• METHODOLOGY
• REPAS
• VALIDATION

ABSTRACT
The passive safety systems base their operation on natural forces (e.g. gravity, gas expansion) that can be consider always reliable; anyway they may fail their mission because of the change of the boundary conditions (e.g. fouling in the pipes, presence of un-condensable gases etc.) that reduce their reliability value to less than one.
Different methodologies have been proposed (e.g. REPAS/RMPS, APSRA) with the aim to evaluate the reliability of the passive systems based on the natural circulation phenomenon to be adopted in the PSA safety study of nuclear power plants.
In this paper the result of the activity aimed at validating the calculation of the reliability applied to an experimental facility is described. The natural circulation loop simulates a passive system with a fixed reliability experimentally obtained that has to be compared with the calculated one.
This activity has been performed in the framework of the IAEA-CRPI31018 titled “Development of Methodologies for the Assessment of Passive Safety System Performance in Advanced Reactors”.
REPAS/RMPS METHODOLOGY
The REPAS constitutes a procedure aiming at the evaluation of the TH-R (thermal-hydraulic reliability) of a passive system.
The general objective of REPAS is to characterize in an analytical way the performance of a passive system in order to increase the confidence toward its operation, to compare performances of active and passive systems and performances of different passive systems. Therefore, the methodology may provide numerical values that can be used in more complex safety assessment study. Furthermore, the methodology can be used to optimize a passive system, though not all the aspects of an optimization process (e.g. the cost of an assigned component or system solution) are taken into account.
The methodology can be subdivided in the following main steps :
Characterization of design/operational status of the system (identification of the mission of the system and of the relevant parameters connected with the TH phenomenon: design and critical parameters);
Definition of nominal values, range of variation and assigned probability distributions to design and critical parameters;
Definition of failure criteria for the system performance (starting from the knowledge of the system mission and the identification of the accident scenario and allowing the definition of design targets for passive system); the failure criteria are established as single targets (e.g., the system shall deliver a specific quantity of liquid within a fixed time) or as a function of time targets or integral values over a mission time (e.g., the system shall reject at least a mean value of thermal power all along the system actuation); in some cases, it can be better to define a global Failure Criterion (FC) of the complete system instead of a specific criterion concerning the passive system; for instance, the FC can be based on the maximal clad temperature during a specified period; in this case, it is necessary to model the complete system and not only the passive system,
Detailed code modelling; once the system mission, accident scenario, and FC are established, a system model has to be developed by means of a best- estimate TH code (e.g., RELAP5);
Direct Monte Carlo simulation applied to TH code; it involves the propagation of the uncertain selected parameters through the considered TH code obtaining a model response (i.e., output variable) which allows, by means of statistic methods, to estimate the probability of failure of the passive function;
Quantitative reliability evaluation.
REPAS methodology was embedded in the Reliability Methods for Passive Safety (RMPS) methodology, developed within the framework of a project called RMPS functions, under the European 5th Framework program.

EXPERIMENTAL FACILITY
The test facility selected for the validation of REPAS methodology is a rectangular shaped loop, where the natural circulation can be induced. The heat source is placed at the bottom horizontal tube and the heat sink (the cooler) on the top horizontal tube.
The two vertical tubes were insulated by means of an Armaflex® layer and can be considered adiabatic. At the heating section the flux is imposed, while at the cooling section the heat sink temperature (H.S. Temp.) is imposed. The vertical tubes and the four bends are made of stainless steel AISI 304, while both the horizontal tubes are made of copper (99.9%). The loop internal diameter D is 30 mm and it is constant over the entire loop length, the thickness is 1.3 mm; the loop height H is 0.988 m and the total length Lt, measured on the tube axis, is 4.100 m, with a Lt/D ratio of 136.7.
The heater is made by an electrical nicromel wire rolled uniformly around the copper tube, connected to a programmable DC power supply (Sorensen DHP 150-33). On the upper part of the loop a coaxial cylindrical heat exchanger is connected to a cryostat (Haake KT90), which is able to maintain constant temperature of -20°C with cooling power of 1 kW, whereas it can remove up to 2.5 kW in a temperature range between -10°C and +30°C. The coolant which flows throw the annulus is a mixture of 50% of water and 50% of glycol, with freezing point at -40°C. An external pump is needed in order to reach a high coolant flow rate (0.60kg/s), which minimizes (<1K) the temperature difference between inlet and outlet section of the heat exchanger (constant temperature along the heat sink). Both heater and cooler were thoroughly insulated. An open expansion tank connected to the top of the loop allows the working fluid to expand as consequence of temperature growing up, keeping atmospheric pressure inside the loop.
All the calibrated thermocouples (±0.1 K) used for this apparatus are shielded T-type with external diameter of 0.5 mm. Twenty thermocouples measure the fluid temperature in 4 sections (A to D) placed 142 mm far from the axis of the closest horizontal tube. In each section one thermocouple is located on the vertical pipe axis, while the other 4 are radially placed at a distance of half radius (7.5 mm) from the tube wall and distributed one each 90°. The temperatures at the inlet and outlet section of the secondary flow of the heat exchanger are evaluated by two thermocouples (tc.27 and 28), and an auxiliary thermocouple checks the internal temperature of the cryostat as well.
Experimental data were acquired and stored by mean of a high-speed data acquisition system by National Instruments (PCI-1200, SCXI-1000, SCXI-1102, SCXI-1303). Acquisition time interval was 1 second and each data was averaged on 100 readings per second.
This facility is sited at University of Genova (Italy) and it is managed by Prof. Misale and Prof. Devia

