A Thermodynamic Perspective on Energy Efficiency

Transcription

1 Thermodynamic Perspective on Energy Efficiency Juan C. Ordonez Department of Mechanical Engineering Energy and Sustainaility Center Center for dvanced Poer Systems Florida State University

2 Nicolas Léonard Sadi Carnot

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4 Thermal engine

5 Engine Efficiencies in times of Carnot Dran after Bejan ET and Cardell From Watt to Clausius

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7 Sources: Bejan (ET); and H.B. Callen (T)

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9 Oserved efficiency

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11 Endoreversile model External irreversiility Linear heat transfer model Chamadal (1957) Novikov (1958) Curzon & lhorn (1975) endoreversile External irreversiility Linear heat transfer model

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13 Recent studies suggest that at maximum poer Taylor expansion

14 What is the maximum poer that can e extracted from a hot stream? What are realistic limits for this poer?

15 1. Poer extraction: T H, P ṁ reversile poer plant. Q atmosphere: T T, P. W rev W rev If the stream interacts only ith the atmospheric temperature reservoir (T ), the maximum poer that can e extracted is the flo exergy: mc p T T T H T 1 ln T The actual poer ill alays e loer than rev ecause of the irreversiilities of the heat transfer eteen the hot stream and the rest of the poer plant. W H (ideal gas)

16 The heat transfer irreversiility is due to: T H, P ṁ T out T, P (i) temperature difference eteen the stream (T) and the heat exchanger surface (T s ) and.. W rev >W reversile poer plant. Q (ii) thermal mixing of the discharged stream. atmosphere: T

17 Hot stream collecting stream poer plant W We use a second stream to collect the poer from the hot stream. This second stream is the orking fluid of the poer producing device. Q atmosphere: T The case here the collecting stream is single phase as studied y Bejan and Errera, 1998.

18 Poer extraction from a hot stream

19 This image cannot currently e displayed. Entropy generation analysis T H ater. m c p. m T out T S W gen ( H h ) Q Q e m h Q + Q e + m s T ( s ) H W me x,h T S gen reversile compartment Ẇ e x,h ( h T s ) ( h T s ) H H W. Q ( ) m e x e,2 T x,1. Q e S m gen No for the heat exchanger, and external cooling alone: ( h h ) m ( h h ) Q H 2 1 e m s ToS Q e ( s ) + m ( s s ) + gen H x,h me m 2 1 T ( e e ) x,2 x,1

20 We can maximize the poer output using: or directly using W W me x,h ( ) m e x e,2 T x,1 S gen minimize In dimensionless form: η II W me x,h m ( e e ) x,2 me x,h x,1

21 [IJHMT Vargas, Ordonez and Bejan, 1999] Maximization of the second la efficiency y selecting the mass flo rate of the ater stream m m

22 m m Optimal system structure Effect of the mass flo rate on the allocation of area among the sections of the heat exchanger

23 T H. m c p T out. m ater 1 liquid 1-x-y / N1 Η oiling y / steam x S / M Effect of the mass flo rate on the allocation of area among the sections of the heat exchanger

24 Concluding remarks Sadi Carnot, laid out the foundations of thermodynamics exploring limits of operation of thermal engines that lead to maximum poer. n interesting question that can e asked is hy do e oserve a pattern in efficiency at maximum poer? This maye linked to symmetry in physical las

25 Concluding remarks Chamadal, Novikov, Curzon and hlorn derived efficiency expression that predicts ell performance of thermal plants. The Novikov Chamadal-Curzon-hlorn expression has een derived in different context: Classical thermodynamics Endoreversile thermodynamics (finite times, finite sizes) Linear Irreversile Thermodynamics

26 Concluding remarks: T H. m c p T out The extraction of poer and refrigeration from a hot stream can e maximized y properly matching the stream ith a receiving stream of cold fluid, across a finite-size heat transfer area. m ater.72.7 counterflo + ideal-gas model for steam There is an associated optimal allocation of heat exchanger inventory: 1 liquid 1-x-y / N1 Η η ΙΙ taulated steam properties.5 oiling y / M N1 Η Optimal mass flo rate ratio steam x S / M

27 Concluding remarks System structure appears as a result of optimization -> maximization of flo access Constructal Design: Generation of architecture under gloal constraints

28 Thank you!

29 cknoledgements: Prof. S.. Sherif Professors. Bejan, J.V. C. Vargas and C. Harman The comments of the revieers of this paper are greatly appreciated. Center for dvanced Poer Systems at Florida State University.

