Design of a supercritical test setup
Introduction
Several theoretical studies concerning organic Rankine cycles show a significant improvement in net
efficiency when using a working fluid operating at supercritical pressures compared to the subcritical
cycle. This is mainly due to the higher exergy efficiency of the supercritical heat transfer process.
Since the late 1950’s, a lot of research has been done concerning the investigation of the heat
transfer phenomena of supercritical fluids, this mainly for water and CO2. As a consequence, a whole
list of heat transfer correlations exists to characterize the heat transfer process, e.g. Petukhov and
Kranoshekov, Jackson et al. ….
Supercritical fluids show certain typical characteristics when approaching the critical and pseudocritical point and some of the existing correlations can qualitatively indicate these phenomena.
The problem with the correlations is that they are formulated for a certain test setup, parameter
range, working fluid and application. This means that the existing correlations cannot be applied
directly to a supercritical organic Rankine cycle without further investigation.
The main goal of this research is to perform a fundamental investigation and understanding of the
heat transfer characteristics of a fluid working at supercritical pressures. For this a supercritical test
facility has to be built.
Supercritical organic Rankine cycle
A typical setup of a supercritical organic Rankine cycle is shown in Figure 1.
Figure 1: Setup of a supercritical Rankine cycle
The main components are:
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a feeding pump of the organic fluid;
a vapour generator;
a turbine or expander;
a condenser;
and if necessary an internal heat exchanger or regenerator.
Simulation results of a realistic supercritical organic Rankine cycle are presented below. For the
calculations the heat transfer process is discretized in 40 steps, because of the severe changes that
occur in the thermo-physical properties of the supercritical fluids.
The specifications of the supercritical organic Rankine cycle are the following:
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Heat source:
o Water
o Inlet temperature heat source = 90°C
o Mass flow rate heat source = 1 kg/s
o Pressure = 1,1 bar
Working fluid
o R125
o Inlet temperature pump = 27°C
o Mass flow rate working fluid = 0,33 kg/s
o Condensing temperature = 30°C
Cooling fluid
o Water
o Inlet temperature heat source = 15°C
o Pressure = 1,1 bar
Isentropic pump efficiency = 75%
Isentropic expander efficiency = 80%
Pinch point condenser and vapour generator = 10°C
The representation of a cycle in a T,s-diagram is shown in Figure 2.
Figure 2: T,s-diagram for a supercritical organic Rankine cycle
The maximum net efficiency of 6,435% is obtained for a supercritical pressure of 1,116 x pcritical (40,37
bar)
The corresponding variables are:
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Expander output = 3,508 kW
Vapour Expansion Ratio = 2,616
Mass flow rate cooling fluid = 1,719 kg/s
Outlet temperature heat source = 80,39°C
Outlet temperature working fluid = 80°C
Outlet temperature cooling fluid = 20,25°C
Inlet temperature supercritical heat exchanger = 29,84°C
Heat input = 40,335 kW
Pump power = 0,912 kW
The maximum expander output of 3,520 kW is obtained for a supercritical pressure of 1,083 x pcritical
(39,17 bar)
The corresponding variables are:
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Net efficiency = 6,414%
Vapour Expansion Ratio = 2,235
Mass flow rate cooling fluid = 1,719 kg/s
Outlet temperature heat source = 80,15°C
Outlet temperature working fluid = 80°C
Outlet temperature cooling fluid = 20,38°C
Inlet temperature supercritical heat exchanger = 29,71°C
Heat input = 41,343 kW
Pump power = 0,868 kW
Figure 3 shows the net efficiency and expander power output as a function of the critical pressure.
Figure 3: Optimization of net efficiency and expander output versus supercritical pressure.
Design of a supercritical heat exchanger
A supercritical heat exchanger, which covers the non-isothermal heating process of Figure 2, can be
designed for the test case supercritical organic Rankine cycle.
For this test case a tube-in-tube heat exchanger is designed according to the input parameters of the
supercritical organic Rankine cycle as calculated above.
Figure 4: Left: Proposed tube-in-tube heat exchanger; right: heating process in the supercritical heat exchanger.
The heat transfer calculations are done using the PETUKHOV-KRANOSCHEKOV correlation for
supercritical heat transfer and the GNIELINSKI correlation for the heat transfer of the heating fluid.
