INTRODUCTION
Everyday nuclear engineers use a variety of computer programs to carry out their work. This must be done because most nuclear reactor experiments are unsafe to accomplish. Even if the physical experiments are safe, these experiments can be expensive and time consuming, making computer simulations the most optimal solutions [1]. At times it is necessary for a nuclear engineer to run calculations on potential accident scenarios in order to better understand the conditions associated with them. This process allows the nuclear industry to predict what may happen during a nuclear accident meaning that these conditions can likely be prevented. Therefore, nuclear engineers will want to use the most accurate nuclear simulation tool to predict these accidents. The most effective nuclear simulation code will make the industry safer.
Two of the more prominent nuclear simulation codes are the TRAC RELAP Advanced Computational Engine (TRACE) and Coolant Boiling in Rod Arrays, the two fluid version (COBRA-TF or CTF) [1][2]. TRACE was developed by the NRC to audit vendor calculations for full plant safety analysis [1]. Similarly, CTF is used for safety analysis, but it analyzes a reactor at the sub-channel level. Both of these are thermal hydraulic codes that were derived using a finite volume analysis. Both of them have been used by different companies or institutions to simulate a variety of conditions including normal operating conditions (steady state conditions) and nuclear accidents conditions (transient conditions). The project being developed here is a code-to-code verification of the point kinetics models in both CTF and TRACE and a verification of TRACE’s ability to perform sub-channel analysis. The point kinetics model is relatively new to CTF and has not been completely verified. This will be done for both a steady power and transient situation. The model built will be a simplified version of a past work that used point kinetics models in both CTF and TRACE. Once the results are evaluated, any differences between the results will be explained by any differences seen in both codes’ input and conservation equations.
DESCRIPTION OF THE ACTUAL WORK
The majority of this work is a code-to-code verification to determine whether or not CTF and TRACE can accurately simulate steady and transient conditions with and without a point kinetics model. Two data sets will be analyzed, one with past work comparing CTF and TRACE and a new, simplified one. This project is still a work in process, and compilation and analysis of the modified data set is not yet complete. On the other hand, analysis of the older data set is complete with some differences observed between TRACE and CTF, especially during a transient. Preliminary research suggests that these differences are primarily caused by modeling differences between the two codes. For example, CTF models entrainment while TRACE does not [2]. Currently, work is being done to add a droplet model into TRACE, but for now it does not have one [1]. This difference in phase modeling may easily cause differences between the two codes. It also implies that CTF may be more accurate than TRACE in this aspect since it is able to model another phase that is not included in TRACE.
Base Model
This project is based off of work started in a Master’s Thesis by Faisal Raja. This thesis compared CTF and TRACE using an implemented point kinetics model of reactor power and feedback mechanisms [3]. The problem posed by this work is a quarter core PWR simulation of a 50% loss of coolant flow accident. 1.8 seconds after this accident condition is introduced in the codes, reactor power drops by 80% over a ten second period in a partial SCRAM to counter the loss of flow accident [3]. Performing this type of transient causes changes to several thermal hydraulic parameters such as pressure, coolant density, and fuel rod axial temperature.
More specifically, the reference work used both codes to compare steady state and then transient conditions. Each code was run with two variations, steady state and transient with and without the point kinetics model. The results showed a nearly identical relationship between the data for steady state with and without the point kinetics model. For example, Fig. 1 shows a comparison of the fuel rod cladding temperatures in the axial direction between CTF and TRACE during steady conditions [3].
Fig. 1 shows that there are indeed some differences between CTF and TRACE especially near the center of the axial direction. The data for CTF looks reasonable as it follows the power profile, but the curve for TRACE should not flatten out. The author of the work suggests that this has been caused by a heat structure initialization on TRACE [3]. The heat structures were not initialized in the most ideal manner to generate the most accurate results. Heat structures with power components were used in Raja’s work to represent the heat transfer elements. These were initialized in the radial direction on the walls of pipes, the structures used in the past work to represent sub-channels [3]. There is a channel component on TRACE, but the author opted not to use it. The geometries and conditions were set based on the mesh schemes of the pipes. In contrast, CTF is a sub-channel based code meaning that data can only be entered at the sub-channel level [2]. This is done with a CTF input deck. Nonetheless, the new work will run a simpler version of this data to potentially fix the issue with the heat structure initialization.
Next, Raja repeated the process with a transient. He obtained drastically different results as neither CTF nor TRACE seemed to align with one another. For example, Fig. 2 shows the results of the axial reactor core pressure for both CTF and TRACE during the loss of flow accident [3].
Fig. 2 clearly shows that there is a large difference between the codes during the transient. During steady state, this same comparison showed nearly identical results between the two codes. This means that initiating the transient has caused more noticeable differences between the codes than were seen during steady state. The issue may have been caused by the fact that the author has chosen not to model point kinetics here [3]. Showing more results of the transient with the point kinetics initiated will be done in the current project. There may also be other problems that the new research and simplification of the models may shed light on.
