5. Performance and Eciency Test of a Refrigeration Plant (Lecture) 1. Vapor Compression Refrigeration Vaporcompression refrigeration! in "#ic# t#e refrigerant undergoes p#ase c#anges! is one of t#e many refrigeration cycles and is t#e most "idely used met#od for airconditioning of $uildings and automo$iles. %t is also used in domestic and commercial refrigerators! largescale "are#ouses for c#illed or fro&en storage of foods and meats! refrigerated truc's and railroad cars! and a #ost of ot#er commercial and industrial serices. il re*neries! petroc#emical and c#emical processing plants! and natural gas processing plants are among t#e many types of industrial plants t#at often utili&e large aporcompression refrigeration systems. Refrigeration may $e de*ned as lo"ering t#e temperature of an enclosed space $y remoing #eat from t#at space and transferring it else"#ere. + deice t#at performs t#is function may also $e called an air conditioner! refrigerator! air source #eat pump! geot#ermal #eat pump or c#iller (#eat pump). ,. -escription of t#e aporcompression refrigeration system T#e aporcompression uses a circulating liuid refrigerant as t#e medium "#ic# a$sor$s and remoes #eat from t#e space to $e cooled and su$seuently re/ects t#at #eat else"#ere. 0igure 1 depicts a typical! singlestage apor compression system.
+ll suc# systems #ae four components a compressor! a condenser! a t#ermal e2pansion ale (also called a t#rottle ale or metering deice)! and an eaporator. Circulating refrigerant enters t#e compressor in t#e t#ermodynamic state 'no"n a saturated apor compressed to a #ig#er resulting in a as #ig#er temperature as and "ell.isT#e #ot! compressed apor pressure! is t#en in t#e t#ermodynamic state 'no"n as a super#eated apor and it is at a temperature and pressure at "#ic# it can $e condensed "it# eit#er cooling "ater or cooling air. T#at #ot apor is routed t#roug# a condenser "#ere it is 1
cooled and condensed into a liuid $y 3o"ing t#roug# a coil or tu$es "it# cool "ater or cool air 3o"ing across t#e coil or tu$es. T#is is "#ere t#e circulating refrigerant re/ects #eat from t#e system and t#e re/ected #eat is carried a"ay $y eit#er t#e "ater or t#e air ("#ic#eer may $e t#e case). T#e condensed liuid refrigerant! in t#e t#ermodynamic state 'no"n as a saturated liuid! is ne2t routed t#roug# an e2pansion ale "#ere it undergoes an a$rupt reduction in pressure. T#at pressure reduction results in t#e adia$atic 3as# eaporation of a part of t#e liuid refrigerant. T#e autorefrigeration e4ect of t#e adia$atic 3as# eaporation lo"ers t#e temperature of t#e liuid and apor refrigerant mi2ture to "#ere it is colder t#an t#e temperature of t#e enclosed space to $e refrigerated. T#e cold mi2ture is t#en routed t#roug# t#e coil or tu$es in t#e eaporator. + fan circulates t#e "arm air in t#e enclo sed spac e across t#e coil or tu$es carrying t#e cold refrigerant liuid and apor mi2ture. T#at "arm air eaporates t#e liuid part of t#e cold refrigerant mi2ture. +t t#e same time! t#e circulating air is cooled and t#us lo"ers t#e temperature of t#e enclosed space to t#e desired temperature. T#e eaporator is "#ere t#e circulating refrigerant a$sor$s and remoes #eat "#ic# is su$seuently re/ected in t#e condenser and transferred else"#ere $y t#e "ater or air used in t#e condenser. To complete t#e refrigeration cycle! t#e refrigerant apor from t#e eaporator is again a saturated apor and is routed $ac' into t#e compressor. . Vapor Compression Cycle T#e t#ermodynamics of t#e apor compression cycle can $e analy&ed on a temperature ersus entropy diagram as depicted in 0igure ,.
+t point 1 in t#e diagram! t#e circulating refrigerant enters t#e compressor as a saturated apor. 0rom point 1 to point ,! t#e apor is isentropically compressed (i.e.! compressed at constant entropy) and e2its t#e compressor as a super#eated apor. 0rom point , to point ! t#e apor traels t#roug# part of t#e condenser "#ic# remoes t#e super#eat $y cooling t#e apor. 6et"een point and point 7! ,
t#e apor traels t#roug# t#e remainder of t#e condenser and is condensed into a saturated liuid. T#e condensation process occurs at essentially constant pressure. 6et"een points 7 and 5! t#e saturated liuid refrigerant passes t#roug# t#e e2pansion ale and undergoes an a$rupt decrease of pressure. T#at process results in t#e adia$atic 3as# eaporation and autorefrigeration of a portion of t#e liuid (typically! less t#an #alf of t#e liuid 3as#es). T#e adia$atic 3as# eaporation process is isent#alpic (i.e.! occurs at constant ent#alpy). 6et"een points 5 and 1! t#e cold and partially apori&ed refrigerant traels t#roug# t#e coil or tu$es in t#e eaporator "#ere it is totally apori&ed $y t#e "arm air (from t#e space $eing refrigerated) t#at a fan circulates across t#e coil or tu$es in t#e eaporator. T#e eaporator operates at essentially constant pressure and $oils of all aaila$le liuid t#ere after adding 78 deg 9elin of super #eat to t#e refrigerant as a safeguard for t#e compressor as it cannot pump liuid. T#e resulting refrigerant apor returns to t#e compressor inlet at point 1 to complete t#e t#ermodynamic cycle. %t s#ould $e noted t#at t#e a$oe discussion is $ased on t#e ideal apor compression refrigeration cycle "#ic# does not ta'e into account real "orld items li'e frictional pressure drop in t#e system! slig#t internal irreersi$ility during t#e compression of t#e refrigerant apor! or nonideal gas $e#aior (if any). 7. Performance of t#e standard aporcompression cycle T#e standard aporcompression cycle is s#o"n on t#e temperatureentropy diagram in 0igure .
T#e processes constituting t#e standard aporcompression cycle to are 1, Reersi$le and adia$atic compression from saturated apor t#e condenser pressure , Reersi$le re/ection of #eat at constant pressure! causing desuper#eating and condensation of t#e refrigerant
7 %rreersi$le e2pansion at constant ent#alpy from saturated liuid to t#e eaporator pressure 71 Reersi$le addition of #eat at constant pressure causing eaporation to saturated apor T#e "or' of compression in ':;'g is t#e c#ange in ent#alpy in process 1, of 0igure 7a or h1 < h2. T#is relation deries from t#e steady3o" energy euation
h1 + q = h, + w
"#ere c#anges in 'inetic and potential energy are negligi$le.
6ecause in t#e adia$atic compression t#e #eat transfer is &ero! t#e "or' euals h1 < h2. T#e di4erence in ent#alpy is a negatie uantity! indicating t#at "or' is done on t#e system. Een t#oug# t#e compressor may $e of t#e reciprocating type! "#ere 3o" is intermittent rat#er t#at steady! process 1, still represents t#e action of t#e compressor. +t a s#ort distance in t#e pipe a"ay 7
from t#e compressor! t#e 3o" #as smoot#ed out and approac#es steady 3o". 9no"ledge of t#e "or' of compression is important $ecause it may $e one of t#e largest operating costs of t#e system. T#e #eat re/ection in ':;'g is t#e #eat transferred from t#e refrigerant in process ,! "#ic# is h3 < h2. T#is 'no"ledge also comes from t#e steady3o" energy euation! in "#ic# t#e 'inetic energy! potential energy! and "or' terms drop out. T#e alue of h3 < h2 is negatie! indicating t#at #eat is transferred from t#e refrigerant. T#e alue of #eat re/ection is used in si&ing t#e condenser and calculating t#e reuired 3o" uantities of t#e condenser cooling 3uid. T#e refrigerating e4ect in ':;'g is t#e #eat transferred in process 71! or h1 < h4. 9no"ledge of t#e magnitude of t#e term is necessary $ecause performing t#is process is t#e ultimate purpose of t#e entire system. T#e coecient of performance of t#e standard aporcompression cycle is t#e refrigerating e4ect diided $y t#e "or' of compression
Coecien t of performanc e=
h1 − h7 h, − h1
(1) =ometimes t#e olume 3o" rate is computed at t#e compressor inlet or state point 1. T#e olume 3o" rate is a roug# indication of t#e p#ysical si&e of t#e compressor. T#e greater t#e magnitude of t#e term! t#e greater t#e displacement of t#e compressor in cu$ic meters per second must $e. T#e po"er per 'ilo"att of refrigeration is t#e inerse is t#e inerse of t#e coecient of performance! and an ecient refrigeration system #as a lo" alue of po"er per 'ilo"att of refrigeration $ut a #ig# coecient of performance. E2ample >o. 1 + refrigeration system using refrigerant ,, is to #ae a refrigerating capacity of 8? '". T#e cycle is a standard aporcompression cycle in "#ic# t#e eaporating temperature is 8 C and t#e condensing temperature is 7, C. (a) -etermine t#e olume 3o" of refrigerant measured in cu$ic meter per second at t#e inlet to t#e compressor. ($) Calculate t#e po"er reuired $y t#e compressor. (c) +t t#e entrance to t#e eaporator "#at is t#e fraction of apor in t#e mi2ture e2pressed $ot# on a mass $asis and a olume $asis@ Aien Refrigerant ,,. Refrigerating Capacity B 8? ' Eaporating temperature B 8 C Condensing temperature B 7, C Reuired (a) Volume 3o" of refrigerant measured in cu$ic meter per second at t#e inlet to t#e compressor. ($) Po"er reuired $y t#e compressor. (c) 0raction of apor in t#e mi2ture e2pressed $ot# on a mass $asis and a olume $asis at t#e entrance of t#e eaporator. =olution
5
Dse Refrigerant ,, Ta$le from Refrigeration and +ir Conditioning $y =toec'er and :ones +t 1! 8 C h1 B hg1 B 7?,.71 ':;'g hf1 B 1?.F18 ':;'g vg1 B G1.?58 L;'g vf1 B ?.FG,5 L;'g
s1 B 1.FG7 ':;'g.9 +t ,! 7, C condensing temperature! constant entropy h2 B 78.F? ':;'g +t ! 7, C h3 B ,5,.5, ':;'g
h4 B h3 B ,5,.5, ':;'g (a) Volume 3o" of refrigerant B wvg w(h1 h4) B 8? '" w(7?,.71 ,5,.5,) B 8? w B ?.57 'g;s Volume 3o" of refrigerant B (?.57 'g;s)(G1.?58 L;'g) B ,.5 L;s B ?.?,5 m;s +ns. ($) Po"er reuired $y compressor B w(h2 h1) B (?.57)(78.F? 7?,.71) B 1.77, '" +ns. G
(c) Let xm B fraction of apor $y mass $asis and xv B fraction of apor $y olume $asis. Hass 6asis h −h ,5, .5 ,− 1E? .F18 xm = 7 f 1 = = ?.,E .71− 1E? .F18 hg1 − hf 1 7? , (ans"er) Volume 6asis
( 1− xm )vf 1 + xmvg1 Total olume B Total olume B (1 ?.,,)(?.FG,5) I ?.,,(G1.?58) B 18.8 L;s
xv =
xmvg1
(
)
= ?.,E ,G1.?E58 = ?.EF
Totalvolume
18.8
(ans"er) 7.1Jeat E2c#angers =ome refrigeration systems use a liuidtosuction #eat e2c#anger! "#ic# su$cools t#e liuid from t#e condenser "it# suction apor coming from t#e eaporator. T#e arrangement is s#o"n in 0igure 5a and t#e corresponding pressureent#alpy diagram in 0igure 5$.
