| 1. |
- Abreu, Leandra, I, et al.
(author)
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Resolvent modelling of near-wall coherent structures in turbulent channel flow
- 2020
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In: International Journal of Heat and Fluid Flow. - : ELSEVIER SCIENCE INC. - 0142-727X .- 1879-2278. ; 85
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Journal article (peer-reviewed)abstract
- Turbulent channel flow was analysed using direct numerical simulations at friction Reynolds numbers Re-tau = 180 and 550. The databases were studied using spectral proper orthogonal decomposition (SPOD) to identify dominant near-wall coherent structures, most of which turn out to be streaks and streamwise vortices. Resolvent analysis was used as a theoretical approach to model such structures, as it allows the identification of the optimal forcing and most amplified flow response; the latter may be related to the observed relevant structures obtained by SPOD, especially if the gain between forcing and response is much larger than what is found for suboptimal forcings or if the non-linear forcing is white noise. Results from SPOD and resolvent analysis were compared for several combinations of frequencies and wavenumbers. For both Reynolds numbers, the best agreement between SPOD and resolvent modes was observed for the cases where the lift-up mechanism from resolvent analysis is present, which are also the cases where the optimal resolvent gain is dominant. These results confirm the outcomes in our previous studies (Abreu et al., 2019; Abreu et al., 2020), where we used a DNS database of a pipe flow for the same Reynolds numbers.
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| 2. |
- Abreu, Leandra, I, et al.
(author)
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Spanwise-coherent hydrodynamic waves around flat plates and airfoils
- 2021
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In: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 927
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Journal article (peer-reviewed)abstract
- We investigate spanwise-coherent structures in the turbulent flow around airfoils, motivated by their connection with trailing-edge noise. We analyse well-resolved large-eddy simulations (LES) of the flow around NACA 0012 and NACA 4412 airfoils, both at a Reynolds number of 400 000 based on the chord length. Spectral proper orthogonal decomposition performed on the data reveals that the most energetic coherent structures are hydrodynamic waves, extending over the turbulent boundary layers around the airfoils with significant amplitudes near the trailing edge. Resolvent analysis was used to model such structures, using the mean field as a base flow. We then focus on evaluating the dependence of such structures on the domain size, to ensure that they are not an artefact of periodic boundary conditions in small computational boxes. To this end, we performed incompressible LES of a zero-pressure-gradient turbulent boundary layer, for three different spanwise sizes, with the momentum-thickness Reynolds number matching those near the airfoils trailing edge. The same coherent hydrodynamic waves were observed for the three domains. Such waves are accurately modelled as the most amplified flow response from resolvent analysis. The signature of such wide structures is seen in non-premultiplied spanwise wavenumber spectra, which collapse for the three computational domains. These results suggest that the spanwise-elongated structures are not domain-size dependent for the studied simulations, indicating thus the presence of very wide structures in wall-bounded turbulent flows.
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| 3. |
- Abreu, Leandra, I, et al.
(author)
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Spectral proper orthogonal decomposition and resolvent analysis of near-wall coherent structures in turbulent pipe flows
- 2020
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In: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 900
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Journal article (peer-reviewed)abstract
- Direct numerical simulations, performed with a high-order spectral-element method, are used to study coherent structures in turbulent pipe flow at friction Reynolds numbers Re-tau = 180 and 550. The database was analysed using spectral proper orthogonal decomposition (SPOD) to identify energetically dominant coherent structures, most of which turn out to be streaks and quasi-streamwise vortices. To understand how such structures can be modelled, the linear flow responses to harmonic forcing were computed using the singular value decomposition of the resolvent operator, using the mean field as a base flow. The SPOD and resolvent analysis were calculated for several combinations of frequencies and wavenumbers, allowing the mapping out of similarities between SPOD modes and optimal responses for a wide range of relevant scales in turbulent pipe flows. In order to explore physical reasons behind the agreement between both methods, an indicator of lift-up mechanism in the resolvent analysis was introduced, activated when optimal forcing is dominated by the wall-normal and azimuthal components, and associated response corresponds to streaks of streamwise velocity. Good agreement between leading SPOD and resolvent modes is observed in a large region of parameter space. In this region, a significant gain separation is found in resolvent analysis, which may be attributed to the strong amplification associated with the lift-up mechanism, here understood as nonlinear forcing terms leading to the appearance of streamwise vortices, which in turn form high-amplitude streaks. For both Reynolds numbers, the observed concordances were generally for structures with large energy in the buffer layer. The results highlight resolvent analysis as a pertinent reduced-order model for coherent structures in wall-bounded turbulence, particularly for streamwise elongated structures corresponding to near-wall streamwise vortices and streaks.
