting damage observed in some commercial CANDU reactors. Therefore, if turbulence-induced excitations are incapable of producing transverse vibration required to cause observed material loss for a single fuel element, then it is most unlikely for a whole fuel bundle to vibrate only by turbulence. From the investigation of Simth and Derken (1998) on a single CANDU-6 fuel bundle, it has been found that the bundle vibration is a mixture of rolling and bending motion; the unsteady forces acting on the bundle is reduced with the inclusion of the straightener in the inlet.
Some of most recent research work revealed that CANDU fuel bundle flow is very complex Zhang and Yu, 2011;Bhattacharya et al., 2012). This is due to the presence of endplates which consist of several ribs and rings contributing to the generation of some local cross-flow around the entrance of the inlet bundle and interfaces between neighbouring bundles. Bhattacharya et al., (2011a), in an experimental work on simulated 43-element CANDU fuel bundle, observed that the bundle lateral vibration frequency is proportional to the inlet velocity of the flow entering the bundle -an indication of the existence of vortex shedding phenomenon. The effect of bundle angular misalignment has been studied by Vijayan et al. (1999). They carried out experiments to measure the pressure drop across various components of the CANDU reactor fuel channel under single-phase flow conditions. The experimental results indicated that the variation in the bundle alignment at the junction can result a maximum variation of ±6% in the pressure drop across the 13-bundle string in a fuel channel. However, they did not evaluate any effect of misalignment on the bundle response or the fluid excitations. Further work on this area in understanding the bundle flow mechanism and also the cause of bundle vibration inside the whole fuel cannel is thus required.

Approach with computational fluid dynamics
Flow inside a CANDU fuel channel is a large scale flow problem. The lack of comprehensive studies of the fuel channel flow in the past was due to the extreme complexities of the flow structure and the large computational demand of the problem. With the rapid advancement in the computing technology and parellel processing technique, numerical solutions for very large scale problem are now possible. Various numerical schemes have been employed in the literature to solve three-dimensional unsteady flow problems. Lee and Jang (1997) investigated the turbulent flow in an array of bare elements by solving the Reynolds Averaged Navier-Stokes (RANS) equations, in conjunction with the non-linear k-ε method. Suh and Lightstone (2004) concluded that the k-ε method is unable to predict secondary flows inside complex subchannel areas in element-bundle geometry. Chang and Tavoularis (2007)  anisotropic turbulence with high accuracy. In LES scheme, the filtered N-S equations are solved in such a way that eddies larger than the mesh size are computed directly, while eddies smaller than the mesh size are modeled implicitly. The advantage of LES is that direct determination of the large eddies yields higher accuracy in modeling the unsteady flow through complex geometries like bundle subchannels because of their geometrydependency and unsteady nature. The small scale eddies are modeled by sub-grid scale (SGS) modeling. Barsamina and Hassan (1997)  reported (Rollet-Miet et al., 1999;Benhamadouche and Laurence, 2003;Baglietto et al., 2006). In LES applications, the Smagorinsky model is commonly used with a constant, C s (Smagorinsky, 1963). This requires the use of additional wall functions in order to dampen the subgrid scale viscosity near the solid boundaries. To resolve this problem, a dynamic subgrid scale (DSGS) model is used (Germano et al., 1991), where the model parameter is dynamically calculated on the basis of the resolved scales. This improvement on the Smagorinsky model was initially proposed by Germano et al. (1991) and then modified by Lilly (1992). Hassan and Barsamian (1999) applied the Smagorinsky model and the DSGS model based on Lilly's modification to a 9 element non-staggered bundle arrangement.
They concluded that LES is a good alternative in solving large scale engineering applications with complex geometries. Kim and No (2004)  It is known that for any structure to be excited it takes two, i.e., both the excitation frequency and the structural mode should match in order to produce a non-zero joint acceptance between these two factors. Now, since the fuel bundles or the string of fuel bundles vibrate inside the fuel channel meaning that there has to be some sources of excitation which combines with the structural modes to provide the energy of vibration to the fuel bundle system. The present study is mainly aimed towards understanding the possible sources of potential fluid excitations in a much comprehensive manner.
Therefore, the mixed cross and parallel flows in the entrance region and the bundle-tobundle interface regions appear to be responsible for producing the large amplitude flow excitations. The flow inside the fuel bundle subchannels is responsible for connecting and forming a very complex and coherent flow pattern inside the bundle-filled fuel channel. For the present investigation, it was found that to properly identify the true flow-induced fuel bundle vibration mechanism, it is necessary to include the entire string of fuel bundles and the pressure tube for modeling the fluid flow (Bhattacharya and Yu, 2013) and the fluidstructure interactions in the CFD models.  To evaluate the effects of bundle-to-bundle angular misalignments on unsteady fluid forces, which are responsible for fuel string vibration;

Motivation and objectives of the present research
 To investigate experimentally the vibration of a short string of simulated fuel bundles with various angular misalignments in a water loop to find the FIV mechanism and also to analyze effect of bundle angular misalignments on the FIV.

Methodology and organization of thesis
To deliver on the objectives of the thesis, both computational and experimental approaches are taken. Detailed methodologies of these approaches are outlined below.

Computational approach
As shown in Fig. 1-2, the flow through a 12-bundle string fuel channel consists of the following distinctive regions: (a) entry to the inlet bundle, (b) interfaces between neighboring bundles, where the fluid particles, due to the bundle geometry, flow in a very complex manner like mixed cross and parallel flow. This leads to enhancement of the lateral fluid force acting on the bundles and ultimately higher bundle side-to-side motion.
Therefore, to understand the bundle flow mechanism accurately, flow should be modeled for multiple bundles, possibly for a complete fuel channel. The methodology considered in this research work is schematically presented in Fig. 1-2 Chang and Tavoularis (2007). Then the computational approach is extended to a half bundle CFD model by considering a clear pipe zone, an interim endplate zone and half of the first bundle zone in the flow model (refer to Case-A of Fig. 1-2). The results from this model are compared with the experimental work of D' Arcy and Schenk (1987). This preliminary work, as described in Chapter 2, is an establishing step of the computational and solution technique being adopted for the CFD models which will provide confidence before extending it to a 12 bundle CFD model. At this juncture, the already tested computational scheme can be extended for a larger flow domain with 12 bundles placed inside a fuel channel. The physical domain for which this numerical model is created represents different cases with various angular misalignment combinations at the bundle-to-bundle interfaces, as sketched in Case-B of Fig. 1-2. The idea of this study is to have an overall view on the fluid flow and its lateral excitations on each of the bundles with several bundle misalignment combinations out of numerous possible hypothetical angular misalignments at different interfaces in a complete fuel channel. This is one of the most significant attempts made to date in regards to capturing comprehensively the flow and its characteristics in the whole fuel channel for a CANDU type reactor. Chapter 3 discusses various aspects of this study with much detail.
From the inherent design of the CANDU fuel channel, there could be countless different combinations of angular misalignment out of the 11 bundle interfaces in a single fuel channel filled with 12 bundles. Both developing and solving CFD models with so many combinations are hard to execute practically, as well as being computationally demanding.
Therefore, the investigation on the effect of angular position on the lateral fluid excitations is carried out with two bundles only. It may not represent though the true fuel channel model, but surely it will give some light to the phenomenon under examination. The computational scheme for this flow problem is taken from the 12-bundle CFD model. Thus a CFD model is prepared consisting of two inlet CANDU-6 bundles (refer to Case-C of Fig.   1-2); the model can take different misalignment configurations between the two bundles, as presented in Chapter 4. This work expands on the possible effect of bundle-to-bundle angular misalignment on the lateral fluid excitations, and thereby identifies some critical misalignment orientations at which fuel bundle may experience higher lateral fluid forces.