The design of the heat exchanger is done taking into account that the speed and pressure drop in the
tube and annulus are within the allowable ranges. The speed ranges were fixed at minimum 0,7 m/s
and maximum 2,8 m/s, the pressure drop is kept below 40 kPa.
To comply with these restrictions, the following setup is chosen for the tube-in-tube heat exchanger:
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Outside diameter of tubes (standard size) = ½ inch
Tube thickness (standard size) = 0,049 inch (= 1,24 mm) (maximum pressure = 250 bar)
Outside diameter of annulus (standard size) = 2 inch
Number of tubes = 5
The simulations gave the following results:
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Needed heat exchange surface (calculated on the outside of the tubes) = 1,757 m²
Needed heat exchange length of 1 tube = 8,807 m
Pressure drop
o Heat source = 32,807 kPa
o Working fluid = 32,489 kPa
Speed
o Heat source = 1,006 m/s (min 1,002 m/s and max 1,009 m/s)
o Working fluid = 1,278 m/s (min 0,677 m/s and max 2,741 m/s)
The heat input per heat exchange area
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o Minimum = 10,82 kW/m²
o Maximum = 48,9 kW/m²
o Mean = 23,67 kW/m²
Heat transfer coefficients
o Heat source = 4547 W/m²K
o Working fluid = 2482 W/m²K
Heat input = 41,579 kW
Outlet temperature heat source = 80,1°C
Outlet temperature working fluid = 80°C
Figure 5: Temperature distribution in the heat exchanger.
Figure 6: Heat transfer coefficients in the heat exchanger.
Figure 7: Specific heat and Prandtl number of the supercritical working fluid.
Figure 8: Dynamic viscosity of the supercritical working fluid.
Figure 9: Density and thermal conductivity of the supercritical working fluid.
Figure 10: Velocities in the heat exchanger.
Figure 11: Pressure drops in the heat exchanger.
Test facility
The test facility will be built similar to the proposed supercritical organic Rankine cycle, so that it
covers a large part of the parameter range of a real possible heating cycle.
The test facility will use the same major components with some adaptations. A scheme of a possible
test facility is given in Figure 12.
Figure 12: Test facility for supercritical heat transfer.
The major changes compared to a supercritical organic Rankine cycle are:
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the use of a pre-heater to set the temperature (enthalpy) at the inlet of the test section;
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the vapour generator (heat exchanger) is changed by a simple tube to perform local
measurements;
as the heat source a DC or AC power supply is used, so that it is possible to measure the wall
temperature over the entire test section;
the expander is removed and the heated working fluid is cooled directly by the after-cooler;
the pump is then only used to compensate for the losses in the system.
Description of the test facility
The supercritical test facility is designed for performing thermo-hydraulic measurements of
refrigerants in the supercritical region, which can be used in supercritical organic Rankine cycles.
Table 1 shows a reduced overview of the working fluids that can be used in transcritical Rankine
cycles, according to the temperature range of the waste heat stream. Working fluids which will be
phased out, working fluids with a low molecular weight, a very low critical temperature and a high
flammability have been deleted.
In this section, a detailed description of the experimental equipment will be given.
Name
Physical data
Tcrit
Type
(°C)
pcrit
(bar)
Molecular
weight (g/mol)
Safety data
Environmental data
ASHRAE
34 ATL
GWP
safety group
(yr)
ODP (100 yr)
R-747 (CO2)
Wet
31,10
73,80
44,01
A1
>50
0
1
HFC-125
Wet
66,02
36,20
120,02
A1
29
0
3500
HFC-410A
-
70,20
47,90
72,58
A1
16,95
0
2088
PFC-218
Isentropic 71,89
26,80
188,02
A1
2600
0
8830
HFC-143a
Wet
72,73
37,64
84,04
A2
52
0
4470
HFC-32
Wet
78,11
57,83
52,02
A2
4,9
0
550
HFC-407C
-
86,79
45,97
86,20
A1
15657
0
1800
HFC-134a
Isentropic 101,03
40,56
102,03
A1
14
0
1430
HFC-227ea
Dry
101,74
29,29
170,03
A1
34,2
0
3220
PFC-3-1-10
Dry
113,18
23,20
238,03
-
2600
0
8600
HFC-152a
Wet
113,50
44,95
66,05
A2
1,4
0
124
PFC-C318
Dry
115,20
27,78
200,03
A1
3200
0
10250
HFC-236ea
Dry
139,22
34,12
152,04
-
10,7
0
1370
PFC-4-1-12
Dry
147,41
20,50
288,03
-
4100
0
9160
B1
7,6
0
900
HFC-245fa
Isentropic 154,05 36,40
134,05
Table 1: Overview of potential working fluids for transcritical ORCs
The test facility will be designed for fluids operating in the range of low-temperature waste heat
applications from 90°C until 150°C. The maximum design pressure will be set at 50 bar for safety
reasons. This results in Error! Reference source not found., which represents the working fluids that
can be tested in the facility.
