GALCIT Colloquium

A flow reconstruction methodology is presented for incompressible, statistically stationary flows using resolvent analysis and data-assimilation. The only inputs necessary for the procedure are a rough approximation of the mean profile and a single time-resolved measurement. The objective is to estimate both the mean and fluctuating states of experimental flows with limited measurements which do not include pressure. The input data may be incomplete, in the sense that measurements near a body are difficult to obtain with techniques such as particle image velocimetry (PIV), or contaminated by noise. The tools developed in this talk are capable of filling in missing data and reducing the amount of measurement noise by leveraging the governing equations. The reconstructed flow is capable of estimating fluctuations where time-resolved data are not available and solving the flow on larger domains where the mean profile is not known.

The first part of the talk is centered on developing the tools necessary for this procedure. The second part of the talk discusses the reconstruction of flow around a NACA 0018 airfoil at zero angle of attack and a chord-based Reynolds number of 10250. The mean profile, obtained from PIV, is data-assimilated and used as an input to resolvent analysis to educe coherent structures in the flow. The resolvent operator for non-amplified temporal frequencies is forced by an approximated nonlinear forcing. The amplitude and phase of the modes are obtained from the discrete Fourier-transform of a time-resolved probe point measurement. The final reconstruction contains less measurement noise compared to the PIV snapshots and obeys the incompressible Navier-Stokes equations.