1989 Volume 25 Issue 1 Pages 69-75
In the initial paper, we have proposed a model-based method to measure unsteady flow in a pipe, in which, based on a distributed-parameter dynamic fluid model, velocity profiles are estimated by a Kalman filter. From then on, we extended the model-based method to the measurement of the entrance flow in a circular pipe. The extension was brought to success by linearizing the nonlinear Navier-Stokes' equation according to the fact that the entrance flow satisfies linear equations at its boundaries.
In this paper, we show the effectiveness of the linearization method for the estimation of the flow velocity profiles in the rectangular duct entrance. First, we linearize the momentum equation of the unsteady fluid in a rectangular duct by the proposed method and derive a lumped dynamic model with an unknown parameter by using the finite element method. Next, using this lumped model, we set up an extended Kalman filter algorithm to estimate the velocity profiles in the rectangular duct entrance. We verify the validity of the estimated results by comparing them with numerical solutions which are calculated by the finite difference method and have been proved to agree well with the real flow by experiments using a beam scanning LDV.
