O n T wo- p h a s e F l o w, H e a t T r a n s f e r P h a s e C h a n g e S i m u l a t i o n i n F u e l A s s e m b l i e s

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1 Report Series - Applications TransAT for Nuclear Science & Technology O n T wo- p h a s e F l o w, H e a t T r a n s f e r P h a s e C h a n g e S i m u l a t i o n i n F u e l A s s e m b l i e s ASCOMP GmbH Edited by: Dr S. Thomas and Dr D. Lakehal Release Date: Sep., 2014 Reference: TRS-A/

2 Table of Contents 1. INTRODUCTION SIMULATION POSSIBILITIES USING TRANSAT (CFD & CMFD) SINGLE-PHASE FLOW & HEAT TRANSFER IN FUEL ASSEMBLIES RANS with IST: The Westinghouse 24-rod Mock-up of SVEA-96 Fuel Bundle RANS with IST: The PBST Test-Case LES with BFC: The Scaled-down PSBT 5x5 case MULTI-PHASE FLOW & HEAT TRANSFER IN FUEL ASSEMBLIES USING ITMs MULTI-PHASE FLOW & HEAT TRANSFER IN FUEL ASSEMBLIES USING PHASE-AVERAGE MODELS DEBORA TEST CASE BARTOLOMEI TEST CASE LEE, PARK & LEE and TU & YEOH TEST CASE D PWR SUB-CHANNEL TEST CASE CONCLUSIONS References

3 Abstract This note shows capabilities of the CMFD code TransAT for various scenarios of multiphase flow and heat transfer simulations in fuel assemblies. The document highlights the unique features of the code compared to others, including meshing complex geometries using the coupled Immersed Surfaces Technology combined with Block Mesh Refinement (IST/BMR), and phase-change physics using either interface tracking or phase-average models. 1. INTRODUCTION Subcooled flow boiling in PWR S occurs in the hot fuel assemblies when heat flux is supplied to the wall, which is initially in contact with flowing liquid. Understanding and predicting this complex phenomenon is crucial for efficient operations, safety, and development of new PWRs, and more generally in light-water cooled reactor (Sugrue et al, 2012). For instance, in U.S. PWR plants (Fig. 1), subcooled flow boiling occurs under normal operating conditions, and determines the margin to Critical Heat Flux CHF (Toderas & Kazimi, 1990). Subcooled flow boiling also determines the rate at which corrosion products in solution in the coolant deposit on the surface of the zirconium alloy cladding, which can lead to localized corrosion and neutronic distortions (axial offset), and ultimately cladding failure (Sugrue et al, 2012). Figure 1: Schematic of subcooled flow boiling in a PWR assembly (not to scale). The mainstream modelling approach for thermal-hydraulics systems involving two-phase flow and heat transfer is based on the Eulerian-Eulerian, two-fluid model (Bestion et al, 2009; Lo, 2006 and In & Chun, 2009), which requires closure laws for the phase-to-phase and wall-to-flow mass, momentum, and energy terms in the governing equations. The wallto-flow constitutive relation for energy captures subcooled boiling heat transfer. Examples of mechanistic boiling heat transfer models are the heat flux partitioning model of Kurul and Podowski (1991) and its recent modified variant of Krepper and Rzehak (2011). 3

4 Consensually, in the partitioning heat flux model, heat removal by the boiling fluid is split into three contributions, (i) the latent heat of evaporation to form the bubbles, (ii) the heat expended in re-formation of the thermal boundary layer following bubble departure, the socalled quenching heat flux, and (iii) the heat transferred to the liquid phase outside the zone of influence of the bubbles by convective heat transfer (Fig. 1). This modeling strategy is generally applicable to low heat flux boiling and has been based on speculative hypotheses supported by a myriad of empirical correlations, assuming that single-phase convection and nucleate boiling are analogous physical processes; e.g. the Rohsenow correlation. The Achilles-Heel of existing wall boiling models is the definition of the bubble departure diameter, which is a critical unknown. The flux-partitioning boiling model is in general implemented within the two-fluid model, except in code TransAT, where it is implemented with the homogeneous mixture model, coded within the general N-phase context. Moving away from rough empiricism towards developing more mechanistic models of boiling heat transfer requires high-quality/resolution DNS or experimental data made available, including nucleation site density, bubble growth rate, bubble departure diameter and frequency, and time-resolved temperature distribution on the boiling surface. While efforts are underway on the experimental side notably to develop better data acquisition/visualization systems, on the CMFD front, the interest has been shifted towards high-end simulation (DNS) of boiling processes, using for example the so-called Interface Tracking Methods (ITMs), in which the topology of the vapor/liquid interface is directly calculated together with the Navier-Stokes equations. This is expected to play a major role in the process of model development too. Note too that alternative treatments of wall heat partitioning a la Kurul and Podowski (1991) are underway, accounting notably for other hydrodynamics phenomena, including the effect of bubble merger and coalescence, bubble size distribution, bubble sliding. This effort includes Kolev s bubble interaction model (1994), and the hybrid numerical-empirical model of Sanna et al (2009). 2. SIMULATION POSSIBILITIES USING TRANSAT (CFD & CMFD) In TransAT, one can resort to various modelling combinations, depending on the needs in terms of physics, the simulation capabilities (grid size and CPU resources). Fig. 2 below presents these various modelling combinations. In short, as to turbulence first, TransAT can simulate flows using either statistical time-average models (RANS, both isotropic and algebraic stress, using wall functions or low-re approaches) or scale-resolving approaches (LES and V-LES). The same structure is available as to multiphase flow structures: use could be made of phase-average models (N-phase approach) or interface tracking methods (ITM), including Level Set and VoF. As to heat transfer phase-change, TransAT offers again two routes: using interfacial and wall heat/mass transfer models (under both phase-average models and ITM) or inter-phase direct heat-flux integration (under ITM). The same is true as to meshing capabilities: TransAT uses either the Body-Fitted Coordinates approach (BFC) or the Immersed Surface Technique (IST) combined with Block Mesh Refinement (BMR) or Local Mesh Refinement (LMR). IST combined with BMR or LMR is infinitely faster than BFC, in particular as to fuel assembly cases involving complex-shaped spacers. These modelling and meshing combination possibilities offer indeed a great deal of flexibility to the users. For instance the combination of ITM and LES is termed as LEIS, short for Large-Eddy & Interface Simulation, and is a unique feature in TransAT. In extending the modelling portfolio of TransAT, a new compressible, high-speed, N-phase formulation has been developed and is under validation; another unique feature in TransAT. The next sections will highlight these modelling combinations in terms of practical examples, with or without direct comparison with experiments. 4