F
=aturated liuid at point coming from t#e condenser is cooled to point 7 $y means of apor at point G $eing #eated to point 1. 0rom a #eat $alance! h3 < h4 B h1 < h6. T#e refrigerating e4ect is eit#er h6 < h5 or h1 < h3. 0igure G s#o"s a cuta"ay ie" of a liuidtosuction #eate2c#anger.
Compared "it# t#e standard aporcompression cycle! t#e system using t#e #eat e2c#anger may seem to #ae o$ious adantages $ecause of t#e increased refrigerating e4ect. 6ot# t#e capacity and t#e coecient of performance may seem to $e improed. T#is is not necessarily true! #o"eer. Een t#oug# t#e refrigerating e4ect is increased! t#e compression is pus#ed fart#er out into t#e super#eat region! "#ere t#e "or' of compression in ':;'g is greater t#an it is close to t#e saturatedapor line. 0rom t#e standpoint of capacity! point 1 #as a #ig#er speci*c olume t#an point G! so t#at a compressor "#ic# is a$le to pump a certain olume deliers less mass 3o" if t#e inta'e is at point 1. T#e potential improements in performance are t#us counter$alanced! and t#e #eat e2c#anger pro$a$ly #as negligi$le t#ermodynamic adantages. T#e #eat e2c#anger is de*nitely /usti*ed! #o"eer! in situations "#ere t#e apor entering t#e compressor must $e super#eated to ensure t#at no liuid enters t#e compressor. +not#er practical reason for using t#e #eat e2c#anger
8
is to su$cool t#e liuid from t#e condenser to preent $u$$les of apor from impeding t#e 3o" of refrigerant t#roug# t#e e2pansion ale. E2ample >o. , + refrigerant ,, apor compression system includes a liuidtosuction #eat e2c#anger in t#e system. T#e #eat e2c#anger "arms saturated apor coming from t#e eaporator from 1? to 5 C "it# liuid "#ic# comes from t#e condenser at ? C. T#e compressions are isentropic in $ot# cases listed $elo". (a) Calculate t#e coecient of performance of t#e system "it#ou t t#e #eat e2c#anger $ut "it# t#e condensing temperature at ? C and an eaporating temperature of 1? C. ($) Calculate t#e coecient of performance of t#e syste m "it# t#e #eat e2c#anger@ (c) %f t#e compressor is capa$le of pumping 1,.? L;s measured at t#e compressor suction! "#at is t#e refrigeration capacity of t#e system "it#out t#e #eat e2c#anger@ (d) it# t#e same compressor capacity as in (c)! "#at is t#e refrigerating capacity of t#e system "it# t#e #eat e2c#anger@ Aien Refrigerant ,, Liuidtosuction #eat e2c#anger Eaporator from 1? to 5 C Condenser at ? C Reuired (a) Coecient of performance of t#e system "it#out t#e #eat e2c#anger $ut "it# t#e condensing temperature at ? C and an eaporating temperature of 1? C. ($) Coecient of performance of t#e system "it# t#e #eat e2c#anger@ (c) Refrigeration capacity of t#e system "it#out t#e #eat e2c#anger@ (d) Refrigerating capacity of t#e system "it# t#e #eat e2c#anger@ =olution
(a) it#out #eat e2c#anger +t 1!G! 1? C! Ta$le +G. (=toec'er and :ones) h1 B h6 B 7?1.555 ':;'g s1 B s6 B 1.FGF1 ':;'g.9 +t ,! ? C! constant entropy! Ta$le +F h2 B 71.F8F ':;'g +t !7 ! ? C! Ta$le +G. h3 B h4 B ,G.GG7 ':;'g +t 5! h5 B h4 B ,G.GG7 ':;'g hG − h5 7?1.555− ,G.GG7
=
h, − h1
=
= 5.7G
71.F8F− 7?1.555
coecient of performance
(ans"er)
($) it# #eat e2c#anger +t G! 1? C ! Ta$le +G (=toec'er and :ones) h6 B 7?1.555 ':;'g +t 1! 1? C eaporator temperature! 5 C! Ta$le +F h1 B 711.875 ':;'g +t ,! ? C! constant entropy! Ta$le +F h2 B 777.7?F ':;'g +t ! ? C! ta$le +G h3 B ,G.GG7 ':;'g.
h3 h4 h4 h5
< h4 B h1 < h6 B h3 I h6 < h1 B ,G.GG7 I 7?1.555 < 711.875 B ,,G.F7 ':;'g B h4 B ,,G.F7 ':;'g hG − h5 7?1.555− ,,G.F7
= h, − h1 = 777.7?F− 711.875= 5.8 coecient of performance
(ans"er)
(c) Refrigerating capacity "it#out #eat e2c#anger 1?
+t 1! v B G5. L;'g Refrigerating Capacity
1,.? s ( hG − h5 ) = 1,.? s ( 7?1.555− ,G.GG7) = G5.EE kg G5.EE kg B ?. '
(ans"er)
(d) Refrigerating capacity "it# #eat e2c#anger +t 1! v B F?.,F51 L;'g Refrigerating Capacity
= 1,.? s ( h1 − h5 ) = 1,.? s ( 7?1.555− ,,G.F7) F?.,F51 kg F?.,F51 kg B ,. '
(ans"er)
7.,+ctual aporcompression cycle T#e actual aporcompression cycle su4ers from ineciencies compared "it# t#e standard cycle. T#ere are also ot#er c#anges from t#e standard cycle! "#ic# may $e intentional or unaoida$le. =ome comparisons can $e dra"n $y superimposing t#e actual cycle on t#e pressureent#alpy diagram of t#e standard cycle! as in 0igure F.
