Data assimilation of mean velocity from 2D PIV measurements of flow over an idealized airfoil

Symon, Sean; Dovetta, Nicolas; McKeon, Beverley; Sipp, Denis; Schmid, Peter J.

doi:10.1007/s00348-017-2336-8

Cited by 54 publications

(44 citation statements)

References 29 publications

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“…A disadvantage of the method though, is that it requires knowledge of the full mean state. However, data assimilation is an active field of research in fluid mechanics, and techniques have recently been developped for two-dimensional mean-flow reconstruction from underresolved/incomplete/noisy measurements (Foures et al 2014;Symon et al 2017). For the method to be applicable outside the lab though, methods should be developped to infer the mean flow from localized sensors only.…”

Section: Resultsmentioning

confidence: 99%

Linear iterative method for closed-loop control of quasiperiodic flows

et al. 2019

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This work proposes a feedback-loop strategy to suppress intrinsic oscillations of resonating flows in the fully nonlinear regime. The frequency response of the flow is obtained from the resolvent operator about the mean flow, extending the framework initially introduced by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to study receptivity mechanisms in turbulent flows. Using this linear time-invariant model of the nonlinear flow, modern control methods such as structured ${\mathcal{H}}_{\infty }$-synthesis can be used to design a controller. The approach is successful in damping self-sustained oscillations associated with specific eigenmodes of the mean-flow spectrum. Despite excellent performance, the linear controller is however unable to completely suppress flow oscillations, and the controlled flow is effectively attracted towards a new dynamical equilibrium. This new attractor is characterized by a different mean flow, which can in turn be used to design a second controller. The method can then be iterated on subsequent mean flows, until the coupled system eventually converges to the base flow. An intuitive parallel can be drawn with Newton’s iteration: at each step, a linearized model of the flow response to a perturbation of the input is sought, and a new linear controller is designed, aiming at further reducing the fluctuations. The method is illustrated on the well-known case of two-dimensional incompressible open-cavity flow at Reynolds number $Re=7500$, where the fully developed flow is initially quasiperiodic (2-torus state). The base flow is reached after five iterations. The present work demonstrates that nonlinear control problems may be solved without resorting to nonlinear reduced-order models. It also shows that physically relevant linear models can be systematically derived for nonlinear flows, without resorting to black-box identification from input–output data; the key ingredient being frequency-domain models based on the linearized Navier–Stokes equations about the mean flow. Applicability to amplifier flows and turbulent dynamics has, however, yet to be investigated.

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Section: Resultsmentioning

confidence: 99%

Linear iterative method for closed-loop control of quasiperiodic flows

et al. 2019

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“…Recent work has investigated the use of data assimilation techniques (e.g. particle filters or ensemble Kalman filters) to estimate the mean flow [55,56,57] or the full flow field [58,59,60,61,62]. In any case, the accuracy of observer-based methods depends on the quality of the reduced-order model, so there is inevitably a tradeoff between low-latency and high-accuracy models.…”

Section: Prior Work In Flow Field Reconstructionmentioning

confidence: 99%

Robust flow reconstruction from limited measurements via sparse representation

Callaham¹,

Maeda²,

Brunton³

2019

Phys. Rev. Fluids

126

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In many applications it is important to estimate a fluid flow field from limited and possibly corrupt measurements. Current methods in flow estimation often use least squares regression to reconstruct the flow field, finding the minimum-energy solution that is consistent with the measured data. However, this approach may be prone to overfitting and sensitive to noise. To address these challenges we instead seek a sparse representation of the data in a library of examples. Sparse representation has been widely used for image recognition and reconstruction, and it is well-suited to structured data with limited, corrupt measurements. We explore sparse representation for flow reconstruction on a variety of fluid data sets with a wide range of complexity, including vortex shedding past a cylinder at low Reynolds number, a mixing layer, and two geophysical flows. In addition, we compare several measurement strategies and consider various types of noise and corruption over a range of intensities. We find that sparse representation has considerably improved estimation accuracy and robustness to noise and corruption compared with least squares methods. We also introduce a sparse estimation procedure on local spatial patches for complex multiscale flows that preclude a global sparse representation. Based on these results, sparse representation is a promising framework for extracting useful information from complex flow fields with realistic measurements.

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“…The equations are spatially discretised using quadratic basis functions for the velocity and linear basis functions for the pressure resulting in approximately 360,000 and 1,000,000 degrees of freedom for the A0 and A10 cases, respectively. The reader is referred to Foures et al (2014); Symon et al (2017) for more details about the algorithm and its implementation.…”

Section: Data-assimilation Of the Mean Velocity Profilesmentioning

confidence: 99%

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

2019

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The flows around a NACA 0018 airfoil at a chord-based Reynolds number of Re = 10250 and angles of attack of α = 0 • and α = 10 • are modelled using resolvent analysis and limited experimental measurements obtained from particle image velocimetry. The experimental mean velocity profiles are data-assimilated so that they are solutions of the incompressible Reynolds-averaged Navier-Stokes equations forced by Reynolds stress terms which are derived from experimental data. Spectral proper orthogonal decompositions of the velocity fluctuations and nonlinear forcing suggest different modelling approaches should be taken based on the angle of attack under consideration. For the α = 0 • case, the cross-spectral density tensors of both the velocity fluctuations and nonlinear forcing are low-rank at the shedding frequency and its higher harmonics. In the α = 10 • case, low-rank behaviour is observed for the velocity fluctuations in two bands of frequencies. Resolvent analysis of the data-assimilated means identifies lowrank behaviour only in the vicinity of the shedding frequency for α = 0 • and none of its harmonics. The resolvent operator for the α = 10 • case, on the other hand, identifies two linear mechanisms whose frequencies are a close match with those identified by spectral proper orthogonal decomposition. It is also shown that the second linear mechanism, corresponding to the Kelvin-Helmholtz instability in the shear layer, cannot be identified just by considering the time-averaged experimental measurements as a mean flow for resolvent analysis. This is due to the fact that experimental data are missing near the leading edge of the airfoil. The α = 0 • case is classified as an oscillator where the flow is organized around an intrinsic instability mechanism while the α = 10 • case behaves like an amplifier whose forcing is unstructured. For both cases, resolvent modes resemble those from spectral proper orthogonal decomposition when the operator is low-rank. To model the higher harmonics where this is not the case, we add parasitic resolvent modes, as opposed to classical resolvent modes which are the most amplified, by approximating the nonlinear forcing from limited triadic interactions of known resolvent modes. The amplifier case is modelled without parasitic modes at frequencies where the resolvent is low-rank. The two cases suggest that resolvent-based modelling can be achieved for more complex flows with limited experimental measurements and the nonlinear forcing need not be approximated unless the flow behaves like an oscillator.

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Data assimilation of mean velocity from 2D PIV measurements of flow over an idealized airfoil

Cited by 54 publications

References 29 publications

Linear iterative method for closed-loop control of quasiperiodic flows

Linear iterative method for closed-loop control of quasiperiodic flows

Robust flow reconstruction from limited measurements via sparse representation

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

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