Simulations and measurements of adiabatic annular flows in triangular, tight lattice nuclear fuel bundle model

Nuclear Engineering and Design 299 (2016) 163–173

Contents lists available at ScienceDirect

Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes

Simulations and measurements of adiabatic annular flows in triangular, tight lattice nuclear fuel bundle model Abhishek Saxena a,∗ , Robert Zboray b , Horst-Michael Prasser a,b a b

ETH Zurich, Laboratory for Nuclear Energy Systems, Department of Mechanical and Process Engineering, Sonneggstrasse 3, 8092 Zürich, Switzerland Laboratory for Thermal-hydraulics, Nuclear Energy and Safety Department, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland

a r t i c l e

i n f o

Article history: Received 28 July 2015 Accepted 31 July 2015 Available online 21 October 2015

a b s t r a c t High conversion light water reactors (HCLWR) having triangular, tight-lattice fuels bundles could enable improved fuel utilization compared to present day LWRs. However, the efficient cooling of a tight lattice bundle has to be still proven. Major concern is the avoidance of high-quality boiling crisis (film dry-out) by the use of efficient functional spacers. For this reason, we have carried out experiments on adiabatic, air-water annular two-phase flows in a tight-lattice, triangular fuel bundle model using generic spacers. A high-spatial-resolution, non-intrusive measurement technology, cold neutron tomography, has been utilized to resolve the distribution of the liquid film thickness on the virtual fuel pin surfaces. Unsteady CFD simulations have also been performed to replicate and compare with the experiments using the commercial code STAR-CCM+. Large eddies have been resolved on the grid level to capture the dominant unsteady flow features expected to drive the liquid film thickness distribution downstream of a spacer while the subgrid scales have been modeled using the Wall Adapting Local Eddy (WALE) subgrid model. A Volume of Fluid (VOF) method, which directly tracks the interface and does away with closure relationship models for interfacial exchange terms, has also been employed. The present paper shows first comparison of the measurement with the simulation results. © 2015 Elsevier B.V. All rights reserved.

1. Introduction To improve the long-term sustainability of nuclear power generation and to achieve better fuel utilization, different innovative reactor concepts have emerged in the last decade with significantly increased conversion ratios nevertheless still relying on well-established light water reactor (LWR) technology. High conversion ratios are obtained by hardening the neutron spectrum via reducing the water fraction in the core adopting usually a triangular, tight-lattice fuel bundle geometry, featuring narrow gaps combined with relatively large diameter rods. The boiling-type, high conversion light water reactor (HCLWR) is a promising concept to achieve the aforementioned goals. Intensive research focusing on this type of HCLWR has been carried out in Japan in the past decades. Iwamura et al. (1999) describe already the research efforts toward a Reduced-Moderation Water Reactor (RMWR), which aims at breeding, high burn-up, long operation cycles and plutonium recycling. By a more step-wise approach on the evolutionary way toward cores with a triangular lattice, it is proposed to start with

∗ Corresponding author. Tel.: +41446328784. E-mail address: [email protected] (A. Saxena). http://dx.doi.org/10.1016/j.nucengdes.2015.07.063 0029-5493/© 2015 Elsevier B.V. All rights reserved.

increasing the density of the rectangular lattice (Kondo et al., 2004). In the second step, triangular fuel rod lattice would lead to hexagonal fuel element cross-sections, which would be combined with Y-shaped control rods (Yamashita et al., 2004). Uchikawa et al. (2007) describe the next evolutionary step toward a light water reactor with flexible fuel cycle (FLWR) for minor actinide (MA) recycling. The FLWR core concept is envisioned in two stages, the first would be a continuation of current LWR technology, where the fuel rod gap is the same as current LWR’s. When loaded with 9% Plutonium containing mixed oxide (MOX) fuel, a conversion ratio of approximately 0.9 can be achieved. The fuel assemblies in the second phase of the FLWR concept have the exact same configuration (rod number, pitch) as before, but with increased Pu content and a larger fuel rod diameter. With 18% plutonium containing fuel, conversion ratios over 1.0 can be realized (Uchikawa et al., 2007), enabling breeding in an LWR. While power output of the first and second phases of the FLWR project are the same, the increased rod diameter decreases interstitial coolant volume. This poses a challenge on cooling the bundle properly, as the same amount of power has to be removed with less coolant. To ensure the thermal-hydraulic feasibility of the concept, and to ensure continuity between the first and second FLWR phases in the same core,

