I. Gryshanova, A. Rak
Investigation of the Correction Factor for Ultrasonic Flow Meters
The main source of errors while applying modern ultrasonic flow measurement principle is the deviation of the actual velocity profile of the measured flow from the calculated one. If the velocity profile is known, the corresponding correction can be evaluated and considered during calibration. However, in practice, the distribution of velocities in the cross section of the pipeline differs from the theoretical one, which leads to errors of hydrodynamic origin.To determine the flow rate of the measuring medium, it is necessary to transform the flow velocity averaged along the acoustic path to the velocity averaged for the cross section of the flow meter. To do this, use the hydrodynamic correction factor, which is a function of the Reynolds number. The inaccuracy of this factor is the largest component of the total error of ultrasonic flowmeters. This is due to the fact that velocity distribution (and hence the hydrodynamic factor) use dependences obtained on the assumption that measuring flow is axisymmetric and the trajectory of the ultrasonic beam lies in the plane passing through the pipeline axis. Nevertheless, most industrial flow media have a distorted profile due to installation effects, which are an integral part of any hydraulic system. As a result, the determined average flow velocity does not correspond to the real one. Therefore, the problem of studying the influence of flow non-symmetry on the value of the hydrodynamic correction factor is relevant. The effect of distortion of the velocity profile on the measurement results of ultrasonic flowmeters was evaluated using theoretical dependences describing non-symmetric velocity profiles. For this purpose, functions based on the power law of velocity distribution in smooth pipes with the imposition of some influence function, which depends on the radial and angular distances from the observation point to the pipeline axis, were used. However, some dependencies can only be applied to approximate real flow profiles.For velocity profiles that do not have axial symmetry, the only correct way to accurately estimate the flow rate is to reconstruct 2D velocity field using algebraic techniques. The implementation of one of these methods was performed based on the inverse Abel’s transform.For velocity profiles that do not have rotational symmetry around the axis of the pipeline, the value of the measured velocity will depend on the angle of orientation of the measuring plane relative to the diametrical plane of the flow meter. The calculation of the actual average flow velocity in the cross section of the meter was obtained from a specific mathematical dependencies describing velocity distribution by integration technique.This research allows us to conclude that it is possible to calculate the performance of ultrasonic flowmeters under conditions of distorted non-symmetric flows at Re > 104 with sufficient accuracy using computational hydrodynamics, integration based on Abel’s transform, methods of theoretical research and mathematical processing.