Analytical model of an ultrasonic cross-correlation flow meter, part 2: Application

An analytical model of an ultrasonic cross-correlation flow meter has been developed to relate the time delay measured by the meter to the mean velocity profile and statistical properties of turbulent pipe flow. In Part 2 of this two-part paper, the cross-correlation and cross-spectrum of the demodulated ultrasonic signal are obtained using the stochastic model of the turbulent velocity fluctuations from Part 1. Calculations of the bulk velocity calibration factor using computational fluid dynamics simulations of fully-developed pipe indicate that the calibration factor has a logarithmic dependence on Reynolds number. In addition, the model was used to investigate the sensitivity of the device to transducer spacing and wall roughness. It was found that increased transducer spacing and increased pipe roughness both decrease the bulk velocity calibration factor.