7 Dynamic Similitude
260
Ω s = 1 (diagonal form). Low specific speed machines have a lower efficiency, as
their channels are long and narrow, causing increased friction losses. High specific
speed machines have a lower efficiency, as rotor work then gets low, causing increased relative weight of losses.
Pump design starts from the specification of the flow rate and the energy rise.
The choice of a rotational speed that optimises the specific speed may be attempted.
From
3/ 4
s
m
E
/ Q
W W D
=
emerges that, with a high head and a low flow rate, the
corresponding rotational speed may be high and may become unrealisable. For a
pump driven by an electric motor, the maximum rotational speed at 50 Hz power
supply amounts to about 2900 rpm (asynchronous motor). In such a case, a suboptimal specific speed might be opted for. The opposite occurs with a low head and
a high flow rate. The optimum rotational speed might be too low to be realisable
in practice. Synchronous rotational speeds are fractions of 3000 rpm and currently
can be: 3000, 1500, 1000 and 750, asynchronous rotational speeds being about 3 %
lower. A gearbox between the motor and the machine may be opted for. The reasoning demonstrates that the choice of rotational speed is a priority. This also applies to
other turbomachines. For this reason, optimisations are always implemented for a
given specific speed. When no solution with an acceptable efficiency can be found
within a design diagram, series connection or parallel connection shall be taken into
consideration (see Sect. 7.5).
The Cordier line that can be drawn in a s
s
D
W −
diagram is universal, with a
good approximation, for all turbomachines (Cordier 1953). Figure 7.7 sketches this
universal diagram. There is a difference between driven (pumps, compressors) and
driving (turbines) machines (source: [5]). The diagram concerns machines with full
through-flow. An additional degree of freedom is generated with partial throughflow. The diagram is always to be applied when designing a turbomachine, but
Fig. 7.6 Maximum attainable efficiency for single-stage compressors and pumps at given Ω s and
D s . (Adapted from [2])
260
Ω s = 1 (diagonal form). Low specific speed machines have a lower efficiency, as
their channels are long and narrow, causing increased friction losses. High specific
speed machines have a lower efficiency, as rotor work then gets low, causing increased relative weight of losses.
Pump design starts from the specification of the flow rate and the energy rise.
The choice of a rotational speed that optimises the specific speed may be attempted.
From
3/ 4
s
m
E
/ Q
W W D
=
emerges that, with a high head and a low flow rate, the
corresponding rotational speed may be high and may become unrealisable. For a
pump driven by an electric motor, the maximum rotational speed at 50 Hz power
supply amounts to about 2900 rpm (asynchronous motor). In such a case, a suboptimal specific speed might be opted for. The opposite occurs with a low head and
a high flow rate. The optimum rotational speed might be too low to be realisable
in practice. Synchronous rotational speeds are fractions of 3000 rpm and currently
can be: 3000, 1500, 1000 and 750, asynchronous rotational speeds being about 3 %
lower. A gearbox between the motor and the machine may be opted for. The reasoning demonstrates that the choice of rotational speed is a priority. This also applies to
other turbomachines. For this reason, optimisations are always implemented for a
given specific speed. When no solution with an acceptable efficiency can be found
within a design diagram, series connection or parallel connection shall be taken into
consideration (see Sect. 7.5).
The Cordier line that can be drawn in a s
s
D
W −
diagram is universal, with a
good approximation, for all turbomachines (Cordier 1953). Figure 7.7 sketches this
universal diagram. There is a difference between driven (pumps, compressors) and
driving (turbines) machines (source: [5]). The diagram concerns machines with full
through-flow. An additional degree of freedom is generated with partial throughflow. The diagram is always to be applied when designing a turbomachine, but
Fig. 7.6 Maximum attainable efficiency for single-stage compressors and pumps at given Ω s and
D s . (Adapted from [2])