Resolvent analysis on the origin of two-dimensional transonic buffet

Kojima, Yoimi; Yeh, C.; Taira, Kunihiko; Kameda, Masaharu

doi:10.1017/jfm.2019.992

Cited by 29 publications

(9 citation statements)

References 38 publications

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“…Jovanović (2004) extended the methodology to unstable systems and Schmid & Brandt (2014) discussed the evolution of perturbations over a finite-time horizon and the modal sensitivity to small changes in the resolvent operator. These efforts enabled the use of resolvent analysis for studying various types of complex fluid flows (Gómez et al 2016;Schmidt et al 2018;Yeh & Taira 2019;Kojima et al 2020;Yeh et al 2020;Liu et al 2021).…”

Section: Introductionmentioning

confidence: 99%

Wing sweep effects on laminar separated flows

et al. 2022

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We reveal the effects of sweep on the wake dynamics around NACA 0015 wings at high angles of attack using direct numerical simulations and resolvent analysis. The influence of sweep on the wake dynamics is considered for sweep angles from $0^\circ$ to $45^\circ$ and angles of attack from $16^\circ$ to $30^\circ$ for a spanwise periodic wing at a chord-based Reynolds number of $400$ and a Mach number of $0.1$ . Wing sweep affects the wake dynamics, especially in terms of stability and spanwise fluctuations with implications on the development of three-dimensional (3-D) wakes. We observe that wing sweep attenuates spanwise fluctuations. Even as the sweep angle influences the wake, force and pressure coefficients can be collapsed for low angles of attack when examined in wall-normal and wingspan-normal independent flow components. Some small deviations at high sweep and incidence angles are attributed to vortical wake structures that impose secondary aerodynamic loads, revealed through the force element analysis. Furthermore, we conduct global resolvent analysis to uncover oblique modes with high disturbance amplification. The resolvent analysis also reveals the presence of wavemakers in the shear-dominated region associated with the emergence of 3-D wakes at high angles of attack. For flows at high sweep angles, the optimal convection speed of the response modes is shown to be faster than the optimal wavemakers speed suggesting a mechanism for the attenuation of perturbations. The present findings serve as a fundamental stepping stone to understanding separated flows at higher Reynolds numbers.

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Section: Introductionmentioning

confidence: 99%

Wing sweep effects on laminar separated flows

et al. 2022

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“…In this subsection, we perform a resolvent analysis of the mean flow. Resolvent analysis has been utilized to uncover the origin of unsteady fluctuations in turbulent boundary layers (Luhar, Sharma & McKeon 2014) and transonic flow over an aerofoil (Kojima et al 2020), in terms of the input-output relation analysis. Through resolvent analysis, we aim to uncover the origin of the trailing-edge noise for the primary tone noise at St = 7.2 and the higher frequency tone at St = 11.2, presented in figure 5(a).…”

Section: Resolvent Analysis Of the Linear Operatormentioning

confidence: 99%

“…Using the spatial window C can aid in studying the optimal energy amplification from forcing to a response in local domains (Schmidt et al 2018;Kojima et al 2020;Yeh et al 2020). In this study, the spatial window is chosen to cover the laminar separation bubbles on both sides of the aerofoil, where the velocity fluctuations are mainly generated.…”

Section: Resolvent Analysismentioning

confidence: 99%

On the origin of quadrupole sound from a two-dimensional aerofoil trailing edge

Kojima

Skene²,

Yeh³

et al. 2023

J. Fluid Mech.

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Tonal noise emitted from the trailing edge of an airfoil is considered using modal analysis techniques to investigate secondary quadrupole tones. We examine the origin of quadrupole sound generated from two-dimensional unsteady laminar flow over a NACA0012 airfoil. In this paper, we consider two flow configurations at Mach numbers of $M_\infty = 0.1$ and 0.05 that lead to different acoustic characteristics: the former has a significant high-frequency quadrupole noise source, whereas the latter does not. We use vortex sound theory, dynamic mode decomposition (DMD), and resolvent analysis to analyze the sound source. First, we employ DMD modes to reveal that the quadrupole sound is only observed in the higher Mach number case. Next, the vortex dynamics in the vicinity of the trailing edge are studied to identify the origin of quadrupole sound. It is found that the quadrupole sound is caused by vortex shedding in the vicinity of the trailing edge. The complex vortex interaction between both sides of the airfoil strengthens the quadrupole source in the higher Mach number case, while it is negligible in the lower one. Furthermore, we perform resolvent analysis to examine the vortex generation over the airfoil. The resolvent mode indicates that the interaction between the vortices on both sides of the airfoil causes a multi-scale vortex structure on the suction-side wall.

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“…encapsulates the region of LSB. This spatial window is implemented in the output matrix C in equation ( 5) by assigning unit weights to its diagonal elements inside the window and zeros otherwise [39,48]. This matrix C defines the output ŷ as the response observed only through this spatial window, while masking out the response outside.…”

Section: Windowed Analysismentioning

confidence: 99%

Resolvent analysis of an airfoil laminar separation bubble at Re = 500,000

Yeh¹,

Benton²,

Taira³

et al. 2020

Preprint

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We perform resolvent analysis to examine the perturbation dynamics over the laminar separation bubble (LSB) that forms near the leading edge of a NACA 0012 airfoil at a chord-based Reynolds number of 500,000 and an angle of attack of 8 degrees. While we focus on the LSB residing over 6% of the chord length, the resolvent operator is constructed about the global mean flow over the airfoil, avoiding numerical issues arising from domain truncation. Moreover, randomized SVD is adopted in the present analysis to relieve the computational cost associated with the high-Re global base flow. To examine the local physics over the LSB, we consider the use of exponential discounting to limit the time horizon that allows for the instability to develop with respect to the base flow. With discounting, the gain distribution over frequency accurately captures the spectral content over the LSB obtained from flow simulation. The peak-gain frequency also agrees with previous flow control results on suppressing dynamic stall over a pitching airfoil. According to the gain distribution and the modal structures, we conclude that the dominant energy-amplification mechanism is the Kelvin-Helmholtz instability. In addition to discounting, we also examine the use of spatial windows for both the forcing and response. From the response-windowed analysis, we find that the LSB serves the main role of energy amplifier, with the amplification saturating at the reattachment point. The input window imposes the constraint of surface forcing, and the results show that the optimal actuator location is slightly upstream of the separation point. The surfaceforcing mode also suggest the optimal momentum forcing in the surface-tangent direction, with strong uni-directionality that is ideal for synthetic-jet-type actuators. This study demonstrates the strength of randomized resolvent analysis in tackling high-Reynolds-number base flows and calls attention to the care needed for base-flow instabilities. The physical insights provided by the resolvent analysis can also support flow control studies that target the LSB for suppressing flow separation or dynamic stall.

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Resolvent analysis on the origin of two-dimensional transonic buffet

Cited by 29 publications

References 38 publications

Wing sweep effects on laminar separated flows

Wing sweep effects on laminar separated flows

On the origin of quadrupole sound from a two-dimensional aerofoil trailing edge

Resolvent analysis of an airfoil laminar separation bubble at Re = 500,000

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