Proceedings of SCCO2 Power Cycle Symposium 2009 RPI, Troy, NY, April 29-30, 2009

THERMODYNAMIC ASPECTS OF CYCLES WITH SUPERCRITICAL FLUIDS Petr Hájek Ústav jaderného výzkumu Řež a.s. Husinec-Řež 130 25068 Husinec-Řež, Czech Republic tel.: +420 266 173 513; fax: +420 266 172 045 Email: [email protected]

Abstract - The supercritical power cycles are taking advantage of real gas behaviour in order to achieve high thermal efficiency. There are two main types of supercritical cycles, one uses water and the other carbon dioxide. The supercritical water cycle enhances thermal efficiency by rising turbine inlet temperature, while the supercritical carbon dioxide (S-CO2) takes advantage of reduction of compressor input work due to properties change close to the critical point (30.98°C, 7.38MPa). Thermodynamic analysis and comparison of different modifications of the S-CO2 cycle from the point of cycle thermal efficiency have been performed. Analyzed cycles were: simple Brayton cycle, pre-compression cycle, recompression cycle, split expansion cycle, partial cooling cycle and partial cooling cycle with improved regeneration. Different computer codes were developed for each cycle to evaluate all thermodynamic states. For optimizing the structure of the cycles, com-pressor inlet and turbine inlet temperatures were held constant (32°C and 550°C) and other pa-rameters such as compressor outlet pressure, turbine pressure ratio were varying. Also some analysis of using S-CO2 in combination with steam cycle was made. For standard PWR is this combined cycle very promising. An experimental S-CO2 loop was built in 1999 in the Czech Republic. The main objective was to obtain experimental data for comparison with previous theoretical studies. This facility was the first of its kind in the world. Its operation and performed measurements have provided many interesting data and thus brought valuable operational experience as well as new objectives for future research and development of S-CO2 cycles. 1. INTRODUCTION One of the main goals in the effort of development of new nuclear reactors is to raise the thermal efficiency. The supercritical power cycles are such candidates and are taking advantage of real gas behaviour in order to achieve higher thermal efficiency. There are two main types of supercritical cycles, one uses water and the other carbon dioxide. Great experience is available in the area of supercritical water cycles from classic fossil power energy, the power cycles with supercritical carbon dioxide are currently in the stage of development, calculations and testing. The main difference is given by the distant positions of the critical points of water and carbon dioxide. Generally speaking, the power cycle with CO2 shows very promising: the calculation with estimative values of components’ efficiency gives high thermal efficiency, low capital costs, short period of construction, non-significant losses caused by corrosion as well as particularly small dimensions of turbomachinery. The direct use of carbon dioxide cycles in nuclear energy is questionable as there is not sufficient world wide experience with this coolant. As a first approach, it seems that the optimal use of carbon dioxide cycles would be in combination with water. Particularly for the case of HPLWR, this solution shows the following advantages: - very high thermal efficiency of combined cycles; - lower capital costs – lower pressure steam part is replaced by CO2; - optimal thermal input for CO2 – condensation part of the steam cycle; - fewer problems with erosion and corrosion – the low-pressure steam part is omitted. Several research institutes in the Czech Republic (e.g. Czech Technical University in Prague, SVUSS Prague, QAI) have analyzed the possibility of using CO2 as energy conversion medium, where all have started with cycles calculation as input to this issue. A number of possibilities of cycle arrangements were analyzed; in all cases, the results depended on predefined efficiency of machineries and heat exchangers. On the other hand, only few organizations have engaged in the preparation of an experimental loop for testing power cycles with supercritical CO2. One facility of this kind was operated between 1999 and 2000, giving some very

