On the wave-cancelling nature of boundary layer flow control

Sasaki, Kenzo; Morra, Pierluigi; Fabbiane, Nicolò; Cavalieri, André V. G.; Hanifi, Ardeshir; Henningson, Dan S.

doi:10.1007/s00162-018-0469-x

Cited by 23 publications

(49 citation statements)

References 47 publications

(69 reference statements)

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“…The implementation of this method in experimental applications would depend on the availability of two simultaneous measurements for constructing the TFs, one of them possibly corresponding to wall-shear stress. The availability of the SISO transfer function also allows for the derivation of linear control laws, as explored in other works by this group, for transitional flows (Sasaki et al 2018a). Furthermore, as long as the wall-normal separation between input and output measurements is kept small, a reasonable prediction is obtained by this method.…”

Section: Discussionmentioning

confidence: 99%

“…The dummy variables (ζ , τ ), which are analogous to (z, t), were introduced for the calculation of the convolution. In order to obtain g IO (ζ , τ ), the problem is formulated in the frequency/spanwise wavenumber space, where the optimal frequency response, in the least squares sense, may be defined from the auto-and cross-spectra of the input and output signals (Bendat & Piersol 2011;Sasaki et al 2017Sasaki et al , 2018a:…”

Section: Single-input Linear Transfer Functionmentioning

confidence: 99%

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Transfer functions for flow predictions in wall-bounded turbulence

et al. 2019

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Three methods are evaluated to estimate the streamwise velocity fluctuations of a zero-pressure-gradient turbulent boundary layer of momentum-thickness-based Reynolds number up to $Re_{\unicode[STIX]{x1D703}}\simeq 8200$, using as input velocity fluctuations at different wall-normal positions. A system identification approach is considered where large-eddy simulation data are used to build single and multiple-input linear and nonlinear transfer functions. Such transfer functions are then treated as convolution kernels and may be used as models for the prediction of the fluctuations. Good agreement between predicted and reference data is observed when the streamwise velocity in the near-wall region is estimated from fluctuations in the outer region. Both the unsteady behaviour of the fluctuations and the spectral content of the data are properly predicted. It is shown that approximately 45 % of the energy in the near-wall peak is linearly correlated with the outer-layer structures, for the reference case $Re_{\unicode[STIX]{x1D703}}=4430$. These identified transfer functions allow insight into the causality between the different wall-normal locations in a turbulent boundary layer along with an estimation of the tilting angle of the large-scale structures. Differences in accuracy of the methods (single- and multiple-input linear and nonlinear) are assessed by evaluating the coherence of the structures between wall-normally separated positions. It is shown that the large-scale fluctuations are coherent between the outer and inner layers, by means of an interactions which strengthens with increasing Reynolds number, whereas the finer-scale fluctuations are only coherent within the near-wall region. This enables the possibility of considering the wall-shear stress as an input measurement, which would more easily allow the implementation of these methods in experimental applications. A parametric study was also performed by evaluating the effect of the Reynolds number, wall-normal positions and input quantities considered in the model. Since the methods vary in terms of their complexity for implementation, computational expense and accuracy, the technique of choice will depend on the application under consideration. We also assessed the possibility of designing and testing the models at different Reynolds numbers, where it is shown that the prediction of the near-wall peak from wall-shear-stress measurements is practically unaffected even for a one order of magnitude change in the corresponding Reynolds number of the design and test, indicating that the interaction between the near-wall peak fluctuations and the wall is approximately Reynolds-number independent. Furthermore, given the performance of such methods in the prediction of flow features in turbulent boundary layers, they have a good potential for implementation in experiments and realistic flow control applications, where the prediction of the near-wall peak led to correlations above 0.80 when wall-shear stress was used in a multiple-input or nonlinear scheme. Errors of the order of 20 % were also observed in the determination of the near-wall spectral peak, depending on the employed method.

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Section: Discussionmentioning

confidence: 99%

Section: Single-input Linear Transfer Functionmentioning

confidence: 99%

Transfer functions for flow predictions in wall-bounded turbulence

et al. 2019

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“…The flow is forced with a spatiotemporally white noise for y < 5. The distributed forcing excites, in addition to unstable Tollmien-Schlichting (T-S) waves, many other stable modes, leading to a more challenging case for estimation in comparison to forcing in a limited upstream region, which is often considered in flow-control problems (Bagheri et al 2009;Belson et al 2013;Sasaki et al 2018).…”

Section: Transitional Flat-plate Boundary Layermentioning

confidence: 99%

Resolvent-based optimal estimation of transitional and turbulent flows

et al. 2020

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“…This behaviour leads to an imperfect cancellation of the incoming streak. Since a destructive interference is the physical mechanism behind flow control of convectively unstable flows (Sasaki et al 2018a;Morra et al 2019), the f x2 -only and optimal forcing actuators lead to a lower performance in terms of transition delay. It should also be noted that the identified actuator presents a peak in its spatial support which is at a higher wall-normal location than the other two (as shown in figure 8); this is probably related to the higher peak of the streak it is identifying inside the flow.…”

Section: Spod In Open-loopmentioning

confidence: 99%

On the role of actuation for the control of streaky structures in boundary layers

et al. 2019

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This work deals with the closed-loop control of streaky structures induced by free-stream turbulence (FST) in a zero-pressure gradient, transitional boundary layer, by means of localized sensors and actuators. A linear quadratic gaussian regulator is considered along with a system identification technique to build reduced-order models for control. Three actuators are developed with different spatial supports, corresponding to a baseline shape with only vertical forcing, and to two other shapes obtained by different optimization procedures. A computationally efficient method is derived to obtain an actuator which aims to induce the exact structures which are inside the boundary layer, given in terms of their first spectral proper orthogonal decomposition (SPOD) mode, and an actuator that maximizes the energy of induced downstream structures. Two free-stream turbulence levels were evaluated, corresponding to 3.0% and 3.5%, and closed-loop control is applied in large-eddy simulations of transitional boundary layers. All three actuators lead to significant delays in the transition to turbulence and were shown to be robust to mild variations in the free-stream turbulence levels. Differences are understood in terms of the SPOD of actuation and FST-induced fields along with the causality of the control scheme when a cancellation of disturbances is considered. The actuator optimized to generate the leading downstream SPOD mode, representing the streaks in the open-loop flow, leads to the highest transition delay, which can be understood due to its capability of closely cancelling structures in the boundary layer. However, it is shown that even with the actuator located downstream of the input measurement it may become impossible to cancel incoming disturbances in a causal way, depending on the wall-normal position of the output and on the actuator considered, which limits sensor and actuator placement capable of good closed-loop performance.

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On the wave-cancelling nature of boundary layer flow control

Cited by 23 publications

References 47 publications

Transfer functions for flow predictions in wall-bounded turbulence

Transfer functions for flow predictions in wall-bounded turbulence

Resolvent-based optimal estimation of transitional and turbulent flows

On the role of actuation for the control of streaky structures in boundary layers

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