The Institute for Neutron Physics and Reactor Technology (INR) at the Karlsruhe Institute of Technology (KIT) is investigating the application of the meso- and microscale analysis for the prediction of local safety parameters for light water reactors (LWR). By applying codes like CFD (computational fluid dynamics) and SP3 (simplified transport) reactor dynamics it is possible to describe the underlying phenomena in a more accurate manner than by the nodal/coarse 1D thermal hydraulic coupled codes. By coupling the transport (SP3) based neutron kinetics (NK) code DYN3D with NEPTUNE-CFD, within a parallel MPI-environment, the NHESDYN platform is created. The newly developed system will allow high fidelity simulations of LWR fuel assemblies and cores. In NHESDYN, a heat conduction solver, SYRTHES, is coupled to NEPTUNE-CFD. The driver module of NHESDYN controls the sequence of execution of the solvers as well as the communication between the solvers based on MPI. In this paper, the main features of NHESDYN are discussed and the proof of the concept is done by solving a single pin problem. The prediction capability of NHESDYN is demonstrated by a code-to-code comparison with the DYNSUB code. Finally, the future developments and validation efforts are highlighted.
The safety evaluation methodologies of nuclear power plants (NPP) are in continuous development and validation and must reflect the state of the art in science and technology. Recent advances in computer and engineering sciences have led to a gradual improvement of the prediction capability of numerical tools regarding key safety-relevant phenomena of nuclear reactors. Currently, conservative and best estimate (BE) safety analysis methodologies are being applied with increasing importance of the BE computer codes within the licensing process of NPP.
Due to the increasing complexity of fuel assemblies (FA) in design and material compositions, a general trend to move towards multiscale and multiphysics simulations aiming to obtain high fidelity simulations is pursued [
This new trend permits a better assessment of the safety margins and contributes to reduction of the conservatism in the applied methodologies for core analysis. The availability of high performance computers allows an increase of the spatial resolution of the thermal hydraulics (TH) and neutron physical phenomena at very detailed scales paving the way for the possibility to directly predict local safety parameters [
In this paper, the novel system NHESDYN (NEPTUNE-SYRTHES-DYN3-SP3) is presented. It consists of the coupling of the neutron kinetic code DYN3D-SP3 [
The far goal of this development is to have a coupled system able to describe both the thermal hydraulic and neutronic phenomena in LWR cores with fewer approximations than the legacy coupled codes such as RELAP5/PARCS [
In this paper, the main features of NHESDYN to solve one single pin problem are presented since the application of NHESDYN to solve pin clusters, fuel assemblies, or even a reactor core is very challenging and too time consuming at the moment. Hence the authors decided to restrict themselves to a simple problem where the potentials of the coupling methodologies can be clearly demonstrated. After the description of the coupling approach and implementation, the validation of NHESDYN is described and discussed in Section
By coupling NEPTUNE-CFD with the heat conduction solver SYRTHES and the NK code DNY3D-SP3, a new code named NHESDYN was created. In this coupling approach, the codes are externally coupled using the Message Passing Interface (MPI) standards for the communication between them. In Figure The SYRTHES code receives the information of the volumetric heat flux from DYN3D-SP3. The fuel temperature gradients plus pin gap and cladding heat conduction are solved. The heat flux is transferred from the cladding to the fluid domain, solving the conjugated heat transfer, between TH codes. The NEPTUNE-CFD code calculates the temperatures, pressure, and velocities of the fluid. DYN3D-SP3 updates the cross-sections by taking the information of the Doppler temperature (calculated by SYRTHES) and moderator temperature and density (calculated by NEPTUNE-CFD).
Simplified communication scheme for the coupled solution NEPTUNE_CFD/SYRTHES/DYN3D_SP3.
Finally, the power calculated by the NK code is passed over to the SYRTHES code to restart again the process. This methodology is repeated at each time step. The codes involved have to wait for the information generated by its predecessor to start the calculation and each code is normally executed one time. This kind of time hierarchy in the coupled solutions is called explicit. The solution can be considered a combination of external and internal coupling. The heat conduction solver SYRTHES is coupled in NEPTUNE-CFD by means of a semi-implicit approach; therefore the thermal hydraulic and heat conduction solver are considered as one. The combination of NEPTUNE-CFD/SYRTHES performs an external coupling with the NK tool.
Because the effort to validate codes used for safety analysis is very large, a preservation of the established codes is of strong importance. Therefore, coupling between existing codes representing different physics fields such as TH and NK is very attractive compared to the option of developing a complete new code. This approach is followed by the route of a combined coupling and it works quite well for the TH/NK systems where well validated codes exist. The TH tool is always one step ahead of the NK calculation.
