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Influence of thickness on the flow field generated by an oscillating cantilever beam

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Abstract

 The aerodynamic performance of oscillating piezoelectric fans has been the focus of many research studies due to their potential as active cooling mechanisms for thermal management applications. These studies have typically focused on commercially available fans with flexible beams that are made to oscillate by tuning the alternating input voltages to the beam’s resonant frequency. Geometric variables such as fan height and length have previously been investigated; however, fan thickness has remained a fixed geometric constraint (\({\mathcal {O}}\sim 0.1\) mm) to allow feasible resonant frequencies to be achieved. This study investigates the influence of beam thickness on the flow field generated by an oscillating beam. The beam in this study is a rigid cantilever that is mechanically oscillated at a fixed amplitude and frequency thereby obviating the requirement to operate at resonance. Thicknesses of 1 and 3.7 mm are considered. A custom-designed particle-image velocity (PIV) facility was used to capture the induced phase-locked and time-averaged flow fields in two planes. The beams were noted to produce markedly different wakes within the oscillation plane. The 1-mm beam induced two distinct diverging jets—consistent with much of the literature on piezoelectric fans. In comparison, the 3.7-mm beam created two strong lateral wake regions with minimal fluid disturbance downstream of the beam tip. Out-of-plane measurements, as well as numerical models, revealed that fluid separation from the 3.7-mm beam is inhibited due to the more dominant influence of viscous friction on the larger, upper and lower surfaces of the rigid structure. The numerical analysis also revealed the significant influence of shed, counter-rotating vortex pairs on the pressure fields around the beam structures during the subsequent half-stroke. The results of this work may inform the design of oscillating fans for use in thermal management applications, as well as contribute to the literature on the complex phenomenon of flapping wing flight.

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Abbreviations

a :

Tip-to-tip amplitude (mm)

c :

Beam chord width (mm)

E :

Young’s modulus (Pa)

F :

Force (N)

f :

Oscillating frequency (Hz)

I :

Identity matrix (–)

L :

Beam length (mm)

p :

Pressure (Pa)

t :

Time (s)

\(U_{\mathrm{Tip}}\) :

Maximum tip velocity (m/s)

u :

Velocity field (m/s)

v :

Poisson’s ratio (–)

X :

Spanwise beam location (mm)

\(\alpha\) :

Normalised thickness (–)

\(\delta\) :

Beam thickness (mm)

\(\Theta\) :

Maximum beam displacement angle (\(^{\circ }\))

\(\theta\) :

Time-dependent angular displacement of the beams (\(^{\circ }\))

\(\mu\) :

Dynamic viscosity (kg/ms)

\(\nu\) :

Kinematic viscosity (\(\text{m}^{2}/\text{s}\))

\(\rho\) :

Density (\(\text{kg/m}^{3}\))

\(\sigma\) :

Stress tensor (–)

\(\phi\) :

Phase angle (\(^{\circ }\))

\(\omega\) :

Vorticity (1/s)

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Acknowledgements

The authors acknowledge the financial support of the Irish Research Council (IRC) for funding under their Government of Ireland Postgraduate Scholarship Scheme: Project ID GOIP/2014/1480.

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Authors and Affiliations

  1. Stokes Laboratories, University of Limerick, Limerick, Ireland

    Ciaran Conway & Jeff Punch

  2. Efficient Energy Transfer Department, Nokia Bell Labs, Blanchardstown, Dublin, 15, Ireland

    Nick Jeffers & Akshat Agarwal

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  1. Ciaran Conway
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  2. Nick Jeffers
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  3. Akshat Agarwal
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  4. Jeff Punch
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Correspondence to Ciaran Conway.

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Conway, C., Jeffers, N., Agarwal, A. et al. Influence of thickness on the flow field generated by an oscillating cantilever beam. Exp Fluids 61, 167 (2020). https://doi.org/10.1007/s00348-020-02997-5

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