30 System structure appears as a result of optimization Constructal Design: Generation of architecture under gloal contraints

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32 Concluding remarks: Ho does the optimal area allocation appears in practice? a) One counterflo heat exchanger, three sections: The three sections rearrange themselves ) Three sections, oiling in contact ith hottest gases: Here a morphing heat exchanger is needed 1.5 liquid oiling 1-x-y / y / N1 Η steam x S / M System structure appears as a result of optimization (Constructal theory)

33 Concluding remarks: Optimal HT area allocation T H. m c p. m T out ater.72.7 ideal-gas model for steam 1 1-x-y / N1 Η η ΙΙ taulated steam properties.5 y / M N1 Η x / S M.2 q L H 4 L x 1.2 y.2 U ~ 5 H LO r

34 Maximization of the second la efficiency using Toluene as orking fluid Duke University Mechanical Engineering and Material Science Department

35 Maximum poer from a hot stream In engineering thermodynamics it is usually assumed that the heat that drives a poer plant is already availale from a hot temperature reservoir. hot cold poer plant W In most applications a fuel is urn, and a hot stream ecomes the input to the poer plant. comustion cold hot stream poer plant W - What is the maximum poer that can e extracted from a hot stream?

36 Thermodynamic optimization methodology: Poer and refrigeration systems are assemlies of streams and hardare (components). The size of the hardare is constrained. Rankine poer cycle Department of Mechanical Engineering

37 fuel heater turine pump condenser Each stream carries exergy (useful ork content), hich is the life lood of the poer system. Exergy is destroyed (or entropy is generated) henever streams interact ith each other and ith components. Our ojective is to optimize the streams and components, so that they generate minimum entropy suject to the constraints. Department of Mechanical Engineering

38 THE METHOD OF THERMODYNMIC OPTIMIZTION Starts ith: SYSTEM Interactions ENVIRONMENT -Thermodynamics provides the asic equations -Flos, flo resistances, losses (irreversiility, dissipation ) and interactions are integrated from related disciplines MODEL CONSTRINED OPTIMIZTION OPTIMIZED SYSTEM Department of Mechanical Engineering

39 MODEL CONSTRINED OPTIMIZTION OPTIMIZED SYSTEM Environment (T P ) We start from the 1 st and 2 nd las of thermodynamics: in T T. Q. W System (M, E, S) de dt n Q i W + mh i in out m h n ds Q i S gen ms + ms dt T i i in out T 1 T 1. Q 1 T 2 T 2. Q 2 T n T n. Q n out Department of Mechanical Engineering

40 MODEL CONSTRINED OPTIMIZTION OPTIMIZED SYSTEM The to las comined (eliminating Q ): n d T W dt i 1 T i in out. ``Exergy nalysis ( E TS) + 1 Q i + m ( h Ts) m ( h Ts) TS gen (E1) destroyed exergy Flo-exergy associated to mass flos ctual ork Exergy, heat transfer interactions In the reversile limit ( S gen ), W rev Non-flo exergy n T ( ) + E T S 1 Q i + m ( h Ts) m ( h Ts) d dt i 1 Ti in out Work in the reversile limit W < W rev Department of Mechanical Engineering

41 MODEL OPTIMIZED SYSTEM CONSTRINED OPTIMIZTION Sustracting them e get the Gouy-Stodola theorem: The destroyed poer is proportional to the rate of entropy generation. W W W lost rev T S gen (E.3) EGM starts from (E.3). We ant to e as close as possile to the reversile limit ( W rev), then e should ork in the minimization of the entropy generation ( S ). gen Department of Mechanical Engineering

42 MODEL OPTIMIZED SYSTEM CONSTRINED OPTIMIZTION CONSTRINED OPTIMIZTION function, constraints and degrees of freedom The FUNCTION to e optimized, is related to PURPOSE e.g: -Max. poer extraction -Min. poer requirement -Max. of exergy collection -Min. ratio destroyed exergy/ supplied exergy CONSTRINTS. e.g: Total volume, area, material amount, operation temperatures. DEGREES OF FREEDOM -Operation temperatures -Charging/discharging times -Dimensions, thickness -Spacing among components -Material properties Department of Mechanical Engineering

43 MODEL OPTIMIZED SYSTEM CONSTRINED OPTIMIZTION The total surface constraint (c1), can e ritten as, U s N µ N s + N + µ U U U s x N s N U mc s constant In the numerical computations, e defined the folloing area fractions p superheater (steam) y oiling 1 x y Preheater (liq. ater) The equations e have until no allo us to compute the temperature distriution. We need the ork output. Department of Mechanical Engineering

