The “Gheorghe Asachi” Technical University of Iasi...

The „Gheorghe Asachi” Technical University of Iasi – an excellent choice for highschool graduates, who decided to opt for a career in the provoking field ofengineering. All our eleven faculties, endowed with laboratories and the latestequipment, where worldwide recognized specialists perform their activity, areready to welcome and assist you in your endeavour. I am convinced that thediploma awarded by our university will become the key of success both in yourcareer and personal life.

We look forward to welcoming you at our university!

The “Gheorghe Asachi” Technical University of Iasi

Romania

LLLP ERASMUS - NANCY - 2013

Gouy – Stodola Theorem

Prof. Dr. Eng. Gheorghe DUMITRASCU“Gheorghe ASACHI” Technical University of Iasi

Mechanical and Automotive Engineering Departmenthttp://www.tuiasi.ro

http://www.mec.tuiasi.ro/indextmtfc.html


http://www.tuiasi.ro/


Assumptions


1. They will be analyzed non steady-state enlarged basic open thermodynamic systems, including both the thermal system and, the external heat reservoirs controlling the heat transfers and, the environment allowing the mass transfers;

2. The working fluid is a mixture of different chemical species, the inlet and outlet compositions might be different because of chemical reactions that can appear during the flow through the thermal system;

3. The inner boundary of the flow path through the thermal system is deformable under the environmental pressure;

Gouy – Stodola Theorem, EnginesFirst Law of Thermodynamics

Second Law of Thermodynamics

( )

∑∑

++−

+++

∂∂

−−−=∂∂

outlet

22

ee0

gZ2

VhmgZ2

Vhm

tVpWQQ

tU

inlet

0smsmTQ

TQ

tSS

outlet0

0irrevgen ≥⋅+⋅−

−−

∂∂

= ∑∑

inlet

M: Mass of the working fluid surrounded by the operating engine inner walls at a certain operational timeV: Working fluid volume defined by the operating engine inner walls at a certain operational timeU: Inner operating engine working fluid energy at a certain operational timeS: Entropy of the working fluid surrounded by the operating engine inner walls at a certain operational time


inlet

outlet

Heat sinkT0

S

MU

Heat sourceT>T0

V

0Q

Q

eW

Gouy – Stodola Theorem, Engines

Combined First and Second Laws of Thermodynamics


( ) ( )

( ) irrevgene

outletinlet

irrevlost

revee

STSTVpU t

gZVsThmgZVsThm

TTQWWW

00

2

0

2

0

0

22

1

−−+∂∂

−

++−−

++−+

−=+=

∑∑

inlet

outlet

Heat sinkT0

S

MU

Heat sourceT>T0

V

0Q

Q

eW


Reversible Engine Power


( ) ( )

( )

methalpy the is gZVhh

where

STVpU t

sThmsThm TTQW

*

e

outletinlet

reve

++=

>−+∂∂

−

−−−+

−=

∑∑

2

0

1

2

0

0*

0*

0

inlet

outlet

Heat sinkT0

S

MU

Heat sourceT>T0

V

0Q

Q

eW


Irreversible Lost Power


irrevgen

irrevlost STW ⋅−= 0

inlet

outlet

Heat sinkT0

S

MU

Heat sourceT>T0

V

0Q

Q

eW

Gouy – Stodola Theorem, Refrigeration Cycles

First Law of Thermodynamics

Second Law of Thermodynamics


( )

∑∑

++−

+++

∂∂

−−−=∂∂

outlet

22

ee0

gZ2

VhmgZ2

Vhm

tVpWQQ

tU

inlet

0smsmTQ

TQ

tSS

outlet0

0irrevgen ≥⋅+⋅−

−−

∂∂

= ∑∑

inlet

Q

0Q

eW

inlet

outlet

Heat sourceT

Heat sinkT0

S

MU

V

M: Mass of the working fluid surrounded by the operating engine inner walls at a certain operational timeV: Working fluid volume defined by the operating engine inner walls at a certain operational timeU: Inner operating engine working fluid energy at a certain operational timeS: Entropy of the working fluid surrounded by the operating engine inner walls at a certain operational time



Combined First and Second Laws of Thermodynamics

( ) ( )

( ) irrevgene

outletinlet

irrevlost

revee

STSTVpU t

gZVsThmgZVsThm

TTQWWW

00

2

0

2

0

0

22

1

−−+∂∂

−

++−−

++−+

−=+=

∑∑Q

0Q

eW

inlet

outlet

Heat sourceT

Heat sinkT0

S

MU

V



Reversible Consumed Power

( ) ( )

