Brochure

V
1
A
1
V
0
A
0
V
2
A
2
8787
For a sudden expansion, as shown in figure 5.7, the following expression is used:
(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
A
1
= Cross-section area at inlet [m
2
]
A
2
= Cross-section area at outlet [m
2
]
The model gives a good estimate of the head loss at large expansion ratios
(A
1
/A
2
close to zero). In this case the loss coecient is ζ = 1 in equation (5.9)
which means that almost the entire dynamic head into the component is
lost in a sharp-edged diuser.
For small expansion ratios as well as for other diuser geometries with
smooth area expansions, the loss coecient ζ is found by table lookup
(MacDonalds) or by measurements.
5.3.3 Mixing loss at cross-section contraction
Head loss at cross-section contraction occurs as a consequence of eddies being
created in the flow when it comes close to the geometry edges, see figure 5.8.
It is said that the flow ’separates’. The reason for this is that the flow because
of the local pressure gradients no longer adheres in parallel to the surface but
instead will follow curved streamlines. This means that the eective cross-
section area which the flow experiences is reduced. It is said that a contraction
is made. The contraction with the area A
0
is marked on figure 5.8. The contraction
accelerates the flow and it must therefore subsequently decelerate again to
fill the cross-section. A mixing loss occurs in this process. Head loss as a
consequence of cross-section contraction occurs typically at inlet to a pipe
and at the impeller eye. The magnitude of the loss can be considerably reduced
by rounding the inlet edges and thereby suppress separation. If the inlet is
adequately rounded o, the loss is insignificant. Losses related to cross-section
contraction is typically of minor importance.
Figure 5.8: Loss at cross-section contraction.
Contraction