Comparison of Hirs' equation of Moody's equation for determining rotordynamic coefficients of annular pressure seals

摘要

The rotordynamic coefficients of an incompressible-flow annular pressure seal were determined using a bulk-flow model in conjunction with two different friction factor relationships. The first, Hirs' equation, assumes the friction factor is a function of Reynolds number only. The second, Moody's equation, approximates Moody's diagram and assumes the friction factor is a function of both Reynolds number and relative roughness. For each value of relative roughness, Hirs' constants were determined so that both equations gave the same magnitude and slope of the friction factor. For smooth seals, both relationships give the same results. For rough seals (e/2 H sub 0 = 0.05) Moody's equation predicts 44% greater direct stiffness, 35% greater cross-coupled stiffness, 19% smaller cross-coupled damping, 59% smaller cross-coupled inertia, and nominally the same direct damping and direct inertia.