5 Figure 2: Schematic of the TransAT modelling combination capabilities. 3. SINGLE-PHASE FLOW & HEAT TRANSFER IN FUEL ASSEMBLIES 3.1 RANS with IST: The Westinghouse 24-rod Mock-up of SVEA-96 Fuel Bundle In Boiling Water Reactors (BWR), the nuclear core consists of multiple parallel channels, connected at the inlet and outlet plena. This particular design feature effectively eliminates coolant cross flows through the entire core and provides a more uniform and controllable enthalpy distribution in various fuel rod assemblies. Thus, the issue of the optimization of the thermal-hydraulic performance of nuclear fuel is shifted from the core-wide to the assembly-wide analysis. This is only an apparent simplification of the task, since the phenomena that govern the phase distribution within fuel assemblies are still very complex, mainly due to various mechanisms such as diversion flows, void drift and turbulent mixing. Clearly, prediction of the thermal-hydraulic performance of fuel rod assemblies and- in particular- prediction of the occurrence of the Critical Heat Flux (CHF) requires that the details of flow and phase distributions are known. Current computational methods cannot be fully trusted in such complex applications and still require significant development of new models as well as thorough validation of the existing ones. One of the important components of the fuel rod assembly, whose important bi-function is to enhance the lateral exchange of flow momentum and energy, is the spacer grid. The experimental rig, schematically shown in Fig. 3 consists of a test section, a water reservoir, a centrifugal pump (15 kw), flow control valves and stainless steel piping, forming a closed loop. The water flow is measured by an electromagnetic flow meter downstream of the pump. From the pump the water enters the plenum connected to the lower part of the vertical test section. The plenum contains a honeycomb flow rectifier suppressing large-scale vortices generated by the pump and tube bends. The test section terminates in another plenum. A weir in the upper plenum maintains a constant water level and a free surface at atmospheric pressure. The water from the upper plenum returns to the reservoir passing a number of baffles giving time for air bubbles trapped in the water to rise to the surface. All the measurements were performed in single-phase water flow. The crosssectional view of the test section, corresponding to one quarter of the SVEA 96 fuel assembly, is shown in Fig. 3. The spacer part in the studied and surrounding sub-channels is presented in the same figure together with the photographs of spacer elements, such as dimple, spring and frame vane. The 24 rods are held in position by five spacers of the thin- 5

6 plate spring construction. The rods could slightly vibrate. The walls of the test section are made of 10mm thick glass plates, allowing visibility techniques to be used to study the flow. Figure 3: Real spacer photography and associated CAD file immersed in a coarse IST grid (for illustration). 3.2 RANS with IST: The PBST Test-Case The PSBT benchmark, based on the NUPEC database (Rubin et al, 2010), focuses on advancement in subchannel analysis of fluid flow in rod bundles, which has very important relevance to the nuclear reactor safety margin evaluation. In this scaled down preliminary work, steady state single phase flow with conjugate heat transfer in a PWR 5x5 rod bundle with three different kind of spacers (the simple spacer, the non-mixing vane spacer and mixing vane spacer; Fig. 4) is simulated and analysed. Turbulence effects are accounted for using a standard k-ε model. The solids, including the spacers and the rods, were modelled using the Immersed Surface Technique (IST). Commercial CMFD package TransAT was used for the simulations. Figure 4: The original CAD files of the two guiding-vane spacers Steady state flow simulations were performed using TransAT employing the k- model for turbulence with wall functions, modified to account for buoyancy forces for the production and dissipation equations. The CAD files depicting the spacers (shown in Fig 4) could be immersed in a Cartesian grid consisting of enough grid cells to mesh the fluid and solid areas (Fig. 5). In TransAT, a minimum of 3 cells is needed to resolve solid components immersed into the Cartesian grid. In this preliminary feasibility study, the problem has been 6

