Application of Finite-time Thermodynamics for Evaluation Method of Heat Engines

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ORC2017 13-15 September 2017, Milano, Italy Takeshi Yasunaga and

1 Application of Finite-time Thermodynamics for Evaluation Method of Heat Engines IV International Seminar on ORC Power Systems, ORC September 2017, Milano, Italy Takeshi Yasunaga and Yasuyuki Ikegami Institute of Ocean Energy, Saga University, Japan 1

2 Contents 1. Motivation & lessons 2. Concept 3. Normalization of TE 4. Summary and future work 2

3 Institute of Ocean Energy, Saga University - Established in Over 40 years of experience of OTEC* (*Ocean Thermal Energy Conversion) <OTEC team:> - System optimization (Experimental, Computational) - Heat exchanger development (Performance test benches, visualization, CFD) 30kW / 15kW OTEC experimental facilities HE test facilities 3

4 In 2013, launched NEW STAGE to connect 4 the grid for the first time in the 21 st century. Ocean Thermal Energy Conversion System in Japan - 100kW - HFC134a - Rankine cycle (2-stages)

5 1. Motivation & lessons 5

6 Development of High Efficiency Thermo-Cycle 1970s,80s- Rankine 1990s- Kalina Working Fluid : HFC22 -> NH3 Working Fluid : NH3-H2O Saga U (Uehara) Working Fluid : NH3-H2O 2011 Double Rankine NH3 HFC134a Increase Net power NOT Thermal efficiency 6

7 Thermal efficiency Avery, H. W. and Wu, C., Renewable Energy from the Ocean - A guide to OTEC - (1994) - Upper bound of thermal efficiency: Warm seawater temp T W and Cold seawater temp T C η th,m = 1 T C T W - At the maximum work condition the thermal efficiency: (Finite-time thermodynamics) The half of Upper η th,ca = 1 T C T W Condition at maximum efficiency and maximum work is different. That is the contradiction of the performance. Propose the normalized thermal efficiency for lowgrade thermal energy conversion An application of ORC - [2] I. I. Novikov, The efficiency of atomic power stations, Nucl. Energy II ; ; Translated from At. Energ. 3; p. 409 [3] F. L. Curzon and B. Ahlborn, Efficiency of a Carnot engine at maximum power output, Am. J. Phys., Vol. 43; p

8 Applicable heat sources Low-grade Thermal Energy Conversion (LTEC) WHR (hot water) Hot-spring Ocean Thermal 8

9 Series of small scale ORC package units commercialized or semi-commercialized in Japan ULVAC ANEST IWATA IHI. KOBELCO. ELECTRA THERMO ACCESS ENERGY 3 kw 11 kw 20 kw 72 kw 110 kw 135 kw Performance Spec. is only Capacity of Products. Why? On the other hand, many researches uses the achievement of increase of the thermal efficiency in their system. Definition of the effective thermal efficiency is required. 9

10 2. Concept 10

11 Thermodynamic model of ideal condition C H,T H T H,O T H,e T T H Q H Reversible heat engine W T H,O T L,O Reversible heat engine T He T Le T L,O Q L T L,e T L Conceptual model C L,T L s Conceptual T-s diagram - Thermal energy is stored in liquid as sensible heat - Specific heat is constant - Ideal heat exchanger (zero pinch temperature) - Reversible heat engine (Carnot cycle) 11

12 Contradiction of the perk of work and thermal efficiency 12

13 Contradiction of the perk of work and thermal efficiency 13

14 Maximum work condition Q H = rc HS T H T H,O C HS = C H +C L, r = C H C HS η th = 1 T L,O T H,O C is the heat capacity flow rate [W/K] (mass flow rate [kg/s] times specific heat [kj/kgk]) W max = r 1 r C HS T H T L 2 Δs = Q H T H,O Q L T L,O = 0 W = η th Q H = f T H,O W will be the one degree of freedom W T H,O = 0 W max η th,ca = 1 T L T H 14

15 3. Normalization of Thermal Efficiency 15

16 Thermal energy in heat source T T H Available thermal energy T stored between high and low T temperature heat source H Q HS = 2r 1 r C HS T H T L T 0 Equilibrium state (Dead state) T L T 0 Q HS /2 Q HS E 16