Current Project
The project that is currently in process takes both the TRACE and CTF models made by Raja and simplifies them. This simplification is down to one sub-channel for CTF and one pipe in TRACE. Both of these will be dimensioned in a similar manner to ensure consistency between both of them. Additionally, the transient will be slightly altered to represent the conditions of a turbine trip. The reactor type will also be changed to a BWR to see if more inconsistencies arise. Moreover, the mesh used on TRACE will be altered to mirror a more fine calculation which will likely improve the alignment of TRACE and CTF. If time allows, the pipe component on TRACE will be changed to a channel. Doing so may improve TRACE results during a transient.
Preliminary Results
The only way to find out whether or not the codes act differently during steady and transient conditions is to model them and compare their results. The work shown earlier in this report by Raja is just the base model used to generate new CTF and TRACE models. Raja’s model does imply that there are some differences between the codes, but the new models will ultimately prove code-to-code verification. Furthermore, the new project will verify the point kinetics models in CTF and TRACE and TRACE’s ability to do sub-channel analysis.
Once the new models are built and if significant differences are seen, evaluating the codes at the mathematical level may give reasons for the differences. In order to accomplish this, the set of conservation equations used by both codes are heavily analyzed. In the main report, all of the equations used by CTF and TRACE are listed with their individual parts explained. The differences start to arise in the amount of equations each code uses. CTF uses a set of nine field equations split into three groups to represent conservation of mass, momentum, and energy. Each set of conservation equations is divided into three phases, liquid, vapor, and dispersed liquid (liquid phase with vapor bubbles intermittent) [2]. Right away this yields one reason why TRACE results to not match those of CTF. TRACE only uses the Two-Fluid Model that only includes six field equations and two phases of matter. TRACE does not model the dispersed phase, leading to slightly different results [1]. This implies that CTF may be more accurate than TRACE in modeling transients due to no droplet model in TRACE at this time.
There are some differences in the actual input of data that may impact how CTF and TRACE interpret results. For example, CTF is a sub-channel based code meaning that all data is input into sub-channels. A sub-channel is defined as the smallest flow area bounded by a combination of fuel rods [4]. The sub-channels used in this project are interior sub-channels meaning that they are surrounded by fuel rods. This means that thermal hydraulic data is entered onto CTF for sub-channel parameters only. In contrast, data was entered by Raja into TRACE into pipes which are slightly different than sub-channels [3]. TRACE has the ability to model any reactor component at the holistic level, including pipes. Furthermore, mesh nodes are input whenever necessary, such as when adding heat structures to the pipe walls [1]. This project could have been done as a single fuel rod or channel component in TRACE, but pipes with breaks and fills for boundary conditions provide were used. The added capability of modeling nearly all reactor components rather than only sub-channels means that TRACE can likely simulate data at a holistic level more accurately than CTF. However, since this project has been simplified with sub-channels, CTF may be better, hence explaining the differences observed during a transient.
Similarly, there are also structural differences between TRACE and CTF. For example, CTF is modeling the spacer grids within the reactor core while TRACE does not in the reference material used [3]. However, one can add spacer grids to TRACE. Spacer grids were not used because pipes were used in TRACE to try to replicate CTF sub-channels. To model spacer grids with pipes, loss coefficients are input where appropriate along the length of the pipes [3]. This slight difference is likely the cause between TRACE and CTF not aligning during a transient. Overall, any problems with structural differences between the codes can likely be fixed by changing the mesh scheme used in both of the codes. Additionally, the new project will include both a pipe and channel model on TRACE. Providing a channel model on TRACE may align its results more closely to those of CTF.
Conclusions
At this time it can be concluded from the initial analysis that the differences seen with the output of both CTF and TRACE are caused by internal differences in each of the codes. The main differences are likely caused by the codes’ equations and their modeling properties. This is explained in detail in the preliminary results section. Furthermore, a modified model that is based off of Raja’s data is now being implemented into both CTF and TRACE. More specifically, the point kinetics model of both CTF and TRACE along with TRACE’s ability to do sub-channel analysis are being verified. The data of the new project will be much simpler than the previous work by only implementing one sub-channel on CTF and one pipe on TRACE. This will allow for a more careful treatment of finite volume mesh discretization. This also means that more testing can be done to the geometry or mesh discretization since fewer channels are being modeled. Overall, it is expected that these new CTF and TRACE results will be closer to one another; however there may be differences that will need to be explained.
REFERENCES
- J. WATSON, “Power Plant Simulation,” Penn State University (2014).
- M. Avramova, R. SALKO, “CTF – A Thermal-Hydraulic Subchannel Code for LWRs Transient Analyses,” RDFMG MNE, Penn State University (2014).
- F. RAJA, “Development and Implementation of Point Kinetics and Associated Models in COBRA-TF,” Penn State University (2011).
- S. KIM, “Nuclear Power Reactor Systems: Definitions of Nuclear Engineering Terms,” Penn State University (2015).