System codes along with necessary nodalizations are valuable tools for thermal hydraulic safety analysis. Qualifying both codes and nodalizations is an essential step prior to their use in any significant study involving code calculations. Since most existing experimental data come from tests performed on the small scale, any qualification process must therefore address scale considerations. This paper describes the methodology developed at the Technical University of Catalonia in order to contribute to the qualification of Nuclear Power Plant nodalizations by means of scale disquisitions. The techniques that are presented include the so-called
In September 1988 the USNRC approved a revision of the ECCS rule (10 CFR part 50) by which BEPU calculations could be used for licensing. Likewise, CSAU methodology (Figure
CSAU methodology.
One of the CSAU methodology requirements (see step 9 in Figure the design of a test facility which “cannot completely satisfy all the scaling requirements. Thus scaling distortions are unavoidable (…).” [ intrinsic limitations of thermalhydraulic codes, namely, the simulation of two-phase flow regime transitions and the impossibility of qualifying their closure equations under transient and nondeveloped flow conditions [
Along these lines, several scaling analysis philosophies have been developed (H2TS [
Even though the main code scaling techniques presented in this paper could be perfectly integrated within the “roadmap to scaling” concept presented in [
This paper, along with that of [
Computational analysis and NPP nodalizations are both a widely used and well-developed application in nuclear engineering not limited to licensing. Most of the tasks, related to the support to plant operation and control, are extensively discussed in two different IAEA safety reports [ TH analysis of PSA sequences, mainly those of Level 1. Analysis of actual transients. NPP start-up test analysis. EOP validation analysis. Transient analysis for training support. Design modifications. Improvement of plant availability.
Results presented by the UPC in [
As regards scaling, plant-scaled calculations (called
Primary pressure (picture from [
U-tube collapsed liquid level (picture from [
UPC scaling-up methodology follows the general guideline given in [
There are two main factors that affect scaling up of ITF posttest simulations: the scaling-down criterion used for the design of the ITF, the differences of configuration between the ITF and the NPP.
In order to analyze both, the UPC scaling-up methodology uses two approaches, “scaled-up nodalizations” and “hybrid nodalizations.” It is crucial that they are not confused with the approaches previously presented. Sections
The “UPC scaling-up methodology” is shown in Figure To identify a specific scenario for qualifying NPP nodalizations with ITF tests that reproduces its related phenomena. A validation matrix must be defined in order to relate the ITF tests with the particular phenomena to be qualified in the selected scenario “ To validate ITF nodalizations and ITF tests selected in the NPP validation matrix “ To perform a preliminary plant scaled calculation with the NPP nodalization “ To analyze and establish the scaling and design effects in the simulation results by using generated scaled-up and hybrid nodalizations To perform an expert judgment by comparing the results of step (C) combined with conclusions of step (D)
UPC scaling-up methodology.
Each of the steps of the “UPC scaling-up methodology” is explained in more detail in the following subsections. The results that are shown are from [
The initial step of the UPC scaling-up methodology requires the analyst to decide the type of scenario for which he wants to validate the NPP nodalization. Once the scenario has been selected, three main features have to be analyzed: the relevant thermal-hydraulic phenomena occurring in the selected scenario, the design of the ITFs employed in the analysis, the choice of ITF experiments.
The aim is that the analyst finds ITFs with similar design to his NPP nodalization in which selected tests include the TH phenomena related to the specific scenario. In that sense, the ITF system description reports, ITF test reports, and, most of all, CSNI code validation matrices [
Once the TH phenomena have been decided upon and the most convenient ITFs have been chosen, an “NPP scenario validation matrix” must be defined in order to ensure which phenomena can be tested by system codes. In Table
NPP SBLOCA/IBLOCA validation matrix.
Test phenomena | Counterpart tests | Counterpart tests | ROSA 2 test 1 | ||
---|---|---|---|---|---|
PKL III G7.1 | ROSA 2 Test 3 | BL-34 (LOBI) | SB-CL-21 (LSTF) | ||
1-phase natural circulation | X | O | |||
2-phase natural circulation | X | X | X | O | |
Reflux and condensation | X | X | X | O | |
Asymmetric loop behavior | X | O | |||
Break flow | X | X | X | O | X |
Phase separation without mixture level formation | X | X | O | O | X |
Mixture level and entrainment on SG secondary side | X | X | X | O | |
Core mixture level | X | X | X | O | X |
Stratification in horizontal pipes | X | X | X | O | X |
Phase separation T-junction and effect on break flow | X | X | O | X | |
ECC-mixing and condensation | X | X | X | O | X |
Loop seal clearing | X | X | X | ||
Pool formation in UP/CCFL | O | X | |||
Core-wide void and flow distribution | X | X | O | X | |
Heat transfer in covered core | X | X | X | O | X |
Heat transfer in preuncovered core | X | X | X | O | X |
Heat transfer on SG primary side | X | X | X | O | X |
Heat transfer on SG secondary side | X | X | O | O | X |
Pressurizer thermalhydraulics | X | ||||
Surgeline hydraulics | X | ||||
1-phase 2-phase pumps behavior | O | ||||
Structural heat and heat losses | X | X | X | O | X |
Noncondensable gas effect | |||||
Boron mixing transport | |||||
CET versus PCT relationship | X | X |
X: totally reproduced, O: partially reproduced.
