MASTER OF. Major Professor ABSORPTION REFRIGERATION SYSTEM. Ltf$ Taiwan Provincial Cheng Kung University Tainan, Taiwan, 1958 REPORT

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1 ABSORPTION REFRIGERATION SYSTEM by Ltf$ CHUN -KING CHENG B.3., Taiwan Prvincial Cheng Kung University Tainan, Taiwan, 1958 A MASTER 1 S REPORT submitted in partial fulfillment f the requirements fr the degree MASTER OF SCIENCE Department f Mechanical Engineering KANSAS STATS UNIVERSITY Manhattan, Kansas 1966 Apprved by: Majr Prfessr

2 L.D A US ii \ *>V TABLE OP NTENTS c. a- SECTION 1. Intrductin Page 1.1. Difference between Cmpressin and Absrptin Refrigeratin Systems Principles f the Absrptin Refrigeratin System and Its Cyclic Analysis 4 1»3» Cyclic Analysis f an Absrptin Refrigeratin System in Terms f Circulating Fluids 9 SECTION 2. First Law and Secnd Law Analysis f an Absrptin Refrigeratin System 2.1. Mass Balance Energy Balance Secnd Law Analysis f an Absrptin Refrigeratin System 21 SECTION 3. Cmputatin f a Typical Ammnia-Absrptin Refrigeratin System 3.1. Principal Determining Factrs Example f a Typical Ammnia-Absrptin Refrigeratin System Cnclusins 6l ACKNOWLEDGEMENT 63 BIBLIOGRAPHY 64 NOMENCLATURE 66 ABSTRACT 70

3 SECTION 1 Intrductin 1.1. Difference between Cmpressin and Absrptin Refrige- (1) (2)* ratin Systems^',v ; Refrigeratin might be defined as the art f prducing and maintaining, in a given space, a temperature level which is lwer than the surrunding temperature level. The reversed Carnt cycle perating as a heat pump remves heat frm a lw temperature surce and rejects it t a higher temperature regin; n ther cycle is mre efficient than this ne fr given high temperature and lw temperature surces. Actual refrigeratin cycles, because f their inherent irreversibilities, perate at lwer efficiencies than the reversed Carnt cycle. In the fllwing discussins, irreversibility fr each prcess in an actual cycle will be cnsidered instead f the reversible prcesses which cnstitute the reversed Carnt cycle. Generally speaking, refrigeratin systems are divided int tw classes cmpressin refrigeratin systems and absrptin refrigeratin systems. In a cmpressin refrigeratin system (see Fig. la), liquid refrigerant passes thrugh a thrttle valve, thereby underging a thrttling prcess t a lwer pressure and temperature. After expansin thrugh the valve, the fluid is evaprated in the cils by means f the absrptin f * All superscripts with specified numbers in parentheses shw bibligraphy which are tabulated n page 6^.

4 Cndenser rlqz? OUt,\v Expansin Hi I Evapratr "-Heat in Fig. tc. Basic cmpressin refrigeratin. -«; Genc-rcrr in Cn C ~ '. cc.* Ht ut Punp M &wsuy tw»»vy v Slutin c r/ Expansin vj velvet j! Strng Ktf el-ccn ';:-;- Abcr&r i "J i Evc;>c;-c?crr" : '- ec ',n Fig. I b. Basic absrptin s f2l cycled * sj... j Jiw. :<j>a r

5 heat frm the evapratr. The dry saturated vapr frm the evapratr is then cmpressed t a higher pressure by supplying mechanical wrk t the cmpressr. During the cmpressin the temperature f the refrigerant increases. The high temperature vapr is then cndensed under cnstant pressure cnditins t the entrance f the thrttle valve. This cmpletes the cycle. Bth cmpressin refrigeratin systems and absrptin refrigeratin systems have the same cndensing prcess, thrttling prcess thrugh the expansin valve and evaprating prcess. The difference between the tw systems is the prcess between the end f the evaprating prcess and the entrance f the cndensing prcess. As mechanical wrk is much mre expensive than an equivalent amunt f heat, it may be desirable t use heat directly as the perating energy instead f using mechanical wrk. The mst successful system perating almst whlly n an input f heat is the absrptin system. The basic absrptin refrigeratin system (see Fig. lb) uses an absrber, generatr, slutin valve and a liquid pump instead f the cmpressr in the cmpressin refrigeratin system and uses tw fluids (such as ammnia and water) instead f ne fluid (such as ammnia) in the cmpressin refrigeratin cycle. In accrdance with the design pressure and temperature at the absrber, the mixed slutin quickly reaches the equilibrium cnditin and finally becmes a strng cncentrated slutin. (A strng cncentrated slutin is ne that has a relatively large amunt f the refrigerant disslved in the absrbing fluid.) During this mixing peratin, cling