164

A. Saxena et al. / Nuclear Engineering and Design 299 (2016) 163–173

2. Experimental setup and conditions Nomenclature k ε Dh u␶ w  y  ϕ u+ y+ u’ U

turbulent kinetic energy dissipation rate hydraulic diameter shear velocity wall shear density distance from wall kinematic viscosity void fraction dimensionless velocity dimensionless wall distance fluctuating velocity field mean velocity field

significant experimental and modeling R&D still has to be done. The use of computational fluid dynamics (CFD) modeling is planned and being done (Ohnuki et al., 2008; Takase et al., 2004; Yoshida et al., 2006). This is accompanied by significant experimental activity to check the accuracy of CFD simulations, and to validate the models for certain phenomena in the numerical approach (Ohnuki et al., 2008). The latter involves mainly critical power, critical heat flux (CHF), pressure drop and spacer tests on different sized fuel bundle models (Yamamoto et al., 2004, 2006; Kureta et al., 2006). Also the 3D void distribution has been studied in great detail using neutron tomography, a non-intrusive technique, by Kureta (2007a, 2007b) and the prediction of a range of codes have been validated against these experimental results (Kureta et al., 2008). Clearly, the influence of geometry and scale in tight lattices should be carefully evaluated for phenomena such as the boiling transition (crises) in the annular flow regime caused by the dryout of the liquid film. It is a severe safety issue for the tight lattice fuel bundles just as it is in conventional rectangular BWR lattices (Lahey and Moody, 1993). Therefore, a thorough understanding of the behavior of annular flows and liquid films is crucial for the HCLWRs. Related to this, the development and use of functional spacers in tight lattice geometries for enhancing the margin to dry out should also be examined in detail. To attack this problem, at first in a simplified manner, we have carried out experiments on adiabatic, air-water annular two-phase flows in a tight-lattice, triangular fuel bundle model. A high-spatialresolution, non-intrusive measurement technology, cold-neutron tomography, has been utilized (Zboray and Prasser, 2013a). The influence of functional spacers on the annular flow has been also studied to better understand the basic functioning of the mixingvane spacer. The main measured quantity is the distribution of the liquid film thickness on the virtual fuel pin surfaces downstream of the spacer (Zboray and Prasser, 2013b). Unsteady CFD simulations have also been performed to replicate and compare with the experiments using the commercial code STAR-CCM+. Large eddies have been resolved on the grid level to capture the dominant unsteady flow features expected to drive the liquid film thickness distribution downstream of a spacer while the subgrid scales have been modeled using the Wall Adapting Local Eddy (WALE) subgrid model. A Volume of Fluid (VOF) method, which directly tracks the interface and does away with closure relationship models for interfacial exchange terms, has been employed. Below the experimental set up and measurement technology is introduced first. Then the computational models and methods are explained in detail. Finally, the first comparison of the measurement results with those of the simulations is shown. Time-averaged film thickness results are compared while liquid film velocity profiles are also obtained with the simulation results.

