Measurement of instantaneous flow rate through estimation of velocity profiles

It is very important, but difficult to measure instantaneous flow rate in the unsteady flow regime, since the variation of velocity profile limits the dynamic accuracy of flowmeters. Consideration of the velocity profile variation is crucial to improving their dynamic performance. This paper presents a new method of measuring the instantaneous flow rate of unsteady flow in a circular pipe by estimating the velocity profile of the flow. The estimation is formulated as a discrete Kalman filter problem where the dynamics of the velocity profile, which is governed by a linear partial differential equation, is approximated using a finite-dimensional model. An instantaneous flowmeter consisting of a laser Doppler velocimeter (LDV) and an 8-bit microcomputer which implements the solution of the filter problem has been developed. Successful measurements of a pulsating flow and a stepwise changing flow by this flowmeter are presented.