The IAEA has coordinated a benchmark project on natural convection phenomena in the upper plenum of the MONJU reactor. JAEA has provided both detailed geometrical data of the plant and complete thermalhydraulic boundary conditions describing a pump trip transient, accomplished during the start-up experiments of the reactor. For the initial conditions of the pump trip transient, extensive sensitivity analyses have been made with the CFD code Trio_U. These calculations show a high sensitivity of the global flow pattern in the MONJU upper plenum depending on the initial order of the numerical scheme and the modelling of the geometrically complex upper core structure. During the pump trip, the formation of a thermal stratification within the plenum has been observed which persists for almost two hours. All calculations have shown a homogenization of the temperature in the plenum after about 15 minutes. A slight reduction of the mixing in the upper plenum could have been achieved by modifying the form of the flow holes in the inner barrel (fillets instead of sharp edges) in order to reduce their axial pressure loss.
The IAEA has coordinated a research project (CRP) between 2008 and 2012 entitled “Benchmark Analysis of sodium Natural Convection in the upper plenum of the MONJU Reactor Vessel.” Eight research organizations from seven countries with an active program on sodium cooled fast reactors—namely, China, France, India, Japan, Republic of Korea, Russian Federation, and USA—contributed to this CRP. Japan Atomic Energy Agency (JAEA) has submitted to the CRP participants the data of sodium thermal stratification measurements in the MONJU reactor vessel upper plenum collected during a plant trip test conducted in December 1995. The benchmark partners have analysed this experiment by applying different codes and methodologies. The benchmark thus helped the members to improve their capability in the field of fast reactor in-vessel Sodium thermalhydraulics.
Sodium cooled fast breeder reactors are under development for more than 50 years. Nevertheless, only very limited data are published to date which allow the validation of CFD codes in general and for natural and mixed convection phenomena in particular.
Within the European Fast Breeder Reactor project, an experimental approach in the RAMONA facility has been largely used to study decay heat removal situations [
Similarity criteria are often used to extrapolate the results of water tests to sodium flow. Such similarity criteria for mixed convection have been evaluated at CEA in two geometrically identical experimental facilities; SUPERCAVNA for water flow and CORMORAN for sodium flow. The generic setup was a horizontal channel connected to a cavity, heated (or cooled) at one wall. The thermal stratification and thermal fluctuations have been measured in both facilities and additional velocity measurements were made in the water tests [
For the mixing of submerged jets encountered at the core outlet, two identical setups have been analysed in [
Accompanying the construction of the Indian prototype fast breeder reactor, thermalhydraulic phenomena of internal heat exchangers have been analysed in detail by using CFD codes. On the primary side, the uniform distribution of the flow at the inlet window connected to the upper plenum has been evaluated in [
Most of the phenomena expected to be important in the thermal stratification formation in the upper plenum of sodium cooled reactors have been analysed experimentally by separate effect tests. The only full scale, integral test published to date is the MONJU reactor pump trip used in the IAEA CRP. These data are used in this paper and are applied for CFD validation on reactor scale.
The MONJU plant is a prototype nuclear power plant with sodium cooled fast breeder reactor. The upper plenum of the MONJU reactor is geometrically very complex. Figure
Sketch of the MONJU upper plenum.
The Fuel Handling Machine (FHM) with its hold down arm is also illustrated in Figure
The UCS is situated above the SA outlets and below the Upper Instrument Structure body (UIS). This region is shown in more detail in Figure
Sketch of the MONJU upper core structure (UCS).
The Flow Guide Tubes (FGTs) are a tube bundle maintained at its top by a perforated plate called Honeycomb Structure (HS). The Fingers (FS) are located above the FGT and the HS. Thermocouples are positioned at the FGT outlet centres, installed at the bottom ends of FS which are connected to the UIS. The main flow passes from the SA into the FGT to enter the Fingers region. 19 Control Rod Guide Tubes (CRGTs) are present inside both regions.
The purpose of the test was the confirmation of plant safety against turbine failure. At 40% nominal power, the main coolant pumps are tripped and the control rods were inserted. The decay heat is removed to the atmosphere through sodium-air heat exchangers. The temporal changes of the vertical distribution of the sodium temperature in the upper plenum was measured along the TCP as shown in Figure
Measured temperature distribution on TCP.
