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Research Papers: Flows in Complex Systems

# Numerical Calculation of Unsteady Flow Fields: Feasibility of Applying the Weis-Fogh Mechanism to Water Turbines

[+] Author and Article Information
Kideok Ro

Professor
Department of Mechanical System Engineering,
Institute of Marine Industry,
Gyeongsang National University,
445 Inpyeong-dong, Tongyeong, Gyeongnam 650-160, South Korea
e-mail: rokid@ gnu.ac.kr

Baoshan Zhu

Department of Thermal Engineering,
State Key Laboratory of Hydroscience and Engineering,
Tsinghua University,
Beijing 100084, China

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the Journal of Fluids Engineering. Manuscript received September 19, 2012; final manuscript received July 3, 2013; published online August 6, 2013. Assoc. Editor: Chunill Hah.

J. Fluids Eng 135(10), 101103 (Aug 06, 2013) (6 pages) Paper No: FE-12-1458; doi: 10.1115/1.4024956 History: Received September 19, 2012; Revised July 03, 2013

## Abstract

In this study, a reciprocating-type water turbine model that applies the principle of the Weis-Fogh mechanism was proposed, and the model's unsteady flow field was calculated by an advanced vortex method. The primary conditions were as follows: wing chord $C=1$, wing shaft stroke length $hs=2.5C$, and the maximum opening angle of the wing $α=36 deg$. The dynamic characteristics and unsteady flow fields of a Weis-Fogh type water turbine were investigated with velocity ratios $U/V$ = 1.0 ∼ 3.0. Force coefficients $Cu$ and $Cv$ acting on the wing in the $U$ and $V$ directions, respectively, were found to have a strong correlation each other. The size of a separated region on the back face of the wing increased as the velocity ratio increased and as the wing approached the opposite wall. The rapid drop in $Cv$ during a stroke increased as the velocity ratio increased, and the average $Cu$ and $Cv$ increased as the velocity ratio increased. The maximum efficiency of this water turbine was 14.1% at $U/V$ = 2.0 for one wing.

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## References

Weis-Fogh, T., 1973, “Quick Estimates of Flight Fitness in Hovering Animals, Including Novel Mechanism for Lift Production,” J. Exp. Biol., 59, pp. 169–230.
Lighthill, M. J., 1973, “On the Weis-Fogh Mechanism of Lift Generation,” J. Fluid Mech., 60, pp. 1–17.
Furber, S. B., and Ffowcs Williams, J. E., 1979, “Is the Weis-Fogh Principle Exploitable in Turbomachinery?” J. Fluid Mech., 94(3), pp. 519–540.
Tsutahara, M., and Kimura, T., 1987, “An Application of the Weis-Fogh Mechanism to Ship Propulsion,” ASME J. Fluids Eng., 109, pp. 107–113.
Tsutahara, M., and Kimura, T., 1988, “A Pilot Pump Using the Weis-Fogh Mechanism and its Characteristics,” Trans. Jpn. Soc. Mech. Eng., Ser. B, 54(498), pp. 393–397.
Tsutahara, M., and Kimura, T., 1994, “Study of a Fan Using the Weis-Fogh Mechanism (An Experimental Fan and its Characteristics),” Trans. Jpn. Soc. Mech. Eng., Ser. B, 60(571), pp. 910–915.
Ro, K. D., and Seok, J. Y., 2010, “Sailing Characteristics of a Model Ship of Weis-Fogh Type,” Trans. Korea Soc. Mech. Eng., Ser. B, 34(1), pp. 45–52.
Ro, K. D., Choi, B. K., Lee, J. H., and Oh, S. K., 2010, “Vibration Characteristics of a Model Ship With Weis-Fogh Type Ship's Propulsion Mechanism,” J. Korea Soc. Mech. Eng., 34(1), pp. 69–75.
Ro, K. D., 2010, “Performance Improvement of Weis-Fogh Type Ship's Propulsion Mechanism Using a Wing Restrained by an Elastic Spring,” ASME J. Fluids Eng., 132, p. 041101.
Kamemoto, K.1995, “On Attractive Features of the Vortex Methods,” Computational Fluid Dynamics Review 1995, M.Hafez and K.Oshima, ed., Wiley, New York, pp. 334–353.
Ro, K. D., Zhu, B. S., and Kang, H. K., 2006, “Numerical Analysis of Unsteady Viscous Flow Through a Weis-Fogh Type Ship Propulsion Mechanism Using the Advanced Vortex Method,” ASME J. Fluids Eng., 128, pp. 481–487.
Uhlman, J. S., 1992, “An Integral Equation Formulation of the Equation of Motion of an Incompressible Fluid,” Naval Undersea Warfare Center Report No. 10-086.

## Figures

Fig. 1

Model of Weis-Fogh-type water turbine

Fig. 2

Analytical model

Fig. 9

Vortex distributions and streamlines around the wing at the center of the water channel (1∼3 correspond to U/V = 1.0~3.0 in Fig. 8)

Fig. 8

Time variation of Cv on the wing for one stroke at different velocity ratios

Fig. 7

Vortex distributions and velocity vectors around wing at different positions (A–C correspond to A–C in Fig. 4(b).)

Fig. 6

Pressure distributions around the wing at the center of the water channel (U/V = 2.0)

Fig. 5

Pressure distributions around the wing at the center of the water channel (U/V = 1.0)

Fig. 4

Time variations of Cu and Cv on the wing at different velocity ratios

Fig. 3

Definition of Fu and Fv on the wing

## Errata

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