CHAPTER 5 ENTROPY GENERATION...Lost Available Work 0 0 ¦ ¦ ¦ t out n i in i gen ms ms T Q dt dS S...
Transcript of CHAPTER 5 ENTROPY GENERATION...Lost Available Work 0 0 ¦ ¦ ¦ t out n i in i gen ms ms T Q dt dS S...
CHAPTER 5 – ENTROPY GENERATION
Instructor:
Prof. Dr. Uğur Atikol
Chapter 5 Entropy Generation (Exergy Destruction) Outline
Lost Available Work
Cycles
Heat engine cycles
Refrigeration cycles
Heat pump cycles
Nonflow Processes
Steady-Flow Processes
Exergy wheel diagrams
System
in
out
Reservoir at T1
Reservoir at T2
Reservoir at Tn
...
Atmospheric temperature and pressure reservoir
at ( ,PoTo )
Lost Available Work
inm
outmdt
dVPWWu 0
0Q
1Q 2Q nQ
0P
dt
dVdt
dVP0
(All modes of work transfer)
uW
W
Atmosphere
magneticshearelectrical WWWdt
dVPW
atmosphereeagainst th
doneWork
Lost Available Work
00
out
n
i ini
igen smsm
T
Q
dt
dSS
out
on
i in
o
i hmhmWQdt
dE
0
Note: is known as methalpy, such that
gzV
hho 2
2
oh
inmoutmSystem
T1 T2 Tn
T0
W
0Q
1Q2Q nQ
First law:
Second law:
Lost Available Work
00
out
n
i ini
igen smsm
T
Q
dt
dSS
out
on
i in
o
i hmhmWQdt
dE
0
genlost
revlostgenrev
out
on
i in
o
i
i
rev
gen
gen
n
i out
o
in
o
i
i
STW
WWWSTWW
sThmsThmQT
TSTE
dt
dW
S
STsThmsThmQT
TSTE
dt
dW
Q
0
0
0
1
00
0
0
1
000
0
0
Hence
that know however we
:generally Therefore
)()(1)(
:hence zero, is reversibleWhen
)()(1)(
:equations twoebetween th Eliminate
Also known as «exergy destruction Xdes» or «Irreversibility»
Lost Available Work
Work producing devices
Work absorbing devices
0 revout WW
0 revin WW
ve is lostW
ve is lostW
)(remember
negativeor positiveeither becan and although positive always is
WWW
WWW
revlost
revlost
The main purpose of studying the lost available work is to diagnose the areas where irreversibilities are taking place in a prosess so that thermodynamic improvements can be made.
Lost Available Work
gen
out
o
in
o
i
n
i i
W
STsThmsThm
QT
TSTVPE
dt
d
dt
dVPWX
dtdVP
P
000
1
000
0
workavailable of Rate
0
0
)()(
1)(
:such that of rate
worka consumes atmosphere then the pressure hasthat
atmosphere eagainst th work doing is system When the
In most flow systems P0 dV/dt = 0, therefore ẊW = Ẇ (i.e., exergy transfer
by work is simply the work itself)
out
in
out
flow mass with exergy flow of Release
m
in
flow masswith
exergy flow
of Intake
m dt
dΦ exergy nonflow
ofon Accumulati revWX
power mechanical available
ofdelivery Maximum
Lost Available Work
1QXnQQ XX .......................
2
1T 2T nT
),(t Environmen 00 PT
out outin in
mΨ
out
o
mΨ
in
o
i
n
i i
dtdΦ
revW
revrevW
sThmsThmQT
TSTVPE
dt
dX
dt
dVPWX
flow masswith exergy flow of Release
0
flow masswith exergy flow of Intake
0
ferheat transwith sfer Exergy tan
1
0
exergy nonflow ofon Accumulati
00
power available ofdelivery Maximum
0
)()( 1 )(
:limit reversible In the
out
in
out
m
in
m
dt
dΦ
revWX
Lost Available Work
1QXnQQ XX .......................