When ITF tests are chosen, it is important to pay attention to counterpart tests (tests with identical boundary conditions performed at facilities at different scales) because they allow to check, for different scales and designs, if the codes and the ITFs nodalizations can reproduce the same phenomena. This will not ensure that these phenomena can be extrapolated to the NPP scale (as already mentioned, this point is not within the scope of this methodology), but it will be very effective for translating ITF modeling experience to NPP nodalization qualification because the analyst can evaluate whether the same modeling criteria have been used for different scales and designs. In the example of Table
In the second step, the analyst should perform posttest analyses of the ITF experiments chosen in the “NPP scenario validation matrix.” The aim of this step is to ensure the quality of the results and to draw conclusions on code modeling. The work of the analyst should therefore be focused on two features: qualifying the ITF nodalizations for several tests beyond those selected in the validation matrix, assuring the robustness of the nodalization to minimize user effect and compensating errors.
About these points, some papers have been presented during the last few years [
Once the ITF nodalization has been qualified and the required tests of the validation matrix have been simulated, phenomena that have been validated for at least two facilities at different scales and designs can be used for qualifying NPP nodalizations. The modeling guidelines derived in both cases need to be consistent. To achieve this, expert judgment will be essential. If counterpart tests have been validated for the same phenomena with the same modeling conclusions, a plant-scaled calculation and scaling and design effect analyses will be performed for the counterpart test in which the design of the ITF is closest to the NPP nodalization.
In [
PKL CET versus PCT curve.
LSTF CET versus PCT curves.
Both nodalizations were previously qualified with the ROSA posttest 3-1 ([
A plant-scaled calculation is a system code simulation in which defined ITF test conditions are scaled up to an NPP nodalization in order to reproduce the same scenario. It allows the behavior of the NPP and ITF nodalizations to be compared under the same conditions in order to check the capabilities of the NPP nodalization and the improvement of nodalization when needed.
In a plant-scaled calculation, experimental conditions and safety actions are adapted without modifying the NPP nodalization. Special care is taken in order to prevent overdetermined systems. The most significant parameters are steady-state conditions, break size, break unit and containment, core power decay curve (if it is experimentally imposed), pump coastdown curves (if they are experimentally imposed), scram set point, isolation set points, ECCS’s set points, ECCS injection curves (pressure versus mass flow curves), blow down set points, specifications of the blow down valves (area, opening and closing ratios), feed water controller, PZR heater controllers (if this is the case).
The scaling-up adjustment is performed by following the scaling criterion and using scaling factors recalculated for the specific NPP nodalization. These are usually different from those used in the ITF design (related to the ITF reference plant). As explained in [ time reducing or linear scaling, time preserving or volume scaling, idealized time preserving.
A greater number of ITF tests have been performed in facilities that have been designed using the power-to-volume scaling criterion, which encompasses time preserving scaling. The following scaling-up techniques will be related to the power-to-volume scaling. A further explanation of this criterion can be found in Section
One of the important points of this activity is the calculation of the NPP scaling factor which was commonly computed as the ratio between the primary liquid volume of the NPP and the ITF. This criterion should be revised given that several NPP components (PZR, SG plenums, pumps…) can differ significantly in volume with those of the ITF reference plant and is due to dissimilar design. The authors of the present paper suggest checking which components and parameters have a local scaling factor close to the reference ITF volumetric factor in the ITF system description report. Subsequently the analyst should calculate the scaling factor as an average of the same local factors applied to the chosen NPP. Normally core power, core volume, and total number of U-tubes (for PWR) are a good reference.
As regards the “UPC scaling-up methodology,” a plant-scaled calculation is a unique calculation with two aims: to check the applicability of the ITF test in the NPP nodalization for phenomena that have been validated in posttest analyses, being a reference for justifying as an expert judgment those discrepancies that appear in comparison with the results of the posttest analysis. Therefore, scaled-up and hybrid nodalizations explained in Sections
In the example of Figure
Plant-scaled calculation is unique and cannot be tuned during scaling and design effect analyses. Only if the expert judgment considers that the NPP must be improved should a second calculation be carried out in order to qualify the NPP nodalization improvements.
