Design of a supercritical test setup

IntroductionSeveral 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 pseudo-critical 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 cycleA 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:

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:

Heat source:o Watero Inlet temperature heat source = 90°Co Mass flow rate heat source = 1 kg/so Pressure = 1,1 bar

Working fluido R125o Inlet temperature pump = 27°Co Mass flow rate working fluid = 0,33 kg/so Condensing temperature = 30°C

Cooling fluido Watero Inlet temperature heat source = 15°Co 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:

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:

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 exchangerA 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:

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:

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 kPao Working fluid = 32,489 kPa

Speedo 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

o Minimum = 10,82 kW/m²o Maximum = 48,9 kW/m²o Mean = 23,67 kW/m²

Heat transfer coefficientso Heat source = 4547 W/m²Ko 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 facilityThe 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:

the use of a pre-heater to set the temperature (enthalpy) at the inlet of the test section;

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.

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.

Physical data Safety data Environmental data

Name Type Tcrit (°C)pcrit

(bar)Molecular weight (g/mol)

ASHRAE 34 safety group

ATL (yr) ODP

GWP (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

HFC-245fa Isentropic 154,05 36,40 134,05 B1 7,6 0 900

Physical data Safety data Environmental data

Name Type Tcrit (°C)pcrit

(bar)Molecular weight (g/mol)

ASHRAE 34 safety group

ATL (yr) ODP

GWP (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 72,73 37,64 84,04 A2 52 0 4470

HFC-134aIsentropic 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

PFC-C318 Dry 115,20 27,78 200,03 A1 3200 0 10250Table 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 R-502.

Physical Properties:

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=1.083 pcrit , m /A=800 kg/m ² s, Q / A=10 kW /m ² (left),

Q / A=80kW /m ² (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:

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=1.083 pcrit , m /A=800 kg/m ² s, Q / A=10 kW /m ² (left), Q / A=100 kW /m ² (right).

The design parameters for the supercritical test setup are given below:

Vertical/horizontal setup Test section

o Length: 2000 mmo Diameter: ½ inch = 12.7 mm (outside) inside 10.21 mmo 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 Wo 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.

Figure 15: Schematic of the fluid loops in the test facility.

Cold water system

Supercritical cooler

Test section

Preheater 2

Preheater 1

Hot water system

Cold water loop Working fluid loop Hot water loop

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 loopA pump provides subcooled refrigerant to the first preheater. This preheater consists of … tube-in-tube 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 air-driven 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 loopA 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 loopThe 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.

PreheaterIn 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 ' 'T w−T b

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 ' '= Qπ D iL

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 ,∈¿+[ LxLH ][ Qm ]¿

The local fluid temperature can be calculated from thermophysical properties of specific enthalpy and system pressure as follows:

T b , x=f (hb , x , P¿)

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:

T w ,i=T w , o+qv4 λw [( Do2 )

2

−(Di2 )2]− qv

2 λw (Do2 )

2

lnD o

Di

Where qv=

Qπ4 (Do2−Di2 )LH

(volumetric heat generation)