Name
Physical data
Tcrit
Type
(°C)
pcrit
(bar)
Molecular
weight (g/mol)
Safety data
Environmental data
ASHRAE
34 ATL
GWP
safety group
(yr)
ODP (100 yr)
HFC-125
Wet
66,02
36,20
120,02
A1
29
0
3500
PFC-218
Isentropic 71,89
26,80
188,02
A1
2600
0
8830
HFC-143a
Wet
37,64
84,04
A2
52
0
4470
HFC-134a
Isentropic 101,03
40,56
102,03
A1
14
0
1430
HFC-227ea
Dry
101,74
29,29
170,03
A1
34,2
0
3220
PFC-3-1-10
Dry
113,18
23,20
238,03
-
2600
0
8600
A1
3200
0
10250
72,73
PFC-C318
Dry
115,20 27,78
200,03
Table 2: Overview of potential working fluids for transcritical ORCs
The working fluids R125 and R134a are simulated in EES to define the input parameter range of the
test facility.
R-125, Pentafluoroethane, is a blend component used in low- and medium-temperature applications.
R-125 is non-toxic, non-flammable, and non-corrosive. R-125 is one replacement refrigerant for R502.
Physical Properties:
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Formula: C2HF5
Molecular mass: 102.02 g/mol
Boiling point (760mmHg): -48.45°C
Critical temperature:66.05°C
Critical pressure: 35.92 bar
Critical density: 0.571 g/cm3
Liquid density: 1.245 g/cm3
Heat of evaporation: 165.0 kJ/kg
Heat capacity (liquid): 1.26 kJ/kg
ODP: 0
GWP: 0.84
Figures 13 and 14 show the T,s-diagrams for R-125 and R-134a which is being heated in the
supercritical test facility. The input parameters correspond with realistic values for a supercritical
heat exchanger.
Figure 13: T,s-diagram for R-125: Tpre-heater = 50°C, 𝒑 = 𝟏. 𝟎𝟖𝟑𝒑𝒄𝒓𝒊𝒕 , 𝒎̇⁄𝑨 = 𝟖𝟎𝟎 𝒌𝒈⁄𝒎²𝒔, 𝑸̇⁄𝑨 = 𝟏𝟎 𝒌𝑾⁄𝒎² (left),
𝑸̇⁄𝑨 = 𝟖𝟎 𝒌𝑾⁄𝒎² (right).
R-134a, Tetrafluoroethane, is an inert gas used primarily as a “high-temperature” refrigerant for
domestic refrigeration and automobile air conditioners. It is a haloalkane refrigerant with
thermodynamic properties similar to R-12, but with less ozone depletion potential and is mainly a
substitute of R-12.
Physical Properties:
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Formula: CH2FCF3
Molecular mass: 102.03 g/mol
Boiling point (760mmHg): -26.1°C
Critical temperature: 101.1°C
Critical pressure: 40.7 bar
Critical density: 0.512 g/cm³
Liquid density: 1.207 g/cm³
Heat of evaporation: 215.0 kJ/kg
Heat capacity (liquid): 1.51 kJ/kg
ODP: 0
GWP: 0.29
Figure 14: T,s-diagram for R-134a: Tpre-heater = 85°C, 𝒑 = 𝟏. 𝟎𝟖𝟑𝒑𝒄𝒓𝒊𝒕 , 𝒎̇⁄𝑨 = 𝟖𝟎𝟎 𝒌𝒈⁄𝒎²𝒔, 𝑸̇⁄𝑨 = 𝟏𝟎 𝒌𝑾⁄𝒎² (left),
𝑸̇⁄𝑨 = 𝟏𝟎𝟎 𝒌𝑾⁄𝒎² (right).
