387
11.2 Thermodynamic Modelling
The isentropic efficiencies are no efficiencies in the strict thermodynamic sense.
Efficiency is, by strict definition, the ratio of the useful part of the work to the total
work with a given process. But, a compressible fluid does not allow a precise definition of the useful part, as this would require detailed knowledge of the real process
path in the h-s diagram. This path is not defined as the real process is unsteady and
moreover, the objective is to define efficiency solely using the states at the start
and the end of the process. Efficiencies defined here are quality numbers, as they
compare the work from two processes, namely that of a lossless steady process and
that of the real one. Strictly spoken, such a quality number is termed effectiveness,
but the two concepts are not distinguished in practice, so that we henceforth will use
the term isentropic efficiency.
11.2.2 Reheat Effect
The problem with the efficiency assessment of a compression or an expansion is
the heating of the fluid by the losses. This causes a shift of a state point in the h-s
diagram to the right side, for a given pressure. The divergence of the isobars thus
increases the enthalpy difference available for work by the fluid, exactly in the
same way as an enthalpy difference increase by external heating. This implies that
part of the work dissipated is recoverable. On the other hand, the work required
to continue compression or to recompress after expansion increases. This effect is
termed reheat effect.
In further analysis, we assume that the kinetic energy change for the overall process is negligible, so that we may state that d ½ v
2
= 0. The total-to-total efficiency
may then be noted by comparing static states. To a compression and an expansion
respectively apply
We then speak of isentropic efficiency, without any further specification.
In order to study the reheat effect, we first consider the series connection of two
compressions with the same isentropic efficiency, as sketched in Fig. 11.12, left.
The isentropic efficiencies are equal:
The isentropic efficiency of the entire compression is lower:
This follows from the divergence of the isobars: 3s
2
3ss
2s
h
h
h
h
−
>
−
.
and
2s
1
2
3s
1
2
s
sre
s
2
1
2
1
1
2s
h
h
h h
h h
,
.
h h
h h
h h
h
h
h
−
−
−
=
=
=
−
−
−
2s
1
3s
2
s1
s2
2
1
3
2
h
h
h
h .
h h
h h
h
h
−
−
=
=
=
−
−
3ss
1
3ss
2s
2s
1
s
3
1
3
2
2
1
h
h
h
h
h
h .
h h
h h h h
h
−
−
+
−
=
=
−
− + −
11.2 Thermodynamic Modelling
The isentropic efficiencies are no efficiencies in the strict thermodynamic sense.
Efficiency is, by strict definition, the ratio of the useful part of the work to the total
work with a given process. But, a compressible fluid does not allow a precise definition of the useful part, as this would require detailed knowledge of the real process
path in the h-s diagram. This path is not defined as the real process is unsteady and
moreover, the objective is to define efficiency solely using the states at the start
and the end of the process. Efficiencies defined here are quality numbers, as they
compare the work from two processes, namely that of a lossless steady process and
that of the real one. Strictly spoken, such a quality number is termed effectiveness,
but the two concepts are not distinguished in practice, so that we henceforth will use
the term isentropic efficiency.
11.2.2 Reheat Effect
The problem with the efficiency assessment of a compression or an expansion is
the heating of the fluid by the losses. This causes a shift of a state point in the h-s
diagram to the right side, for a given pressure. The divergence of the isobars thus
increases the enthalpy difference available for work by the fluid, exactly in the
same way as an enthalpy difference increase by external heating. This implies that
part of the work dissipated is recoverable. On the other hand, the work required
to continue compression or to recompress after expansion increases. This effect is
termed reheat effect.
In further analysis, we assume that the kinetic energy change for the overall process is negligible, so that we may state that d ½ v
2
= 0. The total-to-total efficiency
may then be noted by comparing static states. To a compression and an expansion
respectively apply
We then speak of isentropic efficiency, without any further specification.
In order to study the reheat effect, we first consider the series connection of two
compressions with the same isentropic efficiency, as sketched in Fig. 11.12, left.
The isentropic efficiencies are equal:
The isentropic efficiency of the entire compression is lower:
This follows from the divergence of the isobars: 3s
2
3ss
2s
h
h
h
h
−
>
−
.
and
2s
1
2
3s
1
2
s
sre
s
2
1
2
1
1
2s
h
h
h h
h h
,
.
h h
h h
h h
h
h
h
−
−
−
=
=
=
−
−
−
2s
1
3s
2
s1
s2
2
1
3
2
h
h
h
h .
h h
h h
h
h
−
−
=
=
=
−
−
3ss
1
3ss
2s
2s
1
s
3
1
3
2
2
1
h
h
h
h
h
h .
h h
h h h h
h
−
−
+
−
=
=
−
− + −