44 MODEL OPTIMIZED SYSTEM CONSTRINED OPTIMIZTION Constrained optimization: The total area constraint, can e ritten as, U s N µ N s + N + µ U U U s N N U mc s constant In the numerical computations, e defined the folloing area fractions p x s superheater (steam) y oiling 1 x y Preheater (liq. ater) The equations e have until no allo us to compute the temperature distriution. We need the ork output. Department of Mechanical Engineering

45 Concluding remarks (1/3): T H. m c p T out The extraction of poer from a hot stream can e maximized y properly matching the stream ith a receiving stream of cold fluid, across a finite-size heat transfer area. m ater.72.7 counterflo + ideal-gas model for steam There is an associated optimal allocation of heat exchanger inventory: 1 liquid 1-x-y / N1 Η η ΙΙ taulated steam properties.5 oiling y / M N1 Η Optimal mass flo rate ratio steam x S / M

46 We ant to search for an optimal matching eteen the streams. Thermodynamic optimization Starts ith: SYSTEM Interactions ENVIRONMENT -Thermodynamics provides the asic equations -Flos, flo resistances, losses (irreversiility, dissipation ) and interactions are integrated from related disciplines MODEL CONSTRINED OPTIMIZTION OPTIMIZED SYSTEM

47 The case here the collecting stream experience a phase change as studied y Vargas, Ordonez and Bejan (IJHMT, 1999). T H T T 3. 2 m c p T 4 c s. m T out T T c s T 1 steam superheating oiling liquid ater preheating Temperature distriution along the three sections of the heat exchanger heat transfer surface Florida State University,, S. Chen

48 MODEL ε s CONSTRINED OPTIMIZTION Heat transfer analysis classical effectiveness Ntu analysis Superheater Boiling Preheating ' 1 exp[ N ( 1 µ )] ε 1 exp( N ) ε ' 1 exp[ N s ( 1 µ )] 1 µ exp N ( 1 µ ) 1 µ exp[ N ( 1 µ )] ε s µ T H OPTIMIZED SYSTEM s ( T T ) H T 3 ε µ < 1, µ < 1 T T H H T3 T ε T T 4 [ ] T 1 T 1 ε s T T 2 3 T T h T H T3 µ c fg s ε T µ out ( T T ) 1 T 4 4 m c µ mc N s p s U s m c s s N U mc p N m c µ mc U m c p

49 MODEL CONSTRINED OPTIMIZTION OPTIMIZED SYSTEM Constrained optimization: Maximize poer extraction (efficiency) For fixed total area, Degree of freedom, m The total area constraint T H can e ritten as, U s N µ N s + N + µ U N U s mc p. m c p U U s N T out In the numerical computations, e defined the folloing area fractions x y s 1 x y superheater (steam) oiling Preheater (liq. ater)

50 MODEL OPTIMIZED SYSTEM CONSTRINED OPTIMIZTION

51 ε s Heat transfer analysis classical effectiveness Ntu analysis Superheater Boiling Preheating ' 1 exp[ N ( 1 µ )] ε 1 exp( N ) ε ' 1 exp[ N s ( 1 µ )] 1 µ exp N ( 1 µ ) 1 µ exp[ N ( 1 µ )] ε s µ T H s ( T T ) H T 3 ε µ < 1, µ < 1 T T 4 3 T T 3 ε T T 4 [ ] T 1 T 1 ε s µ T 2 ( T T ) H T m h fg mc p ( T T ) 3 ε T µ out ( T T ) 1 T 4 4 µ m c mc p s µ m c mc p N s U s m c s s N U mc p N U m c

52 Maximization of the second la efficiency y selecting the mass flo rate of the ater stream m m Duke University Mechanical Engineering and Material Science Department

53 m m Effect of the mass flo rate on the allocation of area among the sections of the heat exchanger Duke University Mechanical Engineering and Material Science Department

54 Effect of the heat transfer area size on the match eteen the temperature distriutions of the to streams

55 Effect of heat exchanger size on the second la efficiency and on the allocation of heat transfer area Duke University Mechanical Engineering and Material Science Department

56 Effects of varying the orking-fluid inlet temperature and oiling temperature Duke University Mechanical Engineering and Material Science Department

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58 1 H 4, 1.98, η II,max.5 x opt M opt y opt Notice roustness of the optimal match N Effect of heat exchanger size on the second la efficiency and on the allocation of heat transfer area

