481
13.3 Radial Flow Variation
that downstream of a rotor blade passage, four vortex structures are typically visible
(Fig. 13.14, right): a hub passage vortex together with a counter-rotating vortex in
the corner between the suction side of the blade and the hub (leg of the horseshoe
vortex); a casing passage vortex together with a counter-rotating vortex in the corner between the pressure side of the blade and the casing (the leakage vortex). The
other vortices are typically much weaker.
13.2.6 Loss Assessment
The secondary flow generates a loss that may be expressed by an additional drag coefficient. According to Howell’s measurements on slender rotor blades (high aspect
ratio), approximately applies
With a low aspect ratio, secondary flows are higher. Vavra finds ( c is chord, h is
height):
Both formulae give the same result for c/h = 0.45, which means that Vavra’s formula
must be applied with aspect ratio h/c lower than 2.22. The end boundary layers
themselves generate a loss as well. The associated drag coefficient is approximately
0.02 s/h, with s the blade spacing. The typical magnitude of the loss coefficients
( c/s ≈ 1.33, h/c ≈ 2) is
This means that the primary loss mostly is not dominant within the total loss.
13.3 Radial Flow Variation
13.3.1 S 1 -S 2 Decomposition
Analytical study of the real three-dimensional flow in a turbomachine is impossible and only numerical solution of the flow equations is achievable. An often
used simplification is a quasi-three-dimensional representation of the flow. It is
assumed then that flow within blade passages occurs on circumferential streamsurfaces (surfaces of revolution). The flow is represented two-dimensionally on such
surfaces, denominated S 1 -surfaces or blade-to-blade surfaces. The shape of these
S 1 -surfaces follows from the streamlines within a meridional section, where the
C
C
D
L
,sec
.
.
= 0 018
2
C
C
c
h
D
L
,sec
.
.
= 0 04
2
C
C
C
D prim
D end
D
,
,
,sec
. ,
. ,
. .
= =
=
0 02
001
0 02
13.3 Radial Flow Variation
that downstream of a rotor blade passage, four vortex structures are typically visible
(Fig. 13.14, right): a hub passage vortex together with a counter-rotating vortex in
the corner between the suction side of the blade and the hub (leg of the horseshoe
vortex); a casing passage vortex together with a counter-rotating vortex in the corner between the pressure side of the blade and the casing (the leakage vortex). The
other vortices are typically much weaker.
13.2.6 Loss Assessment
The secondary flow generates a loss that may be expressed by an additional drag coefficient. According to Howell’s measurements on slender rotor blades (high aspect
ratio), approximately applies
With a low aspect ratio, secondary flows are higher. Vavra finds ( c is chord, h is
height):
Both formulae give the same result for c/h = 0.45, which means that Vavra’s formula
must be applied with aspect ratio h/c lower than 2.22. The end boundary layers
themselves generate a loss as well. The associated drag coefficient is approximately
0.02 s/h, with s the blade spacing. The typical magnitude of the loss coefficients
( c/s ≈ 1.33, h/c ≈ 2) is
This means that the primary loss mostly is not dominant within the total loss.
13.3 Radial Flow Variation
13.3.1 S 1 -S 2 Decomposition
Analytical study of the real three-dimensional flow in a turbomachine is impossible and only numerical solution of the flow equations is achievable. An often
used simplification is a quasi-three-dimensional representation of the flow. It is
assumed then that flow within blade passages occurs on circumferential streamsurfaces (surfaces of revolution). The flow is represented two-dimensionally on such
surfaces, denominated S 1 -surfaces or blade-to-blade surfaces. The shape of these
S 1 -surfaces follows from the streamlines within a meridional section, where the
C
C
D
L
,sec
.
.
= 0 018
2
C
C
c
h
D
L
,sec
.
.
= 0 04
2
C
C
C
D prim
D end
D
,
,
,sec
. ,
. ,
. .
= =
=
0 02
001
0 02