26
1 Working Principles
Here, q irr is the dissipation inside the flow. The efficiency of the conversion of the
rotor work (work done by the rotor on the flow) into mechanical energy increase in
the fluid is called internal efficiency, defined as
The work equation for a work delivering machine is
m
irr
W
E
q
D
D
−
= −
−
or
m
irr
E
W q
D
D
−
= −
+
The internal efficiency is the ratio of the rotor work (work done by the flow on the
rotor) to the mechanical energy extracted from the flow, so that
The terminology comes from an interpretation of the heating of the fluid by the
dissipation mechanisms. In simplified turbomachine analyses, heat generated
outside the fluid path by wheel friction, friction in bearings and seals is supposed to be transferred to the surroundings. Heat generated internally by friction
is supposed to stay in the fluid. This means that the flow, not the machine, is
considered to be adiabatic (except when there is explicit heat exchange between
the flow and the surroundings, as in a cooled turbine part of a gas turbine; see
Chap. 11). From now on, this simplification will be assumed. The energy equation is then noted as
(1.32)
Because of the assumption of adiabatic flow, we consider q irr
o
as a mechanical
loss. This means a loss with removal to the surroundings of the heat produced by
the dissipation. A loss with the heat by dissipation absorbed by the fluid is called
a thermodynamic loss or an internal loss. We remark that the definitions of mechanical and internal efficiencies stay valid with another interpretation of heating
due to dissipation. The interpretation only influences the writing of the energy
equation (1.32).
1.6.2 Energy Analysis of an Axial Hydraulic Turbine
Figure 1.9 sketches mean streamlines in the flow through an axial hydraulic turbine.
Inlet: 0 → 1
Absolute frame (no work):
2
1
irr
2
1
0 d v
dp dU dq
r
=
+
+
+
.
m
i
E .
W
D
h
D
=
i
m
m
W
W
.
E
E
D
D
h
D
D
−
=
=
−
2
1 2
p
W
( e
v
U ).
D
D
r
=
+
+ +
1 Working Principles
Here, q irr is the dissipation inside the flow. The efficiency of the conversion of the
rotor work (work done by the rotor on the flow) into mechanical energy increase in
the fluid is called internal efficiency, defined as
The work equation for a work delivering machine is
m
irr
W
E
q
D
D
−
= −
−
or
m
irr
E
W q
D
D
−
= −
+
The internal efficiency is the ratio of the rotor work (work done by the flow on the
rotor) to the mechanical energy extracted from the flow, so that
The terminology comes from an interpretation of the heating of the fluid by the
dissipation mechanisms. In simplified turbomachine analyses, heat generated
outside the fluid path by wheel friction, friction in bearings and seals is supposed to be transferred to the surroundings. Heat generated internally by friction
is supposed to stay in the fluid. This means that the flow, not the machine, is
considered to be adiabatic (except when there is explicit heat exchange between
the flow and the surroundings, as in a cooled turbine part of a gas turbine; see
Chap. 11). From now on, this simplification will be assumed. The energy equation is then noted as
(1.32)
Because of the assumption of adiabatic flow, we consider q irr
o
as a mechanical
loss. This means a loss with removal to the surroundings of the heat produced by
the dissipation. A loss with the heat by dissipation absorbed by the fluid is called
a thermodynamic loss or an internal loss. We remark that the definitions of mechanical and internal efficiencies stay valid with another interpretation of heating
due to dissipation. The interpretation only influences the writing of the energy
equation (1.32).
1.6.2 Energy Analysis of an Axial Hydraulic Turbine
Figure 1.9 sketches mean streamlines in the flow through an axial hydraulic turbine.
Inlet: 0 → 1
Absolute frame (no work):
2
1
irr
2
1
0 d v
dp dU dq
r
=
+
+
+
.
m
i
E .
W
D
h
D
=
i
m
m
W
W
.
E
E
D
D
h
D
D
−
=
=
−
2
1 2
p
W
( e
v
U ).
D
D
r
=
+
+ +