COMPARISON OF INTEGRATION METHODS FOR MULTIPATH ACOUSTIC DISCHARGE MEASUREMENTS

One of the main issues of the acoustic discharge measurement (ADM) is related to the accuracy of the method. The accuracy of the measurements depends on many factors such as the flow situation on site, the local geometry, care devoted to the transducer installation, the electronic devices and also the algorithms applied to evaluate discharge. The robustness of the ADM may also depend on water quality and the size of the measuring section. To estimate the overall accuracy of a measurement, individual sources of errors have to be analysed separately. Important sources of errors arise from flow field distortions which accordingly might demand a higher number of acoustic paths to achieve the desired measuring accuracy. Further sources lie in the installation, the out-of-roundness and deformation of pipes, in cross section and eventually free surface measurement, the employed integration method and also in the protrusion effect of the acoustic transducers within the flow. According to the appendix of the IEC 60041standard the volume flux Q in a conduit can be determined by integrating individual path readings applying a simplified Gauss-Jacobi integration method, where the individual path readings are weighted and added up. One of limitations of this method described in IEC 60041 is that deviations of the integrated discharge from a true discharge value are observed even when ideal velocity distributions are calculated with theoretical equations for turbulent velocity profiles. Since velocity profiles vary as a function of Reynolds number and wall roughness, these deviations are determined by these parameters. The deviations are inherent to the method proposed in IEC 60041 as an assumed uniform velocity profile is used for individual weight calculations. A further limitation of the method is the fixed weighting of the path velocities and thus the need for very accurate positioning of the acoustic transducers with respect to the prescribed distances di of the acoustic paths to the pipe centre. To overcome these limitations Voser [1999] proposes a modified integration method with slightly modified optimum sensor positions and weighting coefficients, thus reducing the integration error by 0.1 up to 0.2 percent. Furthermore, he includes in his method the actual, measured path positions for determination of the weighting coefficients and hereby eliminates the positioning error. He names this method OWICS (Optimal Weighted Integration for Circular Sections). This new method is based on the generalized Gauss-Jacobi method, abandoning the idea of a uniform velocity distribution. Coefficients are optimized on the assumption of turbulent velocity profiles, thus adapting the method better to the physical process. In this paper the background of the integration methods is explained in detail, and advantages of the OWICS integration method are pointed out and demonstrated for selected examples. Quantitative data showing integration uncertainty as a function of the number of paths for ideal and disturbed velocity distributions is provided.