2017 Water Reactor Fuel Performance Meeting September 10 (Sun) ~ 14 (Thu), 2017 Ramada Plaza Jeju Jeju Island, Korea

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1 ACE/ATRIUM 11 Mechanistic Critical Power Correlation for AREVA NP s Advanced Fuel Assembly Design K. Greene 1, J. Kronenberg 2, R. Graebert 2 1 Affiliation Information: 2101 Horn Rapids Road, Richland, WA, 99338, USA, Kenneth.Greene@areva.com 2 Affiliation Information: Paul-Gossen-Str. 100, Erlangen, Germany, Juris.Kronenberg@areva.com; Ruediger.Graebert@areva.com ABSTRACT: ATRIUM 11 * is AREVA NP s new fuel assembly design for BWR reactors. AREVA NP s pioneer work on the development of an 11x11 fuel assembly resulted in the delivery of the first lead fuel assemblies (LFA) in Meanwhile, 5 LFA projects in Europe and in the U.S. are in progress demonstrating the expected excellent operational behavior. All defined goals for the development of ATRIUM 11 fuel assembly have been achieved, e.g.: - fuel reliability due to high pellet-cladding-interaction resistance and robust defense against debris, - operational flexibility due to low linear heat generation rate, - reduced fuel cycle costs due to balanced moderator-to-fuel distribution, - improved TH stability (especially for BWR3 to BWR6 plants) and excellent Dry-out performance. Thermal-hydraulic performance of the ATRIUM 11 design has been tested in AREVA NP s thermal-hydraulics loop KATHY located in Karlstein, Germany. The KATHY loop provides the ability to perform pressure drop, critical power, transient, and stability measurements with BWR test bundles in prototypical full scale geometry. These design verification measurements result in characterization of the fuel assemblies, validation of AREVA NP s steady-state and transient codes, and importantly, the development and validation of the licensing critical power correlation. A mechanistic critical power correlation is applied to the ATRIUM 11 fuel assembly design. The ACE/ATRIUM 11 correlation foundation is an annular flow model describing the three fields liquid film, vapor and liquid droplets. The replacement of the previous purely empirical correlations (e.g. XL type correlations) by a mechanistic correlation: - provides a better agreement between measured and calculated critical power - leads to an accurate prediction of the dryout location in agreement with the experimental data - improves the reliability of the predictions outside of the normal experimental domain, an area that is often problematic. The ACE/ATRIUM 11 correlation is the third mechanistic correlation to be licensed with the U.S. NRC. The first correlation - ACE/ATRIUM 10 - was licensed in Since 2009, ACE correlations have been utilized to monitor Safety Limit Minimum Critical Power Ratio (SLMCPR) of AREVA NP fuel assemblies in nuclear reactors. With licensing of the ACE/ATRIUM 11 correlation in 2017 a significant milestone will be achieved for the reload readiness of the ATRIUM 11 fuel assembly design. KEYWORDS: Dryout, Critical Power, BWR, ATRIUM 11, Mechanistic. * ATRIUM is a trademark of AREVA NP registered in the United States and various other countries 1

2 I. INTRODUCTION ATRIUM 11 is the most advanced member of the ATRIUM fuel assembly family and has been well received by customers. Meanwhile, 40 lead fuel assemblies are in operation in five different reactor cores. Some of them are close to their final burnup (Fig. 1) and showing the expected good appearance of all fuel assembly components. Design features of the ATRIUM 11 fuel assembly and the results of the extensive post-irradiation examinations have been summarized in Ref. 1 and 2. The next highlight of the ATRIUM 11 development and industrialization project will be the delivery of the first reload in Number of Fuel Assemblies Total Number of irradiated Fuel Assemblies: Assembly Burnup [MWd/kgHM] Fig. 1. Achieved burn-up with ATRIUM 11 fuel assemblies (Dec. 2016) The present paper describes one major part of the fuel design development program, namely the characterization of the Critical Heat Flux (CHF) performance. Significant developments in this field have occurred since electrical production nuclear reactors started operating in the 1950 s and 1960 s. Yet the prediction of CHF in a nuclear reactor remains a challenge. The mechanisms are complex and depend on a variety of factors including geometry, flow regime, heat transfer regime, fluid state, surface state, etc. Critical power performance of new fuel assembly designs requires experimental measurements. AREVA NP measures the performance in the KATHY loop located in Karlstein, Germany. It is a state of the art test facility that is used to perform steady-state critical power, single and two-phase pressure drop, transient, and oscillatory dryout/rewet measurements. High quality detailed experimental data are obtained. A database is constructed from the data. Then the data are carefully examined and appropriately tagged as part of the data qualification process. When this is complete, the data are partitioned into two parts, (1) a set for defining or fitting the model, and (2) a set for validating the model. The measured critical power measurements are not used directly in fuel design. They are used to construct and qualify a model or correlation. Critical power correlations are used for Boiling Water Reactor (BWR) core design and monitoring. Collier and Thome describe two types of correlating procedures that have been adopted (Ref. 3, pp ): (a) correlations of an empirical nature which make no assumptions whatever about the mechanisms involved in the critical heat flux mechanism, but solely attempt a functional relationship between the critical heat flux and the independent variables, and (b) correlations where attempts have been made to look at and write down equations for the hydrodynamic and heat transfer processes occurring in the heated channel and to relate these to the actual heat flux condition. 2

