504
13 Axial Compressors
A particular problem arises with connecting stages in series. If, for design rotational speed, stages are matched to each other in the sense that the operating point
of each stage has a sufficient margin against instability and against choking, it is
not guaranteed that a similar margin is kept at lower rotational speed. At a reduced
rotational speed, the pressure build-up is lower and the density in the rear stages is
below the design value. For a constant density fluid, the shape of the velocity triangles of the stages does not change when the stages maintain their flow coefficient
and their work coefficient. So, stage matching is maintained for an operating point
that obeys kinematic similitude. The reduced density rise with a compressor causes
a deviation to the kinematic similitude with increased through-flow velocity in the
rear stages and decreased through-flow velocity in the front stages. So, the tendency
is that rear stages are pushed towards choking and front stages towards stall (we discussed this phenomenon already in Sect. 11.1.4 of Chap. 11 for explaining the need
of adjustable stator vanes). In order to maintain stage matching, incidences may
be set to smaller values than those for optimum efficiency in the first stages and to
larger values in the last stages. These settings diminish the efficiency at the design
operating point somewhat. It is also obvious that a large choking margin of the last
stages is favourable. The Mach number level in the last stages is therefore lower
than in the first ones (see Fig. 13.19). The consequence is that the stall margin of
rear stages is the smallest at design rotational speed, but that the stall margin of the
front stages becomes the smallest at low rotational speed. With increased backpressure, the following effects result: surge in the rear stages at design rotational speed
or a somewhat enlarged or reduced speed, full-span rotating stall with one cell in
the middle stages at reduced speed and rotating stall with several cells at the casing
within the front stages at low rotational speed [4].
High pressure ratio compressors (say r = 20 and above) cannot maintain stage
matching at reduced speed without variable geometry, which means the possibility
for stator vane angle adjustment. The dashed lines in Fig. 13.15 may also be seen as
obtained with global mass flow rate reduction. The figure demonstrates that angle
adjustment of stator vanes at reduced flow rate allows both the readjustment of inlet
rotor velocity ( w 1 ) and of inlet stator velocity ( v 2 ) into the original direction. The
adjustment is attained by a more tangential position of the stator vanes. This means
closing of the compressor. Closing results in a comparable work, and thereby pressure ratio, but with a smaller flow rate than originally. The compressor characteristics are thus shifted towards lower flow rate this way.
With compressors operating with a largely changing load, many stages in the
front part may be provided with variable geometry. This may be done with industrial compressors or compressors of stationary gas turbines for power generation.
Aero-engines operate most of the time in cruise conditions. Actually, compressors
of these gas turbines only have a problem at start-up. Often, only one or two stages
in the front are provided with variable geometry. Installation of bleeds onto the first
stages is an alternative for variable geometry. Sufficient segmentation of the gas
turbine is another method. E.g., some Rolls Royce Trent engine types have three
shafts and no variable geometry (but the Tent800 taken as example in Chap. 12 has
variable geometry in the front stages of the IP-compressor).
13 Axial Compressors
A particular problem arises with connecting stages in series. If, for design rotational speed, stages are matched to each other in the sense that the operating point
of each stage has a sufficient margin against instability and against choking, it is
not guaranteed that a similar margin is kept at lower rotational speed. At a reduced
rotational speed, the pressure build-up is lower and the density in the rear stages is
below the design value. For a constant density fluid, the shape of the velocity triangles of the stages does not change when the stages maintain their flow coefficient
and their work coefficient. So, stage matching is maintained for an operating point
that obeys kinematic similitude. The reduced density rise with a compressor causes
a deviation to the kinematic similitude with increased through-flow velocity in the
rear stages and decreased through-flow velocity in the front stages. So, the tendency
is that rear stages are pushed towards choking and front stages towards stall (we discussed this phenomenon already in Sect. 11.1.4 of Chap. 11 for explaining the need
of adjustable stator vanes). In order to maintain stage matching, incidences may
be set to smaller values than those for optimum efficiency in the first stages and to
larger values in the last stages. These settings diminish the efficiency at the design
operating point somewhat. It is also obvious that a large choking margin of the last
stages is favourable. The Mach number level in the last stages is therefore lower
than in the first ones (see Fig. 13.19). The consequence is that the stall margin of
rear stages is the smallest at design rotational speed, but that the stall margin of the
front stages becomes the smallest at low rotational speed. With increased backpressure, the following effects result: surge in the rear stages at design rotational speed
or a somewhat enlarged or reduced speed, full-span rotating stall with one cell in
the middle stages at reduced speed and rotating stall with several cells at the casing
within the front stages at low rotational speed [4].
High pressure ratio compressors (say r = 20 and above) cannot maintain stage
matching at reduced speed without variable geometry, which means the possibility
for stator vane angle adjustment. The dashed lines in Fig. 13.15 may also be seen as
obtained with global mass flow rate reduction. The figure demonstrates that angle
adjustment of stator vanes at reduced flow rate allows both the readjustment of inlet
rotor velocity ( w 1 ) and of inlet stator velocity ( v 2 ) into the original direction. The
adjustment is attained by a more tangential position of the stator vanes. This means
closing of the compressor. Closing results in a comparable work, and thereby pressure ratio, but with a smaller flow rate than originally. The compressor characteristics are thus shifted towards lower flow rate this way.
With compressors operating with a largely changing load, many stages in the
front part may be provided with variable geometry. This may be done with industrial compressors or compressors of stationary gas turbines for power generation.
Aero-engines operate most of the time in cruise conditions. Actually, compressors
of these gas turbines only have a problem at start-up. Often, only one or two stages
in the front are provided with variable geometry. Installation of bleeds onto the first
stages is an alternative for variable geometry. Sufficient segmentation of the gas
turbine is another method. E.g., some Rolls Royce Trent engine types have three
shafts and no variable geometry (but the Tent800 taken as example in Chap. 12 has
variable geometry in the front stages of the IP-compressor).