Drag reduction by elastic reconfiguration Tristan Leclercq French - - PowerPoint PPT Presentation

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Drag reduction by elastic reconfiguration Tristan Leclercq French - - PowerPoint PPT Presentation

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Drag reduction by elastic reconfiguration Tristan Leclercq French supervisor: Emmanuel de Langre (LadHyX, Ecole Polytechnique) UK supervisor: Nigel Peake (DAMTP, University of Cambridge) The Oak and the Reed [...] the winds for me

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SLIDE 1

French supervisor: Emmanuel de Langre

(LadHyX, Ecole Polytechnique)

  • UK supervisor: Nigel Peake

(DAMTP, University of Cambridge)

Drag reduction by elastic reconfiguration

Tristan Leclercq

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SLIDE 2

The Oak and the Reed

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Jean de La Fontaine (1668)

“[...] the winds for me Are much less dangerous than for thee; I bend, but do not break.You have until now Against their terrible strikes Resisted without bowing your head. But let’s just wait till the end.” The wind redoubled his efforts So that finally it uprooted The oak whose head was reaching heavens And roots were touching the realms of the deads.

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SLIDE 3

Flexibility: and evolutionary advantage?

3

Flexibility correlated to the magnitude of the flow forces

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SLIDE 4

Outline

4

1.

Introduction: static drag reduction by reconfiguration

2.

Self-induced dynamics in steady flow

3.

Dynamic reconfiguration in oscillating flow

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SLIDE 5

Outline

5

1.

Introduction: static drag reduction by reconfiguration

2.

Self-induced dynamics in steady flow

3.

Dynamic reconfiguration in oscillating flow

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SLIDE 6

Static drag reduction by reconfiguration

6

= passive adaptation of the shape in response to a forcing

Reconfiguration

Denny, M., & Cowen, B. J. Exp. Biol., 1997. Vogel, S. J. Exp. Bot., 1989.

Static drag reduction by reconfiguration

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SLIDE 7

Static drag reduction by reconfiguration

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Reconfiguration

Frontal area reduction

Vogel, S. J. Exp. Bot., 1989.

Static drag reduction by reconfiguration

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SLIDE 8

Static drag reduction by reconfiguration

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Reconfiguration

Streamlining

Vogel, S. J. Exp. Bot., 1989.

Static drag reduction by reconfiguration

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SLIDE 9

Static drag reduction by reconfiguration

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Reconfiguration

Drag reduction

Vogel, S. J. Exp. Bot., 1989.

drag force F flow velocity U flexible rigid Frigid Fflexible

Static drag reduction by reconfiguration

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SLIDE 10

Static drag reduction by reconfiguration

10

Gosselin et al., JFM, 2010.

increasing U

Cantilever flat plate, transverse flow

Static drag reduction by reconfiguration

U

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SLIDE 11

Steady flow

static shape ?

Static drag reduction by reconfiguration

11

Does the self-induced dynamics prevent drag reduction by reconfiguration?

Tadrist et al., JFS, 2015 Gosselin et al., JFM, 2010.

Static drag reduction by reconfiguration

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SLIDE 12

Outline

12

1.

Introduction: static drag reduction by reconfiguration

2.

Self-induced dynamics in steady flow

3.

Dynamic reconfiguration in oscillating flow

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SLIDE 13

Model

13

Cantilever, slender, flat plate Clamped transverse to the uniform, steady flow D<<W<<L