EXPERIMENTAL DATA
Fluid temperatures were averaged at the four thermocouple sections in order to compensate three-dimensional effects. The assumption of adiabatic legs is confirmed by the same temperature reading at the top and at the bottom measurement section of each leg.
By analyzing the temperature differences across heater and cooler it is possible to recognize different flow regimes.
This map has been obtained from several experiments.
Attention is focused on the selected area highlighted with the red dashed rectangle corresponding to the region identified by 2 kW heater power and heat sink temperature ranging from 10 to 20 °C, because in this case there are several transitions from stable to instable state.
The stable natural circulation has been considered when the fluid keeps the same direction (does not matter whether clockwise or counter clockwise) during the test; unstable in case the direction of the fluid oscillates during the experiments.
The difference trend of the mean of the temperatures measured at the thermocouples in the upper right and left is the chosen criterion in order to affirm if the system is stable or not (Coordinate Research Project’s meeting-IAEA- Vienna 2011).
The experiments, object of the study, were performed in order to single out the threshold between stable and unstable thermo-hydraulic behaviour with a power of 2.0 kW varying the H.S. Temperature (heat-sink). The list of the experiments executed in the L2 loop is reported in figure 2. The power at the heat sink is fixed at 2.0 kW, while the temperature at the heat sink has been changed in the range 4-18 °C.
From the experiments has been observed that the transition between unstable/stable natural circulation has not a fixed temperature of the heat sink (once the power at the heat source is fixed) but there is an interval of temperature at the heat sink where the facility shows randomly stable/unstable behaviour; increasing the temperature at the heat sink from the lowest one 4°C, the loop shows a greater tendency to stabilize.

REPAS APPLICATION TO THE LOOP L2
REPAS methodology is applied to the loop L2 in order to compare the reliability experimentally estimated and numerically simulated (percentage of the number of stable cases).
The loop behavior has been simulated by mean the best estimate code Relap5 mod3.3.
Several sensitivities analysis and engineering judgement have allowed the identification of the parameters that have mainly the natural circulation behavior, that can cause the failure of the natural circulation varying around their nominal value:
Cooler “Inlet temperature”;
Thickness of the tubes;
Power at heat source.
The next step is the definition of the pdf (probability distribution function) for each of the parameters identified as critical for the analyzed system.
H.S. TEMPERATURE is the only parameter measured during the experiment.
A preliminary analysis on the H.S. Temperature data, is performed in order to remove the transitional zone, identified in the first interval of five thousand seconds for each H.S. Temperature; at this point has been observed that the Gaussian distribution fits the experimental data.
The pdf of the thickness of the tubes and the power at heat source has been modeled using Gaussian distribution by mean engineering judgement; the choice is justified by the fact that the Gaussian function represents well natural phenomena; to represent the variability of the thickness has been hypothesized a range of variation considering the standard manufacturing tolerances for the two different materials of the tubes (in the rectangular loop the vertical tubes and the four bends are made of stainless steel AISI 304, while both the horizontal tubes are made of COPPER), and the technical characteristics of the component to represent the variability of the heat source power.
In this step, DOE method (2^K factorial design) has been applied in order to assign importance to the selected parameters; variance is chosen to describe the objective function and is calculated on the difference between the trend in the time of T (A) (average value of temperature at the thermo-couples in the upper right) and T (D) (average value of temperature at the thermo-couples in the upper left); low values refer to the stability of the system.
At this point, for each of the 8 temperatures of the heat sink identified, a sample size of 100 has been selected. This sample size has been obtained by mean the Wilks’ formula that gives the proper number of independent observations of the random output, minimizing the number of calculations that characterize the system performance.
At this point 100 sets of triples (H.S. temperature, Tube thickness, Power of the heat source) of parameters have been generated by mean Monte Carlo simulation taking into account the pdf of each parameter.
Each one of the identified set has been implemented in the RELAP5 mod3.3 input deck and the calculation has been performed. Totally 800 code results have been obtained.

