Abstract
In this paper, we present a new method for the estimation of the velocity profile of unsteady laminar fluid flow in the entrance region of a circular pipe, in order to measure the flow rate in the pipe. The method is a model-based method which uses a nonlinear dynamic model of the flow and is a unified method which can be applied to both outside and inside of the entrance region.
The dynamic model is derived, initially, by linearizing the Navier-Stokes equation for the axial direction, and secondly, by lumping the distributed parameters of the linear equation. The linearization is done by using the fact that the entrance flow satisfies linear equations at its boundaries and yields a linear partial differential equation with an unknow parameter. The lumping is done by applying the finite element method.
The extended Kalman filter technique is then applied to the linear lumped parameter model with an unknow parameter, and a nonlinear filter to estimate the velocity profile on the pipe section at any point along the pipe is obtained.
The filter is implemented on a numerical simulator and on a real system. Both implementations are executed to yield accurate estimations of the velocity profile. In the real system the velocity profile is measured by a beam scanning laser Dopplar velocimeter which was developed originally in the authors' laboratory, and is compared with the estimated profile. As a result the effectivenss of the filter is shown.