( )

methalpy the is gZVhh

where

STVpU t

sThmsThm TTQW

*

e

outletinlet

reve

++=

<−+∂∂

−

−−−+

−=

∑∑

2

0

1

2

0

0*

0*

0

Q

0Q

eW

inlet

outlet

Heat sourceT

Heat sinkT0

S

MU

V



Irreversible Lost Power

irrevgen

irrevlost STW ⋅−= 0

Q

0Q

eW

inlet

outlet

Heat sourceT

Heat sinkT0

S

MU

V

Gouy – Stodola TheoremConclusions


0→irrevgenS 00 →⋅−= irrev

genirrev

lost STW

revstoragee

revflowe

revQe

reve WWWW ,,,

++=



revstoragee

revflowe

revQe

reve WWWW ,,,

++=

•Relationship Q – W, engines, (heat exergy)

0TT1QW 0rev

Qe >

−=

,

•Relationship Q – W, refrigeration cycles, (heat exergy)

( ) 0TTT

Q1TTQW

0

0revQe <

−−=

−−=

,



revstoragee

revflowe

revQe

reve WWWW ,,,

++=

Relationship flow– W, (flow exergy)

( ) ( )∑∑ −−−=outlet

00revflowe sThmsThmW *

inlet

*,



revstoragee

revflowe

revQe

reve WWWW ,,,

++=

Relationship “energy storage” – W, non steady-state system operation,(storage exergy)

( )STVpU t

W 0erevstoragee −+

∂∂

−=,

Introduction to Irreversible Cycles


Mechanical and Automotive Engineering Departmenthttp://www.tuiasi.ro





Introduction to Irreversible Cycles

AssumptionsNo mass transfer:

and

Non deformable boundary walls:

Steady state operation:

0gZ2

VhmgZ2

Vhmoutlet

22

=

++−

++ ∑∑

inlet

0tVpe =∂∂

0tS and 0

tU

=∂∂

=∂∂

0smsmoutlet

=⋅+⋅− ∑∑

inlet



Introduction to Irreversible Closed CyclesEndo-reversible Carnot Cycle

Entropy Generation by IrreversibilityEnlarged System – including both the thermal system and

the external heat reservoirsRelated to overall Irreversibility (external + internal)

T0

T

(T0+∆T0)

T

(T—∆T)

(T—∆T)

(T0+∆T0)

Q

Q

Q0

Q0

W

W 0TQ

TQ

S0

0overallgen ≥+−=

Entropy Generation by IrreversibilityThermal System – excluding the external heat reservoirs

Related to internal irreversibility

0TT

QTT

QS

00

0cyclegen ≥

∆−+

∆+−=

or Nirrev is the overall irreversibility function related to T and T0,

is the number of internal irreversibility related to (T - ∆T) and (T0 - ∆T0),

Irr is the internal irreversibility function related to other reference temperatures on the cycle

and different from (T - ∆T) and (T0 - ∆T0)


Introduction to Irreversible Closed CyclesEndo-reversible Carnot cycle

Entropy BalanceEnlarged System – including both the thermal system and the

external heat reservoirs

T0

T

(T0+∆T0)

T

(T—∆T)

(T—∆T)

(T0+∆T0)

Q

Q

Q0

Q0

W

W

0TQ

TQ

Irr0

0 =+−

Entropy BalanceThermal System – excluding the external heat reservoirs

Related to internal irreversibility

0TQIrr

TQ

TTQN

TTQ

0

0internalirrev

00

0 =+−=∆−

+∆+

− **

*0T

*T

IrrinternalirrevN

Theat

source1

2rev

2irrev

s

equivalent to a throtling


Cyclic Heat Input

Introduction to Irreversible non-Carnot Closed Cycles

( )1rev2rev21

mqrev21irrev12

qmqrevinputheat

rev2irrev2rev2irrev2

ssTmQQ

sTmQQTThh

−==

∆==

≅⇒=

−− ,

( )rev2irrev2irrev sss ,, −=∆


Cyclic Heat Output

Introduction to Irreversible non-Carnot Closed Cycles

( )3rev4rev43

mqrev43irrev34

qmqrevinputheat

rev4irrev4rev4irrev4

ssTmQQ

sTmQQTThh

−==

∆==

≅⇒=

−− ,

3

4,rev4,irrev

T

s

heatsinkT0

equivalent to a throttling( )rev2irrev2irrev sss ,, −=∆


Irreversible First Law Efficiency - Engines

Introduction to Irreversible non Carnot Closed Cycles

∆θ+−=

∆−−=

−=+

==η=

−qSLT

gen0

qt3r2

mq

gen00

rev

gen0

rev

reve

rev

irreve

revee

irrevirrevengines

smS

1TT1

sTmST

TT1

QST

QW

QWW

QWFLE

( )TTTT1N

TT1 0Carnot

01N

irrev0

irrev

irrev,η=−<−=η

>

Where T is the temperature of the heat source and, is a second law of thermodynamics correction