3 Correlations used in licensing of BWR fuel include the XL series of correlations (e.g. XL10XM) and the MacBeth form correlations (e.g. SPCB). These are all of the former or empirical nature. As fuel designs have increased in complexity, these empirical correlations have become more complex and required more coefficients. Therefore, AREVA NP was inspired to pursue a mechanistic based correlation to provide a robust solution that is able to adequately model future designs as they increase on complexity. This paper provides an introduction to the latter type of correlation the mechanistic approach. This is a significant departure from the traditional empirical type of correlation. In a BWR, the thermal-hydraulic conditions in the core are dominated by annular flow. The mechanisms of hydrodynamics and heat transfer under conditions of annular flow have been investigated since the late 1960s by researchers and collaborators beginning at Harwell (Ref. 4). They have been quite successful at developing a mechanistic model based on three fields liquid annular film, droplet field, and vapor field. This model has been implemented in a number of codes, for example the RINGS code (Ref. 5) and the F-COBRA-TF code (Ref. 6). Both of these codes are subchannel codes and they implement the triangular relationship algorithm for applying the annular flow model. Unfortunately, this approach requires a subchannel code leading to the situation that the calculation takes too long for practical implementation in the core monitoring process. These higher order models provide insight, however, for the capabilities of a mechanistic model and provide the foundation for the development of a licensable mechanistic critical power correlation. II. MECHANISTIC MODELING The annular flow regime is depicted in Fig. 2. Three fields are shown, an annular liquid film on the surfaces of the flow channel, a vapor field in the middle, and a droplet field entrained within the vapor field. The figure also depicts the transport processes between the fields deposition from the droplet field to the annular liquid film, entrainment from the annular liquid film to the droplet field, and evaporation from the annular liquid film and droplet fields to the vapor field. The cooling of the fuel rod surfaces is provided by the annular liquid film that covers these rods. A mass balance equation for the annular liquid film is provided by Hewitt and Govan (Ref. 7) dm& LF 4 q& = D E (1) dz d h In their equation, the liquid film mass flow rate per unit cross-sectional area is m& LF, d is the diameter of the tube, D is the deposition mass flux per unit peripheral area, E is the entrainment mass flux per unit peripheral area, q& is the heat flux, and h is the heat of vaporization. We would like to apply this model to the fuel rods contained in reactor fuel assemblies (i.e. not tube geometry). Multiply through this equation by the cross-sectional flow area of the tube, π d 2 4. dml π dq& = DPh EPh dz h m l is the mass flow rate of the annular liquid film and P h is the perimeter of the heated tube. The geometry must be generalized from a single uniformly heated tube to N fuel rods in the fuel assembly. For a single average rod, the last term can be written in terms of fuel assembly power instead of heat flux. dml q = DPh EPh (3) dz NLh (2) 3

