25
1.6 Energy Analysis of Turbomachines
equations for an average streamline through the rotor. We thus assume that the
active forces, exerted to the flow by the material parts, on average intervene as represented in Fig. 1.5. This means that the work done per time unit may be considered
as the scalar product of the average force and the average flow velocity. This does
not follow from the reasoning with the moment of momentum balance. By applying the control volume, we need not pronounce judgment upon the details of the
internal forces. We spontaneously have no objections against the use of the work
expressed by (1.24) in the work equation (1.5) and the energy equation (1.6) on the
basis of the fundamental laws of thermodynamics. It will be verified in Chap. 2 that
the representation of the work done in Fig. 1.5 is correct for an axial machine. This
verification is less feasible for a more general machine. It requires three-dimensional formulation of the conservation laws.
1.6 Energy Analysis of Turbomachines
In an energy analysis, we write work or energy balances between successive stations in a machine and we define efficiencies.
1.6.1 Mechanical Efficiency and Internal Efficiency
For a work receiving machine, the work transfer from the shaft to the fluid side
of the rotor is expressed by Eq. (1.19). The efficiency of this transfer is called the
mechanical efficiency, defined as
For a work delivering machine, the work transfer from the fluid side of the rotor to
the shaft is expressed by Eq. (1.20). The efficiency of the transfer, also called the
mechanical efficiency, is defined as
Up to now, the difference between the shaft work and the rotor work is the dissipation by wheel friction ( q irr
o ), outside the flow path. In practice, shaft work is
measured at the flange of the driving motor or the driven load. This means that
dissipation by friction in the bearings of the shaft and the seals at the passage of the
shaft through the casing are included in the definition of the mechanical efficiency.
For a work receiving machine (pump), the relation between the rotor work and
the increase of the mechanical energy in the fluid (the head) may be written as
m
shaft
W .
W
D
h
D
=
shaft
m
W
.
W
D
h
D
−
= −
m
irr
W
E
q .
D
D
=
+
1.6 Energy Analysis of Turbomachines
equations for an average streamline through the rotor. We thus assume that the
active forces, exerted to the flow by the material parts, on average intervene as represented in Fig. 1.5. This means that the work done per time unit may be considered
as the scalar product of the average force and the average flow velocity. This does
not follow from the reasoning with the moment of momentum balance. By applying the control volume, we need not pronounce judgment upon the details of the
internal forces. We spontaneously have no objections against the use of the work
expressed by (1.24) in the work equation (1.5) and the energy equation (1.6) on the
basis of the fundamental laws of thermodynamics. It will be verified in Chap. 2 that
the representation of the work done in Fig. 1.5 is correct for an axial machine. This
verification is less feasible for a more general machine. It requires three-dimensional formulation of the conservation laws.
1.6 Energy Analysis of Turbomachines
In an energy analysis, we write work or energy balances between successive stations in a machine and we define efficiencies.
1.6.1 Mechanical Efficiency and Internal Efficiency
For a work receiving machine, the work transfer from the shaft to the fluid side
of the rotor is expressed by Eq. (1.19). The efficiency of this transfer is called the
mechanical efficiency, defined as
For a work delivering machine, the work transfer from the fluid side of the rotor to
the shaft is expressed by Eq. (1.20). The efficiency of the transfer, also called the
mechanical efficiency, is defined as
Up to now, the difference between the shaft work and the rotor work is the dissipation by wheel friction ( q irr
o ), outside the flow path. In practice, shaft work is
measured at the flange of the driving motor or the driven load. This means that
dissipation by friction in the bearings of the shaft and the seals at the passage of the
shaft through the casing are included in the definition of the mechanical efficiency.
For a work receiving machine (pump), the relation between the rotor work and
the increase of the mechanical energy in the fluid (the head) may be written as
m
shaft
W .
W
D
h
D
=
shaft
m
W
.
W
D
h
D
−
= −
m
irr
W
E
q .
D
D
=
+