COMPARISON OF REPAS RESULTS WITH EXPERIMENTAL RESULTS

The main difficulty in the application of the REPAS/RMPS methodology, in this activity, has been to identify an appropriate Performance Indicator (PI) that is able to characterize the entire system behavior using just one value.
The steps to compute the PI can be summarized:
To select a reference case; namely the limit case from stable and unstable behaviors;
For the reference case selected to calculate the absolute value of the mean of the difference between the temperatures at point A and D;
To calculate the integral of the absolute value of the difference T (A)-T (D) minus the value calculated at item 2 in the last 3000 sec. The system is considered stable if it is stable at least in that range (Z ref);
The triple 100 at H.S. temperature of 18 °C has been chosen as reference case (stable case).
To repeat the step 2 and step 3 for each one sensitivity (Zi);
To computed PI for each set point Heat Sink temperature with the formula:

〖PI〗_i= Z_i/Z_ref
We realized that for a PI>1 the system can be considered unstable, instead for 0<PI<1 stable.
A probability value of each set is associated with PI value to obtain the curves of merit (PI=f(log(p)); it is calculated simply multiplying the probability of each parameter and then its logarithm has been plotted; being a continue distribution it is thought as the probability that the distribution assumes values greater (absolute value) than the random generated number.
The same logic has been followed for the experiments; in this case, to associate a probability value to the PI, only two levels for each H.S. temperature have been selected: the one with higher probability (correspondent to the mean value of the Gaussian curve) and the one with lower probability (in the tail of the Gaussian curve).
It can be noted that the curves of merit demonstrate that the stability of the system increases with the increase of the temperature of the Heat Sink, according to experimental data, and the capability of the methodology to reproduce stable and instable cases at the different temperatures, therefore the experiments.

A further graphical confirmation is the capability of the methodology of reproducing stable and instable cases at the different temperatures ; the best simulation has the most similar values of mean and variance compared to those of the experiments, calculated on five segments of the whole period.

However, it’s important to underline that it’s not basic to have exclusively a very small error between RELAP and experimental results to judge the goodness of the methodology; certainly it is a factor considered, but the criticality is associated also to the capability of stabilizing in “the same” time as experiment.
Plotting the number of stabilizations in function of the stabilization’s times, it’s possible to conclude that the stabilization’s time of each experiment is reproduced by the most number of simulations.
It’s interesting, at last, to make a frequency analysis in order to demonstrate that exist a clustering between the simulations at the different H.S. temperatures; in this way it’s formally possible to say that each experiment at a single H.S. temperature has an associated simulation at the same H.S. temperature.
The objective has been performed making the Fast Fourier Transform (fft) on segments of 500 seconds on the whole duration of each simulation, obtaining the waterfall of the fft; this choice is justified by the absence of stationarity; then, to facilitate comprehension and reading of these graphics, z axis has been represented on the xy map (pcolor view) with a color scale from blue, which refers to the lower values of amplitude, to red that refers to the higher value of amplitude.
Frequency analysis allows concluding that:
Stability occurs when low values of amplitude (blu color) persist until the end of the whole period at all frequencies;
Stabilization “way” is different for each H.S. temperature when a transitional zone is present: it means that several couples of amplitudes-frequencies occur before stabilization;
Maximum values of amplitude (red color) are typical of low values of H.S. temperature for the unstable cases (the number of sets characterized by the presence of red color decreases with the increase of H.S. temperature);
It is possible clustering unstable case at the different H.S. temperatures observing that higher values of amplitude occur at several values of frequency and time and that the simulations have a “greater tendency” to stabilize with the increase of H.S. temperature.
It could be interesting in the future for other applications, clustering the eight H.S. temperatures linking up numerically all the typical values of the amplitude-frequency couples in the time.

CONCLUSION
The activity described in this paper deals with the first attempt of validation of the REPAS/RMPS methodology based on available experimental data.
The main concern is connected to the limited amount of experimental data that are not sufficient to perform a rigorous statistical analysis; e.g. for some heat sink temperatures just one value is available.
Moreover due to the simple hardware configuration of the L2 loop, the system is intrinsically unstable and it is difficult to simulate its behavior.
Based on the results of this work is not possible to conclude about the validation of the REPAS/RMPS methodology, but in some steps of the analysis connected to the capability of RELAP5 to simulate the loop behavior and to provide an indication on the trend towards the system stabilization at higher H.S. temperature.
Thus, it needs to repeat the experiments following a statistical procedure trying to make a connection with the simulations; it means to found a number of experiments statistically significant.
The point of start is to consider that, generally, the variable that represents a general phenomenon (its mean) varies with a Gaussian function making n experiments; it means that the histogram of the experimental means on n experiments has a Gaussian shape; the mean of this distribution is associated with the theoretical mean of the phenomenon.
It is reasonable to think that the analyzed phenomenon can be descripted by the variance of the exit temperature: low values indicate stability and high values indicate instability.
The number of the experiments will has to be sufficient to “include” its variability.

At this point it’s possible to apply this procedure for the eight H.S. temperatures and to choose only a value (the max) of the eight founded or to consider different values of n for the different H.S. temperatures.
Matlab and R software have been used to write the programs.