A simple non-dimensional model to describe the flutter onset of two-fin straight labyrinth seals [1] is extended to stepped seals. The effect of the axial displacement of the seal is analyzed first in isolation. It is shown that this fundamental mode is always stable. In a second step, the combination of axial and torsion displacements is used to determine the damping of modes with arbitrary torsion centers. It is concluded that the classical Abbot's criterion stating that seals supported in the low-pressure side of the seal are stable provided that natural frequency of the mode is greater than the acoustic frequency breaks down under certain conditions. An analytical expression for the non-dimensional work-per-cycle is derived and new non-dimensional parameters controlling the seal stability identified. It is finally concluded the stability of stepped seals can be assimilated to that of a straight through seal if the appropriate distance of the torsion center to the seal is chosen.
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