The design parameters for the supercritical test setup are given below:
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Vertical/horizontal setup
Test section
o Length: 2000 mm
o Diameter: ½ inch = 12.7 mm (outside)  inside 10.21 mm
o Tube thickness (standard size) = 0,049 inch (= 1,24 mm) (maximum pressure = 250
bar)
Mass flow rate: mass flux = 500 kg/m²s (0.0409 kg/s)  1500 kg/m²s (0.123 kg/s)
Pressure: from 1.01 pcrit to 1.2 pcrit (R-125: 36.65 bar to 47.18 bar; R-134a: 41.11 bar to 48,84
bar)
Preheater 1:
o Heating the working fluid from room temperature until 45°C for R-125 and 80°C for
R-134a.
o Maximum needed power (for R-125): 5096 W
o Maximum needed power (for R-134a): 12067 W
Preheater 2 (electrical):
o Maximum needed power (for R-134a): 1143 W
Heating test section (electrical):
o Heat flux: 10 kW/m² - 100 kW/m²
 Maximum needed power: 7980 W
The major parameters controlled and measured are system pressure, the mass flow rate of the
working fluid, the temperature at the inlet of the test section, and the wall heat flux provided to the
working fluid.
The facility consists of three fluid loops (Figure 15). Centrally situated is the supercritical fluid loop, in
which the refrigerant is circulated. A hot water loop provides heat to preheater 1, after this
preheater a second electrical preheater is added for fine-tuning of the required temperature at the
test section inlet. The condenser is cooled by a cold water/glycol circuit to remove the heat.
Cold water loop
Cold water
system
Working fluid loop
Supercritical
cooler
Test section
Preheater 2
Preheater 1
Figure 15: Schematic of the fluid loops in the test facility.
Hot water loop
Hot water
system
All measurement data is gathered using National Instruments Labview 8.0 software. Online
calculations are performed for control purposes of the pumps and valves, as well as to check the
thermal stability and measurements uncertainty criteria.
Supercritical fluid loop
A pump provides subcooled refrigerant to the first preheater. This preheater consists of … tube-intube heat exchangers. The working fluid in the central tube is heated on a supercritical isobar to the
desired temperature by the hot water flowing in the annuli. The temperature at the inlet of the test
section is then controlled by an electrical preheater for fine-tuning. In the test section the fluid is
electrically heated until it comes into a supercritical state. Afterwards, the heated fluid is dumped
into a plate condenser. This condenser transfers the heat from the refrigerant to a cold water/glycol
flow and provides subcooled liquid to the pump. The pump in the system compensates only for the
pressure losses.
Figure 16: Test facility for supercritical heat transfer.
In Figure 16 a schematic of the supercritical fluid loop is shown. For experiments with a supercritical
fluid, the loop should be pressurized above the critical pressure of the fluid. For example an airdriven liquid pump can be operated with pressurized air.
The mass flow rate can be precisely controlled via a magnetic drive gear pump (e.g. Micropump
GLHH25, Lesson SCR rated DC Motor) installed in the loop. The flow rate of the working fluid is
controlled by the rotation speed (rpm) controller of the motor (e.g. Lesson Speedmaster), and
adjusted with a needle valve (e.g. Swagelok) installed in the flow bypass line of the loop. The mass
flow rate is measured using a Coriolis mass flow meter (e.g. Rheonik RHM 03 a1 model), which has a
measurement range from … to … kg/s, an accuracy of ...% (of full scale) and a repeatability of …%.
The inlet temperature is the key parameter for calculating the bulk fluid temperature and enthalpy
along the flow direction of the working fluid. The working fluid supplied by the pump is heated to the
desired inlet temperature by passing it through a circulation pre-heater (Watlow Cast X-2000 model,
6 kW), which is controlled using a PID (Proportional Integral Derivative) temperature controller
(Autonics TZ4ST model).
The second preheater and the test section are heated electrically using a DC power supply (Sorensen
SGI series DC power supply, 60 V, 500 A, 30kW) to provide a uniform heat generation rate. The
power supply can be operated in constant power mode, and the voltage and current are adjusted
automatically in relation to the electrical resistance of the test section.
In all locations in the loop, the temperature is measured with K-type ungrounded thermocouples
(0.5-mm diameter). The thermocouples should be calibrated to an accuracy of within ±0.2°C. The
pressure throughout the loop (except in the test section inlet) is measured using a dial-type gauge
pressure meter (Swagelok), and the pressure in the test section inlet is measured with an absolute
pressure transmitter (Setra Model 204 high accuracy pressure transducer), which has a range of up
to 207 bar (3000 psia) and an accuracy of 0.11% (of full scale).
