This paper deals with the validation of the twophase flow models of the CFD code NEPTUNECCFD using experimental data provided by the OECD BWR BFBT and PSBT Benchmark. Since the twophase models of CFD codes are extensively being improved, the validation is a key step for the acceptability of such codes. The validation work is performed in the frame of the European NURISP Project and it was focused on the steady state and transient void fraction tests. The influence of different NEPTUNECFD model parameters on the void fraction prediction is investigated and discussed in detail. Due to the coupling of heat conduction solver SYRTHES with NEPTUNECFD, the description of the coupled fluid dynamics and heat transfer between the fuel rod and the fluid is improved significantly. The averaged void fraction predicted by NEPTUNECFD for selected PSBT and BFBT tests is in good agreement with the experimental data. Finally, areas for future improvements of the NEPTUNECFD code were identified, too.
The validation of the twophase flow modelling capability of CFD codes, for example, NEPTUNECFD, is mandatory for its application in the design and safety evaluation of energy systems. The goal thereby is to demonstrate that the twophase flow models of CFD codes are able to predict the most relevant flow regimes under pre and postcritical heat flux (CHF) conditions. The focus is on the accurate prediction of the pressure drop, void fraction, critical power, departure from nucleated boiling (DNB), and so forth. The ways how the CFD codes are modelling the heat transfer between a solid and the coolant (wall heat transfer) and the liquidvapour interphase heat transfer (bulk heat transfer) differ from code to code. The validation of the twophase flow heat transfer models of NEPTUNECFD requires the understanding of the implemented mathematicalphysical models in the code as well as their interaction with the heat conduction models of the solids and the fluid dynamics. In the medium term a combined application of CFD and system or subchannel codes will lead to a more realistic prediction of safetyrelevant phenomena in nuclear reactors. The simulations performed during this work are focused on the void fraction prediction in rod bundles of light water reactors (LWR) using the NEPTUNECFD 1.0.8. In this paper, the investigations performed to validate the twophase flow models of NEPTUNECFD under steadystate and transient conditions using the database provided by the PSBT and BFBT tests are presented and discussed. This research code is being developed and tested within the European NURISP and NURESAFE projects. First of all, the main features of NEPTUNECFD are presented in detail. Then, the validation work based on both PSBT and BFBT is discussed in detail. Finally, a summary and the main conclusions are given.
The NEPTUNECFD solver is based on a pressure correction approach to simulate multicomponent multiphase flows by solving a set of three balance equations for each field (fluid and/or gas phase) in a Reynolds Averaged Navier Stokes (RANS) approach. These fields can represent many kinds of multiphase flows; among them also is bubbly flow. The solver is based on a finite volume discretization together with a collocated arrangement for all variables. The twofluid models of the NEPTUNECFD are designed specifically for the simulation of twophase transients in nuclear reactors. The models and closure laws used by NEPTUNECFD [
When an averaging operation is performed, the major part of the local information at the interfaces and the physics governing the different types of exchanges at a microscale are lost. As a consequence a number of closure relations (also called constitutive relations) must be supplied to close the balance equations so that they can be mathematically solved. Three different types of closure relations can be distinguished: interfacial mass and heat transfer terms (i.e., the molecular and turbulent transfer terms) and the wall heat transfer terms. In the next paragraphs, a short description of the interfacial and wall transfer terms important for the description for the boiling phenomena will be presented. Details about the NEPTUNECFD models can be found in the theory and user manual [
If the mechanical terms are neglected in comparison to the thermal terms in the averaged form of the energy jump condition, this condition reduces to
The interfacial transfer of momentum
The interfacial area concentration (IAC) transport equation is given by (
The nucleate boiling term (
a single phase flow convective heat flux
a quenching heat flux
evaporation heat flux
The heat flux density due to quenching is written as
The basic wall heat flux partitioning model assumes that the amount of water on the wall is sufficient to remove heat from the wall to be used for evaporation. Superheating of the vapour that occurs at high void fractions is not modelled. Under these assumptions, the basic heat flux partitioning model cannot be used for CHF conditions. In order to take into account the phenomenon of temperature excursion at DNB conditions, the heat flux partitioning model can be generalized as follows:
The NEPTUNECFD code with the twophase heat transfer models explained in Section
The test bench of the PSBT experiment is shown in Figure
Test conditions for steadystate void measurements.