The time discretization has to be small enough to avoid numerical stability problems. Exploring studies have shown that the explicit method of updating the data is free of oscillations only if the time step is small enough. For large time steps some variables develop unphysical oscillations of numerical nature that are not related to the physics of the problem under consideration. The explicit method is conditionally stable. Normally, the time step is selected by the TH code attending to the flow characteristics like the Courant number. In case of the simulation of a transient scenario with externally coupled codes, both codes share the same time step. The time scale of the coupled solutions is always conditioned by the most restrictive time step. TH tools use a smaller time step compared to the NK code. Therefore, NK code has always a sufficient time step in the coupled solution.
A general overview of the data flow between the codes and how it was implemented is described here. First of all, the first step for the communication among the codes is the creation of the MPI groups. A general scheme concerning the group distribution of the different codes is shown in Figure
General distribution of the three MPI groups and the codes included within them.
NHESDYN generates DYN3D-SP3 as a subprocess (spawn operation) and creates a point to point communication with NEPTUNE-CFD. At the same time the NK code creates a point to point communication with SYRTHES. In the MPI, the point to point communication is a client and a server.
In Figure
In Figure
Simplified flow chart for the coupled NHESDYN system.
The information generated takes two different ways. The information from SYRTHES (Doppler temperature) can be transferred directly to DYN3D-SP3 because both are included in the same MPI group. The second way is followed by the information from NEPTUNE-CFD (moderator temperatures and densities) which is sent to the main code. Here, if it applies some operations are performed (e.g., convergence loops for a steady state case). Afterwards, the information is resent to the NK code. By this last operation the NK has enough information to refresh the precalculated cross-sections and solve the transport equation. When the calculation is finished the heat flux is sent again to the TH code which is waiting for the next time step calculation.
In Figure
NHESDYN main steps of execution.
DYN3D-SP3 first performs a steady state run and then the transient calculation is initiated. In this case, both codes run at the same time and the thermal hydraulic boundary conditions can be modified and these modifications can be taken into account by the transient neutronic solver.
The coupling scheme depends on the type of calculation to be done, namely, steady state or transient. In case of the coupled steady state calculation, the neutronic solver and the thermal hydraulic solvers are run sequentially till a converged solution is found. At each time step, the information is exchanged between them; for example, the power is passed from DYN3D-SP3 to the thermal hydraulic solver and they provide the feedback parameters like coolant density or temperature, fuel temperature, and so forth to the neutronic solver for the cross-section update before the neutron transport problem is solved. In Figure
Time advancement description for the codes.
Due to the fact that there are three solvers coupled to each other solving the fluid dynamics (NEPTUNE-CFD), heat conduction and transfer (SYRTHES), and neutronic (DYN3D-SP3), the coupled system may need a lot of iterations to converge since the TH parameters are very sensitive to any power changes. Since SYRTHES uses the same time step as the other code solvers but it is not mandatory to do so, this time step can be modified to speed up the convergence. Hence, high values for the time step of SYRTHES (e.g., 104 seconds) were selected in order to neglect the thermal inertia from the energy equation during the heat conduction solution. By this way, the temperature changes in the fuel will rapidly accommodate to the new power distribution.
As soon as the NK code changes to a transient simulation mode, the time step of SYRTHES will depend on the NEPTUNE_CFD solver, which defines the time step for all involved codes. During the coupled simulation, the NK code waits until the thermal hydraulic solver finalizes the simulation. The following thermal hydraulic variables are monitored and their relative changes will be used as convergence criteria: Doppler temperature, moderator temperature, and moderator density. In addition, the heat flux at the solid-liquid interface is also checked for as convergence criteria. For this purpose, the relative variation of these parameters between the current and the last time step is calculated. The convergence criterion is reached when the relative variation of these variables is below 10−4. Furthermore, to monitor the evolution of the steady state coupled simulation, the main program writes the convergence parameters at each axial level of the TH discretization, that is, local convergence criteria. When all the axial levels are converged then the information is sent to the NK code to perform another time step calculation.
In case of a coupled transient simulation, there is no convergence loop before Step 6 and the TH parameters are sent directly to the NK solver by the main program after they have been collected. Both the TH and the NK solvers are executed in transient mode. To assure that the effects of the thermal inertia are accurately described, SYRTHES uses the same time step as the other solvers. In Figure
For the information exchange between the involved solvers in the coupled system NHESDYN, the definition of an appropriate spatial mapping is very important. This will be described in the next subsection.
