INTERRELATIONS AMONG AERODYNAMIC COMPONENTS
The other chapters of these volumes describe how the design of engine
components may be implemented once the engine type is decided and the
pressure ratios and turbine inlet temperatures have been tentatively selected.
Further elaboration is not required here. Some observations of
mutual interactions among the components remain to be discussed, as well
as some incidental information about individual components that influences
their effectiveness.
Most of the problems in this category were anticipated in the discussions
of the previous sections. Any component that delivers a nonuniform
distribution to components downstream contributes losses and other problems
to those components. Conversely, events in a downstream component
may affect an upstream one. Because of these interactions, potentially
beneficial concepts for one component sometimes have to be deferred to
help another.
Several of the authors in this series have emphasized the close cooperation
among the many disciplines that is mandatory if a design is to be
efficiently executed. Pertinent topics have been discussed in Refs. 1 and 2,
and in the remaining chapters of this volume. One object of this section is
to identify some of the compromises involved in selecting turbine inlet
temperatures, rotor speeds, and rotor diameters. Important interactions
among the aerodynamic components are also reviewed in this section.
Temperature and Speed
Most modern engines can profitably use the highest achievable turbine
inlet temperatures. An obvious exception is a jet engine for subsonic or
low-supersonic speeds. If the bypass ratio of the fans is limited by problems
such as ground clearance, Eq. (1.20) shows that aerothermodynamics can
again constrain the desired temperature. In the other cases, temperature is
limited by material strength, thermal corrosion, and aerodynamic and
cooling losses necessary for surviving high temperatures.
Section 4.3 of Ref. 2 offers a good discussion of the design restraints
imposed by temperature and stress. The same chapter shows how stress
problems are eased by cooling; it also shows how the act of cooling
introduces new losses and how the blade shapes required for cooling invite
still further losses. Chapter 5 of the same reference provides further
material on this subject; Sec. 5.2 in particular gives a good description of
the problems of designing for high temperature.
An effect of temperature on material strength is quantified by Fig. 1.38.
The abscissa is the Larsen-Miller parameter, which correlates the combined
effects of the level and duration of stress and temperature. The ordinate
shows the stress allowed for each value of the abscissa.
Two properties are noteworthy. Temperature has an almost exponential
effect on useful life--the life is about halved for a 25°F increase in
temperature. The second feature concerns the uncertainty of the data. The
discussions cited in Ref. 2 provide evidence about the lack of uniformity in
the temperatures approaching turbines. An educated guess is necessary to
avoid either an unreliable or uncompetitive design. The indicated uncertainty
of the material data is another challenge. Some designers use the
three-sigma data and add an arbitrary value, e.g., 50°F, to the expected
temperature. Since life is so sensitive to temperature, experience with
similar tasks and with one's associates is a valuable asset for making proper
choices.
Figure 1.38 alone would strongly support a choice of low rotor speeds to
avoid high stresses. Low linear and angular blade speeds would result from
this decision. Euler's turbine equation, however, leads to the observation
that power is proportional to the cube of the linear blade speeds and that
high speeds are required for lightweight units. These conflicts are resolved
by making many design iterations to arrive at an attractive balance.
Experience with other engines is again an asset.
Another restraint on speeds is the Mach number relative to the rotors of
fan and compressor blades. This problem is discussed in Chapter 3 of Ref.
2. Fan blade stresses are also a determinant of allowable speed, particularly
when the added weight of part span shrouds (or dampers or clappers,
visible in Fig. 1.27) are used as protection from flutter or to re-enforce the
blades in the event of an impact with a large bird during flight.
Diameters
The diameters of the components are determined principally by the gas
flow rate. Inasmuch as the radial force on a blade is proportional to the
flow area, there is a natural desire to keep this area as low as possible by
maintaining the axial component of the Mach numbers at high subsonic
values.
This solution opens the door to other problems, however. When a
one-dimensional calculation indicates that the axial component of the
Mach number leaving a blade row is about 0.6, the row is probably at
limiting loading. What happens is that the effective axial component of the
Mach number is about 1--the wakes from the blades and the combined
thicknesses of the boundary layers at the tip and casing contract the
effective flow area by the 19% needed to account for the difference.
The Mach number of the flow at the compressor inlet affects the relative
position of the corrected speed lines; see, e.g., Fig. 1.12a. The gas speed is
more or less proportional to the rotating speed, but the rate of change of (WvfT/P) with the airspeed decreases to zero as the throughflow Mach
number approaches 1. (See Fig. 1.39.) The rate of change of corrected
weight flow behaves the same way. This accounts for the crowding of the
speed lines in Fig. 1.12a at their higher values. This situation can be
troublesome and must be avoided.
There are other reasons for using less than the maximum flow rates.
Efficiency suffers when the blade heights become too small and the area of
the flow boundaries offering nothing but friction becomes comparable to or
greater than those areas responsible for the transfer of useful energy.
Again, high velocities approaching combustors must be diffused at the
expense of space and, sometimes, available energy. Moreover, a large
acceleration of flow ahead of an engine nozzle throat usually aids the thrust
coefficient by improving the flow distribution; low upstream velocities are
then beneficial. These are a few of the reasons why diameters are also
selected only after an extensive inquiry of the design iterations.