T#e essential di4erences $et"een t#e actual and t#e standard cycle appear in t#e pressure drops in t#e condenser and eaporator! in t#e su$cooling of t#e liuid leaing t#e condenser! and in t#e super#eating of t#e apor leaing t#e eaporator. T#e standard cycle assumes no drop in pressure in t#e condenser and eaporator. 6ecause of friction! #o"eer! t#e 11
pressure of t#e refrigerant drops in t#e actual cycle. T#e result of t#ese drops in pressure is t#at t#e compression process $et"een 1 and , reuires more "or' t#an in t#e standard cycle. =u$cooling of t#e liuid in t#e condenser is a normal occurrence and seres t#e desira$le function of ensuring t#at 1?? percent liuid "ill enter t#e e2pansion deice. =uper#eating of t#e apor usually occurs in t#e eaporator and is recommended as a precaution against droplets of liuid $eing carried eer into t#e compressor. T#e *nal di4erence in t#e actual cycle is t#at t#e compression is no longer isentropic and t#ere are ineciencies due to friction and ot#er losses. 5. Compressor 5.1Types of Compressors T#e most common compressors used in c#illers are reciprocating! rotary scre"! centrifugal! and scroll compressors. Eac# application prefers one or anot#er due to si&e! noise! eciency and pressure issues. Compressors are often descri$ed as $eing eit#er open! #ermetic! or semi#ermetic! to descri$e #o" t#e compressor and;or motor is situated in relation to t#e refrigerant $eing compressed. Variations of motor;compressor types can lead to t#e follo"ing con*gurations • Jermetic motor! #ermetic compressor • Jermetic motor! semi#ermetic compressor pen motor ($elt drien or close coupled)! #ermetic compressor • pen motor ($elt drien or close coupled)! semi#ermetic compressor •
Typically in #ermetic! and most semi#ermetic compressors (sometimes 'no"n as accessi$le #ermetic compressors)! t#e compressor and motor driing t#e compressor are integrated! and operate "it#in t#e refrigerant system. T#e motor is #ermetic and is designed to operate! and $e cooled $y! t#e refrigerant $eing compressed. T#e o$ious disadantage of #ermetic motor compressors is t#at t#e motor drie cannot $e maintained in situ! and t#e entire compressor must $e remoed if a motor fails. + furt#er disadantage is t#at $urnt out "indings can contaminate "#ole refrigeration systems reuiring t#e system to $e entirely pumped do"n and t#e refrigerant replaced. +n open compressor #as a motor drie "#ic# is outside of t#e refrigeration system! and proides drie to t#e compressor $y means of an input s#aft "it# suita$le gland seals. pen compressor motors are typically aircooled and can $e fairly easily e2c#anged or repaired "it#out degassing of t#e refrigeration system. T#e disadantage of t#is type of compressor is a failure of t#e s#aft seals! leading to loss of refrigerant. pen motor compressors are generally easier to cool (using am$ient air) and t#erefore tend to $e simpler in design and more relia$le! especially in #ig# pressure applications "#ere compressed gas temperatures can $e ery #ig#. Jo"eer t#e use of liuid in/ection for additional cooling can generally oercome t#is issue in most #ermetic motor compressors. 5.,Reciprocating compressors
1,
Reciprocating
compressors
are
pistonstyle!
positie
displacement
compressors. 5.,.1 Performance T"o of t#e most important performance c#aracteristics of a compressor are its refrigerating capacity and its po"er reuirement. T#ese t"o c#aracteristics of a compressor operating at constant speed are controlled largely $y t#e suction and disc#arge pressures. 5.,., Volumetric eciency Volumetric eciencies are t#e $ases for predicting performance of reciprocating compressors. T"o types of olumetric eciencies "ill $e considered! actual and clearance. T#e actual olumetric eciency ηva is de*ned $y !m s volume"owrateentering compressor η va = !m s !isplaceme nt rateof compressor (,) "#ere t#e displacement rate is t#e olume s"ept t#roug# $y t#e pistons in t#eir suction. Clearance volumetric ecienc# depends on t#e ree2pansion of gas trapped in t#e clearance olume! as in 0igure 8.
1
T#e ma2imum olume in t#e cylinder! "#ic# occurs "#en t#e piston is at one end of its str o'e! is $3. T#e minimum olume! or clearance olume! is $c! "#ic# occu rs at ot#er end of t#e pist on stro'e. T#e disc#arge pressure is p!. %n t#e *rst instance! assume t#at t#e suction pressure is p1. Aas trapped in t#e clearance olume must *rst e2pand to olume $1 $efore t#e pressure in t#e cylinder is lo" enoug# for t#e suction ales to open and dra" in more gas. T#e olume of gas dra"n into t#e cylinder "ill $e ( $3 < $1)! and t#e clearance olumetric eciency ηvc for t#is case is ( $3 < $1)(1??);($3 < $c). #en t#e suctio n pressure is p2! t#e inta'e portion of t#e stro'e is reduced to $3 < $2. %n t#e e2treme case "#ere t#e suction pressure #as dropped top3! t#e piston uses its entire stro'e to ree2pand t#e gas in t#e clearance olume and t#e clearance olumetric eciency is ? percent. T#e clearance olumetric eciency can $e e2pressed in anot#er "ay! illustrated in 0igure 8 using p1 as t#e suction pressure. T#e percent clearance m! "#ic# is constant for a gien compressor! is de*ned as
m=
$c 1? $ − $c
() +dding $c < $c to t#e numerator of t#e e2pression for #c gies η vc
=
$ − $c + $c − $1
1? ? 1? ?
$ − $c
=
$c − $1
+ $ − $c
and
17
1?
(7)
ηvc = 1? ?−
$1 − $c $c $1 − 11? 1? ?= 1? ?− $ − $c $ − $c $c
T#erefore
$1 − 1 $c
ηvc = 1? ?− m
(5) %f an isentropic e2pansion is assumed $et"een$c and $1. $1 vsuc = $c v!is (G) "#ere vsuc B speci*c olume of apor entering compressor v!is B speci*c olume of apor after isentropic compression top! Values of t#e speci*c olumes are aaila$le from t#e pressureent#alpy diagram of t#e refrigerant or from ta$les of properties of super#eated apor. =u$stituting Euation (G) into Euation (5) gies
vsuc − 1 v!is
ηvc = 1? ?− m
(F) 5.,. Performance of t#e ideal compressor 0igure s#o"s t#e e4ect of eaporating temperature on clearance olumetric eciency.
15
T#e mass rate of 3o" controls t#e capacity and po"er reuirement more directly t#an t#e olume rate of 3o". T#e mass rate of 3o"! w 'g;s! t#roug# a compressor is proportional to t#e displacement rate in liters per second and t#e olumetric eciency and inersely proportional to t#e speci*c olume of gas entering t#e compressor. %n euation form
w = !isplaceme nt rate×
ηvc 1?
vsuc (8)
E2ample >o. +n ammonia compressor #as a 5 percent clearance olume and a displacement rate of 8? L;s and pumps against a condensing temperature of 7? C. 0or t#e t"o di4erent eaporating temperatures of 1? and 1? C! compute t#e refrigerant 3o" rate assuming t#at t#e clearance olumetric eciency applies. Aien +mmonia compressor 5 K clearance olume -isplacement rate B 8? L;s Condensing temperature B 7? C Eaporating temperatures are 1? C and 1? C. Reuired Refrigerant 3o" rate =olution 1G
Euation (8)
w = !isplaceme nt rate×
ηvc 1?
vsuc
(a) +t 1? C! Ta$le +. (=toec'er and :ones) s1 B 5.F55? ':;'g vsuc B 71F.7FF L;'g +t 7? C! constant entropy! 0ig. +1 v!is B 11,.5 L;'g mB5K Euation (5) and Euation (G).
vsuc − 1 v!is
ηvc = 1? ?− m
71 F.7F F− 1 = 8G.77 5K 11 ,.5
ηvc = 1? ?− 5
w = !isplaceme nt rate×
w = ( 8? s) ×
ηvc 1?
vsuc
8G.77 51? ? 71 F .7F F
= ?.1G Gkg s at 1? C (ans"er)
($) +t 1? C! Ta$le +. (=toec'er and :ones) s1 B 5.7,7 ':;'g vsuc B ,?5.,, L;'g +t 7? C! constant entropy! 0ig. +1 v!is B 5 L;'g mB5K Euation (5) and Euation (G).
vsuc − 1 v!is
ηvc = 1? ?− m
,? 5.,,− 1 = E7.1E EK E5
ηvc = 1? ?− 5
w = !isplaceme nt rate×
ηvc 1?
vsuc
w = ( 8? s) × E7.1E E1? ?= ?.G Fkg s ,? 5 .,,
at 1? C (ans"er)
1F
5.,.7 Po"er reuirement T#e po"er reuired $y t#e ideal compressor is t#e product of t#e mass rate of 3o" and t#e increase in ent#alpy during t#e isentropic compression! % = w∆hi () "#ere % B po"er! ' w B mass rate of 3o"! 'g;s ∆hi B isentropic "or' of compression! ':;'g 0igure 1? s#o"s t#e ariation in ∆hi as t#e eaporating temperature c#anges.
T#e alue of ∆hi is large at lo" eaporating temperatures and drops to &ero "#en t#e suction pressure euals t#e disc#arge pressure ("#en t#e eaporating temperature euals t#e condensing pressure). T#e cure of t#e po"er reuirement in 0igure 1? t#erefore s#o"s a &ero alue at t"o points! "#ere t#e eaporating temperature euals t#e condensing temperature and "#ere t#e mass rate of 3o" is &ero. 6et"een t#e t"o e2tremes t#e po"er reuirement reac#es a pea'. 5.,.5 Refrigerating capacity. T#e refrigerating capacity q is q = w( h1 − h7 ) k& (1?) 18
"#ere h1 and h4 are ent#alpies in ':;'g of t#e refrigerant leaing and entering t#e eaporator! respectiely. T#e refrigerating e4ect h1 < h4' increases slig#tly "it# an increase in suction pressure! as 0igure 11 s#o"s! proided t#at t#e ent#alpy entering t#e e2pansion ale remains constant. T#e increase is due to t#e slig#tly #ig#er ent#alpy of saturated apor at #ig#er eaporating temperatures.
0igure 11 also s#o"s t#e refrigeration capacity calculated "it# Euation (1?). T#e capacity is &ero at t#e point "#ere t#e mass rate of 3o" is &ero. T#e refrigerating capacity is dou$led! for e2ample! $y increasing t#e eaporating temperature from ? to ,? C. 5.,.G Coecient of performance and olume 3o" rate per '" of refrigeration T#e coecient of performance can $e deried from t#e refrigerating capacity of 0igure 11 and t#e po"er from 0igure 1?. T#e result! displayed in 0igure 1,! s#o"s a progressie increase as t#e eaporating temperature increases.
