An apparatus for sealing a circumferential gap between a stationary component and a rotating member is disclosed. The rotating member is configured to rotate about a longitudinal axis and has a radially outer surface disposed at a first non-zero angle with respect to the longitudinal axis. The apparatus includes a stator disposed circumferentially about the longitudinal axis and a shoe configured for translation in a radial direction with respect to the stator. The shoe includes a circumferential surface and a plurality of protrusions extending radially inward from the circumferential surface toward the rotating member, each one of the plurality of protrusions having a length configured to maintain a clearance gap with respect to the rotating member.