Exergy Analysis.ppt

8/9/2019 Exergy Analysis.ppt

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Exergy Analysis

ME 210 AdvancedThermodynamics


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Definitions

Exergy (also called Availability or Work otential!" themaxim#m #sef#l $ork that can be obtained from a system ata given state in a given environment% in other $ords& the most$ork yo# can get o#t of a system

'#rro#ndings" o#tside the system bo#ndaries Environment" the area of the s#rro#ndings not affected by the

rocess at any oint ()or examle& if yo# have a hot t#rbine&the air next to the t#rbine is $arm* The environment is thearea of the s#rro#ndings far eno#gh a$ay that the

temerat#re isn+t affected*! Dead 'tate" $hen a system is in thermodynamic e,#ilibri#m

$ith the environment& denoted by a s#bscrit -ero% at thisoint no more $ork can be done


3/30

Examle

A coal.fired f#rnace is #sed in a o$er lant* /t delivers000 kW at 1000 * The environment is at 00 * Whatis the exergy of the added heat3 4o# can #se t$o stes

to solve this roblem* Determine the maxim#m ercentage of the heat that can beconverted to $ork*

5sing yo#r ans$er from the first art& determine the maxim#m$ork ossible*

This is the maxim#m $ork o#t#t ossible bet$een thegiven state and the dead state& i*e*& the heat+s exergy* /nthis case& 06 of the 000 kW is unavailable energy7itcan+t be converted to $ork*


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Why 't#dy Exergy3

/n the last several decades& exergy analysis has

beg#n to be #sed for system otimi-ation*

8y analy-ing the exergy destroyed by eachcomonent in a rocess& $e can see $here $e

sho#ld be foc#sing o#r efforts to imrove system

efficiency*

/t can also be #sed to comare comonents orsystems to hel make informed design decisions*


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9eversible Work

Wrev(reversible $ork!" the maxim#m amo#nt of$ork it+s ossible to rod#ce (or minim#mnecessary to in#t! in a rocess bet$een giveninitial and final states* :ote that this is differentfrom an isentroic rocess $here $e $ere givenan inlet state and solved for the exit state #sings2;s1* 'ince the exit and inlet states are both

fixed& the rocess is not necessarily isentroic* What t$o conditions $ill ca#se a rocess to beisentroic3


6/30

/rreversibilities

/rreversibility& /" exergy destroyed% $asted

$ork otential* /t reresents energy that

co#ld have been converted into $ork b#t$as instead $asted

What are some so#rces of /3

To have high system efficiency& $e $ant /to be as small as ossible*


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/& cont*

/;Wrev& o#t


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'#rro#ndings Work& Ws#rr

>ere some $ork is

#sed to #sh the

atmosheric air (thes#rro#ndings! o#t of

the $ay% that $ork

can+t be #sed forother #roses*

( ) positive1200 == VVPdVPWsurr


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'#rro#ndings Work& Ws#rr& cont* >ere atm hels #sh the

iston in% this is gained

$ork* /n a rocess $here

the iston goes in and o#t

contin#ally& the s#rro#nding

$ork val#es cancel o#t*

What is Ws#rrfor a control

vol#me3

( ) negative120 VVPWsurr =


10/30

'econd ?a$ Efficiency& //

Thermal efficiency tells #s $hat $e get o#t

comared to $hat $e #t in*

The second la$ efficiency tells #s ho$

m#ch $e get o#t comared to the

maxim#m ossible $e co#ld get o#t& given

the inlet and exit conditions*


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'econd ?a$ Efficiency& cont*

th&max;1.T?@T>;1.00@00;0*B 'ay th;0*C//;0*C@0*B2;0*2 We $ant a high th and //Another $ay to look at this" for

a $ork o#t#t device

//;W#@Wrev


12/30

'econd ?a$ Efficiency& cont*

A general definition"

suppliedexergy

(I)destroyedexergy1

beginning)at theavailables(what'suppliedexergyprocess)after theavailables(what'recoveredexergy

=

=II


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Three Efficiency Definitions

The second t$o are defined for $ork

=5T5T devices

rev

uII

isentropic

actual

in

net

W

W

W

W

Q

W

=

=

=

Law2

Isentropic

Theral

nd

s

th


14/30

Examle

A free-er is maintained at 20) by

removing heat from it at a rate of

8t#@min* The o$er in#t to the free-er is0*0 h& and the s#rro#nding air is )*

Determine a! the reversible o$er& b! the

irreversibility& an c! the second.la$efficiency of this free-er*

9ef" Fengel G 8oles& Thermodynamics& An Engineering Aroach& Cth edition& Mc.Hra$ >ill& 2002*!"


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Exergy

We can calc#late the exergy& I ($ork otential! at a givenstate* The $ork otential is a f#nction of the total energy of thesystem*

(remember that in a control mass& there $ill be no flo$ $ork!

IE(exergy d#e to kinetic energy!" J2

@2 (on a er #nit massbasis IE" gK

Iinternalenergy" #.#oLo(v.vo!.To(s.s0!