1
T#e olume 3o" rate per unit refrigeration capacity is an indication of t#e p#ysical si&e or speed of t#e compressor necessary to deelop 1 ' of refrigeration. + large olume 3o" must $e pumped for aspeci*c gien capacity at lo" eaporating temperature $ecause of t#e #ig# olume. 5.,.F E4ect of condensing temperature T#e response of a reciprocating compressor to c#anges in condensing temperature can $e analy&ed similarly to t#e eaporating temperature. 0igure 1 s#o"s t#e clearance olumetric eciency as calculated from Euation (F) for a compressor "it# an eaporating temperature of ,? C.
,?
+s t#e condensing temperature increases! t#e olumetric eciency drops o4. 6ecause t#e speci*c olume of t#e refrigerant at t#e compressor suction remains constant! only t#e olumetric eciency a4ects t#e mass rate of 3o"! "#ic# s#o"s a corresponding decrease as t#e condensing temperature increases. 0igure 17 s#o"s suc# a progressie decrease.
,1
T#e refrigerating capacity is t#e product of t#e refrigerating e4ect and t#e mass rate of 3o"! $ot# of "#ic# decrease "it# increasing condensing temperature. T#e result is t#at t#e refrigerating capacity drops rat#er rapidly on an increase in condensing temperature. T#e remaining important c#aracteristic is t#e po"er! s#o"n in 0igure 15.
T#e compressor po"er is t#e product of t#e "or' of compression in ':;'g and t#e mass 3o" rate. T#e "or' of compression in ':;'g increases and t#e mass rate of 3o" decreases as t#e condensing temperature increases! so t#at t#e po"er increases to a pea' and t#en $egins to drop o4! a trend similar to t#e po"er as a function of t#e eaporating temperature s#o"n in 0igure 1?. 5.,.8 +ctual olumetric eciency T#e prediction of olumetric eciency on t#e $asis of ree2pansion of apor in t#e clearance olume is a good start to"ard predicting t#e actual olumetric eciency. t#er factors t#at in3uence t#e olumetric eciency are t#e pressure drop across t#e suction and disc#arge ales! lea'age past t#e rings of t#e piston! and lea'age $ac' t#roug# t#e disc#arge and suction ales. +lso cylinder #eating of suction gas reduces t#e olumetric eciency! since immediately upon entering t#e cylinder t#e gas is "armed and e2panded. T#e speci*c olume of t#e gas inside t#e cylinder is conseuently #ig#er t#an "#en entering t#e compressor! "#ic# is t#e position on "#ic# t#e olumetric eciency is $ased. +ll t#e a$oementioned factors result in a lo"er actual olumetric eciency t#an t#at predicted $y t#e ree2pansion of ,,
clearance gas alone. 0igure 1G s#o"s t#e actual olumetric eciency compared "it# t#e clearance olumetric eciency.
T#e a$scissa in 0igure 1G is t#e disc#argetosuction pressure ratio! a conenient parameter on "#ic# to $ase t#e olumetric performance of t#e compressor. T#e cure for t#e actual olumetric eciency as a function of t#e pressure ratio applies to a "ide ariety of eaporating and condensing temperatures. #en t#is cure is aaila$le! along "it# t#e 'no"ledge of t#e displacement rate of t#e compressor! t#e refrigerating capacity of t#e compressor can $e calculated oer a "ide ariety of conditions. 5.,. Compression eciency T#e compression eciency ηc in percent is isentropic workof compressio n!k( kg ηc = × 1? actualworkof compressio n!k( kg (11) "#ere t#e "or' of compression are referred to t#e same suction and disc#arge pressures. T#e compression eciencies for opentype reciprocating compressors are usually in t#e range of G5 to F? percent. =ome of t#e processes t#at reduce t#e compression eciency from its ideal alue of 1?? percent are friction of ru$$ing surfaces and pressure drop t#roug# ales. E2ample >o. 7 T#e catalog refrigerant ,,! fourcylinder! #ermetic operating at for , a r;s. a condensing temperature of 7? compressor C and an eaporating temperature of 7 C s#o"s a refrigeration capacity of 115 '". +t t#is operating points t#e motor ("#ose eciency is ? percent) dra"s 7.5 '. T#e $ore of t#e cylinders is 8F mm and t#e piston ,
stro'e is F? mm. T#e performance data are $ased on 8 C of su$cooling of t#e liuid leaing t#e condenser. Compute (a) t#e actual olumetric eciency and ($) t#e compression eciency. Aien Refrigerant , 0our cylinder! #ermetic compressor at , r;s Condensing temperature B 7? C Eaporating temperature B 7C Refrigeration capacity B 115 '" Bq Hotor eciency B ? K B ηm Hotor B 7.5 '" B P m 6ore B 8F mm B ?.?8F m B ) Piston =tro'e B F? mm B ?.?F? m B 8 C of su$cooling Reuired (a) t#e actual olumetric eciency ($) t#e compression eciency =olution
Reference. Refrigeration and +ir Conditioning $y =toec'er and :ones Ta$le +G! 7 C eaporating temperature. h1 B 7?.8FG ':;'g vsuc B 5.5G8, L;'g s1 B 1.F5FF5 ':;'g.9 +t ,! ta$le +F! constant entropy! 7? condensing temperature h2 B 75.1 ':;'g v!is B 1F.17 L;'g +t ! 7? C condensing temperature! Ta$le +G! 8 C =u$cooling t B 7? 8 B , C
h3 B ,., ':;'g h4 B h3 B ,., ':;'g (a) 0or actual olumetric eciency ,7
-isplacement rate B (7 cyl)(, r;s)M( π;7)(-,) m;cyl.rN(L) -isplacement rate B (7 cyl)(, r;s)M( π;7)(?.?8F), m;cyl.rN(?.?F?) B ?.?78,F m;'g B 78.,F L;'g +ctual rate of refrigerant 3o" !w B q;(h1 < h4) B 115 '" ; (7?.8FG ,., ':;'g) B ?.G85 'g;s +ctual olumetric 3o" rate at t#e compressor suction B w 2 vsuc B (?.G85 'g;s)(5.5G8, L;'g) B F.7, L;s !m s volume"owrateentering compressor η va = !m s !isplaceme nt rateof compressor ηva =
F.7, s 78.,F s
× 1??= FF.5K
(ans"er) ($) 0or compression eciency. +ctual "or' of compression B ηm%m;w B ?. (7.5 ') ; (?.G85 'g;s) B 77.75 ':;'g isentropic workof compressio n!k( kg ηc = × 1? actualworkof compressio n!k( kg ηc =
ηc =
h, − h1 × 1? actualworkof compressio n!k( kg 7 5 .E1− 7? .8F G 77.75
× 1? ?= F?.E (ans"er)
5.,.1?Compressor disc#arge temperatures %f t#e disc#arge temperature of t#e refrigerant from t#e compressor $ecomes too #ig#! it may result in $rea'do"n of t#e oil! causing e2cessie "ear or reduced life of t#e ales! particularly t#e disc#arge ales. %n general t#e #ig#er t#e pressure ratio! t#e #ig#er t#e disc#arge temperature! $ut t#e properties of t#e refrigerant are also crucial. 0igure 1F s#o"s t#e disc#arge temperatures for four refrigerants follo"ing isentropic compression from saturated apor at ? C to arious condensing temperatures. Refrigerants 1, and 5?, #ae lo" disc#arge temperatures "#ile refrigerant ,, e2periences #ig#er temperatures. =ince t#e #ig#est temperature of t#e four refrigerants s#o"n is ammonia! ammonia compressors are euipped "it# "ater cooled #eads.
,5
5.Rotary scre" compressors
Rotary scre" compressors are also positie displacement compressors. T"o mes#ing scre"rotors rotate in opposite directions! trapping refrigerant apor! and reducing t#e olume of t#e refrigerant along t#e rotors to t#e disc#arge point.
,G
5.7Centrifugal compressors
Centrifugal compressors are dynamic compressors. T#ese compressors raise t#e pressure of t#e refrigerant $y imparting elocity or dynamic energy! using a rotating impeller! and conerting it to pressure energy. 5.7.1 Tip speed to deelop pressure + roug# estimate of t#e tip speed of t#e impeller can $e made $y using seeral fundamental relations#ips for tur$omac#inery. T#e torue t#e impeller ideally imparts to t#e gas is T = w( $,t r, − $1t r1 ) (1,) "#ere T B torue in >.m w B mass rate of 3o"! 'g;s $2t B tangential elocity of refrigerant leaing impeller! m;s r2 B radius of e2it of impeller! m $1t B tangential elocity of refrigerant entering impeller! m;s ,F
r1 B radius of inlet of impeller! m %f t#e refrigerant enters t#e impeller in an essentially radial direction! t#e tangential component of t#e elocity $1t B?! and so T = w$,t r, (1) T#e po"er reuired at t#e s#aft is t#e product of t#e torue and t#e rotatie speed % = Tω = w$,t r,ω (17) "#ere % B po"er! ω B rotatie speed! rad;s +t least at ery lo" refrigerant 3o" rates t#e tip speed of t#e impeller and t#e tangential elocity of t#e refrigerant are nearly identical t#erefore r,ω = $,t
% = w$,,t and
(15)
+not#er e2pression for ideal po"er is t#e product of t#e mass rate of 3o" and t#e isentropic "or' of compression! % = w∆hi (1???k( kg) (1G) Euating t#e t"o e2pression for po"er! Euation (15) and (1G)! yields ,
$,t = 1??? ∆hi
(1F) +lt#oug#! Euation (1F) is $ased on some ideali&ations! it can proide an orderofmagnitude estimate of t#e tip speed and can also s#o" important comparisons. E2ample >o. 5 + t"ostage centrifugal compressor operating at G? r;s is to compress refrigerant 11 from an eaporating temperature of 7 C to a condensing temperature of 5 C. %f $ot# "#eels are to $e of t#e same diameter! "#at is t#is diameter@ Aien T"o stage G? r;s! Refrigerant 11! Eaporating temperature B 7 C Condensing temperature B 5 C Reuired -iameter =olution +t 7 C eaporating temperature! Ta$le +7. (=toec'er and :ones) h1 B ?. ':;'g s1 B 1.G8888 ':;'g.9 ,8
+t 5 C condensing temperature! 0ig. +,! constant entropy! h2 B 71? ':;'g ω B G? r;s B 1,?π rad;s Euation 111G! $,,t = 1??? ∆hi
h, − h1 ,
$,,t = 1???
