Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals

As oil fields deplete, in particular in deep sea reservoirs, pump and compression systems work under more strenuous conditions with gas in liquid and liquid in gas mixtures, mostly inhomogeneous. Off-design operation affects system overall efficiency and reliability, including penalties in leakage and rotordynamic performance of secondary flow components, namely seals. The paper details a bulk-flow model for annular damper seals operating with gas in liquid mixtures. The analysis encompasses all-liquid and all-gas seals, as well as seals lubricated with homogenous (bubbly) mixtures, and predicts the static and dynamic force response of mixture lubricated seals; namely: leakage, power loss, reaction forces, and rotordynamic force coefficients, etc., as a function of the mixture volume fraction (β_S), supply and discharge pressures, rotor speed, whirl frequency, etc. A seal example with a nitrogen gas mixed with light oil is analyzed. The large pressure drop (70 bar) causes a large expansion of the gas within the seal even for (very) small gas volume fractions (β_S). Predictions show leakage and power loss decrease as $β→1$⁠; albeit at low β_S (< 0.3) (re)laminarization of the flow and an apparent increase in mixture viscosity, produce a hump in power loss. Cross-coupled stiffnesses and direct damping coefficients decrease steadily with increases in the gas volume fraction; however, some anomalies are apparent when the flow turns laminar. Mixture lubricated seals show frequency-dependent force coefficients. The equivalent damping decreases above and below β_S ∼ 0.10. The direct stiffness coefficients show atypical behavior: a low β_S = 0.1 produces stiffness hardening as the excitation frequency increases. Recall that an all liquid seal has a dynamic stiffness softening as frequency increases due to the apparent fluid mass. The predictions call for an experimental program to quantify the static and dynamic forced performance of annular seals operating with (bubbly) mixtures and to validate the current predictive model results.