Run number  Heat flux (W/cm^{2})  T. inlet (K)  Pressure (MPa) 

Mass flow (kg/s) 

1.2211  194.34  568.4  15.01  46.9  0.3248 
1.2223  150.72  592.6  15.01  22.6  0.3248 
1.2237  129.56  602.6  15.03  12.9  0.3248 
1.4325  129.13  526.8  10.03  57.6  0.1487 
1.4326  129.77  541.8  10.01  42.4  0.1487 
1.6222  107.75  477.2  5.0  59.9  0.1487 
(a) Experimental setup of the PSBT benchmark; (b) crosssectional cut illustrating the location of the heat source; and (c) numerical model in NEPTUNECFD showing the velocity field for case 1.2211.
The turbulent transfer term applied is the
The cross section of the subchannel geometry is illustrated in Figure
Cross section of the four proposed space discretization schemes for the domain (M1, M2, M3, and M4).
To catch the physical phenomena near the wall, for example, the void fraction by the numerical codes, a more refined discretization is necessary. Hence, four different spatial resolutions of the subchannel were tested, all of them consist of structured meshes in order to avoid diffusivity problems and to reduce the number of cells; see Figure
Discretization details of the four meshes applied in the study of the PSBT benchmark.
Subchannel 1 (M1)  Subchannel 2 (M2)  Subchannel 3 (M3)  Subchannel 4 (M4)  

Number of cells  182679  147429  112179  77345 
First cell near the wall (mm)  0.1  0.2  0.3  0.4 
Number of cross cells (X direction)  25  21  17  14 
The case PSBT 1.6222 has been simulated using different meshes (M1 and M4). In Figure
Axial void fraction (VF) profile in the near heated wall region for case 1.6222.
Axial water temperature profile in the near heated wall region and in the subchannel center for case 1.6222.
The heat flux partitioning at the wall is commonly divided into 3 fluxes according to Kurul and Podowski [
Water temperature in the near wall region at 1.4 m elevation as function of the mesh size for 0.1 mm bubble diameter.
Local void fraction (VF) at 1.4 m elevation as function of mesh size for 0.1 mm of bubble diameter.
For the comparison of four different meshes, NEPTUNECFD predicts large gradients of void fraction in the near wall region for the refined meshes (M1) and (M2). These void fraction differences affect the calculated average void fraction over the crosssectional area at the measurement position. The water temperature evolution calculated for the different mesh configurations at two axial locations can be observed in Figure
Water temperature at the near wall region and at the centre of the subchannel of the case 1.2211 as function of mesh size.
The liquid temperature profile is the combination of several phenomena. The liquid phase near the wall is heated by the wall heat flux, which is divided into convective, evaporation, and quenching heat flux. Once the bubbles are generated, they migrate and condense within subcooled liquid in the core of the flow and hence heat the liquid. The molecular and turbulent heat fluxes inside the liquid phase also modify the temperature profile.
The results computed by NEPTUNECFD are summarized in Table
Results for the local and averaged VF for the different meshes applied for the simulation of case 1.2211.
Mesh  Nearest heated wall cell VF (%)  Average VF (%) at measured cross section ( 

M1  67  8.1 
M2  57  6.7 
M3  40  4.6 
M4  15  3.1 
The choice of the coarse mesh to perform the rest of the simulations has been made to preserve the numerical stability while solving the heat transfer problem. In addition, the coarse mesh (M4) is producing maximum
In the previous simulations, a constant bubble diameter (0.1 mm) has been applied. Incidence of other bubble diameters or the selection of an interfacial area equation (IAE) for the simulation is discussed in this subchapter. For the mesh M4 and the case 1.2211 previously studied, three different configurations for the IAC are considered. The first is by applying the previous 0.1 mm constant diameter. In the second configuration the diameter is increased to 0.2 mm. The third applies one IEA, described by (
For the three configurations proposed, the water temperature in the near wall region is illustrated in Figure
Water temperature in the near heated wall region at 1.4 m elevation. Comparison for different bubble diameters. Case 1.2211.
Bubble size distribution in case of using the IAE. Case 1.2211.
VF in the near heated wall region at 1.4 m elevation. Comparison for different bubble diameters. Case 1.2211.
Steam velocity in the near heated wall region at 1.4 m elevation. Comparison for different bubbles diameters. Case 1.2211.