6 water circulates cntinuusly t take ff this heat. The strng slutin is then pumped t the generatr \tfhere almst pure vapr flws t the cndenser and the weak slutin expands thrugh a slutin valve and flws back t the absrber. In the absrber the absrbent and the refrigerant vapr are brught int cntact t facilitate the disslving f vapr cntinuusly. The basic difference described abve can be seen by cmparing the left hand sides f Fig. la and Fig. lb. By far the mst cmmnly used binary mixtures fr absrptin refrigeratin systems are ammniawater, lithium chlride-water, lithium brmide-water. Of these tw systems, the cmpressin refrigeratin system is much simpler in mechanism than the absrptin refrigeratin system. Fr cmparisns, hwever, we have t cnsider sme ther practical and lcal circumstances, such as the investment cst, the availability f heating and cling systems; we can nt assert which system is preferable in general. Further detail in the cmparisn f the absrptin and cmpressin systems, by a purely thermdynamic viewpint with the aid f perfrmance rati and cefficient f perfrmance, will be shwn in Sec Principles f the Absrptin Refrigeratin System and Its Cyclic Analysis Figure 2 shws a mre cmplete diagram f a cnventinal absrptin refrigeratin system than des Fig. lb. The high pressure vapr enters the cndenser where it becmes a liquid. The liquid then passes thrugh the expansin valve where it is thrttled t a lw pressure, lw temperature, and lw quality

7 vapr. This lw pressure and lw temperature refrigerant flws thrugh the evapratr where it absrbs heat as the liquid is vaprized. The lw pressure and lw temperature vapr cming frm the evapratr flws int the absrber where it cmes in cntact with the cl weak slutin. The absrber perates at a pressure slightly lwer than the evapratr pressure. The weak slutin absrbs the vapr which cmes frm the evapratr and thereby becmes a strng slutin. The maximum cncentratin f refrigerant vapr that can be absrbed depends upn the temperature and pressure in the absrber. This maximum absrptin is an imprtant cncept in investigating absrptin refrigeratin systems. Fig. 3 shws, fr example, the maximum cmpsitin f ammnia by weight in a slutin f ammnia and water as a functin f pressure and temperature. During the absrptin prcess, the heat f absrptin, which is the equivalent f the heat f cndensatin f the liquid, must be remved fr the purpse f hlding a lw temperature in the absrber and thereby maintaining a gd absrptin rate. Usually cling water is used t absrb this heat. a- Frm the absrber the strng slutin enters the pump at the system which raises its pressure and sends it thrugh a heat exchanger and t the generatr. The generatr perates at the cndenser pressure and is supplied with steam r ther surces f * "Rich slutin" is als ppularly used as an exchangeable term.

8 «a "6.? \Z <* c E D '5 0) E c C\j 5? E

9 NH,% by C * a weight "= ' i-lo % by weigh"? GO Fig. 3; Biling temperature f aqua Gmmnia slutin affected by pressure end cncentratin.w

10 * f heat thrugh heating cils which drives ff sme f the refrigerant frm the liquid, decreasing the cncentratin f the liquid until it becmes a weak liqur. The vapr distilled frm the slutin in the generatr is cmpsed f refrigerant vapr alng with small quantities f absrbent vapr, and when this mixture is cled in the rectifier, the absrbent vapr saturated with refrigerant is cndensed and flws back int the generatr. By- this means, part f the refrigerant is vaprized frm the strng slutin in the generatr; the remaining slutin is a mixture f liquid absrbent with a relatively small cncentratin f refrigerant disslved in it. This remaining slutin is called the weak slutin. It leaves the generatr, flws thrugh the heat exchanger, the slutin valve and then int the absrber. In the heat exchanger the weak slutin which cmes frm the generatr heats the strng slutin which is sent up frm the absrber thrugh the pump. This reduces the amunt f heat required In the generatr. Neglecting the pressure head lsses due t frictin, we can cnsider that in an absrptin refrigerant system there are tw distinct pressure levels which exist within the unit; the high pressure which exists in the heat exchanger, the generatr, the rectifier and the cndenser; the lw pressure which exists in the absrber and the evapratr. After the weak slutin has been cled in the heat exchanger it enters the slutin valve, which acts as a thrttle valve, where its pres- * Such as electrical heating; but steam heating is preferable due t its lwer cst.

