ANALYSIS AND APPLICATIONS OF A TWO-FLUID MULTI-FIELD HYDRODYNAMIC MODEL FOR CHURN-TURBULENT FLOWS

Proceedings of the 2013 21st International Conference on Nuclear Engineering ICONE21 July 29 - August 2, 2013, Chengdu, China ICONE21-16297 ANALYSIS AND APPLICATIONS OF A TWO-FLUID MULTI-FIELD HYDRODYNAMIC MODEL FOR CHURN-TURBULENT FLOWS Gustavo Montoya Helmholtz-Zentrum Dresden-Rossendorf P.O. Box 510119 01314 Dresden Germany g.montoya-zabala@hzdr.de Yixiang Liao Helmholtz-Zentrum Dresden-Rossendorf P.O. Box 510119 01314 Dresden Germany Dirk Lucas Helmholtz-Zentrum Dresden-Rossendorf P.O. Box 510119 01314 Dresden Germany Eckhard Krepper Helmholtz-Zentrum Dresden-Rossendorf P.O. Box 510119 01314 Dresden Germany Keywords: CFD modeling, CFD validation, churn-turbulent flow, multiphase flow, two-fluid model ABSTRACT Today Computational Fluid Dynamic (CFD) codes are widely used for industrial applications, mostly in the case of single phase flows in automotive or aircraft engineering, but multiphase flow modeling had gain an increasing importance in the last years. Safety analyses on nuclear power plants require reliable prediction on steam-water flows in case of different accident scenarios. This is particularly true for passive safety systems such as the GEKO component of the KERENA reactor. Here flashing may occur in the riser (Leyer and Wich, 2012). In such case, high gas volume fractions and the churn-turbulent flow regime may ensue. In the past, the codes for the prediction of churn-regime have not shown a very promising behavior. In this paper, a two-fluid multi-field hydrodynamic model has been developed based in the Euler-Euler framework. The main emphasis of this work has been on the modeling and applicability of various interfacial forces between dispersed gaseous phases and the continuous liquid, as well as bubblebubble interactions, and the evolution of different bubble sizes in an adiabatic vertical pipe inside the churn-turbulent flow regime. All the expected mechanistic models that intervene in this flow pattern have been taken into account including drag force, wall force, lift force, turbulent dispersion, and bubble induced turbulence. Bubble breakup and coalescence has been defined (Liao et al., 2011), and in order to design a polydispersed model related to reality, the inhomogeneous MUSIG approach (Krepper et al., 2008) has been used to defined an adequate number of bubble size fractions which are arranged into different groups with their own velocity field. Based on these models, a series of simulations were made on the framework of ANSYS CFX 14.0, and all of the calculations were further validated with experimental data extracted from the TOPFLOW facility at the Helmholtz-Zentrum Dresden- Rossendorf. Different water and gas flow rates were used inside the churn-turbulent flow regime, as well as for the transition from bubbly to churn flow. The calculated cross-section averaged bubble size distributions, gas velocities, and time averaged radial profile for the gas fraction have shown a promising agreement with the experimental data. Nevertheless there are also clear deviations which indicate shortcomings of the present modelling. In order to further improve the modeling of this flow regime, a discussion based on the results will be used to shown a series of limitations of the actual modeling and possible solutions to be implemented in future works. 1. INTRODUCTION The applicability of CFD codes for two-phase flows has always been limited to special cases due to the very complex structure of its interface. Furthermore, the additional increase of computational power will not allow reflecting the details of the interface of gas-liquid with practical relevance. Instead, averaging procedures are commonly used in these cases, which at the same time cause the loss of information on the interfacial structure. In order to apply the wide-spread two-fluid model, closure laws are needed to reflect the interfacial mass, momentum and heat transfer (Lucas et al., 2007). Such closure models strongly depend on the flow pattern. When considering vertical pipe flow, it is known that for low gas volume flow rates, bubbly flow occurs (Qi et al., 2012). With increasing gas volume flow rates more and more large 1 Copyright 2013 by ASME

bubbles are generated by bubble coalescence, which leads to a transition to slug or/and churn-turbulent flow. Further increase will finally results in an annular flow pattern. Considering, for example, a heated tube producing steam by evaporation, such as steam generator tubes, all these flow patterns including transitions between them are expected to occur in the system. Up to now, no CFD simulation of such case is possible. This becomes clear, if the complexity of the flow situations is considered. Even in the case of bubble flow, the momentum exchange between liquid and the bubbles strongly depends on the bubble size. An example of this would be the sign change of the lateral lift force action on a bubble at a critical size, which leads to a de-mixing of small and large bubbles. The purpose of this paper is the development, test, and experimental validation of a multifield model of adiabatic gasliquid flows at high gas volume fractions (churn-turbulent flow regime) for which a multiple-size