7 downgraded to simulate an axial heated length of 1m with five spacers along the length of the rod bundle, requiring a total of 6.4 million cells. The project is expected to culminate with the single state temperature analysis of the full PSBT geometry of 3.658m length with 17 spacers in total, which would require about million grid cells, which is reasonable compared to what might be needed with a BFC Grid (~ 100 million cells). Figure 5: IST grid of the entire system with spacers; temperature iso-contours on the solids. Fig. 6 displays a three-dimensional perspective view of the temperature iso-contours taken on the solid walls, showing the details of the flow captured by the IST method. It shows in particular the way heat evolves between the different spacers. Fig. 7 depicts the detailed picture of the heat transfer on the rods and secondary flow-field immediately downstream the upper mixing-vane spacer. The left panel shows clear heat streaks forming on the surfaces of the rods enhanced by the mixing vane structure. The secondary flow is also rather well predicted, although the method is more suitable to be used in the wall function context, avoiding low-re modelling requiring an extreme near-wall refinement. 7

8 Figure 6: Temperature contours on the surface of the entire assembly. 8

9 Figure 7: Temperature contours (left) and secondary flow (right) downstream the 1 st and 2 nd spacers. 3.3 LES with BFC: The Scaled-down PSBT 5x5 case This problem is inspired by the PSBT OECD sub-channel benchmark (Rubin et al., 2010) in terms of radial dimensions, though the expected deliverables are different, in that the focus is on detailed flow and temperature profiles in the subchannel, together with global parameters including the heat transfer coefficient, the onset of nucleation, the pressure drop and the thermal entry length (some only were required in the OECD benchmark). The operating conditions of the present case are made on purpose different from PSBT, namely the power and mass flow rate, which have been adjusted according to the reduced length (1m instead of 3.65m). The PWR fuel assembly consists of a rod bundle with water coolant flowing upward along the rods at a high Reynolds number. The rod diameter is 9.5mm, the rod pitch is 12.6mm and the active fuel length is typically 3.7m. The hydraulic diameter for a unit cell is D e = 11.8mm. The coolant pressure is 15.5MPa with temperature ranging from 290 C to 340 C. The mass flux is G=3700 kg/m2s, corresponding to a Reynolds number Re=GD e/ = , shear velocity ~0.2m/s, and frictional Reynolds number ~10 4. The problem has been scaled down to more reasonable conditions, i.e.. Choosing LES instead of DNS is motivated by the fact that in contrast to channel flow, this problem should involve non-cartesian meshing, e.g. BFC or unstructured grids, which are not adequate for DNS. Finally, the length of the domain was reduced from the PWR case to relax the meshing requirements in the axial direction. Since the distance to the onset of nucleate boiling depends on the integrated power (heat flux times rod surface area) supplied to the fluid, the heat flux was scaled accordingly. The heat flux is to be applied at the rod outer surface. The actual operating conditions are summarized in Table 2. Pressure 15.5 MPa Sat. temp C Inlet temperature 290 C Mass flux 74.1 kg/m 2 s (or Re =300) Heat Flux 50 kw/m 2 Power 1.57 kw Table 2: Test case 2 operating flow conditions. P=13.0 mm 9

10 Fuel Rod Flow outlet Heat flux q Cross flow section =45 0 =0 0 Figure 8: Computational domain: Dimensions & BC s. (lower) Medium (left) and fine (right) grids for LES (x-y). Arrows show 0 0 and 45 0 segments. The dimensions of the simulation domain and boundary conditions are indicated in Fig. 8. The case feature cross-sectional dimensions similar to the PSBT OECD case; rod diameter D = 10 mm and pitch P = 13 mm. The length is reduced from 3.6 m to 1.0 m. A novel approach was used to generate proper boundary conditions for this flow. First, periodic conditions were applied in the radial and circumferential directions to mimic the effect of the neighbouring rods. In the axial direction, however, a hybrid Developed & Developing Flow Hybrid Approach has been developed. It consists of first generating turbulence in a periodic e, then the resulting fluctuating (scaled to maintain the mass flow rate) field is imposed in the entire domain, recycled periodically: temperature is updated using inflow-outflow BC s, together with the steam-water interface in case of two-phase flow calculations. Two BFC grids were employed: the medium one (208 // core blocks) consists of cells providing a near-wall resolution of y+~ , which allows resolving the viscous sublayer. The second grid (832 // core blocks) consists of 1,600x60x60 cells, providing a near-wall resolution of y+~ Fig. 9 below depicts the cross-flow and heat transfer in the bundle. Panel a) and b) present results of a 6 million cell still somewhat under-resolved DNS simulation. The lower panels present LES results obtained with 1.6 million-cell grid (Caviezel et al, 2013). The panels illustrate that dissipation in the numerical method captures some features of a subgrid scale 10

11 model and the wall temperatures of interest are reasonably predicted. What is also of interest is the ability of under-resolved DNS to tackle problems of practical interest. (a) Fine grid: instantaneous (b) Fine grid: time average (c) Medium grid: instantaneous (d) Medium grid: time average Figure 9: Fine vs. medium resolutions: Instantaneous (a and c) and time averaged (b and d) crosssectional velocities and temperature contours. Medium grid Fine grid Figure 10: Mean velocity profiles across the subchannel (0 & 45 ) compared to the DNS of Eggels et al. (1994); medium versus fine mesh simulations. Time averaged results are presented in Figs. 10 and 11, including mean velocity and temperature profiles. Since the flow resembles turbulent flow in a pipe, use was made of available DNS data (Eggels et al, 1994) for comparison. The DNS data are not filtered. The difference with the pipe flow is that the present one has two azimuthal segments, a short one ( =0 ) with low Re effects and a full one ( =45 ) extending to the core with high Re effects (see Fig. 10); the latter one should thus return the imposed shear Reynolds number 11

