Experimental Study of the Static and Dynamic Characteristics of a Long Smooth Seal With Two-Phase, Mainly-Air Mixtures
Authors: Zhang Min , Mclean James E. , Childs Dara W. 
Published: August 2017

A 2-phase annular seal stand (2PASS) has been developed at the Turbomachinery Laboratory of Texas A&M University to measure the leakage and rotordynamic coefficients of division wall or balance-piston annular seals in centrifugal compressors. 2PASS was modified from an existing pure-air annular seal test rig. A special mixer has been designed to inject the oil into the compressed air, aiming to make a homogenous air-rich mixture.
Test results are presented for a smooth seal with an inner diameter D of 89.306 mm, a radial clearance Cr of 0.188 mm, and a length-to-diameter ratio L/D of 0.65. The test fluid is a mixture of air and Silicone oil (PSF-5cSt). Tests are conducted with inlet LVF = 0%, 2%, 5%, and 8%, shaft speed ω = 10, 15, and 20 krpm, and pressure ratio PR = 0.43, 0.5, and 0.57. The test seal is concentric with the shaft (centered), and the inlet pressure is 62.1 bars.
Complex dynamic stiffness coefficients are measured for the seal. The real parts are generally too dependent on excitation frequency Ω to be modeled by constant stiffness and virtual mass coefficients. The direct real dynamic stiffness coefficients are denoted as KΩ; the cross-coupled real dynamic stiffness coefficients are denoted as kΩ. The imaginary parts of the dynamic stiffness coefficients are modeled by frequency-independent direct C and cross-coupled c damping coefficients.
Test results show that the leakage and rotordynamic coefficients are remarkable impacted by changes in inlet LVF. Leakage mass flow rate ṁ drops slightly as inlet LVF increases from zero to 2%, and then increases with further increasing inlet LVF to 8%. As inlet LVF increases from zero to 8%, KΩ generally decreases except it increases as inlet LVF increases from zero to 2% when PR = 0.43. kΩ increases virtually with increasing inlet LVF from zero to 2%. As inlet LVF further increases to 8%, kΩ decreases or remains unchanged. C increases as inlet LVF increases; however, its rate of increase drops significantly at inlet LVF = 2%. Effective damping Ceff combines the stabilizing impact of C and the destabilizing impact of kΩ. Ceff is negative (destabilizing) for lower Ω values and becomes more destabilizing as inlet LVF increases from zero to 2%. It then becomes less destabilizing as inlet LVF is further increased to 8%.
Measured ṁ and rotordynamic coefficients are compared with predictions from XLHseal_mix, a program developed by San Andrés [1] based on a bulk-flow model, using the Moody wall-friction model while assuming constant temperature and a homogenous mixture.
Predicted ṁ values are close to measurements when inlet LVF = 0 and 2%, and are larger than measured values when inlet LVF = 5% and 8%. As with measurements, predicted ṁ drops slightly as inlet LVF increases from zero to 2%, and then increases with increasing inlet LVF further to 8%. However, in the inlet LVF range of 2∼8%, the predicted effects of inlet LVF on ṁ are weaker than measurements.
XLHseal_mix poorly predicts KΩ in most test cases. For all test cases, predicted KΩ decreases as inlet LVF increases from zero to 8%. The increase of KΩ induced by increasing inlet LVF from zero to 2% at PR = 0.43 is not predicted. C is reasonably predicted, and predicted C values are consistently smaller than measured results by 14∼34%. Both predicted and measured C increase as inlet LVF increases. kΩ and Ceff are predicted adequately at pure-air conditions, but not at most mainly-air conditions. The significant increase of kΩ induced by changing inlet LVF from zero to 2% is predicted. As inlet LVF increases 2% to 8%, predicted kΩ continue increasing versus that measured kΩ typically decreases. As with measurements, increasing inlet LVF from zero to 2% decreases the predicted negative values of Ceff, making the test seal more destabilizing. However, as inlet LVF increases further to 8%, the predicted negative values of Ceff drops versus measured values increase. For high inlet LVF values (5% and 8%), the predicted negative values of Ceff are smaller than measurements. So, the seal is actually more stable than predicted for high inlet LVF cases.