An input–output based analysis of convective velocity in turbulent channels

Liu, Chang; Gayme, Dennice F.

doi:10.1017/jfm.2020.48

Cited by 21 publications

(21 citation statements)

References 85 publications

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“…This implies that the use of temporal data from a stationary wallsensor, as input for off-wall opposition control of near wall turbulence, is as effective as using spatial data. It is also noted that the temporal and spatial coherence spectra differ significantly in the region + < 15 and + < 500, which is presumably due to the mismatch between the local mean and the true structure convection velocity in that region (Del Álamo and Jiménez, 2009;Dróżdż and Elsner, 2017;Liu and Gayme, 2020). Figs.…”

Section: Spatial Versus Temporal Coherence Spectrogramsmentioning

confidence: 88%

Near wall coherence in wall-bounded flows and implications for flow control

Samie

Baars

Rouhi

et al. 2020

International Journal of Heat and Fluid Flow

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Opposition-control of the energetic cycle of near wall streaks in wall-bounded turbulence, using numerical approaches, has shown promise for drag reduction. For practical implementation, real-time opposition control is only realizable if there is a degree of coherence between the turbulent velocities passing a sensor and the target point within the flow; for practicality, a sensor (and actuator) should be wall-based to avoid parasitic drag. As such, we here inspect the feasibility of real-time control of the near wall cycle, by considering the coherence between a measurable wall-quantity, being the wall-shear stress fluctuations, and the streamwise and wall-normal velocity fluctuations in a turbulent boundary layer. Synchronized spatial and temporal velocity data from two direct numerical simulations and a fine large eddy simulation at ≈ 590 and 2000 are employed. This study shows that the spectral energy of the streamwise velocity fluctuations that is stochastically incoherent with wall signals is independent of Reynolds number in the near wall region (up to the viscous-scaled wall-normal height + ≈ 20). Consequently, the streamwise energy-fraction that is stochastically wall-coherent grows with Reynolds number due to the increasing range of energetic large scales. This thus implies that a wall-based control system has the ability to manipulate a larger portion of the total turbulence energy at off-wall locations, at higher Reynolds numbers, while the efficacy of predicting/targeting the small scales of the near wall cycle remains indifferent with varying Reynolds number. Coherence values of 0.55 and 0.4 were found between the streamwise and wall-normal velocity fluctuations at the near wall peak in the energy spectrogram, respectively, and the streamwise fluctuating friction velocity. These coherence values, which are considerably lower than 1 (maximum possible coherence) suggest that a closed-loop drag reduction scheme targeting near wall cycle streaks alone (based on sensed friction velocity fluctuations) will be of limited success in practice.

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Section: Spatial Versus Temporal Coherence Spectrogramsmentioning

confidence: 88%

Near wall coherence in wall-bounded flows and implications for flow control

Samie

Baars

Rouhi

et al. 2020

International Journal of Heat and Fluid Flow

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“…Structured input-output analysis shares the advantages of all methods employing analysis of the spatio-temporal frequency response, which this work builds upon (e.g. Farrell & Ioannou 1993;Bamieh & Dahleh 2001;Jovanović & Bamieh 2005;McKeon & Sharma 2010;McKeon, Sharma & Jacobi 2013;McKeon 2017;Illingworth, Monty & Marusic 2018;Vadarevu et al 2019;Madhusudanan, Illingworth & Marusic 2019;Symon, Illingworth & Marusic 2021;Liu & Gayme 2019, 2020a. Of greatest interest in this work is its computational tractability compared with nonlinear approaches and the lack of finite channel size effects that can plague both DNS and experimental studies.…”

