This paper presents the assessment of CATHARE 3 against PWR subchannel and rod bundle tests of the PSBT benchmark. Noticeable measurements were the following: void fraction in single subchannel and rod bundle, multiple liquid temperatures at subchannel exit in rod bundle, and DNB power and location in rod bundle. All these results were obtained both in steady and transient conditions. Void fraction values are satisfactory predicted by CATHARE 3 in single subchannels with the pipe module. More dispersed predictions of void values are obtained in rod bundles with the CATHARE 3 3D module at subchannel scale. Singlephase liquid mixing tests and DNB tests in rod bundle are also analyzed. After calibrating the mixing in liquid single phase with specific tests, DNB tests using void mixing give mitigated results, perhaps linked to inappropriate use of CHF lookup tables in such rod bundles with many spacers.
CATHARE 3 is a new twophase thermalhydraulics system code developed at CEA Grenoble [
Following the BWR Fullsize FineMesh Bundle tests (BFBT) benchmark, the PWR subchannel and bundle tests (PSBT) benchmark [
Single subchannel experiments are simulated by the CATHARE 3 pipe 1D module while rod bundle cases are simulated with the CATHARE 3 3D module meshed at a subchannel scale, that is, one cell per subchannel in a horizontal cross cut. The 3D module for the rod bundle has been coupled with a 1D module in order to improve the inlet flow simulation along the downcomer.
Useful balance equations and closure laws are briefly presented in the following Section
Both 1D and 3D modules of CATHARE 3 solve the same set of balance equations, except that the energy balances are written using enthalpy in the 3D module and internal energy in the pipe module. The closure laws remain identical as far as possible. A firstorder donor cell scheme is used in both modules as far as space discretization is concerned. For time discretization, the pipe module calls a fully implicit scheme, while the 3D module uses a semiimplicit scheme.
Contrary to the preceding BFBT simulations [
For a given generation of steam along a single heated channel, the local void fraction is governed by wall and interfacial friction. In a 3D flow inside a rod bundle, crossflows between adjacent subchannels lead to void dispersion. Also turbulent dispersion or diffusion may affect the temperature map in the single phase region. The void dispersion phenomena can be modelled by a mixing term in the momentum balance equations. The temperature dispersion (caused by nonrandom flow from one subchannel to a neighbour) and diffusion (caused by random fluctuations of flow between adjacent subchannels) are modelled by a single term in the liquid energy balance equation. The velocity diffusion is presently neglected in the momentum equation; its implementation had no effect on results of several tests, either in single phase or two phase flow in bundles.
Consider the following equation:
The mixing term
For a singlephase flow in a tube or a subchannel (far from a spacer grid), the turbulent kinetic energy
At the end, it comes
It is written using internal energy
To summarize, the turbulence is modelled here by two different algebraic terms: one described just above in the energy balance and the
The Departure from Nucleate Boiling appears on a hot wall when the heat flux towards the fluid exceeds the socalled “Critical Heat Flux,” which is assessed in sixequation model of CATHARE 2 and CATHARE 3 using homemade polynomials interpolating CHF lookup tables, given the local values of mass flux, pressure, and steam quality. The tables are based on the 1995 Groeneveld tables [
The PWR Subchannel and Bundle Tests (PSBT) benchmark is proposed by OECD/NRC. Pennsylvania State University (PSU) under the sponsorship of U.S. Nuclear Regulatory Commission (NRC) prepared the specification and organized the benchmark with the Japan Nuclear Energy Safety (JNES) Organization. The Nuclear Power Engineering Corporation (NUPEC) released a database including various single subchannel and fullscale rod bundle tests in boiling conditions, with detailed void distribution and DNB measurements. Both system codes and CFD codes can match their results against the averaged (macroscopic data at subchannel scale) or fine experimental results.
Two phases are proposed:
The first one is devoted to the void distribution and includes four exercises.
Exercise 1—steadystate single subchannel benchmark,
Exercise 2—steadystate bundle benchmark,
Exercise 3—transient bundle benchmark,
Exercise 4—pressure drop benchmark.
The second is devoted to DNB prediction and includes three exercises.
Exercise 1—steadystate fluid temperature benchmark,
Exercise 2—steadystate DNB benchmark,
Exercise 3—transient DNB benchmark.
This benchmark, especially through its accurate measurements, is a very good opportunity to assess the capabilities of system codes such as CATHARE 3 to simulate boiling flows in PWR core geometry.
Four different geometries of single subchannels, for central, side, and corner locations (side and corner are relative to a rod bundle in a square box) have been tested, resulting in void fraction measurements at 1400 mm level inside a 1555 mm long heated subchannel (Figure
Test section for void measurement in a central subchannel.
A set of 39 tests is proposed in the benchmark among a large database of 126 tests. The range of flow pressure is from 50 to 170 Bars and the range of mass flux is 500 to 4200 kg m^{−2} s^{−1}. We calculated the whole database and compared the simulation results versus the measurement data.
Calculations were performed using a quasiuniform 31 cell meshing.
The void fraction has been measured by a
The results are gathered in Figure
Distribution of deviations: “calculated minus measured voidfraction” in the different series of single subchannel PSBT tests.
Test number  Average  Standard dev.  

