Modelling of system behaviour

Various NC systems are relevant within the nuclear technology. As already mentioned in the present report, various computational tools have been applied to the prediction of NC features of those systems. The complexity level of the concerned tools largely varies depending upon

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the simulated system and the objectives of the simulation. Simple analytical models solving approximate equations resembling the fundamental principles of the physics making reference to systems assumed in steady state conditions up to sophisticate codes including numerical solutions of partial differential equations in the three-dimensional space and in transient conditions can be distinguished.

In the following discussion, attention is focused on the application of thermal-hydraulic system codes. Under this category codes like APROS, ATHLET, CATHARE, RELAP5 and TRAC are included, all based upon the solution of a main system of six partial differential equations. Two main fields, one per each of the two phases liquid and steam are considered and coupling is available with the solution of the conduction heat transfer equations within solids interfaced with the fluid phases. A one-dimensional solution for the characteristics of the fluid is achieved in the direction of the fluid motion in time dependent conditions. It should be emphasized that more sophisticate models are also available including three-dimensional solutions and multi-field approaches in two and multiphase fluids. However the present qualification level of those sophisticated computational tools is questionable as well as their actual need in the design or in the safety applications.

The mentioned codes have been applied to the simulation of data measured in experimental facilities of different dimensions and complexity as well to the prediction of the NC performance of existing nuclear power plants and of advanced reactor concepts. The discussion is limited hereafter to the main findings from the applications of the system codes to the simulation of NC in Integral Test Facilities (ITF) that are simulators of PWR, BWR and WWER-440. Mention is made of the scaling problem and of the uncertainty expected in the predictions of NC in NPP.

3.4.1. NC simulation in PWR and WWER-440 ITF

NC experiments have been conducted in all ITF for characterizing the loop features and for constituting databases suitable for code assessment. NC experiments have been conducted in the Lobi, Pkl, Bethsy Pmk and Pactel facilities, the first three simulators of PWR and the last two simulators of WWER-440. In relation to all the ITF, NC experiments with decreasing mass inventories of the primary coolant system have been carried out. The electrical power supplied to the core simulator corresponded to the decay power and ranged between 1.5% and 5%, roughly of the nominal core power. In these situations the NC scenario can be characterized by a diagram showing the core power as a function of the primary system mass inventory.

The applications of system codes have been of help for interpreting the experimental scenarios, for optimizing the features of the nodalizations and for characterizing the code capabilities. A list of significant achievements is given below together with references where details of the analyses can be found.

a) The codes have been used to distinguish five main NC flow patterns depending upon the value of the mass inventory of the primary loop (see also Ref. [7]):

¾ Single phase NC with no void in the primary system excluding the pressurizer and the upper head;

¾ Stable co-current two-phase NC with mass flow rate increasing when decreasing primary system fluid inventory;

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¾ Unstable two-phase NC and occurrence of siphon condensation;

¾ Stable reflux condensation with liquid flowing counter-current to steam in the hot legs:

flow-rate is sufficient to remove core power till loop mass inventory achieves values as low as 30-40% of the nominal values;

¾ Natural circulation with part of core rods in dry-out condition not favorable from the current technological and safety point of view.

b) The code has been used for characterizing the oscillations (third dashed item in the list above), showing the different role of the counter-current flow limitation (CCFL) at the entrance of the U-tubes, the siphon effect and the steam condensation both in the rising part of the tubes. The flow reversal and the different behaviour of parallel groups of U-tubes could also be observed by the help of the code, Ref. [8].

c) Different codes used by different European organizations have been applied to the comparative analysis of the A2-77 experiment carried out in Lobi facility. Capabilities of the codes were characterized as well as the influence upon the results that should be expected owing to the code-user effect, Ref. [9]. Deficiencies were observed in the predictions of pressure drops at low value of the Reynolds number.

d) The application to the study of NC in WWER-440 showed the code capability in predicting the flow stagnation and the consequent rise in system pressure caused by the loop sealing present in the hot leg of this reactor type, Ref. [10]. Clearing of loop seal occurs before dangerous situation for the system are reached and is also predicted by the code.

e) The code has been used to determine the maximum core power at which the PWR systems or PWR simulators can be operated in NC keeping sub-cooled the core. The limit was found close to 10% of the core nominal power, Ref. [11]. Higher limits were found fixing different thresholds for the system operation.

f) The code has been successfully used in predicting NC phenomena measured in systems that are relevant to the AP-600, including NC across the PRHR (pressurized residual heat removal), and the CMT (core make-up tank) systems, Refs [12] and [13].

3.4.2. NC simulation in BWR ITF and NPP

NC experiments have also been performed in ITF that simulate the BWR system performance.

Relevant NC data have also been recorded from the operation of BWR NPP and used for benchmarking system code performance. The flow map for the operation of BWR systems shows the core power as a function of the core flow rate. A parabola like curve in the considered plane is derived from experiments and confirmed from code applications. A steep power increase up to about 50% of nominal core power can be observed from the mentioned diagram when core flow rate achieves roughly 30% of the its nominal value (i.e. value at 100% core power). This implies that the BWR systems can operate at 50% power in NC.

However, in these conditions the system is prone to instabilities, identified in the literature as density wave oscillations (DWO). A wide literature exists related to the DWO that can be considered as a NC phenomenon. A state-of-the-art report on this topic has been recently issued by OECD/CSNI, Ref. [14].

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Lesson learned from the application of system codes to BWR related NC experimental situations are summarized in the following, again including references where details for the analyses can be found.

(a) The curve core power versus core flow rate in NC conditions predictable by system codes is close to the experimental values in relevant ITF, Ref. [15]. The code is also capable of predicting the same curve related to the BWR operation. The capability in predicting the NC flow map in BWR is not affected by the scaling of the system.

(b) The code has been successfully used in predicting the NC measured between core and a heat exchanger installed in a pool outside the main vessel in a configuration that is typical for the SBWR equipped with the IC (isolation condenser), Ref. [16].

(c) The code has capability to predict DWO occurring recorded during the NC in typical BWR conditions, Ref. [17]. However, the prediction is largely affected by the user choices.

3.4.3. Final remarks

The system codes have been widely applied to the prediction of NC in situations relevant to PWR and BWR conditions. The scaling problem has been addressed by demonstrating that the accuracy of the prediction is not affected by the geometric dimensions of the involved systems. No major deficiencies have been detected. It can be concluded that codes are suitable in predicting NC phenomena in conditions relevant to the present generation reactors. An exception is constituted by the predictive capability of DWO. In this case the user may substantially affect the predictive capabilities.

The above conclusions can be extended to a number of systems that are part of the design of advanced reactors like the PRHR and the CMT in the case of the AP-600 and the IC in the case of the SBWR, in relation to which a suitable experimental database exists. However, in this last case, more rigorous procedures may be established where:

¾ Precision requirements are established (e.g. core flow rate in NC must be predicted with an error of 3%);

¾ Measurements are shown to comply with the fixed error-threshold;

¾ Accuracy of the predictions, adopting well established input decks, is shown to lie within established error bands.

¾ Needs for experiments and for development of new models are derived from deficiencies found from the above process.