and Engineering
378
Figure 2 shows the pressure −enthalpy
p
−
h
diagram corresponding to Fig.1. It also shows an ideal superheated Rankine cycle and an actual cycle.
Process 1 →2 shown in Fig.1 and Fig.2 is the isentropic compression by the pump. The
ideal pump power is given by
P
W =
WF
m h
2
−
h
1
1 In contrast, in the actual cycle, the compression by the pump is not exactly isentropic.
Moreover, some losses also occur; hence, the pump power is given by
P
W =
WF
m h
2
−
h
1
η
P
2 Process 2
→ 3 is the heating of the working fluid at a constant pressure in the evaporator.
The heat absorbed by the working fluid is given by
E
Q
=
WF
m h
3
−
h
2
{
h
3
−
h
2
in the actual cycle} 3
Process 3 →4 is the isentropic expansion in the turbineexpander. The ideal
turbineexpander power is given by
T
W =
WF
m h
3
−
h
4
4 On the other hand, process 3
′→4′ is non-isentropic expansion from a certain state in the turbineexpander, which is generally observed in the actual cycle. Using the measured
pressures and temperatures at the inlet and outlet of the turbineexpander, the turbineexpander power is given by
T
W =
WF
m h
3
−
h
4
η
T
5 Process 4
→1 is the cooling of the working fluid at a constant pressure in the condenser. The heat released from the working fluid is given by
C
Q =
WF
m h
4
−
h
1
{
h
4
−
h
1
in the actual cycle} 6
The thermal efficiency of the ORC is calculated as follows:
Net power Total heat input
Turbine power Pump power
Heat gain in Evaporator
R T
P E
W W
Q =
− =
η
7
In the above equations, enthalpies are calculated using the pressure and temperature measured in the experiment. REFPROP ver. 7 developed by the NIST
8
is used in the calculation. The mass flow rate of the working fluid is also measured in the experiment.
3. Experiment on 250 W ORC System
3.1 Experimental Setup
A small ORC system, which has the potential to produce a turbine power of approximately 250 W, was built to elucidate the cycle characteristics. Figure 3 shows a
schematic diagram of the built ORC system. Table 1 shows the principle specifications of the system. HFC245fa was used as the working fluid because of its characteristic of being a
dry liquid, which provides relatively higher efficiency than other fluids in low temperature ranges
9
. The critical temperature of HFC245fa is 427.16 K approximately 154°C, which is considerably higher than the highest temperature expected in the present system. The hot
source was water heated by an electric heater by circulation. Similarly, the cold source was water cooled by a chiller by circulation. Plate-type heat exchangers were used as both the
and Engineering
379
evaporator and the condenser. The measuring points of temperature and pressure shown in Fig.3 correspond to the numbered points shown in Fig.1 and Fig.2. To elucidate the required
turbine efficiency in consideration of the pump power, a clamp-on power meter was used to measure the pump power. All measured data were recorded to and monitored using an
acquisition PC.
Currently, there is no suitable turbineexpander that can function efficiently under the conditions of the present system. Therefore, we installed two expansion valves instead of
the turbineexpander, in order to simulate its functions. It is possible to adjust the expansion ratio in a certain range using these expansion valves. In contrast, a conventional small
turbineexpander has a fixed expansion ratio. The simulated turbine power
T
W
is calculated from Eq.5. The ideal turbine power is calculated from Eq.4. Thus, the effect
of the expansion ratio on the thermal efficiency was experimentally elucidated.