U

x z y D W L

Self-induced dynamics in steady flow

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SLIDE 14

Model

14

Deflection in the xz-plane 2D Euler-Bernoulli beam

Bending stiffness EI Lineic mass m

U

x z L reconfiguration

Self-induced dynamics in steady flow

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SLIDE 15

Self-induced dynamics in steady flow: flutter

15 Self-induced dynamics in steady flow

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SLIDE 16

Model

16

Local models of flow forces

Resistive drag

x z s τ n

U

θ Relative velocity Self-induced dynamics in steady flow

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SLIDE 17

Model

17

Local models of flow forces

Resistive drag Reactive force

Relative velocity Added mass Curvature x z s τ n

U

θ Self-induced dynamics in steady flow

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SLIDE 18

Governing parameters: static equilibrium

18

Cauchy number

resistive drag / restoring bending stiffness

Self-induced dynamics in steady flow

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SLIDE 19

Governing parameters: static equilibrium

19

Cauchy number

resistive drag / restoring bending stiffness

controls level of static reconfiguration

increasing

U

Self-induced dynamics in steady flow

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SLIDE 20

Governing parameters: static equilibrium

20

Cauchy number

resistive drag / restoring bending stiffness

controls level of static reconfiguration Slenderness

resistive drag / reactive (added mass) force

Self-induced dynamics in steady flow

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SLIDE 21

Governing parameters: static equilibrium

21

Cauchy number

resistive drag / restoring bending stiffness

controls level of static reconfiguration Slenderness

resistive drag / reactive (added mass) force

negligible contribution to static equilibrium

Self-induced dynamics in steady flow

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SLIDE 22

Governing parameters: static equilibrium

22

Cauchy number

resistive drag / restoring bending stiffness

controls level of static reconfiguration Slenderness

resistive drag / reactive (added mass) force

negligible contribution to static equilibrium

Self-induced dynamics in steady flow

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SLIDE 23

Governing parameters: dynamic parameters

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Reduced velocity

reactive (added mass) force / restoring bending stiffness

Self-induced dynamics in steady flow

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SLIDE 24

Governing parameters: dynamic parameters

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Reduced velocity

reactive (added mass) force / restoring bending stiffness

drives the instability

Self-induced dynamics in steady flow

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SLIDE 25

Governing parameters: dynamic parameters

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Reduced velocity

reactive (added mass) force / restoring bending stiffness

drives the instability Slenderness

resistive drag / reactive (added mass) force

Self-induced dynamics in steady flow

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SLIDE 26

Governing parameters: dynamic parameters

26

Reduced velocity

reactive (added mass) force / restoring bending stiffness

drives the instability Slenderness

resistive drag / reactive (added mass) force

damping of the instability

Self-induced dynamics in steady flow

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SLIDE 27

Governing parameters: dynamic parameters

27

Reduced velocity

reactive (added mass) force / restoring bending stiffness

drives the instability Slenderness

resistive drag / reactive (added mass) force

damping of the instability

Redundant flow parameters

Self-induced dynamics in steady flow

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SLIDE 28

Governing parameters: dynamic parameters

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Reduced velocity

reactive (added mass) force / restoring bending stiffness

drives the instability Slenderness

resistive drag / reactive (added mass) force

damping of the instability Mass ratio

added mass / total moving mass

Self-induced dynamics in steady flow

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SLIDE 29

Governing parameters: dynamic parameters

29

Reduced velocity

reactive (added mass) force / restoring bending stiffness

drives the instability Slenderness

resistive drag / reactive (added mass) force

damping of the instability Mass ratio

added mass / total moving mass

drives the instability

Self-induced dynamics in steady flow

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SLIDE 30

Non-linear dynamics

30

Stable equilibrium:

Self-induced dynamics in steady flow

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SLIDE 31

Non-linear dynamics

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Periodic limit cycle:

Self-induced dynamics in steady flow

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SLIDE 32

Non-linear dynamics

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Periodic limit cycle:

Self-induced dynamics in steady flow

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SLIDE 33

Non-linear dynamics

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Chaotic motion:

Self-induced dynamics in steady flow

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SLIDE 34

Non-linear dynamics

34

Chaotic motion:

Self-induced dynamics in steady flow

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SLIDE 35

Stable static equilibrium Periodic flapping Chaotic flapping

Kinematic regimes

35 Self-induced dynamics in steady flow

Drag in the different regimes compared to rigid case ? Increasing flow velocity

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SLIDE 36

Drag reduction

36 Self-induced dynamics in steady flow

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SLIDE 37

Drag reduction

37 Self-induced dynamics in steady flow

STABLE UNSTABLE

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SLIDE 38

Drag reduction

38 Self-induced dynamics in steady flow

STABLE CHAOTIC PERIODIC

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SLIDE 39

Drag reduction ?

