Lift coefficient estimation for a rapidly pitching airfoil

Abstract

We develop a method for estimating the instantaneous lift coefficient on a rapidly pitching airfoil that uses a small number of pressure sensors and a measurement of the angle of attack. The approach assimilates four surface pressure measurements with a modified nonlinear state space model (Goman-Khrabrov model) through a Kalman filter. The error of lift coefficient estimates based only on a weighted-sum of the measured pressures are found to be noisy and biased, which leads to inaccurate estimates. The estimate is improved by including the predictive model in an conventional Kalman filter. The Goman-Khrabrov model is shown to be a linear parameter-varying system and can therefore be used in the Kalman filter without the need for linearization. Additional improvement is realized by modifying the algorithm to provide more accurate estimate of the lift coefficient. The improved Kalman filtering approach results in a bias-free lift coefficient estimate that is more precise than either the pressure-based estimate or the Goman-Khrabrov model on their own. The new method will enable performance enhancements in aerodynamic systems whose performance relies on lift.

All you need is time to generalise the Goman–Khrabrov dynamic stall model

“…2015, 2019; Sedky, Jones & Lagor 2020; An et al. 2021). It accurately models dynamic stall load hysteresis over a wide range of reduced frequencies and flow conditions where dynamic stall is characterised by a progressive increase of trailing-edge separation.…”

“…Once X 0 (α) is obtained, τ 1 and τ 2 are empirically determined by applying (2.1) to unsteady experimental or numerical training data. The best-fit values of τ 1 and τ 2 are considered to be constant for a large range of pitching frequencies for a specific airfoil shape (Williams et al 2015;Le Provost et al 2018;Williams & King 2018;An et al 2021).…”

“…The Goman-Khrabrov model predicts well the attached flow regime, the magnitude and timing of the first lift peak, and the general decaying lift trend post dynamic stall, which occurs at t = t ds . It is a first-order model that neglects higher-order features in the flow field and cannot reproduce the higher harmonics of the load fluctuations due to subsequent vortex shedding seen in figure 1 (Culler & Farnsworth 2019;An et al 2021).…”

“…The state-space Goman-Khrabrov model (Goman & Khrabrov 1994) is a first-order model with two empirical parameters that provides a good compromise between interpretability and simplicity. The model has received renewed interest in the past decade for active control applications (Williams et al 2015(Williams et al , 2019Sedky, Jones & Lagor 2020;An et al 2021). It accurately models dynamic stall load hysteresis over a wide range of reduced frequencies and flow conditions where dynamic stall is characterised by a progressive increase of trailing-edge separation.…”

Experimental Study of Dynamical Airfoil and Aerodynamic Prediction

“…Juliano et al [16] found that the pressure field on an oscillating airfoil can have distinct patterns at different locations that are difficult to capture using pressure sensors. Similarly, An et al [17] develop a method for estimating the instantaneous lift coefficient on a rapidly pitching airfoil that uses a small number of pressure sensors and a measurement of the angle of attack. Gao et al [18] detected unsteady boundary layer transition on a pitching airfoil using a statistical criterion calculated from thirty surface-pressure transducer measurements.…”