In Figure
Axial VF profile at the centre of the subchannel. Comparison for 3 different bubbles diameters. Case 1.2211.
The pressure drop in the channel is calculated also for the different bubble sizes. The simulated results are presented in Figure
Pressure drop calculated for the 3 different bubble diameters. Case 1.2211.
By using an IAE there are more parameters to control. One of the most important measures is to clip the value of the minimum bubble diameter. Very small bubble size can lead to numerical instabilities regarding the nondrag forces applied like the added mass force or the turbulent dispersion force. For the simulations the smallest bubble diameter of 0.01 mm is allowed in the computational domain.
The VF calculated by NEPTUNECFD for the six cases selected from the PSBT database is illustrated in Table
Comparison of predicted and measured void fraction.
Run number  PSBT  NEPTUNECDF  Relative error (%)  ANSYS CFX 12.1 SST  Relative error (%) 

VF (%)  VF (%)  VF (%)  
1.222300  31.100  20.280  −34.790  21.200  31.833 
1.223700  44.000  31.850  −27.610  29.100  33.864 
1.221100  3.800  3.100  −18.420  11.700  −207.895 
1.432600  53.100  58.890  10.900  50.600  4.708 
1.432500  33.500  40.470  20.810  34.300  −2.388 
1.622200  30.600  41.620  36.010  26.600  13.072 
Three experiments are overpredicted (1.2223, 1.2237, and 1.2211) and the other three are underpredicted (1.4326, 1.4325, and 1.6222) by NEPTUNECFD. In Table
The axial VF profile for each case is illustrated in Figure
Axial VF evolution for each case compared against experimental data.
The BFBT void distribution benchmark [
The test section of the experiment is a full sized
(a) Test section with the location of the Xray densitometers and the heated section. (b) Cross section of the tested rod bundle and the selected portion to be modelled. (c) Numerical model of the simulated domain. (d) Water velocities calculated by NEPTUNE_CFD.
To reproduce in the test bench the turbine trip without bypass and the recirculation pump trip, the BFBT database provides the evolution of the water mass flow rate, the system pressure, and the power. This data is used as boundary condition for NEPTUNECFD. In Figures
Test section outlet pressure evolution measured for turbine trip and recirculation pump trip experiment.
Test section mass flow rate evolution measured for turbine trip and recirculation pump trip experiment.
Test bench measured power evolution for turbine trip and recirculation pump trip experiment.
Normalized radial FA power coefficients for turbine trip and recirculation pump trip experiment in the context of the BFBT experiment.
The numerical simulation is performed with the models explained in Section
The time step is adaptive depending on the Courant number. The time step width ranges from 1 to 3 ms. The drag and nondrag forces, lift, added mass, and turbulent dispersion force, are computed for the simulation.
The nodalisation of the PSBT test section was done following the best practice guidelines for the use of CFD codes. The nearest wall heated region cell has a constant width of 0.3 mm. The mesh is composed of 135 axial levels and 12 cross cells in each subchannel. Globally the NEPTUNECFD nodalisation has 211928 cells. The maximum
Taking into account the radial symmetry of the FA only 1/8 of the fluid domain is modelled with two symmetry planes (Figure
(a) NEPTUNECFD model; (b) NEPTUNECFD+SYRTHES model; green ring represents the insulator and the clad according to the real benchmark geometries.
The averaged void fraction for the crosssectional area of the FA is calculated each 0.02 seconds at the three axial levels (
Computed void fraction results corresponding to two configurations are illustrated. The first is by modelling the problem with NEPTUNECFD standing alone and the second configuration takes into account the wall thermal inertia effect by adding the SYRTHES code to NEPTUNECFD.
Figure
(a) Location of the measured axial levels. Local VF distribution calculated by NEPTUNE_CFD at different times for the turbine trip scenario: (b) second 7, (c) second 11.5, (d) second 20, (e) second 30, and (f) second 50.
The comparison between the evolution of the calculated void averaged calculatedby NEPTUNECFD and SYRTHES and the experimental data is shown in Figure
Comparison of the BFBT VF data and its measurement error (±2%) with the VF evolution predicted by NEPTUNE/SYRTHES at three axial levels during the turbine trip experiment.
