Analyse und Fehleroptimierung der mehrpfadigen akustischen Durchflussmessung in Wasserkraftanlagen

III Abstract The exact knowledge of the discharge in hydro power plants is of major importance for field acceptance tests, for continuous efficiency monitoring, for water manage¬ ment and accounting of the gross hydraulic energy, for leak detection in pipes and for the calibration of secondarv discharge measurement devices. The acoustic discharge measurement (ADM) bases on the superposition of the pro¬ pagation velocity of an acoustic signal with the fluid velocity. With the measure¬ ment of the transit time of a downstream and upstream propagated signal the mean flow velocity can be derived between transducers which are mounted at the pipe wall with a angle of 30 to 60 degrees to the mean flow. Additional laterally shifted transducer pairs increase the measurement accuracy. The aim of this work is the analysis of the major error sources and the improvement of the measurement accuracy for a given number of transducers. In practical use it is assumed that the signal propagates along a straight line ("acou¬ stic path") between the two transducers. In reality the ray path is slightly bent due to the varying flow and sound velocities in the pipe. In the first part of this thesis, calculations based on methods using geometrical acoustics have proven, that with exception of the very rare case of very high air bubble concentrations paired with a strong variation of bubble diameter along the acoustic piath the measurement error due to the bend ing of the ray path can indeed be neglected. The multipath ADM consists typically of 4 to 8 acoustic paths (8 or 16 transducers) arranged in one or two measuring planes. In general, the measured path readings are summed up using a quadrature integration method according to Gauss-|acobi to evaluate discharge in each of the measuring planes. Inherent to this method is a systematic error of about ±0.15%. In this thesis, a modified quadrature formula is presented which almost fully eliminates all svstemafic errors. A further part of this thesis is dedicated to the detailed analysis of the three major sources of errors ot the multipath ADM, including an error depending on the velocity profile ("integration error"), an error resulting from the transducer protrusion into the pipe ("protrusion error"), and a geometrical error, which can pri¬ marily be attributed to an imprecise positioning of the transducers in the measuring section ("installation error"). To investigate the integration error, a software program based on a triangulation rou¬ tine was developed. With this program scattered velocity data m circular pipes may be interpolated and integrated, which is basis for the numerical simulation of the ADM including the calculation of the measuring error as a I unction of the mounting angle. Divided into the groups "single bends", "double bends", "vanes" and "contrac¬ ting cones" integration errors ot about 20 velocity records from different sources were computed and compared to measured data trom held and laboratory measu¬ rements. Based on the results of the simulation calculations guide lines for an opti-The exact knowledge of the discharge in hydro power plants is of major importance for field acceptance tests, for continuous efficiency monitoring, for water manage¬ ment and accounting of the gross hydraulic energy, for leak detection in pipes and for the calibration of secondarv discharge measurement devices. The acoustic discharge measurement (ADM) bases on the superposition of the pro¬ pagation velocity of an acoustic signal with the fluid velocity. With the measure¬ ment of the transit time of a downstream and upstream propagated signal the mean flow velocity can be derived between transducers which are mounted at the pipe wall with a angle of 30 to 60 degrees to the mean flow. Additional laterally shifted transducer pairs increase the measurement accuracy. The aim of this work is the analysis of the major error sources and the improvement of the measurement accuracy for a given number of transducers. In practical use it is assumed that the signal propagates along a straight line ("acou¬ stic path") between the two transducers. In reality the ray path is slightly bent due to the varying flow and sound velocities in the pipe. In the first part of this thesis, calculations based on methods using geometrical acoustics have proven, that with exception of the very rare case of very high air bubble concentrations paired with a strong variation of bubble diameter along the acoustic piath the measurement error due to the bend ing of the ray path can indeed be neglected. The multipath ADM consists typically of 4 to 8 acoustic paths (8 or 16 transducers) arranged in one or two measuring planes. In general, the measured path readings are summed up using a quadrature integration method according to Gauss-|acobi to evaluate discharge in each of the measuring planes. Inherent to this method is a systematic error of about ±0.15%. In this thesis, a modified quadrature formula is presented which almost fully eliminates all svstemafic errors. A further part of this thesis is dedicated to the detailed analysis of the three major sources of errors ot the multipath ADM, including an error depending on the velocity profile ("integration error"), an error resulting from the transducer protrusion into the pipe ("protrusion error"), and a geometrical error, which can pri¬ marily be attributed to an imprecise positioning of the transducers in the measuring section ("installation error"). To investigate the integration error, a software program based on a triangulation rou¬ tine was developed. With this program scattered velocity data m circular pipes may be interpolated and integrated, which is basis for the numerical simulation of the ADM including the calculation of the measuring error as a I unction of the mounting angle. Divided into the groups "single bends", "double bends", "vanes" and "contrac¬ ting cones" integration errors ot about 20 velocity records from different sources were computed and compared to measured data trom held and laboratory measu¬ rements. Based on the results of the simulation calculations guide lines for an opti-