71?− E ?.E ,
$,,t = 1??? $,t
= EF.G5m s per stage
r,ω = $,t ), ,
( 1,?π ) = EF.G
), = ?.51 8m (ans"er) 5.5=croll compressors
,
=croll compressors are also positie displacement compressors. T#e refrigerant is compressed "#en one spiral or$its around a second stationary spiral! creating smaller and smaller poc'ets and #ig#er pressures. 6y t#e time t#e refrigerant is disc#arged! it is fully pressuri&ed.
5.GControls %n simple commercial refrigeration systems t#e compressor is normally controlled $y a simple pressure s"itc#! "it# t#e e2pansion performed $y a capillary tu$e or simple t#ermostatic e2pansion ale. %n more comple2 systems! including multiple compressor installations! t#e use of electronic controls is typical! "it# ad/usta$le set points to control t#e pressure at "#ic# compressors cut in and cut out! and temperature control $y t#e use of electronic e2pansion ales. %n addition to t#e operational controls! separate #ig# pressure and lo" pressure s"itc#es are normally utili&ed to proide secondary protection to t#e compressors and ot#er components of t#e system from operating outside of safe parameters. %n more adanced electronic control systems t#e use of 3oating #ead pressure! and proactie suction pressure! control routines allo" t#e compressor operation to $e ad/usted to accurately meet di4ering cooling demands "#ilst reducing energy consumption. G. Condensers and Eaporators T#e most "idely used types of condensers and eaporators are s#ellandtu$e #eat e2c#angers (0igure 18) and *nnedcoil #eat e2c#angers (0igure 1). ?
G.1 erall #eattransfer coecient T#e oerall #eattransfer coecient for an eaporator or condenser is t#e proportionality constant! "#ic#! "#en multiplied $y t#e #eattransfer area and t#e mean temperature di4erence $et"een t#e 3uids! yields t#e rate of #eat transfer. %f #eat 3o"s across a tu$e! as in 0igure ,?! $et"een refrigerant on t#e outside and "ater on t#e inside! for e2ample! under steady state conditions t#e rate of #eat transfer q in "atts is t#e same from t#e refrigerant to t#e outside surface of t#e tu$e! from t#e outside to inside surface of t#e tu$e! and from t#e inside surface of t#e tu$e to t#e "ater.
1
T#e e2pressions for q in eac# of t#ese transfers are! respectiely! q = ho *o ( to − tos ) (18)
q=
k *m( tos − tis ) x (1)
q = hi *i ( tis − ti ) (,?) "#ere q B rate of #eat transfer! ho B #eattransfer coecient on outside of tu$e! ;m ,.9 *o B outside area of tu$e! m, to B refrigerant temperature! C tos B temperature of outside surface of tu$e! C k B conductiity of tu$e metal! ;m.9 x B t#ic'ness of tu$e! m tis B temperature of inside surface of tu$e! C ,
*imBB#eattransfer mean circumferential area of tu$e! h coecient on inside of m tu$e! ;m ,.9 *i B inside area of tu$e! m , ti B "ater temperature! C To e2press t#e oerall #eattransfer coecient t#e area on "#ic# t#e coecient is $ased must $e speci*ed. T"o accepta$le e2pressions for t#e oerall #eattransfer coecient are q = +o*o ( to − ti ) (,1) q = +i *i ( to − ti ) and (,,) "#ere +o B oerall #eattransfer coecient $ased on outside area! ;m ,.9 +i B oerall #eattransfer coecient $ased on inside area! ;m ,.9 0rom Euations (,1) and (,,) it is clear t#at+o*o B +i*i. T#e D alue is al"ays associated "it# an area. 9no"ledge of +o or +i facilitates computation of t#e rate of #eat transfer q. To compute + alue from (18) 'no"ledge t#e indiidual #eattransfer coecients! *rstt#e diide Euation $y ho*of o! Euation (1) $y k*m;2! and Euation (,?) $y hi*i! leaing only t#e temperature di4erences on t#e rig#t sides of t#e euations. >e2t add t#e t#ree euations! giing ,
q qx q + + ho*o k*m hi *i
( + t)(os − t)is + tis − ti = ( to − t)os
q qx q + + ho*o k*m hi *i
= to − ti
(,) +lternate e2pressions for to < ti are aaila$le from Euation (,1) and (,,)
to − ti =
q +o*o
=
q +i *i
(,7) Euating Euations (,) and (,7) and canceling q proides an e2pression for computing t#e D alues 1
+o*o
=
1
+i *i
=
1
ho*o
+
x 1 + k*m hi *i (,5)
G.,Liuid in tu$es #eat transfer and pressure drop T#e e2pression for t#e #eattransfer coecient for 3uids 3o"ing inside tu$es is of t#e form ,u= CRen Prm "#ere n and m are e2ponents. T#e constant C and e2ponents in t#e euation are
$)ρ h) = ?.?, k µ
?.8
cpµ k
?.7
(,G) "#ere h B conection coecient! ;m ,.9 ) B %- of tu$e! m k B t#ermal conductiity of 3uid! ;m.9 $ B mean elocity of 3uid! m;s ρ B density of 3uid! 'g;m µ B iscosity of 3uid! Pa.s cp B speci*c #eat of 3uid! :;'g.9 Euation (,G) is applica$le to tur$ulent 3o"! "#ic# typically preails "it# t#e elocities and properties e2perienced in most commercial eaporators and condensers. E2ample >o. G + refrigerant ,, condenser #as four "ater passes and a total of G? copper tu$es t#at are 17 mm %- and #ae , mm "all t#ic'ness. T#e conductiity of copper is ? ;m.9. T#e outside of t#e tu$es is *nned so t#at t#e ratio of outside to inside area is 1.F. T#e cooling"ater 3o" t#roug# t#e condenser tu$es is .8 L;s. (a) Calculate t#e "aterside coecient if t#e "ater us at an aerage temperature of ? C! at "#ic# temperature k B ?.G17 ;m.9! ρ B G 'g;m! and µ B ?.???8? Pa.s.
($) Dsing a mean condensing coecient of 17,? ;m,.9! calculate t#e oerall #eattransfer coecient $ased on t#e condensing area. Aien Refrigerant ,, condenser 7 passes! total of G? copper tu$es 17 mm %-! , mm "all t#ic'ness Conductiity of copper is ? ;m.9 Ratio of outside to inside area B 1.F Cooling "ater t#roug# condenser tu$es B .8 L;s ater at ? C
k B ?.G17 ;m.9! ρ B G 'g;m ! and µ B ,?.???8? Pa.s. Hean condensing coecient B 17,? ;m .9 Reuired (a) ater side coecient! hi. ($) erall #eattransfer coecient $ased on t#e condensing area! +o. =olution (a) aterside coecient
$)ρ h) = ?.?, k µ
?.8
cpµ k
?.7
) B 17 mm B ?.?17 m k B ?.G17 ;m.9 ρ B G 'g;m µ B ?.???8? Pa.s cp B 71? :;'g.9 $=
− .8× 1? m s . = * G?tu-es π ( ?.?17m) , 7 pass 7
$ = 1.G75Fm s ?.8 ( )(.G75F )( )?.?17 ( )(EEG ) 1 = ?.?, ?.G1 7 ?.???8?
) 7 h( ?.?1
h = F!1 & m, ⋅ / (ans"er) ($) erall #eattransfer coecient 1
+o*o
=
1
ho*o
+
x k*m
+
1
hi *i
7
71E? ?.???8? ?.G1 7
?.7
1
+o
=
1
ho
+
x*o *o + k*m hi *i
ho B 17,? ;m,.9 k B ? ;m.9 *o ; *i B 1.F 1
1
*o
,
,
1.F
*m = ( *o + *i ) =
*o +
*o ; *m B 1.,5,G x B , mm B ?.??, m hi B F!1 ;m,.9 1
+o
=
1
+
17,?
( ?.??, )( 1.,5EG ) E?