bubble approach has been implemented by dividing each of the gas structures into an specified number of groups, each of which represents a prescribed range of sizes. The simulations were performed using the computational fluid dynamic code from ANSYS, CFX 14.0. A complete threefield and four-field model, including the continuous liquid field and two to three gas fields representing bubbles of different sizes, were first tested for numerical convergence and then validated against TOPFLOW experimental data (Lucas et al., 2010; Beyer et al., 2008). The simulations were made with the objective of predicting the evolution of bubble concentration from the inlet of the channel to fully-developed conditions eight meters downstream along an adiabatic vertical pipe. 2. NOMENCLATURE Notation C D Drag coefficient. C L Lift coefficient. C cc Interphase drag force coefficient for the FAD turbulence dispersion model. C TT Turbulent dispersion coefficient. C VV Virtual mass coefficient. C W Wall force coefficient. C μ Coefficient for viscocity. d b Bubble diameter. D h,k Maximum horizontal dimension of the bubble. EE k Modified Eötvos number. g Acceleration due to gravity. m k Volumetric mass transfer term into field-k from other fields representing the same phase. i M kk Interfacial momentum transfer per unit time between the fields k and j. p Absolute pressure. ε S c Source term for the turbulent eddy dissipation. r d Drag radius [m]. RR k Reynolds number of the k-phase. S Source term. t Time [s]. v k Phase-k averaged velocity. v m Mass averaged mixture velocity. w rrr Relative velocity. Greek letters α Void fraction. ε Turbulent eddy dissipation term. κ Turbulent kinetic energy. μ Viscocity. ρ k Density of the phase-k. σ tc Turbulent Schmidt number for the continuous phase volume fraction. τ k Total shear stress term. μ τ k Total shear stress term due to viscocity. RR τ k Total shear stress term due to the Reynolds number. ω Turbulent frequency term. Superscripts i Interfacial. D Drag. NN Non-drag. VV Virtual mass. TT Turbulent dispersion. L Lift. W Wall. Subscripts c Continuous phase. d Dispersed phase. j Index. k k-phase. 3. COMPUTATIONAL FLUID DYNAMICS (CFD) MODEL FORMULATION FOR CHURN-TURBULENT FLOWS A three to four-field multiphase CFD modeling was created to simulate two-phase churn-turbulent flow regime in a vertical pipe. Such a multifield modeling concept of multiphase flows is based on ensemble averaging the respective governing equations for each component fluid. When using such modeling along adequate closure laws, this approach should be capable of representing flow regimes from bubbly through churn-turbulent to annular flow. With the present available CFD-models, it is not possible to describe transitions between flow regimes. In order to model the adiabatic flow, the resultant conservation equations shown in (1) and (2) are commonly used, representing the mass and momentum conservation equations respectively. (α k ρ k ) d + (ρ k α k v k ) = m k (1) 2 Copyright 2013 by ASME

(α k ρ k v k ) + (ρ t k α k v k v k ) = α k p k + α k τ k + ρ k α k g i + M kk j i + m m,k v m m (2) The drag force is known for playing a major role in the axial direction (Drew, 1992). The drag contribution model use in this research work is given as M D d,k ρ c = 3 α 4 d,k C d D,k v c v d,k v c v d,k (5) b Where m k = m m m,k In the aforementioned equations, α k represents the volume fraction of the field-k, while m m,k is the volumetric mass transfer term from other fields which represents the same phase into field-k. The term τ k = τ μ k + τ Rr k = μ k ( v k + v T k ) 2 μ 3 k v k I is the total shear stress term. i The variable M kk represents the interfacial momentum transfer per unit time between two different fields. 3.1 Description of the Mechanistic Models for Interfacial Forces One of the most important factors for the correct representation of the hydrodynamics on multiphase flows is the adequate designation of mechanistic closure laws which allow the modeling of the principle mass and momentum interactions at the fluid interfaces. Due to the averaging of the conservation equations, some information is lost, but has to be reintroduced by the use of these closure relations. The closure laws objective is to account for the mass and momentum transfer between the different fields and phases while providing the functional form expected for the interfacial forces. Still, the presented models are limited by the need of local condition dependent coefficients derived from the fact that the closure laws have been developed for ideal bubbly flow and are now being applied to churn-turbulent flow conditions. The system is assumed to be under adiabatic conditions which translate into the consideration of momentum exchange only at the bubble interface. The different forces that interact at the interface of the flow can be divided into drag and non-drag components with their respective mechanistic models. M k i = M k D + M k NN (3) The interfacial non-drag forces include the lift force, the wall force, the turbulent dispersion force, and the virtual mass force. For reasons that will be explained later in this chapter, the virtual mass force was not taken into account for the present model. Other contributions such as the Basset force may be