Brochure

W
1,kanal
W
1
β
1
β´
1
9090
5. Pump losses
5.3.5 Incidence loss
Incidence loss occurs when there is a dierence between the flow angle and
blade angle at the impeller or guide vane leading edges. This is typically the
case at part load or when prerotation exists.
A recirculation zone occurs on one side of the blade when there is dierence
between the flow angle and the blade angle, see figure 5.11. The recirculation
zone causes a flow contraction after the blade leading edge. The flow must
once again decelerate after the contraction to fill the entire blade channel
and mixing loss occurs.
At o-design flow, incidence losses also occur at the volute tongue. The de-
signer must therefore make sure that flow angles and blade angles match
each other so the incidence loss is minimised. Rounding blade edges and vo-
lute casing tongue can reduce the incidence loss.
Model
The magnitude of the incidence loss depends on the dierence between rela-
tive velocities before and after the blade leading edge and is calculated using
the following model (Pfleiderer og Petermann, 1990, p 224):
(5.1)
(5.2)
(5.3)
(5.4)
(5.5)
(5.6)
(5.7)
(5.8)
(5.9)
(5.10)
(5.11)
(5.12)
(5.13)
(5.14)
(5.15)
constantPPP
loss, shaft sealloss, bearingloss, mechanical
=+=
g2
V
HH
2
dyn, inloss, friktion
⋅ ζ = ⋅ ζ =
g2D
LV
fH
h
2
loss, pipe
=
O
A4
D
h
=
ν
=
h
VD
Re
Re
64
f
laminar
=
0.0047
32mm
0.15mm
k/D Relative roughness:
110500
sm101
0.032m3.45m s
VD
Re
Reynolds number:
sm3.45
m0.032
4
sm(10/3600)
A
Q
VMean velocity:
h
26
h
22
3
==
=
⋅
⋅
=
ν
=
=
π
==
−
sm
sm
gD
LV
f
H
h
loss, pipe
1.2 m
9.8120.032m
)3.45(2m
0.031
2
Pipe loss:
2
2
2
=
⋅⋅
⋅
==
g2
V
HH
2
1
dyn,1loss, expansion
⋅ ζ = ⋅ ζ =
2
2
1
A
A
1






− = ζ
g2
V
A
A
1H
2
0
2
2
0
loss, contraction
⋅






− =
g2
V
HH
2
2
dyn,2
loss, contraction
⋅ζ=⋅ζ=
g2
ww
g2
w
H
2
1, kanal1
2
s
loss, incidence
⋅
−
ϕ=
⋅
ϕ=
2
2
design1 loss, incidence
k)QQ(kH +−⋅=
m
22
6
4
22
3
2
loss, disk
DU
102
103.7k
)e5D(DUkρ
P








⋅ ν
⋅ =
+ =
−
( ) ( )
( )
( )
B
5
2
3
A
5
2
3
B
loss, disk
A
loss, disk
Dn
Dn
PP =
(5.16)
(5.17)
(5.18)
(5.19)
leakageimpeller
QQQ +=
( )
g8
DD
HH
2
gap
2
2
2
stat, impellerstat, gap
−
ω − =
g2
V
1.0
g2
V
s
L
f
g2
V
0.5H
222
stat, gap
++=
gap
leakage
stat, gap
VA
Q
1.5
s
L
f
2gH
V
=
+
=
where
ϕ = Emperical value which is set to 0.5-0.7 depending on the size of the recir-
culation zone after the blade leading edge.
w
s
= dierence between relative velocities before and after the blade edge
using vector calculation, see figure 5.12.
Figure 5.12: Nomenclature for incidence loss
model.
Figure 5.11: Incidence loss at inlet to impeller
or guide vanes.