Experimental approach
Ideally, a test loop with 12 bundles placed in it should be used for the experimental study.
But due to various limitations e.g., space, driving pump etc., the experiments could be collectively will deliver the material and the results that meet the objectives of the present research study

Conclusion and future work
The findings from the present research study are summarized in Chapter 5. Some possible avenues for expanding the current work, towards achieving the larger goal to addressing the fuel bundle vibration induced by the flow in a more comprehensive way, are also provided in Chapter 5.

FLOW MODELING SCHEME INSIDE FUEL CHANNEL
The flow regime inside the fuel channel where heavy water fluid particles travel from the clear pipe zone to an entirely different and complex bundle subchannels through a number of thin endplates in the interface zones is of importance to this study. The theory behind the development of the computational model and also some idealized flow models will be discussed in this chapter. The scheme adopted for the computational model as elaborated in the coming sections will be generic to the next chapters.

Approach for modeling
In an ideal situation, the flow domain inside the fuel channel containing 12 bundles with bearing pads and spacer pads attached to them along with the end-fittings at the two ends of the bundle string should be modeled. However, this leads to an enormous and very complicated computational model which might not be feasible practically, at least as of now.
Therefore, in this research study, primarily a meshing scheme is developed for a much

Assumptions made in model building
Like any other research, the present research also has certain assumptions made while developing the computational model. They are as mentioned here.
The first assumption that is made while developing all the computaional model is that the boundary of the flow domain, i.e., the walls of the fuel bundle structure, is fixed and hence cannot move. However, in actual practice they are not. Thus, the present computational work lacks to some extent to capture the real flow and the associated fluid-structure interaction phenomenon.
Another important aspect is that in real CANDU bundles, the bearing pads and the spacer pads are installed to support the bundle inside the pressure tube and to avoid inter-element impacting, respectively. These pads are not considered while preparing the computational models, to avoid more complexity. It may be useful to mention here that the projected area of obstruction by all 18 bearing pad considered together is in the range of about 2% of the overall pipe flow area. Therefore, influence in changing the bundle subchannel flow pattern is deemed to be minor and hence, neglected in the current study.
It is to be noted that the above assumptions are followed for all the computational models developed in the current research.

Modeling of a sector of bundle flow
This flow problem contains one sixth of a 37-element CANDU fuel bundle with air as the flowing fluid as studied by Chang and Tavoularis (2007).  Table 2-1, are created and solved using LES to simulate the parallel flow problem studied by Chang and Tavoularis (2007). The value of z  is kept to a fixed value of 4 mm because in that direction the flow domain has the longest dimension. Since the highest skewness value of the cell volumes for the three meshes is 0.7, which is less than 0.9 required of a quality grid, the mesh distribution attained is good.

Solution of the computational model
As described earlier, the computational models are solved using the LES scheme. Now, when the LES technique is employed to solve the three-dimensional filtered unsteady N-S equations, flow structures larger than the scaling filters are resolved directly; whereas, subgrid scales are used to model structures smaller than the filter scale (Chung, 2002). The filtered momentum and continuity equations for incompressible flow without body forces can be written as (Sagaut, 2006), where, u i , are the flow velocity components; p is the pressure;  is the density; and  is kinematic viscosity; the over-bar denotes the filtered quantity; and ij  is the subgrid stress components. Leonard (1974) expressed the subgrid stress term in the form of a triple summation as, represent the Leonard tensor, cross-stress tensor and Reynolds subgrid tensor, respectively, with a view to decomposing the non-linear term j i u u to finally arrive at (Sagaut, 2006), These are turbulent stresses for grid filters, which can ultimately be determined by filtered velocity fields through interaction among (i) resolved scales transferring energy to small scales, (ii) unresolved scales transferring energy to either large or small scales, and (iii) small scales producing energy from small scales to large scales (Chung, 2002).
In the Smagorinsky subgrid model, the subgrid stress components are modeled as, where, C s  is the mixing length and C s is the Smagorinsky constant having a value between 0.1 and 0.2;  is the filter length scale or cubic root of the cell volume, i.e., usually the size of the computational grids. In the current study, the value of C s is taken as 0.1, which is default value in FLUENT.
A cluster of supercomputers, in conjunction with a parallel processing scheme, are utilized to obtain a numerical solution. A steady-state solution is first sought using the k- method.
The converged steady-state solution is subsequently used as the initial condition for obtaining an unsteady state solution with LES.

Results
The time-averaged streamwise velocities (U/U max ) around the outer-middle element are compared in Fig. 2-2 for  = 60 o and  = 180 o at which data were measured for a longer range of r/d ratios. Here r is the local radial co-ordinate; d is the element diameter; and  is the orientation angle. It is worth mentioning here that these data are taken at locations starting from r/d ratio of 0.514, but not exactly on the element outer surface where a no-slip boundary condition is imposed. It can be seen that for both  values, the simulation results obtained using the present CFD models, with LES approach those of Chang and Tavoularis (2007) as the mesh grid size becomes finer. The present measurements and obtained trend are in good agreement with the already measured trend, but based on the results obtained from balancing the conflicting needs for accuracy and affordability of computations, Mesh-I is adopted for a more comprehensive verification against the independently obtained results in Fig. 2-3. An examination of the results reveals that there is good agreement among the three sets of results independently obtained by experiments and URANS (Chang and Tavoularis 2007), and LES in this study. Only minor differences are observed for  = 120 o at higher r/d ratios where a small under-prediction is noticed.

Modeling of a full section bundle flow with the inlet endplate
As described at the beginning of this chapter, the flow modeling of a complete CANDU fuel channel is a large-scale complex problem. It would be, therefore, appropriate to test the computational scheme adopted and verified in a 60 o sector parallel flow model, as elaborated in section 2.3, for a much simplified flow domain before implementing it into a full scale fuel channel model with 12 bundles. Thus, a small CFD model is developed to examine this issue, which is discussed briefly in the following sub-sections.