function linking the heat transfer to the involved mean thermodynamic temperatures

t3r2mq

SLT TT−=θ

Enlarged System Entropy Balance Equation

0TQN

T

Q

0

0irrev =+−


Irreversible First Law Efficiency - Refrigeration Cycles


rev

gen00

TT

rev

irrevloste

rev

reve

irrevloste

reve

rev

e

rev0W

eirrev

irrevionrefrigerat

QST

TT1

1

QW

QW

1

WWQ

WQ

WQCOPFLE

0

e

−−−=

+−=

+−=−===

<

<

,

,

∆θ+−

−=

∆θ−−

−=

−qSLT

gen0

qt5r4

mqSLT

gen00irrev

smS

1TT1

1

sTmST

TT1

1COP

( )0Carnot0

1N

irrev0

qSLT

gen0

irrev TTCOPTT

TTNT

T

Tsm

S1T

TCOPirrev

,=−

<−

=

−

∆θ+

=>

t5r4mq

SLT TT−=θWhere T is the temperature of the heat source and, is a second law of thermodynamics correction

function linking the heat transfer to the involved mean thermodynamic temperatures

Enlarged System Entropy Balance Equation

0TQN

T

Q

0

0irrev =+−


Conclusions

1. ηirrev and COPirrev includes explicitly the overall irreversibility (internal and external one)

2. has the meaning of the overall number of irreversibility, it evaluates both

the external irreversibility due to the heat transfer at finite temperature differences, and the internal ones.

3. When Sgen → 0 then Nirrev → 1 ,

4. The correction function θSLT links the heat input at temperature T to the heat absorbed by the working

fluid at temperature Tmq < T

∆θ+=

qSLT

genirrev sm

S1N



Conclusions – Engines

T0 = 273,15 K

( )TTTT1N

TT1FLE 0Carnot

01N

irrev0

irrevirrevengines

irrev,η=−<−=η=

>



Conclusions – Refrigeration cycles

T0 + 293,15 K


( )0Carnot0

1N

irrev0

qSLT

gen0

irrev TTCOPTT

TTNT

T

Tsm

S1T

TCOPirrev

,=−

<−

=

−

∆θ+

=>

INFLUENCE OF WORKING FLUID PROPERTIES ON INTERNAL IRREVERSIBILITY OF POWER SYSTEMS

Gheorghe DUMITRASCU

Engineering Thermodynamics, Thermal Machines, and Refrigeration Dept.,

“Gh. Asachi” Technical University of Iasi,

ROMANIA,

[email protected], http://www.tuiasi.ro


mailto:[email protected]


THE WAY TO OPTIMIZE THE IRREVERSIBLE CYCLES

The optimization of cycles: first and second law efficiencies (exergy analysis), entropy generation minimization, and sometimes Novikov–Curzon–Ahlborn maximum power issue.

The paper presents a concise method to evaluate directly the irreversibility, inside a unique criterion uniting first and second laws, called here the irreversible first law efficiency.

Key words: NTUS, second law effectiveness of external heat exchangesirreversible maximum power,number of internal irreversibility, number of external irreversibilityirreversible first law efficiency


Presenter

Presentation Notes

Vezi Novikov-Curzon-Ahlborn issue, format pdf, atasat la e-mail and Consideratii privind posibilitatea definirii Irreversible First Law Efficiency, format pdf, atasat la e-mail

Engines Reversibility Principle- engineering realm -

The possible ideal engine cycles in temperature – entropy diagram

s1=s2 s3=s4

3

4

2 3

1 4

T

T

T0

dT

dT0

QR

2

s

c1-2=c3-4 ( )04312 ln TTcssss n=−=−

TT

rev01−=η

Any ideal cycle is characterized by no entropy generation

All Complete Reversible Engine Cycles

.0Sgen =

Non – CARNOT complete Reversible Engine Cycles


Presenter

Presentation Notes

Vezi Novikov-Curzon-Ahlborn issue, format pdf, atasat la e-mail and Consideratii privind posibilitatea definirii Irreversible First Law Efficiency, format pdf, atasat la e-mail

Introduction“Optimization of Irreversible Cycles” , FTT or FST

The ideal cycles are characterized by no entropy generation,

The Finite Time Thermodynamics (FTT), or Finite Speed Thermodynamics (FST) is a featureof the originator works of:

CHAMBADAL (1957) and NOVIKOV (1958) – studies about nuclear cycles, CURZON et AHLBORN (1975) – the time-based thermodynamic analysis in view of the real

heat transfer made at finite temperature difference, YAN et al. (1989), GROSU et al. (2004), CHEN et al. (1997, 1999) – analyzed the

irreversible cycles with three external heat sinks

THE IDEAL REVERSIBLE CYCLES ARE CONSIDERED AS USELESS, THEY MIGHT SUPPLY THEMAXIMUM ENGINES WORK, BUT NO POWER. THE REQUIRED TIME BY THE REVERSIBLE

HEAT TRANSFER AT INFINITESIMAL TEMPERATURE DIFFERENCE REQUIRES AN INFINITEPROCESS TIME (I.E. THE POWER, WHICH IS RATIO WORK PER TIME IS IN FACT ZERO).

.0Sgen =


Presenter

Presentation Notes

The Irreversible First Law EfficiencyExternal Irreversibility

Endo-Reversible CARNOT Engine

The second law effectiveness of the heat exchange with the heat source

T

s

T

T0

∆T

∆T0

3

1 4

2

Heat exchanger at the hot reservoir

Heat exchanger at the cold sink

Endoreversible

CARNOT cycleqsm

UANTUS∆

=

Number of Transfer Units per Reversible Entropy Variationdue to reversible heat transfer

( ) revq QsTTmTUAQ

=∆∆−=∆=

Basic Equations

⇒+

=∆1NTUS

1TT ( )1NTUS

NTUSsTmsTTmQ qq +∆=∆∆−=

( ) ⇒<+

==ε∞→

11NTUS

NTUSQ

Q

NTUSII

The second law effectiveness at the heat exchange at the hot reservoir

( ) 0T ss

sTmQQQ

NTUSqq

qIIrev

IINTUSII

→∆∆=∆

⇒∆ε=ε=ε=

∞→

∞→

,max

revQQ max <


Presenter

Presentation Notes

For the sake of simplicity we supposed for CARNOT sq = (sq )A = sq0

The second law effectiveness of the heat exchange with the heat sinkT

s

T

T0

∆T

∆T0

3

1 4

2

Heat exchanger at the heat source

Heat exchanger at the heat sink

EndoreversibleCARNOT cycle

Basic Equations

The second law effectiveness of the heat exchange at the cold sink

0q

000 sm

AUNTUS,∆

=

( ) 0q000000 sTTmTAUQ ,∆∆+=∆=

⇒−

=∆1NTUS

1TT0

00 ( )1NTUS

NTUSsTmsTTmQ0

00q00q000 −

∆=∆∆−= ,,

( ) ⇒>−

==ε∞→

11NTUS

NTUSQ

Q

0

0

NTUS0

00II

0

, ( )0T ss

sTmQQQ

0NTUS0q0q

0q00II0IINTUS000

0

0

→∆∆=∆

⇒∆ε=ε=ε=

∞→

∞→

,,,

,,min,

minQQ0 >


Number of Transfer Units per Reversible Entropy Variationdue to reversible heat transfer



Presenter

Presentation Notes

For the sake of simplicity we supposed also sq,0 = (sq,0 )A = sq = (sq )A

The dependence second law effectiveness – NTUS

0 0.5 1 1.5 2

∞→NTUS Decreasing

irreversibility: 0→∆T

sTmQQ ∆=→

max

0NTUS←∞ Decreasing

irreversibility: 00 T∆←

0min0 QQsTm

←=∆

ε → 1 The best way

1 ← ε0 The best way




The Power

εε

τ−ε∆=

εε

−ε=

−=−=

II

0IIIIq

II

0IIII

00

11sTmQ

Q1Q

Q

Q1QQQP ,,

max

minmax

The Irreversible First Law Efficiency

extirrII

0III N1111 ,

,

τ−=

εε

τ−=η

The Second Law Efficiency

11N11

N11IIextirr

extirr

II =η⇒→⇒

τ−

τ−

=η ,

,




Considerations on the Real Power Cycles

The real power cycles are also internally irreversible, respectively: the heat transfer processes, 2–3 and 4–1, are non-isothermal; the adiabatic processes, 2–3 and 4–1, are non-isentropic; the external heat reservoirs have finite heat capacities, respectively are non-

isothermal; the mean log temperature difference pertaining to the heat transfers has a value that it

is not equalizing the difference of the mean thermodynamic temperatures.

This dissimilarity can be solved step by step by introducing the necessary amendment coefficients in order to take into account also the internal irreversibility.