2
1T 2T nT
),(t Environmen 00 PT
WX
lostWX
Actual work
Lost available work Lost exergy Exergy destruction Irreversibilities
Lost available work is defined as the difference between the maximum available work Wrev and the actual work W. Alternatively it can be defined as:
WrevWlost XXX )(Same as Ẇlost Same as Ẋdes
Lost Available Work
out
m
n
i
QnX
1
in
m
dt
dΦ
revWX WX
lostWX
Exergy inflow Exergy outflow
Exergy balance of the open system discussed can be shown on a flow diagram as follows:
Lost Exergy in Cycles
W
X
i
n
i
Qlost
Q
i
n
i i
revW
XXW
T
TQX
TTQ
QT
TX
revW
)(
1
0
0
1
0
)(
:cyclesin operating systems closed
for work availablelost theTherefore
1
as expressed becan ) , ,(fer heat trans ofcontent Exergy
1)(
is power) available (maximumpower availablefor valueceiling The
cycles. ofnumber integralan in operate that systems closed asConsider
Tn T2 T1
Q1 Q2 Qn Closed system
Cycles
W T0
Heat Engine Cycles
Heat Engine
Sink TL
Ẇ
HQ
LQ
genLlost
H
LHWQlost
L
lost
H
H
L
Lgen
LH
STW
WT
TQXXW
TT
W
T
Q
T
QS
WQQ
H
:as expressed becan Also
1
be toassumed is etemperatur
if follows as expressed becan
0
0
: thatstate laws second andFirst
0
Source TH Obtained by applying the
definition of entropy to the 2 reservoirs. QH is -ve
Heat Engine Cycles
revLQ , revW
HQ
HT
LT
HT
LQ W
HQ
LT
0 0
lostW
Temperature -energy diagram for a heat engine cycle proposed by Adrian Bejan
lostW
genS1tan
gengen
genLlost
L
lost
SS
STW
T
W
1tanor tan
, since
tan
Reversible Irreversible
Heat Engine Cycles
HeatEngine
EQH
II x EQH
De
stru
ction of Exergy
Comparison between the first- and second-law efficiency of a heat-engine cycle
XQH
II XQH
Exergy transfer by heat transfer
H
LHrevWQ
Q
WII
T
TQXX
X
X
H
H
1)( where
HeatEngine
High Temperature Reservoir at TH
Low Temperature Reservoir at TL
QH
QL
W x Q = HI
Heat Engine Cycles Second-law efficiency of a heat-engine cycle can also be expressed as follows:
revW
genL
revW
lostrevW
revW
WII
X
ST
X
WX
X
X
)(1
)(
)(
)(
H
LIII
H
X
HLHII
H
QII
I
W
Q
WII
H
I
T
T
Q
TTQ
Q
X
XW
X
X
Q
W
HQ
H
H
1
)1(
Therefore, ) (i.e.,
it with associatednsfer exergy tra theas same theis transfer that workknow We
and
Relationship between first and second law efficiencies:
Ambient TH
They are closed systems in communication with two heat reservoirs
(1) the cold space (at TL) from which refrigeration load QL is extracted
(2) the ambient (at TH) to which heat QH is rejected
Refrigeration Cycles
Refrigerator
Refrigerated space TL
Ẇ
HQ
LQ
lost
L
HL
L
HL
W
W
T
TQ
Qlost
lostH
H
H
L
Lgen
HL
WT
TQW
WT
TQXXW
WT
T
T
Q
T
QS
WQQ
L
HL
L
1 gRearrangin
)(1
:follows as expressed becan . is which ambient,
theof re temperatu theis etemperatur-state dead Here
0
0
: thatstate laws second andFirst
numbernegative a is
input Work
negative be will termThissign ve)(
a with itself be will
1
0
Obtained by applying the definition of entropy to the
2 reservoirs. QL is -ve
Refrigeration Cycles Temperature -energy diagram for a refrigeration cycle proposed by Adrian Bejan
LQrevW
HQ
HT
LT
HT
LQ W
HQ
LT
0 0
lostW lostW
genS1tan
gengen
genHlost
L
lost
SS
STW
T
W
1tanor tan
, since
tan
Reversible Irreversible
Refrigeration Cycles Energy conversion vs exergy destruction during a refrigeration cycle
Refr
ige
rato
r
High Temperature Reservoir at TH
Low Temperature Reservoir at TL
QH
QL
W
W
QCOP L
revWLQ
loss
L
L
XXW
genHQ
Q
W
revWII
STX
X
X
X
)(or when 0when
input work Minimum
)(
)(
1or 1
1
1 that Noting
and II
LH
II
L
HII
LH
rev
rev
L
TTCOP
T
TCOP
TTCOP
COP
COP
W
QCOP
Refrigerator
-XW
-XQL
Ex
ergy
de
structio
n
Heat-Pump Cycles Energy conversion vs exergy destruction during a heat-pump cycle
W
QCOP H
Heat-
pu
mp
High Temperature Reservoir at TH
Low Temperature Reservoir at TL
QH
QL
W
Heat-pump
-XW
-XQH
WXW
H
H
LQ Q
T
TX
H
1
)()(1
or ndestructio
Exergy
WQT
TW
HQrevgenL
XW
H
H
L
ST
lost
lostH
H
L WQT
TW
1 arranging-reor
Heat-Pump Cycles
Heat-pump
-XW
-XQH
WXW
H
H
LQ Q
T
TX
H
1
ndestructioExergy
II)(
)(
: workactual by thet requiremen work minimum thedividingby calculated is cycle pump-heat theof efficiency law-second The
genLQ
Q
W
revW
STX
X
X
X
H
H
HL
II
H
LII
HL
rev
rev
H
TTCOP
T
TCOP
TTCOP
COP
COP
W
QCOP
1or 1
1
1 that Noting
and II
fixed. are and as long as
system theofproperty amic thermodyna is
tyavailabili Nonflow or
where
)(
: to from
equation above theintegrate and 2 1 process
aconsider shown system closed For the
)()(1)(
: workavailablefor equation General
00
00
00
1
021
21
000
1
000
0
workavailable of Rate
PT
A
vPsTea
VPSTEA
STXAAX
tttt
STsThmsThmQT
TSTVPE
dt
d
dt
dVPWX
n
i
geniQW
gen
out
o
in
o
i
n
i i
W
Nonflow Processes
Tn T2 T1
Q1 Q2 Qn Closed system
Cycles W T0
Nonflow Processes
)()(
)()(
:fullin exergy nonflow The
out. dropequation original in the termslast two that theNote
)(
:as expressed becan delivers
system closed amax work thereservoir,only theis atmosphere When the
)(
000000
000000
exergy nonflow theasknown is This
0
1
021
vvPssTeeaa
VVPSSTEEAAΦ
AAX
STXAAX
revW
n
i
geniQW
The nonflow exergy is the reversible work delivered by a fixed-mass system during a process in which the atmosphere is the only reservoir.
