Handbook of Turbomachinery Second Edition Revised - Ventech!

or
Dp 00
rotor ¼ Xrotor
1
2 r W 2 1 þ W 2 2
2
ð33Þ
With rotors, incidence loss can be significant, so we include that contributor
in the expression for the rotor loss coefficient:
Xrotor ¼ Xprofile þ Xsecondary þ Xtrailing edge þ Xincidence
ð34Þ
Other losses associated with the rotor are tip clearance and windage losses.
Turbine rotors operate with a small clearance between the tips of the blades
and the turbine housing. Flow leaks across this gap from the high-pressure
side of the blade to the low-pressure side, causing a reduction in the pressure
difference at the tip of the blade. This reduces the tangential force on the
blade, decreasing the torque delivered to the shaft. Tip clearance effects can
be reduced by ‘‘shrouding’’ the turbine blades with a ring, but this
introduces manufacturing and mechanical integrity challenges. The loss
associated with tip clearance can be modeled either using a pressure loss
coefficient or directly as a reduction in the turbine efficiency. The specific
models differ with turbine type and will be discussed in following sections.
Windage losses arise from the drag of the turbine disk. As the disk
spins in the housing, the no-slip condition on the rotating surface induces
rotation of the neighboring fluid, establishing a radial pressure gradient in
the cavity. This is commonly referred to as disk pumping. For low-head
turbines operating in dense fluids, the windage losses can be considerable.
Windage effects are handled by calculating the windage torque from a disk
moment coefficient defined as
Gwindage ¼ 2Cm
1
2 ro2 r 5 disk
ð35Þ
The output torque of the turbine is reduced by the windage torque. Values
of the moment coefficient Cm depend on the geometry of the disk cavity and
the speed of the disk. Nece and Daily [4–6] are reliable sources of moment
coefficient data.
Diffuser Losses
Losses in the diffuser arise from sources similar to those in other flow
passages, namely, friction and flow turning. The diffuser loss can be
expressed in terms of a loss coefficient for accounting in turbine
performance, but diffuser performance is usually expressed in terms of
Copyright © 2003 Marcel Dekker, Inc.