Abstract
A new method to measure the instantaneous flow rate of unsteady flows in a circular pipe with the help of an estimating filter theory is presented. It is very important but difficult to measure the instantaneous flow rate. The variation of the velocity profile of unsteady flow often degrades the dynamic accuracy of the flowmeters. The velocity profile should be taken into consideration.
The dynamics of the velocity profile variation in a circular pipe is governed by a linear partial differential equation. In this paper, the equation is approximated with a finite partial fraction expansion of its Laplace-transformed solution. Utilizing this finite dimensional model, the velocity profile estimation problem is formulated as a discrete Kalman filter problem and solved in a general form.
By means of this filter, an instantaneous flowmeter which consists of a laser Doppler velocimeter and an eight bits microcomputer has been developed. The filter of eighth order is implemented on the computer and is operated in real time. The instantaneous flow rate of a pulsating flow and a stepwise changing flow has been measured successfully by this flowmeter.
