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Research Papers: Gas Turbines: Microturbines and Small Turbomachinery

On Scaling Down Turbines to Millimeter Size

[+] Author and Article Information
R. T. Deam

Faculty of Engineering and Industrial Sciences,  Industrial Research Institute Swinburne, P.O. Box 218, Hawthorn, Victoria 3122, Australiardeam@groupwise.swin.edu.au

E. Lemma

Faculty of Engineering and Industrial Sciences,  Industrial Research Institute Swinburne, P.O. Box 218, Hawthorn, Victoria 3122, Australiaelemma@swin.edu.au

B. Mace

 Micromachines Ltd., 20 Queen Street, Melbourne, Victoria 3000, Australiabm@alphalink.com.au

R. Collins

 Micromachines Ltd., 20 Queen Street, Melbourne, Victoria 3000, Australiaracoll@ozemail.com.au

J. Eng. Gas Turbines Power 130(5), 052301 (Jun 12, 2008) (9 pages) doi:10.1115/1.2938516 History: Received January 24, 2007; Revised April 24, 2008; Published June 12, 2008

The purpose of this work is to establish the maximum theoretical efficiency that a viscous flow turbine (such as a Tesla turbine) can achieve. This is very much in the spirit of the Betz limit for wind turbines. The scaling down of viscous flow turbines is thought not to alter this result, whereas the scaling down of conventional turbines, whether axial or radial flow, results in an ever lowering of their efficiencies. A semiempirical scaling law is developed for conventional gas turbines using published machine performance data, which is fitted to a simple boundary layer model of turbine efficiency. An analytical model is developed for a viscous flow turbine. This is compared to experimental measurements of the efficiency of a Tesla turbine using compressed air. The semiempirical scaling law predicts that below a rotor diameter of between about 11mm and 4mm, a practical Brayton cycle is not possible. Despite that, however, and for rotor diameters less than between about 7mm and 2mm, a viscous flow turbine, compressor, or pump will be more efficient than a conventional design. This may have a significant impact on the design of microelectromechanical system devices.

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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Practical air breathing Brayton cycle machine efficiencies

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Figure 2

Brayton cycle thermal efficiency versus turbine component efficiency, assuming 20°C inlet temperature to the compressor (thick lines simple cycle; thin lines with regenerator)

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Figure 3

Schematic of heat losses from turbine casing

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Figure 4

Comparison of practical Brayton cycle machine efficiencies with the semiempirical scaling law for different turbine inlet temperatures with Ẇ0=200W

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Figure 5

Comparison of NASA closed Brayton cycle machine efficiencies with the semiempirical scaling law

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Figure 6

1D viscous flow turbine

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Figure 7

Possible scaling laws for viscous and conventional turbines at MEMS scale

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