Several steps must be performed using the MPI-features for the exchange of information of the different solvers considering the peculiarities of each spatial nodalization. For this purpose, the information has to be prepared before and after each data exchange between solvers. One has to make sure that the axial and radial discretization of any problem used by the different solvers are compatible with each other and to assure that the information exchange is self-consistent. For the neutronic SP3 solver, a fuel rod is radially treated as one homogenized cell while in the axial direction it can be subdivided into any number of cells. The SYRTHES solver, on the other hand, can discretize the fuel pin (fuel, gap, and cladding) in different radial rings and axial nodes. Finally, the CFD solver allows a very detailed discretization of the fluid domain including a large number of cells. The spatial refinement of the fluid domain is problem dependent. Those different discretization approaches of the involved codes represent a real challenge to be solved by the coupled system. To avoid mesh dependencies in the communication, a “virtual interface” is created before the information exchange is done between solvers. Doing so, the important values to be passed from one domain to another are approximated to continuous functions. These functions are described by 4th degree polynomial approximations. Due to the simplicity of the case a 4th degree polynomial is enough to describe the axial profiles. In case of setting a more complex problem, for example, different burn up or enrichment, other approaches need to be investigated.
Then, the real information exchanged between codes is done via these approximations. By this innovative approach, the amount of information to be treated and sent by the MPI code is considerably reduced. In Figure
Spatial mapping for a pin: (a) NEPTUNE-CFD/SYRTHES model, (b) averaged TH values at each axial level, (c) polynomial approximation of TH parameters, (d) DYN3D-SP3 model, (e) computed power, and (f) polynomial approximation of the axial power.
Since the involved codes are already in the process of validation, the coupled NHESDYN system will be verified and validated by a code-to-code comparison. For this purpose, the DYNSUB system, developed at KIT by coupling DYN3D-SP3 with the subchannel code SUBCHANFLOW [
The test problem consists of one pin surrounded by the coolant with the thermal conditions given in Table
Nominal conditions for the simulations according to the OECD/NEA and US NRC PWR MOX/UO2 core transient benchmark adapted for a single pin geometry.
Power (kW) | Inlet temp. (K) | Pressure (MPa) | Mass flow (kg/s) |
---|---|---|---|
21.68 | 560 | 15.5 | 0.28 |
The dimensions of the fuel rod are exhibited in Table
Rod geometry considered for the validation based on the the OECD/NEA and US NRC PWR MOX/UO2 core transient benchmark.
Fuel radius (mm) | Clad inner radius (mm) | Rod radius (mm) |
---|---|---|
3.951 | 4.010 | 4.583 |
For a consistent code-to-code comparison between NHESDYN and DYNSUB we made sure that both coupled codes use the same thermophysical material data for the fuel, gap, and cladding, for example, thermal conductivity, density, and the heat capacity as defined in [
In DYNSUB, a constant heat transfer coefficient (HTC) of 104 W/m2 K is used. In NHESDYN, the temperature gradient over the gap is calculated by solving locally the conduction within a solid using the thermophysical properties of helium. This is a simplification of the complex heat transfer phenomena that can take place in the gap, normally a combination of conduction, convection, and radiation. The difference between these two solution approaches leads to significant changes in the Doppler temperature prediction. To reduce the difference, the same HTC is used in both codes. After a NHESDYN steady state calculation, an averaged HTC of 11710 W/m2 K is calculated based on the heat transfer area, the heat flux, and gradient of the fuel rod gap temperature. This value is used in DYNSUB as the HTC over the fuel rod gap. In Figure
(a) Plant view of a 17
NEPTUNE-CFD describes the fluid domain where the mass flow rate is imposed at the inlet (the bottom of the subchannel) and the pressure is set at the outlet (the top of the subchannel) as boundary conditions.
The fluid domain is 12.6 mm in the
In the coupled code NHESDYN, the solid domain is solved by SYRTHES while the fluid domain is solved by NEPTUNE-CFD. In Figure
Fuel pin with a fluid domain with different discretizations: (a) and (b) correspond to a coarse mesh and (c) and (d) to a refined mesh.
Since the modelling of the heat transfer over the fuel gap is very important, a mesh sensitivity study was performed with the goal to find out the most appropriate meshing of both fuel and fluid domains for the coupled simulations. In SYRTHES, a coarser and a refined mesh of the fuel and clad are considered; the number of cells in the gap is 2; see Table
Specifications of the test matrix for the sensitivity study of the influence of a mesh refinement on the prediction of fuel and cladding temperatures.
Case | Mesh type | Gap boundary nodes properties |
---|---|---|
Run_1 (R1) | Refined | He |
Run_2 (R2) | Coarse | He |
Run_3 (R3) | Coarse | UO2-Zircaloy |
Then, three NHESDYN steady sate simulations and one DYNSUB were performed for the three cases illustrated in Table
Comparison of the axial Doppler temperature distribution calculated by DYNSUB and by NHESDYN using three different resolutions (R1, R2, and R3).
