Unscented Kalman Filter (ukf)-based Nonlinear Parameter Estimation For A Turbulent Boundary Layer

A turbulent boundary layer is a ubiquitous element of fundamental and applied fluid mechanics. Unfortunately, accurate measurements of turbulent boundary layer parameters (e.g. friction velocityu tau tau(w)) are challenging, especially for high-speed flows (Smitset al2011). Many direct and/or indirect diagnostic techniques have been developed to measure wall shear stress (Vinuesaet al2017). However, based on various principles, these techniques generally give different results with varying uncertainties. The current study introduces a nonlinear data assimilation framework based on the unscented Kalman filter (UKF) that can fuse information from (i) noisy and discretized measurements from stereo particle image velocimetry (SPIV), a Preston tube, and a MEMS shear stress sensor, as well as (ii) the uncertainties of the measurements to estimate the parameters of a turbulent boundary layer. A direct numerical simulation of a fully developed turbulent channel flow is used first to validate the data assimilation algorithm. The algorithm is then applied to experimental boundary layer data at Mach 0.3 obtained in a blowdown wind tunnel facility. Drag coefficients from control volume analysis of the SPIV and wall pressure data and laser interferometer skin friction measurements are used for independent cross-validation. The UKF-based data assimilation algorithm is robust to the uncertain and discretized experimental data and is able to provide accurate estimates of turbulent boundary layer parameters with quantified uncertainty.