presented but neglected due to its small effect (Guillen et al, 2009). The total force acting at the interface of the flow can be expressed as the superposition of several component forces. M k i = M k D + M k VV + M k TT + M k L + M k W (4) For the drag coefficient calculation, the expression proposed by Ishii and Zuber (1979) has been used. The next equations represent the correlations for the drag coefficient for spherical cap, ellipse, and distorted bubbles respectively. C D,k (ccc) = 8 3 (1 α k) 2 C D,k (eeeeeee) = 2 3 EE1 2 (6) C D,k (ddddddddd) = min (C D,k (eeeeeee), C D,k (ccc) ) It is important to note that other researchers have reported some significant overestimation of this drag coefficient so that one has to artificially increase the bubble size for the simulation to match the observed flow data when applied to churnturbulent flow conditions (Chen et al., 1995; Tsuchiya et al., 1997). The non-drag interfacial forces are dominant and control the gas profile in the radial direction. The turbulent volume fraction dispersion force is included with the objective of take into account the increased in mixing due to turbulence in the multiphase flow. The turbulent dispersion force transport the gaseous phase in a direction opposing the void fraction gradient. The model that was used in this research is the one known as Favre average drag model (FAD) proposed by Burns (2004). M c TT = M c TT = C TT C cc v tc α d σ tc α d α c α c (7) In the prior equation, the C cc represents the interface drag force coefficient. Therefore, this model depends on details of the drag force correlation that is being used. The term σ tt refers to the turbulent Schmidt number for the continuous phase volume fraction, which is commonly taken to be 0.9 (CFX- Theory User Manual, ANSYS V14.0). The coefficient for turbulent dispersion (C TT ) is commonly take as. In order to account for the momentum exchange due to lift between the continuous and dispersed gaseous phases, the interfacial lift force closure law is used. L M d,k = C L ρ c α d,k (v d,k v c ) ( v c ) (8) The lift coefficient (C L ) is calculated as proposed by Tomiyama et al. (2002). 3 Copyright 2013 by ASME

C L,k = min 0.288 ttth(0.121rr k ), f(ee k ) fff EE k < 4 C L,k = f(ee k ) fff EE k < 4 (9) C L,k = 0.27 fff EE k > 10 In this case, f(ee k ) is defined as shown in equation (10). The critical bubble diameter (Lucas et al., 2006) at which the lift force change sign can be found by solving the roots of this correlation which gives a value of 5.8 mm under atmospheric pressure and room temperature for air bubbles in water (Tomiyama, 1998). f(ee k ) = 0105EE k 3 159EE k 2 204EE k + 0.474 (10) The modified Eötvös number or Eo k is calculated as EE k = g(ρ c ρ d )D h,k 2 σ (11) From an empirical correlation by Wellek et al. (1966) for aspect ratio of an elliptical shape bubble, the maximum horizontal dimension of the bubble, D h,k can be calculated as 3 0.757 D h,k = D k 1 + 0.163EE k (12) In order to account for the hydrodynamic force produce on a bubble which moves in close proximity to a wall, the interfacial wall force is used. The model chose for this force is the one proposed by Tomiyama (1998). M W d d,k = C b α 1 W 2 y 2 ρ cw 2 rrr n r (13) The wall coefficient (C W ) used in this investigation was the one proposed by Hosokawa et al. (2002), who studied the influence of the Morton number, and proposed a correlation which is valid for both high and low Morton numbers provided that the bubble does not collide with the wall (Rzehak et al., 2012). 7 C W = max RR 1.9, 217EE k (14) k The effect of the wall is generally observed as a sharp spike in the bubble void fraction near the wall, that affects the small bubbles and in a weaker manner also the large bubbles. Another of the interfacial non-drag forces named in equation (4) is the virtual mass or added mass force, which is in charge of accelerating the flow around a bubble as it moves through the liquid. As it has been said prior in this section of the present work, this force has been neglected. The reason for doing this is due to that in churn-turbulent flow regime, one of the distinguished characteristics of the flow is the existence of large-fast rising bubbles. These large bubbles do not have a close wake and so the concept of added mass is not applicable. On the other hand, the small bubbles do have a close wake, but in this regime they suffer strong recirculation, moving downwards near the wall region. For this reason, the inclusion of the added mass contributions to the small bubbles would lead to severe convergence difficulties (Krishna et al., 2001). Furthermore, it has been reported (Guillen et al., 2009) that for churn-turbulent regime this force can be neglected since its effect is very small, and does not affect the overall gas profile. For the simulations presented in this work, it has been assumed that between seventeen to nineteen groups of bubbles of different diameters enter the flow channel. These bubbles will eventually start to coalesce forming a large spectrum of new and larger than the original bubbles. The opposite process will also occur making the large bubbles breakup into smaller ones. A mechanistic and accurate mass transfer model, which should be also computationally effective, is needed in