4 Figure adapted from Ref. 3, p Fig. 2. Fields and Transport Processes in Vertical Annular Flow The entrainment rate is taken to be proportional to the mass flow rate of the liquid film which is the source of the entrainment. This approach leads to the correct behavior when the annular liquid film disappears there is no more entrainment. Let EP = m (4) h γ l e l where γ l e has the units of inverse length and can be considered to be the inverse memory length for entrainment. Similarly, the deposition rate can be taken to be proportional to the available liquid droplets DP = m (5) h γ e l e where γ e l is the inverse memory length for deposition. This also has the correct behavior in that when the droplet mass flow rate reaches zero, there is no more deposition. Place equations 4 and 5 into equation 3. dml q = γ e lme γ l eml (6) dz NLh This differential equation provides a mechanistic model of the annular liquid film. It is a balance equation the rate of change of mass flow rate of the liquid film is provided on the left side of the equation. Liquid film mass flow rate is decreased by entrainment and evaporation and increased by deposition. This equation is integrated along the heated length of the fuel rod. Power is increased until onset of dryout is reached mechanistically when the mass flow rate of the liquid film just reaches zero at some point along the length of the rod. The power in Equation 6 is taken to be uniformly distributed across the heated surface. But nuclear fuel assemblies have non-uniform axial power shapes and a distribution of power between the fuel rods. The average linear heat generation rate per rod is given by q NL. Allowing for axial and radial variation in the power distribution, ( ) ( ) q f z z fr z q ( z) = f z ( z) fr ( z) q = (7) NL Therefore, Equation (6) can be generalized for non-uniform axial power shapes, dm q f z ( z l ) fr ( z) = γ e lme γ l eml (8) dz NLh where f z ( z ) is the normalized axial power shape and fr ( ) z is the normalized radial power factor. 4

5 In a nuclear reactor fuel assembly, the rods are positioned and fixed by spacers. It is common knowledge that spacers have a significant influence on critical power. The empirically based correlations generally include the effect of spacers implicitly only through the measurements. This affects the robustness of the model because these models do not predict the location of onset of dryout consistent with the measurements. In the mechanistic model, the influence of spacers is included explicitly. The influence of spacers is derived from Ref. 5. Within the annular flow liquid film model, the effect of the spacers is superimposed on the deposition term, dml γ ( ) ( ) ( ) s z z q f s z z fr z = γ e lm e 1 Dse γ l eml dz + (9) NLh Where D s is a deposition coefficient representing the magnitude of the effect of the spacer, γ s is the inverse spacer memory length representing the axial effect of the spacers, and z s is the location of the upstream spacer. Equation (9) provides a mechanistic correlation form for modeling annular flow dryout. It has been adapted to reactor geometry and nonuniform axial power shapes. m e is determined by satisfying the conservation and energy equations of the three phases liquid annular film, droplet, and vapor. A fully mechanistic correlation is not possible. This situation was also the case for Hewitt and collaborators. At this point, one must rely on experimental data and empirical models to arrive at closure relationships. It is a form because there remain some unknowns to clarify (closure relationships). The inverse memory lengths for deposition and entrainment must be determined. Hewitt and Govan provided relationships for tube geometry in Ref. 7. Design specific experimental data are needed to describe some of these terms. III. APPLICATION OF THE MECHANISTIC DRYOUT MODEL With some further algebraic manipulation, the model, with appropriate closure relations, is applied to the ATRIUM 11. The comparison of calculated critical power to measured critical power is in good agreement as shown in Fig. 3. The mean ECPR is (expected) and the standard deviation is about 2.7%. In the next comparison (Fig. 4), the accuracy of the model at predicting the axial location of dryout is assessed. Because we explicitly account for the influence of the spacers in the model, it is capable of predicting the axial location of dryout. This feature results in a prediction of the axial location of dryout that matches the expected location from the experiment. Onset of dryout will occur only in a limited number of axial locations within the fuel assembly. The model axial location prediction error is calculated by taking the difference between the calculated axial location of dryout and the measured location of dryout in terms of the spacer. So for example, if dryout is measured just below spacer 2 and dryout is calculated just below spacer 1, the error in the prediction is 2 1 = 1. Differences between the upper most assembly in the heated length and the end of the heated length are marked as a difference of 0.5. It is observed that the model for ATRIUM 11 is very accurate, predicting over 80% of the axial locations of dryout exactly. In the event that the prediction does not match the measurement, most of the predictions miss by no more than one spacer span axially. The ACE/ATRIUM 11 critical power correlation behavior with mass flow rate is shown in Fig. 5. The Experimental Critical Power Ratio (ECPR), defined as the calculated critical power divided by the measured critical power, is plotted on the y-axis. The x-axis shows the mass flow rate. A trend line is also shown that indicates there is no trend of the correlation with mass flow rate. The correlation predicts the effect of flow rate at high flows as well as at low flows. Fig. 6 shows the ECPR as a function of pressure. No significant trends are apparent. Fig. 7 shows the effect of inlet subcooling, also showing the good performance of the ACE/ATRIUM 11 critical power correlation. In order to achieve the correct behavior in the CHF model, some empirically based correlations will use a functional form that mathematically imposes a condition on behavior. For example, the CHF is a linear function of the inlet subcooling (MacBeth correlation). But it is observed that no such functional exists in the mechanistic annular liquid film model (or the ACE correlation). It is common to take the data from a single test and plot the critical power as a function of inlet subcooling for each mass flow rate (see Fig. 8). For the test shown, the agreement between the predictions and the measurements is very good. What is 5

