Design of a Supercritical Test Setup

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 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 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:

·  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  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:

·  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 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:

·  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 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

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:

·  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

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

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 Table 2, 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)
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-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
PFC-C318 / Dry / 115,20 / 27,78 / 200,03 / A1 / 3200 / 0 / 10250

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 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=1.083pcrit, mA=800 kgm²s, QA=10 kWm² (left), QA=80 kWm² (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=1.083pcrit, mA=800 kgm²s, QA=10 kWm² (left), QA=100 kWm² (right).

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

·  Vertical/horizontal setup

·  Test section

o  Length: 2000 mm

o  Diameter: ½ inch = 12.7 mm (outside) à 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) à 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):