Model description
A computational model consisting of (i) a pipe of 6D in length, where D is the inner diameter of the pressure tube, (ii) all endplate subchannels formed by the circular rings and radial ribs, (iii) the bundle subchannels formed by fuel element outer surfaces, and (iv) finally the gap subchannels formed between the outer fuel element surfaces and the pressure tube inner surface, is created using GAMBIT and FLUENT to simulate the entrance flow

Meshing Scheme
A sectional view of the grid in the A-A plane, used for the flow problem in Fig of the grid are given in Table 2-2. In addition to the LES approach with Dynamic Smagorinsky Model as described in section 2.3.1, the energy equation is added to the solver as follows: where e is the energy obtained using with h being the enthalpy. Constant specific heat is considered for the present problem, so the enthalpy may be written as The accuracy of the LES technique, primarily dependent on the size and quality of the meshes, can be evaluated using the three Kolmogorov microscales -the length scale , the time scale  and the velocity scale  . According to Tennekes and Lumley (1972), the Kolmogorov scales may be determined from the following equations, where, the Reynolds number Since the near-wall mesh resolution is of critical importance in LES, the thickness of the first layer of cells near a wall must meet the requirement: y + = 1, which is followed in the current study. Details pertaining to the boundary layer are provided in Table 2

Domain Partitioning, Boundary Conditions
The present model domain is segregated into several regions to handle different geometries of the pipe section, the endplate subchannels and the bundle subchannels. Each transition zone consists of a different geometry and these different geometrical regions were connected to each other by the interface surfaces. This allows a transition through nonconformal meshes.
The inlet face is defined as the velocity inlet since the mean axial flow is known a priori at this cross-section. The outlet surface is specified as the outflow, which defines no z-gradient of flow parameters. This is in accordance to the actual situation since at the mid-span of the CANDU bundle fluid particle has almost minimal z-gradient (Zhang and Yu, 2011). The inner wall of the tube surrounding the bundle and the outer walls of all elements are defined as walls with the no-slip condition. This is, however, worth mentioning here that modeling a half of the bundle and analyzing its behavior in isolation of the other neighboring bundles would not be fully correct for an ideal situation. Because, even at the middle of the bundle the fluid has influence from the interface zone having the other endplate which is not modeled. However, the idea of this half bundle model is to verify the extent of ability of the CFD model to predict the flow features. This will be carried out by comparing the results with that of experimental work from literature.

Validation of the results
The results of this half bundle CFD model are compared with the measurement done by

Results
Results on the z-velocity and corresponding pathlines are shown in the coming sub-sections.  The contour at the axial location of 15D h further downstream does not show the reversal of flow, which is understandable, but some periodic distribution of flow, with a periodicity of 120 o in the azimuthal direction, can be observed.

Results of z-velocity
From Fig. 2-10, it can be noticed that fluid particles shift from its original flow path to a different one; but, the flow is showing a pattern that near the half way of the bundle it reflects lesser movement in the transverse direction.

Flow development after endplate
Typical flow development with time is shown by Fig. 2-11 by a series of images. Pathlines are shown by lines varying from darker to lighter for four source surfaces to locations away from the four sources, respectively. These pathlines are generated from four different tiny surfaces at pre-selected locations. Two surfaces are on the left side and the other two are on the right side, as shown by each image. Surfaces created on the left side are at centre of the subchannels and represent a wide-gap region; whereas, surfaces created on the right side are between two elements and represent a narrow-gap region. To have a clearer view for better understanding, elements are not shown for row (a) and only a few elements are shown for row (b) and row (c). The three columns represent three different instants of time. A very interesting phenomenon is noticed for the source at the bottom-right location. Flow coming from this source area shows strong swirling motion in its path although the deviation is small. This observation can be verified in the isometric images where this effect is seen to be very prominent.
Another important observation is that, for all images, flow coming from a source near the endplate rib similar to sources at the top-left, top-right and bottom-right, gets deviated much more than that coming through the clear subchannel area, similar to the source at the bottom-left. This confirms that the presence of the endplate ribs/rings influences the flow to behave like cross-flow around the entrance region and helps generate wakes. Ultimately, due to the combined effect of all these ribs/rings, the bundle experiences a swirling-like flow through subchannels, as seen in Fig. 2-10.

Summary
From both the one-sixth sector and full cross-section bundle model, it is observed that the computational scheme adopted is capable of predicting the flow features in bundle subchannels of various asymmetric geometries. One of the findings from this part of study is the occurrence of swirling flow inside the bundle. Results demonstrate that the flow in the vicinity of the inlet bundle is far from the commonly perceived parallel flow. On the contrary, it is a mix of cross and parallel flow, and the presence of endplate ribs and rings are the reason behind this. However, in order to judge the fluid behavior inside the fuel channel more precisely, modeling a comprehensive flow model considering all 12 bundles would be appropriate and this is investigated in the following chapter. The present work deals with an application of a previously validated LES scheme (Bhattacharya et al., 2012) with an aim to developing a CFD model for a complete string of 12 bundles and assesses the nature of the flow and flow-induced excitations onto different bundles inside the fuel channel. The reason for selecting the LES scheme used in this work and details associated with the scheme are already described in much detail in earlier chapters and therefore, not included here. However, for clarity, readers are advised to please refer to Chapter 2 for further details on the CFD modeling schemes and its solution techniques adopted in this study.
The CANDU fuel bundles are not axi-symmetric structures. The angular position of fuel bundle is not controlled during refueling. The fuel bundles can take on difference angular positions inside the fuel channel. In this study, to address the effect of the possible angular misalignments between different bundles on the flow characteristics inside a complete CANDU fuel channel with 12 bundles, three different CFD models are created: (a) one with all bundles fully aligned to each other, (b) one with misalignment existing at two different bundle interfaces, and (c) another with all misaligned interfaces. The focus of this study is to see the effect of the angular misalignments on the flow and flow-induced unsteady lateral forces on each bundle in the string.

Description of the flow domain
As mentioned earlier, three different CFD models are developed with the complete length of a CANDU-6 fuel channel containing string of 12 bundles. The first model has all fuel bundles perfectly aligned to each other inside the pressure tube, as illustrated for Model-1 of  Fig. 3-1). Thus, with these three models, the nature of the flow and flow-induced unsteady forces onto the different bundles can be captured comprehensively. Please note that, the first bundle (BD-1) and the last bundle (BD-12) are always referred here with respect to the coolant's inlet and outlet flow direction, respectively (refer Fig. 3-1).

Solution scheme
For solving the computational problems mentioned in the previous section, the LES scheme, which is already tested and validated, is employed. The details for the LES scheme implemented in this study are not elucidated in this section and can be found in Chapter 2.
The time step size in this study is chosen to be 510 -5 s, which is well below the large eddy turn-over-time (LETOT) of 2.410 -4 s. The mean axial flow velocities considered is 2.4 m/s at the inlet corresponding to an average velocity of 6 m/s through the bundle subchannels and the corresponding Reynolds number is 4.8610 4 . The temperature everywhere in the fluid (water) is assumed to be 300 o C. A static pressure of 10 MPa is used at the inlet to simulate operating conditions similar to in-situ.

Computational resource
Each of the computational models has about 55 millions grid cells. Therefore, the enormity of such a large scale numerical problem requires very efficient, accurate and high performance computing resources. The numerical solution is obtained for the three dimensional unsteady flow using a cluster of 60 high performance computer, in conjunction with a parallel processing scheme. The cluster consists of eight shared-memory machines that are high-end Sun SPARC Enterprise M9000 Servers. Each of these servers consists of 64 quad-core 2.52 GHz Sparc64 VII processors; also the servers have a total of 2 TB of memory (8 GB per core). A steady-state solution is first sought using the k- model. The

Validation
The previously verified computational scheme, as described in Chaper 2, is extended to develop this 12 bundle flow model. To avoid redundancy, the details for this validation are not mentioned here and readers are requested to kindly refer to Chapter 2 for further insight.