+
1.F F!1
+o = 1?G?& m, ⋅ / (ans"er) +s t#e 3uid 3o"s inside t#e tu$es t#roug# a condenser or eaporator! a pressure drop occurs $ot# in t#e straig#t tu$es and in t#e D$ends or #eads of t#e #eat e2c#anger. =ome drop in pressure is also attri$uta$le to entrance and e2it losses. T#e e2pression for pressure drop of 3uid 3o"ing in straig#t tu$es is $, ∆p = f ρ ) , (,F) #ere ∆p B pressure drop! Pa f B friction factor! dimensionless B lengt# of tu$e! m =ince t#e pressure drop in t#e straig#t tu$es in an eaporator or condenser may represent only 5? to 8? percent of t#e total pressure drop! e2perimental or catalog data on t#e pressure drop as a function of 3o" rate are desira$le. %f t#e pressure drop at one 3o" is 'no"n! it is possi$le to predict t#e pressure drop at ot#er 3o" rates. T#e e2pression aaila$le to straig#t tu$es! Euation (,F)! indicates t#at t#e pressure drop is proportional to t#e suare of t#e elocity and t#us t#e suare of t#e 3o" rate. T#e ot#er contri$utors to pressure drop resulting from c#anges in 3o" area and direction are also almost e2actly proportional to t#e suare of t#e 3o" rate! so if t#e pressure drop and 3o" rate ∆p1 and w1 are 'no"n! t#e pressure drop ∆p2 at a di4erent 3o" rate w2 can $e predicted
w ∆p, = ∆p1 , w1
,
(,8) G.Liuid in s#ell #eat transfer and pressure drop. 5
%n s#ellandtu$e eaporators! "#ere refrigerant $oils inside tu$es! t#e liuid $eing cooled 3o"s in t#e s#ell across $und les of tu$es! as s#o"n sc#ematically in 0igure ,1.
T#e liuid is directed $y $aOes so t#at it 3o"s across t#e tu$e $undle many times and does not s#ortcircuit from t#e inlet to t#e outle t. T#e analytical prediction of t#e #eattransfer coecient of liuid 3o"ing normal to a tu$e is complicated in itself! and t#e comple2 3o" pattern oer a $undle of tu$es ma'es t#e prediction een more dicult. %n order to proceed "it# t#e $usiness of designing #eat e2c#angers! engineers resort to correlations t#at relate tu$es and $aOes. =uc# an euation $y Emerson can $e modi*ed to t#e form
h)
= ( termscontrolle! -#geometr# ) (Re?.)(G
k
) ?.
Pr
µw µ
?.17
(,) "#ere µ B iscosity of 3uid at $ul' temperature! Pa.s µw B iscosity of 3uid at tu$e"al temperature! Pa.s T#e Reynolds num$er in t#is euation is 0);µ! "#ere 0 is t#e mass elocity or mass rate of 3o" diided $y a c#aracteristic 3o" area. ne important reali&ation emerges from a Euation (,)! for a gien eaporator or condenser "#en "ater 3o"s in t#e s#ell outside t#e tu$es
&ater− si!eheat− transfercoecien t = ( const) ( "owrate) ?.G (?) T#e conection coecient aries as t#e ?.G po"er of t#e 3o" rate compared "it# t#e ?.8 po"er for 3o" inside tu$es. T#e pressure drop of liuid 3o"ing t#roug# t#e s#ell across tu$e $undles is also dicult to predict analytically! $ut "#en an e2perimental point is aaila$le for one 3o" rate! predictions of t#e pressure drop at ot#er 3o" rates can $e made uite accurately. 0igure ,, s#o"s t#e "ater pressure drop ta'en from catalog data of a "aterc#illing eaporator. T#e application e2ponent in t#e pressuredrop3o"rate relations#ip #ere is 1..
G
E2ample >o. F + s#ellandtu$e condenser #as a D alue of 8?? ;m ,.9 $ased on t#e "ater side are and a "ater pressure drop of 5? 'Pa. Dnder t#is operating condition 7? percent of t#e #eattransfer resistance is on t#e "ater side. %f t#e "ater 3o" rate is dou$led! "#at "ill t#e ne" D alue and t#e ne" pressure drop $e@ Aien +1 B 8?? .m,.9 ∆p1 B 5? 'Pa 7?K of #eat transfer resistance is on t#e "ater side ater3o" rate dou$led Reuired >e" D alue B +2 =olution +1 B 8?? ;m,.9 h1 B aterside coecient 1
h1
1 = ?.7? +1
h1 =
1
1 ?.7? 8? ?
= ,!??
&ater− si!eheat− transfercoecien t = ( const) ( "owrate) ?.G for eaporator replace ?.G $y ?.8 for condenser.
&ater− si!eheat− transfercoecien t = ( const) ( "owrate) ?.8 F
0or w2 ; w1 B ,
h, w, = h1 w1
?.8
, h, = ( ,??? )( ) , ?.8 = 78, .,& m ⋅ /
Remaining resistance B (?.G?)( 1 ; 8?? ) B ?.???F5 >e" DValue 1
+,
=
1
1
+ ?.???F5=
h,
+ ?.???F
78, .,
+, = EG7& m, ⋅ / (ans"er) >e" Pressure -rop
w ∆p, = ∆p1 , w1
,
w, =, w1
∆p, = 5?( ,) , = ,??k%a (ans"er)
G.7E2tended surface *ns. T#e $ar *n! s#o"n in 0igure , is a rudimentary *n "#ose performance can $e predicted analytically and "ill $e used to illustrate some important c#aracteristics.
8
T#e *ns are of lengt# and t#ic'ness ,# m. T#e conductiity of t#e metal is k ;m.9! and t#e airside coecient is hf ;m,.9. To sole for t#e temperature distri$ution t#roug# t#e *n! a #eat $alance can $e "ritten a$out an element of t#ic'ness !x m. T#e #eat $alance states t#at t#e rate of #eat 3o" entering t#e element at position 1 from t#e end of t#e *n plus t#at transferred to t#e element from t#e air euals t#e rate of #eat transferred out of t#e element at position , to"ard t#e $ase. 0or one#alf a *n "idt# and a *n dept# of m! t#e #eat $alance in sym$ols is !t !t k#1 + 1!xh f ( ta − t ) = k#1 !x1 !x, (1) "#ere ta B temperature of air t B temperature of *n Canceling and factoring gies !t !t k# − = !xhf ( ta − t ) !x, !x1 (,) 0or t#e di4erential lengt# !x t#e c#ange in t#e temperature gradient is !t − !t = ! !t !x= !,t !x !x, !x, !x1 !x !x () =u$stituting into Euation (,)! "e get !,t hf ( ta − t )
!x,
=
k#
(7) 6y soling t#e secondorder di4erential euation (7) t#e temperature distri$ution t − t- t#roug#out cos# 2( − x)t#e *n can $e s#o"n to $e = ta − tcos#2 (5)
"#ere t- B temperature of $ase of *n! C
2=
hf k#
#en a *nned coil cools air! points in t#e *n fart#er a"ay from t#e $ase are #ig#er in temperature t#an points close to t#e $ase. T#e net result of t#e #ig#er temperature of most of t#e *n is t#at less #eat is transferred t#an if t#e entire *n "ere at temperature t-. T#e ratio of t#e actual rate of #eat transfer to t#at "#ic# "ould $e transferred if t#e *n "ere at temperature t- is called t#e n eectiveness.
actualq 5ine4ectiven ess= η = q if 3nwereat -asetemperatu e (G) =#arper and 6ro"n found t#at t#e *n e4ectieness for t#e $ar *lm at 0igure , can $e represented $y tan#2 η= 2 T#e $ar *n is not a common s#ape $ut t#e dominant type of *nned surface is t#e rectangular plate mounted on cylindrical tu$es. T#e net result is a rectangular or suare *n mounted on a circular $ase! one section of "#ic# is s#o"n in 0igure ,7a.
T#e *n e4ectieness of t#e rectangular plate *n is often calculated $y using properties of t#e corresponding annular *n (0igure ,7$)! for "#ic# a grap# of t#e *n e4ectieness is aaila$le! as in 0igure ,5. T#e corresponding annular *n #as t#e same area and t#ic'ness as t#e plate *n it represents.
7?
E2ample >o. 8 Compute t#e *n e4ectieness of an aluminum rectangular plate *n of a *nned aircooling eaporator if t#e *ns are ?.18 mm t#ic' and mounted on a 1Gmm- tu$es. T#e tu$e spacing is 7? mm in t#e direction of air 3o" and , 75 mm ertically. T#e airside coecient is 55 ;m .9. Aien ?.18 mm t#ic'! 1Gmm - tu$es Tu$e spacing 7? mm in t#e direction of air 3o" 75 mm ertically +irside coecient B 55 ;m,.9 B hf Reuired 0in e4ectieness =olution hf B 55 ;m,.9 +lumimum 0ins! k B ,?, ;m.9 ,# B ?.???18 mm # B ?.???? mm
2=
hf k#
=
55
( ,?)( , ?.????E )
= 55m−1
Euialent e2ternal radius.
