In one embodiment, a method for controlling seal clearance in a turbine engine includes positioning a seal ring within a turbine engine, the seal ring having an inner annular surface and an outer annular surface, the inner annular surface and the outer annular surface both being circular but non-concentric, rotating the seal ring within the engine until the seal ring is placed in an aligned orientation at which a center of a circle that defines the inner annular surface coincides with a centerline of the engine, and securing the seal ring while in the aligned orientation.