6 also apparent in this plot is that the prediction is consistent with expectation (linear behavior of critical power with inlet subcooling). Empirically based correlations rely on experimental data to achieve the correct behavior. If one gets outside of the base of experimental data, it is not unusual in the empirical correlations to observe non-physical behavior this is simply an artifact of the curve fitting process. One of the advantages of choosing a correlation form that has a mechanistic basis is that the correct physical behavior is built in. Thus, the mechanistic model behaves correctly at conditions where test data may not be available. IV. APPLICATION AND LICENSING Consistency between core monitoring and the areas of fuel design, thermal limits calculation, and transient analysis is important. For BWR core monitoring, it is not yet practical to use a sub-channel model in a code like F-COBRA-TF due to the calculation time and computational resources required. A fast computation of the critical power ratio (CPR) during core monitoring is a requirement. The calculation of the critical power by the ACE correlation is very efficient the CPR of every assembly in the core can be calculated on a single modern processor in 1 2 seconds. This is quite reasonable and although a bit longer than the calculation time from existing empirically based correlations, the overall coupled neutronics and thermalhydraulics solution for core monitoring is not significantly extended. The first critical power correlation to incorporate the annular flow mechanistic model as its base correlation form was the ACE/ATRIUM 10 Correlation. The correlation was reviewed and approved by the U.S. Nuclear Regulatory Commission in Subsequently, the ACE/ATRIUM 10XM correlation has been reviewed and approved and the ACE/ATRIUM 11 critical power correlation is near the end of review. The ACE correlation has been well received by customers and regulators and is in use in operating plants in the U.S. and Taiwan. Licensing of the ACE correlation for use in Europe is underway with the first application expected in conjunction with ATRIUM 11 reloads Percent Fig. 3. Comparison of Calculated Critical Power to Measured Critical Power Measured Spacer - Calculated Spacer Fig. 4. Accuracy of Prediction of Axial Location of Dryout 6

7 ECPR Mass Flow Rate (kg/s) Pressure (bar) Inlet Subcooling (kj/kg) Fig. 5: ECPR vs. Mass Flow Rate Fig. 6: ECPR vs. Pressure Fig. 7: ECPR vs Inlet Subcooling V. CONCLUSIONS Fig. 8. Comparison of Predicted Critical Power (Lines) and Measured Critical Power (Symbols) in One Test The use of a mechanistic correlation for core monitoring of critical power ratio (thermal limits) is a significant step forward in robust modeling of fuel performance. The model provides good behavior both at experimentally observed conditions and at conditions for which experimental data is either unavailable or cannot be collected due to physical limitations of the experimental facility. The model has proven reliable in fuel design, analysis, and in core monitoring. REFERENCES 1. S. COLE, N. GARNER, R. GRAEBERT, and P. MOLLARD, ATRIUM 11 Validation of Performance and Value for BWR Operations, TOP FUEL 2015, Zurich, Switzerland, Sept , S. COLE, N. GARNER, S. MAZURKIEWICZ, V. SCHOSS, and P. MOLLARD, ATRIUM 11 Operating Experience, TOP FUEL 2016, Boise, ID, Sept 11 15,

8 3. J. G. COLLIER and J. R. THOME, Convective Boiling and Condensation, 3 rd Ed., pp , Oxford University Press Inc, New York, NY (1996). 4. P. B. WHALLEY, P. HUTCHINSON, and G. F. HEWITT, The Calculation of Critical Heat Flux in Forced Convection Boiling, Proceedings of the 5 th International Heat Transfer Conference, Tokyo, Japan, (290), P. KNABE and F. WEHLE, Prediction of Dryout Performance for Boiling Water Reactor Fuel Assemblies Based on Subchannel Analysis With the RINGS Code, Nuclear Technology, Vol. 119, Dec P. POHL, H. GABRIEL, J. KRONENBERG, S. OPEL, and K. GREENE, Dryout Prediction by the Advanced Subchannel Code F-COBRA-TF to Support ACE/ATRIUM 11 Dryout Correlation Validation, PHYSOR 2014, Kyoto, Japan, Sept. 28 Oct. 3, G. F. HEWITT and A. H. GOVAN, Phenomena and Prediction in Annular Two-Phase Flow, ASME Winter Annual Meeting, Dallas, TX, pp