74
2 Basic Components
The value of the tangential force coefficient C Fu with present-day, optimally functioning, turbine cascades is about 1.0–1.2. The separation value is 1.4–1.6. These
values are the same for constant density and variable density fluids and do not
depend on the outlet Mach number for compressible fluids. The tangential force
coefficient may very reliably be applied to turbine cascades. With pump, fan and
compressor cascades, application of C Fu is possible as well. The optimal value is
about 1.0–1.2 as well, but values show a much larger spreading than with turbines
(see next section).
2.2.9 The Lieblein Diffusion Factor
With strongly decelerating cascades, the lift potential is also determined by the inlet
velocity level. Therefore, the lift coefficient C L2 , but as well C L1 , is not universally
applicable. Figure 2.16 shows typical velocity distributions near the blade surface
(boundary layer edge) of a strongly accelerating turbine cascade and a strongly
decelerating compressor cascade. The figure demonstrates that the tangential force
with the turbine is strongly correlated to the outlet dynamic pressure. The correlation is much weaker with the compressor cascade, due to the strong acceleration downstream of the leading edge stagnation point, both on suction and pressure
sides. Consequently, the tangential force is also determined by the value of the inlet
dynamic pressure. Deceleration is limited with fans and pumps and the tangential force coefficient can be applied more reliably than with compressors. When
studying axial turbines, axial fans and axial pumps, the tangential force coefficient,
according to Eq. (2.29) may be applied. With compressor cascades, the concept of
the diffusion factor is mostly used to determine the lift capacity of a cascade. This
concept was introduced by Lieblein in the 1950s and there have been some variants.
A diffusion factor is the ratio of the deceleration at the suction side ( w max − w 2 ) to
a reference velocity, mostly w 1 . The diffusion factor in that sense will be discussed
in Chap. 13 (axial compressors). With axial and radial fans and pumps, the concept
of local diffusion factor may be used as well. It is the ratio of ( w max − w 2 ) to w max .
Fig. 2.16 Velocity distribution near the blade surface in a highly loaded turbine cascade ( left) and
a highly loaded compressor cascade ( right)
2 Basic Components
The value of the tangential force coefficient C Fu with present-day, optimally functioning, turbine cascades is about 1.0–1.2. The separation value is 1.4–1.6. These
values are the same for constant density and variable density fluids and do not
depend on the outlet Mach number for compressible fluids. The tangential force
coefficient may very reliably be applied to turbine cascades. With pump, fan and
compressor cascades, application of C Fu is possible as well. The optimal value is
about 1.0–1.2 as well, but values show a much larger spreading than with turbines
(see next section).
2.2.9 The Lieblein Diffusion Factor
With strongly decelerating cascades, the lift potential is also determined by the inlet
velocity level. Therefore, the lift coefficient C L2 , but as well C L1 , is not universally
applicable. Figure 2.16 shows typical velocity distributions near the blade surface
(boundary layer edge) of a strongly accelerating turbine cascade and a strongly
decelerating compressor cascade. The figure demonstrates that the tangential force
with the turbine is strongly correlated to the outlet dynamic pressure. The correlation is much weaker with the compressor cascade, due to the strong acceleration downstream of the leading edge stagnation point, both on suction and pressure
sides. Consequently, the tangential force is also determined by the value of the inlet
dynamic pressure. Deceleration is limited with fans and pumps and the tangential force coefficient can be applied more reliably than with compressors. When
studying axial turbines, axial fans and axial pumps, the tangential force coefficient,
according to Eq. (2.29) may be applied. With compressor cascades, the concept of
the diffusion factor is mostly used to determine the lift capacity of a cascade. This
concept was introduced by Lieblein in the 1950s and there have been some variants.
A diffusion factor is the ratio of the deceleration at the suction side ( w max − w 2 ) to
a reference velocity, mostly w 1 . The diffusion factor in that sense will be discussed
in Chap. 13 (axial compressors). With axial and radial fans and pumps, the concept
of local diffusion factor may be used as well. It is the ratio of ( w max − w 2 ) to w max .
Fig. 2.16 Velocity distribution near the blade surface in a highly loaded turbine cascade ( left) and
a highly loaded compressor cascade ( right)