71
π ( re )
,
−
1G
,
,
, 1G ( = )(7?) 75 − π ,
re B ,.7 mm B ?.?,7 m ri B 8 mm B ?.??8 m (re ri) B (?.?,7 ?.??8)(55) ?.88 re;ri B ,.7 mm ; 8 mm B 0rom 0ig. ,5 0in E4ectieness B ?.G8 +ns. T#e airside areaarea of a and *nned eaporator is composed of t"o portions! t#e prime t#econdenser e2tended or area. T#e prime area *p is t#at of t#e tu$e $et"een t#e *ns! and t#e exten!e! area *e is t#at of t#e *n. =ince t#e prime area is at t#e $ase temperature! it #as a *n e4ectieness of 1.?. %t is to t#e e2tended surface t#at t#e *n e4ectieness less t#an 1.? applies. Euation for t#e oerall #eattransfer coecient can $e reised to read x 1 1 1 1 = = + + +o*o +i *i hf ( *p + η*e ) k*m hi *i G.5Aas 3o"ing oer *nned tu$es #eat transfer and pressure drop + precise prediction of t#e airside #eattransfer coecient "#en t#e air 3o"s oer *nned tu$es is complicated $ecause t#e alues is a function of geometric factors! e.g.! t#e *n spacing! t#e spacing and diameter of t#e tu$es! and t#e num$er of ro"s of tu$es deep. Dsually t#e coecient aries appro2imately as t#e suare root of t#e face elocity of t#e air. + roug# estimate of t#e airside coecient hf can $e computed from t#e euation deried from illustratie data in t#e +R% standard. ?.5
hf = 8$
(F) "#ere $ is t#e face elocity in meters per second. T#e drop in pressure of t#e air 3o"ing t#roug# a *nned coil is also dependent upon t#e geometry of t#e coil. 0igure ,G s#o"s t#e pressure drop of a commercial cooling coil "#en t#e *nned surfaces are dry.
7,
+s e2pected! t#e pressure drop is #ig#er for coils "it# a larger num$er of *ns per meter of tu$e lengt#. T#e ordinate is t#e pressure drop per num$er of ro"s of tu$es deep! so t#e alues "ould $e multiplied $y G for a si2ro" coil! for e2ample. 0or t#e coil series "#ose pressure drops are s#o"n in 0igure ,G t#e pressure drop for a gien coil aries as t#e face elocity to t#e 1.5G po"er. T#at e2ponent is fairly typical of commercial plate*n coils. G.GReuired condensing capacity T#e reuired rate of #eat transfer in t#e condenser is predominantly a function of t#e refrigerating capacity and t#e temperatures of eaporation and condensation. T#e condenser must re/ect $ot# t#e energy a$sor$ed $y t#e eaporator and t#e #eat of compression added $y t#e compressor. + term often used to relate t#e rate of #eat 3o" at t#e condenser to t#at of t#e eaporator is t#e heatre7ection ratio
rateof heatre7ecte! at con!enser !k& 8eat− re7ection ratio= rateof heata-sor-e! at evaporator !k& (8)
7
+ grap# of typical alues of #eatre/ection ratios is s#o"n in 0igure ,F.
#en t#e motor driing t#e compressor is #ermetically sealed! some of t#e #eat associated "it# ineciencies of t#e electric motor is added to t#e refrigerant stream and must ultimately $e remoed at t#e condenser. T#e #eatre/ection ratios of t#e #ermetically sealed compressors are usually slig#tly #ig#er t#an t#ose of t#e opentype compressor. G.FCondensing coecient T#e $asic euation for calculating t#e local coecient of #eat transfer of apor condensing on a ertical plate (0igure ,8) "as deeloped $y >usselt $y pure p#ysical analysis.
77
T#e euation for t#e local condensing coecient is , hcvx gρ hfgx = k 7µk∆t
17
() #ere hcv B local condensing coecient on ertical plate! ;m ,.9 x B ertical distance measured from top of plate! m g B acceleration due to graity B .81 m;s , ρ B density of condensate! 'g;m hfg B latent #eat of apori&ation! :;'g µ B iscosity of condensate! Pa.s ∆t B temperature di4erence $et"een apor and t#e plate! 9 T#e mean condensing coecient oer t#e total #eig#t of t#e plate is
hcv
h !x gρ h k =∫ = ?.E7 ?
,
cv
fg
µ∆t
17
, & m ⋅/
(7?) T#e euation for t#e mean condensing coecient for apor condensing on t#e outside of #ori&ontal tu$es is 17
gρ ,hfgk , µ∆t,) & m ⋅ /
hct = ?.F, 5
(71) "#ere , B num$er of tu$es in ertical ro" ) B 9) of tu$e! m
E2ample >o. Calculate t#e mean condensing #eattransfer coecient "#en refrigerant 1, condenses on t#e outside of t#e #ori&ontal tu$es in a s#ellandtu$e condenser. T#e outside diameter of t#e tu$es is 1 mm! and in t#e ertical 75
ro"s of tu$es t#ere are respectiely! t"o! t#ree! four! t#ree! and t"o tu$es. T#e refrigerant is condensing at a temperature of 5, C and t#e temperature of t#e tu$es is 77 C. Aien Refrigerant 1,. - B 1 mm Vertical ro"s of tu$es B ,! ! 7! ! and , tu$es Condensing temperature B 5, C Temperature of tu$es B 77 C Reuired Hean condensing #eattransfer coecient < hcon! =olution Condensing Coecient
gρ ,hfgk µ∆t,)
17
hcon!= ?.F, 5
Ta$le +5 at 5, C. (Refrigeration and +ir Conditioning =toec'er and :ones) hfg B F?.F ,51.??7 ':;'g B 11. ':;'g hfg B 11! :;'g ρ B 1 ; (?.81F L;'g) B 1,?, 'g;m Ta$le 155! Liuid Refrigerant 1,. (Refrigeration and +ir Conditioning =toec'er and :ones) µ B ?.???1F P+.s k B ?.?5, ;m.9 , B (, I I 7 I I,) ; 5 B ,.8 ∆t B 5, C 77 C B 8 9
gB .81 m;s, ) B 1 mm B ?.?1 m
( E.81 )( 1,?, () , 11E )( !EE) ?.?5E1 )( )( 8 )(,.8 ? ) .?1E ( ?.???1F7
17
hcon!= ?.F,5
hcon!= 1?G5& m, ⋅ / (ans"er) G.80ouling factor +fter a "atercooled condenser #as $een in serice for some time its + alue usually degrades some"#at $ecause of t#e increased resistance to #eat transfer on t#e "ater side due to fouling $y t#e impurities in t#e "ater from t#e cooling to"er. T#e ne" condenser must t#erefore #ae a #ig#er + alue in anticipation of t#e reduction t#at "ill occur in serice. T#e #ig#er capacity "it# ne" euipment is proided $y specifying a fouling factor 1; h ,
m .9;.1T#is x* e2pands * *for t#e+ alue into 1 term
+o
=
ho
+
o
k*m
+
o
h4 *i
+
o
hi *i (7,) 7G
=eeral di4erent agencies #ae esta$lis#ed standards for t#e fouling factor to $e used. ne trade association speci*es ?.???1FG m ,.9;! "#ic# means t#at t#e condenser s#ould leae t#e facto ry "it# a 1; +o alue of ?.???1FG *o;*i less t#an t#e minimum reuired to meet t#e uoted capacity of t#e condenser.
G.-esuper#eating Een "#en t#e refrigerant condenses at a constant pressure! its temperature is constant only in t#e condensing portion. 6ecause t#e apor coming from t#e compressor is usually super#eated! t#e distri$ution of temperature "ill $e as s#o"n in 0igure ,.
6ecause of t#e distortion in t#e temperature pro*le caused $y t#e desuper#eating process! t#e temperature di4erence $et"een t#e refrigerant and t#e cooling 3uid is no longer correctly represented $y t#eT)
2T)= ( tc −)t( i
− )tc − to tc − ti ln tc − to
(7) %t is common practice to use Euation (7) any"ay "it# t#e follo"ing /usti*cation. +lt#oug# t#e temperature di4erence $et"een t#e refrigerant and cooling 3uid is #ig#er in t#e desuper#eating section t#an calculated from Euation (7)! t#e conection coecient in t#is section is normally lo"er t#an t#e condensing coecient. T#e t"o errors compensate some"#at for eac# ot#er! and t#e application of Euation (7) along "it# t#e condensing coecient oer t#e entire condenser area usually proides reasona$ly accurate results. G.1?
Eaporators %n most refrigerating eaporators t#e refrigerant $oils in t#e tu$es and cools t#e 3uid t#at passes oer t#e outside of t#e tu$es. Eaporators t#at $oil refrigerant in t#e tu$es are often called directe2pansion eaporators! and 0igure ? s#o"s an aircooling eaporator and 0igure 1 a liuid cooler.
7F
G.11
6oiling in t#e s#ell %t is dicult to predict t#e $oiling coecient accurately $ecause of t#e comple2ities of t#e mec#anisms. 0urt#ermore! t#e coecients follo" some di4erent rules "#en t#e $oiling ta'es place in t#e s#ell outside t#e tu$es! in contrast to $oiling inside t#e tu$es. =ome trends t#at usually occur "ill $e presented. T#e classic prediction for t#e #eattransfer coecient for pool $oiling of "ater at atmosp#eric pressure is s#o"n in 0igure ,.
78
T#e tests "ere conducted $y immersing a #eated "ire in a container of "ater. %n t#e $oiling regi me *: t#e $oiling is called nucleate -oiling! "#ere $u$$les form on t#e surface and rise t#roug# t#e pool. T#e euation of t#e cure is appro2imately
q = C∆tto7 * "#ere
q B rate of #eat transfer! * B #eattransfer area! m, C B constant ∆t B di4erence in temperature $et"een metal surface and $oiling 3uid!