2.1. The fuel bundle model The setup comprises of a flow channel featuring the tight lattice geometry complemented by a recirculation auxiliary system closing the two-phase flow loop operated at near ambient temperature and pressure. The scheme of the loop and the subchannel is illustrated in Fig. 1. The channel geometry models four neighboring subchannels (quadruple subchannel test section) of a conceptual FLWR fuel rod bundle at a scale approximately twice that of the actual bundle (see Fig. 2a). The investigation focuses on the middle subchannel (subch2 in Fig. 2a) as it is not limited by the presence of walls, which pose unrealistic no-slip boundary conditions that are not present in a full fuel bundle, whereas such unrealistic boundaries are present in the other three subchannels. The channel is constructed entirely out of Anticorodal-110® (EN AW-6082). For details on the test section see Zboray and Prasser (2013b). We have investigated here a simple, generic spacer geometry shown in Fig. 2c. It comprises split vanes that have been developed in the context of low-quality CHF problems to promote crossflow between subchannels (Shin and Chang, 2009) and resembles in geometry to the ULTRAFLOWTM spacer developed for the ATRIUMTM fuel assemblies by AREVA (Kraemer et al., 1995). The spacer grid is placed just above of the start of the thin-wall section (see Fig. 1a). The spacer is constructed out of 0.6 mm thick aluminum sheets welded together. Note that as the vanes are quite tiny the uncertainty in the actual inclination angle could be around 3◦ . 2.2. The neutron imaging method The imaging of the subchannels has been performed at the cold neutron beam line, ICON, at the SINQ spallation neutron source at the Paul Scherrer Institute, Switzerland. For details on the beam line see Kaestner et al. (2011). The imaging optics consisted of a 1024 × 1024 pixels, cooled ANDOR CCD camera equipped with an f/2.0 100 mm Nikon macro lens focusing on a Li6 -doped scintillator/converter screen through a mirror at 45◦ angle. A field of view (FOV) of about 6 × 6 cm2 has been achieved with a pixel resolution of the digitized images of 59.5 ␮m/pixel. The camera and mirror are placed in a light-tight box, whose only opening is covered by the scintillation screen. The image pre-processing and tomographic reconstruction is performed as described in Zboray and Prasser (2013a, 2013b). Projections of the empty channel (no flow) are used as references for reconstruction and the raw projection data are corrected for spectral (beam hardening) and scattering effects based on Monte Carlo (MC) simulations as described in Zboray and Prasser (2013a). The liquid film thickness (LFT) is determined by integrating the liquid hold-up profile over the liquid film obtained from the reconstructed gray-scale image. As is shown by Zboray and Prasser (2013a) the LFT obtained in such a way has a minimal bias (around −2% or less) and its statistical uncertainty is typically 7–9% for the present measurements. Artifacts occurring in the reconstructed image, their significance as well their suppression or compensation are thoroughly discussed in Zboray and Prasser (2013a). Experimental results are shown in details in Section 4. 2.3. Test conditions We have investigated three flow combinations, summarized in Table 1, with and without the spacer shown in Fig. 2. The experiments with spacer have been carried out using two field-of-views (FOVs), one focusing at the spacer and one above the spacer. All

A. Saxena et al. / Nuclear Engineering and Design 299 (2016) 163–173

165

Fig. 1. The scheme of the test section including the bundle model and the two-phase flow loop.

Fig. 2. Cross-sectional view of the upper, thin-walled part of the tight lattice bundle model (a). Note that the grooves, used to hold the spacer in place (shown by dashed lines), are only present at the first 5 cm of the thin-wall section. A reconstructed cross section of the empty bundle with a spacer in it at the level of the spacer vanes (b). The photo of the spacer used in this study is shown in (c). Note that (b) shows the vanes looking from the grid (bottom) toward the vanes (top), which explains the apparent “discrepancy” in the vane inclination between (b) and (c).

Fig. 3. Quadruple tight-lattice subchannel geometry (a) used for experiments and (b) used for computations. Table 1 Matrix of the experimental conditions. Air flow (N m3 /h)

Water flow (l/h)

Jair (m/s)

Jwater (m/s)

1–ˇ

P inlet (bar)

Variations:

Exp1

58

454

34.74

0.60

0.0170

Exp2

49

454

28.87

0.60

0.0204

Exp3

38

454

22.85

0.60

0.0256

3.6 3.7 3.3 3.4 2.9 3.0

No spacer Spacer (2 FOVs) No spacer Spacer (2 FOVs) No spacer Spacer (2 FOVs)

166

A. Saxena et al. / Nuclear Engineering and Design 299 (2016) 163–173

3. The computational model

Fig. 4. Simulation methodology.

tests were carried out at ambient temperature of approximately 20 ◦ C. The two-phase flow can be characterized by the superficial gas and liquid velocities: Jg =

V˙ g A

and

Jl =

V˙ l , A

(1)

where A is the channel cross section and V˙ is the volumetric flow rate. Further, the gas volume flow fraction is defined as: ˇ=

V˙ g . V˙ g + V˙ l

(2)

Note that 1 − ˇ, the liquid volume flow fraction is given there. Note that pressure values in Table 1 are measured at the channel bottom at the air inlet junction (green piece in Fig. 1), therefore the actual static pressure at the height of the FOV is lower. Using the Friedel correlation for two-phase pressure drop (Friedel, 1979), taking acceleration pressure drop due to presence of gas and form losses, the total pressure drop from the air inlet to the FOV has been estimated and the gas superficial velocity in Table 1 is given taking this correction into account.

