Correction of Flow Metering Coefficients Using Two-Dimensional Curve Fitting

Abstract

Swirl flows are either tumbling motions of main flows or circulating secondary flows in the cross-section of pipe, which makes accurate flow metering difficult without installing a long straight pipe upstream of a flow meter. However, there are many situations, where such long upstream/downstream pipelines cannot be installed due to limited space in the installation site for flow metering. The relative deviations of flow rates between the testing and the reference flow meters can be reduced by introducing a correction formula. The correction formula considers flow parameters such as curve number, swirl factor, Reynolds number and two non-dimensional numbers regarding installation of flow meters. Nonetheless, there are certain flows where the correction formula is not effective due to strong swirl flows. Two-dimensional curve fitting is introduced in the present study to solve some of difficulties in compensating flow rates due to swirl flows upstream/downstream of flow control elements, i.e., a contraction pipe, an expansion pipe, a single elbow and a butterfly valve. This method minimizes the gap between the measured and the estimated flow rates by applying the Levenberg-Marquardt algorithm. 2nd or 4th order polynomials with two independent variables, i.e., Reynolds number and a non-dimensional location of testing flow meter, are chosen to test their ability to compensate flow rates. From this study, the relative deviations were maintained within ±2% by applying the two-dimensional curve fitting.