Essais & Simulations n°115

Dossier Incertitudes de

Dossier Incertitudes de mesure ‘root sum of the squares’ is reasonable in this instance as described further. Figure 3: 1/4 scale mock-up in flow test loop EVEREST 3.1. Characterization and estimation of uncertainty sources Identification step provides a list of uncertainty sources: • physical model, • time and space discretization, • input data, • iterative convergence, • round-off, • computer programming; From this large but not exhaustive list, the physical model and the space discretization source are evaluated as a unique source. First, because all of them have a common origin: simplifications from real phenomenon. Turbulence model, boundary conditions, physical properties Figure 4: “K” coefficient vs. Reynolds number and geometry are considered on this group. On the other hand no affordable method exists (in terms of time calculation). Thus estimation of uncertainty is made by 1/4 scale model data comparison. EDF R&D operates its own flow test loop (with a ±0.4 % flowmeter) where a 1/4 scale model is installed (see Figure 3). Using equation (4), an experimental “K” coefficient can be calculated accurately. Then the mean deviation between experimental and CFD, “K” coefficients are calculated for various flow rates. A normal (or Gaussian) distribution is chosen to cover amply “K” coefficient deviation data. For extrapolating from 1/4 scale to full scale model an analysis based on a dynamic similitude law is made. For the same Reynolds number (2.106) two simulations are made, the first one at 1/4 scale conditions (temperature of 26 °C and D=0.2m) and the second one at full scale conditions (temperature of 289 °C and D=0.78m). Results show that “K” coefficients are comparable. The second part of this analysis is the evolution of “K” coefficient vs. Reynolds number for scaled and full model (see Figure 4): “K” coefficient is quite stable and no important dependencies exist. Regarding input data, EDF R&D evaluates its influence by a sensitivity test of the velocity and the temperature inputs. Taking advantage of actual measurements from PWR, three levels for CFD input data are chosen. First a nominal value (T nom and V nom ) is defined based on nominal operating conditions. Then minimum and maximum values are defined from safety limits. Finally CFD simulations are executed for different combinations of levels (T min / V max , T max / V min , etc.). Results are analyzed by a statistical approach. A mean value and a standard deviation are calculated based on a normal distribution (conventional coverage factor of 2σ). As said above, “K” coefficient is computed using equation (4) where the differential pressure is taken from simulations results. “K” coefficient varies lightly as a function of sampling number used for calculation. Analyze of all CFD results permits to choose an optimal sampling number. Variations of differential pressure are computed for the last 500 iterations where convergence is guaranteed. Once more an average and standard deviation is calculated from the last 500 iterations via normal distribution method. For round-off and computer programming uncertainty sources are insignificant and not considered in this study. Uncertainty estimation, as shown above, deals only with differential pressure calculation from equation (4) due to CFD errors. Thermal expansion might also have an effect on “K” coefficient uncertainty due to temperature difference, from 25°C to 289°C. Based on well-know coefficient of thermal expansion for stainless steel, an estimation is done for “K” coefficient for low and nominal operating temperatures. Results show the effect is small but not negligible: deviation reaches 1 %. 3.2. Estimation of uncertainty budget Physical model and discretization uncertainty represent systematic error that might be corrected when reference values are available. In this case that’s not possible because the bias is known only for scaled model. Input data uncertainty represents a random error that must be related to physical model and discretization uncertainty. Those uncertainty sources are not independent and Essais & Simulations • OCTOBRE 2013 • PAGE 44

Dossier Incertitudes de mesure covariances must also be taken into account when calculating the combined uncertainty. Uncertainties due to iterative convergence and thermal expansion are mutually independents and can be combined by quadratic summation method. Uncertainty budget is finally expressed as: (5) Acknowledgements This study was a collaborative work involving various EDF teams: the authors are grateful for the help and contribution of both STEP department (scale model experiments and uncertainty method) and MFEE department (CFD expertise) from the EDF R&D as well as nuclear operators who provided essential plant data. Note: an extended version of this paper has been accepted for presentation at the International Congress of Metrology [DEN-13] where: σ total uncertainty budget of K coefficient; σ inp uncertainty of inputs data; σ mod uncertainty of physical model and space discretization; σ conv uncertainty due to iterative convergence; σ ther uncertainty due to thermal expansion; 4. CONCLUSION The current method to calculate RCS flow rate in nuclear power plants can be influenced by the temperature heterogeneity in the hot leg of the primary loop. A method using the existing elbow taps at the outlet of the steam generator should be able to solve this issue. EDF R&D has developed a new method in order to get a continuous, accurate and absolute measurement of the RCS flow rates that is independent of the loop temperature measurements. Once known, the uncertainty of the K coefficient, from the equation (3), can be used to calculate the global uncertainty of the flow rate measurement. Due to the redundancy of the differential pressures on PWRs, the global uncertainty of the method is below 3%. Thus this RCS flow measurement is more accurate than the RCP114. Real tests were performed on the Civaux plant (two 4-looper 1,450MW units). All measurements are coherent with the RCP114 flow rate. This can be considered as a first validation of the method. Due to its generic character, such a methodology could be advantageously used in other application fields. Olivier Deneux 1 and Mario Arenas 1 1EDF R&D, STEP Department, 6 quai Watier, 78401 Chatou, France Références [ARC-04] F. Archambeau, N. Méchitoua, and M. Sakiz, “Code_Saturne: a Finite Volume Code for the Computation of Turbulent Incompressible Flows”, International Journal on Finite Volumes, Vol. 1, 2004 [CRA-09] M. A. Crabtree, “Industrial Flow Measurement”, Master’s thesis, University of Huddersfield, 2009 [DEN-11] O. Deneux, J. M. Favennec, and J. Veau, “Suivi de débit dans une conduite hydraulique fermée”, patent INPI n° 1156689, 2011 [DEN-13] O. Deneux , M. Arenas, “CFD and Metrology in Flowmetering: RCS Flow Measurement with Elbow Taps and its Uncertainty”, Accepted for presentation at the 16 th International Congress of Metrology, S2 Session, Paris, France. October 2013. [GUM-100] GUM : “Evaluation of measurement data-Guide to the expression of uncertainty in measurement”, JCGM 100. 2008 [MIL-76] R.W. Miller, “Flow Measurement Engineering Handbook”, 1976 [OBE-00] W.L. Oberkampf, T.G. Trucano, “Validation Methodology in Computational Fluid Dynamics”, Sandia National Laboratories, 2000 Essais & Simulations • OCTOBRE 2013 • PAGE 45