A dealiasing method for use with ultrasonic pulsed Doppler in measuring velocity profiles and flow rates in pipes

Abstract

The ultrasonic pulsed Doppler method (UDM) is a powerful tool for measuring velocity profiles in a pipe. However, the maximum detectable velocity is limited by the Nyquist sampling theorem. Furthermore, the maximum detectable velocity (also called Nyquist velocity), vmax, and the maximum measurable length are related and cannot be increased at the same time. If the velocity is greater than vmax, velocity aliasing occurs. Hence, the higher velocity that occurs with a larger pipe diameter, i.e. under higher flow rate conditions, cannot be measured with the conventional UDM. To overcome these limitations, dual-pulse repetition frequency (dual PRF) and feedback methods were employed in this study to measure velocity profiles in a pipe. The velocity distributions obtained with the feedback method were found to be more accurate than those obtained with the dual PRF method. However, misdetection of the Nyquist folding number using the feedback method was found to increase with the flow velocity. A feedback method with a moving average is proposed to improve the measurement accuracy. The method can accurately measure the velocity distributions at a velocity five times greater than the maximum velocity that can be measured with the conventional UDM. The measurement volume was found to be among the important parameters that must be considered in assessing the traceability of the reflector during the pulse emission interval. Hence, a larger measurement volume is required to measure higher velocities using the dual PRF method. Integrating velocity distributions measured using the feedback method with a moving average makes it possible to accurately determine flow rates six times greater than those that can be determined using the conventional pulsed Doppler method.