The Doppler temperature is calculated taking into account the fuel center line and the fuel outer surface. It can be seen that the Doppler temperature for the cases R1 and R2 is very close to the one of DYNSUB (reference solution). For case 3 the Doppler temperature is largely underpredicted compared to the reference value. In addition, the radial temperature profiles along the fuel rod radius predicted by NHESDYN for the three cases (R1, R2, and R3) and by DYNSUB are compared to each other in Figure
Radial temperature distribution over the radius of the fuel pin at 1.8 m elevation. Comparison of DYNSUB and different NHESDYN resolutions (R1, R2, and R3).
Comparison of the axial evolution of the cladding temperatures for DYNSUB and different NHESDYN resolutions (R1, R2, and R3).
The axial coolant temperature distribution calculated for the three cases (R1, R2, and R3) and by DYNSUB is shown in Figure
Comparison of the axial moderator temperature evolution predicted by DYNSUB and by NHESDYN using three resolutions (R1, R2, and R3).
Evolution of
In a steady state case the coupled system reaches convergence after four NK iterations. The TH needs more time to develop a temperature and density profile after a change in the power; to reach a steady scenario for the TH hundreds of iterations are needed by executing the convergence loop. Case R1 provides the best result regarding
To test and validate the new NHESDYN coupled system by a code-to-code comparison with the DYNSUB code, the following three transient cases are defined. Case 1: variation of the coolant temperature at fuel rod inlet. Case 2: variation of the coolant mass flow rate. Case 3: variation of the system pressure.
These transient cases are used to check the robustness and numerical stability as well as the prediction accuracy of NHESDYN.
The initial conditions for all transient cases are given in Table
The simulations performed have been tested with the two mesh refinement cases R1 and R2.
In this postulated transient case, the inlet temperature is decreased 10 degrees from the initial 560 K within few seconds and it remains at this condition for six seconds. Later on, the temperature returns to nominal conditions. Due to the temperature reduction, the moderator density increases leading to a better moderation of the fast neutrons and hence the power increases.
In Figure
Water inlet temperature evolution imposed and averaged water temperature of the domain for different NHESDYN resolutions (R1 and R2) and DYNSUB.
The evolutions of the Doppler temperature as predicted by NHESDYN (R1 and R2) and by DYNSUB are compared to each other, Figure
Comparison of the pin averaged Doppler temperature computed with DYNSUB and with NHESDYN using two different resolutions (R1 and R2).
In Figure
Comparison of the total power and reactivity evolution predicted by DYNSUB and NHESDYN using different resolutions (R1 and R2).
For this postulated transient, it is assumed that the moderator mass flow rate is progressively decreased from the nominal value down to 50% of the nominal conditions, that is, from 0.28 kg/s to 0.14 kg/s within 14 seconds. It remains at this value for four seconds and then it increases with the same change rate till nominal conditions are achieved.
By decreasing the moderator flow and keeping all other parameters at the nominal values, the coolant will heat up leading to a reduction of the neutron moderation and hence of the multiplication factor. The moderator temperature predicted at the axial elevation of 2 m by NHESDYN and DYNSUB is illustrated in Figure
Comparison of the moderator temperature evolution for two heights in the
In Figure
Comparison of the local Doppler temperature evolution during the transient at the axial height 2 (2 m) predicted by DYNSUB and NHESDYN using two different resolutions (R1 and R2).
The predicted total power by NHESDYN and DYNSUB is presented in Figure
Comparison of the power evolution calculated by DYNSUB and NHESDYN using two resolutions (R1 and R2).
A depressurization scenario is defined to study the robustness of NHESDYN when two phase flow conditions appear in the fluid domain. Such conditions are expected to occur when a pipe break in the primary circuit happens. It was assumed that the outlet pressure is decreased from nominal value of 15.5 MPa to 7.1 MPa within 15 seconds (Figure
Outlet pressure imposed by NHESDYN during the transient. And void fraction evolution predicted by NHESDYN R1 and R2.
As it can be seen in Figure
To make the problem more challenging, a pressure oscillation was defined from second 26 to second 41 as shown in Figure
When the void appears, large density gradients in the moderator are expected. The decrease of the density of the moderation leads to a reduction of the neutron moderation and a negative reactivity is produced. On the other hand if the moderation is improved an increase in the power is expected. The refined mesh provided by case R1 has an earlier onset of boiling and generates more void than the coarse mesh provided by case R2. The local density evolution at the axial height of 3.63 m is illustrated in Figure
Comparison of the local moderator density evolution for axial heights in the
Before the boiling starts (around 24.5 seconds) the moderator density decreases due to the pressure decrease; this fact provides negative reactivity and the power decreases too; see Figure
Comparison of the power evolution for the depressurization transient scenario calculated with DYNSUB and NHESDYN using two resolutions (R1 and R2).