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Proceedings of SCCO2 Power Cycle Symposium 2009 RPI, Troy, NY, April 29-30, 2009

interesting results mainly in the part of recuperation. Much effort was spent to find arguments supporting these experimental results. After years, these arguments seem clearer today, thus giving significant occasions for improving the cycles thermal efficiency, especially in the connection with SCWR Projects. 2. CYCLES CALCULATION Different types of thermodynamic cycles were analyzed by the above-mentioned partners; input parameters and assumptions were as follows: - thermodynamic properties of analyzed medium (predominantly from the NIST Database); - efficiency of all compressors and turbines; - minimum temperature drop of heat exchanger; - pressure losses in the loop. The pressure losses were neglected in most cases, assuming that they are not important for supercritical media. For the combined cycles (SCWR and S-CO2), these input analyses were not made, however, a possibility was examined of using S-CO2 instead of the low-pressure part of a standard PWR. The input data for this calculation were taken from the real operational data of the Czech nuclear cycles in NPP’s Dukovany and Temelin; i.e. the high-pressure part of the turbine was left unchanged and the low-pressure part was substituted by the above mentioned thermodynamic cycle with supercritical carbon dioxide. In this case, the output thermal efficiency has grown up to 39,6%.

Fig. 1: Thermal efficiency against turbine pressure ratio for 6 different cycles A to F with supercritical carbon dioxide. Next, different power conversion cycles solely with supercritical carbon dioxide were analyzed, while compressor inlet and turbine inlet temperatures were held constant (32°C and 550°C); the results of these calculations are plotted in Fig. 1 (cycle efficiency against turbine pressure ratio). Comparison of results for 6 different cycles has shown that the cycle “C” – cycle with regeneration and divided compression – exhibits the highest thermal efficiency. In these cycles, the heat exchanger plays a very important role due to abrupt changes of most thermalhydraulic parameters through the critical point, e.g. density, viscosity and especially isobaric heat capacity coefficient. As seen in Fig. 2, at low temperatures the thermal capacity is higher for low pressures, while at high temperatures the thermal capacity is higher for high pressures; the point of intersection of the low-pressure and the high-pressure curves will have a major impact on the (intermediate) heat exchanger.

Fig. 2: Isobaric heat capacity vs. temperature for pressures between 10 and 50MPa (step 5MPa).

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Proceedings of SCCO2 Power Cycle Symposium 2009 RPI, Troy, NY, April 29-30, 2009

CpH CpD

Qztr

CpH

T

The 4 options as represented in the schemes on Fig. 3 have been evaluated. The “Schema 4” is only complementary, for this situation was not found within the investigated area of CO 2 properties.

T T22

T22 Tz Tx

Qztr

Ty

CpD

Ty

Tz Tx T3

T11 T11

Cp

Cp

Schema 3

Schema 1

T

T CpH

T22

CpD CpH Qztr

Qztr

Tz Tx Ty

CpD

T22 Tz Tx Ty T11

T11

Cp

Cp

Schema 2

Schema 4

Fig. 3:Possibility of cp variation in IHX Apart from that, thermal efficiency of the cycle is also very influenced by thermal efficiency of the turbo machinery. To get a first estimate of the value of this efficiency, a preliminary design of the compressor and turbine would have to be made, or it can be estimated from similarity with other media, where enough practical experience is available. 3. EXPERIMENTAL LOOP WITH SUPERCRITICAL CO2 An experimental loop represented on HIGH PRESSURE ENERGETIC LOOP II. Fig. 4 and 5 was built in the research institute SVUSS Bechovice between the years 1995 and 1999; support was realized through governmental funding of the task called ”Analysis of high pressure cycle”. Medium used in the loop is carbon dioxide and the loop is equipped with energy conversion machine realized as a piston engine. The loop is computer controlled and can measure temperature, pressure, power and other properties in the following ranges: LEGEND:

CS BA

V 16

V 15

V 12

V 14

V 13

V 11

V8

V 10

V9

V7

V4

V6

V5

V2

V1

HAND OPERATED VALVE

V3

SAFETY VALVE

ELECTRIC VALVE

T 11

BACK PRESSURE VALVE

T8

P2

THERMOCOUPLE

T 26

PRESSURE SENSOR

n1

SPEED SENSOR

F

FORCE SENSOR

T9

T7

T5

T8

T6

T4

V 15

T3

T 10

V 16

MANOMETER

T 20

P

GEAR BOX

B

HYDRODYNAMIC BREAK

V

HEAT EXCHANGER

CH

COOLER

K

Temperature Pressure Flow rate

20-300 C; up to 50MPa; up to 12m3/hr.