At this point, it is important to remark that the models implemented regarding interfacial interactions like mass, heat transfer, and momentum are designed for bubbly flow only. The water is set as continuous phase and the vapour is set as the disperse phase; this condition is valid for bubbly flow. When the amount of void in the fluid exceeds 60%, the regime is no longer bubbly flow. Therefore, the results of the second and third elevation cannot be considered reliable and more developments in the modelling are necessary to properly describe the flow at those elevations. The description of different flow regimes in the same domain requires the definition of a change of continuous and dispersed phase at each location. Nevertheless the code is able to trace the tendency of the void generation in line with the experimental data even in those flow regimes.
Figure
Normalized values of power, mass flow, and pressure evolution provided by the turbine trip experimental data together with relative error between VF predicted by NEPTUNECFD/SYRTHES and experimental VF data at axial level
The coupling of NEPTUNECFD with SYRTHES leads to a significant improvement due to the accurate steam temperature calculation. In addition SYRTHES contributes to relax the temperature calculation and the solidliquid interface increasing the time step and accelerating the simulation.
Figure
Saturation, steam, clad, and liquid temperature calculated by NEPTUNECFD/SYRTHES. Comparison against the steam temperature calculated with NEPTUNECFD stand alone.
The temperatures from Figure
Using the experience acquired from the turbine trip simulation, another exercise of the BFBT database is simulated. For this case, only the simulation combining NEPTUNECFD and SYRTHES is performed.
The comparison between the experimental data provided by the BFBT database and the computed void fraction of NEPTUNECFD/SYRTHES is illustrated in Figure
Comparison of the BFBT VF data and its measurement error (±2%) with the VF predicted by NEPTUNE/SYRTHES at three axial levels during the recirculation pump trip experiment.
For this case the prediction fits well with the experimental data during the void increase between seconds 11 and 13. At this time there is no power peak and the void rises due to the decrease of mass flow. At this point the simulation is underestimating the experimental data only at the first axial level. For the lapse of time between seconds 15 and 42, an overprediction occurs for all axial levels. At the last third of the transient when the mass flow increases up to nominal conditions, the void predicted is slightly underestimated for axial levels 1 (
Figure
Local water temperature at 3 different axial levels, (a) 0.67 m, (c) 1.72 m, and (c) 2.7 m. Calculated by NEPTUNECFD/SYRTHES for the recirculation pump trip (second 30).
Local void distribution at 3 different axial levels, (a) 0.67 m, (c) 1.72 m, and (c) 2.7 m. Calculated by NEPTUNECFD/SYRTHES for the recirculation pump trip (second 30).
In Figure
Local steam temperatures evolution at the bulk and near the heated wall calculated by NEPTUNE_CFD/SYRTHES during the recirculation pump trip. Comparison of two different time scales returning to saturation for the steam.
The validation basis of NEPTUNECFD has been extended by using LWRrelevant transient test data obtained in both a PWRspecific (NUPEC PSBT) and a BWRspecific (NUPEC BFBT) test facility. It is the first time that the twophase flow models of NEPTUNECFD have been validated using transient data obtained for tests representing the LWR plant conditions of postulated transients like a turbine trip or a recirculation pump trip. This validation process has clearly shown the status of the twophase flow modelling of NEPTUNECFD. It is possible to summarize the global conclusions about the NEPTUNECFD capabilities, identifying its strengths and weaknesses.
According to the interfacial exchange terms, the main flow regime currently implemented in NEPTUNECFD is the bubbly flow, which is good enough to describe the flow with a certain void concentration (<60%). However, in BWR the amount of void generated is beyond the limits of the bubbly flow, and other flow regimes (slug flow or annular flow) must be taken into account for an accurate description of safetyrelevant phenomena. How to model the transition between flow regimes describing a whole flow map is an open issue for CFD codes.
A study of the sensitivity to the bubble size has been performed applying two constant bubble sizes (0.1 and 0.2 mm) and a variable size with an IAE for the PSBT experiments. The heat and mass exchange is strongly influenced by the IAC. Bubbles may rise close to the heated wall and eventually depart from it and migrate into subcooled liquid where they condense. Smaller diameters produce more IAC and more condensation. Hence, for smaller selected bubble sizes, reduced void fraction will appear in the domain. The smaller bubble size generated by the IAE produces more interfaces, and thus the condensation is stronger and the void predicted is less than the other two bigger bubbles selected (0.1 and 0.2 mm).