The simulations were performed in a quadruple subchannel tight lattice geometry using the commercial code STAR-CCM+ which solves the Navier–Stokes equations using a finite volume method on an unstructured grid. The flow conditions for the simulation have been chosen corresponding to the conditions for Experiment 3 (Fig. 3). As highlighted in Fig. 4, as a first step, a realizable k–epsilon simulation was performed in a 1 m long geometry without spacers to obtain inlet conditions for the subsequent simulations. Outlet conditions from this step were then used as inlet conditions for the LES calculations. A development length of 10 hydraulic diameters has been included upstream of the spacer in the final geometry to allow the fluctuations in the velocity field at the inlet to develop the fluctuations in the volume fraction field from a time-averaged value. Due to manufacturing tolerance and the actual positioning of the grid in the subchannel geometry, slight differences in the spacer geometry might be expected. 3.1. Inlet conditions The inlet conditions were obtained by simulating air-water flow in a 1-m section of the geometry without spacers using a realizable k–ε two-equation turbulence model. Local cylindrical coordinate systems were defined for each of the six rods and an initial film thickness of 0.3 mm was set corresponding to the inlet conditions of the experiments along with a flat velocity profile calculated from the superficial velocities of each phase.

Fig. 5. Time-averaged inlet (a) volume fraction field and (b) axial velocity field for LES obtained from unsteady k–ε simulation without spacer.

Fig. 6. Time-averaged liquid fraction and axial velocity near spacer.

A. Saxena et al. / Nuclear Engineering and Design 299 (2016) 163–173

167

Fig. 7. Time-averaged tangential velocity (with the origin at the center of the middle subchannel) at (a) the tip of the spacer vanes, (b) at 10 mm downstream and (c) at 20 mm downstream.

Fig. 8. Time averaged liquid film thickness distribution on (a) Pin 1, (b) Pin 2 and (c) Pin 3 around the spacer.

168

A. Saxena et al. / Nuclear Engineering and Design 299 (2016) 163–173

Fig. 9. Liquid film thickness distribution on (a) Pin 1, (b) Pin 2 and (c) Pin 3 spatially averaged from 10 to 40 mm downstream of spacer.

This initial simulation, which was averaged over a time period of 10 flow through times based on the average velocity of the liquid film, was performed to provide the inlet volume fraction profile, the velocity profile, the turbulent intensity and the turbulent length scale information for the main case where they were evaluated as: u Turbulent intensity = , U

 u =

k3/2⁄∈ Turbulent length scale = C

2k , U= 3

 Ux2 + Uy2 + Uz2

(3)

(4)

wherein isotropy of turbulent stresses is assumed. Fig. 5 shows the obtained inlet conditions. Calculation of turbulent inlet profiles in the form of pseudorandom coherent motions superimposed on to mean values is seen important in the growth and sustenance of turbulence in the computational domain. This is borne out of the fact that the grid scale

structures always include a time-varying component and need to be taken into account at the inlet by some mechanism to generate stochastic fluctuations in the grid-scale quantities that look like ‘turbulence’. The Synthetic Eddy Method (SEM) of Star-CCM+, proposed by Jarrin et al. (2009), was used to generate these fluctuations. 3.2. Physical models Large Eddy Simulation (LES), originally proposed by Smagorinsky (1963), is a turbulence modeling approach which is being increasingly used to tackle problems of industrial relevance in recent times. Since the solution of a turbulent flow contains different length and time scales, a direct numerical solution (DNS) of such a flow requires the resolution of the smallest energy dissipating length and corresponding time scales. Although DNS is being progressively used for low to medium Reynolds number

A. Saxena et al. / Nuclear Engineering and Design 299 (2016) 163–173

169

Fig. 10. Time-averaged liquid film thickness distribution on (a) Pin 1, (b) Pin 2 and (c) Pin 3.

flows, it is still computationally prohibitive to use for almost all of engineering applications. LES methodology, on the other hand, involves a resolved velocity field evaluated by filtering the Navier–Stokes equations and an unresolved subgrid velocity field that is modeled. For a numerical LES, the filter width, given by the mesh size, is a function of space for an unstructured mesh. Since the large eddies are directly computed with LES, these models are expected to perform better than two equation Reynolds Averaged Navier Stokes (RANS) models which typically perform well when the flow is fully turbulent, mostly attached and has no adverse pressure gradients. A Wall Adapting Local-Eddy (WALE) viscosity subgrid model is used for the unresolved turbulent stresses to scale the eddy viscosity near the walls appropriately. The Volume of Fluid (VOF) approach, originally proposed by Hirt and Nichols (1981), is an interface tracking method that solves for the volume fraction variable ˚ through an additional transport equation: ∂˚ + v · ∇˚ = 0 ∂t