The second law effectiveness of the heat exchange with the heat source

qsmUANTUS∆

=

Number of Transfer Units per Entropy Variation

Basic Equations

The second law effectiveness at the heat source

Tmq0

TmqΔTmq

ΔTmq0

T

s( ) qmqmqTmq sTTmCTUAQ ∆∆−=∆= ∆

⇒+⋅

=∆∆ 1CNTUS

1TTT

mqmq ( )1CNTUS

CNTUSsTmsTTmQT

Tqmqmqmq +⋅

⋅∆=∆∆−=

∆

∆

( ) ⇒<+⋅

⋅==ε

∆

∆∆

→∞→∞

11CNTUS

CNTUSCQ

Q

T

Ts

ANTUSII q

( )

( )→∞

→∞∆∆

→∞→∞

∆∆

=∆

∆=

⇒∆ε=ε=

ANTUSq

qs

mq

treansferheat

meanT

ANTUSqmqIIII

ss

C T

TC

sTmQQ

q,

max

maxQQ <


Any Endo-Reversible Engine


Presenter

Presentation Notes

Aici am considerat ca sq corespunde unui schimbator de caldura si am adoptat conventia de la (first law) effectiveness of Hex pentru evaluarea fluxului termic maxim maximorum.

The second law effectiveness of the heat exchange with the heat sink

0q

000 sm

AUNTUS∆

=

Number of Transfer Units per Entropy Variation

Basic Equations

The second law effectiveness at the heat sink

Tmq0

TmqΔTmq

ΔTmq0

T

s( ) 0q0mq0mq0mq000 sTTmCTAUQ

0T∆∆+=∆=

∆

⇒−⋅

=∆∆ 1CNTUS

1TT0T0

0mq0mq ( )1CNTUS

CNTUSsTmsTTmQ0T0

0T00q0mq0q0mq0mq0 −⋅

⋅∆=∆∆−=

∆

∆

( ) ⇒>−⋅

⋅==ε

∆

∆∆

→∞→∞

11CNTUS

CNTUSCQ

Q

0T0

0T0s

ANTUS0

00II 0q

0

,

( )→∞

→∞∆∆

→∞→∞

∆∆

=∆

∆=

∆ε=ε=

ANTUS0q

0qs

mq

treansferheat

mean0T

ANTUS0q0mq0II0II0

00q s

sC

TTC

sTmQQ

,

,min,

minQQ0 >⇒


Any Endo-Reversible Engine


Presenter

Presentation Notes

Aici am considerat ca sq0 corespunde unui schimbator de caldura si am adoptat conventia de la (first law) effectiveness of Hex pentru evaluarea fluxului termic minim minimorum.

1 – 2r irreversible adiabatic compression, 2r – 3r irreversible heating 3r – 4r irreversible adiabatic expansion, 4r – 1 irreversible cooling

r2t3q sss −=∆

int,irrq

14irr

43irr

32irr

21irrq

t5r40q

Ns

sssss

sss

⋅∆=

=∆+∆+∆+∆+=

−=∆−−−−

( )1

ss

1Nq

irrirr >

∆

∆+= ∑ int

int,

4t

1=5r

2t 2r

3t 3r

4r

5t

21irrs −∆

32irrs −∆

43irrs −∆

14irrs −∆

s

T

The Irreversible First Law EfficiencyInternal Irreversibility

Any Basic Irreversible Engine


Presenter

Presentation Notes

Nu putem suprapune un ciclu teoretic echivalent peste ciclul real (nu avem unul unic) dar putem compara procele ireversibile cu cele ireversibile

engineintirrt3r2

mq

t5r4mq

qt3r2

mq

0qt5r4

mq

t3r2

t5r40

t3r2engine

NTT

1sTmsTm

1

Q

Q1

QP

,−

−

−

−

−

−

−

−=∆⋅⋅

∆⋅⋅−=

=−==η

4t

1=5r

2t 2r

3t 3r

4r

5t

21irrs −∆

32irrs −∆

43irrs −∆

14irrs −∆

s

T




4t

1=5r

2t 2r

3t 3r

4r

5t

21irrs −∆

32irrs −∆

43irrs −∆

14irrs −∆

s

T 1T

TC

sTmsTm

QQ

mq

t3r2mq

sqmq

qt3r2

mq32

t3r2

II q<=

∆

∆==ε

−

∆

−

−

−

max

1TT

CsTmsTm

QQ

0mq

t5r4mq

s0q0mq

0qt5r4

mq54

t5r4

0II 0q>=

∆

∆==ε

−

∆

−

−

−

min,

1C

CN

0q

q

s

s

II

0IIextirr >

εε

=∆

∆,,

int,,int,,

irrextirrirrs

s

II

0II

mq

0mqengine NN11N

C

C

TT

10q

q ⋅τ

−=εε

−=η∆

∆

The Irreversible First Law EfficiencyExternal and Internal Irreversibility



1 – 2r irreversible adiabatic compression, 2r – 3r internal irreversible heating by heat regeneration, 3r – 4r irreversible heating, 4r – 5r irreversible adiabatic

expansion, 5r – 6r internal irreversible cooling by heat regeneration, 6r – 1 irreversible cooling.