11 9 sure is reduced frm the high pressure t the lw pressure, and then flws int the absrber. The refrigerant which was vaprized in the generatr cntains sme absrbent vapr. Since this absrbent vapr will cndense at a much lwer temperature than the refrigerant vapr, this mixed slutin is passed thrugh a rectifier t cndense the absrbent vapr in rder t btain pure refrigerant vapr. In the rectifier the refrigerant vapr is cled sufficiently t cndense the surplus absrbent which is separated and returned t the generatr. It is imprtant t keep the absrbent vapr t a minimum t prevent the accumulatin f liquid r slid state absrbent in the cndenser r refrigerant cils. 1«3«Cyclic Analysis f an Absrptin Refrigeratin System in Terms f the Circulating Fluids ^ Attentin has been previusly directed t the principles f the absrptin refrigeratin system in terms f the prcesses that ccur in each piece f apparatus. Nxtf, the system vrill be analyzed frm the viewpint f the fur sub-cycles which cnstitute the whle system. (1) Refrigerant Vapr Cycle After the strng slutin in the generatr is heated t the pint f driving ff sme f the refrigerant vapr, with a small amunt f absrbent, this vapr passes thrugh the rectifier where the absrbent is cndensed and the refrigerant cled. The absrbent is separated and returned t

12 10 the generatr while the refrigerant vapr passes thrugh the cndenser where it is cndensed. The liquid then flws thrugh the expansin valve t the evapratr where it takes up heat and is revaprized. Frm the evapratr it passes int the absrber and is absrbed by the cled weak slutin. This weak slutin is thus changed t a strng slutin which is pumped by the refrigerant pump thrugh the heat exchanger t the generatr. This cmpletes the cycle. (2) Weak Slutin Cycle When the strng slutin is subjected t high temperature in the generatr, sme f the refrigerant in it is vaprized thus prducing a weak slutin. This weak slutin is cllected at the bttm. f the generatr. In rder t maintain cnstant liquid levels in the generatr and the absrber, the flw f strng slutin t the generatr must be f such value that it equals the sum f the flws f weak slutin frm the generatr and the refrigerant t the cndenser. The weak slutin flws frm the generatr t the heat exchanger where it is cled. It then flws t the absrber where it absrbs the cld refrigerant cming frm the evapratr, and is further cled. The absrptin changes the weak slutin t a strng slutin.

13 11 (3) Strng Slutin Cycle As mentined in the refrigerant vapr cycle, the strng slutin frmed in the absrber by the unin f refrigerant vapr and weak slutin is picked up by the pump, frced thrugh the heat exchanger where it is warmed, and then passes t the generatr t be heated further. (4) Cling Water Cycle When the cling water is cld, it is cmmn practice t let the water circulate first thrugh the cndenser. Here it liquefies the refrigerant and cmes frm the cndenser sufficiently cld t be used in the absrber. Frm the absrber cling water is circulated thrugh the rectifier. In warm weather, where a suitable supply f cld water is nt available, separate water supplies are maintained fr the cndenser, the absrber and the rectifier. Whether separate cling water supplies are used r nt, in either case the water cming frm the cling systems may be passed t the sewer discharge r carried either t cling twers r spray pnds t be re-used. Whereas sme pwer is used in sending such water thrugh the cling prcess f either spray pnds r cling twers, there are certain advantages in reusing this water. The water used and reused des nt scale s badly, since it has nly s much hardness t depsit, and nce this is separated the water is practically nn-scaling. Further, unless very

14 12 cheap water Is available, it is seldm pssible t secure it, either by pumping r by purchase, at as lw a cst as by cling it either by sprays r cling twers. The fur sub-cycles which have been described abve can be seen frm Fig. ^ n page 13.