(5)

where v is the flow velocity field. The method reconstructs the interface geometrically and hence is naturally mass conserving for incompressible flows. For sharp interfaces, a special discretization scheme for the convective term of the volume fraction is particularly needed to avoid excessive spreading. The advection scheme used for the volume fraction is HRIC (High-Resolution Interface Capturing), which provides a smooth blending of HRIC in low CFL (Courant-Friedrichs-Lewy) regions and upwind scheme in high CFL regions of the flow. The final scheme includes factors for sharpening the interface for surface tension dominated flows and an angle factor to avoid wrinkling of the interface when the flow is parallel to it. The time step was chosen to be 1e−05 s to keep the CFL number close to 1 at the interface. In order to keep the interface sharp, the sharpening factor was increased to 0.1 as recommended for surface tension dominated flows. A bounded-central scheme was used for the convective term along with a second-order implicit

time-stepping method implying a third-order truncation error in space and time coordinates. 3.3. Mesh A mixed prism-layer polyhedral unstructured mesh was used for the simulations with the prism layer being used to resolve the liquid film and the interface with the gaseous phase along with the wall layers on the spacer while the polyhedral cells were used primarily in the gas core region. Two mesh sizes were tested to evaluate the effect of mesh size on the computational results with a 15 million cell coarse mesh and a 40 million cell fine mesh. Target surface sizes of 0.4 mm and 0.2 mm were used for mesh 1 and mesh 2, respectively. The prismatic layers extended up to a wall distance of 0.4 mm from the rods, within the maximum film thickness given by the experiments for these flow rates with the film having a resolution of 5–15 cell layers in the wall normal direction at the inlet. The wall y+ was found to be <5 on all walls. The dynamic nature of the topography of the interface in the flow being simulated in this work prohibits one to obtain mesh independent results since the interactions between the two phases depend extensively on the mesh size particularly near the interface. As many researchers, e.g. Lorencez et al. (1997), have found, turbulence on the gas side near a gas-liquid interface essentially behaves like wall turbulence and, correspondingly, mass and momentum transfer at the interface would depend on the smallest resolved eddies near the interface which typically scale as the distance from the interface itself. Since grid sized eddies are resolved and subgrid scale features are suppressed by additional turbulent viscosity in an LES computation, one might expect the mesh size to play an important role in determining the interface dynamics especially due to the effects of entrainment and deposition. For this reason, simulations were performed for flow conditions corresponding to Exp. 3 since these flow rates correspond to the lowest relative velocities of the phases which would limit the length scale of the smallest eddies near the interface. Dependence of liquid film thickness (LFT) distribution around the pins on the mesh size can be seen in Section 4.1. Better results

170

A. Saxena et al. / Nuclear Engineering and Design 299 (2016) 163–173

Fig. 11. Liquid film thickness distribution on (a) Pin 1, (b) Pin 2 and (c) Pin 3 spatially averaged from 10 to 40 mm downstream of spacer.

are obtained using a finer mesh which might imply a direct effect of the resolution of interface flow dynamics due to better capturing of mass and momentum transfer between the two phases. Coarser mesh, particularly near the interface, allows the spatial gradients to be inaccurately resolved resulting in an accumulation of liquid in streaks as revealed in the higher magnitude peaks in the liquid film distribution in Fig. 7. Insufficient resolution of relevant eddies near the interface could also relate to the inability of capturing the time resolved entrainment process from the liquid film into the gas core. Statistics for both simulations were gathered for an additional 10 flow through times after allowing the flow to develop for a similar time based on the mean liquid film velocity. Since better results are obtained using the finer mesh, all the results and comparisons are done using results from the simulation using this grid. 4. Results Since spacers are known to play an important role in determining the flow behavior which affects the local heat transfer in rod

bundles, it is imperative to delve into the highly resolved details of the flow. Fig. 6 shows the mean liquid phase fraction and the mean axial velocity cross sectional profiles at the plane where the spacer vanes start. An increase in the axial velocity can be observed in certain regions in the central subchannel due to the blockage provided by the spacer itself along with low velocity regions next to them. This increase and reduction in velocity manifests itself in high and low axial shear zones acting on the liquid film, which coupled with the tangential shear field, mainly drives the LFT distribution. A high time-averaged liquid fraction can also be observed along and on top of the spacer walls in all the four subchannels due to accumulation of the liquid at the surfaces. Looking at the tangential velocity field, one can observe flow features with opposite rotational sign being formed at the vane tips in Fig. 7(a)), where the blue/black region indicates clockwise flow motion and the pink region the counter-clockwise flow motion. This counter clockwise rotating tangential field then slowly merges with the field near the pins, while the clockwise flow merges in

