Investigations on static and dynamic properties of liquid annular seals by a new transient numerical method with circular whirl model

Annular seals are employed in centrifugal pumps to inhibit leakage for reducing the effect of leaking fluid on the main flow. However, the seals generate fluid excitation forces while controlling the leakage flow, which seriously compromises the stability of the pump rotor system. Therefore, it is necessary to investigate the static and dynamic properties of annular seals. In this paper, a transient numerical method based on a circular whirl model is developed to predict leakage flow rates and dynamic coefficients of annular seals. The reliability of the numerical method is verified through the experiment and the bulk-flow method. In addition, the influences of seal taper and length-to-diameter ratio on the static and dynamic properties of the seal are investigated. The results reveal that the trends of dynamic coefficients and leakage flowrate with pressure difference from the transient numerical method agree well with the experimental data. Moreover, its predictions of direct stiffness, direct damping, and leakage flow rate are more precise than those of the bulk-flow method. With an increase in seal taper, the whirl-to-frequency ratio of the divergent seal becomes negative and causes seal instability. Under the same taper conditions, the convergent seal exhibits at least 4.8% lower leakage flow rate than the divergent seal. With increasing length-to-diameter ratio, the direct stiffness coefficients of various taper seals change from positive to negative, thereby weakening the support for the rotor system. Furthermore, the seals with varying tapers exhibit decreased leakage flow rates, with the constant seal having the minimum value and the divergent seal having the maximum value.