Series 1: standard central subchannel  43 

4.8% 
Series 2: central subchannel close to a thimble  43 

5.3% 
Series 3: lateral subchannel  20 

6.0% 
Series 4: corner subchannel  20 

3.2% 
All series  126 

5.0% 
PSBT single subchannel test comparison (thimble means a central subchannel close to an unheated thimble).
Some examples of void axial profiles simulated by CATHARE 3 in various flow conditions in the standard central subchannel are shown on Figure
PSBT single subchannel test comparison: axial void profiles of 5 tests in a standard central subchannel.
Several types of rod bundles were tested, most of them including a
Power distribution in the bundle B7: red: 100%, green: 85%, blue: unheated thimble.
The heated part of the rod bundle was modelled by a 3D grid, with
An array of void fraction values in the different subchannels was measured at 3 different levels along the upper part of the heated length, reconstructed by 6 chordal averaged values in
Sensitivity to the void diffusion term.
Only the averaged value of the 4 central subchannel void fractions was available in the benchmark database, and this is the compared data versus the void calculated by CATHARE 3 hereafter on Figure
PSBT rod bundle test comparison of predicted and measured void fraction in central region at 3 different elevations along the heated length; lower: 2216 mm; medium: 2669 mm; upper: 3177 mm.
The points are more dispersed than for the single subchannel tests. The statistics of the results (difference: computed minus measured void fraction given in absolute %) is presented in Table
PSBT rod bundle comparison statistics for void fraction tests.
Series  5  6  7  8  All gathered 

Power profile  Uniform  Cosine  Cosine  Uniform  
Central thimble  No  No  Yes  No  
Average 





Standard deviation 





The series number correspond to 3 different bundles; the series 8 is tested with the same bundle as series 5 as repeated cases, which appear to be less satisfying.
A set of 12 transient tests is proposed in the benchmark, including power increase (PI), flow reduction, temperature increase (TI), and depressurization in each of the 3 same tested bundles as in the steady tests of the exercise 2. The void fraction was also measured at the same 3 elevations during the transient.
The flow parameters (pressure, flow rate, and inlet temperature) were measured outside of the main vessel, near the inlet nozzle (referred as Coolant Inlet on Figure
PSBT test vessel and flow channel structures.
Hence, except for the “Temperature Increase” transients, as the inlet temperature remains quasiconstant during the transient, the same computational domain was considered as in the previous steady tests, that is, the heated length in the rod bundle only and the requested inlet conditions were applied at the bottom of the heated length.
An example of comparison is given below (Figure
Comparison of void fraction transient predicted by CATHARE 3 and measured in PSBT 7TPI test.
For this 7TPI test, the location of the inlet temperature measurement is not sensitive because the temperature remains more or less constant during the transient. However, for Temperature Increase tests, this location must be at the boundary of the computational domain. Otherwise, a temperature delay would induce a bias in the simulation. Hence, for these TI transients, another domain has been set up, adding the downcomer as an axial module upstream the 3D module simulating the whole rod bundle.
An example of simulation is presented on Figure
Comparison of void fraction transient predicted by CATHARE 3 and measured in PSBT 7TTI test.
The comparison is less satisfying than for the other test 7TPI. All maximum void fractions are underpredicted and while the time of void take off is well predicted, the time of maximum void is delayed and the void curves seem to be widened. This seems to be the consequence of a too large axial diffusion of void and perhaps also of the temperature step in the inlet part of the domain.
No data is available for codetodata comparison for this exercise, except a single value given at the beginning of one transient test (7TPI) in nonboiling steadystate condition. The benchmark specifications recommended the pressure loss coefficients to be used for every type of spacer grid. Using these values, CATHARE 3 predicted the overall bundle pressure drop at 1.85 kg cm^{−2}, while the measured pressure drop is 1.6 kg cm^{−2}. This can be considered as a satisfying bias, considering the constant pressure loss coefficient with no dependency on the flow Reynolds number.
This exercise is particularly useful to assess the code capabilities for turbulent dispersion and diffusion in singlephase flow.
In a
Rod power distribution in fluid temperature measurement tests; red rod power 100%, yellow 25%.
Nine tests at high pressure (from 50 to 170 bars) are proposed for simulations in a wide range of mass fluxes (between 500 and 4700 kg/m^{2}s). In Figure
Sensitivity of the temperature profile to the turbulent diffusion term.
A first step of analysis allowed us to calibrate the turbulent viscosity used in the liquid energy balance (also in the void mixing term which is not useful in this exercise). Figure
The profiles of half of the proposed tests are correctly predicted. The other tests show unbalanced measured temperatures at the outlet compared to inlet flow parameters and bundle power and hence, comparisons are not significant.
In the Table
Test parameters for temperature measurements.
Test number  Pressure (kg/cm^{2}a)  Mass flux (10^{6} kg/m^{2} hr)  Inlet temperature (^{°}C)  Power (MW) 