Results
The present chapter will concentrate only on the flow features for different bundles along the whole length of the fuel channel considering various misalignment configurations. To demonstrate this, various flow parameters, like flow velocities, fluid excitaion force, for each fuel bundle, are considered for analysis and discussion. It is observed from earlier studies (Zhang and Yu, 2011;Bhattacharya et al., 2012a), that the fluid excitaions for bundle lateral motion primarily come from the region around the endplates, i.e., the inlet and the interface zones, where the flow is mainly mixed of cross and parallel flow, compared to the almost parallel flow at the mid-bundle locations. Thus, the analysis in the subsequent sections will be done for parameters in transverse, i.e., x and y direction, with z being the longitudinal or axial direction of the flow model. The next subsections present contours, time histories, mean and RMS values for different parameters for different bundles to showcase the flow characteristics for the whole bundle string.
From the description of the three models, as depicted in section 3.2.1, it can be seen that Model-3 is entirely different from the other two models due to the fact that only in Model-3 all interfaces are with misaligned bundle orientations (Fig. 3-1). However, except for two specific interface locations, i.e., between BD-4 & 5 and BD-8 & 9, all interfaces of model 1 and 2 are with fully aligned bundle orientation. Therefore, from this aspect, it is assumed that results from Model-3 will have remote chance of similarity with other two models but, between model 1 and 2 similar results can be expected except for those two misaligned interfaces, as indicated above. Thus, a comparative study of flow parameters around these two interfaces would be a legitimate and logical approach in order to examine the effect of the angular misalignment on the bundle subchannel flow. This is worked out in the following sections.

Velocity contours at various interfaces
In Fig. 3-2

Velocity vectors at various interfaces
First, in Fig. 3-4, radial velocity vectors are presented. It is very clearly noticeable that in both the cross sections, i.e., BD-4 & 8, radial components are not so significant in case of model-1 compared to that of Model-2, where presence of strong radial vectors is visible in various subchannels. Moreover, it should also be emphasized here that the occurrence of the strong radial vectors in the subchannels of the flow domain is localized to opposite sides of the vertical axis, towards left in case of BD-4 and towards right in case of BD-8. This can be explained in this way, that for the flowing fluid of BD-8, the BD-9 is rotated in the direction opposite to that of flowing fluid of BD-4 entering BD-5 (refer to Fig. 3-1). Fig. 3-4 In-plane radial velocity vectors (10x scale).
In order to see the vectors more clearly by their length and orientation, a zoom-in view is also produced for a portion in the upper half of the cross-section, as shown in Fig. 3-5. It is very clear from these vectors plots that the misaligned interfaces create considerably higher (from 0.7 m/s to 2.37 m/s in aligned and misaligned cases, respectively, i.e., almost 3 times higher for the maximum value) transverse flow motion across various subchannels. Therefore, going by this observation, BD-4 and BD-8 should be subjected to opposite transverse fluid excitations, which would be investigated in the section 3.4.4 of this chapter.

Discussion on x-force (F x )
The

Discussion on y-force (F y )
Not surprisingly, are found similar outcomes from the time histories of the lift force or the yforce of different bundles (Fig. 3-9). One can easily notice that the overall range of amplitude varies between ±30 N and the large deviation from the mean is observed again for the BD-4, 5, 8 & 9, which are located around the misaligned interfaces. Also, like x-force, the fluctuations of fluid excitation force in y-direction for remaining bundles, which are located away from misalignment zones, is also significantly influenced by the presence of interface zones and hence they too are amplified to a considerable amount.
This in turn hints that the presence of only two misaligned interfaces out of a total 11 of them can influence the lateral fluid excitations for all other bundles which are even away from the misaligned interface locations. Thus, the results presented here are an indication to the fact that bundle-to-bundle angular misalignment should not be ruled out for the true evaluation of the fluid forces experienced by the fuel bundles.

PSDs for the x and y-forces in different bundles
Power spectral densities (PSDs) of the fluid forces in x and y directions are also evaluated for each fuel bundle for the recorded fluid force history data. The PSDs are determined and plotted using a Matlab script (See Appendix). Observations on the PSD plots are discussed in the next section.

PSDs of x-forces
The PSDs of the x-forces on different bundles are shown in Fig. 3-10. The results reveal that for Model-1, there is almost no shift in the evolution of these frequencies of the fluid lateral forces for different bundles. On the contrary, for both of the plots (b) and (c) i.e., for Model-2 and Model-3, it is observed that the fluid excitation frequencies evolve without showing any trend and keep on changing for different bundles. Moreover, from the very same plots, it can also be found that compared to fully aligned situation, misaligned bundle interface produces more number of sharp spikes in their respective spectra making the bundles subjected to more number of fluid excitation frequencies.

PSDs of y-forces
In Fig. 3

Mean and RMS values of x and y-force for different bundles
It is important to investigate the lateral fluid forces acting on each bundle in the complete length of the 12 bundle string inside the pressure tube. The RMS values of the recorded data are evaluated after deducting the mean from the original data and processed further with the help of Microsoft Excel tool.

Mean and RMS of x-forces
The mean values of the x-force of different bundles are shown in Fig. 3 figure (Fig. 3-12), it is also seen that the mean value of the transverse fluid forces change to a reasonable extent if all the interfaces in the bundle string are with misaligned bundle configuration, as seen for Model-3.
While investigating the RMS values, it is found that the fluctuations are very small in case of Model-1, but is observed to be quite high for Model-2 and -3 both. For Model-2, BD-4, 5, 6, 8, 9 & 10 show considerable rise in the RMS values. This is because they contain the two misaligned interfaces; whereas, for BD-1, 2, 3, 7, 11 & 12, fluctuations remain comparable to that of Model-1. This is because these bundles are situated far from the misaligned interfaces which turned out to be one of the major sources of the lateral fluid forces.

However, for Model-3, except BD-1, RMS values of all remaining bundles show large
variations from that of model-1 and they keep changing from BD-2 to BD-12, which is as expected, because Model-3 has all bundles misaligned with each other.

Mean and RMS of y-forces
The mean and RMS values of the y-forces for different bundles are presented in Fig. 3-13. Like the x-force results, for the RMS values, for Model-1 no significant fluctuation is noticed; but, for Model-2, it is very high for BD-4, 5 & 9. This is again because of the fact that these bundles constitute the misaligned interface zones and thereby creating large amount lateral fluid forces acting on these bundles. Whereas, BD-1, 2, 3, 7, 9 & 10 exhibit fluctuating force almost matching with the corresponding bundle of Model-1; reason behind this is the location of these bundles being far away from the misaligned interfaces. The results from Model-3 are almost similar to that of the x-force results and hence proving the significance of the misaligned interfaces.

