# Second-order sensitivity in the cylinder wake: Optimal spanwise-periodic wall actuation and wall deformation

@article{Boujo2018SecondorderSI, title={Second-order sensitivity in the cylinder wake: Optimal spanwise-periodic wall actuation and wall deformation}, author={Edouard Boujo and Andrea S. Marcano Fani and François Gallaire}, journal={Physical Review Fluids}, year={2018} }

Two-dimensional (2D) flows are efficiently controlled with spanwise waviness, i.e. spanwise-periodic (SP) wall blowing/suction/deformation. We tackle the global linear stability of 2D flows subject to small-amplitude 3D SP control. Building on previous work for parallel flows (Boujo et al. 2015), an adjoint method is proposed for computing the 2nd-order eigenvalue sensitivity. Such control has a zero 1st-order linear effect, so the 2nd-order quadratic effect prevails. The sensitivity operator…

## 10 Citations

### Optimal spanwise-periodic control for recirculation length in a backward-facing step flow

- Engineering
- 2019

Three-dimensional control is considered in the flow past a backward-facing step (BFS). The BFS flow at Reynolds number $Re=500$ (defined with the step height and the maximum inlet velocity) is…

### Sensitivity gradients of surface geometry modifications based on stability analysis of compressible flows

- EngineeringPhysical Review Fluids
- 2020

We derive a discrete framework for the calculation of eigenvalue sensitivity to geometric deformations. We apply the technique to the steady compressible Navier-Stokes and Reynolds-averaged…

### Second-order adjoint-based sensitivity for hydrodynamic stability and control

- MathematicsJournal of Fluid Mechanics
- 2021

Abstract Adjoint-based sensitivity analysis is routinely used today to assess efficiently the effect of open-loop control on the linear stability properties of unstable flows. Sensitivity maps…

### Viscous flow due to non-uniform cylinder with non-uniform stretching (shrinking) and porous velocities

- EngineeringPhysica Scripta
- 2019

A theoretical investigation is accomplished by considering a viscous flow over a porous and stretching (shrinking) cylinder of non-uniform radius. The stretching (shrinking) and injection (suction)…

### The effect of streaks on the instability of jets

- PhysicsJournal of Fluid Mechanics
- 2021

Abstract The presence of elongated streaks of high and low streamwise velocity in the shear layer of circular jets breaks the axisymmetry of their steady-state solution. If the streaks are considered…

### Brachistochronous motion of a flat plate parallel to its surface immersed in a fluid

- PhysicsJournal of Fluid Mechanics
- 2022

Abstract We determine the globally minimum time $T$ needed to translate a thin submerged flat plate a given distance parallel to its surface within a work budget. The Reynolds number for the flow is…

### Convergence enhancement of SIMPLE-like steady-state RANS solvers applied to airfoil and cylinder flows

- EngineeringJournal of Wind Engineering and Industrial Aerodynamics
- 2022

### Stability Analysis of Incompressible Boundary-Driven Flows in Rectangular Cavities

- Materials Science
- 2020

### Optimum Control of Flow around a Circular Cylinder with Non-Uniform Suction

- Engineering
- 2019

In the present study, numerical investigations were performed to determine the optimum non-uniform suction profiles to control the flow around a circular cylinder in the range of Reynolds numbers…

## References

SHOWING 1-10 OF 48 REFERENCES

### Second-order sensitivity of parallel shear flows and optimal spanwise-periodic flow modifications

- PhysicsJournal of Fluid Mechanics
- 2015

The question of optimal spanwise-periodic modification for the stabilisation of spanwise-invariant flows is addressed. A second-order sensitivity analysis is conducted for the linear temporal…

### Optimal wavy surface to suppress vortex shedding using second-order sensitivity to shape changes

- Engineering
- 2016

### Second-order perturbation of global modes and implications for spanwise wavy actuation

- PhysicsJournal of Fluid Mechanics
- 2014

Abstract Sensitivity analysis has successfully located the most efficient regions in which to apply passive control in many globally unstable flows. As is shown here and in previous studies, the…

### Controlled reattachment in separated flows: a variational approach to recirculation length reduction

- EngineeringJournal of Fluid Mechanics
- 2014

Abstract A variational technique is used to derive analytical expressions for the sensitivity of recirculation length to steady forcing in separated flows. Linear sensitivity analysis is applied to…

### Stabilization of absolute instability in spanwise wavy two-dimensional wakes

- PhysicsJournal of Fluid Mechanics
- 2013

Abstract Controlling vortex shedding using spanwise-varying passive or active actuation (namely three-dimensional control) has recently been reported as a very efficient method for regulating…

### A self-consistent formulation for the sensitivity analysis of finite-amplitude vortex shedding in the cylinder wake

- PhysicsJournal of Fluid Mechanics
- 2016

We use the adjoint method to compute sensitivity maps for the limit-cycle frequency and amplitude of the Bénard–von Kármán vortex street in the wake of a circular cylinder. The sensitivity analysis…

### Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows

- Mathematics, PhysicsJournal of Fluid Mechanics
- 2007

This article deals with the first Hopf bifurcation of a cylinder flow, and more particularly with the properties of the unsteady periodic Kármán vortex street regime that sets in for supercritical…

### Flow around a helically twisted elliptic cylinder

- Physics, Engineering
- 2016

In the present study, we conduct unsteady three-dimensional simulations of flows around a helically twisted elliptic (HTE) cylinder at the Reynolds numbers of 100 and 3900, based on the free-stream…

### Numerical study on the effect of shape modification to the flow around circular cylinders

- Engineering, Physics
- 2016

### Structural sensitivity of the first instability of the cylinder wake

- EngineeringJournal of Fluid Mechanics
- 2007

The stability properties of the flow past an infinitely long circular cylinder are studied in the context of linear theory. An immersed-boundary technique is used to represent the cylinder surface on…