15 1 I ' _ 13 L. It t >.-. (vrrgeranv Week z.^lir. Strng slutin M Clina wafer 1 1! Gcnercvr N i : 51 plv i i ; Q'AOAzr,: «i X 1 i f If, Pusrn /"7s v v,.:v. i bvprvi in C! -.'- - ft «*

16 Ik SECTION 2 First Law and Secnd Lav; Analysis f an Absrptin Refrigeratin System Althugh the analysis f the reversible cycle by means f the reversed Garnt relatin is useful fr determining the limiting cnditins, we shall nw cnsider a mre detailed analysis f a real cycle with irreversibilities. In this sectin the analysis cnsists f mass and energy balances arund the varius cmpnents as well as arund the whle system. A schematic diagram f an absrptin refrigeratin system is shwn in Fig. 5 A binary mixture with apprpriate prperties (fr example, NH~ - RgO, HpS^ - R-O) is vaprized in the generatr by the additin f a quantity f heat Q at the generatr S pressure P. As a result vapr refrigerant, fr example, ammnia, is prduced. Let x = dente pure absrbent and x = 1 dente pure refrigerant cncentratin. The pressure P- a is chsen s that the entire refrigerant vapr can be liquefied in the cndenser. Fr the fluid flw thrugh the expansin valve, the cndensate is thrttled t the lwer pressure P, T and the saturatin temperature falls. In this way the liquid can evaprate at a lwer vaprizatin temperature, T, with the additin f the heat quantity Q (the s-called refrigeratin capacity). The cl refrigerant vapr (3)* cming frm the evapratr * Specified numbers in parentheses, ( ), refer t the crrespnding sectins which is labeled in Fig. 5-

17 15 T,- Fig.5. Typical absrptin refrigeratin system

18 16 is sent int the absrber where it is absrbed by the cl slutin with the remval f an amunt f heat Q. The refrigeratin prcess f the absrptin system is based n the fact that a cld vapr can be absrbed by a warm liquid slutin. The weak slutin f cmpsitin, x, cmes frm the generatr, passes thrugh the heat exchanger, is thrttled in the slutin valve t the absrber pressure, P L, and passes int the absrber. The cld vapr f state (3) is induced, and this is absrbed by the weak slutin, thereby becming a strng slutin. The absrptin f vapr prduces heat. In rder t maintain the absrber at a sufficiently lw temperature, cling water is circulated thrugh cils in the absrber. The enriched cld slutin is pumped t the higher generating pressure, P, warmed thrugh the heat exchanger, and is again vaprized in the generatr. The rectifier prvides the final drying effect by cling and delivering pure refrigerant vapr t the cndenser. The drip frm the rectifier is returned t the generatr. In this way the ttal cycle cntinuusly wrks withut interruptin Mass Balance^ ' ^' In steady-state perating cnditins, the quantities f mass supplied t and remved frm each apparatus must be equal. This refers bth t the ttal quantity f the mixture as well as t a simple cnstituent. Fr the purpse f finding the rate f flw f pure refrigerant t the cndenser, let M, where n = 1, 2, 2a, 3t ^. ^i 5,..., 10, dente the mass f fluid that crsses the varius

19 17 sectins indicated n Fig. 5» Hence, at the absrber, the refrigerant mass balance is M 5 x 5 = (M 5 - M 3 )x w + M 3 x 3 (1) in which x = x r = x^ = x, dentes the weight cncentratins f s the strng liquid slutin, and x w = x jj, = x i a = x 8 = X 10' dentes weight cncentratin f the weak slutin. Fr each pund f refrigerant absrbed frm the evapratr, the amunt f refrigerant circulated in terms f the weight cncentratins f strng slutin (x ) and f weak slutin (x^) is g M 1 - x This means that fr each pund f the refrigerant vapr prduced, the specific slutin quantity G must be pumped frm the absrber thrugh the heat exchanger t the generatr. The quantity f weak slutin that flws back t the absrber is M - M 1 - x G-l = -5-g-i = -^ (lb m /lb m Of Hj\ (3) Frm equatins (2) and (3) we can see that the smaller the degassing breadth, x - x, the larger must be the specific slutin circulated; nevertheless, this is still restricted by the chemical cmpsitin f the refrigerant absrbent slutin. Further M l = M 2 = M 2a - M 3 (4)

