Handbook of Turbomachinery Second Edition Revised - Ventech!

manner similar to that of a vaneless radial pump being run with reverse
throughflow. On its way to the center of the disk, the working fluid
undergoes an enthalpy increase and a static pressure decrease. The enthalpy
change distribution, and thus the pressure change distribution as a function
of radius, could be readily computed from Euler’s equation if the tangential
velocity distribution on the face of the disk were known. This velocity
distribution is a strong function of the disk velocity, the geometry of the
disk, and the nature of the enclosure in which the disk is rotating. The
limiting conditions for this velocity distribution would be a free vortex (in
the case where the rotating disk did not influence the fluid’s motion) and a
forced vortex if the fluid motion matched the disk motion. In reality, for a
smooth-surfaced turbine disk, the actual velocity distribution is found to be
somewhere between these two limiting cases. A situation similar to that just
described exists on the rotor outlet side of the turbine disk. For more specific
information as to the calculation of these velocity distributions, see Refs. 9
and 10. H. F. Rue et al. [10] undertook a fairly extensive test program with
both water and liquid hydrogen flowing radially inward as well as radially
outward over both ribbed and smooth disks. Rib height on the ribbed disks
was also varied, as were the clearance between the disks and the housing in
which they rotated. Measurements of static pressures on the disk face were
obtained at several radii and could be used to deduce velocity distributions
across the disk face. The central idea in Rue’s effort was that the fluid
angular velocity at a given radius was a fraction of the disk angular velocity.
The fluid-to-disk velocity ratio is known as K. If this ratio is known across a
given radial increment, the difference in static pressure across this increment
can be computed from
Where
DP ¼ r
g K2 o 2 RDR ð19Þ
DP ¼ change in static pressure across a given radial increment.
r ¼ fluid density.
K ¼ fluid-to-disk angular velocity ratio.
o ¼ disk angular velocity.
R ¼ disk radius.
DR ¼ change in disk radius.
If the ‘‘delta’’ terms are reduced to differentials, the pressure force on the
entire disk face can be found by integrating radially across the disk. It
should be noted here that Stepanoff 11 had previously suggested the idea of
Copyright © 2003 Marcel Dekker, Inc.