Correlation study of flow features among different bundles
The fluid flow throughout the string of bundles is a continuous media as fluid particles are connected by the subchannels of bundles, however complicated they may be. Results from previous subsections showed that different bundle position could influence the flow features in the neighbouring bundles to a large extent; but how much the fluid properties, e.g., velocity, fluid excitation etc., are correlated to each other is not yet shown with cogent data or expression. Upcoming sections of this thesis will shed some light on this matter, with the help of correlation studies.
To examine the similarity (or dissimilarity) of flow among different bundles, a crosscorrelation study is carried out on the time history of the flow parameters recorded during the simulation solution time. In time history analysis, the cross-correlation between two time series describes the normalized cross-covariance function. If, for the 12-bundle flow model, (F t ) i and (F t ) j represent two stationary flow properties corresponding to i th and j th bundle, respectively, then the cross-covariance of these pair of time histories would be as, where, μ i and μ j are the mean values of (F t ) i and (F t ) j , respectively, E is an operator which determines the expected values of the corresponding expression on which it is acting. Now, the cross-correlation coefficient, which is the normalized cross-covariance function, can be expressed as below, where, σ i and σ j are the standard deviations of the two time histories (F t ) i and (F t ) j , respectively, under consideration. From this relation, if (F t ) i = (F t ) j for all t, then the crosscorrelation coefficient represents simply the auto-correlation coefficient. The correlation coefficients are evaluated and plots generated using a Matlab script (See Appendix).
As far as the fuel bundle motion is concerned, it is also important to figure out the correlation or coherence of the flow features in the frequency domain, especially the fluid excitations. Revealing this would lead towards finding the possible matching of fluid excitation frequencies with the bundle frequencies, if there is any, which can be utilized for a larger scope of future study in the dynamics of the bundle behavior inside a fuel channel. This is executed again with the help of a Matlab script (See Appendix) for different flow parameters recorded during the simulation solution. The parameter plotted is the coherence magnitude with respect to frequency for two time histories using Welch's averaged and modified periodogram method (Welch, 1967). The Matlab script therefore estimates the coherence between (F t ) i and (F t ) j for the recorded period of time as a function of frequency, as expressed below, where, P(f) i,i , P(f) j,j are the power spectral densities of the above two time histories and the P(f) i,j is the cross-power spectral densities of those time histories. The C(f) i,j values determine how good (F t ) i is related to (F t ) j at each frequencies and provides a value from 0 to 1, with 1 being the highe st coherence. Hence, the coherence values will always be 1 for all frequencies in case (F ) = (F ) . This is verified in the next section which deals with the e. Therefore, a strategy is developed aiming to cover the whole range of correlation combinations in order to deliver the objectives of this t i t j results of the current study.
In a single fuel channel, altogether there are 12 bundles; thus the number of possible bundlepair combinations could be: ( 12 Č 2 +12) equalling 78. Here, Č denotes conventional notation of combination and the addition of 12 corresponds to 12 additional combinations of each bundle with themselves, i.e., the auto-correlations. Therefore, for any flow parameter there could be 78 total combinations among 12 bundles for which cross-correlation coefficient can be determined. Consolidating all of those hundreds of correlation plots in this manuscript is not plausible to demonstrat study, as elaborated in the next paragraph. as shown in Fig. 3-14, collectively will be able to find out the relation is influenced due to the presence of the bundle angular misalignm

54
It can be clearly noticed that a strong correlation is seen in all combinations of bundle pairs selected; this implies that flow properties of different bundles placed at the midway of the fuel channel are highly correlated for the completely aligned bundle arrangement.
If we see Fig. 3-16, which refers to Model-2, from (a) observation similar to Fig. 3-15 (a) can be noticed. A comparison between part (b) of both Fig. 3-15 and Fig. 3-16 reveals that strongest correlation occurs for C(τ) 6,6 in Model-2, as expected. All other bundle-pair combinations exhibit almost no correlation or very week correlation, as opposed to what is seen for Model-1. This can be explained as, the fluid flow features loose their resemblance from bundle to bundle due to the presence of misaligned interfaces. In Fig. 3-16 (c), it can be observed that a very weak correlation is present for these set of bundles unlike what is noticed in Fig. 3-15 (c). This is justified since misaligned interfaces change the pattern of the flow in the bundle subchannels and hence weaker correlation.
The correlation of bundle-pair in their progressive increment from BD-1 to BD-12 is shown in Fig. 3-17. From Fig. 3-17 (a), it is observed that except for first 3 to 4 bundles, all other combinations exhibits strong correlation meaning that flow nature is very much coherent in the most part of the bundle string barring few from the inlet end. The reason for this is explained above. As expected, the misaligned interfaces break the inter-bundle coherence of the flow parameter showing the weakest correlation values, as seen in Fig. 3-17 (b).
The change in the flow pattern in case of misaligned interfaces will obviously reflect onto the fluid forces acting on the bundles; this is examined here with combination "P". Now, looking at Fig. 3-18 (a), it can be seen that the nature of the flow for the first three bundles at the inlet and the last couple of bundles at the outlet end is the most uncorrelated ones. Other than these, remaining all bundle-pairs possess a much strong coherent flow, as expected.
From Fig. 3-18 (b), it is observed that the flow similarity observed in case Model-1 is lost in Model-2 emphasising the influence of the bundle angular misalignment.

Correlation x-velocities, x-and y-forces in frequency domain
Until now it is demonstrated that how much the fluid flow in one bundle is correlated to that of another bundle by selecting several bundle-pair combinations. They represent correlation in time domain only at different time lags, however, with a spatial comparison for different bundles since the bundles are placed at different axial locations inside the fuel channel.
However, it is hard to conclude that that at which frequencies the flow parameters are mostly correlated, but knowledge of those frequencies is of specific interest to the current study as far as fuel bundle vibration is concerned. This is discussed next. From theory, the coherence will have a value of unity for all frequencies, only in case of auto-correlation i.e., when a time history pertaining to any bundle being compared with itself. This is exactly what is observed for C(f) 1,1 and C(f) 6,6 in Fig. 3-19 (a) and Fig. 3-19 (b), respectively. However, for all other bundle-pair combinations, the matching frequencies are very much scattered without showing any specific trend. The plots in Fig. 3-19 (b) are found with a coherence value of around 0.8, as opposed to Fig. 3-19 (a), for frequencies less than 250 Hz. The part (c) of Fig. 3-19, where specific bundle-pair combinations are selected, demonstrates even higher coherence values, reaching almost unity for frequencies less than 250 Hz again and also at 280 Hz, 350 Hz for C(f) 9,10 combination. Therefore, in a string of fully aligned bundles, the bundles placed away from the ends of the string have more coherent flow with rest of the bundles and the coherence is more prominent in case of frequencies less than 250 Hz.
The coherence plots for Model-2 which considers misaligned bundles are shown in Fig. 3-20. The coherence is noticed to be very week, mostly reduced to less that 0.5, for the whole range of the frequencies considered in both part (a)

Summary
This 12-bundle computational work is novel from the following perspective: (

Introduction
During refueling in a CANDU reactor, the angular positions of the fuel bundles are not controlled. As a result, the fuel bundles in a fuel channel tend to have different angular orientations and therefore, the possibility of angular misalignments among a string of fuel bundles exists. If any two adjacent bundles are resting inside the pressure tube with such an angular orientation that their components, viz., bundle-elements, endplate-ribs/rings, are in perfect alignment for the two bundles, then the configuration is considered as a fully aligned interface; and if not, then it yields a misaligned interface. A simpler case of bundle-tobundle interface configuration considering 30 o angular rotation for one bundle is illustrated in Fig. 4-1, and the results for several other angular misalignment configurations are presented and discussed later.

