Handbook of Turbomachinery Second Edition Revised - Ventech!

momentum exchange between working fluid and rotor is not taking place,
and the blade passage is filled with fluid that may be thought of as stagnant.
As the blade passage begins to encounter the active portion of the nozzle,
the ‘‘high-’’energy working fluid entering the passage must displace the
‘‘stagnant’’ fluid before the intended momentum exchange can occur. When
the blade passage leaves the active nozzle arc, an analogous process occurs.
The ‘‘high-energy’’ fluid that is resident in the blade passage when the
passage just leaves the nozzle arc can undergo diffusion while traversing the
passage, thus lowering the net momentum exchange. The smaller an
individual arc of admission, the larger the role these losses assume as a
percentage of the total intended energy exchange. For this reason, the active
nozzle arc fraction should be made as large as possible. This could take the
form of consolidating several ‘‘small’’ arcs into a single ‘‘large’’ arc. Further
enlargement would require a decrease in rotor diameter so that the required
annular flow area would be maintained. However, a decrease in rotor
diameter lowers the stage velocity ratio, which, as described earlier, tends to
reduce stage efficiency. If efficiency is of concern, an iterative design/analysis
process would be needed to optimize the rotor diameter/nozzle arc
combination. General trends in this situation are illustrated in Fig. 12.
This figure illustrates the effects of varying nozzle arc configurations on
stage efficiency. Additionally, a single ‘‘large’’ arc is preferable (from a
thermo/fluid mechanic standpoint) to several ‘‘small’’ arcs. However, a
single arc (or any nonsymmetrical admission) imposes a net bending load on
the rotor. The ability of the rotor and bearings to react to this type of load
should be checked as part of the design process. If this load is found to be
excessive, a more nearly symmetrical nozzle arc may need to be substituted.
The second major type of partial-admission loss is what may be
termed a rotor pumping loss. As the rotor blades traverse the inactive
portion(s) of the nozzle arc, the blade flow passages are immersed in ‘‘lowenergy’’
fluid. The rotor blades (and to a lesser extent the turbine disk)
behave in this instance like a radial-flow pump, imparting a tangential
component of momentum to the fluid. This pumping action absorbs turbine
power, detracting from the rate of shaft work generation. This parasitic loss
is calculable from basic Euler considerations if the velocity distribution
across the disk and blades as a function of radius is known. Unfortunately,
the vortex flows associated with fluid adjacent to a rotating disk (the
geometry of which is variable) is an extremely complex problem and must be
modeled at a very fundamental level to be solved effectively. Consequently,
no general forms of ‘‘pumping loss’’ correlations exist to this author’s
knowledge.
Contemporary examples of partial-admission turbines in rocket engine
systems include the turbine in the Agena engine (a highly successful 16,000-
Copyright © 2003 Marcel Dekker, Inc.