Abstract
Recently, the study on the model-based method of the measurement of unsteady pipe flow has developed rapidly and a lot of fruitful applications have been reported. These applications, however, are all limited to the measurement of unsteady laminar flow, although the application to unsteady turbulent flow is strongly needed in practice. For this reason, not only is it necessary to make the model-based measurement method applicable for unsteady turbulent pipe flow, but also is it more needed to build up a unified model-based measurement method which is applicable for both laminar and turbulent flows without any special distinctions.The aim of this paper is to present a unified model-based method to estimate velocity profiles as well as flow rates for both the turbulent and the laminar flows in a pipe.In this paper, a dynamic model of fluid in the pipe including a time-varying unknown parameter is derived by, first, considering a distributed parameter system governing the flow with suitable expression for eddy viscosity, and then lumping it by using the finite element method. The extended Kalman filtering technique is applied to the model to yield a nonlinear estimator for simultaneous estimation of the unknown parameter and the velocity profile. Experiments using a beam scanning laser-Doppler velocimeter (LDV) ara done to verify the proposed estimator. Successful results show that the method is effective not only for turbulent flow but also for laminar flow.
