Handbook of Turbomachinery Second Edition Revised - Ventech!

Eq. (43) for axial turbines; for radial-inflow turbines, the rotor tip speed is
used.
Reynolds Number
The Reynolds number for a turbine is usually defined as
Re ¼ rUtipdtip
m
ð44Þ
where m is the viscosity of the working fluid. Sometimes odtip is substituted
for Utip, resulting in a value twice that of Eq. (44). The Reynolds number
relates the viscous and inertial effects in the fluid flow. For most
turbomachinery operating on air, the Reynolds number is of secondary
importance. However, when turbomachinery is scaled (either larger or
smaller), the Reynolds number changes, resulting in a change in turbine
efficiency. Glassman [1] suggests the following for adjusting turbine losses to
account for Reynolds number changes:
1 Z0 a
1 Z0 ¼ A þ B
b
Reb
Rea
0:2
ð45Þ
where Z 0 indicates total-to-total efficiency and A and B sum to 1.0. That all
the loss is not scaled by the Reynolds number ratio reflects that not all losses
are viscous in origin. Also, total-to-total efficiency is used since the kinetic
energy of the exit loss is not affected by Reynolds number. Glassman [1]
suggests values of 0.3–0.4 for A (the nonviscous loss) and from 0.7 to 0.6 for
B (the viscous loss).
Equivalent or Corrected Quantities
In order to eliminate the dependence of turbine performance maps on the
values of inlet temperature and pressure, corrected quantities such as
corrected flow, corrected speed, corrected torque, and corrected power were
developed. Using corrected quantities, turbine performance can be
represented by just a few curves for a wide variety of operating conditions.
Corrected quantities are not nondimensional. Glassman [1] provides a
detailed derivation of the corrected quantities. The corrected flow is defined
as
pffiffi
w y
wcorr ¼ ð46Þ
d
Copyright © 2003 Marcel Dekker, Inc.