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Research Papers

On the Leakage, Torque, and Dynamic Force Coefficients of Air in Oil (Wet) Annular Seal: A Computational Fluid Dynamics Analysis Anchored to Test Data

[+] Author and Article Information
Luis San Andrés

Fellow ASME
Mechanical Engineering Department,
Texas A&M University,
College Station, TX 77843

Jing Yang

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

Xueliang Lu

Mechanical Engineering Department,
Texas A&M University,
College Station, TX 77843

1Corresponding author.

2A wet gas is made up to 5% liquid volume fraction [1].

Manuscript received June 25, 2018; final manuscript received June 28, 2018; published online September 21, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(2), 021008 (Sep 21, 2018) (11 pages) Paper No: GTP-18-1347; doi: 10.1115/1.4040766 History: Received June 25, 2018; Revised June 28, 2018

Subsea pumps and compressors must withstand multiphase flows whose gas volume fraction (GVF) or liquid volume fraction (LVF) varies over a wide range. Gas or liquid content as a dispersed phase in the primary stream affects the leakage, drag torque, and dynamic forced performance of secondary flow components, namely seals, thus affecting the process efficiency and mechanical reliability of pumping/compressing systems, in particular during transient events with sudden changes in gas (or liquid) content. This paper, complementing a parallel experimental program, presents a computational fluid dynamics (CFD) analysis to predict the leakage, drag power, and dynamic force coefficients of a smooth surface, uniform clearance annular seal supplied with air in oil mixture whose inlet GVF varies discretely from 0.0 to 0.9, i.e., from a pure liquid stream to a nearly all-gas content mixture. The test seal has uniform radial clearance Cr = 0.203 mm, diameter D = 127 mm, and length L = 0.36 D. The tests were conducted with an inlet pressure/exit pressure ratio equal to 2.5 and a rotor surface speed of 23.3 m/s (3.5 krpm), similar to conditions in a pump neck wear ring seal. The CFD two-phase flow model, first to be anchored to test data, uses an Euler–Euler formulation and delivers information on the precise evolution of the GVF and the gas and liquid streams' velocity fields. Recreating the test data, the CFD seal mass leakage and drag power decrease steadily as the GVF increases. A multiple-frequency shaft whirl orbit method aids in the calculation of seal reaction force components, and from which dynamic force coefficients, frequency-dependent, follow. For operation with a pure liquid, the CFD results and test data produce a constant cross-coupled stiffness, damping, and added mass coefficients, while also verifying predictive formulas typical of a laminar flow. The injection of air in the oil stream, small or large in gas volume, immediately produces force coefficients that are frequency-dependent; in particular the direct dynamic stiffness which hardens with excitation frequency. The effect is most remarkable for small GVFs, as low as 0.2. The seal test direct damping and cross-coupled dynamic stiffness continuously drop with an increase in GVF. CFD predictions, along with results from a bulk-flow model (BFM), reproduce the test force coefficients with great fidelity. Incidentally, early engineering practice points out to air injection as a remedy to cure persistent (self-excited) vibration problems in vertical pumps, submersible and large size hydraulic. Presently, the model predictions, supported by the test data, demonstrate that even a small content of gas in the liquid stream significantly raises the seal direct stiffness, thus displacing the system critical speed away to safety. The sound speed of a gas in liquid mixture is a small fraction of those speeds for either the pure oil or the gas, hence amplifying the fluid compressibility that produces the stiffness hardening. The CFD model and a dedicated test rig, predictions and test data complementing each other, enable engineered seals for extreme applications.

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References

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Figures

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Fig. 1

Cross-sectional view (X direction) of the wet seal test rig with fluid path. Taken from Refs. [9] and [10].

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Fig. 6

Drag power Ploss/Ploss,l from CFD predictions and test data [10] versus inlet GVF. Pressure drop ΔP = 1.5 bar, rotor speed 3500 RPM.

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Fig. 3

CFD predicted (cross-film) average GVF, static pressure ratio (P/Ps), axial velocity (W) of oil and air, and circumferential velocity swirl ratio of oil and air versus seal axial distance (Z/L). Inlet GVF = 0.2 → 0.9. (L/D = 0.36, Cr = 0.203 mm). Pressure drop ΔP = 1.5 bar, rotor speed 3500 RPM: (a) GVF, (b) static pressure ratio on rotor wall, (c) axial velocity W (m/s), and (d) swirl ratio α = Uθ/(ΩR).

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Fig. 7

Direct and quadrature parts of seal dynamic complex stiffnesses (H, h) from CFD and BFM versus test data versus excitation frequency. Inlet GVF = 0.0 → 0.9. (L/D = 0.36, Cr = 0.203 mm). Pressure drop ΔP = 1.5 bar, rotor speed 3500 RPM (58.3 Hz). Test data taken from Ref. [10].

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Fig. 4

Contours of GVF along seal axial direction (Exaggerated clearance). Inlet GVF = 0.2, 0.4, 0.6, 0.8, and 0.9. (L/D = 0.36, Cr = 0.203 mm). Pressure drop ΔP = 1.5 bar, rotor speed 3500 RPM.

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Fig. 5

Contours of axial velocity along seal axial direction (Exaggerated clearance). Inlet GVF = 0.2, 0.4, 0.6, 0.8, and 0.9. (L/D = 0.36, Cr = 0.203 mm). Pressure drop ΔP = 1.5 bar, rotor speed 3500 RPM.

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Fig. 8

Direct damping coefficient (C) from CFD and BFM versus test data versus excitation frequency. Inlet GVF = 0.0 → 0.9. (L/D = 0.36, Cr = 0.203 mm). Pressure drop ΔP = 1.5 bar, rotor speed 3500 RPM (58.3 Hz). Test data taken from Ref. [10].

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Fig. 9

Effective damping coefficient (Ceff) from CFD and CFD versus test data versus excitation frequency. Inlet GVF = 0.0 → 0.9. (L/D = 0.36, Cr = 0.203 mm). Pressure drop ΔP = 1.5 bar, rotor speed 3500 RPM (58.3 Hz). Test data taken from Ref. [10].

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Fig. 10

Direct dynamic stiffness HR predicted by BFM versus excitation frequency. Inlet GVF = 0, 0.05, 0.1, 0.15, and 0.2. Pressure drop ΔP = 1.5 bar, rotor speed 3500 RPM (58.3 Hz).

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Fig. 2

View of mesh for test annular seal. Inset showcases mesh density at inlet section. (L/D = 0.36, Cr = 0.203 mm).

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Fig. 11

Sound speed (a/al) versus GVF. al = 1470 m/s (GVF = 0) and ag = 353 m/s (GVF = 1) at 34 °C. a/al = 0.24 at GVF =1.

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