Description of flow domain
This study considers CFD models which are developed, as shown in Fig. 4    To meet the accuracy requirement of the LES scheme, the whole domain is discretized using an adequately fine mesh distribution, with endplate and bundle regions having the fine meshes and the upstream pipe flow region having coarse meshes. The grid distribution in various subchannels for the bundle and endplate regions along with the boundary layer distribution in the respective region in a cross section of the xy-plane is kept same as described for CFD model in Chapter 2 (refer Fig. 2-7). To comply with the demand of LES in regard to the near-wall mesh resolution, which is of critical importance, the thickness of the first layer of cells near the walls is restricted to a very low value to ensure y + equals 1 on most surfaces, while modeling boundary layer regions.

Flow domain discretization
When considering numerical solutions of turbulent flow, determination of a suitable timestep size becomes one of the foremost requirements and key tools (Choi and Moin, 1994).
For the present research, the time step size is based on the large eddy turn-over-time (LETOT), which is evaluated from the Kolmogorov time scale  (as mentioned in Eq. (6) of Chapter 2) to be 2.410 -4 seconds. The time step size in this study is chosen to be 510 -5 seconds. Two different mean axial flow velocities, 2.4 m/s and 4.8 m/s, are considered at the inlet corresponding to an average velocity of 6 m/s and 12 m/s through bundle subchannels and a Reynolds number of 4.8610 4 and 9.7210 4 , respectively. Some details of the flow parameters considered in the current study are mentioned in Table 4-1. The boundary conditions at different part of the flow domain are followed to be similar as described for the entrance flow model in Chapter 2. The computational models are solved at high temperature (300 o C) and high pressure (10 MPa) with water used as fluid.

Solution technique and Computational resource
The LES technique, associated with Smagorinsky SGS model, is employed to solve threedimensional filtered unsteady N-S equations. The LES scheme, as described in the Chapter 2, is followed for all the CFD models considered in this study. The detailed description of this LES scheme is, therefore, not repeated in this chapter and can be referred to Chapter 2 for any further information.
Using a cluster of supercomputers (36 in numbers), in conjunction with a parallel processing scheme, the numerical solutions are obtained for the three dimensional unsteady flow through the first two inlet CANDU fuel bundles. The convergence criteria is set to a value of 0.001 for flow parameters; with the time step size considered for several models, there is 2 (minimum) to 8 (maximum) iterations for every time steps in the LES solutions, thus conforming the non-linearity in solving the N-S equations.

Validation and grid sensivity study
Like in Chapter 2, the numerical approach is validated comparing results from two different studies: (i) numerical and (ii) experimental. In regard to numerical scheme, the LES technique is verified first with the work done by Chang and Travoularis (2007). Then, the results from the current simulation is compared with experimental results documented by D'Arcy and Schenk (1987) for local axial flow velocity contours in certain subchannel part of the bundle cross-section. In both of these comparison, good agreement is achieved. For the details on the validation for this present study and also for grid sensitivity study please refer to Chapter 2.

Bundle-to-bundle angular misalignment
The 37-element bundle structure, considered in the present study, exhibits a periodicity of however, fluid excitation forces in the lateral direction on the bundle i.e., F x and F y are evaluated and discussed for all different misaligned interfaces. In Fig. 4-4, the reference rotating plane is shown by a dashed line, which is rotated every time by 5 o to get the next misaligned configuration. It is noted that, the actual resting angular position of a fuel bundle is random although fuel bundles tend to have their most preferred orientations from the operating experiences.

Results
In this section, numerical results obtained from the CFD models are analyzed and discussed.
Various cases are considered and results produced for different parameters. The total duration of solution for all different models is 0.5 s from which only 0.4 s (i.e., 0.1 s to 0.5 s) is considered for data processing because the solution became stable after 0.1 s.
The contours are presented as viewed from the upstream towards the downstream. Every contour plot consists of the endplate profile projected on it for better understanding of the effect due to the endplate, if any. It is to be noted here that although the contours exhibit flow parameters at certain moment, however, their distribution or the pattern remains similar at different time instants on that surface with very small changes in the magnitude. The discussion in the following section involves detailed review of the interface flow and its effect on the fluid forces experienced by the BD-1 with the help of Fig. 4-5 to Fig. 4-9.
Then, emphasis is given on the effect of different angular misalignments in the bundle-tobundle interface region, as can be seen from Fig. 4-10   However, for (c) and (d), higher velocity is observed around locations right before and after the endplate ribs/rigs and their junctures.

Discussion on x-velocities
Like in the case of y-velocity, the contour corresponding to the midplane i.e., Fig. 4-6  respectively. In (a), (c) and (d) of Fig. 4-6, it is seen that lateral velocity components are magnified before and after the endplate ribs/rings, proving again the influence of these endplate components in modifying the parallel bundle subchannel flow.

Tangential velocity
Distribution of tangential velocity components through the bundle subchannels at crosssections of various axial locations are illustrated in Fig. 4-7. In Fig. 4-7 (a) and Fig. 4-7 (c), the middle and inner subchannel regions behind and ahead of the endplate for the BD-1 are seen with high tangential velocity, with Fig. 4-7 (a) showing strong negative tangential velocity in the endplate ribs. The intensity of the tangential velocity component is found to be decreased in Fig. 4-7 (b) with more flow continuity established through the bundle subchannels, enhancing the presence of swirling like flow in the BD-1. This is, however, not evidenced in the case of BD-2, shown in Fig. 4-7 (d); but the existence of negative tangential velocity is again found after the interface endplate ribs, elaborating the importance of considering endplates and the bundle-to-bundle interface regions while modeling the bundle subchannel flow.

Radial velocity
The radial velocity components can also contribute towards the bundle lateral motion and hence, it is important to discuss it at this point in time. The contours of radial velocity components, which are shown in Fig. 4-8, display that the highest magnitude is attained for both locations right after the endplate for two bundles, i.e, (a) and (d). At the halfway through the BD-1, a radial continuity of flow through bundle subchannels with a low value is observed, as shown in Fig. 4-8 (b). In Fig. 4-8 (c), the locations between the adjacent elements in same endplate ring are found to show higher magnitude of the radial velocity components. This is because, at those locations, fluid particles tend to cross the interface endplate rings and thus spread in radial direction, providing higher bundle lateral movement.

Lateral fluid forces
Fluid forces on the BD-1 are presented in this section through Fig. 4-9. Due to bundle sagging, the CANDU fuel bundle has maximum gap between the outer elements and the pressure tube inner wall at the top. The bundle tends to move upwards under the influence of the lift force. It may be better to mention here that, from the operating experiences of the CANDU reactors, lateral fluid forces are of more interest while dealing with fuel bundle vibration. Hence, time histories and PSDs for the x-force (F x ) and the y-force (F y ), which are responsible for bundle side-to-side and vertical motion, respectively, for the BD-1 are presented here as the lateral fluid force.     Hz for U of 4.8 m/s. The lift force (F y ) is found with dominant frequencies spread over around 65 Hz to 120 Hz for U of 2.4 m/s; and around 35 Hz to 220 Hz for U of 4.8 m/s. All these frequencies discussed here show that if the fuel bundles contain any of its natural modes in the vicinity of these frequencies, then the bundle will get energy for its vibration from these frequencies.

