This model upgrade is intended to embrace a variety of high-speed noncontact seals and bearings traditionally used in gas turbine applications. In this case, the heatenergy exchange between the hardware and the working medium may be far from being negligible. This very fact calls for including a separate energy equation in the set of flow-governing equations cited in Appendix E. The boundary conditions on insertion of this equation involve such variables as the local convection heat transfer coefficient and the local “wall” and flow-stream temperatures.

Given the fact that the rotor-to-housing clearance width is extremely small, the problem of friction choking (in a Fanno-process type of mechanism) is indeed part of this compressible flow problem. Unfortunately, the occurence of this choking type requires external intervention during the flow solution process. During the iterative procedure, where the momentum-equations convection terms are continually linearized, and once the nodal magnitudes of velocity vector are attained, the intervention process begins by computing the corresponding nodal magnitudes of Mach number. These are then examined to see if the Mach number is in excess of unity anywhere in the computational domain (the seal exit station in particular), which is impossible in a subsonic nozzle-like passage. Referring to the simple annular seal in Figure 16.20, the term nozzle here is applicable in the sense that the blockage effect of the boundary layer growth over the solid walls causes, in effect, a streamwise reduction in the cross-flow area, turning what is physically a constant-area passage into a subsonic nozzle in the sense of rising displacement thickness (a fraction of the boundary layer thickness that depends on the boundary-layer velocity profile).