Unscented Kalman filter (UKF) based nonlinear parameter estimation for a turbulent boundary layer: a data assimilation framework

TL;DR

This paper presents a novel data assimilation framework using the Unscented Kalman Filter to accurately estimate turbulent boundary layer parameters from noisy and incomplete measurements, validated through simulations and wind tunnel experiments.

Contribution

It introduces a UKF-based nonlinear data assimilation method that fuses multiple measurement types to estimate boundary layer parameters more accurately than existing techniques.

Findings

The algorithm accurately estimates boundary layer parameters from noisy data.

It is robust to measurement uncertainties and data gaps.

Validated with both numerical simulations and experimental data.

Abstract

A turbulent boundary layer is an essential flow case of fundamental and applied fluid mechanics. However, accurate measurements of turbulent boundary layer parameters (e.g., friction velocity $u_\tau$ and wall shear $\tau_w$), are challenging, especially for high speed flows (Smits et al., 2011). Many direct and/or indirect diagnostic techniques have been developed to measure wall shear stress (Vinuesa et al., 2017). However, based on different principles, these techniques usually give different results with different uncertainties. The current study introduces a nonlinear data assimilation framework based on the Unscented Kalman Filter that can fuse information from i) noisy and gappy measurements from Stereo Particle Image Velocimetry, 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 boundary layer flow at Mach 0.3 is used first to validate the data assimilation algorithm. The algorithm is then applied to experimental data of a flow at Mach 0.3, which are obtained in a blowdown wind tunnel facility. The UKF-based data assimilation algorithm is robust to uncertain and gappy experimental data and is able to provide accurate estimates of turbulent boundary layer parameters.