4t

1=7r

2t 2r

3t3r

4r

6t

T

s

5r5t6r

7t


Any Irreversible Engine with Internal Heat Transfer (Internal Regeneration of Heat)

r3t443q ssss −=∆=∆ −

( ) ( )r6t5t6r5

mqr2t3t3r2

mq ssTssT −=− −−

( )

76irr

65irr

54irr

43irr

32irr

21irr

t6r5mq

t3r2mq

r2t3qt7r60q

ssssss

TT

1ssssss

−−−−−−

−

−

∆+∆+∆+∆+∆+∆

+

−−+∆=−=∆




4t

1=7r

2t 2r

3t3r

4r

6t

T

s

5r5t6r

7t

( ) ( ) 1TT

1s

ssss

1N t6r5mq

t3r2mq

q

r2t3

q

irrirr >

−

∆−

+∆

∆+= −

−∑ intint,

int,irrt4r3mq

t7r6mq

qt4r3

mq

0qt7r6

mq0engine

NTT

1

sTmsTm

1Q

Q1

QW

−

−

−

−

−=

=∆⋅⋅

∆⋅⋅−=−==η




4t

1=7r

2t 2r

3t3r

4r

6t

T

s

5r5t

6r

7t

0

0 ,0,int

, ,int

1

11

εη

ε

τ

∆

∆

= − =

= − ⋅ ⋅

q

q

smq IIengine irr

mq II s

irr ext irr

CTN

T C

N N


Any Irreversible Co-generation Engine

r2t332q ssss −=∆=∆ −

( )

∆

∆+∆=∆

+∆=−=∆=∆

∑∑=

=

−

−

q

engineirr

q

1432y

4321x

yxirr

qt6r4140q

ss

1ss

sssss

int,,,

,,,

( )

∆

∆−∆+∆=∆−∆=−=∆=∆ ∑

−−q

cogengine

irrqcog14t6t515

cog0q s

ss1sssssss int

,




( )

cogirrt3r2

mq

t6r4mq

32t3r2

mq

54t5r4

mq14t6r4

mq

32

5414

32

54overall

NTT

1

sTmsTsTm

1

Q

QQ1

Q

QP

int,−

−

−−

−−

−−

−

−−

−

−

−=

=∆⋅⋅

∆⋅−∆⋅⋅−

=−

−=+

=η

( )

∆

∆−

∆

∆+=

−−

−

−

∑32

cogt6r4

mq

t5r4mq

32

engineirrcog

irr ss

TT

ss

1N intint, For endo-reversibility 0Ncog

irr →int,




For endo-reversibility and 0Ncogirr →int,

int,,

int,,

irrextirr

irrs

s

II

0II

mq

0mqoverall

NN11

NC

C

TT

10q

q

τ−=

=εε

−=η∆

∆

1overall →η


Numerical Results

The computational procedure assumed the following restrictive conditions. Variable heat capacities of gases, fourth degree temperature polynomials;Adiabatic exponents of the reversible processes computed as the ratio of enthalpy variation to internal energy variation.In the case of engine heated by combustion, they were considered negligible dissociation during combustion, and the mass and energy balance equations of combustion gave the flue gases composition, the excess air value, and the fuel mass flow rate.


Numerical Results

First Figures compare the oxy-combustion with 90% mass fraction of O2 in the oxygenated air, and the air combustion, for an open Joule – Brayton cogeneration cycle. The restrictive conditions were: maximum temperature on the cycle, 1200°C; isentropic efficiency of the compressor, 0.88; isentropic efficiency of the gas turbine, 0.94; pressure loss coefficient in the combustion chamber, 0.98; the fuel mass composition of 15% H2 and 85% C; higher heating value of the fuel ~46,000 kJ/kg.Next Figures compare six possible working fluids, air, O2, N2, CO2, H2 and He, in a closed Joule –Brayton engine cycle externally heated, e.g. by solar energy. The restrictive conditions were: maximum temperature on the cycle, 1000°C; the minimum temperature on the cycle, 20°C; isentropic efficiency of the compressor, 0.88; isentropic efficiency of the gas turbine, 0.94; pressure loss coefficient in the heat exchanger connecting the external hot source, 0.98; pressure loss coefficient in the heat exchanger connecting the external cold sink, 0.98; variable heat capacities; adiabatic exponent computed as the ratio of heat capacities at constant pressure and constant volume.