12 at the subchannel center point, in the form of y+ centerline= Re. The mean flow profiles are plotted in Fig. 9, compared to DNS. As explained earlier, the =0 segment profile achieves a lower y+ than the =45 one. The profiles match very well the DNS data of Eggels et al (1994), in particular the fine grid one which does not show the slight grid effect returned by the medium grid simulation. This preliminary important result pleads in favour of a high quality LES simulation achieved by TransAT. Another important measure is the normalized temperature variance >, which is plotted in Fig. 11 on both segments, at various crossflow locations, comparing once more the medium and fine grid results. It is only for this higher-order quantity that the grid resolution shows an effect, with differences in peak values of about 5% in the =0 segment and up to 10% in the =45 one. The medium grid results still show a grid effect (kink). The fine grid results exhibit variations in this quantity with elevation, which is not always the case in the medium grid results. This may be an artefact of normalization; it could have shown a self-similar behaviour if it were normalized by the average wall temperature. We also suspect that the fine grid simulations require still more time to reach statistical convergence, in particular for second-order turbulent quantities. Be it as it may, the results are similar to DNS data of a heated channel flow. Fine grid: segment 0 Fine grid: segment 45 Figure 11: Mean temperature profiles across the subchannel at various locations. Global parameters results are presented in Table 3. The LES results are compared here to existing analytical and experimental correlations. The pressure drop between medium and fine grid is accurate to 2.2% and 5% compared to the correlation. As to the heat transfer coefficient (HTC), there are uncertainties for the case of interest, which in fact belongs to the transitional cases regime, according to Incropera and DeWitt (1996), for which the correlations, in particular the Colburn one (or Dittus-Boelter), could give up to 25% error. When accounting further for the effect of neighbouring rods using the Weisman correction (here =1.826p/D-1.043=1.33), the deviations between LES and correlation is high, and is precisely 33%. If this correction is not accounted for, the LES results (fine grid in particular) are comparable to the Colburn correlation, within -5%. With more sophisticated correlations e.g. the Gnielinski and Petukov (see Incropera and DeWitt, 1996), the analysis changes, in that the LES data are 6% than Gnielinski s correlation and 1.9% only than Petukov s one. Quantity Med. grid Fine grid Analytical/Exp. Pressure drop P [Pa] Heat transfer coefficient (HTC) at X ONB [kw/m 2 K] 1.62 (Colburn) 2.16 (Colburn -W*) 1.44 (Gnielinski) (Gnielinski -W) 1.50 (Petukov) 2.0 (Petukov -W) 12

13 Distance to X ONB [m] Min-max Min-max (Colburn) 0.79 (Colburn -W) Thermal entry length [m] Min-max Min-max *W means with the Weisman (1959) correction factor Table 3: Test case 2 operating flow conditions The distance to the onset of boiling is questionable in the same way, since it is directly based on the HTC correlation employed (here we took the Colburn one only). The simulation results are within a few percent s deviations from the Colburn correlation, but 24-35% off the Colburn Weisman variant, which is in line with the HTC deviations reported. Finally, as stated previously, there is no such a constant line indicating XONB since the simulations have clearly shown that the effect of the secondary flow motion makes it rather undulating by 5-7% around the mean. 4. MULTI-PHASE FLOW & HEAT TRANSFER IN FUEL ASSEMBLIES USING ITMs The hydrodynamics of the convective boiling two-phase flow is the focus of this section. One expects here the nucleating small bubbles to grow to non-spherical shapes due to intense shearing - and migrate to the core flow, possibly featuring coalescence, before condensing. Starting from this hypothesis, the modeller aiming at using ITMs - faces a dilemma as to the way nucleation should be seeded, since there is no other alternative. Intuitively, the choice would be to initiate individual resolved (super-grid) bubbles on the rod where the wall temperature reaches saturation. But this could be questionable since it appeals to making various hypotheses as to the statistical distribution of the bubbles, their size and concentration, and the intensity of the nucleation of the sites. In other words, the potential to make errors on the wall regions, which are instantaneously favourable for bubble growth, is obviously high. Thus to avoid additional modelling assumptions, we have taken another novel route where boiling incipience is triggered using an unresolved (sub-grid) vapour film instead of individual super-grid bubbles, without a-priori experimental evidence. Here the only information available is the wall temperature. With the present boiling incipience idea by means of a SGS vapour film, the physics of nucleate boiling cannot be captured immediately past the onset of nucleate boiling where nucleation of individual bubbles dominate heat transfer, unless the vapour film breaks in a later stage into individual bubbles. But this again raises the issue of grid-dependent simulations; an insufficient resolution should rather return large (discontinuous) patches of vapour on the surface, as is the case in near-chf situations. The simulations started from the existing LES data basis, and initiated an ultra-thin-film of vapour instantaneously on the rod surface where at T wall= T sat. The film grows by the action of heat/mass transfer from the wall; here use is made of the Level-Set technique (Sussman et al., 1994) to track the vapour-water interface. Because a BFC grid is employed, a fastmarching approach on a narrow-band is used to re-distance the interface and conserve mass; traditional re-initialization techniques are indeed suitable for Cartesian grids only. A dynamic contact angle model based on the Yong s triple force decomposition has been employed. Combing advanced ITMs and LES is known as LEIS, short of Large-Eddy & Interface Simulation (Lakehal, 2010). A near-interface damping approach is employed (Liovic & Lakehal, 2007a,b). As to phase-heat transfer, direct heat flux integration is performed to capture the exact rate of mass transfer across the interface, without resorting to a model. The qualitative results shown next were obtained after time steps only, which took 3 weeks on 892 processors. We estimate another time steps before concluding. 13

