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Electrostatically driven synthetic microjet arrays as a propulsion method for micro flight

Part I: principles of operation, modeling, and simulation

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Abstract

A novel propulsion method suitable for micromachining is presented that takes advantage of Helmholtz resonance, acoustic streaming, and eventually flow entrainment and thrust augmentation. In this method, an intense acoustic field is created inside the cavity of a Helmholtz resonator. Flow velocities at the resonator throat are amplified by the resonator and create a jet stream due to acoustic streaming. These jets are used to form a propulsion system. In this paper a system hierarchy incorporating the new method is described and the relevant governing equations for the Helmholtz resonator operation and acoustic streaming are derived. These equations can predict various device parameters such as cavity pressure amplitude, exit jet velocity and generated thrust. In a sample embodiment, an electrostatic actuator is used for generation of the initial acoustic field. The relevant design parameters for the actuator are discussed and an equivalent circuit model is synthesized for the device operation. The circuit model can predict the lowest order system resonance frequencies and the small signal energy conversion efficiency. A representative resonator performance is simulated and it is shown that velocities above 16 m/s are expected at jet nozzles. The calculated delivered thrust by this resonator with 0.7 μm diaphragm displacement amplitude is 3.3 μN at the resonance frequency.

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Abbreviations

A cor :

Area correction factor

A D :

Diaphragm area

A E :

Effective throat area

A T :

Geometric throat area

c :

Speed of sound

d 0 :

Initial actuator gap

f:

Frequency of operation

h T :

Throat height

L :

Perforation hole depth

l :

Perforation hole opening size

L C :

Diaphragm-throat distance

L D :

Diaphragm length

L E :

Equivalent inertia length of the throat

L T :

Geometric throat length

L V :

Equivalent viscous length of the throat

M :

Distance between perforation holes

t :

Diaphragm thickness

V bias :

DC bias voltage

V c0 :

Initial cavity volume

μ:

Air viscosity

σ:

Diaphragm residual stress

ε0:

Permitivity of vacuum

ρair:

Air density

ω c :

Cavity resonance frequency

ρ D :

Diaphragm density

ω D :

Diaphragm resonance frequency

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Acknowledgements

The authors would like to thank the Defense Advanced Research Projects Agency (DARPA) for providing the support for this work through contract# N00019-98-K-0111. The help of Christopher Morris in the preparation of the manuscript is appreciated.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Washington, Campus Box 352500, Seattle, WA, 98195, USA

    Babak A. Parviz

  2. Department of Electrical Engineering and Computer Science, Center for Wireless Integrated Micro Systems, University of Michigan, Ann Arbor, MI, 48109-2122, USA

    Khalil Najafi

  3. Aerospace Engineering Department, University of Michigan, Ann Arbor, MI, 48109-2122, USA

    Michael O. Muller, Luis P. Bernal & Peter D. Washabaugh

Authors
  1. Babak A. Parviz
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  2. Khalil Najafi
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  3. Michael O. Muller
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  4. Luis P. Bernal
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  5. Peter D. Washabaugh
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Correspondence to Babak A. Parviz.

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Parviz, B.A., Najafi, K., Muller, M.O. et al. Electrostatically driven synthetic microjet arrays as a propulsion method for micro flight. Microsyst Technol 11, 1214–1222 (2005). https://doi.org/10.1007/s00542-005-0599-0

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