A. Saxena et al. / Nuclear Engineering and Design 299 (2016) 163–173

171

Fig. 12. Liquid film thickness distribution on downstream and upstream faces of spacer vanes 2 and 3.

the center of the middle subchannel. The field also decreases in magnitude as one travels further downstream as expected. 4.1. Liquid film distribution on pins Analyzing the time-averaged film thickness distribution on the pins, film thinning can be observed at the spacer locations due to the high shear stresses from the gas side. Due to the blockage imposed by the presence of the spacers, the gas phase is accelerated in the space between the spacer side wall and the pin causing high relative velocities at the interface which in turn is responsible for the local thinning of the liquid film (Fig. 8). Comparing LFT distribution around the spacer, one can find discrepancies in the measured and computed results. This might be due to the asymmetric placement of the spacer grid in the experiments as mentioned in Zboray and Prasser (2013b). Generally lower magnitude of LFT on all three pins, averaged over the height of the

spacer body, is predicted by the LES (see Fig. 9). Zboray and Prasser (2013b) attributed the occurrence of peaks around 60◦ and 120◦ due to the proximity of the spacer vanes to the rod surface which caused a merging of the liquid film on the spacer grid with that on the rod surface resulting in a high LFT. Liquid film thickness distribution comparison is made in Fig. 11 for the three pins where the film thickness has been spatially averaged over 30 mm (10–40 mm) of axial length downstream of the spacer. High film thickness on the pin surface is observed on all the three pins at 60◦ and 120◦ azimuthal angles with a trough around a region of 80–90◦ . LES results are found to be slightly offset as a function of the azimuthal angle compared to the experiments which might be due to the asymmetric placement of the spacer grid in the experiments and the slight inaccuracy in the vane angle mentioned above. For example, the dominant peak on the pin surface is found around 110–115◦ in the experiments compared to around 120◦ for the LES results. Results from neutron tomography

Fig. 13. Mean axial velocities for vane 3 on (a) inward tilting and (b) outward tilting face for vane 3.

172

A. Saxena et al. / Nuclear Engineering and Design 299 (2016) 163–173

Fig. 14. Time-averaged streamwise velocity profiles in liquid film on (a) Pin 1, (b) Pin 2 and (c) Pin 3.

experiments conducted by Zboray and Prasser (2013b) show slight variations in the maximum and minimum liquid film thickness for different flow rates around the azimuthal center of the rods. A sharp line of separation which can be seen in the LFT distribution at roughly 90◦ , the so called “split effect”, can be seen in the plots in Fig. 10 and is typical for such vane geometry and arrangement. Since the LFT distribution is primarily expected to be driven by the gas shear, thinning of the liquid film is found in zones of high velocities in the gaseous phase. Similarly, accumulation of liquid would be found in regions where the gas shear is low and where a convergent tangential gas shear is exerted. Peaks can also be observed near the periphery of the pins due to pooling effects wherein the curved pin surface meets the flat walls of the geometry creating a groove for the liquid to get accumulated in. 4.2. Liquid film distribution on spacer vanes One of the contributing factors in the estimation of liquid film thickness (LFT) distribution directly downstream of the spacer on the rods is the role played by the spacer vanes in depositing the dispersed liquid droplets from the gas core onto the rods themselves. Comparison of LFT distribution on the spacer vanes is presented in this section. On observing this distribution on spacer vanes 2 and 3, one can find higher time averaged film thickness on the vane face inclined inwards toward the center of the gas core compared the face inclined toward the outside. This is expected since the inward tilting vane face provides a direct obstruction to the dispersed phase in the gas core enhancing the deposition of liquid