Section: Introductionmentioning

confidence: 99%

Structured input–output analysis of transitional wall-bounded flows

Liu

Gayme

2021

J. Fluid Mech.

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Input–output analysis of transitional channel flows has proven to be a valuable analytical tool for identifying important flow structures and energetic motions. The traditional approach abstracts the nonlinear terms as forcing that is unstructured, in the sense that this forcing is not directly tied to the underlying nonlinearity in the dynamics. This paper instead employs a structured-singular-value-based approach that preserves certain input–output properties of the nonlinear forcing function in an effort to recover the larger range of key flow features identified through nonlinear analysis, experiments and direct numerical simulation (DNS) of transitional channel flows. Application of this method to transitional plane Couette and plane Poiseuille flows leads to not only the identification of the streamwise coherent structures predicted through traditional input–output approaches, but also the characterization of the oblique flow structures as those requiring the least energy to induce transition, in agreement with DNS studies, and nonlinear optimal perturbation analysis. The proposed approach also captures the recently observed oblique turbulent bands that have been linked to transition in experiments and DNS with very large channel size. The ability to identify the larger amplification of the streamwise varying structures predicted from DNS and nonlinear analysis in both flow regimes suggests that the structured approach allows one to maintain the nonlinear effects associated with weakening of the lift-up mechanism, which is known to dominate the linear operator. Capturing this key nonlinear effect enables the prediction of a wider range of known transitional flow structures within the analytical input–output modelling paradigm.

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“…x < 500, which is presumably due to the mismatch between the local mean and the true structure convection velocity in that region (Del Álamo and Jiménez, 2009;Dróżdż and Elsner, 2017;Liu and Gayme, 2020). Figures 3(a) and 3(b) compare the γ 2 uuτ t and γ 2 uuτ s spectrograms at Re τ ≈ 590 and ≈ 2000, respectively.…”

Section: Spatial Versus Temporal Coherence Spectrograms 100mentioning

confidence: 99%

Near wall coherence in wall-bounded flows and implications for flow control

Samie,

Baars,

Rouhi

et al. 2020

Preprint

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Opposition-control of the energetic cycle of near wall streaks in wall-bounded turbulence, using numerical approaches, has shown promise for drag reduction. For practical implementation, opposition control is only realizable if there is a degree of coherence between the sensor-actuator pairs of the control system (and for practicality these sensors and actuators should typically be wall-based to avoid parasitic drag). As such, we here inspect the feasibility of real-time control of the near-wall cycle, by considering the coherence between a measurable wall-quantity, being the wall-shear stress fluctuations, and the streamwise and wall-normal velocity fluctuations in a turbulent boundary layer. Synchronized spatial and temporal velocity data from two direct numerical simulations and a fine large eddy simulation at Re τ ≈ 590 and 2000 are employed. This study shows that the spectral energy of the streamwise velocity fluctuations that is stochastically incoherent with wall signals is independent of Reynolds number in the near wall region (up to the viscous-scaled wallnormal height z + ≈ 20). Consequently, the streamwise energy-fraction that is stochastically wall-coherent grows with Reynolds number due to the increasing range of energetic large scales. This thus implies that a wall-based control system has the ability to manipulate a larger portion of the total turbulence energy at off-wall locations, at higher Reynolds numbers, while the efficacy of predicting/targeting the small scales of the near-wall cycle remains indifferent with varying Reynolds number. Coherence values of 0.55 and 0.4 were found between the streamwise and wall-normal velocity fluctuations at the near wall peak in the energy spectrogram, respectively, and the streamwise fluctuating friction velocity. These coherence values, which are considerably lower than 1 (maximum possible coherence) suggest that a closed-loop drag reduction scheme targeting near wall cycle of streaks alone (based on sensed friction velocity fluctuations) will be of limited success in practice as the Reynolds number grows.

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An input–output based analysis of convective velocity in turbulent channels

Cited by 21 publications

References 85 publications

Near wall coherence in wall-bounded flows and implications for flow control

Near wall coherence in wall-bounded flows and implications for flow control

Structured input–output analysis of transitional wall-bounded flows

Near wall coherence in wall-bounded flows and implications for flow control

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