17 Normalized thermal efficiency Conventional thermal efficiency η th = W Q H = rc HS W T H T H,O Change the denominator to available thermal energy η th,nor = W Q HS = W 2r 1 r C HS T H T L Normalized thermal efficiency Normalized thermal efficiency only depends on the heat source condition and independent from the heat transfer rate to heat engine 17

Normalized thermal efficiency takes into account the external irreversibility To apply the heat source thermal energy based on the equilibrium state to thermal efficiency is equivalent to take into

18 Normalized thermal efficiency takes into account the external irreversibility To apply the heat source thermal energy based on the equilibrium state to thermal efficiency is equivalent to take into account the external irreversibility (Q) [11] A.Bejan, Graphic Techniques for Teaching Engineering Thermodynamics, Mechanical Engineering News, (1997), pp [12] P. Salamon, K. H. Hoffmann, S. Schubert, R. S. Berry, B. Anderson, What conditions make minimum entropy production equivalent to maximum power production, J. Non-Equilibrium Thermodynamics, Vol. 26, (2001), pp

19 Comparison between normalized thermal efficiency and conventional thermal efficiency The normalized thermal efficiency will be less than Curzon-Ahlborn efficiency Normalized thermal efficiency Curzon-Ahlborn thermal efficiency In case T H =80 o C, T L =30 o C, r=0.5, C HS =1 kw/k. 19

20 Comparison between normalized thermal efficiency and conventional thermal efficiency The trend of normalized thermal efficiency corresponds to the work output In case T H =80 o C, T L =30 o C, r=0.5, C HS =1 kw/k. 20

Application of normalized thermal efficiency to Rankine cycles Maximum power output Thermal

normalized thermal efficiency will lead to the maximization of work output from a heat engine,

[15] that T H =80 o C, T L =30 o C, C HS =233 kw/k. [15] T. Morisaki and Y.

21 Application of normalized thermal efficiency to Rankine cycles Maximum power output Thermal efficiency Normalized thermal efficiency In the design stage of ORC on LTEC, the maximization of normalized thermal efficiency will lead to the maximization of work output from a heat engine, instead of the conventional thermal efficiency. The heat source condition corresponds to Ref. [15] that T H =80 o C, T L =30 o C, C HS =233 kw/k. [15] T. Morisaki and Y. Ikegami, Maximum power of a multistage Rankine cycle in lowgrade thermal energy conversion, Applied Thermal Engineering, Vol.69, (2014), pp

22 4. Summary and future work 22

23 Summary Still the field of Low-grade thermal energy conversion (LTEC) system uses the thermal efficiency as the performance evaluation and try to achieve higher thermal efficiency. The effective thermal efficiency is required for the effective evaluation of the system. In the field of the LTEC, the normalized thermal efficiency is proposed and the maximization of normalized thermal efficiency will maximize the power output of the system. η th,nor = W Q HS = W 2r 1 r C HS T H T L 23

24 Future work - To extend the concept to exergy efficiency for Low-grade thermal (Not to misread the normalized thermal efficiency) - To apply the normalized thermal and exergy efficiencies to the design optimization for Low-grade thermal energy conversion - To extend the idea to the other heat source systems 24

25 Thank you so much for your attention. Grazie mille Takeshi Yasunaga, Dr. Eng. Assistant Professor Institute of Ocean Energy, Saga University (IOES) Contact:

26 Q HS = (mc p ) H T H T H,O + (mc p ) L T L,O T L = C H T H T H,O + C L T L,O T L Q HS = C H T H T 0 + C L T 0 T L T w T 0 : dead state (Equilibrium state) T T 0 = rt H + (1 r)t L T 0 Q HS = 2r(1 r)c HS T H T L T c E(Q)

PERFORMANCE ANALYSIS OF SOLAR DRIVEN HEAT ENGINE WITH INTERNAL IRREVERSIBILITIES UNDER MAXIMUM POWER AND POWER DENSITY CONDITION

PERFORMANCE ANALYSIS OF SOLAR DRIVEN HEAT ENGINE WITH INTERNAL IRREVERSIBILITIES UNDER MAXIMUM POWER AND POWER DENSITY CONDITION VO.1, NO.3, OCTOBER 2006 ISSN 1819-6608 PERFORMANCE ANASIS OF SOAR DRIVEN EAT ENGINE WIT INTERNA IRREVERSIBIITIES UNDER MAIMUM POWER AND POWER DENSIT CONDITION A. Biswas, K. M. Pandey and R. Deb Department