1,721,007 research outputs found
A Nonlinear Control Strategy for Finite-amplitude Perturbations in a Boundary-layer Flow
Get PDFAbstractThe present work describes an optimal control strategy, based on the full Navier-Stokes equations, aiming at hampering the rapid growth of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow. An optimization strategy is used to find the blowing and suction control law at the wall providing the maximum damping of the perturbation energy at a given target time. Two optimally-growing finite-amplitude initial perturbations have been employed to initialize the flow. The nonlinear control procedure can drive such perturbations back to the laminar state, provided that the target time of the minimisation and the region in which the blowing and suction is applied have been suitably chosen. On the other hand, an equivalent control procedure based on the linearized Navier-Stokes equations is much less effective, being not able to lead the flow to the laminar state when finite-amplitude disturbances are considered
Hairpin-like optimal perturbations in plane Poiseuille flow
Get PDFIn this work it is shown that hairpin vortex structures can be the outcome of a nonlinear optimal growth process, in a similar way as streaky structures can be the result of a linear optimal growth mechanism. With this purpose, nonlinear optimizations based on a Lagrange multiplier technique coupled with a direct-adjoint iterative procedure are performed in a plane Poiseuille flow at subcritical values of the Reynolds number, aiming at quickly triggering nonlinear effects. Choosing a suitable time scale for such an optimization process, it is found that the initial optimal perturbation is composed of sweeps and ejections resulting in a hairpin vortex structure at the target time. These alternating sweeps and ejections create an inflectional instability occurring in a localized region away from the wall, generating the head of the primary and secondary hairpin structures, quickly inducing transition to turbulent flow. This result could explain why transitional and turbulent shear flows are characterized by a high density of hairpin vortices. © Cambridge University Press 2015
Nonlinear optimal perturbation of turbulent channel flow as a precursor of extreme events
Get PDFThis work aims at studying the mechanisms behind the occurrence of extreme dissipation events in a channel flow, identifying nonlinear optimal perturbations as potential precursors of these events. Nonlinear optimal perturbations with respect to a generic turbulent instantaneous snapshot are computed for the first time using a direct-adjoint algorithm in the channel flow at Reτ ≈ 180. The resulting initial perturbation displays the upstream tilting characteristic of Orr's mechanism and is positioned along the interfaces between two opposite-sign velocity streaks of the pre-existing turbulent field. Such a perturbation induces a sudden breakdown of the pre-existing structures and a heavier tail in the dissipation probability density function distribution. Different mechanisms are at play during this process: the high shear present at the interface between coherent low- and high-momentum regions is exploited to break down the larger structures and drive energy to small scales. This energy cascade is fed by an enhanced lift-up effect that produces intense streaks near the wall. It is found that the optimal perturbation grows exponentially during the first phase of its evolution reflecting the existence of a secondary modal instability of the streaks. To corroborate the results, the conditional spatiotemporal proper orthogonal decomposition (POD) analysis of Hack & Schimdt (J. Fluid Mech., vol. 907, 2021, A9) is performed both in the perturbed and in the unperturbed flow, showing a clear agreement between the two cases and with the reference study. Thus, the optimal perturbation at initial time can be considered as a precursor of extreme events
Numerical study of the effect of freestream turbulence on by-pass transition in a boundary layer
Get PDFWe use direct numerical simulations in the presence of free-stream turbulence having different values of intensity, Tu, and integral length scale, L, in order to determine which kind of structures are involved in the path to transition of a boundary-layer flow. The main aim is to determine under which conditions the path to transition involves structures similar to the linear or non-linear optimal perturbations. For high values of Tu and L, we observe a large-amplitude path to transition characterized by localized vortical structures and patches of high- and low-momentum fluctuations. Such a scenario is found to correlate well with the Λ and hairpin structures resulting from the time evolution of non-linear optimal perturbations, whereas, for lower Tu and L, a larger correlation is found with respect to linear optimal disturbances. This indicates that a large-amplitude path to transition exists, different from the one characterized by elongated streaks undergoing secondary instability. To distinguish between the two transition scenarios, a simple parameter linked to the streamwise localisation of high- and low-momentum zones is introduced. Finally, an accurate law to predict the transition location is provided, taking into account both Tu and L, valid for both the transition scenarios
Global three-dimensional optimal perturbations in a Blasius boundary layer
No full textThe three-dimensional global optimal and near-optimal perturbations in a flat-plate boundary layer are studied by means of an adjoint-based optimization, and their non-linear evolution is investigated by means of DNS. © 2010 Springer Science+Business Media B.V
Large-scale coherent structures in turbulent channel flow: a detuned instability of wall streaks
Get PDFIn this paper it is shown that a modal detuned instability of periodic near-wall streaks originates a large-scale structure in the bulk of the turbulent channel flow. The effect of incoherent turbulent fluctuations is included in the linear operator by means of an eddy viscosity. The base flow is an array of periodic two-dimensional streaks, extracted from numerical simulations in small domains, superposed to the turbulent mean profile. The stability problem for a large number of periodic units is efficiently solved using the block-circulant matrix method proposed by Schmid et al. (Phys. Rev. Fluids, vol. 2, 2017, 113902). For friction Reynolds numbers equal or higher than, it is shown that an unstable branch is present in the eigenspectra. The most unstable eigenmodes display large-scale modulations whose characteristic wavelengths are compatible with the large-scale end of the premultiplied velocity fluctuation spectra reported in previous computational studies. The wall-normal location of the large-wavelength near-wall peak in the spanwise spectrum of the eigenmode exhibits a power-law dependence on the friction Reynolds number, similarly to that found in experiments of pipes and boundary layers. Lastly, the shape of the eigenmode in the streamwise-wall-normal plane is reminiscent of the superstructures reported in the recent experiments of Deshpande et al. (J. Fluid Mech., vol. 969, 2023, A10). Therefore, there is evidence that such large-wavelength instabilities generate large-scale motions in wall-bounded turbulent flows
