Optimal Sensor Placement for the Estimation of Turbulence Model Parameters in Cfd

The optimal placement of sensors for the estimation of turbulence model parameters in computational fluid dynamics is presented. The information entropy (IE), applied on the posterior uncertainty of the model parameters inferred from Bayesian analysis, is used as a scalar measure of uncertainty. Using an asymptotic approximation, the IE depends on nominal values of the CFD model and prediction error model parameters. It is derived from the sensitivities of the flow quantities predicted by the flow model with respect to the model parameters. A stochastic optimization algorithm is used to perform the minimization of the IE in the continuous design space. Robustness to uncertainties in the nominal model parameters and flow conditions is addressed. Information redundancy due to sensor clustering is addressed by introducing spatially correlated prediction error models. The algorithm is applied to the turbulent flow through a backward-facing step where the optimal locations of velocity and Reynolds shear stress profiles of sensors are sought for the estimation of the parameters of the Spalart-Allmaras turbulence model.