Handbook of Turbomachinery Second Edition Revised - Ventech!

interpolations from existing designs and that new designs are executed using
a ‘‘cut-and-try’’ approach. Rodgers [24] says that minimal applicable
cascade test information exists (such as that used to develop many of the
axial-flow turbine loss models) and that exact analytical treatment of the
flow within the rotor is difficult due to the strong three-dimensional
character of the flow. Glassman [1] presents a description of radial-inflow
turbine performance trends based on both analytical modeling and
experimental results and also describes design methods for the rotor and
stator blades. More recently, Rodgers [24] has published an empirically
derived performance prediction method based on meanline quantities for
radial-inflow turbines used in small gas turbines. Balje [3] presents analytical
performance predictions in the form of efficiency versus specific speed and
specific diameter maps.
For our purposes, we will use the results of Kofskey and Nusbaum
[25], who performed a systematic experimental study investigating the effect
of specific speed on radial-inflow turbine performance. Kofskey and
Nusbaum used five different stators of varying flow area to cover a wide
range of specific speeds (0.2 to 0.8). Three rotors were used in conjunction
with these stators in an attempt to attain optimum performance at both
extremes of the specific speed range. Results of their testing are presented in
Fig. 17, which shows the maximum efficiency envelopes for both total-tototal
and total-to-static efficiencies. These efficiencies were measured from
scroll inlet flange to rotor exit and include the effects of tip clearance. Axial
tip clearance was approximately 2.2% of the inlet blade height, while the
radial tip clearance was about 1.2% of the exit blade height. Efficiencies
above 0.90 were measured for both total-to-total and total-to-static
efficiencies. The turbine tested was designed for maximum efficiency and
likely represents a ‘‘maximum attainable’’ performance level. For predicting
the performance of new turbine designs, the efficiency obtained from this
data should likely be derated to account for nonoptimum factors in the new
design such as constraints on scroll size, different blade counts, etc.
Tip clearance losses in a radial-inflow turbine arise from two sources:
axial clearance at the rotor blade inlet, and radial clearance at the rotor
blade exit. Of the two, the radial clearance is by far the more important.
Futral and Holeski [26] found that for axial clearances in the range of 1–7%
of inlet blade height, an increase in clearance of 1% (say from 2% to 3% of
inlet blade height) caused a decrease in total-to-total efficiency of only
0.15%. For radial clearances in the range of 1–3% of exit blade height,
Futral and Holeski measured a 1.6% decrease in total-to-total efficiency for
a1% increase in radial clearance, roughly 10 times greater than the change
for axial clearance. In a radial-inflow turbine, the majority of flow turning in
the rotor is done in the exit portion of the blading, called the exducer.
Copyright © 2003 Marcel Dekker, Inc.