20 ^ 18 M 5 = M 6 = M? = Mg + 1 (i+) In assuming the fluid flws steadily, the amunts f material stred in the generatr and the rectifier d nt change with time. Fr the refrigerant flw in the generatr, x? M? = x 8 W 8 +1 (5) Substituting the assumed values fr x n and x Q, r x and x, int 7 s w* (5) we can get the values f M~ and M. T find the amunt f vapr leaving the generatr and the amunt f cndensate returning t it, we equate the quantities flwing int and ut f the rectifier; we have m q = m (6) Fr the refrigerant alne, we have x 9 M 9 = x 10 M 1Q 1 (7) where x^, as has been shwn abve, is identical with X. The cncentratin Xq, n the ther hand, is that fr the refrigerant and absrbent in the vapr phase which is in equilibrium with the weak slutin (liquid phase) at the pressure and temperature existing in the generatr. T find the maximum values f x Q and x, Q, we can refer t tables and charts which give the maximum cncentratins f the refrigerant and absrbent, fr bth the vapr and liquid phases, as functins f the pressure and temperature Energy Balance^ Fr any piece f apparatus, the energy equatin fr steady flw, neglecting the change in kinetic energy and ptential

21 19 energy terms, is E = 2 ( Mh ) ut " 2 < Mh) (8) in where E dentes the wrk input fr the pump r heat transfer fr all ther pieces f equipments, 2(Mh) dentes the enthalpy f Qut all the fluids that flw ut while 2(Mh) dentes the enthalpy ln fr all the fluids that flw in, based n unit mass f the refrigerant flwing thrugh the evapratr. (1) Heat Exchanger Neglecting heat transfer with the surrundings, the equatin is M? h? * M^ - M 6 h 6 - M 8 hg = (9) (2) Generatr In the generatr, the energy input f the strng slu- * tin is M? h 7, the energy supplied by the drips frm the rectifier is M. the energy leaving with the weak slutin, as it flws int the heat exchanger, is Mghg, and the 10^10 energy leaving with the vapr as it flws t the rectifier is M h. Hence the energy balance is q Q E = Q g = M 8 h 8 * M 9 h 9 ' n 7 h 7 " M 10 h 10 (10) where Q dentes the amunt f heat supplied t the gener atr per unit mass f refrigerant passing thrugh the evapratr.

22 20 (3) Similarly, fr the rectifier, the cndenser, the evapratr and the absrber, we can get the simplified energy equatins accrding t equatin (8) as fllws: Q r = h + M h l l0 10 * M h (11) 9 9 Q c = h 2 " h l ( 12 > % = h 3 - h 2a C13) Q a = M 5 h 5 - M^h 4a - h 3 (14) where Q, Q, Q and Q represent the amunt f net heat transfer in the rectifier, the cndenser, the evapratr and the absrber, respectively. (4) Pump Wrk This can be calculated apprximately by the usual equatin fr ideal pump wrk 144 G V (P - P ) % - hr ci5) i'n which Q dentes the ideal pump wrk input in BTU per pund f refrigerant vapr which circulates thrugh the evapratr; P~ and P, dente the generatr and the evapratr pressure in punds per square inch abslute, respectively; V" s dentes the specific vlume in cubic feet per pund f strng slutin as it enters the pump frm the absrber. Or, by equatin (8) % = M 6 h 6 - lj[ 5 h 5 = n 6< h 6 " h 5 ) < l6 >

23 21 (5) Overall Heat Balance Fr a heat balance, all energies supplied t and remved frm the whle system are identical. Summarizing the abve energy equatins, we have Q + a Q + c Q + r Q + Q + Q = (1?) g p e (6) Steam Cnsumptin A cmmercial tn f refrigeratin is equal t the absrptin f heat in the evapratr at the rate f 288,000 BTU per day r 12,000 BTU per hur. The value f 12,000 BTU per hur is based n the heat required t melt ne tn f ice in ne day r Hj4 x ~jp = 12,000 BTU/hur, where 144 BTU is the latent heat f fusin f ice at atmspheric pressure. Thus the steam cnsumptin in the generatr per tn per hur is 5a. 12,000 (18 ) where h~ is the latent heat f the heating medium (such as fg steam) at the temperature f the heating cil Secnd Law Analysis f An Absrptin Refrigeratin System (1) Intrductin The Secnd Law f thermdynamics states that n prcess can be devised whse sle result is the absrptin f heat frm a reservir (surce) f ne temperature and transfer f this heat t a reservir f higher temperature; r by itself

