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Research Papers: Other (Seals, Manufacturing)

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

[+] Author and Article Information
K. Nagai

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

S. Kaneko

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

H. Taura

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

Y. Watanabe

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

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received March 21, 2017; final manuscript received August 21, 2017; published online October 19, 2017. Assoc. Editor: Mihai Arghir.

J. Tribol 140(3), 032201 (Oct 19, 2017) (16 pages) Paper No: TRIB-17-1101; doi: 10.1115/1.4037846 History: Received March 21, 2017; Revised August 21, 2017

Numerical and experimental analyses were carried out to investigate the static characteristics of liquid annular seals with helical grooves in a seal stator. In the numerical analysis, the momentum equations with turbulent coefficients and the continuity equation, which were averaged across the film thickness, were numerically solved to obtain the leakage flow rate and the pressure distributions in the seal clearance. To accurately define the location of the step between the groove and the land regions in the calculation domain, these governing equations were 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. The numerical analysis included the effects of both fluid inertia and energy loss due to expansion during the passage of fluid from the land region to the helical groove region and that due to contraction from the groove region to the land region. In the experimental analysis, the leakage flow rate and the fluid-film pressure distributions in the seal clearance were measured for the helically grooved seals with different helix angles of the helical groove. The numerical results of leakage flow rate and pressure distributions agree reasonably with the experimental results, which demonstrates the validity of the numerical analysis. The leakage flow rate of the helically grooved seals was influenced by two factors: fluid energy loss during passage through the step between the groove and the land, and the pumping effect by which the spinning motion of the rotor pushes the flow back upstream along the helical grooves. Under a low range of rotor spinning velocity, the leakage flow rate decreased with helix angle because the effect of fluid energy loss in the steps was significant. By contrast, under a high range of spinning velocity, the quantitative difference in the leakage flow rate due to the helix angle decreased compared to that under a low range because the reduction in the leakage flow rate due to the pumping effect was pronounced for a larger helix angle. The effects of helix angle and rotor spinning velocity on the leakage flow rate are explained qualitatively using a simplified model.

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References

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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

Flow passing through step between land and groove regions: sudden expansion (a) and contraction (b) sections

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Fig. 4

Schematic view of experimental apparatus

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Fig. 5

Geometry of helically grooved seal

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Fig. 6

Relationship of leakage flow rate Q to rotor spinning velocity N for all seals tested: (a) pd = 1000 kPa and (b) pd = 294 kPa

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Fig. 7

Variation in leakage flow rate with rotor spinning velocity, ΔQ, versus helix angle γ

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Fig. 8

Numerical results of relationship of leakage flow rate Q to eccentricity ratio ε at equilibrium position: (a) N = 1200 rpm and (b) N = 7200 rpm

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Fig. 9

Axial distributions of circumferentially averaged pressure for three types of seals: helically grooved seal, circumferentially grooved seal, and smooth-surface seal; pd = 1000 kPa, N = 1200 rpm

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Fig. 10

Axial distributions of circumferentially averaged pressure for helically grooved seal with three different helix angles; pd = 1000 kPa, N = 1200 rpm

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Fig. 11

Pressure distributions in seal clearance for helically grooved seal; γ = 29.6 deg, pd = 1000 kPa, and N = 1200 rpm: experimental (a) and numerical (b) results

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Fig. 12

Pressure distributions in seal clearance for helically grooved seal; γ = 8.08 deg, pd = 1000 kPa, and N = 1200 rpm: experimental (a) and numerical (b) results

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Fig. 13

Numerical results of relationship of fluid-film force f to eccentricity ratio ε at equilibrium position; pd = 1000 kPa, N = 1200 rpm

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Fig. 14

Numerical results of relationship of fluid-film force components (a) fε and (b) fθ to eccentricity ratio ε at equilibrium position; pd = 1000 kPa, N = 1200 rpm

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Fig. 15

Numerical results of circumferential distributions at z = 6 mm of fluid-film pressure p and local film thickness, h (= cr (1 + ε·cos θ) + λ·gd) (λ = 0 for smooth-surface seal); pd = 1000 kPa, N = 1200 rpm, and ε = 0.3. θ (=Θ − ψ) is the angular coordinate in the direction of rotor spinning measured from the maximum film thickness position of the smooth-surface seal.

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Fig. 16

Numerical results of axial distributions of mean circumferential velocity averaged along the circumferential direction, u¯xm; pd = 1000 kPa, N = 1200 rpm, ε = 0, and α = 0.1

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Fig. 17

Flow rate vectors with simplified model: (a) due to axial pressure difference between both ends of seal and (b) due to rotor spinning motion

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Fig. 18

Relationship between leakage flow rate Q and rotor spinning velocity N for various helix angles γ, as predicted using the simplified model; pd = 1000 kPa: predictions based on experimental (a) and numerical (b) results

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