Axial-Radial Numerical Modeling of Annular Seals by Mimetic FDM

Annular pressure seals are critical components used in turbomachinery. The annular seal is a thin annular clearance region “sealing” between a high-pressure region and a low-pressure region of a rotating machine by limiting the leakage of the working fluid. The working fluid leakage is limited by the cross-sectional area allowed to the flow, and frequently further limited by axisymmetric grooves machined into the rotor or stator within which the fluid expands, contracts, and recirculates. Modern analysis techniques of such seals tend to fall into two categories. Either the seal model is greatly simplified through assumptions and application of empirical factors, or the seal is modeled using 3-D CFD techniques in generalized fluid dynamics codes. The method of simplification is referred to as “Bulk Flow” analysis due to the use of radially averaged “bulk” values for flow variables. This model takes those radially averaged values and assumes a circumferential solution based on small orbit circular whirling motion. The 3-D momentum equations are thus reduced to a series of 1-D equations in the axial direction with shear forces modeled empirically through Blasius type friction factors. These 1-D equations can be solved rapidly at the expense of accuracy and flexibility in seal geometry types. Comparatively, 3-D CFD codes require large 3-D meshes and the solution of the full 3-D Navier-Stokes equations accompanied by turbulence model. The CFD solutions are accurate within the precision of the boundary conditions used at the expense of much greater computational cost and engineer expertise requirements.

A 2-D seal code is developed with an axial-radial grid to strike a balance between the 1-D bulk flow method and 3-D generalized CFD. This 2-D seal code distinguishes itself through rigorous application of modern numerical and code techniques. The code allows the 0th and 1st order solution of the geometrically perturbed and incompressible cylindrical Reynolds Averaged Navier-Stokes equations to model the seal’s eccentric annular region with an assumed small and circular whirl orbit. Currently a single one-equation turbulence model is included to model the transport of turbulent kinetic energy for high Reynolds number flows. The 0th order solution provides the user with leakage results, wall shear stress, and initial pressure differential estimates. The 1st order solution refines the pressure differential estimate and models the circumferential variation to obtain rotordynamic coefficients from multiple whirl speed cases.