order to be used for modeling the interactions between the different sizes of bubbles (Kumbaro and Podowski, 2006; Monahan et al., 2005). Liao et al. (2011) proposed an approach for bubble breakup and coalescence for the inhomogeneous multiple bubble size group (MUSIG) model. Their main objective was to consider a major number of important mechanisms presented in bubble breakup and coalescence in turbulent gas-liquid mixtures. The interactions that were considered for the coalescence mechanism are coalescence due to turbulence, laminar shear, wake-entrainment, and eddy capture. For bubble breakup they consider the effect due to turbulent fluctuation, laminar shear, and interfacial slip velocity. This approach was implemented in the framework of ANSYS CFX via user fortran routines, and applied to the case of turbulent air-water mixtures in a large vertical pipe in order to be validated for bubbly flow conditions in the aforementioned paper. The implementation used in the actual research work is similar to the one presented there with only slight changes in the calculation of the wake entrainment and turbulence contributions for the coalescence model. The turbulence approach used for the liquid phase is the k- ω based SST model, which accounts for the transport of the turbulent shear stress and produces highly accurate predictions of the onset and the amount of flow separation under adverse pressure gradients. This model behaves better than the baseline (BSL) approach, which even by combining the advantages of the Wilcox and the k-ε models, fails to properly predict the onset and the amount of flow separation from smooth surfaces (CFX-Theory User Manual, ANSYS V.14.0). In general, the k- ω model counts with various advantages over the k-ε approach, such as the treatment when in low Reynolds number close to the wall. This model does not need the complex non-linear damping functions required for the k-ε, and for that matter can be considered as more accurate and robust. Finally, the bubble induced turbulence effect was taken into account by the implementation of the Rzehak and Krepper (2012) approach, which is based in a two equation turbulence model with additional source term description for the particle 4 Copyright 2013 by ASME

induced turbulence. The source term describing the bubble effects for the k-equation is shown in the next correlation, and it is formulated as an assumption that all energy lost by the bubble due to drag is converted to turbulent kinetic energy. S c k = F c D. v c v c (15) The source term for the ω-equation is formulated as S c ω = 1 C μ k c S c ε ω c k c S c k (16) In the last equation, C μ has a standard value of 9. This model has been compared with others approaches, such as Sato enhanced turbulence, showing a better prediction on the actual model. 3.2 Description of the Inhomogeneous Multiple Size Group model (MUSIG) Krepper et al. (2005) proposed an association of different dispersed phases and the algebraic multiple size group model in order to combine both, the adequate number of bubble size classes for the simulation of coalescence and breakup and a limited number of dispersed gaseous phases, with the purpose of limiting the computational effort. The gaseous dispersed phase is divided into a number of N velocity groups (or phases), where each velocity group is characterized by its own velocity field. Then, the overall bubble size distribution is further represented by dividing the bubble diameter range within each of the velocity groups j into a number, M j (j = 1 N), bubble sub-size fractions (see Figure 1). The population balance model considers bubble coalescence and breakup that are applied to the sub-size groups, which means that the mass exchange between the sub-size groups can exceed the size ranges assigned to the velocity clusters (Krepper et al., 2009). Figure 1: Improvement of the polydispersed approach: the size fractions M j are assigned to the velocity field V j (Krepper et al., 2008). In order to control the lower and upper boundaries of the intervals for the bubble size fractions, equal distribution of bubble diameter, equal bubble mass, or user definition of the bubble diameter ranges for each distinct bubble diameter fraction could be used. The subdivision should be based on the physics of bubble motion for gas structures of different sizes, for example, dissimilar behavior of distinctively sized bubbles with respect to lift force or turbulent dispersion. Extensive validation made by Krepper et al. (2007 & 2008), have shown that in most cases N = 2 or 3 velocity groups should be sufficient in order to capture the main phenomena, at least in bubbly regimes. 