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| 4. |
- Abreu, Leandra I., et al.
(author)
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Wavepackets in turbulent flows around airfoils
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Other publication (other academic/artistic)abstract
- Motivated by the recent analysis by Sano et al. 2019, Phys. Rev. Fluids, vol. 4, p. 094602, of spanwise-coherent structures in the turbulent flow around airfoils and their connection to trailing-edge noise, we carry out a thorough characterisation of such structures in three simulation databases. We analyse two different numerical simulations of incompressible flow in turbulent regime, both at chord Reynolds number of 400,000: a large-eddy simulation for a NACA 0012 profile at zero angle of attack, and a direct numerical simulation for a NACA 4412 airfoil with an angle of attack of 5 degrees. Snapshots of the flow field were analysed using Spectral Proper Orthogonal Decomposition (SPOD), in order to extract the dominant coherent structures of the flow. Focus is given to the aforementioned spanwise-coherent fluctuations, which two-dimensional disturbances in the computational domain due to the use of periodic boundary conditions. The leading SPOD modes show that the most energetic coherent structures are wavepackets, extending over the whole turbulent boundary layers around the airfoils with significant amplitudes near the trailing-edge. Higher amplitudes are observed in the region of stronger adverse pressure gradient at the suction side of the NACA 4412 airfoil. To understand how such structures in the turbulent field can be modelled, the linear response of the flow using the singular value decomposition of the linearised resolvent operator was performed, using the mean field as a base flow and considering a locally parallel approximation. Such analysis shows that the leading SPOD modes can be associated to optimal, linearised flow responses, particularly for stations far from the trailing edge; the latter introduces a discontinuity in boundary conditions, and the locally parallel approximation becomes questionable. We then focus on evaluating the dependence of such wavepackets on the domain size, to ensure that these structures are not an artifact of the use of periodic boundary conditions in small computational boxes. To do so, we performed an incompressible LES of a zero-pressure gradient turbulent boundary layer (ZPGTBL), for three different spanwise sizes: Lz=32 δ*, Lz=64 δ* and Lz=128 δ*, where δ* is a reference displacement thickness in a region of developed turbulent flow, with Reynolds number matching the values in the airfoil simulations. The signature of such wavepackets is seen in non-premultiplied spanwise wavenumber spectra, which reaches, for the three domain sizes, a plateau for spanwise wavelengths going to infinity (or wavenumbers going to zero); this plateau is representative of the spanwise-coherent structures seen in the airfoil simulations. Similar SPOD and resolvent analyses were carried out for the zero spanwise wavenumber of the ZPGTBL, and the same coherent wavepackets were observed for the three domains, with very similar amplitudes. Such wavepackets were also accurately modelled using the optimal resolvent response. These results confirm that the spanwise-elongated structures are not domain-size dependent for the studied simulations, and are thus a feature of turbulent boundary layers.
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| 5. |
- Alarcón, José Faúndez, et al.
(author)
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Role of streak secondary instabilities on free-stream turbulence-induced transition
- 2024
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In: Journal of Fluid Mechanics. - : Cambridge University Press. - 0022-1120 .- 1469-7645. ; 988
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Journal article (peer-reviewed)abstract
- We study the stability of a zero-pressure gradient boundary layer subjected to free-stream disturbances by means of local stability analysis. The dataset under study corresponds to a direct numerical simulation (DNS) of a flat plate with a sharp leading edge in realistic wind tunnel conditions, with a turbulence level of 3.45 % at the leading edge. We present a method to track the convective evolution of the secondary instabilities of streaks by performing sequential stability calculations following the wave packet, connecting successive unstable eigenfunctions. A scattered nature, in time and space, of secondary instabilities is seen in the stability calculations. These instabilities can be detected before they reach finite amplitude in the DNS, preceding the nucleation of turbulent spots, and whose appearance is well correlated to the transition onset. This represents further evidence regarding the relevance of secondary instabilities of streaks in the bypass transition in realistic flow conditions. Consistent with the spatio-temporal nature of this problem, our approach allows us to integrate directly the local growth rates to obtain the spatial amplification ratio of the individual instabilities, where it is shown that instabilities reaching an -factor in the range [2.5,4] can be directly correlated to more than 65 % of the nucleation events. Interestingly, it is found that high amplification is not only attained by modes with high growth rates, but also by instabilities with sustained low growth rates for a long time.