PUMP STATION COOLING BASIN

PN

UNDERGROUND BASIN

VSV

BELLOWS VALVES PRESSURE GAS BOTTLE

ø 10/2

CH 4 ø 54/6

V5

V6

ø 10/2 V7

V 14

V8

V 11 V1

V 12

V2

V9 V 10 V3

V 13

T 16

T 16

V4 P3

P4 T 22

P2

TL3

T2

T1 P0

P2

M

P6

V 23

ø 10/2

ø 10/2

C T 12

TL

T 14

T 18

ø 10/2

COMPRESSOR

BA

T 3

CH 3

ELECTRIC HEATER

CS

T 2

CH 2

VSV

ENGINE

T 12

ø 10/2

M

T 13

CH 1

K

V 21

TS

P6

ø 10/2

HIGH PRESSURE PUMP

T

T 1

PRESSURE SWITCH

C

T 19

ø 54/6

PUMP

TS

R

F

ø 10/2 n1

P

OA 1

V 22

n2

V 20

CARBON DIOXID

TL2

TL1

V 17

B

T2

CARBON DIOXID

V 19 T23

COOLING WATER

P7

V 18

T 25

HIGH PRESSURE AIR

P8

T24

OA 2

P PN

OIL

Fig. 4: Scheme of the experimental loop with supercritical carbon dioxide. To our best knowledge, this loop was one of the first of its kind with such parameters. Purpose of the performed tests and measurements was to check and address the possibilities for realization of energetic devices working with a new medium and within improved range of properties Fig. 5: Photograph of the facility.

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Proceedings of SCCO2 Power Cycle Symposium 2009 RPI, Troy, NY, April 29-30, 2009

. Today the thermo-energetic machines work in the area of steam (every energetic machine) or in the area of gas (combustion engine, gas turbine). The controlled area is characterized by values of pressure and temperature, which are higher than critical values. The phase change from liquid to gas proceeds without the two-phase steam-liquid change and it is characterized by high volume energy of the medium.

DEVICE FOR TESTING THERMODYNAMIC PROPERTIES

LEGEND: T 1 - 15

- INTERNAL THERMOCOUPLE

T 16 - 21 - EXTERNAL THERMOCOUPLE H 1,2,3 H 4,5 I1 I2 TC

- EXTERNAL HEATING

- EXTERNAL HEAT INSULTATION

G

- POWER DRIVER UNIT

S

- DISPLACEMENT SENSOR

F

L N

RC

S P

- SERVOVALVE INPUT

V2

G

H1

V

V1

RC

M1

H2

H4

- PRESSURE SENSOR

- COVER - PRESSURE GAS BOTTLE

Z

- POWER SUPPLY

RC

- CONTROL UNIT

R

- SWITCHBOARD

PC

- PERSONAL COMPUTER

O

- HEATING SWITCHS - VALVE - MANOMETER - CARBON DIOXID - PISTON

Z

B

- PRESS

PC

- VESSEL

V TL

B

F

- HEAT CERAMIC INSULTATION

- THERMOCOUPLE UNIT - STEP DRIVER PUMP - CHECK STEP DRIVER

P

L

- INTERNAL HEATING

M M1

V3

M

I1

H5

P F

RC

T 1 - T 15

H3

S

V4

R T 16 - 21

I2

TL K

TC O

Fig. 6: Scheme of the autoclave.

The first challenge was to obtain definite thermodynamic data for optimization of thermodynamic process of the analyzed cycle. The individual data can be used with certain limitations, as there does not a general physical model for a wide range of pressures and temperatures.

Fig. 7: Photograph of the autoclave.