14 Fig. 12 shows instantaneous temperature contours on the rod with the vapour-water interface at positions of T sat, at the end portion of rod. The film shown in a transparent way suggests the occurrence of a patchy discontinuous structure of the interface. It is likely that the film has not yet disintegrated into individual bubbles detaching towards the core flow. The film is better visualized in Fig. 13, which does not show the temperature contours on the rod; note that the film has been increased in size for visualization purposes only. The size of the film is better depicted in Fig. 14 with a black line, displaying cross sections coloured by temperature. It shows the turbulence activity and secondary flow motion as well. Figure 12: Instantaneous temperature contours on the rod with vapour at positions of T sat Figure 13: Vapour-water interface at positions of T sat Figure 14: Cross-sectional temperature contours and interface. 5. MULTI-PHASE FLOW & HEAT TRANSFER IN FUEL ASSEMBLIES USING PHASE-AVER AGE MODELS 14

15 For solving the subcooled boiling problems in the following section, the channels are long and thin (typically 5m long and 20mm width). The grid requirement to capture the sharp interfaces in such slender domains is enormous. To resolve the issue, the Eulerian multiphase (phase-average) model under its homogeneous form (Manninen et al, 1996) is used to capture the evolution of the two phases with heat transfer. The vapor phase is modeled as the secondary phase in the primary liquid flow. Under the original homogeneous form of the Eulerian model, the conservation equations are solved for the mixture quantities, including density, viscosity, velocity, pressure and temperature, and phase volume fractions. The Eulerian Ensemble-Averaged model owing to its lower grid resolution is faster to run. The details of the interface topology are not captured as well as the Level-Set method, but it provides good comparison when looking at flow quantities, like velocity, void fraction, temperature etc. 5.1 DEBORA TEST CASE The motivation behind presenting the results of the DEBORA experiments (Manon, 2000; Garnier et al, 2001) is that because we could compare the results of three different codes, albeit using the same wall boiling model (Kurul and Podowski, 1991). Here we compare the results of FLUENT and NEPTUNE (Lavieville et al, 2005) using the two-fluid approach against TransAT s results using the N-phase mixture model. DEBORA experiments consist of Freon R12 flowing upwards in a vertical pipe heated with a constant heat flux of 58.2 kw/m 2 under a pressure of bar. At the inflow, the liquid is subcooled and is heated as it flows upwards and vapor bubbles are nucleated at the wall. These bubbles break away from the wall and are dispersed in the turbulent flow. Internal diameter of the pipe is 19.2mm. The whole pipe can be divided into three sections: inlet adiabatic section 1m long, heated section 3.5m long and outlet adiabatic section 0.5m long. The test cases are similar those simulated by Vyskocil and Macek [2008]. The summary is listed in Table 4. Case Mass flux T inlet T sat Bubble diameter No. kg/m 2 /s C C mm Table 4: Selected DEBORA test cases The bubble diameter is assumed to be constant for each case and does not vary within the radial profile. The bubble diameters are different for every case. Computationally, the grid is axisymmetric covered by 14 cells in the radial direction and 1000 cells in the axial direction. The standard k-ε model is employed with wall functions for both velocity and thermal fields. The turbulent dispersion coefficient is also employed for the diffusion of void fraction. Properties of Freon-12 are extracted from the NIST Web Book (NIST, 2013). Initial flow conditions are set according to the experiment, with a prescribed ratio of eddy-to-molecular viscosity of 20. The numerical schemes used are second order in space. The void fraction is initialized in the entire domain at Following are the results for the test case. The section is taken at the end of the heated part of the pipe. 15

16 The contours of void fraction, liquid temperature and streamwise gas velocity between 4.5m and 4.6m axially are shown in Fig. 15. It indicates a jump in the void fraction close to the wall and the gas velocity is well developed at the end of the heated section. The liquid temperature in the axial region is heated up close to the saturation temperature. Radial profiles of the void fraction profiles are compared in Figures From the 6 test cases selected, the void fraction profiles compare well with the data. The vapour formation at the wall gives a jump in the void fraction in that area. This behaviour is well captured for all the cases by TransAT, except for Case 7, where the data show a sudden spike in the vapour formation that all the CFD simulations fail to capture. As the inlet temperature increases (constant mass flow rate), the void fraction at the wall increases. Results of TransAT and Fluent show similar trends whereas NEPTUNE predictions do not return sufficient drop in void fraction away from the wall. Figure 15: Contours of void fraction, liquid temperature, streamwise gas velocity and temperature for Case 7 Figure 16: Void Fraction Comparison for Case 2 & 3: T in = C and T in = C Figure 17: Void Fraction Comparison for Case 4 & 5: T in = C and T in = C 16

