Non-contacting annular seals are used in turbomachinery to reduce the leakage of working fluid. The leakage is caused by a pressure differential across the seal and is reduced through textures cut into the surface of the seal. Three common types of non-contacting annular seals are labyrinth seals, hole-pattern seals, and helical groove seals. Labyrinth seals have circumferentially cut grooves as their surface texture. Helical groove seals have continuously cut grooves following a helical path along the surface. Hole-pattern seals have holes patterned across the surface. Each surface texture causes different flow patterns and sealing mechanisms.
These non-contacting annular seals can have textures cut across the surface of the rotor, the surface of the stator, or both. The goal of this study is to determine the degree to which the flow of seals with textures on both surfaces can be viewed as the superposition of the flow for a seal with the rotor surface textured and a smooth stator combined with the flow for a seal with the stator surface textured and a smooth rotor. To accomplish this goal, simulations were run in ANSYS CFX for each seal type and configuration for a variety of rotor speeds and pressure ratios to compare superimposed solutions to standard 3D solutions.
The ability to superimpose solutions to a differential equation — and therefore a fluid dynamics system — is determined by the linearity of the differential equation. By comparing the superimposed solution with the standard solution, this study will quantify the degree of non-linearity in the system. The degree of divergence away from linearity will be compared against the rotor speed and pressure ratio, which are proportional to the Reynold’s number. The Navier-Stokes equation contains a non-linear inertial force term. The relative significance of the inertia forces is predicted by the Reynold’s number so a strong correlation is expected between the Reynold’s number and the agreement between the flow found by superposition and the flow found by the actual seal model.
The other application of this research is to the computational modeling of annular seals. Annular seals can be computationally demanding and time consuming to model. This is especially true for seals with texture on both surfaces where millions of finite volumes may be needed in the simulation in order to find a convergent solution. For rotor speeds with strong agreement between the actual flow and the superimposed flow, superposition can be applied to perform faster simulations of seals with texture on both surfaces.