The other chapters of these volumes describe how the design of engine
components may be implemented once the engine type is decided and the
pressure ratios and turbine inlet temperatures have been tentatively selected.
Further elaboration is not required here. Some observations of
mutual interactions among the components remain to be discussed, as well
as some incidental information about individual components that influences
their effectiveness.
Most of the problems in this category were anticipated in the discussions
of the previous sections. Any component that delivers a nonuniform
distribution to components downstream contributes losses and other problems
to those components. Conversely, events in a downstream component
may affect an upstream one. Because of these interactions, potentially
beneficial concepts for one component sometimes have to be deferred to
help another.
Several of the authors in this series have emphasized the close cooperation
among the many disciplines that is mandatory if a design is to be
efficiently executed. Pertinent topics have been discussed in Refs. 1 and 2,
and in the remaining chapters of this volume. One object of this section is
to identify some of the compromises involved in selecting turbine inlet
temperatures, rotor speeds, and rotor diameters. Important interactions
among the aerodynamic components are also reviewed in this section.
Temperature and Speed
Most modern engines can profitably use the highest achievable turbine
inlet temperatures. An obvious exception is a jet engine for subsonic or
low-supersonic speeds. If the bypass ratio of the fans is limited by problems
such as ground clearance, Eq. (1.20) shows that aerothermodynamics can
again constrain the desired temperature. In the other cases, temperature is
limited by material strength, thermal corrosion, and aerodynamic and
cooling losses necessary for surviving high temperatures.
Section 4.3 of Ref. 2 offers a good discussion of the design restraints
imposed by temperature and stress. The same chapter shows how stress
problems are eased by cooling; it also shows how the act of cooling
introduces new losses and how the blade shapes required for cooling invite
still further losses. Chapter 5 of the same reference provides further
material on this subject; Sec. 5.2 in particular gives a good description of
the problems of designing for high temperature.
An effect of temperature on material strength is quantified by Fig. 1.38.
The abscissa is the Larsen-Miller parameter, which correlates the combined
effects of the level and duration of stress and temperature. The ordinate
shows the stress allowed for each value of the abscissa.
Two properties are noteworthy. Temperature has an almost exponential
effect on useful life--the life is about halved for a 25°F increase in
temperature. The second feature concerns the uncertainty of the data. The
discussions cited in Ref. 2 provide evidence about the lack of uniformity in
the temperatures approaching turbines. An educated guess is necessary to
avoid either an unreliable or uncompetitive design. The indicated uncertainty
of the material data is another challenge. Some designers use the
three-sigma data and add an arbitrary value, e.g., 50°F, to the expected
temperature. Since life is so sensitive to temperature, experience with
similar tasks and with one's associates is a valuable asset for making proper
choices.
Figure 1.38 alone would strongly support a choice of low rotor speeds to
avoid high stresses. Low linear and angular blade speeds would result from
this decision. Euler's turbine equation, however, leads to the observation
that power is proportional to the cube of the linear blade speeds and that
high speeds are required for lightweight units. These conflicts are resolved
by making many design iterations to arrive at an attractive balance.
Experience with other engines is again an asset.
Another restraint on speeds is the Mach number relative to the rotors of
fan and compressor blades. This problem is discussed in Chapter 3 of Ref.
2. Fan blade stresses are also a determinant of allowable speed, particularly
when the added weight of part span shrouds (or dampers or clappers,
visible in Fig. 1.27) are used as protection from flutter or to re-enforce the
blades in the event of an impact with a large bird during flight.
Diameters
The diameters of the components are determined principally by the gas
flow rate. Inasmuch as the radial force on a blade is proportional to the
flow area, there is a natural desire to keep this area as low as possible by
maintaining the axial component of the Mach numbers at high subsonic
values.
This solution opens the door to other problems, however. When a
one-dimensional calculation indicates that the axial component of the
Mach number leaving a blade row is about 0.6, the row is probably at
limiting loading. What happens is that the effective axial component of the
Mach number is about 1--the wakes from the blades and the combined
thicknesses of the boundary layers at the tip and casing contract the
effective flow area by the 19% needed to account for the difference.
The Mach number of the flow at the compressor inlet affects the relative
position of the corrected speed lines; see, e.g., Fig. 1.12a. The gas speed is
more or less proportional to the rotating speed, but the rate of change of (WvfT/P) with the airspeed decreases to zero as the throughflow Mach
number approaches 1. (See Fig. 1.39.) The rate of change of corrected
weight flow behaves the same way. This accounts for the crowding of the
speed lines in Fig. 1.12a at their higher values. This situation can be
troublesome and must be avoided.
There are other reasons for using less than the maximum flow rates.
Efficiency suffers when the blade heights become too small and the area of
the flow boundaries offering nothing but friction becomes comparable to or
greater than those areas responsible for the transfer of useful energy.
Again, high velocities approaching combustors must be diffused at the
expense of space and, sometimes, available energy. Moreover, a large
acceleration of flow ahead of an engine nozzle throat usually aids the thrust
coefficient by improving the flow distribution; low upstream velocities are
then beneficial. These are a few of the reasons why diameters are also
selected only after an extensive inquiry of the design iterations.
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