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Research Papers: Other (Seals, Manufacturing)

Numerical and Experimental Analyses of Dynamic Characteristics for Liquid Annular Seals With Helical Grooves in Seal Stator

[+] Author and Article Information
K. Nagai

Graduate School of Nagaoka
University of Technology,
Department of Energy and
Environment Science,
Kamitomioka-machi 1603-1,
Nagaoka-shi 940-2188, Niigata, Japan
e-mail: s091057@stn.nagaokaut.ac.jp

S. Kaneko

Department of Mechanical Engineering,
Nagaoka University of Technology,
Kamitomioka-machi 1603-1,
Nagaoka-shi 940-2188, Niigata, Japan
e-mail: kaneko@mech.nagaokaut.ac.jp

H. Taura

Department of Mechanical Engineering,
Nagaoka University of Technology,
Kamitomioka-machi 1603-1,
Nagaoka-shi 940-2188, Niigata, Japan
e-mail: htaura@vos.nagaokaut.ac.jp

Y. Watanabe

EBARA Corporation,
Honfujisawa 4-2-1,
Fujisawa-shi 251-8502, Kanagawa, Japan
e-mail: watanabe.yusuke@ebara.com

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received May 2, 2017; final manuscript received November 12, 2017; published online April 10, 2018. Assoc. Editor: Mihai Arghir.

J. Tribol 140(5), 052201 (Apr 10, 2018) (17 pages) Paper No: TRIB-17-1167; doi: 10.1115/1.4039428 History: Received May 02, 2017; Revised November 12, 2017

Numerical and experimental analyses were carried out to investigate the dynamic characteristics of liquid annular seals with helical grooves in the seal stator. In the numerical analysis, the governing equations were the momentum equations with turbulent coefficients and the continuity equation, all averaged across the film thickness and expressed using an oblique coordinate system in which the directions of coordinate axes coincided with the circumferential direction and the direction along the helical grooves. These governing equations were solved numerically to obtain the dynamic characteristics, such as the dynamic fluid-film forces, dynamic coefficients, and whirl-frequency ratio (WFR). The numerical analysis included the effect of both fluid inertia and energy loss at the steps between the helical groove and the land sections. In the experiments, the dynamic fluid-film pressure distributions, which were induced by a small whirling motion of the rotor about the seal center, were measured to obtain the dynamic characteristics. The equivalent numerical results reasonably agree with the experimental results, demonstrating the validity of the numerical analysis. The value of the tangential dynamic fluid force induced by the rotor whirling motion decreased with increasing the helix angle γ. Consequently, the values of the cross-coupled stiffness coefficient and WFR decreased with increasing γ and became negative for large γ. In general, pump rotors rotate with a forward whirling motion under normal operating conditions. Hence, the negative value of WFR for helically grooved seals contributes to rotor stability by suppressing the forward whirling motion of the rotor.

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Figures

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Fig. 1

Liquid annular seal with helically grooved stator and coordinate system

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Fig. 2

Inner surface of seal stator

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Fig. 3

Schematic view of experimental apparatus

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Fig. 4

Geometry of helically grooved seal

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Fig. 5

Small whirling motion of rotor about seal center and dynamic fluid-film forces

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Fig. 6

Dynamic force coefficients versus ratio of whirling angular velocity to spinning angular velocity at a centered position of seal; ε0 = 0, N = 1200 rpm: (a) tangential force coefficient Ft/ew and (b) radial force coefficient Fr/ew

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Fig. 7

Stiffness coefficients versus rotor spinning velocity at a centered position of seal; ε0 = 0: (a) main stiffness Km and (b) cross-coupled stiffness Kc

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Fig. 8

Numerical results for fluid-film force components versus eccentricity ratio at equilibrium position of rotor center [42]; pd = 1000 kPa, N = 1200 rpm: (a) Fluid film component along line of centers fε0 and (b) Fluid film component perpendicular to line of centers fϑ0

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Fig. 9

Damping coefficients versus rotor spinning velocity at a centered position of seal; ε0 = 0: (a) main damping Cm and (b) cross-coupled damping Cc

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Fig. 10

Main added-mass coefficients versus rotor spinning velocity at a centered position of seal; ε0 = 0

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Fig. 11

WFR versus rotor spinning velocity at a centered position of seal; ε0 = 0

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Fig. 12

Numerical results for stiffness coefficients versus eccentricity ratio at equilibrium position of rotor center; N = 1200 rpm: (a) Kxx, (b) KYY, (c) KXY, and (d) KYX

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Fig. 13

Numerical results for damping coefficients versus eccentricity ratio at equilibrium position of rotor center; N = 1200 rpm: (a) Cxx, (b) CYY, (c) CXY, and (d) CYX

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Fig. 14

Numerical results for added mass coefficients versus eccentricity ratio at equilibrium position of rotor center; N = 1200 rpm: (a) Mxx, (b) MYY, (c) MXY, and (d) MYX

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Fig. 15

Numerical results for WFR versus eccentricity ratio at equilibrium position of rotor center; N = 1200 rpm

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