Abstract
It is well known that turbulence models based on the eddy viscosity hypothesis are those to formulate the eddy viscosity and each model involves one or more undetermined coefficients. In general, the undetermined coefficients take different values if the conditions of the flow are different, and have to be prescribed with the aid of empirical information. However, the turbulence models derived from the eddy viscosity hypothesis are subject to specified steady flows. Therefore, it is hard to say that whether or not the prediction of unsteady turbulent flow by those models describe the real flow. For this reason, it is important to develop a dynamic measurement method of the eddy viscosity of turbulent flow.
In this paper, we present a model-based method for measurement of the eddy viscosity of unsteady turbulent flow in a pipe. First, we lump a modified Navier-Stokes' equation which includes the eddy viscosity as an unknown time-and space-varying parameter by using the finite element method and derive a finite-dimensional dynamic model. Then, we set up an algorithm for estimating the eddy viscosity by applying the extended Kalman filtering techniques Finally, we verify the validity of the algorithm by carrying out many numerical simulations and experiments for sinusoidally changing turbulent flow. The results show that the proposed method is effective.
