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Research Papers: Multiphase Flows

Gas-Enabled Resonance and Rectified Motion of a Piston in a Vibrated Housing Filled With a Viscous Liquid

[+] Author and Article Information
L. A. Romero

Computational Mathematics,
Sandia National Laboratories,
P.O. Box 5800, MS 1320,
Albuquerque, NM 87185-1320,
e-mail: lromero@sandia.gov

J. R. Torczynski

Fluid Sciences and Engineering,
Sandia National Laboratories,
P.O. Box 5800, MS 0840,
Albuquerque, NM 87185-0840
e-mail: jrtorcz@sandia.gov

J. R. Clausen

Fluid and Reactive Processes,
Sandia National Laboratories,
P.O. Box 5800, MS 0828,
Albuquerque, NM 87185-0828
e-mail: jclause@sandia.gov

T. J. O'Hern

Thermal and Fluid Experimental Sciences,
Sandia National Laboratories,
P.O. Box 5800, MS 0840,
Albuquerque, NM 87185-0840
e-mail: tjohern@sandia.gov

G. L. Benavides

Advanced Surety Mechanisms,
Sandia National Laboratories,
P.O. Box 5800, MS 0333,
Albuquerque, NM 87185-0333
e-mail: glbenav@sandia.gov

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 4, 2015; final manuscript received November 16, 2015; published online February 18, 2016. Assoc. Editor: Bart van Esch.

J. Fluids Eng 138(6), 061302 (Feb 18, 2016) (19 pages) Paper No: FE-15-1140; doi: 10.1115/1.4032216 History: Received March 04, 2015; Revised November 16, 2015

We show how introducing a small amount of gas can completely change the motion of a solid object in a viscous liquid during vibration. We analyze an idealized system exhibiting this behavior: a piston in a liquid-filled housing with narrow gaps between piston and housing surfaces that depend on the piston position. Recent experiments have shown that vibration causes some gas to move below the piston and the piston to subsequently move downward against its supporting spring. We analyze the analogous but simpler situation in which the gas regions are replaced by bellows with similar pressure–volume relationships. We show that the spring formed by these bellows (analogous to the pneumatic spring formed by the gas regions) enables the piston and the liquid to oscillate in a mode with low damping and a strong resonance. We further show that, near this resonance, the dependence of the gap geometry on the piston position produces a large rectified (net) force on the piston. This force can be much larger than the piston weight and tends to move the piston in the direction that decreases the flow resistance of the gap geometry.

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References

Figures

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Fig. 1

Photographs of an experiment showing that, under certain conditions, vertical vibration can cause a piston in a housing filled with liquid and a small amount of gas to move downward against its supporting spring [13]

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Fig. 2

Schematic diagrams of the cross sections of the actual and simplified systems. Left: the actual system has a complicated inner gap and gas regions above and below the piston [13]. Right: the simplified system analyzed herein has a uniform inner gap and bellows instead of gas. The spring supporting the piston is not shown. The real gaps are much narrower than those shown above.

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Fig. 3

Numerical damping and added-mass matrices computed from unsteady Stokes simulations vary little over a wide frequency range

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Fig. 4

The unsteady Stokes and quasi-steady piston amplitudes agree closely around the resonance frequency

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Fig. 10

The rectified force Frect on the piston is plotted over a wide frequency range for immobilized bellows. No resonance is observed. The rectified force is negative (downward) and is many orders of magnitude smaller than when the bellows are allowed to move.

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Fig. 5

The decoupled and coupled piston amplitudes from Eqs. (96) and (87) agree closely around the resonance

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Fig. 6

The decoupled and coupled values of γ0, defined in Eq. (108), agree closely around the resonance

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Fig. 9

The rectified force Frect, normalized by the piston weight mPg0, is plotted around the resonance frequency for five values of the piston position ZP: 0.3, 0.4, 0.5, 0.6, and 0.7 cm. The rectified force increases as the piston is moved upward and the inner gap becomes shorter.

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Fig. 7

The quantities R11 (solid curve) and R12 (dashed curve) normalized by the rectified force Frect are plotted around the resonance frequency. Since these terms are small and R13 is even smaller, the approximate expression for Frect in Eq. (107) is reasonably accurate.

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Fig. 8

The rectified force Frect, normalized by the piston weight mPg0, is plotted around the resonance frequency, with γ0 from Eq. (108). The driving amplitude is g1 = 10 g0, and Frect is proportional to g12. Under these conditions, the piston would be levitated.

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