A unique testing autoclave-like device (see Fig. 6 and 7) was developed for obtaining the thermodynamic data. It enables direct measurement of thermodynamic properties, in contrast to other devices that provide other (indirect) quantities that are then converted to thermodynamic properties through different physical models. 4. EXPERIMENTAL RESULTS The most significant outcomes of the experiments are the three following: - the piston units had such a bad mechanical efficiency, that direct data especially from the brake could not be used; - the measurement and evaluation of thermo-physical properties shows certain deviations in the area of very high pressures, so that the precision of results is more than questionable; - the most important outcome of the operation turned out to be the set of data obtained for the intermediate heat exchanger. As an example, the following heat exchanger demonstrates well the result: High temperature (°C) = 92,36; Low temperature (°C) = 14,88; High pressure (MPa) = 22,8; Low pressure (MPa) = 9,23. The heat exchanger of standard tubular design is illustrated on Fig. 8. The regenerated heat was in this case 3 times higher than theoretical, while the cooling heat represented only 27% of theory. These values led to values of total thermal efficiency of the cycle that exceed the theoretical limit, the Carnot efficiency. Similar effect appeared during other measurements near the critical point of CO 2.

Fig. 8: Intermediate heat exchanger. 5. DISCUSSION ON RESULTS Several years were dedicated to finding reasons for such “optimistic” results. The first idea was to use the measured thermodynamic data from the high-pressure autoclave mentioned above, but the accuracy of the data was not satisfactory enough, especially at higher temperatures. Another explanation was based on the published experimental results on heat transfer in water in the supercritical region. Temperature drop during uniform heating is at first very surprising (see the red curve on Fig. 9); however, the temperature drop is significant enough to allow investigation of the phenomenon. Fig. 9: Wall temperature vs. bulk fluid

enthalpy fort he case of supercritical water [taken from Lycklama and Laurien, 2007].

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Proceedings of SCCO2 Power Cycle Symposium 2009 RPI, Troy, NY, April 29-30, 2009

This effect is explained by flow acceleration. Change of the flow rate can be achieved through changes in profile or, as mentioned above, through changes in density – at constant pressure achieved through changes in temperature. The equation describing this effect is: ∆h = ∆w2/2 where h is enthalpy and w flow rate. Straightforward interpretation of this equation is that a part of thermal energy is changed into kinetic energy. This process is of course connected with pressure drop – the pressure decreases. This can have two consequences:

1

Temperature drop If a nozzle is installed at a certain place in the intermediate heat exchanger, the speed increases – if the speed is increased on the high-pressure side, it will cause local decrease of temperature and the heat transfer will be enhanced (see Fig. 10). T

S

2

Pressure drop The second consequence is caused by changes in shape of isobaric heat capacity (induced by the pressure drop) vs. temperature (see Fig. 11). In extreme cases, flow acceleration may induce the same shape of isobaric heat capacity for both isobars, or even an interchange.

Fig. 10: Temperature effect in the Brayton cycle P=10MPa

Tx2

P=15MPa

Tx1

P=20MPa P=25MPa

Tx

2

Coming from the equation ∆h = ∆w /2, the above mentioned T processes can lead to threefold increase in heat transfer in the intermediate heat exchanger. Fig. 11: Isobaric heat capacity vs. temThe next question is where the described increase is at maximum and perature for different pressures. where it can be exploited. The following graphs (Fig. 12) show the temperature differences for the most common media used in energy power cycles. In all cases, the maximum effect is near the critical point. All data were calculated for the same enthalpy drop using the NIST database; the higher limit of flow rate was at approx. 60 m/s, lower limit at 5m/s. The graphs show that the temperature differences are very low for helium, they are much larger for water; however, they do not occur in the area of intermediate heat exchanger but in the area of turbine. The optimal medium from this comparison is carbon dioxide – the highest temperature differences are achieved in the area of supposed heat exchanger. P [MPa]

[°c]

