Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow

Cherubini, Stefania; Robinet, Jean-Christophe; Palma, P. De

doi:10.1017/jfm.2013.576

Cited by 19 publications

(21 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The knowledge of these nonlinear mechanisms may allow one to design effective control strategies to delay transition by using wall suction or spanwise oscillations of the boundaries. 49,50 The aim of the present paper is to extend the analysis of the NLOP to the case of the ASBL, following the approach that the authors have employed for the BBL, discussing similarities and differences between these two cases, and highlighting the role of the suction at the wall.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear optimals in the asymptotic suction boundary layer: Transition thresholds and symmetry breaking

2015

Self Cite

View full text Add to dashboard Cite

The 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. C 2015 AIP Publishing LLC. [http://dx.

show abstract

Section: Introductionmentioning

confidence: 99%

Nonlinear optimals in the asymptotic suction boundary layer: Transition thresholds and symmetry breaking

2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…The aforementioned approach is also known as model predictive control (MPC). Cherubini et al (2013) applied MPC to a three-dimensional boundary layer flow with optimally growing perturbations as initial conditions and successfully brought the flow back to the laminar state. They also compared the performance of linear and nonlinear controllers.…”

Section: Nonlinear Optimal Controlmentioning

confidence: 99%

Nonlinear optimal control of transition due to a pair of vortical perturbations using a receding horizon approach

Xiao

Papadakis

2018

J. Fluid Mech.

View full text Add to dashboard Cite

This paper considers the nonlinear optimal control of bypass transition in a boundary layer flow subjected to a pair of free stream vortical perturbations using a receding horizon approach. The optimal control problem is solved using the Lagrange variational technique that results in a set of linearised adjoint equations, which are used to obtain the optimal wall actuation (blowing and suction from a control slot located in the transition region). The receding horizon approach enables the application of control action over a longer time period, and this allows the extraction of time-averaged statistics as well as investigation of the control effect downstream of the control slot. The results show that the controlled flow energy is initially reduced in the streamwise direction and then increased because transition still occurs. The distribution of the optimal control velocity responds to the flow activity above and upstream of the control slot. The control effect propagates downstream of the slot and the flow energy is reduced up to the exit of the computational domain. The mean drag reduction is 55% and 10% in the control region and downstream of the slot, respectively. The control mechanism is investigated by examining the second order statistics and the two-point correlations. It is found that in the upstream (left) side of the slot, the controller counteracts the near wall high speed streaks and reduces the turbulent shear stress; this is akin to opposition control in channel flow, and since the time-average control velocity is positive, it is more similar to blowingonly opposition control. In the downstream (right) side of the slot, the controller reacts to the impingement of turbulent spots that have been produced upstream and inside the boundary layer (top-bottom mechanism). The control velocity is positive and increases in the streamwise direction, and the flow behavior is similar to that of uniform blowing.

show abstract

“…Their study aimed at controlling both streaks developing in flat-plate boundary layers and Görtler vortices evolving along concave surfaces. Cherubini et al (2013) applied a nonlinear optimal control strategy with blowing and suction, starting with the full Navier-Stokes equations, and using the method of Lagrange multipliers to determine the largest decrease of the disturbance energy. A closed-loop optimal control technique based on wall transpiration was derived and tested by Papadakis et al (2016), in the framework of a flat-plate laminar boundary layer excited by freestream disturbances.…”

Section: Optimal Control Approachmentioning

confidence: 99%

Hampering Görtler vortices via optimal control in the framework of nonlinear boundary region equations

Sescu

Afsar

2018

J. Fluid Mech.

View full text Add to dashboard Cite

The control of stream-wise vortices in high Reynolds number boundary layer flows often aims at reducing the vortex energy as a means of mitigating the growth of secondary instabilities, which eventually delay the transition from laminar to turbulent flow. In this paper, we aim at utilizing such an energy reduction strategy using optimal control theory to limit the growth of Görtler vortices developing in an incompressible laminar boundary layer flow over a concave wall, and excited by a row of roughness elements with span-wise separation in the same order of magnitude as the boundary layer thickness. Commensurate with control theory formalism, we transform a constrained optimization problem into an unconstrained one by applying the method of Lagrange multipliers. A high Reynolds number asymptotic framework is utilized, wherein the Navier-Stokes equations are reduced to the boundary region equations (BRE), in which wall deformations enter the problem through an appropriate Prandtl transformation. In the optimal control strategy, the wall displacement or the wall transpiration velocity serve as control variables, while the cost functional is defined in terms of the wall shear stress. Our numerical results indicate, among other things, that the optimal control algorithm is very effective in reducing the amplitude of the Görtler vortices, especially for the control based on wall displacement.

show abstract

Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow

Cited by 19 publications

References 47 publications

Nonlinear optimals in the asymptotic suction boundary layer: Transition thresholds and symmetry breaking

Nonlinear optimals in the asymptotic suction boundary layer: Transition thresholds and symmetry breaking

Nonlinear optimal control of transition due to a pair of vortical perturbations using a receding horizon approach

Hampering Görtler vortices via optimal control in the framework of nonlinear boundary region equations

Contact Info

Product

Resources

About