This step shows how the scaling criterion affects the simulation of phenomena validated in the ITF posttest analyses. Scaled-up nodalizations are developed at this level by comparing ITF posttest simulation with ITF scaled nodalizations that have the same size as the NPP nodalization.
Power-to-volume scaling is one of the most common methods used in ITF design. It considers that there is no interaction between different phases of the coolant. Scaling conditions result due to the application of conservation equations (mass, momentum, and energy) under some requirements and implications. Considering one directional flux along the system and normalizing all parameters with respect to its reference scale, the conservation equations applied are
If pressures, water properties, lenghts, and time are preserved (subindex
And considering that similarity has been achieved between both systems for (
This demonstration is given in greater detail in [
As flow areas change with Friction effects: as Environment heat losses and passive structure storage energy: the transversal flow surfaces will change with different scaling factors because of the hydraulic diameter, affecting the heat conduction and convection:
This implies that the ratio between passive heat losses and core heat power will change from the reference plant to the ITF thus generating scaling distortions. Froude number: as explained in [
Scaled-up nodalizations are developed by following certain scaling criterion. The UPC has developed a “Power-to-Volume Scaling Tool (PVST)” which enables RELAP5mod3 input decks to be scaled by following the power-to-volume scaling criterion. This software scales hydrodynamic components, heat structures, control system variables, general tables, and unit trips using an input scaling factor (
In order to analyze the origin of power-to-volume scaling distortions, two options have been included in the software: scaling environment and passive heat structures preserving their heat impact whatever the scale, scaling input nodalizations preserving the Froude number in horizontal components.
To analyze the scaling effect, several scaled-up nodalizations must be generated using the calculated NPP scaling factor (see Section
This step must be repeated for all the scaling distortions detected until the user achieves an idealized scaled-up nodalization in which the analyzed phenomenon is simulated in the same way as in the ITF posttest analysis.
In [ Sc-up nodalization A: a regular scaled-up nodalization, Sc-up nodalization B: a regular scaled-up nodalization preserving environment heat losses, Sc-up nodalization C: a regular scaled-up nodalization preserving environment heat losses and Froude number.
Comparison between the posttest Sc-up nodalization A and Sc-up nodalization B showed that the increasing system pressures during the reflux and condensation phase were due to a decrease in environment heat losses (see Figure
System pressures.
Break mass flow rate.
Core exit temperature.
The final result of the analysis carried out in this section is an ITF scaled-up nodalization in which scaling effects were minimized by following the established rationale. Such nodalization will be used in the next step.
In this step, the analyst must be able to justify the discrepancies that appear in a plant scaled calculation by means of the differences in design between the ITF and the NPP. In that sense, hybrid nodalizations are compared with the plant scaled calculation and the idealized scaled-up nodalization obtained from the scaling effect analyses. Some components of the NPP nodalization are copied and added to the ITF scaled-up nodalization obtained in the previous step. This allows the impact of each tested component on the simulation to be differentiated.
The work of the analyst in the design effect analyses has to be focused on two main features: to identify which components and differences in the configuration might affect the phenomena to be validated; to develop a group of hybrid nodalizations in series for detecting sources of design distortion. Each component has to be added individually to the previous hybrid nodalization in order to distinguish which components may cause a distortion of the results and which do not. Although some discrepancies could be justified by two or more combined sources of design distortion, it will not be necessary to evaluate them separately as all of them are part of the NPP nodalization. Sequential analyses reveal both the effect of each component and that of them all together.
In [ PZR (differences in scaling ratio—mass of water—and surge line height), UTs (differences in exchanging surface that could affect reflux and condensation), LSTF downcomer-to-hot leg bypass (which has an effect on water stratification in the hot leg that could modify discharge across the break), vessel passive heat structures (could alter vapor generation), vessel geometries excluding the core (PKL and LSTF vessels have different water distribution around the core as a result of a different reference plant—KWU and Westinghouse, resp.).
Core exite temperature.
Once all possible design distortion sources were listed, hybrid nodalizations were prepared for the idealized scaled-up nodalization in which scaling effects were minimized (nodalization C in Figure PKL hybrid base nodalization: Sc-up nodalization C with LSTF heat losses and LSTF Froude number, PKL hybrid A nodalization: PKL hybrid base nodalization with LSTF PZR, PKL hybrid B nodalization: PKL hybrid A nodalization with LSTF U-tubes, PKL hybrid C nodalization: PKL hybrid B nodalization with LSTF downcomer bypass, PKL hybrid D nodalization: PKL hybrid C nodalization with LSTF vessel passive heat structures, PKL hybrid E nodalization: PKL hybrid D nodalization with LSTF hydrodynamic components, LSTF vessel walls heat structures and LSTF material properties.
