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 The wind redoubled his efforts Are much less dangerous than for thee; So that finally it uprooted I bend, but do not break. You have until now The oak whose head was reaching heavens Against their terrible strikes And roots were touching the realms of the deads. Resisted without bowing your head. But let’s just wait till the end.” Jean de La Fontaine (1668) 2
Flexibility: and evolutionary advantage? � Flexibility correlated to the magnitude of the flow forces 3
Outline Introduction: static drag reduction by reconfiguration 1. Self-induced dynamics in steady flow 2. Dynamic reconfiguration in oscillating flow 3. 4
Outline Introduction: static drag reduction by reconfiguration 1. Self-induced dynamics in steady flow 2. Dynamic reconfiguration in oscillating flow 3. 5
Static drag reduction by reconfiguration Denny, M., & Cowen, B. J. Exp. Biol. , 1997. Vogel, S. J. Exp. Bot. , 1989. Reconfiguration = passive adaptation of the shape in response to a forcing 6 Static drag reduction by reconfiguration
Static drag reduction by reconfiguration Vogel, S. J. Exp. Bot. , 1989. Reconfiguration Frontal area reduction 7 Static drag reduction by reconfiguration
Static drag reduction by reconfiguration Vogel, S. J. Exp. Bot. , 1989. Reconfiguration Streamlining 8 Static drag reduction by reconfiguration
Static drag reduction by reconfiguration drag force F rigid flexible F rigid F flexible flow velocity U Vogel, S. J. Exp. Bot. , 1989. Reconfiguration Drag reduction 9 Static drag reduction by reconfiguration
Static drag reduction by reconfiguration � Cantilever flat plate, transverse flow increasing U U Gosselin et al., JFM , 2010. 10 Static drag reduction by reconfiguration
Static drag reduction by reconfiguration � Steady flow static shape ? Gosselin et al., JFM, 2010. Tadrist et al., JFS, 2015 Does the self-induced dynamics prevent drag reduction by reconfiguration? 11 Static drag reduction by reconfiguration
Outline Introduction: static drag reduction by reconfiguration 1. Self-induced dynamics in steady flow 2. Dynamic reconfiguration in oscillating flow 3. 12
Model � Cantilever, slender, flat plate � Clamped transverse to the uniform, steady flow � D<<W<<L z U y L W x D 13 Self-induced dynamics in steady flow
Model � Deflection in the xz-plane � 2D Euler-Bernoulli beam � Bending stiffness EI � Lineic mass m z reconfiguration U L x 14 Self-induced dynamics in steady flow
Self-induced dynamics in steady flow: flutter 15 Self-induced dynamics in steady flow
Model � Local models of flow forces � Resistive drag z U θ τ Relative velocity n s x 16 Self-induced dynamics in steady flow
Model � Local models of flow forces � Resistive drag � Reactive force z U θ τ Relative velocity Added mass n s x Curvature 17 Self-induced dynamics in steady flow
Governing parameters: static equilibrium � Cauchy number � resistive drag / restoring bending stiffness 18 Self-induced dynamics in steady flow
Governing parameters: static equilibrium � Cauchy number � resistive drag / restoring bending stiffness controls level of static reconfiguration U increasing 19 Self-induced dynamics in steady flow
Governing parameters: static equilibrium � Cauchy number � resistive drag / restoring bending stiffness controls level of static reconfiguration � Slenderness � resistive drag / reactive (added mass) force 20 Self-induced dynamics in steady flow
Governing parameters: static equilibrium � Cauchy number � resistive drag / restoring bending stiffness controls level of static reconfiguration � Slenderness � resistive drag / reactive (added mass) force negligible contribution to static equilibrium 21 Self-induced dynamics in steady flow
Governing parameters: static equilibrium � Cauchy number � resistive drag / restoring bending stiffness controls level of static reconfiguration � Slenderness � resistive drag / reactive (added mass) force negligible contribution to static equilibrium 22 Self-induced dynamics in steady flow
Governing parameters: dynamic parameters � Reduced velocity � reactive (added mass) force / restoring bending stiffness 23 Self-induced dynamics in steady flow
Governing parameters: dynamic parameters � Reduced velocity � reactive (added mass) force / restoring bending stiffness drives the instability 24 Self-induced dynamics in steady flow
Governing parameters: dynamic parameters � Reduced velocity � reactive (added mass) force / restoring bending stiffness drives the instability � Slenderness � resistive drag / reactive (added mass) force 25 Self-induced dynamics in steady flow
Governing parameters: dynamic parameters � Reduced velocity � reactive (added mass) force / restoring bending stiffness drives the instability � Slenderness � resistive drag / reactive (added mass) force damping of the instability 26 Self-induced dynamics in steady flow
Governing parameters: dynamic parameters � 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 27 Self-induced dynamics in steady flow
Governing parameters: dynamic parameters � 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 28 Self-induced dynamics in steady flow
Governing parameters: dynamic parameters � 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 29 Self-induced dynamics in steady flow
Non-linear dynamics � Stable equilibrium: 30 Self-induced dynamics in steady flow
Non-linear dynamics � Periodic limit cycle: 31 Self-induced dynamics in steady flow
Non-linear dynamics � Periodic limit cycle: 32 Self-induced dynamics in steady flow
Non-linear dynamics � Chaotic motion: 33 Self-induced dynamics in steady flow
Non-linear dynamics � Chaotic motion: 34 Self-induced dynamics in steady flow
Kinematic regimes � Stable static equilibrium � Periodic flapping Increasing flow velocity � Chaotic flapping Drag in the different regimes compared to rigid case ? 35 Self-induced dynamics in steady flow
Drag reduction 36 Self-induced dynamics in steady flow
Drag reduction STABLE UNSTABLE 37 Self-induced dynamics in steady flow
Drag reduction STABLE PERIODIC CHAOTIC 38 Self-induced dynamics in steady flow
Drag reduction ? STABLE PERIODIC CHAOTIC 39 Self-induced dynamics in steady flow
Drag reduction ? � Magnification of drag during « snapping » events � Short duration � Rare � Random 40 Self-induced dynamics in steady flow
Drag reduction � 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 41 Self-induced dynamics in steady flow
Outline Introduction: static drag reduction by reconfiguration 1. Self-induced dynamics in steady flow 2. Dynamic reconfiguration in oscillating flow 3. 42
Model � Uniform oscillatory flow z A U(t) L x 43 Dynamic reconfiguration in oscillating flow
Model � Uniform oscillatory flow Additional flow force: virtual buoyancy 44 Dynamic reconfiguration in oscillating flow
Model � Uniform oscillatory flow Additional flow force: virtual buoyancy � Neutrally buoyant flat plate 45 Dynamic reconfiguration in oscillating flow
Model � Uniform oscillatory flow Additional flow force: virtual buoyancy � Neutrally buoyant flat plate Neglect virtual buoyancy 46 Dynamic reconfiguration in oscillating flow
Model � Uniform oscillatory flow Additional flow force: virtual buoyancy � Neutrally buoyant flat plate Neglect virtual buoyancy Neglect structural inertia 47 Dynamic reconfiguration in oscillating flow
Model � Uniform oscillatory flow Additional flow force: virtual buoyancy � Neutrally buoyant flat plate Neglect virtual buoyancy Neglect structural inertia Stable to fluid-structure instabilities 48 Dynamic reconfiguration in oscillating flow
Governing parameters � Mass ratio fixed 49 Dynamic reconfiguration in oscillating flow
Governing parameters � Mass ratio fixed � Slenderness 50 Dynamic reconfiguration in oscillating flow
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