4. DESCRIPTION OF THE EXPERIMENTAL FACILITY The simulations presented in this research work have been validated using an experimental database for air/water twophase flows in vertical stainless steel pipes with nominal diameter of 50 mm and 200 mm, that has been extracted from the thermal-dynamic test facility TOPFLOW at the Helmholtz- Zentrum Dresden-Rossendorf (see figure 2). This database provides information about the evolution of two-phase flow along the pipe height. In order to achieve this, several measurements with varying distances between the gas injection and the measurement plane were made for different combination of gas and water flow rates with superficial gas velocities (j G ) varying from 025 to 18.97 m/s, and liquid superficial velocities (j L ) from 405 to 4.047 m/s. Desalinated water was used in the experiments. The pressure at the gas injection is kept constant at 0.25 MPa. The advantage of such boundary condition lies in that the measure data represents the evolution along the pipe as if the gas injection was in a fixed position and the measurement plane varies. The temperature in the system was also kept constant at 30 C. The test section DN200 is equipped with six gas inlet locations which allowed the injection of air or steam via orifices in the pipe wall. To have such injection via wall orifices allow the two-phase flow to rise smoothly to the measurement plane without having any influence from the feeder within the tube at any other location along the flow (Beyer et al., 2008). The liquid phase was supplied from the bottom of the test section. The measurement plane is kept constant at the top of the system, and consists in two wire-mesh sensors. The lower sensor is used for obtaining data on the gas volume fraction profiles and bubble size distributions, while the second one is to determine gas velocities by cross-correlation of both sensors. The results of these experiments are the time averaged radial profiles of the gas fraction, the gas velocity, the time and cross-section averaged bubble sized distributions, and the gas fraction data regarding the resolved bubble sized and spatial distribution. Furthermore, there is also an extensive analysis of the encountered flow patterns and a study of the effect of the orifice s diameter in the gas injection (Beyer et al., 2008). In the present studies, the 1 mm orifices for the injection of the gas were used. As expected from the literature (Ohnuki et al., 2000; Prasser et al., 2007), no slug pattern in the DN200 pipe was observed. It was reported a criterion for the analyzed of the observed flow pattern in the experiments based on the 5 Copyright 2013 by ASME

maximum observable diameter, and the visualizing of the void fraction. For bubbly flow this diameter must be less than 50 mm and present a mono-modal bubble sized distribution, while in the churn-turbulent flow there should be a bimodal bubble sized distribution with bubbles of diameter similar to those encountered in the bubbly flow and also bigger gas structures of diameter less than 400 mm. Figure 2: Vertical test section of the TOPFLOW facility with variable gas injection system. 5. COMPUTATIONAL GRID AND BOUNDARY CONDITIONS gas phase have been taken from the experimental data given by TOPFLOW at L/D = 1.1, including gas velocity, mass flow rate and size fractions. In principle, the TOPFLOW data regarding the gas phase was arrange into two velocity groups. The first velocity group contains six bubble size fractions up to 5.8 mm, while the second group is organized into twelve to fourteen bubble size fractions larger than the limit size of the first velocity group. The defined number of size fractions is dependent of the test case. This limitation in the size in order to establish the difference between one gas field and the other is given by the change on the sign of the Tomiyama lift force coefficient. A logarithmic distribution is used for the calculation of the different size groups. The smallest size bubble that can be measured by the wire mesh sensor of the TOPFLOW facility is about 2 mm. Some first calculations will be given when considering an extra field for the separation of very large cap bubbles. In this case, a third velocity group is defined based on the maximum cap bubble limit diameter correlation proposed by Ishii and Zuber (1979). This diameter was calculated to be around 10.8 mm, reducing the second gas field to mere three gas fractions, and leaving the third gas field with eleven size fractions. A more in-depth explanation about the reason for these considerations will be given in the results and discussion section of this paper. The simulations are based to replicate the experimental conditions established in TOPFLOW air-water flow in a vertical test section experiments. An axisymmetric 40 x 800 grid with refined cell size of mm near the wall, and mm near the inlet, were used to represent the 9765m x 8m system. There are 40 nodes along the radial direction and 800 axial nodes. Taking advantage of the symmetry, only a segment of the pipe was modeled, establishing a so-called 2D axisymmetric approximation with its respective symmetry planes (see figure 3). Three cases from the TOPFLOW experimental studies were taken for the validation of the presented model as it can be seen in table 1. Cases 127 and 129 are both under churnturbulent flow regime conditions, while case 118 is considered to be in transition from bubbly to churn-turbulent flow. Table 1: Initial conditions used in the simulations Run number Superficial liquid velocity (m/s) Superficial gas velocity (m/s) 118 17 0.219 127 0.405 0.342 129 17 0.342 The data corresponding to the inlet conditions at the continuous phase in the multiphase modeling (turbulent kinetic energy, and turbulent dissipation) were taken from fully developed single phase simulations made on the same computational grid, while the velocity profile is calculated from the TOPFLOW experiments. The boundary conditions for the Figure 3: 3D pipe geometry, 2D axisymmetric approximation, and 2D axisymmetric mesh with unequal node distribution (segmented in the axial direction). At the wall boundary, a no slip condition was used. A symmetry boundary condition was established along the pipe 6 Copyright 2013 by ASME

