About the Negative Direct Static Stiffness of Highly Eccentric Straight Annular Seals

Experimental results indicating negative direct static stiffness of highly eccentric straight gas annular seals were very recently presented by Childs and Arthur (2013, “Static Destabilizing Behavior for Gas Annular Seals at High Eccentricity Ratios,” ASME Paper No. GT2013-94201). This instability occurred at zero rotation speed and at high eccentricities. Up to then only gas annular seals with zero rotation speed, operating in centered position and with choked exit section were known as being susceptible of developing negative direct static stiffness. The seals and the working conditions presented by Childs and Arthur (2013, “Static Destabilizing Behavior for Gas Annular Seals at High Eccentricity Ratios,” ASME Paper No. GT2013-94201) had clearly no choked exit section. The present work advances a theoretical explanation of results reported by Childs and Arthur (2013, “Static Destabilizing Behavior for Gas Annular Seals at High Eccentricity Ratios,” ASME Paper No. GT2013-94201). The analysis is based on the numerical solution of the bulk flow equations of the flow in the annular seal. Theoretical results show a negative static stiffness at high eccentricities and zero rotation speeds. Other seal geometries and working conditions were tested and showed that the decrease of the direct static stiffness at high eccentricities and zero rotation speeds is a characteristic of all straight annular seals whether the fluid is compressible or not. Nevertheless with increasing rotation speed, the static stiffness becomes again positive and may increase with increasing eccentricity. The negative static stiffness is then limited to very specific working conditions: high eccentricities and zero rotation speed.