Research Papers

Pump Grooved Seals: A Computational Fluid Dynamics Approach to Improve Bulk-Flow Model Predictions

[+] Author and Article Information
Tingcheng Wu

Research and Development, Siemens,
500 Paul Clark Dr,
Olean, NY 14760
e-mail: wutingcheng29@gmail.com

Luis San Andrés

Fellow ASME Mechanical Engineering Department,
Texas A&M University,
College Station, TX 77843
e-mail: lsanandres@tamu.edu

1Corresponding author.

Manuscript received June 25, 2019; final manuscript received June 25, 2019; published online July 31, 2019. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(10), 101005 (Jul 31, 2019) (10 pages) Paper No: GTP-19-1308; doi: 10.1115/1.4044283 History: Received June 25, 2019; Revised June 25, 2019

In multiple stage centrifugal pumps, balance pistons, often comprising a grooved annular seal, equilibrate the full pressure rise across the pump. Grooves in the stator break the evolution of fluid swirl and increase mechanical energy dissipation; hence, a grooved seal offers a lesser leakage and lower cross-coupled stiffness than a similar size uniform clearance seal. To date, bulk-flow modelbulk-flow models (BFMs) expediently predict leakage and rotor dynamic force coefficients of grooved seals; however, they lack accuracy for any other geometry besides rectangular. Note that scalloped and triangular (serrated) groove seals are not uncommon. In these cases, computational fluid dynamics (CFD) models seals of complex shape to produce leakage and force coefficients. Alas, CFD is not yet ready for routine engineer practice. Hence, an intermediate procedure presently takes an accurate two-dimensional (2D) CFD model of a smaller flow region, namely a single groove and adjacent land, to produce stator and rotor surface wall friction factors, expressed as functions of the Reynolds numbers, for integration into an existing BFM and ready prediction of seal leakage and force coefficients. The selected groove-land section is well within the seal length and far away from the effects of the inlet condition. The analysis takes three water lubricated seals with distinct groove shapes: rectangular, scalloped, and triangular. Each seal, with length/diameter L/D = 0.4, has 44 grooves of shallow depth dg ∼ clearance Cr and operates at a rotor speed equal to 5,588 rpm (78 m/s surface speed) and with a pressure drop of 14.9 MPa. The method validity is asserted when 2D (single groove-land) and three-dimensional (3D) (whole seal) predictions for pressure and velocity fields are compared against each other. The CFD predictions, 2D and 3D, show that the triangular groove seal has the largest leakage, 41% greater than the rectangular groove seal does, albeit producing the smallest cross-coupled stiffnesses and whirl frequency ratio (WFR). On the other hand, the triangular groove seal has the largest direct stiffness and damping coefficients. The scalloped groove seal shows similar rotordynamic force coefficients as the rectangular groove seal but leaks 13% more. For the three seal groove types, the modified BFM predicts leakage that is less than 6% away from that delivered by CFD, whereas the seal stiffnesses (both direct and cross-coupled) differ by 13%, the direct damping coefficients by 18%, and the added mass coefficients are within 30%. The procedure introduced extends the applicability of a BFM to predict the dynamic performance of grooved seals with distinctive shapes.

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Fig. 6

Predicted mass flow rate versus mesh set. Triangular, scalloped, and rectangular groove shapes. Pressure drop ΔP/N = 4 bar over single land-groove section, rotor speed Ω = 5,588 rpm (nominal).

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Fig. 5

CFD predicted velocity profiles, axial and circumferential, at both left and right cross section of a rectangular groove-land section, ΔP/N  = 0.4 MPa: (a) axial velocity and (b) circumferential velocity

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Fig. 4

Depiction of mesh for flow domain in a single groove-land section: (a) rectangular, (b) triangular, and (c) scalloped groove shapes (scaled)

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Fig. 3

Schematic views of shallow depth groove shapes for a pump annular seal (not to scale, Ll: land length, Lg: groove length, Ll/Lg = 1): (a) rectangular groove, (b) triangular groove, and (c) scalloped groove

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Fig. 2

Flowchart of the process to modify a BFM with CFD simulations

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Fig. 1

Geometry of a circumferentially grooved annular liquid seal (not to scale)

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Fig. 7

2D CFD predictions for (a) static pressure on rotor surface and (b) static pressure contours within land-groove section. Pressure drop ΔP/N  =  4 bar and rotor speed Ω = 5,588 rpm (RΩ = 78 m/s).

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Fig. 8

Schematic view of three-control-volume model utilized in a BFM [4,11]

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Fig. 9

Streamlines for flow along axial direction within a ½ land-groove- ½ land section of a (a) rectangular, (b) scalloped, and (c) triangular groove shapes

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Fig. 10

Axial and circumferential velocity profiles across film at a ½ land section and for three groove shapes. Pressure drop ΔP/N = 4 bar, rotor speed Ω = 5,588 rpm (RΩ = 78 m/s): (a) axial velocity and (b) circumferential velocity.

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Fig. 11

Wall shear stresses (on rotor and stator surfaces) in a groove-land section for three types of grooved seals: (a) rotor surface and (b) stator surface

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Fig. 12

Schematic view of cut lines to obtain a mean velocity magnitude in a groove section

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Fig. 13

Friction factors for rectangular-groove-land section predicted by CFD and from a Blasius friction factor model with modified coefficients: (a) rotor surface and (b) stator surface

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Fig. 14

Friction factors for scalloped-groove-land section predicted by CFD and from a Blasius friction factor model with modified coefficients: (a) rotor surface and (b) stator surface

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Fig. 15

Friction factors for triangular groove land section predicted by CFD and from a Blasius friction factor model with modified coefficients: (a) rotor surface and (b) stator surface

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Fig. 16

Schematic views of shallow depth groove shapes for a pump annular seal: (a) rectangular (nominal shape), (b) scalloped, and (c) triangular. The insets show shapes not to scale.



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