centerline. The meshing software utilized was ANSYS ICEM CFD. The mesh unequal distribution, with a finer spacing at the inlet and wall of the pipe was established with the intention of capturing the developing flow at the inlet as well as the effect of high gradients of velocity and bubble concentration near the wall of the tube. 5. RESULTS AND DISCUSSION Extensive testing has been performed on the proposed modeling approach using the experimental conditions corresponding to various data series from TOPFLOW experiments with the objective of validating a number of models previously proposed for bubbly flows, and now implemented on churn-turbulent flow regime. The radial concentrations of the different defined gas fields, as well as the gas and liquid velocity magnitude profiles, can be seen in figure 4 to 9 for the complete channel. In order to plot the whole channel, an unequal ratio height to length has been used in the presented images. The left side in each of the domains represents the wall boundary. For all three cases, it can be seen that the small bubbles field or gas 1, remains near the wall along the channel, while the largest bubbles field or gas 2, are distributed in a way in which the maximum value of volumetric concentration is higher at the center of the pipe. It can also be observed in the images how the highest velocity values appear at the center of the pipe for both, liquid and gas phases. The experiment 127, which presents a lower superficial liquid velocity, showed a better distribution for the second gas field across the whole domain. Figure 5: Distributions of velocity for each dispersed and continuous field in experiment 118. Figure 6: Distributions of void fraction for each dispersed field in experiment 127. Figure 4: Distributions of void fraction for each dispersed field in experiment 118. Figure 7: Distributions of velocity for each dispersed and continuous field in experiment 127. 7 Copyright 2013 by ASME

Figure 8: Distributions of void fraction for each dispersed field in experiment 129. the TOPFLOW facility experiments are only accurate for sizes larger than 2 mm (Prasser et al., 2007). When the superficial gas velocity is increased in experiment 129 (see figure 12), the behavior of the bubble size distribution remains similar as in 118. There is only a slight increment of the probability of appearance of larger bubbles, which slightly decrease the overall appearance of the smaller ones. Still, the underprediction observed for the smaller bubbles distribution peak is highly reduced as to the observed one in the experiment 118. Once the superficial liquid velocity decreased in experiment 127 as in comparison with 129 (see figure 11), there is the appearance of even larger bubbles in the experimental data. In turn, an overprediction of smaller bubble sizes close to both the inlet boundary (L/D = 1.7) and the outlet (L/D = 39.9) is observable on these case, in contrast to the typical underprediction found in the prior two simulations. This last deviation results from the effect of reducing the liquid superficial velocity to less than half, which in turn also increase the turbulence parameters and for that matter increase the breakup on the whole domain. Bubble Size Distribution (% / mm) Figure 9: Distributions of velocity for each dispersed and continuous field in experiment 129. A quantitative analysis of experiment 118 through the bubble size distribution study (see figure 10) showed an overall good prediction of the experimental trend with a constant underprediction of bubbles with smaller sizes, which is followed by an overprediction of bubbles ranging from about 10 to 35 mm. This last deviation is more visible close to the inlet boundary (L/D = 1.7), and gradually decreases until the highest measurement level (L/D = 39.9). Bubbles which sizes are larger than 40 mm are constantly underpredicted for all measurement heights. The behavior observed for the values smaller than 35 mm can be explained in part due to too high coalescence at the beginning of the pipe, which in turn creates an underprediction of the smaller bubbles. This could be improved by diminishing the coefficient for wake entrainment in the coalescence model. It can also be observed that for the bubble size distribution, the smallest bubble size in the simulations differs from the experiments, but there is no possibility of real comparison since 0 20 40 60 80 100 120 140 160 Bubble Size (mm) Figure 10: Validation of bubble size distribution against the experiment 118. Bubble Size Distribution (% / mm) 3.0 2.5 0 30 60 90 120 150 180 210 240 270 300 Bubble Size (mm) Figure 11: Validation of bubble size distribution against the experiment 127. 8 Copyright 2013 by ASME

