8.5 Internal Parallel and Series Connection Of Rotors
305
external volute wall, with a chosen section profile (Fig. 8.17), follows from constant
angular momentum as
and the flow rate through a section on the position angle f as
which results in
.
f
=
b
r
f( )
8.4.8 Return Channels
In multistage pumps, the liquid must be led from the diffuser ring outlet diameter
to the smaller diameter of the suction eye of the next stage. With radial rotors, the
liquid turns 180° in the meridional view, between the diffuser and the return channel. This usually occurs within a ring-shaped, vaned or vaneless chamber with a
constant cross section. If this space features vanes, the liquid follows continuous
channels from the diffuser (with vanes) until the suction eye of the next stage. This
is the best solution from a flow point of view, but requires more complicated castings. As the velocity within the channels has to decrease, their cross section area
should increase. Therefore, it is usually not possible to provide the return channels
with parallel side walls. Further, the area increase must run gradually in order to
prevent boundary layer separation. This often necessitates vanes with a variable
thickness. The return vanes end radially or are somewhat more curved ( ε = 5°) in
order to compensate for the flow deviation. The vane shape is determined by methods applying to rotor blades. Remark that continuous diffuser and return channels
are standard design practice with mixed-flow stages connected in series (Fig. 8.12).
8.5 Internal Parallel and Series Connection Of Rotors
8.5.1 Reason for Internal Parallel or Series Connection
At pump design, flow rate, head and rotational speed are known. Flow rate and head
are imposed by the application. The rotational speed follows from the choice of the
specific speed. At a first design stage, a specific speed is chosen for optimum efficiency. The optimum value is about unity. A deviation from this choice is mostly required to attain a rotational speed that is suitable for a driving motor. If the specific
, with
,
=
=
=
u
u
C
dQ v dA
bdr
v r C
r
b
a
r
r
bdr
Q
Q C
,
2
r
f
f
p
=
= ∫
305
external volute wall, with a chosen section profile (Fig. 8.17), follows from constant
angular momentum as
and the flow rate through a section on the position angle f as
which results in
.
f
=
b
r
f( )
8.4.8 Return Channels
In multistage pumps, the liquid must be led from the diffuser ring outlet diameter
to the smaller diameter of the suction eye of the next stage. With radial rotors, the
liquid turns 180° in the meridional view, between the diffuser and the return channel. This usually occurs within a ring-shaped, vaned or vaneless chamber with a
constant cross section. If this space features vanes, the liquid follows continuous
channels from the diffuser (with vanes) until the suction eye of the next stage. This
is the best solution from a flow point of view, but requires more complicated castings. As the velocity within the channels has to decrease, their cross section area
should increase. Therefore, it is usually not possible to provide the return channels
with parallel side walls. Further, the area increase must run gradually in order to
prevent boundary layer separation. This often necessitates vanes with a variable
thickness. The return vanes end radially or are somewhat more curved ( ε = 5°) in
order to compensate for the flow deviation. The vane shape is determined by methods applying to rotor blades. Remark that continuous diffuser and return channels
are standard design practice with mixed-flow stages connected in series (Fig. 8.12).
8.5 Internal Parallel and Series Connection Of Rotors
8.5.1 Reason for Internal Parallel or Series Connection
At pump design, flow rate, head and rotational speed are known. Flow rate and head
are imposed by the application. The rotational speed follows from the choice of the
specific speed. At a first design stage, a specific speed is chosen for optimum efficiency. The optimum value is about unity. A deviation from this choice is mostly required to attain a rotational speed that is suitable for a driving motor. If the specific
, with
,
=
=
=
u
u
C
dQ v dA
bdr
v r C
r
b
a
r
r
bdr
Q
Q C
,
2
r
f
f
p
=
= ∫