Page 194 - Fluid Mechanics and Thermodynamics of Turbomachinery

Three-dimensional Flows in Axial Turbomachines 175

FIG. 6.4. Variation of fluid angles and Mach numbers of a free-vortex compressor stage
with radius (adapted from Howell 1945).

A further serious disadvantage is the large amount of rotor twist from root to tip
which adds to the expense of blade manufacture.
Many types of vortex design have been proposed to overcome some of the disad-
vantages set by free-vortex design and several of these are compared by Horlock
(1958). Radial equilibrium solutions for the work and axial velocity distributions of
some of these vortex flows in an axial compressor stage are given below.

2. Forced vortex
This is sometimes called “solid-body” rotation because c varies directly with r.
At entry to the rotor assume h 01 is constant and c 1 D K 1 r.
With eqn. (6.6a)

2
d c d
x1 2
DK 1 .K 1 r /
dr 2 dr
and, after integrating,

2 2
c 2 D constant 2K r . (6.10)
x1 1
2
K 1 /r . Thus, as
After the rotor c 2 D K 2 r and h 02 h 01 D U.c 2 c 1 / D .K 2
the work distribution is non-uniform, the radial equilibrium equation in the form