Numerical and analytical estimation of the hydrodynamic coefficients of a radial seal under whirling vibrations

Turbulent leakage flow passes through the radial seals and spiral cases of turbine runners. A small deviation of the runner changes the radial seal flow, inducing a strong pressure gradient. Reaction fluid forces act on the runner which hence whirls. These forces are modeled by dynamic force coefficients on the shaft-line dynamics. We determine those coefficients to predict whirl vibrations. The radial and tangential forces are written as quadratic and linear polynomials of the whirl frequency. The polynomial coefficients correspond to the runner dynamic coefficients. A computational fluid dynamics (CFD) simulation computes these forces for different whirl frequencies of a disk-like structure. Harmonic analyses on a vibroacoustic finite element model (FEM) yield the same forces, which are interpolated to obtain the dynamic coefficients. These numerical models are compared with an analytical potential flow theory model for a plain annular seal geometry. CFD considers more physics than the other methods as it includes the fluid shear. Parametric studies on a clearance-and-side-chamber geometry highlight that hydrodynamic coefficients vary with runner frequency, axial mass flow rate, runner angular frequency and radial seal clearance. The resulting runner dynamic coefficients improve the shaft line analysis, as more physical phenomena are considered on a real geometry.