Results of Figure
Core exite temperature.
Core exite temperature.
Expert judgment is the final step of the “UPC scaling-up methodology.” Once the design effect analysis and ITF posttest analyses modeling have been carried out, the analyst should make a decision on whether the NPP can be considered as qualified for the studied phenomenology or whether the NPP nodalization requires improvement. Expert judgment relies on the conclusions from the design effect analysis, the NPP nodalization handbook, knowledge from ITF modeling.
Once the design effect analysis has been concluded, the user has valuable information about the NPP components that can explain observed discrepancies. When such components are identified, their specification must be thoroughly checked and the analyst must ensure that these components have been consistently modeled. In that sense, the scaling-up methodology” is used in the qualification process and continuous improvement of the nodalization.
If the specifications of an NPP component are well transcribed, the analyst, bearing in mind his ITF modeling knowhow, has to judge the significance of the modeling details of the component for the tested phenomena in the specific scenario. If after expert judgment, it is considered that a nodalization improvement is required, a second plant scaled calculation will be necessary, comparing its results with the idealized scaled-up nodalization and one new hybrid nodalization with the new component. Otherwise, it is considered that NPP nodalization is qualified for these phenomena. When all the NPP validation matrix phenomena are validated, the NPP nodalization will be qualified for plant applications and support to plant operation in the specific scenario.
It could occur that after the design effect analysis step, no distortion sources are found that could justify the tested phenomenon discrepancies. In that case, the expert judgment should conclude that the ITF test validation must be reevaluated and the code capabilities be reviewed. In that sense, it would be another evidence of the robustness of the methodology for validating and guaranteeing quality modeling. In any case, in order to avoid these conclusions and to facilitate the work of the analyst, counterpart tests with different scales and designs should be selected to the furthest extent in the NPP scenario validation matrix. These tests should be then validated for the same phenomena with consistent modeling procedures (see Section
Computational analysis and NPP nodalizations have a widely used and sound application on nuclear engineering. In that sense, the quality assurance procedures take a key role in the continuous improvement of NPP integral nodalizations. In the present paper one of the steps of the qualification methodology has been presented in order to take advantage of the modeling experience acquired from the ITF posttest analyses. Three are the pillars that support this systematic procedure: judicial selection of the experimental transients, full confidence in the quality of the ITF simulations, and simplicity in justifying discrepancies that appear between ITF- and
Two scaling techniques have been introduced in order to find out how ITF simulated transients change from ITF to NPP nodalizations: the “scaled-up nodalizations,” which allow effects of the ITF scaling-down criterion to be checked, and the “hybrid nodalizations,” which help the user to establish how design differences modify the results. The exercise of explaining discrepancies between ITF posttests and
The main concepts and guidelines have been presented along with the rationale of its usage and a representative amount of application results. The presented results are strictly those that are needed to introduce the concepts. Another paper [
Future work will be devoted to enhancing the effectiveness of the tools to a wider field of application.
Three-dimensional
Area
Associació Nuclear Ascó i Vandellós
Advanced plant experiment
Best estimate plus uncertainty
Counter current flow limitation
Core exit temperature
Code of federal regulations
Cold leg
Code scaling, applicability, and uncertainty
Consejo de Seguridad Nuclear
Committee on the Safety of Nuclear Installations
Pipe diameter
Emergency core coolant systems
Emergency operation procedures
Fractional scaling analysis
Gravitational acceleration
Heat transfer coefficient
International Atomic Energy Agency
Intermediate loss-of-coolant accident
Integral test facility
Thermal conductivity
Friction factor
Scaling factor
Kraftwerk Union
Length
LWR off-normal behaviour investigation
Loss-of-coolant accident
Large scale test facility
Nuclear Energy Agency
Nuclear power plant
Organization for Economic Cooperation and Development
Pressure
Peak cladding temperature
Primärkreislauf
Probabilistic safety assessment
Purdue University Multidimensional Integral Test Assembly Facility
Pressurizer
Heat flux
Volumetric flow rate
Rig of safety assessment
Small break loss-of-coolant accident
Time
Temperature
Thermal hydraulics
Universitat Politècnica de Catalunya
United States Nuclear Regulatory Commission
Velocity
Volume
Water-Cooled Water-Moderated Power Reactor
Mass flow rate.
Density
Perimeter
Power.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This paper contains findings that were produced within the OECD-NEA ROSA2 and OECD-NEA PKL2 projects. The authors are grateful to the management board of both projects for their consent to this publication. The authors also want to thank Spanish Safety Council that has partially funded this research.