The thermal stratification front moved upward after the reactor scram and reached the top of the IB after about two hours.
A simplified CAD model has been developed at ANL [ All of the SA outlets are taken as hexagonal. The top of the SA outlets is placed on the levels 0.87 m, 0.9 m, and 0.93 m above the support plate to distinguish the different channels easily. In /10/, all SA outlets are located 0.93 m above the support plate. The ON is rotated to respect the hexagonal core configuration (only half of the outlet nozzle is modelled). Internal structures like FHM and TCP which are placed in a nonsymmetrical way in the upper plenum are not modelled.
Within the UCS, only the Control Rod Guide Tubes (CRGTs) are realized in the CAD model. FGT and FS are not treated explicitly due to their small size and geometrical complexity. However, the external frontiers of the FGT and Fingers regions are realized with the intention of forming in that way two subregions which allow a specific macroscopic modelling by means of porous media with directional pressure loss correlations.
The FGT and FS regions are densely packed tube bundles. The correlation (
Parameters for the pressure loss correlation.
Direction |
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Axial | 0.316 | 0.25 |
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Transverse | 4.03 | 0.27 |
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The axial velocity and transversal velocity are calculated as a function of tube direction vector
The HS is modelled as perforated plate without any thickness. The singular pressure loss which is applied on the plate is predicted from a grid pressure loss correlation [
The tubes in the fingers region reduce the volume accessible by the sodium flow. A volumetric porosity of 0.83 is thus defined in the Navier-Stokes equations for the FS region to simulate the acceleration of the flow outside of the tubes due to mass conservation considerations.
ANL has provided the CAD model of the simplified 60° geometry in IGES format. This model has been imported into the commercial mesh generator ICEMCFD. The UCS regions FGT and FS are defined as internal sub-domains, and the HS is implemented as an internal, semi permeable wall. Three pure tetrahedral meshes of 300.000 elements (coarse mesh) and 1.25 million elements (intermediate mesh) and 3.3 million elements (fine mesh) have been created. The coarse and intermediate meshes are shown in Figure
Coarse and intermediate meshing in a horizontal cut plan.
The coarse and fine meshes are created with a Delaunay procedure which leads to a better approximation of boundary layers on solid surfaces. The intermediate mesh is created with an Octree procedure which leads to a more homogeneous mesh inside of the plenum. Where possible, a similar thickness of the first wall near layer of cells has been defined for all meshes. The
Liquid sodium is used as coolant in the MONJU reactor. The default values of the thermo-physical data used at CEA for 400°C are given in Table
Physical properties of sodium at 400°C.
Quantity | Value | Unit |
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Density | 858 | kg |
Dynamic viscosity | 2.81 * 10−4 | kg |
Therm. conductivity | 69.7 | W |
Heat capacity | 1284 | J |
Therm. expansion coefficient | 2.68 * 10−4 | K−1 |
In the temperature range of interest (380°C to 512°C), the fluid can be treated in first approximation as incompressible. This simplification allows the application of the Boussinesq hypothesis to simplify the Navier-Stokes equations. All physical properties are treated as temperature independent, and buoyancy effects are taken into account only via the gravitational acceleration.
Trio_U [
For unstructured, tetrahedral grids, a hybrid Finite Volume Element method (FVE) is applied. This method approximates a continuous problem by a discrete solution in the space of the finite elements by maintaining the balance notation of finite volumes. In Trio_U, the main unknowns as velocity and temperature are located in the centre of the faces of an element (P1NC). Thus, the number of control volumes for the momentum and scalar conservation is approximately two times the number of elements. The pressure is discretized in both the centre (
Fundamental numerical scheme used in the Trio_U calculations.
General | Dimension | 3D calculation |
Fluid | Sodium at 400°C | |
Mesh | Tetrahedral mesh | |
Discretization |
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Time scheme | 1st order Euler explicit | |
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Navier-Stokes |
Convection | 2nd order upwind |
Diffusion | 2nd order centred | |
Pressure solver | Cholesky method | |
Thermal effects | Boussinesq hypothesis | |
Wall law | Logarithmic wall law | |
Turbulence | RANS | |
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Turbulence |
Turbulence model | High Reynolds |
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2nd order upwind | |
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2nd order centred | |
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Energy transport |
Convection | 2nd order upwind |
Diffusion | 2nd order centred | |
Wall law | Logarithmic wall law | |
Turbulence | Turbulent Prandtl Number |
To reach a steady-state solution, a transient is calculated until all unknowns reach constant values. This procedure guarantees physically correct solutions at any time of the transient.
