Unsteady flow dynamics reconstruction from mean flow and point sensors: an experimental study

Abstract

This article presents a reconstruction of the unsteady behaviour of a round jet at a Reynolds number equal to 3300, from the sole knowledge of the time-averaged flow field and one pointwise unsteady measurement. The reconstruction approach is an application of the work of Beneddine et al. (J. Fluid Mech., vol. 798, 2016, pp. 485-504) and relies on the computation of the dominant resolvent modes of the flow, using a parabolised stability equations analysis. To validate the procedure, the unsteady velocity field of the jet has been characterised by time-resolved particle image velocimetry (TR-PIV), yielding an experimental reference. We first show that the dominant resolvent modes are proportional to the experimental Fourier modes, as predicted by Beneddine et al. (J. Fluid Mech., vol. 798, 2016, pp. 485-504). From these results, it is then possible to fully reconstruct the unsteady velocity and pressure fluctuation fields, yielding a flow field that displays good agreement with the experimental reference. Finally, it is found that the robustness of the reconstruction mainly depends on the location of the pointwise unsteady measurement, which should be within energetic regions of the flow, and this robustness as well as the quality of the reconstruction can be greatly improved by considering a few pointwise measurements instead of a single one. The effects of other experimental parameters on the reconstruction, such as the size of the interrogation window used for the TR-PIV processing and the accuracy of the positioning of the sensors, are also investigated in this paper.

A tale of two airfoils: resolvent-based modelling of an oscillator versus an amplifier from an experimental mean

“…The majority of the aforementioned studies have utilised a mean obtained from simulations although a growing number have considered experimental means (Sasaki et al 2017;Beneddine et al 2017;He et al 2019). The objective in this article is to obtain a reduced-order representation using a partially known mean obtained from experiments.…”

Resolvent-based estimation of space–time flow statistics

“…This strategy explicitly assumes that the spectral content at frequencies of interest is dominated by the leading resolvent mode, and the method performs well when the matching points are located in regions where this hypothesis is valid. Specifically, excellent PSD estimates were obtained for the flow over a backward-facing step (Beneddine et al 2016) and an initially laminar jet (Beneddine et al 2017).…”

“…This strategy explicitly assumes that the spectral content at frequencies of interest is dominated by the leading resolvent mode, and the method performs well when the matching points are located in regions where this hypothesis is valid. Specifically, excellent PSD estimates were obtained for the flow over a backward-facing step (Beneddine et al 2016) and an initially laminar jet (Beneddine et al 2017).Zare et al (2017) developed a method that uses arbitrary known entries in the spatial covariance tensor to estimate the remaining unknown entries. Their approach is also based on linearized flow equations and entails solving a convex optimization problem that determines a matrix controlling the structure and statistics of the associated nonlinear forcing terms.…”

Data-based, reduced-order, dynamic estimator for reconstruction of nonlinear flows exhibiting limit-cycle oscillations

“…..m , that satisfy the conditions given by Eqs. (7). Any velocity field V can then be projected onto this first k modes to produce the approximate flow field V (refer to Eq.…”

“…Semaan [5] computed optimal sensor placements using machine learning. Other reduced order modelling strategies, such as the resolvent analysis [6] have been used for estimation of laminar (but also turbulent) flows using limited measurements [7][8][9][10]. More recent trends use sparse representation and compressive sensing [11,12].…”