59 5 N 6 H 4 5 N 1 H 4 4 Η Η gas ater 4 M opt.48 out gas ater 4 M opt.45 out 1 1 oiling section steam section liquid ater section 1 oiling section steam section liquid ater section 1 1 S S Effect of the heat transfer area size on the match eteen the temperature distriutions of the to streams

60 1 N 1, Η 4, 1.98 η ΙΙ, max.5 M opt x opt y opt Effect of varying the orking-fluid inlet temperature Effect of varying the oiling temperature

61 .72 U /U s 1 and U /U s 1.7 U /U s 1 U /U s η ΙΙ.68 N1 Η m M m Effect of overall heat transfer coefficients on the second la efficiency

62 Concluding remarks : Optimal matching among the hot and collecting stream (counterflo configuration, optimal mass flo rate ratio, optimal allocation of heat exchanger inventory) Collecting stream is single phase IJHMT Bejan and Errera, 1998 Collecting stream experience phase change IJHMT Vargas, Ordonez and Bejan, 1999 Collecting stream experience phase change and oiling section is in contact ith hottest gases SME HT Charlotte Ordonez and Chen, 24

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64 3. Optimal Matching for Refrigeration: Refrigeration system driven y a hot stream through a counterflo heat exchanger

65 Thermodynamics ( c ) ( T T ) + Q Q m p r 2 1 L T2 QL Q ( mc ) ln + p r T1 TLC TC Constraint: + + H L Heat Transfer: Q (U) (TC T ) Q N H L (U) UH mc L (T L T r <1 1 exp ε 1 r exp T p H r >1 1 exp ε 1 1 r exp LC ) r ( mc p) r [ N H ( 1 r) ] [ N ( 1 r) ] H mc ( T ) 2 T1 εr H T1 T 1 [ N H ( 1 r )] [ N ( 1 r )] 1 H p ( T ) 2 T1 ε H T1

66 T T p T mc Q q x H y L y x 1 p L L T mc Q q p mc U U ~ p H H mc U U ~ p L L mc U U ~ Dimensionless groups:

67 n optimal matching for refrigeration.2 q L H 4 L x.2 y U ~.2 5 H LO r r mc p ( mc p) r Illustration of the existence of an optimal capacity rate ratio

68 THE EFFECT OF THE HOT-STREM INLET TEMPERTURE ON THE OPTIML LLOCTION OF HET EXCHNGER INVENTORY

69 Here the heat exchanger area allocation has een optimized Maximized refrigeration rate and optimal capacity rate ratio of the countreflo system

70 Effects of refrigeration temperature

71 Effects of the matching stream inlet temperature

72 EFFECT OF HOT SIDE OVERLL HET TRNSFER COEFFICIENT ON THE REFRIGERTION RTE ND THE EXISTENCE OF N OPTIML CPCITY RTE RTIO.

73 2. Phase change under limiting collecting temperatures Placing the oiling section in contact ith the hottest gases ill prevent pipe overheating (materials constraints). n alternative configuration:

74 T H. m c p T out. m ater Temperature distriution along the three sections of the heat exchanger

75 This image cannot currently e displayed. MODEL CONSTRINED OPTIMIZTION T H OPTIMIZED SYSTEM. m c p. m Entropy generation analysis T out T ater S W gen m h ( H h ) Q Q e Q + Q e + m s T ( s ) H W me x,h T S gen reversile compartment Ẇ e x,h ( h T s ) ( h T s ) H H W. Q ( ) m e x e,2 T x,1. Q e S m gen No for the heat exchanger, and external cooling alone: ( h h ) m ( h h ) Q H 2 1 e m s T Q e ( s ) + m ( s s ) + H 2 1 T ( e ) Sgen mex,h m x,2 ex,1

76 MODEL CONSTRINED OPTIMIZTION OPTIMIZED SYSTEM We can maximize the poer output using: or directly using W W me x,h ( ) m e x e,2 T x,1 S gen minimize In dimensionless form: η II W me x,h m ( e e ) x,2 me x,h x,1

77 .72 ideal-gas model for steam Optimal matching.7 η ΙΙ taulated steam properties.68 N1 Η m M m Maximization of the second la efficiency y selecting the mass flo rate of the ater stream

78 Concluding remarks: Optimal ratio is roust ith respect to total surface area Η oiling section gas ater steam section S 4 N 1 H M opt.45 liquid ater section out 1 1 4, 1.98, 1.8 H 1 η II,max.5 x opt M opt y opt N

79 Optimal area allocation is roust ith respect to refrigeration temperature