Turbulence is treated with the Reynolds averaging concept where the instantaneous velocity
The production of turbulence kinetic energy is calculated by
Buoyancy effects for incompressible flows are treated by
The empirical coefficients listed in Table
Coefficients of the high Reynolds number
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0.09 | 1.0 | 1.3 | 1.44 | 1.92 | 1.0 | 0.9 |
To take into account the effect of thermal stratification, the following assumption is made [ for stable stratification with reduced buoyancy effects: For unstable stratification with full buoyancy effects:
This extension of the standard
For each SA outlet, the time-depending mass flow rate and temperature are given in the data description report [
All walls are treated as adiabatic. Standard logarithmic wall functions [
Before the pump trip at 40% power, the temperature field and the velocity flow were well established in the upper plenum. A first calculation was performed in order to obtain this initial condition. The boundary conditions for the calculation are the conditions at the beginning of the test [
A reduced Froude number Fr of the jet leaving the upper core structure is calculated from
A three-step procedure was applied to ensure convergence of the solution on both the meshing and the numerical scheme. In this procedure, solutions converged on coarser meshes were interpolated on finer meshes to define the new initial condition for the subsequent calculation on the finer mesh. Initializing with a reposing ( Initializing with the solution Initializing with the solution
Identical solutions
In Figure
(a) Momentum dominated solution (
A two-step procedure was applied to ensure convergence of the solution on the meshing. Initializing with a reposing ( Initializing with the solution
Identical solutions
In Figure
It has been tested if it is possible to change the solution from the buoyancy dominated flow to the momentum driven flow by changing the numerical scheme. Initializing with the solution
The coldest sodium leaving the core region has a temperature of 418°C. When initialising the upper plenum with this temperature, buoyancy forces act instantly on the hotter jet. These buoyancy forces are minimized by initialising the upper plenum at the temperature of the hottest sodium (513°C) leaving the core region. Starting from a reposing (
The possible influence of the upper core structure (UCS) on both the thermal stratification and the flow pattern within the upper plenum is not a priori evident. To show the possible effect of the UCS on the flow, an additional sensitivity calculation without UCS has been performed. Initializing with the solution
Convergence tests on further mesh refinements have not been made. The solution
Using different modelling options, three different steady solutions have been achieved which can be distinguished regarding the driving physical process: a momentum dominated solution S1; a buoyancy dominated solution S2; a mixed convection solution S3.
The calculated temperature profiles along the TCP are compared in Figure
Comparison of the axial temperature profiles.
From these temperature profiles it seems not possible to identify the flow pattern present in the upper plenum before the pump trip. JAEA has estimated from many scaled tests using sodium and water that the momentum dominated solution ought to be close to the real behaviour. According to JAEA, this assumption is supported by the two measured temperature changes in the middle part of the plug, 3 m and 3.75 m above the vessel bottom. However, the momentum dominated solution S1 presented in Figure
Various sensitivity calculations have been performed to assure that the presence of the two solutions is not related to incomplete convergence on the mesh or on the numerical scheme. The effects of the sensitivity studies are summarized in Table
Influence of varied parameters on the solution.
Objective | Initialisation | Varied parameter | Solution |
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Convergence of solution S1 | Reposing flow; |
Coarse mesh; 1st order convection scheme | S1c |
Solution S1c; | Intermediate mesh; 2nd order convection scheme | S1i | |
Solution S1i; | Fine mesh; 2nd order convection scheme | S1f | |
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Convergence of solution S2 | Reposing flow; |
Intermediate mesh; 2nd order convection scheme | S2i |
Solution S2i; | Fine mesh; 2nd order convection scheme | S2f | |
Solution S2f; | Coarse mesh; 1st order convection scheme | S2c | |
Reposing flow; |
Intermediate mesh; 1st order convection scheme | S2i | |
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Effect of UCS | Solution S2i; without UCS | Intermediate mesh; 2nd order convection scheme | S3i |
The following conclusions of the sensitivity calculations can be made. A bifurcation into momentum (S1) and buoyancy (S2) dominated solutions is observed. Each solution has been verified to be meshing independent. The momentum dominated solution seems to be attained by using initially coarse meshes and low-order convection scheme (initializing with a reposing fluid). The buoyancy dominated solution seems to be attained by using initially finer meshes and higher order convection schemes (initializing with a reposing fluid). Once a steady-state solution is achieved (either S1 or S2), this solution cannot be altered by changing the numerical scheme and/or the mesh refinement (all solutions were converged on the fine mesh and 2nd order numerical scheme). The modelling of the UCS can have a strong influence on the flow pattern (solution S3).