At that time, a sudden power decrease occurs due to the negative reactivity provided by the moderator density. During the pressure oscillation the void generated oscillates affecting the moderator density and power due to the strong coupling of neutronic and thermal hydraulic processes. The power peaks fit in time with the guided pressure peaks which increase the saturation temperature and the neutron moderation. In Figure
Comparison of the total averaged Doppler temperature evolution predicted by DYNSUB and NHESDYN using two resolutions (R1 and R2).
In this paper, the main features of coupled system NHESDYN are described in detail. The peculiarities of the communication between the involved solvers in the frame of the MPI implementation are also presented. The testing and validation of the prediction capability of NHESDYN are carried out by a code-to-code comparison with DYNSUB, which has the same neutronic solver but a subchannel code instead of NEPTUNE-CFD/SYRTHES. For this purpose, a single pin problem was defined. Three postulated transient scenarios were defined to check the prediction accuracy of this new coupled system, namely, variation of the coolant inlet temperature, variation of the mass flow rate, and variation of the system pressure. These transient scenarios were then predicted by NHESDYN and DYNSUB using the same material properties for the fuel rod as defined in OECD/NEA and US NRC PWR MOX/UO2 core transient benchmark [
Based on the code-to-code comparison, it can be stated that NHESDYN is able to predict the behaviour of the fuel rod under all postulated conditions satisfactorily. By this it is demonstrated that the coupling approach and the information exchange among the solvers are consistent and are working properly. The real advantages of the new system NHESDYN compared to DYNSUB can only be shown, when a pin cluster or a fuel assembly is simulated with a very detailed resolution as usual for CFD codes. Hence the work presented here is the first step in the development of NHESDYN as a high fidelity simulation tool. The promising results obtained till now and presented here are very encouraging for the further development and testing of NHESDYN in solving large problems as fuel rod clusters of fuel assemblies of a PWR core. By this way, NHESDYN makes feasible multiphysics simulations describing the TH phenomena in a multiscale sense, for example, at a micro- and mesoscale, and hence local safety parameters such as clad temperature and pin power can be estimated using a refined space discretization if demanded.
NHESDYN showed a stable and robust behaviour dealing with rapid boundary conditions changes as defined in the three scenarios which are challenging especially for CFD codes.
The steady state analyses provided satisfactory predictions of the main thermal hydraulic parameters with a good agreement with the reference code in both axial and radial spatial profiles. The convergence loop for the steady state works properly and ensures a converged solution as initial condition for transient simulations. The designed main program drives properly the transition steady state to transient.
During the transients, a small delay in the evolution of the moderator temperature was calculated by NHESDYN compared to DYNSUB. The reason for it may be the different spatial discretization used in the thermal hydraulic solvers of NHESDYN (NEPTUNE-CFD) and DYNSUB (SUBCHANFLOW).
The code-to-code comparison has demonstrated the prediction capability of NHESDYN for both steady state and transient test problems.
Finally, the modularity of the developed coupling scheme makes it possible, for example, to replace the serial SP3-transport solver by a parallel Monte Carlo one, so that the coupled system can be run fully in a parallel mode in the frame of high fidelity simulations for reactor design and safety.
Despite the fact that the proof of concept for NHESDYN was very satisfactory, there are several developments that are necessary to fully take advantage of this MPI-based coupled approach. The following investigations should be performed in the near future. Extension of the mapping scheme to deal with pin clusters or fuel assemblies is done. The radial mapping for these cases must be extended for a consistent consideration of the feedbacks of larger computational domains. Then, additional effects and feedbacks can be analysed such as cross flow and pins with different power. Extension of the coupling scheme for the analysis of boron dilution transients in PWR cores or fuel pin arrangements is done. Simulation of BWR relevant transient cases for fast (e.g., rod drop accidents) and slow transients such as pressure, coolant temperature, and coolant mass flow rate perturbations is done.
The MPI-based implementation of NHESDYN facilitates high fidelity simulations of fuel rod clusters and large problems using a very detailed spatial resolution.
Since the SYRTHES solver is not parallel, it limits the overall performance of NHESDYN. Hence NEPTUNE-CFD/SYRTHES should be replaced by commercial CFD codes numerically stable, robust, and more user friendly such as ANSYS CFX [
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.