39 Self-induced dynamics in steady flow

STABLE CHAOTIC PERIODIC

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SLIDE 40

Drag reduction ?

40

Magnification of drag during « snapping » events

Short duration Rare Random

Self-induced dynamics in steady flow

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SLIDE 41

Drag reduction

41

Flutter enhances the drag compared to static equilibrium Drag still drastically reduced by flexibility on average Magnification of drag due to flexibility during short,

rare, random snapping events

Larger mass ratio or slenderness stabilizes the system

Larger domain of stability for the static reconfiguration Smaller amplitude of flapping Larger domain of periodic limit cycle

Self-induced dynamics in steady flow

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SLIDE 42

Outline

42

1.

Introduction: static drag reduction by reconfiguration

2.

Self-induced dynamics in steady flow

3.

Dynamic reconfiguration in oscillating flow

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SLIDE 43

Model

43

Uniform oscillatory flow

x z L

U(t)

A

Dynamic reconfiguration in oscillating flow

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SLIDE 44

Model

44

Uniform oscillatory flow

Additional flow force: virtual buoyancy

Dynamic reconfiguration in oscillating flow

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SLIDE 45

Model

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Uniform oscillatory flow

Additional flow force: virtual buoyancy

Neutrally buoyant flat plate

Dynamic reconfiguration in oscillating flow

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SLIDE 46

Model

46

Uniform oscillatory flow

Additional flow force: virtual buoyancy

Neutrally buoyant flat plate

Neglect virtual buoyancy

Dynamic reconfiguration in oscillating flow

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SLIDE 47

Model

47

Uniform oscillatory flow

Additional flow force: virtual buoyancy

Neutrally buoyant flat plate

Neglect virtual buoyancy Neglect structural inertia

Dynamic reconfiguration in oscillating flow

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SLIDE 48

Model

48

Uniform oscillatory flow

Additional flow force: virtual buoyancy

Neutrally buoyant flat plate

Neglect virtual buoyancy Neglect structural inertia Stable to fluid-structure instabilities

Dynamic reconfiguration in oscillating flow

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SLIDE 49

Governing parameters

Dynamic reconfiguration in oscillating flow 49

Mass ratio fixed

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SLIDE 50

Governing parameters

Dynamic reconfiguration in oscillating flow 50

Mass ratio fixed Slenderness

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SLIDE 51

Governing parameters

Dynamic reconfiguration in oscillating flow 51

Mass ratio fixed Slenderness Flow parameters

Amplitude L A

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SLIDE 52

Governing parameters

Dynamic reconfiguration in oscillating flow 52

Mass ratio fixed Slenderness Flow parameters

Amplitude Frequency

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SLIDE 53

Small-amplitude case

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Neglect geometrical non-linearities

Dynamic reconfiguration in oscillating flow

x z L A

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SLIDE 54

Small-amplitude case

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Neglect geometrical non-linearities

x z L A

Dynamic reconfiguration in oscillating flow

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SLIDE 55

Small-amplitude case

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Neglect geometrical non-linearities