Turbine
Evaporator Condenser
Pump Surge
Tank 1
2 3
4
Cold Source
P
to
T
ti
P
pi
T
hs
T
pi
P
C
T
co
T
cs
P
E
T
to
T
ho
P
ti
T
po
P
po
Expansion valves
Hot Source
Flow meter
m
Fig.3 Schematic diagram of built ORC system Table 1 Principle specifications of built ORC system
Working Fluid R245fa CF
3
CH
2
CHF
2
, molecular weight:134.05 Boiling temperature: 14.9°C
Heat Exchangers Evaporator and Condenser
Brazed plate heat exchanger Heat conduction area: 0.4 m
2
Hot source Water; temperature range: 60~100°C
Heater Electrical heater
adjustable by variable resistor Maximum output: 3.5 kW
Cold source Water; temperature range: 10~20°C
TurbineExpander Simulated by expansion valve control
Working fluid pump Diaphragm pump, maximum pressure: 0.9 MPa
Maximum volume flow rate: 0.52 Lmin
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380
b T
hs
level 70 °C,
η
R
= 12.3 Cold Source:
= 0.11 kgs T
cs
= 10.9 °C
T
co
= 14.0 °C
C
= 1.59 kW η
C
= 85 Hot Source:
= 0.16 kgs T
hs
= 70.4 °C
T
ho
= 66.4 °C
E
= 1.73 kW η
Ε
= 73
Q Q
cw
m
hw
m
P
= 48.8 W
WF
= 0.0077 kgs T
pi
= 14.8 °C
T
po
= 15.3 °C
P
pi
= 0.16 MPa P
po
= 0.57 MPa η
P
= 14.1
W
m
T
= 226 W T
ti
= 67.0 °C
T
to
= 26.7 °C
P
ti
= 0.57 MPa P
to
= 0.16 MPa
W
a T
hs
level 60 °C,
η
R
= 10.1
P
= 48.1 W
WF
= 0.0083 kgs T
pi
= 14.8 °C
T
po
= 15.2 °C
P
pi
= 0.16 MPa P
po
= 0.45 MPa η
P
= 14.4
W
m Hot Source:
= 0.16 kgs T
hs
= 60.5 °C
T
ho
= 57.4 °C
E
= 1.93 kW η
Ε
= 92
Q
hw
m Cold Source:
= 0.11 kgs T
cs
= 10.8 °C
T
co
= 12.8 °C
C
= 1.73 kW η
C
= 82
Q
cw
m
γ
ext
= 8 γ
ext
= 27
T
= 196 W T
ti
= 58.4 °C
T
to
= 26.5 °C
P
ti
= 0.45 MPa P
to
= 0.16 MPa
W
c T
hs
level 80 °C,
η
R
= 14.7 Cold Source:
= 0.11 kgs T
cs
= 10.9 °C
T
co
= 15.1 °C
C
= 1.48 kW η
C
= 85 Hot Source:
= 0.16 kgs T
hs
= 82.2 °C
T
ho
= 77.6 °C
E
= 1.74 kW η
Ε
= 62
Q Q
cw
m
hw
m
γ
ext
= 38
d T
hs
level 90 °C,
η
R
= 4.9
P
= 50.1 W
WF
= 0.0071 kgs T
pi
= 14.6 °C
T
po
= 15.4 °C
P
pi
= 0.16 MPa P
po
= 0.75 MPa η
P
= 16.2
T
= 262 W T
ti
= 77.7 °C
T
to
= 27.7 °C
P
ti
= 0.76 MPa P
to
= 0.16 MPa
W W
m Cold Source:
= 0.11 kgs T
cs
= 11.1 °C
T
co
= 15.4 °C
C
= 1.41 kW η
C
= 86 Hot Source:
= 0.16 kgs T
hs
= 90.6 °C
T
ho
= 83.8 °C
E
= 1.49 kW η
Ε
= 47
Q Q
cw
m
hw
m
P
= 49.6 W
WF
= 0.0066 kgs T
pi
= 14.9 °C
T
po
= 15.4 °C
P
pi
= 0.16 MPa P
po
= 0.83 MPa η
P
= 11.2
W
m
T
= 81.1 W T
ti
= 83.4 °C
T
to
= 57.3 °C
P
ti
= 0.84 MPa P
to
= 0.17 MPa
W
γ
ext
= 53
Fig.4 Steady-state energy balance of built ORC system
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381
3.2 Energy Balance in Steady State