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| 6. |
- Blanco, Diego C. P., et al.
(author)
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Linear and nonlinear receptivity mechanisms in boundary layers subject to free-stream turbulence
- 2024
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In: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 979
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Journal article (peer-reviewed)abstract
- Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free-stream turbulence are considered in the present work. Within an input-output model, where nonlinear terms of the incompressible Navier-Stokes equations are treated as an external forcing, we manage to separate inputs related to perturbations coming through the intake of the numerical domain, whose evolution represents a linear mechanism, and the volumetric nonlinear forcing due to triadic interactions. With these, we perform the full reconstruction of the statistics of the flow, as measured in the simulations, to quantify pairs of wavenumbers and frequencies more affected by either linear or nonlinear receptivity mechanisms. Inside the boundary layer, different wavenumbers at near-zero frequency reveal streaky structures. Those that are amplified predominantly via linear interactions with the incoming vorticity occur upstream and display transient growth, while those generated by the nonlinear forcing are the most energetic and appear in more downstream positions. The latter feature vortices growing proportionally to the laminar boundary layer thickness, along with a velocity profile that agrees with the optimal amplification obtained by linear transient growth theory. The numerical approach presented is general and could potentially be extended to any simulation for which receptivity to incoming perturbations needs to be assessed.
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| 7. |
- Brito, Pedro P. C., et al.
(author)
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Experimental control of Tollmien-Schlichting waves using pressure sensors and plasma actuators
- 2020
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Reports (other academic/artistic)abstract
- This manuscript shows the successful application of the inverse feed-forwardcontrol (IFFC) technique for the cancellation of Tollmien–Schlichting (TS)waves. Active wave cancellation of two-dimensional broadband TS disturbancesis performed with a single dielectric barrier discharge (DBD) plasma actuator.The measurements required for the IFFC are performed with microphones,instead of hot wires most used for this task, in order to reduce the spaceoccupied by the sensors and assess the suitability of simpler and cheaperdevices. The experiments are conducted in an open-circuit wind-tunnel witha NACA0008 wing profile. An attenuation of the TS-wave amplitude of oneorder of magnitude is achieved. Direct numerical simulations (DNS) are alsoperformed, and compared to the outcome of the experiments. The modeling ofboth actuator and sensors in the DNS is not based on data from the presentexperiments. The plasma actuator used is a mapping of the force field inFabbiane et al., J. Fluid Mech. 2015, to the NACA0008 wing profile, whereasthe microphones are modeled as pressure probes. Despite these modellingchoices, a remarkable level of agreement between the DNS and the experimentsis achieved. However, the control performance is better in the DNS, withattenuations of three orders of magnitude of TS-wave amplitude. Furtheranalysis of experiments and simulations shows that the limiting factor in theexperiments is the ambient low-frequency acoustic waves in the wind tunnel,which are sensed by the microphones, acting as noise in the analysis of TS-waveevolution and thus leading to lower coherences between sensors and actuators.This in turn leads to a suboptimal control kernel in the experiment.179
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| 8. |
- Brito, Pedro P. C., et al.