Bubble Size Distribution (% / mm) 0 20 40 60 80 100 120 140 160 180 200 Bubble Size (mm) Figure 12: Validation of bubble size distribution against the experiment 129. In terms of the total radial void fraction, there is a very good agreement between the experiment 127 and the corresponding simulation (see figure 14). Once the liquid superficial velocity is increase in the experiment 129, a good fit with the simulations can be found for the lower levels (L/D = 1.7), but a peak appears between the wall and the center of the pipe for the next shown higher measurement plane (see figure 15). For posterior higher measurement positions these deviation disappear obtaining a similar trend as in experiment 127. While maintaining the same liquid superficial velocity, and decreasing the gas velocity, an analogous behavior of the total radial void fraction is encountered (see figure 13). Total Void Fraction ( ) 0.9 0.8 0.7 0.6 0.4 0.3 0.2 0.1 0 2 4 6 8 0.10 Figure 13: Validation of the radial total void fraction against the experiment 118. In principle, it appears as if this deviation at L/D = 7.9 could be cause by a too large lift force in comparison with the turbulent dispersion. Furthermore, parametric sensitive studies made by Tselishcheva et al. (2010) have shown that both a negative lift coefficient and a too low drag force coefficient could produce similar behaviors in the total void fraction as the one observed in the highest level of the studied system (L/D = 39.9). As it was said prior to this section, the correlation proposed by Ishii and Zuber (1979) is known for overpredict the drag coefficient at churn-conditions. Total Void Fraction ( ) 0.9 0.8 0.7 0.6 0.4 0.3 0.2 0.1 0 2 4 6 8 0.10 Figure 14: Validation of the radial total void fraction against the experiment 127. Total Void Fraction ( ) 0.9 0.8 0.7 0.6 0.4 0.3 0.2 0.1 0 2 4 6 8 0.10 Figure 15: Validation of the radial total void fraction against the experiment 129. A study of the averaged gas velocities for the three experimental cases was also prepared. The observed behavior of the trend in the gas velocities for the three cases is analogous to the overall radial void fraction in terms of the expected deviations. For experiment 127, the velocities for all the evolution of the flow through the pipe qualitatively fit the experimental data very well (see figure 17). For both, experiment 118 (see figure 16) and 129 (see figure 18), the simulation fit almost perfectly the experiments for the height which is closer to the inlet boundary as expected, but for the measurement level L/D = 7.9, the velocity presents a similar peak as the one seem in figure 13 and 15, which attenuates eventually before achieving higher positions (L/D = 39.9). From the bubble size distribution charts, it is already possible to observed that many of the deviations appears to have their base in the misconception than the largest bubbles behave in the same way as it is expected from bubbly flow conditions. For that matter, an approach has been model in 9 Copyright 2013 by ASME

which a third dispersed velocity field has been used for further subdivision of the overall gas phase. Average Gas Velocity (m / s) 4.0 3.5 3.0 2.5 0 2 4 6 8 0.10 Figure 16: Validation of the gas averaged velocity against the experiment 118. Average Gas Velocity (m / s) 2.5 0 2 4 6 8 0.10 Figure 17: Validation of the gas averaged velocity against the experiment 127. In the first set of simulations, the new gas field shares the same closure models as the other gas phases, while in the other shown approach, the modeling has been made by neglecting the lift force in the newly added dispersed field. In this research paper, preliminary results are shown to validate this approach by comparison against the prior mentioned experiment 129. It can be observed that the addition of the third gas phase greatly improves the bubble size distribution in terms of the underprediction encountered with the two-gas field approach, especially for the higher positions of the measurement planes (see figure 19). On the other hand, there was not a visible effect on the simulation by the elimination of the lift force on the third gas phase. Bubble Size Distribution (% / mm) 0 20 40 60 80 100 120 140 160 180 200 Bubble Size (mm) Figure 19: Validation of bubble size distribution against the experiment 129 using a three gas field model. In terms of the radial total void fraction, it can be observed that the peak encountered at L/D = 7.9 in figure 15, is no longer visible with the three-field simulation (see figure 20). This comes at the cost of the accuracy for the radial total void fraction at the lower measurement levels. The lack of lift force in this case, only shifted slightly the total void fraction to lower values for the higher measurement planes. Average Gas Velocity (m / s) 4.0 3.5 3.0 2.5 0 2 4 6 8 0.10 Figure 18: Validation of the gas averaged velocity against the experiment 129. Total Void Fraction ( ) 0.9 0.8 0.7 0.6 0.4 0.3 0.2 0.1 0 2 4 6 8 0.10 Figure 20: Validation of the radial total void fraction against the experiment 129 using a three gas field model. 10 Copyright 2013 by ASME

