An aerodynamic seal assembly for a rotary machine includes multiple sealing device segments disposed circumferentially intermediate to a stationary housing and a rotor. Each of the segments includes a shoe plate with a forward-shoe section and an aft-shoe section having multiple labyrinth teeth therebetween facing the rotor. The sealing device segment also includes multiple flexures connected to the shoe plate and to a top interface element, wherein the multiple flexures are configured to allow the high pressure fluid to occupy a forward cavity and the low pressure fluid to occupy an aft cavity. Further, the sealing device segments include a secondary seal attached to the top interface element at one first end and positioned about the flexures and the shoe plate at one second end.