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Static and Rotordynamic Analysis of a Plain Annular (Liquid) Seal in the Laminar Regime with a Swirl Brake for Three Clearances
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The author conducts tests using a smooth annular seal with a radius of 101.6 mm (4.00 in) with three radial clearances (0.127, 0.254 and 0.381 mm) referred as 1X, 2X and 3X respectively, producing the radial clearance to radius ratios (Cvr/R) of 0.0025,0.005 and 0.0075. The seals have axial length of 45.72 mm (1.80 in), producing the length to diameter ratio of 0.45. ISO VG 46 oil is used as the testing fluid at a temperature range of 46.0-49.0 degrees Celsius to keep fluid flow laminar. A high pre-swirl insert is used to induce high fluid swirl to the swirl brakes (SBs). Each SB comprises of 36 square cuts with an axial depth of 5.08 mm (0.2 in), radial height of 6.35 mm (0.25 in) and circumferential width of 6.35 mm (0.25 in). The author conducts static and dynamic measurements at = 2, 4, 6, 8 krpm, = 2.07, 4.14, 6.21, 8.27 bar (30, 60, 90, 120 psi), and eccentricity ratios, = 0.00, 0.27, 0.53, and 0.80. Static measurements include leakage rate, pre-swirl ratio and outlet swirl ratio, and the static load required to produce the eccentricity ratios. Dynamic measurements comprise rotor-stator relative displacements, stator acceleration, and applied dynamic load. The measurements are used to calculate stiffness, damping, virtual mass and effective damping coefficients for the seals. Most importantly, SBs are shown to be effective in minimizing inlet fluid rotation at the 3X clearance but ineffective at the 1X and 2X clearance. When SBs are used with the 3X clearance seal, the cross-coupled stiffness variables have the same sign meaning that the seal would have a WFR of zero and would not produce destabilizing forces on a pump rotor. However, at the 3X clearance, the smooth annular seal has a negative direct stiffness K that could eventually “suck” the rotor into contact with the stator wall, along with dropping the natural frequency of the pump rotor, further reducing its dynamic stability. Dynamic measurements are compared to predictions based on a model developed by Zirkelback and San Andrés . Most of the predictions agree well with the test data. Notable exceptions are the direct and cross-coupled stiffness coefficients for the 3X clearance. Predictions showed positive direct stiffness and opposite signs for the cross-coupled stiffness coefficients; whereas, the data showed negative direct stiffness and the same positive sign for the cross-coupled stiffness coefficients. Also, for the 1X clearance seal, measured direct damping was higher than predicted at w > 2krpm by about 25%. For the 1X clearance seal, measured cross-coupled damping was lower than predicted by approximately 2-5 times. At most of the test conditions, measured direct virtual mass coefficients are about 6 times greater than predicted but follow the same general trend. For the 1X and 3X clearance seals, predictions are lower than measured data while predictions match test data well for the 2X clearance seals. The model predicts the whirl frequency ratio WFR very well for the 1X and 2X clearance seals at all test conditions but fails to predict zero WFR for the 3X clearance sea
Najeeb, Ovais Ahmed Bin (2017). Static and Rotordynamic Analysis of a Plain Annular (Liquid) Seal in the Laminar Regime with a Swirl Brake for Three Clearances. Master's thesis, Texas A & M University. Available electronically from