Laminar–Turbulent Transition Control Using Passivity Analysis of the Orr–Sommerfeld Equation

Damaren, Christopher J.

doi:10.2514/1.g001763

Cited by 6 publications

(4 citation statements)

References 25 publications

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“…relaminarize it). Similar approaches have been applied to the Blasius boundary layer [67,68] and for control of channels with sensing and actuation limited to the wall [69]. The notion of passivity has also been used in recent work to study a wider class of input-output properties [50].…”

Section: Low Dimensional Shear Flow Models Have Been Used To Provide ...mentioning

confidence: 99%

An input-output inspired method for permissible perturbation amplitude of transitional wall-bounded shear flows

Liu,

Gayme

2020

Preprint

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The precise set of parameters governing transition to turbulence in wall-bounded shear flows remains an open question; many theoretical bounds have been obtained, but there is not yet a consensus between these bounds and experimental/simulation results. In this work, we focus on a method to provide a provable Reynolds number dependent bound on the amplitude of perturbations a flow can sustain while maintaining the laminar state. Our analysis relies on an input-output approach that partitions the dynamics into a feedback interconnection of the linear and nonlinear dynamics (i.e., a Luré system that represents the nonlinearity as static feedback). We then construct quadratic constraints of the nonlinear term that is restricted by system physics to be energy conserving (lossless) and to have bounded input-output energy. Computing the region of attraction of the laminar state (set of safe perturbations) and permissible perturbation amplitude are then reformulated as Linear Matrix Inequalities (LMI), which provides a more computationally efficient solution than prevailing nonlinear approaches based on sum of squares programming.The proposed framework can also be used for energy method computations and linear stability analysis. We apply our approach to low dimensional nonlinear shear flow models for a range of Reynolds numbers. The results from our analytically derived bounds are consistent with the bounds identified through exhaustive simulations. However, they have the added benefit of being achieved at much lower computational cost and providing a provable guarantee that a certain level of perturbation is permissible.

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Section: Low Dimensional Shear Flow Models Have Been Used To Provide ...mentioning

confidence: 99%

An input-output inspired method for permissible perturbation amplitude of transitional wall-bounded shear flows

Liu,

Gayme

2020

Preprint

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“…2r }e where q os,r = e{q os }, q os,i = m{q os }, q sq,r = e{q sq }, q sq,i = m{q sq }, then the methods of Damaren [8] can be used to derive a statespace model of the form in Eqs. (1) and (2).…”

Section: Spatial Discretisation Using Finite Elementsmentioning

confidence: 99%

“…In a previous work [8], we studied the passivity property in two dimensions in the context of the Orr-Sommerfeld equation with actuation inputs implemented as wall-normal velocity. A dual output (based on energy analysis) was shown to be the second spatial derivative (normal direction) of the streamwise velocity perturbation at the wall.…”

Section: Introductionmentioning

confidence: 99%

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Transition control of the Blasius boundary layer using passivity

Damaren

2018

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The control problem for linearised three-dimensional perturbations about a nominal laminar boundary layer over a flat plate (the Blasius profile) is considered. With a view to preventing the laminar to turbulent transition, appropriate inputs, outputs, and feedback controllers are synthesised that can be used to stabilise the system. The linearised Navier-Stokes equations are reduced to the Orr-Sommerfeld and Squire equations with wall-normal velocity actuation entering through the boundary conditions on the wall. An analysis of the work-energy balance is used to identify an appropriate sensor output that leads to a passive system for certain values of the streamwise and spanwise wavenumbers. Even when the system is unstable, it is demonstrated that strictly positive real feedback can stabilise this system using the special output.

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Transition control of the blasius boundary layer using linear robust control theory

Damaren

2023

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The paper considers control system design for linearized three-dimensional perturbations about a nominal laminar boundary layer over a flat plate (the Blasius profile). The objective is prevention of the laminar to turbulent transition using appropriate inputs, outputs, and feedback controllers. They are synthesized with a view to reducing transient energy growth, a known precursor to important transition scenarios. The linearized Navier–Stokes equations are reduced to the Orr–Sommerfeld and Squire equations with wall-normal velocity actuation entering through the boundary conditions on the wall. The sensor output is taken to be the wall-normal derivative of the wall-normal vorticity measured on the plate. Several multivariable output controllers are examined, including simple constant gain output feedback, loop transfer recovery, and $$H_{\infty }$$ H ∞ loop shaping. Reduced order compensators are developed using balanced truncation and analyzed for robustness using the gap metric between reduced order models and full order models. It is demonstrated that the level of minimum transient energy growth that can be achieved is similar for these diverse controller methodologies but falls short of that which can be achieved using optimal state feedback.

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Laminar–Turbulent Transition Control Using Passivity Analysis of the Orr–Sommerfeld Equation

Cited by 6 publications

References 25 publications

An input-output inspired method for permissible perturbation amplitude of transitional wall-bounded shear flows

An input-output inspired method for permissible perturbation amplitude of transitional wall-bounded shear flows

Transition control of the Blasius boundary layer using passivity

Transition control of the blasius boundary layer using linear robust control theory

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