Effect of angular misalignment
The results discussed in the earlier sections provide an insight on the importance of the entrance and the interface regions in a string of bundles for having better knowledge on bundle lateral vibrations. In this section, the effect of the various angular misalignments in the bundle-to-bundle interface region is analyzed. Initially, a comparative study is (S1 to S6) for the pathlines indicated by the black dots; their selection is made to cover the clear subchannel regions and the regions beside the endplate ribs. As expected, pathlines coming from S1, S2, S3 and S5 show maximum scatter compared to the other pathlines.
These locations are situated beside the endplate ribs, enabling the flow to follow certain path, influenced by the differential pressure right after the endplate. The development of the flow can also be seen very clearly through an isometric view, as shown in Fig. 4-10 (b). The pathline generation for misaligned interface is elaborated with the help of Fig. 4-11.
From Fig. 4-11 (a), it is clear that presence of misaligned interface influences fluid particle to scatter more compared to aligned interface, as seen from Fig. 4-10 (a). In addition, there are areas where fluid particles start to swirl in its own path, which is not at all seen for the aligned scenario. From the isometric view, shown in Fig. 4-11 (b), it is noticed that the flow deviations after the inlet endplate are present like the aligned model. However, unlike aligned condition, fluid particles in case of misaligned interface model undergo significant wakes of higher magnitude after the interface endplate, as shown in Fig. 4-11 (b). Thus, this observation draws the importance of misalignment in the bundle-to-bundle interface region.

Mean and RMS values lateral fluid forces
To see the effect of misalignment on the bundle side-to-side force (F x ) and the lift force (F y ), the time histories and the PSDs are compared for the inlet bundle, which can be seen in Fig.   4-14. The mean is again deducted from the raw data and the fluctuation part is produced.
For every plot the corresponding RMS and the mean values are shown separately. It is very important to mention that not only the mean values are increased with misaligned interface scenario, but, the fluctuation range or the RMS values are also increased for both the F x and F y , when there is 30 o angular misalignment. The F x has the dominant spikes at 30 Hz, 55 Hz and 90 Hz; whereas, for F y the frequencies are spread over a wide spectrum of band. Thus, this is very much of interest that the misaligned interface between bundles can produce considerably higher lateral fluid forces compared to that of fully aligned case. Fig. 4-14 Comparison of x-force and y-force for aligned and misaligned interfaces.
The next is to develop several CFD models with different angular misalignments starting from 0 o to 60 o with an increment of 5 o . All configurations considered can be found in Fig.   4-4. For each of these orientations, the F x and F y on the BD-1 is recorded and processed for further analysis. The RMS and the mean values for each case are and can be found in Table   4-2. The mean as well as the RMS are presented by plots with different angular misalignments in Fig. 4-15. From the two graphs of Fig. 4-15, it is clearly seen that the mean values vary with the change in the angular misalignments for both F x and F y . For the F y, the mean follows a decreasing trend and for F x it has increasing trend. Also, the change in the RMS values for x and y-fore is noticed to be significant. This is very important that angular misalignments influence the inlet bundle to experience lateral fluid excitations, much higher in magnitudes, about 3 times higher for RMS values and more than one order of magnitude for mean values.

Findings from the computational study
In this study, comprehensive CFD models for a two-bundle string are developed for the first

Introduction
This section describes an experimental investigation carried out on flow-induced vibration of two simulated 43-element CANDU fuel bundles with angular misalignment in an outreactor fresh water loop. Experimental data are presented and discussed for a range of (a) bundle angular misalignment and (b) mass flow rate in the subsequent sections.

Description on test facility
The experimental setup, as shown in Fig  In addition to the above mentioned accelerometer, a non-contact differential variable reluctance transducer, NC-DVRT-1.5 from MicroStrain Inc., is installed at a location shown in Fig. 4-18 (b) to monitor the lateral (horizontal) movement of the bundle in relation to the supporting tube. The sensor measured directly the gap between a target face on the fuel bundle and its own face at the sensor head. When the face of the sensor probe comes in close proximity to a ferrous or highly conductive material, the reluctance of the coils within the sensor changes and provides the output as a voltage signal. The typical repeatability of this type of sensor is ±2 μm; the frequency range is 0 to 800 Hz. The sensor has a sensitivity of 5 V/mm with a measuring range of 1.5 mm and an error of 0.2 % .
A sampling rate of 19.531 kHz is used to sample all signals for a duration of 6.71 seconds for each test. It is to be noted that this sampling frequency is a pre-set value in the system corresponding to 20 kHz frequency; with this pre-set frequency the maximum measurement duration can be attained up to 6.71 sec. Since highest sensing frequency of the sensor is below 2.5 kHz, the adopted sampling rate is well above the Nyquist frequency. No aliasing problem is anticipated.

Experiments
For a two-bundle string, the bundle orientation angles (α 1 and α 2 ) are defined in Fig. 4-19.
The angular misalignment () is defined in this figure as the difference between the angular positions. In a CANDU reactor, the bundle orientation angle is not a controlled parameter during fuelling and refuelling. Therefore, a distinct possibility of angular misalignments exists between neighbouring fuel bundles. The fuel elements for a 43-element simulated bundle are designed to have a rotational periodicity of seven (or 51.4) in the azimuthal direction. Except for the two central webs, the ring-rib sub-assembly of the 43-element endplate also has a rotational periodicity of seven. Considering this dominating structural periodicity for the 43-element CANDU bundle, it is assumed that the effects of the angular misalignments are largely periodic with a periodicity of 51.4 o for the bundle-obstructed pipe flow.

Fig. 4-19 Present experimental domain with misalignment between bundles explained.
In the current study, the angular position of the first (or inlet) bundle is fixed to be the design position (α 1 = 0) while the second bundle is rotated from the perfectly aligned position (α 2 = 0) to the next nearly perfectly aligned position (α 2 = 51.4) with an increment of 5.14.
All experiments were performed in the room temperature. A static pressurization of 20 psi is applied to the close loop. The Reynolds numbers, water mass flow rates, mean flow velocities both in the pipe and inside the bundle, the shaft speeds at different flow conditions are given in Table 4-3. Simultaneous sampling of the acceleration and displacement signals in each test is done through the data acquisition system; the data are stored for processing and analysis. It is worth metiontioning here that the mounting of the sensors used and associated cables require some amountt of material removal from the respective fuel element -a minor modification to the original bundle structure.  Fig. 4-21. In addition to this figure, the repeatability can also be verified from Fig. 4-22 and Fig. 4-23 where statistics of the measured signals are plotted for more number of tests.
Due to the fine repeatability, only one set of measurement was taken and used in this study.

Results and Discussions
Large number of vibration data in the time domain obtained for a range of configuration and operational parameters are processed and analyzed in this section.

Stationarity of recorded vibration signals
A stationary time signal is one whose statistical properties such as mean, variance, autocorrelation, etc. remain constant over time. A turbulent flow, after an initial transient period, can reach a statistically stationary state in which their statistics are independent of time (Pope, 2000) even though the flow variables vary with time.  The mean value calculated from these 30 different measured means and standard deviations (or the population mean) are shown by a dotted line in each plot. It can be clearly seen that the mean and standard deviations are the same as the reference mean. The small differences from the reference mean, as noticed in the plots, are caused by the random error incurred during the tests, which can hardly be avoided from a practical point of view.