By using an IAE it is assumed that there is a single bubble size per cell. If all bubbles have locally the same size, they will condense at the same speed and their diameter will decrease. If a multisize model is applied, the small bubbles will decrease and collapse rapidly leaving the bigger ones, which increase the mean bubble size. Therefore, the assumption of a single bubble size can lead to an underestimation of the bubble mean size in this case, affecting the void generation.
NEPTUNECFD alone cannot solve heat conduction in solid domains. For this reason it is coupled with SYRTHES which is in charge of calculating the temperature in solid domains. The capabilities of the NEPTUNECFD coupled with SYRTHES have been demonstrated by the prediction of thermal inertia at the walls. By applying SYRTHES, the simulations of the turbine trip are in better agreement with experimental data compared with the application of NEPTUNECFD standalone. In addition, this heat conduction solver helps to reasonably control steam and water temperatures in the near wall region by computing a proper heat transfer coefficient at the solid/fluid interface. The use of SYRTHES has a positive contribution to the NEPTUNECFD prediction capabilities. However, it is not parallelized and hence it penalizes the computational time.
Due to the different mesh distribution applied for each code (tetra volumes for SYRTHES and hexa volumes for NEPTUNECFD), a careful mesh design is required to match the nodes at the solid/liquid interface and have a good energy balance at the interface.
The classical 3 fluxes formulation for the wall/fluid heat transfer assumes three fluxes: quenching, convection, and evaporation. If boiling occurs in this region and the amount of liquid decreases, the water enthalpy rises and the temperature can be several degrees above saturation. To avoid this problem, the fourflux model decomposition (see (
The near wall cells size results as an agreement between the thermal and momentum modeling. This agreement consists in solving the heat transfer problem properly without penalizing excessively the
By setting a very refined axial nodalisation (more than 200 axial levels for the presented domains), the code struggles calculating the pressure field. It is recommended to enlarge the cells in the axial direction in the locations where large amounts of steam are generated.
According to the results obtained during the validation process, the subcooled and saturated boiling description can be considered sufficient enough in its range of applicability. Even if further developments are required, NEPTUNECFD has demonstrated to be a valid TH tool for the twophase flow modeling in LWR applications.
Interfacial area concentration (m^{2}/m^{3})
Wall thermal diffusivity (m^{2}/s)
Liquid thermal diffusivity (m^{2}/s)
Thermal capacity of the liquid (J/(mol·K))
Gas heat capacity at constant pressure (J/(mol·K))
Sauter mean bubble diameter (m)
Bubble detachment diameter (m)
Bubble detachment frequency (Hz)
Interfacialaveraged enthalpies (kJ)
Heat transfer coefficient
Jakob number
Thermal conductivity (W/(m·K))
Latent heat of vaporization (kJ/kg)
Interfacial transfer of momentum
Active nucleation sites density
Nusselt number
Liquid Prandtl number
Péclet number
Convective heat flux (W/m^{2})
Evaporation heat flux (W/m^{2})
Quenching heat flux (W/m^{2})
Volumetric heat flux (W/m^{3})
Interfacial heat flux density
Bubble Reynolds number
Stanton number
Temperature of phase
Nondimensional liquid temperature
Quenching time (s)
Wall friction velocity (m/s)
Phase
Walladjacent cell
Void fraction
Mass transfer condition (Kg)
Kinematic viscosity (m^{2}/s)
Time scale returning to saturation (s)
Bubble nucleation source terms
Bubble coalescence source term
Bubble breakup source term
Wall conductivity (W/(m·K))
Phase
Boiling water reactor full bundle test
Boiling water reactor
Commissariat de l’Energie Atomique
Computational fluid dynamics
Critical heat flux
Departure from nucleated boiling
Electricité de France
Interfacial area equation
Interfacial area concentration
Institut de Radioprotection et de Sûreté Nucléaire
The International Association for the Properties of Water and Steam
Karlsruhe Institute of Technology
The Nuclear Power Engineering Corporation
Reynolds Averaged Navier Stokes
Sauter mean bubble diameter
Shear stress turbulence model
Organisation for Economic Cooperation and Development
Pressurized water reactor subchannel and bundle tests
Pressurized water reactor
Void fraction.
The authors hereby declare that no conflict of interests is present between them and the commercial entities mentioned in the context of the paper.
The authors thank the Program “Nuclear Safety Research” of KIT for the financial support of the Research Topic “Multiphysics Methodologies for Reactor Dynamics and Safety” and the EU Project NURISP.