Resolvent analysis of separated and attached flows around an airfoil at transitional Reynolds number

Thomareis, Nikitas; Papadakis, George

doi:10.1103/physrevfluids.3.073901

Cited by 26 publications

(14 citation statements)

References 35 publications

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“…The mode shapes for intermediate frequencies have a mix of both linear mechanisms as seen for ω = 12 in figure 16. These results are consistent with Thomareis & Papadakis (2018) and Yeh & Taira (2019), who computed resolvent modes for a NACA 0012 airfoil at similar Reynolds numbers and angles of attack from time-averaged DNS and large-eddy simulation (LES) data, respectively. The latter study also identified two branches in the eigenspectrum of the LNS operator which were grouped into wake or shear layer modes.…”

Section: A10 Case: Multiple Linear Mechanismssupporting

confidence: 87%

“…For low Reynolds number bluff body wakes, this could be as few as a single point (see Gómez et al 2016b;Symon et al 2019). In a similar vein, Beneddine et al (2016) and Thomareis & Papadakis (2018) have been able to estimate the spectra at various points of the flow using only the aforementioned measurements. The success of the method relies on the low-rank nature of the (linear) resolvent operator, which one obtains after linearising the Navier-Stokes equations around the (turbulent) mean flow, and treating the nonlinear terms as a source of intrinsic forcing (McKeon & Sharma 2010).…”

Section: Introductionmentioning

confidence: 94%

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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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Section: A10 Case: Multiple Linear Mechanismssupporting

confidence: 87%

Section: Introductionmentioning

confidence: 94%

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

2019

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“…The resolvent operator is derived from the Navier-Stokes equations linearized about the turbulent mean flow and constitutes a transfer function in the frequency domain between terms that are nonlinear and linear with respect to fluctuations to the mean. Resolvent analysis has proven to be a useful tool for understanding and modelling a wide range of flows, including wall-bounded flows (Sharma & McKeon 2013;Morra et al 2019), free-shear flows (Jeun, Nichols & Jovanović 2016;Schmidt et al 2018) and aerodynamic wakes (Thomareis & Papadakis 2018;Symon, Sipp & McKeon 2019;Yeh & Taira 2019). Whereas Beneddine et al (2016) constructed their model using only the first singular mode of the resolvent operator (obtained via singular value decomposition), our model relaxes this a priori assumption and allows the known data to self-select the relevant portion of the resolvent operator.…”

Section: Introductionmentioning

confidence: 99%

Resolvent-based estimation of space–time flow statistics

2019

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We develop a method to estimate space-time flow statistics from a limited set of known data. While previous work has focused on modeling spatial or temporal statistics independently, space-time statistics carry fundamental information about the physics and coherent motions of the flow and provide a starting point for low-order modeling and flow control efforts. The method is derived using a statistical interpretation of resolvent analysis. The central idea of our approach is to use known data to infer the statistics of the nonlinear terms that constitute a forcing on the linearized Navier-Stokes equations, which in turn imply values for the remaining unknown flow statistics through application of the resolvent operator. Rather than making an a priori rank-1 assumption, our method allows the known input data to select the most relevant portions of the resolvent operator for describing the data, making it well-suited for highrank turbulent flows. We demonstrate the predictive capabilities of the method using two examples: the Ginzburg-Landau equation, which serves as a convenient model for a convectively unstable flow, and a turbulent channel flow at low Reynolds number. * Email address for correspondence: towne@umich.edu power spectral densities (PSDs) using knowledge of the mean flow field and power spectra at a few locations. This is accomplished using a least-squares fit at each frequency between the known power spectra and the leading singular response mode obtained from the resolvent operator (McKeon & Sharma 2010), which is derived from the linearized Navier-Stokes equations. 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. The optimization problem is subject to two constraints on the estimated covariance tensor: it must reproduce the known entries and obey a Lyapunov equation that relates the forcing and flow statistics. The constrained optimization problem is computationally demanding and requires a customized algorithm (Zare et al. 2015(Zare et al. , 2017.The objective of the present paper is to build on these previous methods to estimate unknown two-point space-time flow statistics. Both the PSDs (one-point temporal statistics) and spatial covariances (two-point spatial statistics) are subsets of two-point space-time correlations, so our approach represents a generalization of these previous m...

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“…The analysis is performed in frequency space, relies on a mean flow as input, and is specific to a given frequency. It has been used to study the flow over airfoils [11,13,10], however mainly for control purposes and accurate pressure predictions were not provided. In fact, Symon et al [10] remarked that it would be great to see a resolvent pressure prediction for an airfoil.…”

Section: Introductionmentioning

confidence: 99%

Resolvent Method Surface Pressures for Airfoil Trailing-Edge Noise Prediction

Wagner¹,

Sandberg²

2020

Australasian Fluid Mechanics Conference (AFMC)

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We present the first resolvent method-based prediction of airfoil trailing-edge noise. Said noise prediction is obtained by using resolvent method pressure predictions as input to Amiet's theory. This framework is tested by comparing the noise prediction to results obtained from using DNS data as input to Amiet's theory. We subsequently analyse whether the resolvent method predicts the incident, scattered or total pressure field, to establish which expression of Amiet's theory to use. The resolvent method is found to capture the total pressure field, even accounting for the interaction of the incident and scattered pressure fields. The analysis is conducted for an acoustically sharp NACA0012 airfoil at zero incidence, and marks an exciting step in the development of a low-cost, physics-driven, hybrid computational aeroacoustics approach.

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Resolvent analysis of separated and attached flows around an airfoil at transitional Reynolds number

Cited by 26 publications

References 35 publications

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

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

Resolvent-based estimation of space–time flow statistics

Resolvent Method Surface Pressures for Airfoil Trailing-Edge Noise Prediction

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