Acceleration measurements
Altogether there are about 700 numbers of recorded measurements and so, it is hardly possible to present all time domain signals. Therefore, the time histories of the bundle vibration from the accelerometers are presented in Fig. 4-24

Displacement measurements
The time histories of the displacement sensor measurement are presented in Fig. 4

Acceleration PSDs
In the current study, a total of 11 different bundle misalignment configurations are

Displacement PSDs
In Fig. 4-29, PSD plots for the displacement sensor at mass flow rate of 17.97 kg/s is presented. From this figure, a few other dominant frequencies in addition to the pump blade passing frequency are noticed. The 25 Hz frequency is observed to be shifting between 25 Hz and 30 Hz at various bundle misalignment combinations; this demonstrates that the frequency of the displacement response vary with the misalignment angles.
From the PSDs of the acceleration and the displacement response, it is noticed that the frequency of bundle motion is sensitive to the misalignment angle. To date, this is an important observation with respect to CANDU fuel bundle motion. However, it is of more relevance to find out, if at all, the effect of angular misalignment on the bundle lateral response, as discussed in details in the following sub-section.

Effect of Angular Misalignment on Bundle Acceleration response
In Fig. 4  From these plots of both mean and the RMS values, it can very distinctively be seen that bundle-to-bundle misalignment configurations indeed affect the bundle lateral motion.

Effect of Angular Misalignment on Bundle Displacement response
The mean and RMS values corresponding to displacement response are plotted in Fig. 4-31 for different flow rates at all selected misalignment combinations. The values in the plots represent the actual bundle lateral movement inside the PVC pipe of the testing loop. Like well outside the error band of the sensor, but still too small (between 1 μm and 16 μm) to produce considerable amount of fluctuation which could be harmful for the tube containing the bundles. However, it is to be noted here that inside the pressure tube, the actual CANDU fuel bundle has very limited space to move, about 1.5 mm at the top (max). The researches carried out in the past showed that the recorded RMS vibration amplitude for the bundle remains within 10 μm (Pettigrew, 1993) and the gross bundle motion in the pressure tube is as low as 25 μm (Norsworthy et al., 1994). Moreover, fretting is a phenomenon with very small amplitude vibration capable of causing potential damage in long term application.
Therefore, the amount fluctuations recorded from the displacement measurement due to the different misalignment configurations are of practical significance to CANDU fuel bundle application concerning the pressure tube fretting induced wear.

Effect of Flow Velocity on Bundle Response at Various Angular Misalignment
Since the present experiment is conducted at various flow velocities, it would be better to provide information regarding the effect of flow velocities on the bundle response at different misalignment angles. This is described in this sub-section with the help of Fig.   4-32. In this figure, the acceleration and the displacement RMS values of the recorded measurements are plotted for four randomly selected misalignment angles from the 11 predefined combinations at different bundle flow velocities ranging from 2.4 m/s to 7.7 m/s. From all eight plots it is very clearly seen that the RMS values increase with the increase of the flow velocity, which is well expected. Except for few cases, which are minor, the change in the RMS amplitude with respect to the flow velocity is smooth and almost consistent for each misalignment angle condition.

Findings from the experimental work
Experiments are carried out to investigate flow-induced vibration of a two simulated CANDU fuel bundle string with angular misalignment.

Summary
The bundle-to-bundle angular misalignment is found to influence both the lateral fluid excitations and the lateral bundle motion. Both numerical and experimental studies reveal that there exist some misalignment combinations, at which the bundle experiences much higher lateral fluid forces and vibrates with considerably higher amplitude. This is one of the most significant findings to date in the field of flow-induced vibrations of CANDU fuel bundle structure. angle. Therefore, in order to assess proper fluid forces on the fuel bundles and to measure bundle transverse motion due to the coolant flow, bundle-to-bundle angular misalignment should be considered -so that the mechanism of flow-induced vibration in fuel bundle structure is understood well.

Major Accomplishments
The main accomplishments from the current research work can be summarized as:  Developed a comprehensive computational fluid dynamics model for a fuel channel filled with a string of 12-bundles and obtained solutions using large eddy simulation for the first time -a significant achievement to date.
 Discovered that the fully aligned fuel bundles produce minimal lateral fluid excitations and misaligned fuel bundles produce large amplitude excitations.
 Predicted the lateral fluid excitations for individual bundles in a string of 12 bundles at diffferent angular misalignment.
 Observed that one of the major sources of bundle lateral vibration is the coherent nature of the flow among the multiple bundles inside the fuel channel exhibiting fluid excitations of frequencies spread over a wide band in the power spectra.
 Examined lateral fluid excitations at various angular misalignment combinations for a short bundle string with finer increment of misalignment angle and noted some critical bundle positions with higher fluid forces.
 Found good correlation of flow among different bundles and the coherence is reduced with the presence of the misaligned interfaces.
 Experimentally investigated that bundle lateral motion is higher in the case of misaligned bundle interfaces and lower in the fully aligned case.

Significance of this research
This research presents some new results from LES simulations of highly turbulent coolant flow in a string of CANDU fuel bundles with a focus on the effect of the angular misalignment of the individual fuel bundles. One of the the main merits of the present work is the application of high-performance computing to a complex, large-scale practical problem of considerable relevance to the operation of CANDU reactors. An analysis of a complete fuel channel of a nuclear reactor using LES is at the forefront of current research worldwide. The present study contributes to enhancing the state-of-the-art, by a successful application of the CFD technique to a particular problem of the CANDU design.
The current study will help evaluate the lateral fluid excitations on individual fuel bundles in a fuel channel, and will also provide better understanding and information of the influence of the bundle angular misalignment on the fluid forces and the bundle response. Also, from the results of the present research, it can be mentioned that if by any means the bundle angular positions are locked with respect to the neighboring bundles, the effective lateral fluid excitations can be reduced considerably. Therefore, this research could benefit the nuclear industry, in terms of gaining in-depth kowledge on the flow mechanism and the flow-induced vibration of the fuel bundles for a full length fuel channel.

Future work
Firstly, the real fluid-structure interaction phenomemon can be explored and solved for the fuel bundle study using the user defined function ( Secondly, in past studies on the fuel bundle structure subjected to axial flow, while calculating the critical flow velocity for the bundle, only one bundle has been considered at the most. This is highly under-estimating the fact that inside the fuel channel due to the hydraulic drag of the coolant, bundles are in contact with their neighboring ones almost always, and thus these bundles behave more like a string than an independent separate bundle. Therefore, the critical flow velocity calculated for a single bundle can reasonably differ from that of a whole string of bundles. So, in such a situation, if the critical flow velocity based on the complete bundle string is falling on the vicinity of the natural frequency of the bundle string, fluid-elastic instability is bound to happen, and the whole string will start vibrating. This will cause severe damage to the pressure tube. So, it is very important to calculate the proper critical flow velocity for the whole string of bundles in order to see whether the operating flow velocity in the actual reactor is falling near the calculated threshold value. This is has not yet been evaluated to date, and if ascertainable, can be a significant milestone in understanding the mechanism(s) of fuel bundle vibration in CANDU reactors.