24 22 heat can nt flw, by any means, uphill. In accrdance with this statement, fr the purpse f the transfer f a certain amunt f heat frm a cld strage temperature t the surrunding temperature, there must exist a prcess which can cause this heat transfer; hwever, the Secnd Law f thermdynamics has nt restricted the kinds f necessary cmpensating prcess. Therefre, the prcess may be selected as mechanical wrk f cmpressin, r by thermal energy input cmbined with fluids that have suitable prperties. The absrptin refrigeratin system is cnsidered t be a successful system in utilizing the cmbinatin f the recrded methds. Furthermre, there are a number f additinal ways by which it might be pssible t effect varying degrees f imprvement in the perfrmance f an absrptin refrigeratin system. T discuss all such methds in detail is beynd the scpe f this reprt. Befre we cnsider the prblem t imprve the perfrmance f an absrptin refrigeratin system we have t have a cncept f determining the minimum heat expenditure required t attain a desired cling capacity. In this sectin, entrpy change fr each prcess, perfrmance rati, cncepts f availability and irreversibility are invlved. (2) Entrpy Changes N cycle is mre efficient than a cmpletely reversible cycle. If each prcess f a cycle underges a revers-

25 23 ible prcess, and all ther systems assciated with the cycle underg reversible prcess, the ttal change f entrpy f the universe is zer. Nevertheless, if any prcess f a cycle underges an irreversible prcess, the entrpy f the universe must be increased due t the entrpy creatin during this prcess. This als means that the amunt f entrpy change due t the irreversibility is the direct measurement f the resulting lss n efficiency due t the irreversible prcess. Since entrpy is a state prperty, the entrpy change f any prcess, regardless f the reversibility r irreversibility f the prcess, can be evaluated by the integral f -sr alng any reversible path, r by the equatinal frm S II " 3 I - {"'f'rev ("I in which subscripts I and II dente initial and final state f a prcess, respectively. Fr a cyclic analysis, the end state being the same as the initial state, <j> ds = 0. Furthermre, by the Clausius inequality 'M f T < (20) where the equal sign indicates the limiting r reversible cycle, while P~p < hlds fr any cycle which is cmpsed f irreversible prcesses. The general frm f the entrpy balance equatins, fr any prcess, can be expressed by

26 24 2S in + treated + ' f = 2S ut + * 3 stred < 21 > in which 2S in and 2S Qut are entrpy fluxes due t the fluid flw, and T is the temperature f the fluid which emits the heat which is transferred. In the fllwing discussins, in which the system is in steady state cnditin, the last term f the abve equatin is zer. Further, in an analysis f an absrptin refrigeratin system, as has been shwn diagramatically n Fig. 5. we shall cnsider the surrundings, r atmsphere, as the cling water that flws t the cndenser. The temperature f this cling water (r atmsphere) is designated as T n. The temperature f the steam supplying heat t the generatr and the refrigerated space are each assumed t be cnstant and are designated as T and T, respectively. g e Further, in an analysis f a practical prblem, a finite temperature difference must exist in each heating r cling prcess, s that the heat can be transferred. Nevertheless, if we assume that in the absrber there is a great amunt f cling water which circulates thrugh the absrber, the temperature f the absrber can be taken as the cling water inlet temperature instead f taking the average temperature f the cling water in the absrber. This will be dne als fr the cndenser and fr the rectifier. The ttal heat flxv t the surrunding, r cling water at temperature T Q, is cmpsed f the heat transferred frm the absrber (Q_), that transferred frm the cndenser C*

