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Le point sur les incertitudes de mesure

Dossier Incertitudes de mesure accurately and absolutely measure RCS flow, both continuously and independently of the loop temperature measurements. The original approach mingles both CFD simulation and experimental test on a scale flow bench. CFD is able to predict the elbow tap coefficient with a relevant value (with potential bias as small as possible) and associated accuracy, smaller than that of the heat balance method. 2. ELBOW TAP TECHNOLOGY FOR FLOW MEASUREMENT 2.1. Method Description Studies and scientific literature already exist about the possibility to measure a flow in a pipe elbow [CRA-09] [MIL-76]. This method, called elbow tap, is considered as a differential pressure primary device. Indeed the square root of the differential pressure between the flow going along the inner section of the elbow and the flow going along the outer section of the elbow is in principle proportional to the flow rate. Different factors have an influence on the relation between the square root of the differential pressure and the flow rate. In order to develop an accurate elbow tap method applied to RCS flow measurement (see the pipe elbow on Figure1), it is important to identify the most influential factors in the Figure 1: Elbow tap pressure lines on a RCS pipe in a nuclear power plant loop mathematical formula. In order to build this formula, linking the square root of the differential pressure and the flow rate, the flow is assumed to be inviscid (i.e. an ideal fluid with no viscosity). Then the Euler equation over a radial axis can be written: (1) In a first approach, the following basic assumptions are made: the velocity of the fluid is uniform over the whole cross section: vθ (r)=V, the pipe diameter is much lower than its radius of curvature. It is therefore possible to integrate the Euler equation over a diameter. This gives the following mathematical equation where both the flow rate and the differential pressure appear: (2) This equation is true in an ideal case. In real conditions, this one can be approximated with equation (3). The “K” coefficient still depends on the flow condition, where “K” is close to 10π/4 with a correction factor resulting from the real flow conditions. At operating conditions, the fluid temperature is around 289°C, the pressure is 155bar and the flow is very turbulent. (3) 2.2 Elbow tap for RCS flow measurement Equation (3) used by EDF R&D requires the knowledge of a «K» coefficient. This coefficient can be seen as a calibrating coefficient. Even if some influence factors appear directly in the formula, the “K” coefficient may still depend on flow conditions such as the inlet velocity profile of the flow, the fluid temperature, the exact geometry of the pipe elbow, etc. So the “K” coefficient is not exactly a «universal» constant and may vary in accordance with the conditions of the flow change. The aim of the calibration of equation (3) is to figure out a value for this coefficient as relevant as possible for a RCS flow measurement in terms of exactness and uncertainty. EDF R&D has developed a methodology in order to achieve that. EDF owns a varied range of data that can help the study of this “K” coefficient. Those data come from the following sources: measurements from nuclear power plants (EDF owns and operates 58 PWRs, see above), experiments on a 1/4 scale model flow test loop, called EVEREST, where the flow rate, the temperature of the fluid and the pressure of the fluid are lower than those of real plant operation condition (see the section concerning the experimentation on a scale model), simulation from a CFD code developed by EDF (this open-source code is named: Code_Saturne®); The conclusions that can be made from those sources are different. Indeed to compute out the “K” coefficient from the nuclear plants measurements, a reference value of the RCS flow rate is required. But the unique current method to get the RCS flow rate value is the RCP114, which is the method we want to improve. Since the RCS pump curve may evolve during the plant life, the pump Δp flow rate measurement. EVEREST is a 1/4 scale model **Essais** & **Simulations** • OCTOBRE 2013 • PAGE 42

Dossier Incertitudes de mesure test bench where inlet parameters are lower than real values. Getting conclusions from those experiments only may not be relevant enough. So the methodology developed by EDF R&D to find out the value for the K coefficient consists in doing some simulations with Code_Saturne® [ARC-04]. The real measurements on-site and the experiments on EVE- REST will be used to validate the method and to carry out the accuracy calculation. 2.3 A four step methodology The first step of the methodology consists in creating a pipe computational domain that is adequate enough to represent the RCS flow. The computational domain represents the outlet water box of the steam generator and the 40° pipe elbow following. It is important to model the water box because its effect on the flow may be important. The computational grid must have at least two millions cells to ensure the mesh convergence and can be conforming or non-conforming. The mesh convergence was studied with different grids containing one million, two millions and four millions cells. The main flow characteristics and the pressure values stop evolving from a two millions cells simulation to a four million cells simulation. Thus two millions cells are enough for this study. The second step consists in defining the parameters of the simulation. One important choice regards the turbulence model. A LES model is much time consuming and cannot be applied with such a complex flow. So the right choice is to use a RANS model. Different RANS models have been developed such as k ϵ or k (1) , first order models, or R ij SSG, second order model. Numerical experiments have been performed from which it seems that the standard Figure 2: CFD of the RCS flow kϵ model is not precise enough for our purpose and that the R ij SSG do not improve that much the results but is more time consuming. So the turbulence model SST k (1) has been chosen for this study. Finally the inlet values have to be specified such as the velocity of the fluid at the inlet of the water box (supposed to be constant and uniform), the density of the fluid, the viscosity of the fluid, etc. Those values can be evaluated from the operating condition of a nuclear power plant. For a French 1,450MW PWR, those operating conditions are a cold leg temperature of 289°C, a pressure of 155 bar and a flow rate of 24,840 m3h-1. The third step is then the simulation. The time resolution of the simulation has to be quite small, 10 -2s in this study. The simulation is well converged after 2,000 to 3,000 iterations. A picture of the global geometry of the pipe and the simulation can be seen on Figure 2. The fourth and final step is the post-processing of the results. The CFD gives the pressure field in the whole domain. Thus it is now possible to get the pressure in the different tap locations. Then a K coefficient can be computed using equation (4) since the last unknown was the differential pressure (the (4) flow rate being an inlet parameter of the simulation). Eventually four “K” coefficients are computed from the four differential pressures: one for each tap of the inner surface. The four differential pressures are directly taken from the CFD results. A patent has protected this methodology since July 2011 [DEN-11]. Since measuring a flow rate from an elbow tap is not innovative, the patent is based on the calibrating process, using CFD, for measuring an industrial flow rate with high accuracy. 3. UNCERTAINTY QUANTIFICA- TION OF “K” COEFFICIENT As described in a large number of publications, the uncertainty quantification in CFD is based on identification and estimation of the effects of all sources of uncertainty. A well accepted technique is the V&V [OBE-00] method that defines Verification as the activity to evaluate the numerical error, and Validation as the activity to evaluate physical uncertainties. Inspired on V&V, EDF’s method consists of the identification and characterization of each source of uncertainty. Then different groups are defined and a method for its estimation is applied. The choice of a realistic method for each uncertainty source is based on available data at EDF: actual measurements from PWRs and experimental data on a 1/4 scale model flow test loop. Some sources have been identified but neglected because not significant, and the others identified and estimated with a conservatism approach for safety reasons. The last step consists of estimating the total uncertainty of the “K” coefficient. Combined uncertainty is calculated with conservative hypotheses. The quadratic summation also known as **Essais** & **Simulations** • OCTOBRE 2013 • PAGE 43

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