x z L A

Dynamic reconfiguration in oscillating flow

Keulegan-Carpenter structural linear oscillator added mass resistive drag

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SLIDE 56

Small-amplitude case

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Very small amplitude

Dynamic reconfiguration in oscillating flow

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SLIDE 57

Small-amplitude case

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Very small amplitude

linear oscillator with monochromatic forcing

Dynamic reconfiguration in oscillating flow

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SLIDE 58

Small-amplitude case

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Very small amplitude

linear oscillator with monochromatic forcing MODAL REGIME

Dynamic reconfiguration in oscillating flow

Mode 1 Mode 2 Mode 3

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SLIDE 59

Small-amplitude case

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Moderately small amplitude

Dynamic reconfiguration in oscillating flow

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SLIDE 60

Small-amplitude case

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Moderately small amplitude

Dynamic reconfiguration in oscillating flow

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SLIDE 61

Small-amplitude case

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Moderately small amplitude

Dynamic reconfiguration in oscillating flow

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SLIDE 62

Small-amplitude case

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Moderately small amplitude

  • uter solution

CONVECTIVE REGIME

Dynamic reconfiguration in oscillating flow

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SLIDE 63

Small-amplitude case

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Moderately small amplitude

  • uter solution

boundary layer CONVECTIVE REGIME

Dynamic reconfiguration in oscillating flow

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SLIDE 64

Large-amplitude case

Dynamic reconfiguration in oscillating flow 64

Geometric saturation

U(t)

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SLIDE 65

Large-amplitude case

Dynamic reconfiguration in oscillating flow 65

Geometric saturation

Reversal time

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SLIDE 66

Large-amplitude case

Dynamic reconfiguration in oscillating flow 66

Geometric saturation

Reversal time Quasi-static reconfiguration out of reversal

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SLIDE 67

A << W : modal regime

Inertia-dominated regime Linear oscillator response

W << A << L : convective regime

Drag-dominated regime Convection with the fluid particles + elastic BL

L << A : saturated regime

Drag-dominated regime Reversal time + QS reconfiguration

Kinematic regimes

67 Dynamic reconfiguration in oscillating flow

Drag in the different regimes compared to rigid case ? Increasing flow amplitude

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SLIDE 68

Small-amplitude case

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Modal regime

Dynamic reconfiguration in oscillating flow

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SLIDE 69

Small-amplitude case

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Modal regime

Dynamic reconfiguration in oscillating flow

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SLIDE 70

Small-amplitude case

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Modal regime

Dynamic reconfiguration in oscillating flow

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SLIDE 71

Small-amplitude case

71

Modal regime

Dynamic reconfiguration in oscillating flow

  • 1/2
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SLIDE 72

Convective regime

Small-amplitude case

72 Dynamic reconfiguration in oscillating flow

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SLIDE 73

Convective regime

Small-amplitude case

73 Dynamic reconfiguration in oscillating flow

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SLIDE 74

Convective regime

Small-amplitude case

74 Dynamic reconfiguration in oscillating flow

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SLIDE 75

Convective regime

Small-amplitude case

75 Dynamic reconfiguration in oscillating flow

  • 1/4
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SLIDE 76

Large-amplitude case

Dynamic reconfiguration in oscillating flow 76

Flow magnitude is minimum around reversal Maximum force is in the QS regime

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SLIDE 77

Large-amplitude case

Dynamic reconfiguration in oscillating flow 77

Quasi-static reconfiguration out of reversal

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SLIDE 78

Large-amplitude case

Dynamic reconfiguration in oscillating flow 78

Quasi-static reconfiguration out of reversal

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SLIDE 79

Large-amplitude case

Dynamic reconfiguration in oscillating flow 79

Quasi-static reconfiguration out of reversal

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SLIDE 80
  • 1/3

Large-amplitude case

Dynamic reconfiguration in oscillating flow 80

Quasi-static reconfiguration out of reversal

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SLIDE 81

Dynamic reconfiguration in oscillating flow

81 Magnification of drag due to flexibility in the modal regime, at the resonances Drag proportional to characteristic bending length

Rigid case:

structural length

Modal regime:

wavelength

Convective regime:

boundary layer thickness

Saturated (or quasi-static) regime:

bending length Dynamic reconfiguration in oscillating flow

Increasing flow amplitude

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SLIDE 82

Thank you !

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