17 Figure 18: Void Fraction Comparison for Case 6 & 7: T in = C T in = 73.7 C 5.2 BARTOLOMEI TEST CASE Figure 19: Problem Setup for the Bartolomei Test Case. The next set of simulations experiments of Bartolomei et al. (1982). The set-up of experiments is illustrated schematically in Fig. 19. Like in the DEBORA experiments (Manon, 2000; Garnier et al, 2001), the heated lower section of the pipe sub-cooled boiling occurs and steam is produced. The section above is adiabatic and vapor condensation occurs due to the mixing of the vapor generated near the heated wall in the lower section with the still subcooled liquid core. The pipe diameter is mm, the heated section length is L 0 =1 m and the total pipe length is L=1.4 m. Subcooled water at temperature T l enters the pipe at pressure P l =6.89 MPa and mass flux G l. Heat flux at the channel wall in the heated section of the pipe is q=const. Saturation temperature for these conditions is T sat =558 K. The wall heat boundary condition in the non-heated upper section of the pipe is q=0. Other conditions are listed in Table 5. Heat flux mass flux T inlet T sat MW/m 2 kg/m 2 /s K K Table 5: Parameters for the Bartolomei Test Case. 17

18 Figure 20: Radial distribution of void fraction.at different axial locations Fig. 20 illustrates development of radial heating of water, changing of void fraction and transport of steam due to lift and turbulent dispersion forces. By the end of the heated section the water near the heated wall reaches saturation temperature, while the water at the center of the pipe remains approximately 30K sub-cooled, The vapor fraction decreases in the adiabatic section of the pipe due to condensation caused by turbulent mixing of the two-phase mixture from the near-wall region with the sub-cooled liquid in the central region. The experimental and numerical profiles of void fraction as shown in Fig. 21 are in reasonably good agreement, although the discrepancy cannot be ignored. One probable reason for the discepancy between the experimental results and the simulation results is that the assumption of the bubble diameter and shape. The heat transfer rate predicted for spherical bodies for condensation and evaporation is likely not to be accurate for complex two-phase flow structures. The volumetric interfcial area balance equation proposed by Yao at al (2004) to describe the geometrical structure of the two-phase flow, which takes into account turbulence induced bubble coalescence and breakup, and modeling of the nucleation of new bubbles on the volumteric interfacial area. Figure 21: Average void fraction as a function of distance along the pipe. 5.3 LEE, PARK & LEE and TU & YEOH TEST CASE Radial distribution of void fraction in a vertical (concentric) annulus in flow of subcooled boiling water was studied in experiments of Lee, Park & Lee (2002), Tu & Yeoh(2003) and Yeoh & Tu (2005). Schematic of the experimental section is presented in Fig. 22. The experimental section is made as an annulus with inner diameter 19 mm, 37.5 mm, length m and heated section of the inner pipe 1.67 m in length. Subcooled water is fed upwards. The measurements were taken at the elevation of 1.61 m from the inlet. The operating conditions are listed in Table 6. 18

19 Figure 22: Problem Setup. Heat mass flux flux T inlet T sat MW/ m 2 kg/m 2 / s K K Table 6: Computational Parameters. Simulation was performed for the experiments with q=152.3 kw/m2, G l=474 kg/(m 2 s), P=0.14 MPa (saturation temperature T sat=383 K), ΔT sub=11.5 K. The results from the TransAT simulations are compared to the simulations performed by Ustinenko et al (2008) using STAR-CD. The void fraction predictions match quite well with the published results as seen in Fig. 23. Figure 23: Void Fraction Distribution (Radial) D PWR SUB-CHANNEL TEST CASE The present investigation is based on the CFD simulations for the international OECD/NRC PWR subchannel and bundle tests (PSBT) benchmark (Rubin et al, 2010) provided by the Nuclear Power Engineering Corporation (NUPEC), Japan. The benchmark specification essentially compares and assesses numerical models and codes for the prediction of detailed subchannel void distributions to full-scale experimental data on a PWR rod bundle. 19

20 Figure 24: Schematic of the NUPEC PWR Test Facility. Figure 24 shows the schematic of the corresponding subchannel test section with an effective heated length of L H=1555mm and the measurement cross section being located L M=1400mm downstream the horizontal inlet of the coolant to the subchannel test section. As can be seen from the schematic diagram, no special measures had been undertaken in the experiment to control flow conditions or level of turbulence at the inlet cross section of the subchannel test section, e.g. flow straighteners, honeycombs or similar, and it is hoped that the length of the test section is sufficiently long (L/D~112) to prevent too large influence from deviations of the necessary inlet condition assumptions in the CFD setup from the real but unknown experimental inlet conditions. Testcase Measured Pressure [MPa] Inlet Temperature [ C] Power [kw] Mass Flux [kg m -2 s -1 ] Table 7: Computational Parameters for the S1 subchannel. The sub-channel test section, as shown in Fig. 24, simulates a single channel of a PWR fuel assembly. The effective heated length is 1500 mm where the void measurement section is located near close to the top end at 1400 mm from the bottom of the heated section. For the CFD analyses 10 tests in the pressure region of 5 to 15 MPa, the mass flux range of kg m -2 h -1 heating powers of kw and inlet subcooling of about 15 to 50 K were selected (see Table 7). The S1 subchannel consists of a typical central subchannel of a fuel assembly where all four adjacent walls of heater rods are homogeneously heated by constant power over the total length of the heated part of the test section. Due to the 90 symmetry, only 1/4th of the geometry will be simulated in the CFD simulations. 20