9 To "rite t#e euation in anot#er form diide $ot# sides $y ∆t q = hr = C∆t,to *∆t "#ere hr is t#e $oiling coecient! ;(m ,.9). T#e alue of hr increases as t#e temperature di4erence increases! "#ic# p#ysically are due to t#e greater agitation. T#e distur$ance frees t#e $u$$les of apor from t#e metal surface sooner and allo"s t#e liuid to come into contact "it# t#e metal. T#e rate of eaporation can increase to a pea'! point :! "#ere so muc# apor coer t#e metal surface t#at t#e liuid can no longer intimately contact t#e metal. + furt#er increase in t#e temperature di4erence decreases t#e rate of #eat transfer. T#e grap# in 0igure , is useful in predicting t#e trends for #eat transfer coecients for $oiling outside tu$e $undles. Jo4mann summari&ed t#e "or' of seeral inestigators to proide t#e $and s#o"n in 0igure .
7
G.1,
6oiling inside tu$es #en refrigerant $oils inside t#e tu$es! t#e #eattransfer coecient c#anges progressiely as t#e refrigerant 3o"s t#roug# t#e tu$e. T#e refrigerant enters t#e eaporator tu$e "it# a lo" fraction of apor. +s t#e refrigerant proceeds t#roug# t#e tu$e! t#e fraction of apor increases! intensify t#e agitation and increasing t#e #eattransfer coecient. #en t#e refrigerant is nearly all apori&ed! t#e coecient drops o4 to t#e magnitude applica$le to apor transferring #eat $y forced conection. 0igure 7 s#o"s local coecients t#roug#out a tu$e for t#ree di4erent leels of temperature.
5?
T#e #eattransfer coecient is #ig#est for t#e #ig# eaporating temperature! pro$a$ly $ecause at #ig# eaporating temperatures and pressures t#e apor density is #ig#! permitting a greater fraction of t#e metal to $e "etted "it# liuid. G.1
Pressure drop in tu$es T#e pressure of t#e refrigerant drops as it 3o"s t#roug# tu$etype eaporators. T#e e4ect of pressure drop on system performance is t#at t#e compressor must pump from a lo"er suction pressure! "#ic# increases t#e po"er reuirement. n t#e ot#er #and a #ig# refrigerant elocity can $e ac#ieed if more pressure drop is permitted! and t#is #ig# elocity improes t#e #eattransfer coecient. Typical pressure drops for airconditioning eaporators are 15 to ? 'Pa.
F. E2pansion -eices T#e last of t#e $asic elements in t#e aporcompression cycle! after t#e compressor! condenser! and eaporator! is t#e e2pansion deice. T#e purpose of t#e e2pansion deice is t"ofold it must reduce t#e pressure of t#e liuid refrigerant! and it must regulate t#e 3o" of refrigerant to t#e eaporator. 51
F.1Capillary tu$es T#e capillary tu$e seres almost all small refrigerant systems and its application e2tends up to refrigerating capacities of t#e order of 1? '. + capillary tu$e is 1 to G m long "it# an inside diameter generally from ?.5 to ?., mm. T#e name is a misnomer! since t#e $ore is too large to permit capillary action. Liuid refrigerant enters t#e capillary tu$e! and as it 3o" t#roug# t#e tu$e! t#e pressure drops $ecause of friction and acceleration of t#e refrigerant. =ome of t#e liuid 3as#es into apor as t#e refrigerant 3o"s t#roug# t#e tu$e. >umerous com$inations of $ore and lengt# are aaila$le to o$tain t#e desired restriction. nce t#e capillary tu$e #as $een selected and installed! #o"eer! t#e tu$e cannot ad/ust to ariations in disc#arge pressure! suction pressure! or load. T#e compressor and e2pansion deice must arrie at suction and disc#arge conditions "#ic# allo" t#e compressor to pump from t#e eaporator t#e same 3o" rate of refrigerant t#at t#e e2pansion deice feeds to t#e eaporator. + condition of un$alanced 3o" $et"een t#ese t"o components must necessarily $e temporary. F.,=election of a capillary tu$e T#e designer of a ne" refrigeration unit employing a capillary tu$e must select t#e $ore and lengt# of t#e tu$e so t#at t#e compressor and tu$e *2 a $alance point at t#e desired eaporating temperature. 0inal ad/ustment of t#e lengt# is most often cut and try.Q + longer tu$e t#an desired is *rst installed in t#e system "it# t#e pro$a$le result t#at t#e $alance point "ill occur at too lo" an eaporating temperature. T#e tu$e is s#ortened until t#e desired $alance point is reac#ed. F.Arap#ical met#od of capillary tu$e selection Arap#s to facilitate t#e selection of capillary tu$es are $ased on data $y Jop'ins and reised "it# data $y #itesel. T#e *rst grap# (0igure 5) presents t#e refrigerant 3o" rate as a function of t#e entering pressure to t#e capillary tu$e for a tu$e t#at is 1.G mm in diameter and ,.? m long.
5,
T#e arious cures in 0igure G represent performance at a ariety of inlet conditionsmagnitudes of su$cooling and fraction of apor.
5
T#e companion grap# to 0igure 5 is t#e one in 0igure G! presenting correction factors to t#e 3o" rate of 0igure 5 for ot#er lengt#s and diameters. F.7Constantpressure e2pansion ale T#e constantpressure expansion valve maintains a constant pressure at its outlet! t#e entrance to t#e eaporator. %t senses t#e eaporator pressure! and "#en t#at pressure drops $elo" t#e control point! t#e ale opens "ider. #en t#e eaporator pressure rises a$oe t#e control point! t#e ale partially closes. F.50loat Vales T#e "oat valve is a type of e2pansion ale "#ic# maintains t#e liuid at a constant leel in a essel or an eaporator. + 3oat s"itc# "#ic# opens completely "#en t#e liuid leel drops $elo" t#e control point and closes completely "#en t#e leel reac#es t#e control point "ill gie t#e same net performance as a modulating type of 3oat control. F.G=uper#eatcontrolled (t#ermostatic ) e2pansion ale T#e most popular type of e2pansion deice for moderatesi&ed refrigeration systems is t#e super#eatcontrolled ale! usually called a thermostatic expansion valve. T#e name may $e misleading $ecause control is actuated not $y t#e temperature in t#e eaporator $ut t#e magnitude of super#eat of t#e suction gas leaing t#e eaporator. T#e super#eat e2pansion ale regulates t#e rate of 3o" of liuid refrigerant in proportion to t#e rate of eaporation in t#e eaporator. 0igure F is a p#otograp# of a t#ermostatic e2pansion ale.
F.FHanufacturers ratings to t#ermostatic e2pansion ales. 57
T#e catalogs of manufacturers of e2pansion ales usually s#o" t#e refrigerating capacity associated "it# t#e 3o" rate of "#ic# t#e ale is capa$le. %n order to proide some resere capacity! most manufacturers s#o" t#e refrigerating capacity at per#aps F5 percent of t#e full 3o" rate of t#e ale. T#e 3o" rate t#roug# t#e ale is a function of t#e pressure di4erence across t#e ale! and t#e elocity t#roug# t#e fully opened ale can $e computed from t#e #ydraulic formula
) ms = C ,( pressure $elocit# !i4erence (77) "#ere C is an e2perimentally determined constant and t#e pressure di4erence is in 'Pa. +lt#oug# t#e refrigerant follo"ing t#e t#rottling process in t#e ale is a mi2ture of apor and liuid. Euation (77) applies to liuid $ecause t#e apori&ation does not occur until after t#e 3uid #as passed t#roug# t#e ale. T#e liuid is momentarily in a metasta$le condition.
E2ample >o. 1? T#e catalog of an e2pansion ale manufacturer speci*es a refrigerating capacity of 75 ' for a certain ale "#en t#e pressure di4erence across t#e ale is 5?? 'Pa. T#e catalog ratings apply "#en aporfree liuid at F.8 C enters t#e e2pansion ale and t#e eaporator temperature is 7.7 C. #at is t#e e2pected rating of t#e ale "#en t#e pressure di4erence across it is 1,?? 'Pa@ Aien Refrigerating capacity B 75 ' Pressure di4erence B 5?? 'Pa +t F.8 C entering e2pansion ale. Eaporator temperature is 7.7 C Reuired E2pected rating "#en pressure di4erence is 1,?? 'Pa. =olution
= C ,( pressure ) ms $elocit# !i4erence it# all ot#er data as constant e2cept for pressure di4erence and refrigerating capacity.
∝ ,( pressure ) ms ;efrigeratin g Capacit# !i4erence T#en >e" Refrigerating Capacity 1,??k%a = ( 75k&) 5??k%a B G.F ' (ans"er) F.8Electric e2pansion ale
55
T#e electric e2pansion ale! s#o"n sc#ematically in 0igure 8! uses a t#ermistor to sense t#e presence of liuid in t#e outlet stream of t#e eaporator.
#en no liuid is present! t#e temperature of t#e t#ermistor increases! "#ic# drops its resistance and permits a greater current 3o" t#roug# t#e #eater at t#e ale. T#e ale is t#ere$y opened! allo"ing an increased refrigerant 3o" rate. ne of t#e applications of t#e electric e2pansion ale is for #eat pumps! "#ere t#e 3o" rate of refrigerant is reersed in order to c#ange from #eating to cooling. =ince its control is independent of refrigerant pressures! t#e electric e2pansion ale can function "it# 3o" t#roug# t#e ale in eit#er direction. E>-
5G
