Efficient Aeroelastic Energy Harvestingfrom HVAC Ducts

Xiaokun MaChristopher D. Rahn

Department of Mechanical and Nuclear EngineeringThe Pennsylvania State University

October 28th 2015

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Galloping energy harvester with equilateral triangle cross-section tip body(Sirohi, 2011, Journal of Intelligent Material Systems and Structures)

Aeroelastic Energy Harvesters

Vortex shedding induced energy harvester(Weinstein, 2012, Smart Materials and Structures)

Flapping-leaf generator(Li, 2009, SMASIS)

Galloping energy harvester with rectangular cross-section tip body(Zhao, 2012, SMASIS)

• Vortex induced vibration

• Galloping

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Flow-induced self-excited generator(Bibo, 2011, Journal of Intelligent Material Systems and Structures)

Aeroelastic Energy Harvesters

Piezoaeroelastic airfoil(Erturk, 2010, Applied Physics Letters)

• Flutter • Harmonica inspired device

Alternative beam geometries(Roundy, 2005, Pervasive Computing)

• Strain distribution

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• Device Design and Model

• Stability Analysis

• Performance Comparison

• Conclusions and Future Work

Outline

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• Device design Mounted to a HVAC duct wall Air flow scoop above, and electronics and connectors underneath PVDF unimorph pinned at the top and bottom using compliant hinges Transverse vibration opens and closes the air gap Self-excited above a critical flow speed

• Model parameters PVDF unimorph (from Measurement Specialties, Inc.): Chamber dimension: Inflow speed:

Design

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• Transversal beam dynamics

• Electrical circuit equation

Model

Stretching effect for pinned-pinned beam

Strain due to stretching Strain due to bending

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• Pressure dynamics Bernoulli equation (inviscid, irrotational, laminar, and steady flow):

Area of the aperture:

Continuity equation (compressible flow):

Pressure dynamics:

Model

A single-mode reduced-order model is sufficient to approximate the local dynamics(Bibo, 2011, Journal of Intelligent Material Systems and Structures)

𝑤 (𝑥 , 𝑡 )=∅ (𝑥 )𝑞 (𝑡 )=sin ( 𝜋𝐿 𝑥 )𝑞 (𝑡 )

Nonlinear state space model

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Beam dynamicsElectrical circuit

equationPressure dynamics

• Device Design and Model

• Stability Analysis

• Performance Comparison

• Conclusions and Future Work

Outline

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• Linearized model: • Design parameters: air gap width , inflow speed

Stability Analysis

Cantilever Pinned-pinned beam

𝑣0=3𝑚/ 𝑠

𝑊 𝑔=2𝑚𝑚

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Limit cycle frequency

126.1

Limit cycle frequency

2234

Stability Analysis

CantileverPinned-pinned beam

• The critical inflow speed of the pinned-pinned beam increases much faster when the air gap width increases

• At the same wind speed, the air gap width of the cantilever can be chosen in a wider range to ensure instability

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• How do air gap width and critical inflow speed interact with each other?

• Device Design and Model

• Stability Analysis

• Performance Comparison

• Conclusions and Future Work

Outline

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Performance Comparison

Displacement Maximum Strain Power

Cantilever

Pinned-pinned beam

() () () (1% strain)

()

Cantilever 126.1 912 2.13% 1.72 0.808

Pinned-Pinned Beam 2234 51.5 0.179% 0.658 3.68

4x higher average power 12

• Air gap width , inflow speed

11x smaller maximum strain

Tunable Axial Stiffness

• The beam midpoint vibration amplitude increases but the limit cycle frequency decreases when the axial stiffness is reduced

• The average power increases and exceeds of the cantilever when

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• What if we can use an axially flexible pinned-pinned boundary condition?

𝒇(𝑯𝒛) 𝑨𝒘(𝒎𝒎)

𝑷𝒂𝒗𝒆(𝒎𝑾)

• Device Design and Model

• Stability Analysis

• Performance Comparison

• Conclusions and Future Work

Outline

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Conclusions and Future Work• Conclusions

The stability analysis can serve as a design guideline to choose crucial parameters Compared with the cantilever design, the pinned-pinned beam has a much higher limit cycle

frequency and more efficient mode shape The maximum strain in the pinned-pinned beam is 11 times smaller than the cantilever The pinned-pinned beam generates 4 times more average power than the cantilever with the

same maximum strain The tunable axial stiffness design generates higher power output

• Future Work Experimental validation of the model Investigate the tunable axial stiffness design and fabrication

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Thank you!16

Acknowledgment• This work was supported by the National Science Foundation ASSIST Nanosystems ERC

under Award Number EEC-1160483