(author)
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Experimental control of Tollmien-Schlichting waves using pressure sensors and plasma actuators
- 2021
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In: Experiments in Fluids. - : Springer Nature. - 0723-4864 .- 1432-1114. ; 62:2
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Journal article (peer-reviewed)abstract
- This manuscript presents a successful application of the inverse feed-forward control (IFFC) technique for control of the Tollmien-Schlichting (TS) waves over a wing profile placed in an open-circuit wind tunnel. Active cancellation of two-dimensional broadband TS disturbances is performed using a single dielectric barrier discharge (DBD) plasma actuator. The measurements required for the IFFC are performed with microphones, instead of hot wires often used for this purpose, in order to reduce the space occupied by the sensors and assess the suitability of simpler and cheaper devices. An attenuation of the TS-wave amplitude of one order of magnitude is achieved. Direct numerical simulations (DNS) are also performed and compared to the outcome of the experiments. The plasma-actuator model used in DNS is a mapping of the force field used by Fabbiane et al. (In: Proceedings of TSFP-9, Melbourne, 2015a) to the actual geometry, whereas the sensors (microphones) are modeled as pressure probes. Despite these modelling choices, a good agreement between the results of DNS and the experiments is achieved. However, the control performance is better in the DNS, with attenuation of three orders of magnitude of TS-wave amplitude. Further analysis of experiments and simulations shows that the limiting factor in the experiments is the ambient low-frequency acoustic waves in the wind tunnel. These waves are sensed by the microphones and act as noise in the analysis of TS-wave evolution and thus leading to lower coherence between sensors and actuators. This in turn leads to a suboptimal control kernel in the experiment.Please confirm if the inserted city and country are correct in Affiliations [Aff1, Aff2]. Amend if necessary.Confirmed. It is correct.Please confirm if the corresponding author is correctly identified. Amend if necessary.Confirmed. The corresponding author is Pedro P. C. Brito.
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| 9. |
- Freire, Guilherme A., et al.
(author)
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Actuator and sensor placement for closed-loop control of convective instabilities
- 2020
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In: Theoretical and Computational Fluid Dynamics. - : Springer. - 0935-4964 .- 1432-2250.
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Journal article (peer-reviewed)abstract
- This work deals with the characterization of the closed-loop control performance aiming at the delay of transition. We focus on convective wavepackets, typical of the initial stages of transition to turbulence, starting with the linearized Kuramoto–Sivashinsky equation as a model problem representative of the transitional 2D boundary layer; its simplified structure and reduced order provide a manageable framework for the study of fundamental concepts involving the control of linear wavepackets. The characterization is then extended to the 2D Blasius boundary layer. The objective of this study is to explore how the sensor–actuator placement affects the optimal control problem, formulated using linear quadratic Gaussian (LQG) regulators. This is carried out by evaluating errors of the optimal estimator at positions where control gains are significant, through a proposed metric, labelled as $$\gamma $$γ. Results show, in quantitative manner, why some choices of sensor–actuator placement are more effective than others for flow control: good (respectively, bad) closed-loop performance is obtained when estimation errors are low (respectively, high) in the regions with significant gains in the full-state-feedback problem. Unsatisfactory performance is further understood as dominant estimation error modes that overlap spatially with control gains, which shows directions for improvement of a given set-up by moving sensors or actuators. The proposed metric and analysis explain most trends in closed-loop performance as a function of sensor and actuator position, obtained for the model problem and for the 2D Blasius boundary layer. The spatial characterization of the $$\gamma $$γ-metric provides thus a valuable and intuitive tool for the problem of sensor–actuator placement, targeting here transition delay but possibly extending to other amplifier-type flows.
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| 10. |
- Kern, J. Simon, et al.
(author)
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Space-time Proper Orthogonal Decomposition of the onset of leading edge dynamic stall
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Other publication (other academic/artistic)abstract
- The increased availability of large scale computing hardware brings the analysis of fully three-dimensional non-autonomous flow cases within reach. In these flow scenarios, the simplifying assumption of temporal homogeneity is not applicable and with it many data-driven analysis techniques that rely on it. Within the well-established modal decomposition framework of Proper Orthogonal Decomposition (POD), we can treat time in the same way as the spatial dimensions and apply the method to statistical ensembles of non-autonomous flows in order to extract coherent structures in space and time from the resulting experimental or numerical data, leading to the space-time POD formulation. This extension of the existing method is demonstrated on the model problem of the complex Ginzburg--Landau equation, modified to include non-autonomous parameter variations. Subsequently, the space-time POD analysis is carried out on a numerical dataset of 25 realisations of the onset of leading edge dynamic stall on a NACA0009 airfoil section subject to low levels of background disturbances. The space-time POD, combined with extended POD, is used to extract the spatio-temporal structure of energetic wavetrains during the bursting of the laminar separation bubble close to the leading edge, which are found to be statistically relevant phenomena in the context of incipient dynamic stall. The potential of the space-time POD methodology to objectively extract coherent structures from ensembles of non-autonomous data is demonstrated.
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