7.2 Characteristic Numbers of Turbomachines
259
7.2.4 Design Diagrams
Flows with optimum efficiency may be determined for a given turbomachine. The
shape parameters (characteristic numbers) take a certain value with these flows.
Ω s and D s may be determined that way. The same Ω s and D s values may also correspond to the optimum flows in a machine with a slightly different shape (a strong
deviation is not possible). The optimum efficiencies for both machines are not the
same then. So, there is a shape corresponding to the maximum efficiency for each
combination of Ω s and D s . A diagram rendering the maximum possible efficiency
for given values of Ω s and D s may be drawn as sketched for single-stage compressors and pumps in Fig. 7.6 (source: [2]). For the compressors, the volume flow rate
is determined with the inlet density and the head with the isentropic enthalpy rise. In
principle, such a diagram may be composed by studying all machines on the market
and by including each time the machine with the best efficiency for given Ω s and D s
at optimum flows. But this is unfeasible in practice. Diagrams of the Fig. 7.6 kind
occurring in the literature are always calculated. The calculation method is normally
verified for only a limited number of test machines, making the diagrams only partially reliable (see also Sect. 7.4.1: effect of Reynolds number and Sect. 7.4.2: effect
of relative roughness).
One machine shape yielding maximum efficiency corresponds to a chosen specific speed. In the Fig. 7.6 diagram, a line may be drawn rendering the corresponding values of the specific diameter. This line is called the Cordier line. Note that
optimisation for a given specific diameter would generate another line. Optimisation is however always implemented for a given specific speed. As a function of
specific speed, there is always an absolute maximum efficiency attained at about
Fig. 7.5 Pump rotor shapes. a Ω s = 0.2–0.7; b Ω s = 0.7–1.5; c Ω s = 1.5–3; d Ω s = 2.5–6. (From [7];
permission by Springer)
259
7.2.4 Design Diagrams
Flows with optimum efficiency may be determined for a given turbomachine. The
shape parameters (characteristic numbers) take a certain value with these flows.
Ω s and D s may be determined that way. The same Ω s and D s values may also correspond to the optimum flows in a machine with a slightly different shape (a strong
deviation is not possible). The optimum efficiencies for both machines are not the
same then. So, there is a shape corresponding to the maximum efficiency for each
combination of Ω s and D s . A diagram rendering the maximum possible efficiency
for given values of Ω s and D s may be drawn as sketched for single-stage compressors and pumps in Fig. 7.6 (source: [2]). For the compressors, the volume flow rate
is determined with the inlet density and the head with the isentropic enthalpy rise. In
principle, such a diagram may be composed by studying all machines on the market
and by including each time the machine with the best efficiency for given Ω s and D s
at optimum flows. But this is unfeasible in practice. Diagrams of the Fig. 7.6 kind
occurring in the literature are always calculated. The calculation method is normally
verified for only a limited number of test machines, making the diagrams only partially reliable (see also Sect. 7.4.1: effect of Reynolds number and Sect. 7.4.2: effect
of relative roughness).
One machine shape yielding maximum efficiency corresponds to a chosen specific speed. In the Fig. 7.6 diagram, a line may be drawn rendering the corresponding values of the specific diameter. This line is called the Cordier line. Note that
optimisation for a given specific diameter would generate another line. Optimisation is however always implemented for a given specific speed. As a function of
specific speed, there is always an absolute maximum efficiency attained at about
Fig. 7.5 Pump rotor shapes. a Ω s = 0.2–0.7; b Ω s = 0.7–1.5; c Ω s = 1.5–3; d Ω s = 2.5–6. (From [7];
permission by Springer)