27 25 (Q ), and the rest frm the rectifier (Q ). Cnsequently, c r the ttal amunt f entrpy increase f the cling water is Q a + Q c + Q r S a+ c+r ^-Tg ~ U2) Equatins f entrpy balances fr these three prcesses, accrding t the equatin 2 s created = 2S Qut - 2S ln - / -$ under steady state cnditins, are, fr each pund f refrigerant cndensed, S. dq r. = (M-S- - M,, S,. - S_) - f a^ (23) created, a 5 5 4a 4a 3 T Q * " S. dq. = (S - S n ) - / 2- created, c 2 1' J -7JT T c (24) x ' S created,r " < S 1 M 10 S 10 " M <?V " ' ^ (25) S^^, *-~j ^ represents the amunt f entrpy creatin ere iceu. 1 s. due t the mixing f fluids f different temperatures in the absrber. In the cndenser, if the pressure drps due t fluid frictin, and a finite temperature difference is cnsidered t exist between the cndensing refrigerant and the cling water, the ttal amunt f entrpy creatin due t these tw irreversibilities is S created,c = AS f.c +AS at c Q Q = as + (=2. ) (26) 1,0 i X c where subscripts f and AT dente the frictin and the c finite temperature difference, (T - T«), in the cndenser, c u

28 26 respectively. This methd f analysis is still available fi" ther apparatus, such as the evapratr, the generatr, r the absrber, if the finite temperature differences are nt neglected. In the evapratr, in the present analysis, we still assume that the amunt f heat received by the refrigerant in the evaprating cil is transferred frm a large reservir at the saturatin temperature f the refrigerant in the evapratr s that the finite temperature difference is neglected. The amunt f entrpy flw frm the dq e refrigerated space t the evaprating refrigerant is / e Hence the equatin f entrpy balance fr the evaprating prcess becmes ^ treated, ' e = (3 2a " S 2> " J " e '"> Similarly, fr the generating prcess, treated. g = < M V 9 " V? " M 10 S 10> " / "** < 28 > The pumping prcess is cnsidered here t be an lsentrpic prcess, i.e. S created,p = (29) Fr the heat exchanger, the slutin valve, and the expansin valve, we assume that there are n heat transfers t r frm surrundings, i.e. Q = Q = Q = 0. Hence, X V S 27S the equatins f entrpy balances fr these three apparatus are

29 S created,ex. = M 6 (S 7 " S 6> * V S^ " V ( ) S created,vs. = M^ (S i4-a " V (31) S created f ve. = S 2a " S 2 (32) The Clausius inequality fr the nn-ideal cycle is <&Q Q p- Q e Q a Q r Q c g e a r c and fr each prcess 11 do Further, AS. = universe ES created = A3,. - (3 + 3 ) (35) atmsphere e g'»->-" in which atmsphere : ' e +:i g + created,g created, a * created,c created, r created, e created, ex S, (36) created, vs created, ve x J ' (3) Perfrmance Rati The amunt f wrk and/r heat required t mve a certain quantity f heat frm the cld strage rm is an imprtant factr in the analysis f an refrigeratin system. In a cmpressin refrigeratin system, this factr is expressed by "cefficient f perfrmance"; hwever, in an * Sme authrs use "heat rati" as an exchangeable term,

30 28 absrptin refrigeratin system the ttal energy input is the sum f the mechanical wrk which is dne by the slutin pump and the thermal energy which is supplied frm the heat surce temperature, T. Therefre, befre cnsidering the perfrmance rati, we have t cnsider, with the aid f the Secnd Law, hw much equivalent quantity f heat is cnsidered t be supplied frm the heat surce temperature, T, crrespnding t the actual pump wrk input. This equivalent amunt f heat may be expressed by the relatin Frm equatins (17) and (33), we have 2g % Q a + Q e + Q r T g e l + T T (38) Substituting equatin (17) int (38), and after rearranging, we get % v^ Q* 2 -\* T T _ T V^ T (39) The perfrmance rati, <$, f an absrptin refrigeratin system is defined^ 10 ' as Q 3 *a = Q-TT- " 1 W> S PP g Q + Q S Tg -T S * In this sectin the subscripts a and k dente absrptin refrigeratin systems and cmpressin refrigeratin systems, respectively.

31 29 Substituting equatin (39) int the denminatr f equatin (40), we get i % % e g whe re (0P) rev " tttv (*«> e is the cefficient f perfrmance f a refrigeratin prcess f a reversed Carnt cycle (with mechanical drive) between the surrunding temperature, T Q, and the refrigerated space temperature, T, and <1>rev - ^V^ <*3) s is the thermal efficiency f a Carnt engine which perates between the heat surce temperature, T, and the surrunding S temperature, T Q. If the energy is assumed t be supplied by the quantity f equivalent heat, (Q + Q ), S PP the perfrmance rati, <, f the absrptin refrigeratin system will then ex be the limiting case f a reversible cycle; that is & = (CP) v (*]) (UU) ^ct.niax. 'rev v ' *'rev This is the cmbined, ideal case f a reversible refrigeratr perating between the surrunding temperature, T n, and the refrigerated space temperature, T, with cefficient f

