Research Papers

Mechanical Models of Low-Gravity Sloshing Taking Into Account Viscous Damping

[+] Author and Article Information
M. Utsumi

Senior Researcher
Machine Element Department,
Technical Research Laboratory,
IHI Corporation,
1 Shin-Nakaharacho,
Isogo-ku, Yokohama,
Kanagawa Prefecture 235-8501, Japan
e-mail: masahiko_utsumi@ihi.co.jp

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 26, 2012; final manuscript received September 3, 2013; published online October 23, 2013. Assoc. Editor: Thomas J. Royston.

J. Vib. Acoust 136(1), 011007 (Oct 23, 2013) (11 pages) Paper No: VIB-12-1361; doi: 10.1115/1.4025439 History: Received December 26, 2012; Revised September 03, 2013

Mechanical models of damped low-gravity sloshing are developed using a proposed analytical method for arbitrary axisymmetric tanks. It is shown that (a) the complex amplitudes of the force and moment caused by the conventional mechanical model do not coincide with the complex amplitudes of the force and moment calculated from the modal equation of sloshing and (b) these differences arise not only from the damping ratio but also from the surface tension although the surface tension does not cause energy dissipation. A mechanical model for correcting these differences is developed. The mass of this correction model is found to be equal to the mass of the liquid that fills the domain bounded by the meniscus and the plane that includes the contact line of the meniscus with the tank wall. With decreasing Bond number, the correction model mass as well as the damping ratio increase and, therefore, the correction becomes important. The force and moment caused by the conventional uncorrected mechanical model have phase lag with respect to the force and moment calculated from the modal equation of sloshing near the resonant frequency. Therefore, the correction is important for the dynamics and control analysis of a space vehicle.

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Fig. 1

Computational model and coordinate systems

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Fig. 3

Mechanical model for correction (the original features are shown in gray to reinforce the fact that the correction is in addition to the original features and not in place of them)

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Fig. 6

Mass mC of correction model

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Fig. 4

Eigenfrequency ω/2π (Hz)

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Fig. 9

Uncorrected moment My,mech and corrected moment My,mech+My,C (Bo=0.1, filling level is 25.3%)

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Fig. 7

Uncorrected force Fx,mech and corrected force Fx,mech+Fx,C (Bo = 0.1, filling level is 25.3%)

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Fig. 8

Vector figures for phase difference between uncorrected force Fx,mech and corrected force Fx,mech+Fx,C

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Fig. 10

Dimensionless eigenfrequency ω/(g/b)1/2

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Fig. 11

Dimensionless height of the sloshing mass l1/b

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Fig. 12

Force correction factor (Fx,mech+Fx,C)/Fx,mech and moment correction factor (My,mech+My,C)/My,mech (Bo=0.1, filling level is 25.3%)

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Fig. 14

Domain VC (gray domain)

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Fig. 13

Uncorrected moment My,mech and corrected moment My,mech+My,C (Bo = 0.1, filling level is 17.6%)




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