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Research Papers: Gas Turbines: Structures and Dynamics

A Computational Fluid Dynamics Modified Bulk Flow Analysis for Circumferentially Shallow Grooved Liquid Seals

[+] Author and Article Information
Luis San Andrés

Mast-Childs Chair Professor
Fellow ASME
Turbomachinery Laboratory,
Texas A&M University,
College Station, TX 77843
e-mail: lsanandres@tamu.edu

Tingcheng Wu

Turbomachinery Laboratory,
Texas A&M University,
College Station, TX 77843
e-mail: wutingcheng29@gmail.com

Hideaki Maeda

Torishima Pump Mfg. Co., Ltd.,
1-1-8, Miyata-cho,
Takatsuki 569-8660, Osaka, Japan
e-mail: h-maeda@torishima.co.jp

Ono Tomoki

Torishima Pump Mfg. Co., Ltd.,
1-1-8, Miyata-cho,
Takatsuki 569-8660, Osaka, Japan
e-mail: tm-ono@torishima.co.jp

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 3, 2017; final manuscript received July 4, 2017; published online September 19, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(1), 012504 (Sep 19, 2017) (9 pages) Paper No: GTP-17-1266; doi: 10.1115/1.4037614 History: Received July 03, 2017; Revised July 04, 2017

In straight-through centrifugal pumps, a grooved seal acts as a balance piston to equilibrate the full pressure rise across the pump. As the groove pattern breaks the development of fluid swirl, this seal type offers lesser leakage and lower cross-coupled stiffnesses than a similar size and clearance annular seal. Bulk-flow models (BFMs) predict expediently the static and dynamic force characteristics of annular seals; however they lack accuracy for grooved seals. Computational fluid dynamics (CFD) methods give more accurate results, but are not computationally efficient. This paper presents a modified BFM to predict the rotordynamic force coefficients of shallow depth, circumferentially grooved liquid seals with an accuracy comparable to a CFD solution but with a simulation time of bulk-flow analyses. The procedure utilizes the results of CFD to evaluate the bulk flow velocity field and the friction factors for a 73 grooves annular seal (depth/clearance dg/Cr = 0.98 and length/diameter L/D = 0.9) operating under various sets of axial pressure drop and rotor speed. In a groove, the flow divides into a jet through the film land and a strong recirculation zone. The penetration angle (α), specifying the streamline separation in the groove cavity, is a function of the operating conditions; an increase in rotor speed or a lower pressure difference increases α. This angle plays a prominent role to evaluate the stator friction factor and has a marked influence on the seal direct stiffness. In the bulk-flow code, the friction factor model (f = nRem) is modified with the CFD extracted penetration angle (α) to account for the flow separation in the groove cavity. The flow rate predicted by the modified bulk-flow code shows good agreement with the measured result (6% difference). A perturbation of the flow field is performed on the bulk-flow equations to evaluate the reaction forces on the rotor surface. Compared to the rotordynamic force coefficients derived from the CFD results, the modified bulk-flow code predicts rotordynamic force coefficients within 10%, except that the cross-coupled damping coefficient is over-predicted up to 14%. An example test seal with a few grooves (L/D = 0.5, dg/Cr = 2.5) serves to further validate the predictions of the modified BFM. Compared to the original bulk-flow analysis, the current method shows a significant improvement in the predicted rotordynamic force coefficients, the direct stiffness and damping coefficients, in particular.

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References

Figures

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Fig. 1

Geometry of a circumferentially grooved annular liquid seal

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Fig. 2

Schematic views (front and side) of grooved seal with spinning and whirling rotor (not to scale)

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Fig. 3

Schematic view of rotor whirl and spinning motion in a rotating coordinate system (ωt = 0) (drawing not to scale)

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Fig. 4

Depiction of mesh for flow domain in seal: inlet section and groove and land sections

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Fig. 5

Applied boundary conditions (in rotating frame) at inlet and exit planes of seal

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Fig. 6

Computational fluid dynamics predictions: components of grooved seal reaction force, FX/e and FY/e, versus whirl frequency: (a) radial direction and (b) tangential direction. Nominal operating condition ΔP = 29.9 MPa, rotor speed = 5588 rpm (curve fits shown).

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Fig. 7

Schematic view of three-control-volume model utilized in a BFM [18]

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Fig. 8

Computational fluid dynamics derived normalized bulk-flow velocities along the seal length direction. Seal at nominal operating condition.

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Fig. 9

Example of flow in 50th groove of seal: streamlines to obtain penetration angle (α) from separation streamline (seal at nominal operating condition)

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Fig. 10

Penetration angle (α¯) versus parameter β = ΔP/[(1/2) ρR)2]. CFD Results derived from multiple operating conditions.

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Fig. 11

Computational fluid dynamics and bulk-flow (BF) derived axial direction friction factor (frz) on the rotor surface: (a) Z/L: 0 ∼ 1 and (b) groove and land sections at Z/L = 0.796 ∼ 0.810 (58th groove). Grooved seal at nominal operating condition.

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Fig. 12

Computational fluid dynamics and bulk-flow (BF) derived circumferential direction friction factor (f) on the rotor surface: (a) Z/L: 0 ∼ 1 and (b) groove and land sections at Z/L = 0.796 ∼ 0.810 (58th groove). Grooved seal at nominal operating condition.

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Fig. 13

Computational fluid dynamics and bulk-flow (BF) derived axial direction friction factor (fsz) on the stator surface: (a) Z/L: 0 ∼ 1 and (b) groove and land sections at Z/L = 0.796 ∼ 0.810 (58th groove). Grooved seal at nominal operating condition.

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Fig. 14

Computational fluid dynamics and bulk-flow (BF) derived circumferential direction friction factor (f) on stator surface: (a) Z/L: 0 ∼ 1 and (b) groove and land sections at Z/L = 0.796 ∼ 0.810 (58th groove). Grooved seal at nominal operating condition.

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Fig. 15

Computational fluid dynamics and bulk-flow (BF) components of grooved seal reaction force, FX/e and FY/e, versus whirl frequency (ω): (a) radial direction and (b) tangential direction. ΔP = 20 MPa, rotor speed = 4570 rpm.

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