To see a derivation of this last e,#ation& see the aendices on

the $eb site* The oN stands for the dead state (atmoshericconditions!* /f a iston is at atmosheric ress#re andtemerat#re (the dead state!& it can+t do any $ork*

!" #" internal energy flow wor$ X X X X X= + + +


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Exergy of a Flosed 'ystem

Exergy of a closed system& er #nit mass , can befo#nd be adding all the terms

This gives #s the maxim#m $ork $e co#ld ossibly geto#t of a system*

5s#ally $e $ill be more interested in the change in

exergy from the beginning to end of a rocess* )or a closed system&

( ) ( ) ( )

2

2o o o o oV

u u P v v T s s gZ = + + +

2 1 % = =


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)or a control vol#me

Icv;IclosedLIflo$$ork;Icv@m (exergy er #nit mass! Iflo$ $ork;Wflo$.Wagainstatmos(here;v.ov

:o$ combine terms" #Lv;h% #oLovo;ho

( ) ( ) oooooooocv vPPvgzV

ssTvPvPuu ++++=2

2

( ) ( ) gzV

ssThh ooocv ++= 2

2


18/30

Fhange in exergy

/f $e only have one fl#id stream

/f $e have m#ltile streams

( ) ( ) ( )122

12

2121212

2zzg

VVssThh o +

+==

++

++=

1

21

1112

22

222

22

gzV

sThmgzV

sThm oo


19/30

Exergy 8alance We $ill #se these e,#ations in an exergy balance to

solve for s#ch ,#antities as reversible $ork or exergydestroyed*

Iin.Io#t.Idestroyed;Isys

Idestroyed is otential $ork that $as destroyed d#e toirreversibilities like friction*

Exergy can be transferred (Iin.Io#t! by heat& $ork& andmass flo$


20/30

Exergy Transfer by >eat Transfer

As $e add heat to a system& $e

increase its ability to do $ork*

'ee Aendix 8 on $eb for adisc#ssion of ho$ to deal $ith cold

sinks*

===H

oHHheatT

TQQXW 1axax


21/30

Exergy Transfer by Work and Mass

)lo$ /f $e do $ork on a system& $e increase its

ability to do $ork*

I$ork;W.Ws#rr for bo#ndary $ork I$ork;W for all other kinds of $ork

9emember

Imass;m

( )120 VVPWsurr =


22/30

Idestroyed

Idestroyed;/;To'gen

'ee Aendix F on the $eb for a

derivation*

9evie$ from ME 2O

'sys;'in.'o#tL'gen


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Entroy Henerated& 'gen

)or a steady.state control vol#me& this leads #s to

)or a control mass& this becomes

>ere Tkis the temerat#re of the heat so#rce or heatsink (not the system temerat#re!*

=k

k

in

ii

out

eegenT

QsmsmS

=k

kgen

T

QSSS 12


24/30

)inal E,#ation for Isys for control

mass

( )[ ] 12121 XXSTVVPWQT

Tgenook

k

o =

P Terms in Q R are W.Ws#rr;W#

P /f $e $ant to find Wrev& then To'gen;0 and

W#;Wrev

P :ote that if heat transfer is to@from the

s#rro#ndings& the S term dros o#t*


25/30

Examle

A 12.ftrigid tank contains 9.1Ca at 0 sia

and C06 ,#ality* >eat is transferred no$ to the

refrigerant from a so#rce at 120) #ntil theress#re rises to B0 sia* Ass#ming the

s#rro#ndings to be at )& determine a! the

amo#nt of heat transfer bet$een the so#rce and

the refrigerant and b! the exergy destroyedd#ring the rocess*

9ef" Fengel and 8oles


26/30

)inal E,#ation for Isys for control

vol#me

( )[ ] 12121 XXmmSTVVPWQ

T

Teeiigenook

k

o =+

( ) 01 =+

eigenok

k

o

mSTWQT

T

)or m#ltile fl#id streams& #nsteady flo$"

)or one fl#id streams& steady flo$"

To find Wrev& set 'gen;0* /f adiabatic& S;0*


27/30

'et # the follo$ing roblems*

1* 9efrigerant at T1 and 1is throttled to a ress#re of 2*)ind the reversible $ork and exergy destroyed d#ringthis rocess* The atmoshere has a temerat#re of To*

2* Air at T1and 1$ith a velocity of J1enters a no--le andexits at 2and T2$ith a velocity of J2* There is a heatloss S from the no--le to the s#rro#ndings at To* )indthe exergy destroyed d#ring this rocess*

* Air enters a comressor at ambient conditions (Toand

o! and leaves at 2and T2* The comressor isdeliberately cooled& and there is a rate of heat loss of Sto the s#rro#ndings* The o$er in#t to the comressoris W9* )ind the rate of irreversibility& /& for this rocess*


28/30

Examle

'ee hando#t


29/30

Exergy Analysis for a Fycle& 1 fl#id

stream& steady flo$

( )

=

+

+

+

=

+++=

=

=

ink

in

outk

outo

lake

incond

o

turbine

chambercomb

boiler

o

pump

condgenturbinegenboilergenpumpgengen

kiegen

geno

T

Q

T

QmTI

T

Qss

T

Qss

T

Qss

T

Qssm

SSSSS

T

QssmS

STI

&&

&1

212

&&&&

*coponentafor


30/30

'econd ?a$ Efficiency for a Fycle

IW

W

W

W

actualnet

actualnet

reversiblenet

actualnet

II

+==

&

&

&

&

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Exergy Analysis.ppt

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