droplets. As was also observed in the experiments, more liquid is flowing along the less inclined edges of the vanes compared to the more inclined edges and again mostly on the inward tilting vane face. Fig. 12 shows the time averaged LFT distribution comparison on the spacer vanes. The results also reveal that the film collected on the spacer eventually drains off of the vane tip back into the gas core. Fig. 13 shows the time-averaged axial velocity distribution of the liquid film on the inward and outward tilting faces of vane 3. As can be seen, higher velocities are found near the tip of the vane for the inward tilting vane indicating acceleration along the vane face due to the high shear force and the acceleration of the gas itself due to blockage, while higher velocities near the base and lower velocities near the tip of the outward tilting vane face are found due to the decreased shear forces in response to the gas expansion and separation directly above the vane base. 4.3. Velocity profile in liquid film Time averaged dimensionless axial velocity profiles have been extracted and shown in Fig. 14 in the liquid film on all three pins. Profiles are plotted at 10 mm and 30 mm downstream of the spacer and at an azimuthal angle of 110◦ along with the law of the wall where in a linear profile is calculated for y+ less than 11 and a log profile for y+ greater than 11 where: u u = u +



with u =

w 

y+ =

yu

v

(6)

A. Saxena et al. / Nuclear Engineering and Design 299 (2016) 163–173

As can be seen, the velocity profiles do not follow the universal velocity profile (UVP) in a turbulent boundary layer and is higher, especially in the log region, due to the additional momentum transfer from the shearing gas phase through the interface. This is also consistent with the results of Dobran and Flavio (1983) who introduced a damping of the turbulent mixing length close to the gas-liquid interface. Recent experimental results from Ashwood et al. (2015) have confirmed this behavior and have found velocity profiles deviating from a UVP and have proposed modifying the coefficients in the buffer and the log layer. Velocity profiles were found to be similar in the liquid film on all the three pins both qualitatively and quantitatively. Since the first mesh point lies within a y+ of 5 on all wall surfaces, the velocity at that point is expected to match well with the velocity given by a linear profile which can be seen in the plots below. It is to be noted that an all y+ wall treatment has been used for the simulation which uses a blended formulation using a linear and log profile. 5. Conclusions The analysis shows the capability of the current computational methodology in predicting the void fraction distribution in a BWR subchannel in the context of vertical annular flow in a tight subchannel geometry. Although the work is limited in its scope, in its inability to effectively resolve the dispersed phase and consequently its effect on the bulk flow, it lays down a platform for resolving flow details affecting the performance of a spacer. The comparison with experiments shows considerable agreement in terms of LFT distribution downstream of the spacer. Since it is expensive to perform full scale experiments for spacer optimization, this work shows the promise of complex 3D simulations for estimating void fraction in BWR subchannels. Acknowledgements The authors would like to acknowledge the help of Dr. Anders Kaestner and Dr. Eberhard Lehmann of the neutron imaging group of PSI for the opportunity to use the ICON beam line for the experiments. References Ashwood, A.C., Vanden Hogen, S.J., Rodarte, M.A., Kopplin, C.R., Rodríguez, D.J., Hurlburt, E.T., Shedd, T.A., 2015, January. A multiphase, micro-scale PIV measurement technique for liquid film velocity measurements in annular two-phase flow. Int. J. Multiph. Flow 68, 27–39, ISSN 0301-9322. Dobran, Flavio, 1983. Hydrodynamic and heat transfer analysis of two-phase annular flow with a new liquid film model of turbulence. Int. J. Heat Mass Transf. 26 (8), 1159–1171. Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. In: European Two-Phase Flow Group Meeting, Ispra, Italy, June Paper E2.

