Optimal sensor location for model parameter estimation in CFD

Abstract

In this paper the optimal sensor location problem for the estimation of model parameters in computational fluid dynamics is presented. A Bayesian formulation is used to quantify the uncertainties in the model parameters using the measurements provided by a sensor configuration and the information entropy is minimized using a gradient-based algorithm, to optimally locate the sensors in order to obtain as much as possible information from the measurements. The information entropy is expressed in terms of the derivatives, with respect to the model parameters, of the flow quantities predicted by the model. These derivatives are computed using the differentiation of the model equations with respect to the model parameters. Herein, the algorithm is applied to the turbulent flow through a backward facing step where the optimal locations of sensors that measure velocity and Reynolds stress profiles are sought for the optimal identification of the parameters of the Spalart Allmaras turbulence model.