Steady-flow Processes
sThb
STHB
STbmbmX
STsThmsThmQT
TSTVPE
dt
d
dt
dVPWX
o
o
gen
outin
n
i
iQ
gen
outb
o
inb
on
i
X
i
i
W
iQ
0
0
0
1
000
1
)(
000
0
workavailable of Rate
:as defined isport each at ty availabili flow The
)(
)()(1)(
: workavailablefor equation General
Steady-flow Processes
gen
r
kkoutfinf
n
i
iQW
f
f
o
gen
r
kkoutin
n
i
iQW
gen
outin
n
i
iQW
STxmxmXX
bbx
x
sThb
bPT
rk
STbmbmXX
STbmbmXX
0
11
0
0000
000
0
11
0
1
)()()(
Hence
:as exergy flow definecan then we
such that , is ),( conditions talenvironmen standardat evaluatedty availabili flow theIf
.exchangersheat stream- twoand devices stream-single be wouldexamplespopular Most
and 1between streams ofnumber theis where
)()()(
as written becan
)(
slide previous in the obtained
equation The mix.not do streams the wheredevices through flow stream-multiConsider
Remember the flow exergy from Chp 4 The flow work is done against the fluid upstream in excess of the boundary work against the atmosphere such that exergy associated with this flow work:
xflow = Pv – P0v = (P – P0)v
Steady-flow Processes
gen
out
f
in
f
n
i
iQW
gen
outin
n
i
iQW
H
STxmxmXX
STbmbmXX
T
T
0
1
0
1
0
)(
:equation following thederive topossible isit
)(
equation the Using. etemperaturreservoir catmospheri
theand raturehigh tempe abetween operating cycle Rankine aConsider
Ẇt Ẇp
TH
T0
LQ
HQ
1
2 3
4
ẊQH
Boiler
1)( fxm
3)( fxm
2)( fxm
4)( fxmẊWt
-ẊWp
Pump
Cond.
Turb.
HQII X
Steady-flow Processes gen
out
f
in
f
n
i
iQW STxmxmXX 0
1
)(
ẊQH
Boiler
1)( fxm
3)( fxm
2)( fxm
4)( fxmẊWt
-ẊWp
Pump
Cond.
Turb.
HQII X
destroyedExergy
,0
outflowExergy
4
inflowExergy
3
,043
destroyedExergy
,0
outflowExergy
3
inflowExergy
2
,032
)()(
or
)()(0
:)( turbine theof case In the
)()(
or
)()(0
:boiler theof case In the
turbgenfWf
turbgenffW
tW
boilergenffQ
boilergenffQ
STxmXxm
STxmxmX
WX
STxmxmX
STxmxmX
t
t
t
H
H
Steady-flow Processes
gen
out
f
in
f
n
i
iQW STxmxmXX 0
1
)(
ẊQH
Boiler
1)( fxm
3)( fxm
2)( fxm
4)( fxmẊWt
-ẊWp
Pump
Cond.
Turb.
HQII X
)()(
)()(0
:)( pump theof case In the
finite. is )(exergy exit thehence and an greater th
is which , iscondenser theof ratureexit tempe The
)()(0
:condenser theof case In the
diagram theonshown not isit small, so isIt
,02
,021
10
1
ambient thetocondenser fromfer heat trans
todue destroyed isexergy stream of
portiont significanA
,014
fWpumpgenf
pumpgenffW
pW
f
condensergenff
xmXSTxm
STxmxmX
WX
xT
T
STxmxm
p
p
p
HOMEWORK Determine (by drawing an exergy wheel diagram) the
exergy flow with the associated exergy destruction components of each component of a simple vapor-compression refrigeration cycle. Write down the exergy balance equations for each component and state any assumptions made.
Mechanisms of Entropy Generation or Exergy Destruction
Heat Transfer across a Finite Temperature Difference
Flow with Friction
Mixing