21 The simulations are run unsteady (with adaptive time-stepping) till the flow properties become quasi-constant. Fig. 25 shows the evolution of the vapour production over time, till steady state is reached. The production of vapour is generated towards the end of the heated section. The maximum production can be seen close to the exit. Due to the high speed of the flow through the channel, the vapour produced does not drift towards the axis of symmetry. Figure 25: Evolution of the void fraction for test case (Scale 1:20 lengthwise) It is vital to know the minimum grid resolution to confidently perform accurate simulations. Table 8 below shows the cell sizes used for running the test case in order to know the grid resolution needed for grid independence. It also shows the additional computational resources that are required to run the test case at higher grid resolution. The wall clock time going from a cell-size 5.31 mm to mm goes up 12 times with the number of processors going up to 128 from 1. Table 8: Computational Setup for the grid independence Fig. 26 shows the average void fraction taken at a location close to the exit. It is seen that the void fraction increases with better grid resolution. Between grid resolution of mm and the mm, the average void fraction is nearly constant. In the interest of balancing the computational resources and accuracy, a grid resolution of mm is acceptable. Figure 27 shows the steady state void fraction distribution close to the exit. For four different test cases listed in Table 7. It can be seen that the larger quantities of vapour are produced when the inlet temperature is higher and when the fluid velocity is lower. 21

22 Figure 36: Average Void Fraction with increasing grid resolution. Figure 27: Steady State Void Fraction Distribution for test cases , , and Fig. 28 shows the cross-sectional averaged void fraction distribution for the six test cases. The results from TransAT are compared to the experimental results and CFX (Frank et al, 2011 and Krepper & Rzehak, 2013). TransAT show good agreement with the experiments and performs better than CFX in four of the six test cases. 22

23 Figure 28: Steady State Void Fraction Distribution for four test cases (1.2211, , and ) 6. CONCLUSIONS This note describes the way computational thermal-hydraulics is migrating to more sophisticated meshing techniques for problems involving complex geometries as well as more complex physics. The proposed techniques for complex geometries, called IST/BMR, helps describe the wall-surface of any component simply using CAD-based information. The CAD file is immersed in a Cartesian grid. The method can be successfully combined to generate realistic transient simulations of turbulent flows in reasonable computing times, since it reduce the grid size and thus the simulation time. Further, the BMR technique helps to better solve the boundary layer zone along with the IST technique. In BMR, more refined sub-blocks are automatically generated around solid surfaces. An unlimited number of subblocks of various refinements can be generated, leading to a saving of up to 75% of cells in 3D. The advanced turbulence models involved in solving the complicated problems include LES, Steady and Unsteady RANS. The methods for capturing heat transfer, including phase change go from Level-Set to Ensemble-Averaged Model depending on the scale of the problem. Plans are afoot at ASCOMP to create a hybrid approach that combines the level of detail of the Level-Set Method and the large-scale applicability of the Ensemble-Averaged Method. In conclusion, through several examples, the ability of TransAT to simulate different aspects of industrial thermal-hydraulics is demonstrated. With a combination of advanced physical models, numerical algorithms and computational resources, ASCOMP can tackle the most complex problems within a reasonable time-frame. References G. G. Bartolomei, V. G. Brantov, Y. S. Molochnikov, Y. V. Kharitonov, V. A. Solodkii,,G. N. Batashova, & V. N. Mikhailov, An experimental investigation of true volumetric vapor content with subcooled boiling in tubes, Thermal Engineering, 29(3), (1982). D. Bestion, D. Lucas, M. Boucker, H. Anglart, I. Tiselj, Y. Bartosiewicz, "Some lessons learned from the use of Two-Phase CFD for Nuclear Reactor Thermalhydraulics", N13-P1139, Proc. of NURETH-13. Kanazawa, Japan, September 27-October 2 (2009). 23