The test tube is constructed from a stainless steel 316L seamless tube with inner and outer diameters
of 10.21 and 12.70mm (½” tube), respectively. The heated length of the test section is 2000mm (L/Di
= 196). The electrodes for heating the test section are attached to both sides of the test tube, which
is electrically isolated with two dielectric fittings (Swagelok). For measurement of the local wall
temperature, 4x40 K-type thermocouples are installed at intervals of 50mm along the tube. The
thermocouples should be calibrated to an accuracy of within ±0.2°C. Each thermocouple can be
clamped to the outer surface of the tube via a component fabricated from poly ether ether ketone
(PEEK) material and a bolt. The thermocouple junctions then should be pushed enough on the outer
surface of the test section by tightening a bolt screw. And, before experiments, test section is
insulated by the fiber–glass material. In the test section, the bulk fluid temperature is measured at
both the inlet and outlet, and pressure is measured in the inlet position only using an absolute
pressure transmitter (e.g. by Rosemount). The thermocouples are coupled with the Keithley and then
connected to the data acquisition system Labview.
Hot water loop
A large insulated hot water vessel of 2000 litre is used as hot water source for the preheater. A 55
kW gas boiler is used to heat up the water of the hot vessel. An expansion vessel is necessary to
compensate for thermal expansion. On top of the hot vessel, a de-aerator is installed. The
temperature of the hot vessel is monitored at the bottom, the centre and the top using K-type
thermocouples. The inflow and outflow temperature of the boiler are measured.
Cold water loop
The fluid in this loop is a water/glycol (70%/30% by volume) mixture. A cold vessel o f900 litre is used
as cold source for the refrigerant condenser and the pressure control circuit. The flow rate to the
condenser is controlled by a 3-way valve. A 37 kW chiller, outside the building, controls the cold
source temperature. The chiller is switched on and off by a thermostatic device inside the cold vessel.
Preheater
In the test facility 2 preheater are used. Preheater 1 is a tube-in-tube heat exchanger, which is fed
with water from the hot water loop. The working fluid is heated from room temperature until 45°C
for R-125 and 80°C for R-134a. The second preheater is an electrical preheater which can set the
value of the inlet temperature at the beginning of the test section to the desired value.
Data reduction
To develop the heat transfer correlation, heat transfer rates from the inner wall of the test section to
the fluid should be evaluated from the measured parameters in the steady-state heat transfer
experiment. The local heat transfer coefficient can be defined as follows:
ℎ=
𝑞′′
𝑇𝑤 − 𝑇𝑏
The heat flux at the inner surface of the tube can be determined by dividing the total applied power
by the heated area. The total applied power is the product of voltage and current imposed by the
power supply system.
𝑞 ′′ =
𝑄̇
𝜋𝐷𝑖 𝐿
In the experiments, the local fluid temperature cannot be directly measured to avoid flow
obstruction. Instead of direct measurement, the local fluid temperature can be obtained with the
assumption that the specific enthalpy of the fluid increases linearly with axial locations in case of
uniform heat flux conditions.
ℎ𝑏,𝑥 = ℎ𝑏,𝑖𝑛 + [
𝐿𝑥 𝑄̇
][ ]
𝐿𝐻 𝑚̇
The local fluid temperature can be calculated from thermophysical properties of specific enthalpy
and system pressure as follows:
𝑇𝑏,𝑥 = 𝑓(ℎ𝑏,𝑥 , 𝑃𝑖𝑛 )
Since the inner wall temperature cannot be directly measured in the experiment, the temperature at
the inner surface should be calculated from the measured value at the outer wall by using a heat
conduction model of cylindrical tube in case of a uniform heat generation as follows:
𝑇𝑤,𝑖 = 𝑇𝑤,𝑜 +
Where 𝑞̇ 𝑣 = 𝜋
𝑄̇
(𝐷 2 −𝐷𝑖 2 )𝐿𝐻
4 𝑜
𝑞̇ 𝑣 𝐷𝑜 2
𝐷𝑖 2
𝑞̇ 𝑣 𝐷𝑜 2 𝐷𝑜
[( ) − ( ) ] −
( ) 𝑙𝑛
4𝜆𝑤 2
2
2𝜆𝑤 2
𝐷𝑖
(volumetric heat generation)