8.1 Cavitation
291
at the inlet of the rotor), the blade angle is β 1 ≈ − 63°. Some researchers argue, similarly as with radial fans, that optimum internal efficiency is attained by minimisation of the relative speed w 1 at the tip [7, 10]. The corresponding values then are
λ = 0 and σ = 1 and the blade angle becomes β 1 ≈ − 55° (as with the radial fan). With
a smaller magnitude of the blade angle corresponds a higher through-flow velocity.
The rotor inlet is thus narrower with optimisation for losses instead of cavitation.
Optimisation for losses is possible with uncritical cavitation, which is the case for
the second and following stages in a multistage pump.
The results achieved allow deriving what typical values of blade speed and inflow
speed may be. We assume, as an example,
30m/s
=
2
u
(attained with 2
d = 200 mm
and n = 2900 rpm). With moderately backward curved blades, v 2u may amount to
about 20 m/s. Rotor work is then 600 J/kg. With an internal efficiency of 0.8, the
head amounts to 48 m. With a diameter ratio 0.4,
12m/s
=
1
u
. To β 1 = -72° corresponds
3.9m/s
=
1
v
. This is a rather high speed, much higher than what is typically
chosen for a suction pipe, being 2–2.5 m/s. So, normally, a convergent duct part just
upstream of the pump is required (so-called suction nozzle). The through-flow velocity may be increased after the first stage in a multistage pump. For the example,
the blade angle corresponding to 5 m/s is −67°. The example demonstrates that,
mostly, a blade angle in the order of −63° or −55° cannot be chosen. A high throughflow velocity is sometimes possible, in case of direct suction as with the axial pump
in Fig. 1.3. The example also shows that deceleration between the inlet of the eye
of the rotor (velocity v 0 ) and the inlet of the blades of the rotor (velocity v 1 ) is not
a realistic option. One might deduce from (8.13) that deceleration ( ζ < 1) would be
beneficial for reduction of the NPSH r . This is not a correct conclusion, however,
as deceleration would mean a substantial increase of the entrance loss, so a higher
value of λ. This means that with a pump, the optimum value of the velocity factor
ζ, in principle, is unity (in some pumps there is a slight acceleration). So, there is a
big difference here with fans.
8.1.5 Net Positive Suction Head of the Installation
The total pressure at the suction flange results from the pressure within the suction
reservoir minus the pressure drop by the suction height and the head loss within the
suction pipe. From the work equation between the suction reservoir and the suction
flange follows
H s is the suction height, positively calculated when the centre of the rotor inlet is
above the liquid level of the suction reservoir. The pressure in the reservoir, above
the liquid surface, is represented by p r , which mostly equals atmospheric pressure.
The NPSH supplied to the pump by the installation is called the available value and
is denoted by NPSH a . Its value is
r
r
+ + =
+
+
+
2
s
s
r
s
irr ,s
p
v
p 0 0
gH q .
2
291
at the inlet of the rotor), the blade angle is β 1 ≈ − 63°. Some researchers argue, similarly as with radial fans, that optimum internal efficiency is attained by minimisation of the relative speed w 1 at the tip [7, 10]. The corresponding values then are
λ = 0 and σ = 1 and the blade angle becomes β 1 ≈ − 55° (as with the radial fan). With
a smaller magnitude of the blade angle corresponds a higher through-flow velocity.
The rotor inlet is thus narrower with optimisation for losses instead of cavitation.
Optimisation for losses is possible with uncritical cavitation, which is the case for
the second and following stages in a multistage pump.
The results achieved allow deriving what typical values of blade speed and inflow
speed may be. We assume, as an example,
30m/s
=
2
u
(attained with 2
d = 200 mm
and n = 2900 rpm). With moderately backward curved blades, v 2u may amount to
about 20 m/s. Rotor work is then 600 J/kg. With an internal efficiency of 0.8, the
head amounts to 48 m. With a diameter ratio 0.4,
12m/s
=
1
u
. To β 1 = -72° corresponds
3.9m/s
=
1
v
. This is a rather high speed, much higher than what is typically
chosen for a suction pipe, being 2–2.5 m/s. So, normally, a convergent duct part just
upstream of the pump is required (so-called suction nozzle). The through-flow velocity may be increased after the first stage in a multistage pump. For the example,
the blade angle corresponding to 5 m/s is −67°. The example demonstrates that,
mostly, a blade angle in the order of −63° or −55° cannot be chosen. A high throughflow velocity is sometimes possible, in case of direct suction as with the axial pump
in Fig. 1.3. The example also shows that deceleration between the inlet of the eye
of the rotor (velocity v 0 ) and the inlet of the blades of the rotor (velocity v 1 ) is not
a realistic option. One might deduce from (8.13) that deceleration ( ζ < 1) would be
beneficial for reduction of the NPSH r . This is not a correct conclusion, however,
as deceleration would mean a substantial increase of the entrance loss, so a higher
value of λ. This means that with a pump, the optimum value of the velocity factor
ζ, in principle, is unity (in some pumps there is a slight acceleration). So, there is a
big difference here with fans.
8.1.5 Net Positive Suction Head of the Installation
The total pressure at the suction flange results from the pressure within the suction
reservoir minus the pressure drop by the suction height and the head loss within the
suction pipe. From the work equation between the suction reservoir and the suction
flange follows
H s is the suction height, positively calculated when the centre of the rotor inlet is
above the liquid level of the suction reservoir. The pressure in the reservoir, above
the liquid surface, is represented by p r , which mostly equals atmospheric pressure.
The NPSH supplied to the pump by the installation is called the available value and
is denoted by NPSH a . Its value is
r
r
+ + =
+
+
+
2
s
s
r
s
irr ,s
p
v
p 0 0
gH q .
2