016232  169.1  2.10  251.5  0.42 
015252  150.0  1.95  113.9  0.41 
Temperature profiles in 2 fluid temperature measurement tests.
Using the available correct tests, a satisfying value of the temperature dispersion parameter has been selected, and implemented in CATHARE 3 for the other void and DNB simulations.
As for the void fraction tests proposed in phase I, different bundles were tested. The DNB is detected both in experiments and simulation by a significant rise of the wall temperature (more than 11°C) when the bundle power is slowly increased.
We calculated 6 test series in 5 different bundles corresponding to several geometries and power profiles, as shown in Table
Results of 6 series of DNB simulations in rod bundles.
Bundle  Rods  Spacers  Radial power  Axial power  Calculated tests  Predicted power  Std dev  Small flow rate tests 

A0 




9  96.80%  6.24%  0 
A2 




11  87.70%  17.04%  2, overpredicted 
A3 




8  79.46%  3.90%  0 
A4 




20  78.44%  3.07%  2, over 5 std dev 
A4 




27  78.50%  3.72%  0 
A8 




24  81.79%  8.70%  2, overpredicted 
Some statistics of the simulation results (relative power: computed over data in % of experimental data) are given in Table
One can see that the result for bundle A0 is satisfying results while the others show a significant bias.
The A3 bundle, featuring a
The results in the bundle A2 are weakened by two tests at very low flow rate (330 kg m^{−2} s^{−1}), which are overpredicted contrary to the 9 other tests; this enlightens the large value of the standard deviation for this bundle. A similar behaviour exists in series 4 and series 8 where the 2 tests at very low flow rate show significant differences (larger DNB power) compared to the other tests. Generally speaking, the location of the first detected DNB matches better in the series 4 than in the series 8.
The general underprediction of the DNB power in rod bundles may be linked to the use of lookup tables in a 3D analysis; such tables can predict CHF or DNB given 3 parameters: mass flux, pressure, and steam quality. These tables were built using 1D analysis of numerous tests. But in a 3D analysis, the steam quality and the mass flux must obey a local definition with local void fraction and velocities and may display wrong values. As a consequence, the code computation of the local CHF may deviate from the recommended value. Better results can be expected when this point is improved.
Moreover, the better results for the A0 bundle seem point out that the CHF is better predicted with 13 spacers than with 17. The number of 13 is closer to the usual number of spacers in industrial bundles and CHF experiments used to build up the lookup tables. So, the DNB predictions would depend strongly on the spacer number, either through the CHF calculated with the lookup tables, or through the mixing effects simulated in the 3D computation. From this point of view, CATHARE 3 is not able now to predict the DNB power at subchannel scale with accuracy better than 20% in a new bundle.
Given the underprediction of the highvoid fraction noticed in the preceding sections, the predicted DNB power should have been overpredicted because the local CHF increases when the local void fraction decreases. This also shows that these lookup tables are not convenient for the analysis of the PSBT tests. It has to be noted that the original purpose of the 3D module of CATHARE2 and 3 was an improvement of the code behaviour in very large volumes within the reactor vessel such as the downcomer and the lower plenum. Applying this module in core subassemblies at subchannel scale is beyond the usual scope of the module, and the BFBT and PSBT benchmarks were just opportunities to check the module capabilities.
Several tests were proposed in the benchmark specification report, in the rod bundles A4 and A8 (see Table
The 1D and 3D modules of the CATHARE 3 system code were used for the simulations of PSBT benchmark tests. Results of void fraction in phase I and temperature measurements and DNB power measurements in phase II have been compared to calculation results. The void comparisons show that our models of wall and interfacial friction, coupled with void dispersion, lead to satisfactory results, with a slight bias towards void underprediction, for both single subchannels and full rod bundles.
The exercise 1 of phase II, devoted to singlephase mixing and cross flows in liquid phase, shows good results as far as the experimental heat balance of the tests remains satisfactory.
In the exercise 2 of benchmark phase II, steady DNB simulations in 5 different rod bundles show significant underprediction of the critical power in the whole bundle (20% bias). The main reason should be a poor local CHF assessment, more than a rough mixing model. The analysis of transient tests for exercise 3 confirmed this behaviour. The CHF lookup tables in CATHARE 3 underpredict the CHF values in the PSBT rod bundles, which have 17 spacer grids. Improving these features would require improving the modelling of the interaction between spacer grids, turbulence, and local CHF or using CHF correlations designed for specific bundles.
Wall friction phase multiplier
Internal energy
Wall friction coefficient
Gravity
Enthalpy
Turbulent kinetic energy
Interfacial friction coefficient
Laplace length
Pressure
Void dispersion coefficient
Prandtl number
Heat flux
Time
Temperature
Velocity
Phase volume fraction
Boiling/condensation rate
Friction area (or heated area) over control volume
Molecular heat conductivity
Dynamic viscosity
Kinematic viscosity
Phase density
Surface tension
Interfacial stress
Wall stress
Interface
Any phase
Liquid phase
Wall
Turbulent.
This work was made in the frame of the development of the NEPTUNE project, which is jointly developed by the Commissariat à l’Energie Atomique et aux énergies alternatives (CEA, France) and Electricité de France (EDF) and also supported by the Institut de Radioprotection et de Sûreté Nucléaire (IRSN, France) and AREVANP.