Finally, the addition of a third gas phase in terms of gas averaged velocity also in this case makes the peak observable in the two-field approach not visible anymore (see figure 21). A constant overprediction of averaged gas velocities for the values at the center of the pipe, and a constant underprediction close to the wall can be seen. The elimination of the lift force for the third gas phase did not produce an important effect in terms of the averaged gas velocity. Average Gas Velocity (m / s) 4.0 3.5 3.0 2.5 0 2 4 6 8 0.10 Figure 21: Validation of the gas averaged velocity against the experiment 129 using a three gas field model. These deviations obtained for the higher measurement levels could be the result of a too low drag force coefficient. As prior stated, it has been shown that both the underprediction of the drag coefficient and a negative lift force could create such trends in the prediction of total void fraction and gas velocity. Since the effect of neglecting the lift force appear to have little effect in the third gas-field simulations (see figure 22), studies have to be made to consider the effect of other forces that could be producing the higher concentration of gas-3 at the center of the pipe, independently of the lift force, such as the wall lubrication force. Further studies should be made on the subject. Total Void Fraction ( ) 0.7 0.6 0.4 0.3 0.2 0.1 Gas 1 Gas 2 Gas 3 Total Gas Gas 1 w/o Lift Force Gas 2 w/o Lift Force Gas 3 w/o Lift Force Total Gas w/o Lift Force 0 2 4 6 8 0.10 Figure 22: Comparison of the total void fraction for the dispersed phases in the 3-field model with and without lift force at L/D = 39.9. There are other factors which will be studied in future research works such as the effect of the turbulence modeling. In most of the simulations and modeling approaches defined in the last few years for churn-turbulent flow, including this work, the Reynolds-averaged Navier-Stokes (RANS) turbulence approach is the easiest and favorite choice in terms of description for the turbulence of the continuous phase. It is known (Bestion, 2011) that the RANS approach is not suitable for the overall prediction of the churn-regime due to its incapacity for notfiltering of the large scales produce by the largest bubbles (third gas field), not being able to predict the intermittency produce by the passage of these bubbles. Other factor affecting the third gas field is the effect produced by the confinement of the pipe in the simulation, which has not been taking into account before. A possible future modification in the drag force equation could account for the addition of this effect in the simulations. A different possible approach would be the complete resolution of the interface on the third gas field. A suitable technique for such modeling would be the Generalized Two Phase flow approach or GENTOP (Hänsch et al. 2012) currently being developed at the HZDR. While this is a very promising method, it would also bring many challenges and higher computational time simulations due to that it will require three dimensional transient calculations. 6. CONCLUSIONS The current presented work has shown the achievement of a series of important objectives in the studies of the churnturbulent flow as a significant phenomenon which occur in flashing and GEKO risers for safety research in the nuclear industry. It has been shown that while results using a bimodal gas distribution and bubbly flow closure laws produce promising and relatively good results, they cannot yet predict the expected physics at this flow regime. The modeling flow at churnturbulent flow conditions should be based on at least three gas field approach or trimodal distribution based on small spherical bubbles, larger spherical bubbles, and large deformable cap bubbles. In general, while the acknowledgement and consideration of the existence of a third gas field in comparison of the traditionally expected bimodal distribution in the churnturbulent flow regime (Krishna et al. 2001), predicted the physics behind the experiments in churn-conditions in a much more realistic way than before, there is still not achievement of an optimal modeling approach. This occurs because the expected behavior of the third gas phase should differ of the other two dispersed fields. It is expected that further studies and modifications on the specific closure and turbulence models in order to acknowledge the actual physics behind the churnregime, which are in some specific ways very different to those encountered under bubbly flow conditions, will improve in a greatly manner the current modeling at these flow conditions. 11 Copyright 2013 by ASME

Future works will include further studies on the closure laws and its effect on the third gas field, as well as tests on the turbulence modeling for these largest and deformable dispersed structures (churn-turbulent bubbles). The inclusion and study of the confinement effect of the pipe on the third gas field by implementation on the drag force equation will be also a next step on the future simulations. ACKNOWLEDGMENTS This work is carried out in the frame of a current research project funded by the energy company E.ON Kernkraft GmbH. REFERENCES 1. Bestion, D. Applicability of two-phase CFD to nuclear reactor thermalhydraulics and elaboration of Best Practice Guidelines. Nucl. Eng. Des, In Press (2011). 2. Beyer, M.; Lucas, D.; Kussin, J.; Schütz, P. Air-water experiments in a vertical DN200-pipe. FZD-505 TOPFLOW Wissenschaftlich-Technische Berichte (2008). 3. Burns, A.; Frank, T.; Hamill, I.; Shi, J. 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