Numerical Results

The dependence number of internal irreversibility – compression ratio for the basic engine cycle


Numerical Results

The dependence overall number of internal irreversibility – compression ratio for the cogeneration cycle


Numerical Results

The dependence specific power output on compression ratio for the basic engine cycle


Numerical Results

The dependence irreversible first law efficiency (thermodynamic efficiency) on compression ratio for the basic engine cycle


Numerical Results

Comparison of the dependence irreversible first law efficiency (thermodynamic efficiency) on compression ratio for both the basic engine cycle and the engine cycle with internal regeneration of heat, only for

CO2 as working fluid


Numerical Results

The dependence number of internal irreversibility on compression ratio for the basic engine cycle


Conclusions

This paper deals with a new optimization criteria, the irreversible first law efficiency applied to the real cycles. This new approach emphasizes the overall irreversibility by the means of the numbers of internal and external irreversibility, directly inside the first law efficiency.It yields that the maximum power is not unique, as it was assumed untill now, respectively depends on the nature of the working fluid and on the restrictive conditions.The irreversible first law efficiency conducts to the reversible limit, i.e. the reversible Carnot engine, respectively offers the simplest comparison.


Conclusions

For complex cycles, we have only to deal carefully with the entropy variations and thermal interactions during the heat transfer processes.

Important remark: the second law effectiveness, defined in this paper, takes into account only the thermal interactions connecting the working fluids with external heat reservoirs, the internal heat exchanges of complex cycles, e.g. in the case of combined cycles, the heat transfer between the top cycle and the bottom one is included in the number of internal irreversibility; for instance, refer to the simple manner to manage the internal heat exchange of Power Cycles with Internal Heat Transfer.


Conclusions

The direct method presented in this presentation is a concise one, equivalent to exergy analysis, since the lost exergy is proportional to the entropy irreversibly generated. The comparison of possible fluids used in a closed Joule – Brayton cycle, externally heated, shows that CO2 offers a substantial potential for internal regeneration of heat, see the below table, that includes the difference of temperatures of the fluid leaving the turbine and the compressor.


Conclusions

Table 1. The difference between temperatures of the fluid leaving the turbine and the compressor, [°C]

Compression Ratio Air O2 N2 CO2 He H2

5,00 401 423 397 593 123 367

10,00 158 191 152 431 41 115

15,00 17 57 9 337

20,00 272

25,00 221



Mechanical and Automotive Engineering Department

Prof. PhD, Michel FEIDTINSTITUT NATIONAL POLYTECHNIQUE DE LORRAINE ET UNIVERSITE HENRI POINCARE

LABORATOIRE D'ENERGETIQUE ET DE MECANIQUE THEORIQUE ET APPLIQUEEC.N.R.S. UMR 7563

1LLLP ERASMUS - NANCY - 2013

The Influences of the Condenser and Evaporator Effectiveness on the Heat Pump Performances

Overview

1. Introduction

2. Mathematical model

3. Results and discussion

4. Conclusions

2LLLP ERASMUS - NANCY - 2013

1. Introduction First and Second Laws Relationship – CV-HP

• First Law – Energy Balance

3

4t1

2t 2r

3t3r

4r1t

s

T

21irrs −∆

32irrs −∆

43irrs −∆

14irrs −∆

( )int∑∆+∆=

∆+∆+∆+∆+∆=−=∆

−=∆−−−−

irrevq

43irrev

32irrev

21irrev

14irrevqr2t30q

r4t1q

ss

ssssssss

sss


( )( )

0QQQQW

0sTmssTmQQQ

0sTmssTmQQQ

00

0qt3r2

mqr2t3t3r2

mqt3r2c0

qt1r4

mqr4t1t1r4

mqt1r4e

<−=+=

<∆=−===

>∆=−===−−

−

−−−


• First Law – Energy Balance

4

4t1

2t 2r

3t3r

4r1t

s

T

21irrs −∆

32irrs −∆

43irrs −∆

14irrs −∆

( )

1IrrTT

IrrTT

1NTT

NTT

1QQ

QQ

sTsTmsTm

QQQ

COP

e

c

e

cge

HP

irrt1r4mq

t3r2mq

irrt1r4mq

t3r2mq

0

0

qt1r4

mq0qt3r2

mq

0qt3r2

mq

0

0HP

−=

−=

−

=

=∆−∆

∆=

−=

−

−

−

−

−−

−

..