173

Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225. Iwamura, T., Okubo, T., Shimada, S., Usui, S., Shirakawa, T., Nakatsuka, T., Kugo, T., Nakano, Y., Wada, S., 1999. Research on Reduced-Moderation Water Reactor (RMWR). Nippon Genshiryoku Kenkyujo JAERI, Research, pp. 68. Kraemer, W., Proebstle, G., Uebelhack, W., Keheley, T., Tsuda, K., Kato, S., 1995. The ULTRAFLOW spacer – an advanced feature of ATRIUM fuel assemblies for boiling water reactors. Nucl. Eng. Des. 154, 17–21. Kaestner, A., Hartmann, S., Kühne, G., Frei, G., Grünzweig, C., Josic, L., Schmid, F., Lehmann, E.H., 2011. The ICON beamline – a facility for cold neutron imaging at SINQ. Nucl. Inst. Meth. A 659, 387–393. Kondo, T., Mochida, T., Yamashita, J., 2004. Technology development issues for highconversion BWRs using island-type MOX fuel. Nucl. Tech. 145, 257–265. Kureta, M., Tamai, H., Ohnuki, A., Sato, T., Liu, W., Akimoto, H., 2006. Critical power experiment with a tight-lattice 37-rod bundle. J. Nucl. Sci. Tech. 43 (2), 198–205. Kureta, M., 2007a. Development of a neutron radiography three-dimensional computed tomography system for void fraction measurement of boiling flow in tight lattice rod bundles. J. Power Energy Syst. 1 (3), 211–224. Kureta, M., 2007b. Experimental study of three-dimensional void fraction distribution in heated tight-lattice rod bundles using three-dimensional neutron tomography. J. Power Energy Syst. 1 (3), 225–238. Kureta, M., Tamai, H., Yoshida, H., Ohnuki, A., Akimoto, H., 2008. Development of design technology on thermal-hydraulic performance in tight-lattice rod bundles: V-estimation of void fraction. J. Power Energy Syst. 2 (1), 271–282. Lahey, R.T., Moody, F.J., 1993. The Thermal-Hydraulics of a Boiling Water Nuclear Reactor, 2nd ed. American Nuclear Society, La Grange Park, IL. Lorencez, C., Nasr-Esfahany, M., Kawaji, M., Ojha, M., 1997. Liquid turbulence structure at a sheared and wavy gas-liquid interface. Int. J. Multiph. Flow 23 (2), 205–226. Jarrin, N., Prosser, R., Uribe, J.C., Benhamadouche, S., Laurence, D., 2009, June. Reconstruction of turbulent fluctuations for hybrid RANS/LES simulations using a synthetic-eddy method. Int. J. Heat Fluid Flow 30 (3). Ohnuki, A., Kureta, M., Yoshida, H., Tamai, H., Liu, W., Misawa, T., Takase, Akimoto, H., 2008. Development of design technology on thermalhydraulic performance in tight-lattice rod bundle: I – master plan and executive summary. J. Power Energy Syst. 2 (1), 229–239. Shin, B.S., Chang, S.H., 2009. CHF experiment and CFD analysis in a 2 × 3 rod bundle with mixing vane. Nucl. Eng. Des. 239, 899–912. Smagorinsky, J., 1963. General circulation experiments with the primitive equations. Part I: the basic experiment. Mon. Weather Rev. 91, 99–152. Takase, K., Yoshida, H., Ose, Y., Akimoto, H., 2004. Large-scale direct simulation of two-phase flow structure around a spacer in a tight-lattice nuclear fuel bundle. In: Proc. Third International Conference on Computational Fluid Dynamics, ICCFD3, Toronto, 12–16 July 2004. Uchikawa, et al., 2007. Conceptual design of innovative water reactor for flexible fuel cycle (FLWR) and its recycle characteristics. J. Nucl. Sci. Tech. 44 (3), 277–284. Yamashita, J., Kawamura, F., Mochida, T., 2004. Next-generation nuclear reactor systems for future energy. Hitachi Review 53 (3), 131–135 http://www.scopus. com/inward/record.url?eid=2-s2.0-6344284716&partnerID=40&md5=f6b6614 d0c9d6a2dddc8ad271ba6af14. Yamamoto, Y., Hiraiwa, K., Morooka, S., Abe, N., 2004. Critical power performance of tight lattice bundle. JSME Int. J. Ser. B 47 (2), 344–350. Yamamoto, Y., Akiba, M., Morooka, S., Shirakawa, K., Abe, N., 2006. Thermal hydraulic performance of tight lattice bundle. JSME Int. J. Ser. B 49 (2), 334–342. Yoshida, H., Tamai, H., Ohnuki, A., Takase, K., Akimoto, H., 2006. Current status of thermal/hydraulic feasibility project for reduced-moderation water reactor (2) – development of two-phase flow simulation code with advanced interface tracking-method. Nucl. Eng. Tech. 38 (2), 119–128. Zboray, R., Prasser, H.-M., 2013a. Measuring liquid film thickness in annular twophase flows by cold neutron imaging. Exp. Fluids 54 (1596). Zboray, R., Prasser, H.-M., 2013b. Neutron imaging of annular flows in a tight lattice fuel bundle model. Nucl. Eng. Des. 262, 589–599.