Compressible flow through a fixed blade row
In the blade rows of high-performance gas turbines, fluid velocities approaching, or even exceeding, the speed of sound are common and compressibility effects may no longer be ignored. A simple analysis is outlined here for the inviscid flow of a perfect gas through a fixed row of blades which, nevertheless, can be extended to the flow through moving blade rows.
The radial equilibrium equation, Eq. (6.6a), applies to compressible flow as well as incompressible flow. With constant stagnation enthalpy and constant entropy, a free-vortex flow therefore implies uniform axial velocity downstream of a blade row, regardless of any density changes incurred in passing through the blade row. In fact, for high-speed flows there must be a density change in the blade row, which implies a streamline shift as shown in Figure 6.1. This may be illustrated by considering the free-vortex flow of a perfect gas as follows. In radial equilibrium,
For this free-vortex flow the pressure, and therefore the density also, must be larger at the casing than at the hub. The density difference from hub to tip may be appreciable in a high velocity, high swirl angle flow. If the fluid is without swirl at entry to the blades, the density will be uniform. Therefore, from continuity of mass flow there must be a redistribution of fluid in its passage across the blade row to compensate for the changes in density. Thus, for this blade row, the continuity equation is
where ρ2 is the density of the swirling flow, obtainable from Eq. (6.24).