12

CO2 - temperature drop

210 250 290 330 370

1000 5000 9000 13000 17000 21000 25000

Helium - temperature drop

90

3

130 170

2

210 250 290 330 370

1

1000 5000 9000 13000 17000 21000 25000

0

410

170

4

330

0

130

50

250

2

-30 10 50 90 130 170 210 250 290 330 370

1000 5000 9000 13000 17000 21000 25000

90

5

10

170

4

50

6 -30

90

6

10

10

8

0,98 0,96 0,94 0,92 0,9 0,88 0,86 0,84 0,82 0,8 0,78 0,76

-30

-30 10 50 90 130 170 210 250 290 330 370

10

10 50 90 130 170 210 250 290 330 370 410

Water - temperature drop

Fig. 12:Temperature drop affected by FA for different media

To achieve a feasible technical solution, optimization of pressure losses with respect to possible profit in thermal efficiency is critical. First FLUENT calculations of the nozzles have been started in UJV, however, only preliminary results are available, see Fig. 13; convergence as well as hardware capabilities are among important issues.

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Proceedings of SCCO2 Power Cycle Symposium 2009 RPI, Troy, NY, April 29-30, 2009

Temperatures field

Pressures field

Flow rate

Fig. 13:Nozzle: preliminary results from FLUENT calculation Preliminary results of the calculations in FLUENT show an important outcome – the dimensions of the nozzle must be large, so introduction of a nozzle would probably not be applicable for small power sources.

6. GENERAL THEORY CORRECTIONS For practical application, the theory development seems be most suitable the serie of pictures with comments. 1. Well known Carnot cycle, it is very easy to confirm maximal thermal efficiency in given limits of temperature, it can be donned for ideal and also for real media.

T

S

2. For the Brayton cycle, no configuration can lead to thermal efficiencies higher than the Carnot limit, as can be demonstrated by calculation.

3. For the Brayton cycle with flow acceleration on the high pressure isobar, the balance of heat transfer is reversed and the theoretical Carnot efficiency will be exceeded.

T

S

T

S

4. Extremely corrected Brayton cycle with flow acceleration. The picture is in direct disagreement with the statement Tenv. of the 2nd law of thermodynamics. It is shown here only as an example that T the Carnot limit may not be so resolute as S generally accepted. However, this example does probably not allow for technical application; the speed would be too high as well as the pressure losses. For heat exchangers, a technically achievable temperature difference is necessary, for which in this case an appropriate source with sufficient heat content would be the greatest challenge (could it be the ocean?).

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Proceedings of SCCO2 Power Cycle Symposium 2009 RPI, Troy, NY, April 29-30, 2009

7. NEW APPROACH TO THE CONVERSION CYCLES For a feasible application based on the above mentioned theoretical corrections, combined cycles appear to be the most promising; it may apply for supercritical water steam cycles as well. The decrease in thermal efficiency of the steam part by induced increase of the lower temperature should not be as significant compared to the added value brought by S-CO2. Apart from the increase in thermal efficiency, smaller dimensions of the entire system and fewer problems with corrosion are other benefits.

HP

R

IP

HPLWR part Condenser 100°C

IHX T-CO2

Cooler

CO2 part

Fig. 14, 15: HPLWR cycle and its modification 8. CONCLUSION Essential ways of confirming the large effect of flow acceleration in the areas near the critical point are as follows: - calculations according to the equation ∆h = ∆w2/2; - experiments confirming the hear transfer deterioration; - experiments in the supercritical water loop SCWL (installed in UJV Rez). The alternative of using low temperature cycles in nuclear energy is further connected with large improvement in safety and lifetime of power plants; however, detailed analysis of the technical solution is essential to confirm its feasibility. Compared to other ways of improving the parameters of power plants, including new reactor types, fusion energy etc., the outlined solution is simple in terms of calculation as well as experimental confirmation. International collaboration is highly desirable in order to confirm the hypotheses.

ACKNOWLEDGEMENTS Martin Kulhánek1) part of cycles calculation, Otakar Frýbort1) part of FLUENT calculation

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