int,

int,

( )c

e32

ref

t3r2mq

irrq

irrirr T

TT

TNIrr or, 1

ss

1N −

−

=>∆

∆+= ∑

int,int

int,



• Second Law – entropy balance• Internal irreversibility

5

4t1

2t 2r

3t3r

4r1t

s

T

21irrs −∆

32irrs −∆

43irrs −∆

14irrs −∆

0TQ

IrrTQ HP)-(CV e.g.or

0TQ

IrrTQor 0

TQ

NT

Q

c

c

e

e

32ref

014

reft3r2

mq

0irrt1r4

mq

=−

=−=− −−−−

int,



• United First and Second Laws

6

4t1

2t 2r

3t3r

4r1t

s

T

21irrs −∆

32irrs −∆

43irrs −∆

14irrs −∆

1COP

COPCOPR where

TTCOPRIrr HP)-(CV e.g.or

TTCOPRIrror

TT

COPRN

HP

HP

c

e

32ref

14ref

t3r2mq

t1r4mq

irr

−=

=

== −

−

−

−

int,



7

Thermal Relationships of a Solar Assisted Compression

Vapor Heat Pump (CV-HP)

SC

E

K

CTV

Tsco Tsci

Tho Thi



8

• Solar collector

– Collector temperature under non-flow conditions

– Collector plate temperature

– Inlet temperature of the solar heat carrier

– Outlet temperature of the solar heat carrier

ηo is optical efficiency of solar collector, Ta is environmental temperature, UL is solar collector

heat-loss coefficient; εsc is solar collector effectiveness; I is total solar radiation.

L

oas U

ITT η+=

L

sssc U

ITT η−=

scsc

sscsci C

IATTε

η−=

sc

sscisco C

IATT

η+=



9

• Heating systemInlet/outlet temperatures of the useful heat carrier, were imposed by considering that the

heating system asks:

at Ta = TaN = 253.15K, Thi = ThiN = 323.15K and, Tho = ThoN = 333.15K;

at Ta = TaS = 288.15K, Thi = ThiS = 303.15K;

for 253.15 K < Ta < 288.15 K:

Troom = 295.15K.

807143.4675714286.0 +⋅−≅ aho TT


( )( ) ( )ahi

aNroom

aroom

hoNhiN

hohi

aNheating

aheating TTTTTT

TTTT

TQTQ

⇒−−

≅−−

=


10

• Evaporator

evaporator heat rate

evaporator temperature

Where εe is evaporator effectiveness.


( )sciscosce TTCQ −=

sce

escoe C

QTT

ε−=


11

• Heat pump irreversibility (entropy and energy balance)

cc

c

e

e Q 0TQ

TQIrr

⇒=−

( )c

e

c

e

HP

HP

TTCOPR

TT

COP1COPIrr =

+=



12

• CondenserCondensing temperature

Where εc is condenser effectiveness

hc

choc C

QTT

ε+=


By CoolPack, and for adopted restrictive conditions inside the heatpump, it was interpolated, by square roots, the irreversibility, for303.15K < Tc < 338.15K, and, 258.15K < Te < 288.15K:

• refrigerant R22, errors: +1.1%, – 3.1%


• refrigerant R410A, errors: +1.1%, – 6.6%

• refrigerant R407c, errors: +1.1%, – 4.9%


• refrigerant R134a, errors: +1.1%, – 3.6%


13

e

c

TT8506271909710030COPR .. +−=

e

c

TT5683381602290COPR .. +−=

e

c

TT5512542683264721COPR .. +−=

e

c

TT27284443123710456421COPR .. +−=

e

c

TT9518862751023481361COPR .. +−=

e

c

TT9103469052197969440COPR .. +−=



14

• Power balance

cece QQQQW −=+=

WQ

COP cHP

=



• The correlated compilation of previous equations allowed in MathLab to find out numerical results, depending only on εeand εc. Figures 2 to 5 show selected numerical results for:

15

75.0;75.0;1000;1000

;2;95.0;50;15.273 22

====

====

scshsc

Loa

KgKJC

KgKJC

KmWU

mWIKT

εη

η



16

Fig.2. R22

Fig.3. R717

( )ceW εε ,

( )ceW εε ,



17

Fig.4. R22

Fig.5. R717

( )ceHPCOP εε ,

( )ceHPCOP εε ,


18

3. ConclusionsThe presentation presents a mathematical algorithmable in modeling the influences of evaporator andcondenser effectiveness upon the all operationalfeatures of a heat pump: power, heat rates, andtemperatures. The model start with the external heatsources imposed parameters and, combine these onesby the internal irreversibility of the heat pump (entropybalance).


The “Gheorghe Asachi” Technical University of Iasi...

Documents

Transcript of The “Gheorghe Asachi” Technical University of Iasi...