Passive control of fluid-structure instabilities by means of - - PowerPoint PPT Presentation

Passive control of fluid-structure instabilities by means of piezo-shunts

Marco CARINI, Jean-Lou PFISTER & Olivier MARQUET

AEROFLEX project

Piezo-electricity : a wide range of applications

Piezo-electricity : Electric response of certain mate- rials to a mechanical stress due to their microscopic structure Sensing & Actuation from everyday life . . . . . . to the Aerospace Research Our Goal : using piezos to control fluid-structure instabilities

Carini, Pfister & Marquet 2 / 12 31 January 2017

2D Model problem

Fluid region Solid region Rigid cylinder + elastic plate + piezo patches. Re = U∞D/ν = 80, density ratio mρ = 50 and bending stiffness K = 0.3. Electro-mechanical coupling only acting for bending modes (transverse effect +

• pposite poiling direction).

Carini, Pfister & Marquet 3 / 12 31 January 2017

Modelling framework

Arbitrary Lagrangian Eulerian approach Lagrangian for the solid. Eulerian description for the fluid.

• Eqs. in the underformed configuration

Fully coupled nonlinear fluid-electro-mechanical system in compact form B ∂q ∂t = R(q). Linearization around a fixed equilibrium solution qB, i.e. R(qB) = 0, with q(x, t) = ˆ q(x)eλt λBˆ q = ∂R(q) ∂q

• qB

ˆ q, which is a Generalised Eigenvalue Problem, for λ = σ + ıω ∈ C :

Carini, Pfister & Marquet 4 / 12 31 January 2017

Base flow & Leading (unstable) modes

Base flow No Piezos Piezos

Carini, Pfister & Marquet 5 / 12 31 January 2017

Global spectrum

Without vs With Piezos

• 0.25
• 0.2
• 0.15
• 0.1
• 0.05

0.05 0.5 0.75 1 1.25 1.5

σ ω

Added electrical stiffness effect

Carini, Pfister & Marquet 6 / 12 31 January 2017

Connecting a R-shunt circuit

1st order electr. dynamics dQe dt + 1 RCp Qe = 0, τe = RCp is the characteristic electrical time. Energy dissipation by Joule’s effect, Pe = CpV 2

e /τe.

For τe → 0, electro-mechanical coupling becomes negligible (short-circuit). For τe → ∞, electro-mechanical coupling becomes maximal (open-circuit).

Carini, Pfister & Marquet 7 / 12 31 January 2017

Varying the electrical resistance

Leading eigenvalue

−6 −4 −2 1 2 3 −0.06 −0.03 0.03 0.06

σ log10 τe

−6 −4 −2 1 2 3 0.7 0.8 0.9 1 1.1

ω log10 τe

Carini, Pfister & Marquet 8 / 12 31 January 2017

Varying the electrical resistance (continued)

Increasing τe

• 0.2
• 0.15
• 0.1
• 0.05

0.05 0.6 0.8 1 1.2 σ ω

Carini, Pfister & Marquet 9 / 12 31 January 2017

System energy analysis

Leading mode

−6 −4 −2 1 2 3 0.4 0.8 1.2

Es% log10 τe

−6 −4 −2 1 2 3 4 8 12

Pe% log10 τe

×10−4

Carini, Pfister & Marquet 10 / 12 31 January 2017

Conclusions

A conjecture on two possible distinct stabilization mechanisms : Frequency desynchronization by means of the added electric stiffness (original flutter mode). Electrical damping through Joule effect (new selected flutter mode).

Carini, Pfister & Marquet 11 / 12 31 January 2017

Thanks for your attention.

(Any Questions ?)