Nonlinear optimals in the asymptotic suction boundary layer: Transition thresholds and symmetry breaking
Get PDFThe effect of a constant homogeneous wall suction on the nonlinear transient growth of localized finite amplitude perturbations in a boundary-layer flow is investigated. Using a variational technique, nonlinear optimal disturbances are computed for the asymptotic suction boundary layer (ASBL) flow, defined as those finite amplitude disturbances yielding the largest energy growth at a given target time T. It is found that homogeneous wall suction remarkably reduces the optimal energy gain in the nonlinear case. Furthermore, mirror-symmetry breaking of the shape of the optimal perturbation appears when decreasing the Reynolds number from 10?000 to 5000, whereas spanwise mirror-symmetry was a robust feature of the nonlinear optimal perturbations found in the Blasius boundary-layer flow. Direct numerical simulations show that the different evolutions of the symmetric and of the non-symmetric initial perturbations are linked to different mechanisms of transport and tilting of the vortices by the mean flow. By bisecting the initial energy of the nonlinear optimal perturbations, minimal energy thresholds for subcritical transition to turbulence have been obtained. These energy thresholds are found to be 1-4 orders of magnitude smaller than those provided in the literature for other transition scenarios. For low to moderate Reynolds numbers, the energy thresholds are found to scale with Re-2, suggesting a new scaling law for transition in the ASBL. © 2015 AIP Publishing LLC
Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow
No full text"The present work provides an optimal control strategy, based on the nonlinear Navier–Stokes equations, aimed at hampering the rapid growth of unsteady finite- amplitude perturbations in a Blasius boundary-layer flow. A variational procedure is used to find the blowing and suction control law at the wall providing the maximum damping of the energy of a given perturbation at a given target time, with the final aim of leading the flow back to the laminar state. Two optimally growing finite-amplitude initial perturbations capable of leading very rapidly to transition have been used to initialize the flow. The nonlinear control procedure has been found able to drive such perturbations back to the laminar state, provided that the target time of the minimization and the region in which the blowing and suction is applied have been suitably chosen. On the other hand, an equivalent control procedure based on the linearized Navier–Stokes equations has been found much less effective, being not able to lead the flow to the laminar state when finite-amplitude disturbances are considered. Regions of strong sensitivity to blowing and suction have been also identified for the given initial perturbations: when the control is actuated in such regions, laminarization is also observed for a shorter extent of the actuation region. The nonlinear optimal blowing and suction law consists of alternating wall-normal velocity perturbations, which appear to modify the core flow structures by means of two distinct mechanisms: (i) a wall-normal velocity compensation at small times; (ii) a rotation-counterbalancing effect al larger times. Similar control laws have been observed for different target times, values of the cost parameter, and streamwise extents of the blowing and suction zone, meaning that these two mechanisms are robust features of the optimal control strategy, provided that the nonlinear effects are taken into account.
Minimal energy thresholds for sustained turbulent bands in channel flow
No full textIn this work, nonlinear variational optimization is used for obtaining minimal seeds for the formation of turbulent bands in channel flow. Using nonlinear optimization together with energy bisection, we have found that the minimal energy threshold for obtaining spatially patterned turbulence scales with Formula Presented for Formula Presented. The minimal seed, which is different to that found in a much smaller domain, is characterized by a spot-like structure surrounded by a low-amplitude large-scale quadrupolar flow filling the whole domain. This minimal-energy perturbation of the laminar flow has dominant wavelengths close to Formula Presented in the streamwise direction and Formula Presented in the spanwise direction, and is characterized by a spatial localization increasing with the Reynolds number. At Formula Presented, the minimal seed evolves in time, creating an isolated oblique band, whereas for Formula Presented, a quasi-spanwise-symmetric evolution is observed, giving rise to two distinct bands. A similar evolution is found also at low Formula Presented for non-minimal optimal perturbations. This highlights two different mechanisms of formation of turbulent bands in channel flow, depending on the Reynolds number and initial energy of the perturbation. The selection of one of these two mechanisms appears to be dependent on the probability of decay of the newly created stripe, which increases with time, but decreases with the Reynolds number
Stability of the flow over superhydrophobic micro roughnesses: The influence of the interface
No full textSuperhydrophobic surfaces are known for their drag reduction properties. However, the interface between the lubricant and the overlying flow may easily become unstable, leading to the depletion of the superhydrophobic layer and to a consequent drag increase. In this paper, we investigate the modal and non-modal instability of the flow over longitudinal trapezoidal superhydrophobic riblets, including, for the first time, the gas/liquid interface dynamics in the stability analyses. A two-dimensional stability problem, obtained with a domain transform technique and interface modelling using a linearised Young–Laplace equation, is coupled with the n−periodic stability framework introduced by Schmid et al. (2017). The latter technique, using a Bloch wave formalism, allows the computation of the stability of an array of n riblet units of given periodicity at a reasonable numerical cost. For small periodicities, the most unstable mode is a fundamental instability stemming from the three-dimensionalisation of a Tollmien–Schlichting wave. Conversely, in the case of large riblet periodicities, a subharmonic mode linked to capillarity effects becomes the most unstable. Nonmodal transient growth analysis shows that the superhydrophobic riblets have a weak effect on the overall growth. However, riblets having small periodicities induce a slight stabilisation of the flow, while large ones induce an increase of the energy growth on detuned perturbations. The resulting energy growth mechanism induces interface deformations encompassing more than one subunit
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