24 D. Caviezel, M. Labois, C. Narayanan and D. Lakehal,, Highly resolved multiphase flown topology in vertical pipes and risers, International Conference on Multiphase Flow 2013 ICMF2013 (Paper 860), May (2013). J.G.M. Eggels, F. Unger, M. H. Weiss, J. Westerweel, R. J. Adrian, R. Friedrich, and F. T. M. Nieuwstadt. "Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment." Journal of Fluid Mechanics 268, (1994). T. Frank, F. Reiterer and C. Lifante, Investigation of the PWR subchannel void distribution benchmark (OECD/NRC PSBT benchmark) using ANSYS CFX, NURETH-14, paper 85, Toronto, Canada, September (2011). J. Garnier, E. Manon & G. Cubizolles, Local measurement on flow boiling of Refrigerant 12 in a vertical tube, Multiphase Science and Technology, Vol.13, pp.1-58 (2001). W.K. In, and T.-H. Chun, "CFD Analysis of a Nuclear Fuel Bundle Test for Void Distribution Benchmark, N13-P1259", Proc. of NURETH-13, Kanazawa, Japan, Sep. 27-Oct. 2 (2009). H. Incropera & J. DeWitt,. Introduction to Heat Transfer, Wiley & Sons. Third Ed N.I. Kolev, The influence of mutual bubble interaction on the bubble departure diameter, Experimental thermal and fluid science, 8(2), pp (1994). E. Krepper, and R. Rzehak. "CFD for subcooled flow boiling: Simulation of DEBORA experiments", Nuclear Engineering and Design, 241(9), pp (2011). E. Krepper and R. Rzehak, CFD Analysis of a void distribution benchmark of the NUPEC PSBT tests, The 15 th International Topical Meeting on Nuclear Reactor Thermalhydraulics, NURETH-15, paper 336, Pisa, Italy May (2013). N. Kurul, and M. Z. Podowski, Multidimensional Effects in Forced Convection Subcooled Boiling, Proc. of 9th Int. Heat Transfer Conference, Jerusalem, Israel, August (1990). M. Labois & D. Lakehal, Very-Large Eddy Simulation (V-LES) of the flow across a tube bundle, Nuclear Engineering and Design, 241, 6, pp (2011). D. Lakehal, LEIS for the prediction of turbulent multifluid flows applied to thermalhydraulics applications, Nuclear Engineering and Design, 240, 9, pp (2010). J. Lavieville, E. Quemerais, S. Mimouni, M. Boucker, N. Mechitoua: NEPTUNE CFD V1.0 Theory Manual, EDF (2005). T. H. Lee, G. C. Park & D. J. Lee, Local flow characteristics of subcooled boiling flow of water in a vertical annulus. Int. J. Multiphase Flow, Vol.28, p (2002). P. Liovic, D. Lakehal, Interface-turbulence interactions in large-scale bubbling processes, Int. J. Heat & Fluid Flow, 28, , 2007a. P. Liovic, D. Lakehal, Multi-Physics Treatment in the Vicinity of Arbitrarily Deformable Fluid-Fluid Interfaces, J. Comp. Physics, 222, , 2007b. 24

25 S. Lo, Progress in modeling boiling two-phase flows in boiling water reactor fuel assemblies, Proc. of Workshop on Modeling and Measurements of Two-Phase Flows and Heat Transfer in Nuclear Fuel Assemblies, October 10-11, KTH, Stockholm, Sweden (2006). M. Manninen, V. Taivassalo and S. Kallio, On the mixture model for multiphase flow, Espoo, Technical Reseacrh Centre of Finland, VTT Publications, pp (1996). E. Manon, Contribution à l'analyse et à la modélisation locale des écoulements bouillants sous-saturés dans les conditions des réacteurs à eau sous pression, Thèse de Doctorat. Ecole Centrale Paris (2000). NIST Chemistry WebBook, Thermophysical Properties of Dichlorodifluoromethane (R12), A. Rubin, A. Schoedel, and M. Avramova, OECD/NRC Benchmark Based on NUPEC PWR Subchannel and Bundle Tests (PSBT). Volume I: Experimental Database and Final Problem Specifications, NEA/NSC/DOC(2010)1, January A. Sanna, C. Hutter, D.B.R. Kenning, T.G. Karayiannis, K. Sefiane, R.A. Nelson, Nucleate Pool Boiling Investigation on a Silicon Test Section with Micro-Fabricated Cavities, ECI International Conference on Boiling Heat Transfer, Florianópolis, Brazil, 3-7 May (2009). R. Sugrue, T. McKrell and J. Buongiorno, On the effects of orientation angle, subcooling, masflux, heat flux and pressure on bubble growth and detachment in subcooled flow boiling, Advances in Nuclear Energy Disciplines (ANED) Series, MIT-ANED-TR-001 (2012). M. Sussman, P. Smereka & S. Osher, A level set approach for computing solutions to incompressible two-phase flow, Journal of Computational physics, 114(1), (1994). N. Todreas and M. Kazimi, Nuclear Systems I: Thermal Hydraulics Fundamentals, Taylor and Francis Group (1990). J. Y. Tu & G. H. Yeoh, Development of a numerical model for subcooled boiling flow, Third Int. Conf. CFD in the Minerals and Process Industries CSIRO, Melbourne, Australia, December (2003). F. Unger, and R. Friedrich. "Numerical Simulation of Fully Developed Turbulent Pipe Flow." Notes on Numerical Fluid Mechanics 38, (1993). V. Ustinenko, M. Samigulin, A. Ioilev, S. Lo, A. Tentner, A. Lychagin, A. Razin and V. Girin, Y. Vanyukov, "Validation of CFD-BWR, a new two-phase computational fluid dynamics model for boiling water reactor analysis" Nuclear Engineering and Design, 238(3), (2008). L. Vyskocil and J. Macek, Boiling Flow Simulation in NEPTUNE CFD and FLUENT Codes, XCFD4NRS, Grenoble, France, Sep. (2008). W. Yao and C. Morel, Volumetric interfacial area prediction in upward bubbly two-phase flow, Intl. J. Heat Mass Transfer, 47, (2004). G. H. Yeoh & J. Y. Tu, A unified model considering force balances for departing vapour bubbles and population balance in subcooled boiling flow, Nucl. Engineering Design, Vol.235, p (2005). 25

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