A dependency of the flow pattern on the experimental management has been observed at CEA in sodium mixed convection experiments. In a small scale experiment comparable to the MONJU pump trip experiment, a momentum dominated flow similar to the solution S1 has been observed for mixed convection conditions after reducing the inlet flow velocity from an initially higher value to the target value. A buoyancy dominated flow similar to S2 has been observed for identical mixed convection conditions after increasing the flow velocity from an initially lower value to the target value. It cannot be excluded that the flow pattern in the MONJU plenum before the pump trip is as sensitive to the plant management before experiment as the CEA experiment was to the initial conditions. Today, almost 20 years after the experiment, it seems hardly possible to know from numerical simulations the flow pattern at the beginning of the experiment without any doubt.
The intermediate mesh, 2nd order discretization schemes, and the 1st order explicit Euler time marching scheme are applied to analyse the transient of the pump trip experiment. The Courant-Friedrich-Levy stability condition is respected during the whole transient (CFL = 1). The calculation is initialized with solution
The thermal stratification in the symmetry plane, 2 minutes and 10 minutes after the pump trip, is given in Figures
(a) The flow field in the symmetry plane at
During the 3rd CRP meeting, an underestimation of the flow passing through the flow holes (FH) of the inner barrel has been identified by the benchmark participants as a potential source of uncertainty regarding long-term stratification formation. The exact form of the holes is not known. JAEA has provided circular holes with sharp edges in the CAD file [
The reference transient calculation with FH with sharp edges has been repeated with FH with rounded edges. During the transient, the overall flow patterns of sharp edge and round edge calculations look somewhat different [
(a) Axial temperature profiles at
Sofu [
Later then about 10 minutes after the pump trip, an axially linear temperature distribution is present in the upper plenum at elevations higher than about 2 m above the support plate (see Figure
In the framework of an IAEA CRP, benchmark analyses of sodium convection in the upper plenum of the MONJU reactor vessel have been performed at CEA by using the CFD code Trio_U. In angular direction only 1/6 of the MONJU upper plenum has been taken into account in the modelling. This reduced domain was discretized in up to 3.3 million tetrahedral elements. A high Reynolds number turbulence model (
For the steady-state initial condition before the pump trip transient, a bifurcation of the solutions into a “momentum dominated solution” and a “buoyancy dominated solution” was observed. Such a bifurcation has also been found experimentally at CEA in mixed convection experiments. Initializing the coarsest mesh with a reposing fluid and using a 1st order convection scheme, the momentum dominated solution was attained. Initializing the intermediate mesh with a reposing fluid and using a 2nd order convection scheme, the buoyancy dominated solution was attained. After successively refining the mesh and using 2nd order numerical schemes, each of the two solutions can be considered as meshing independent, because each solution was identical on the two finest grids. The experimentally found temperature stratification seems not to be a good indicator to distinguish the flow fields of the two solutions. For a more profound understanding, further numerical analysis is necessary. This concerns the solution procedure (iterative methods as SIMPLE instead of a transient calculation as presented) and may be the use of more sophisticated turbulence modelling approaches.
The pump trip experiment has shown the formation of a thermal stratification within the plenum. The calculations with the intermediate mesh predict well the stratification formation in the first 10 minutes of the pump trip. In the experiment, the stratification persists for more than two hours, whereas all calculations of Trio_U have shown a homogenization of the temperature in the plenum after about 15 to 20 minutes (significant overestimation of the internal mixing). Further analysis is under way to better understand the overestimation of the mixing in the upper plenum. Special attention will be turned on balancing in reposing fluids linear temperature gradients by the pressure.