32 30 perfrmance, (GP), and a reversible heat engine, perating between the heat surce temperature, T, and the surrunding s temperature, T Q, which is supplied heat by the amunt (Q + Q ). and which perates with the thermal efficiency 6 PP C ). In an actual case, where irreversibilities exist, the actual perfrmance rati, $, f an absrptin refrigeratin system must be less than the ideal, r maximum, value, <. Or, expressing this in equatinal frm, we have & x < $ (45) a x a, max Furthermre, the value f < (which is the revers- ^ctmax. ible case) depends upn the temperatures T, T~ and T ; its value can be greater than r smaller than unity. Hwever, the perfrmance rati, $, gives a cncept fr measuring the fractin f energy input (Q^ + Q ) which can be cnverted int the refrigerating capacity Q. The qutient *a,inax gives the efficiency rati f the prcess in which < d> < 1. The difference 1-6 (47) P= dentes the degree f irreversibility, which shws that as a result f irreversibility the p-th part f the input energy (Q- + Qnn is degraded. ) Obviusly, we can nt directly cmpare the perfrmance rati, $, f an absrptin refrigeratin system with the

33 31 cefficient f perfrmance, (CP) k, f a cmpressin refrigeratin system (equal t the rati, J Q e A^ cnp# ) even if these tw different types f refrigeratrs were assumed t be perated between the same temperature range f T Q and T Q, Hwever, a cmparisn can be made between ( cp ) a (the cefficient f perfrmance f the absrptin cycle) and (CP) k. Cnsider a thermdynamic efficiency term, \ fc, defined as the rati f the sum f the increase in available energies f the fluid in the generatr and in the pump, and the T sum f the heat terms, Q and = &-sr Q-. Fr the ideal s x p ^.g case, in which there is n degradatin f energy in the T - T generatr r the pump, " t = -*» ; in the actual case r rr < x.. The cefficient f perfrmance is defined It kt.max (CP)_ - * - f W) while, as given abve It s T g r p r (GP) k ~ W cmp, Further details will be shwn numerically in Sec (4) Cncepts f Availability and Irreversibility^ ' * ' * In basic analyses fr prblems f thermdynamics, it is ften maintained that thermdynamics is cncerned with reversible prcesses and equilibrium states, and that prblems assciabed with irreversibility lie utside its scpe. On the ther hand, the First Law f thermdynamics states that

34 32 heat and wrk are mutually cnvertible, but, since energy can neither be created nr destryed, the ttal energy assciated with an energy cnversin remains cnstant. Hwever, the thermdynamic analysis f a system exchanging heat and wrk with its surrundings can nt be mre than the tabulatin f energies received and rejected by the system when the analysis is based slely n the First Law f thermdynamics. Hwever, the Secnd Law analysis, n the ther hand, is based n the cncept f available and unavailable energy assciated with the degradatin f available energy by irreversibilities. High grade energy may be transfrmed int the mechanical wrk with nly small lsses. The lsses f high grade energy are due t the mechanical r electrical imperfectins within the devices themselves, but nt because f sme theretical limitatin f energy transfrmatin. Fr instance, f the ttal amunt f rtary shaft wrk which is. delivered t a pump r cmpressr, a large fractin f it is delivered t the fluid as mechanical energy with nly a minr fractin f it degraded by frictin. Of lwer grade energy, such as thermal energy, nly sme part f it (the available energy) can be transfrmed int the useful wrk while the rest f it is unavailable energy which can nt be used as rtary shaft wrk. Suppse that there is a state f a system which is nt at the dead state, then it will naturally and simultaneusly change its cnditins twards

35 34 be delivered by the fluid t the surrundings is the quantity given by a reversible engine which brings the fluid frm state (I) t the state (D) which is in equilibrium with the surrundings. The maximum amunt f wrk is established by assuming that the heat given ut by the fluid is delivered in an indefinitely large number f steps t a series f Garnt engines which wrk between the temperature f the fluid at any instant as surce and the temperature f the surrundings. The wrk delivered by the engines may be cnsidered t be stred as mechanical energy in external systems. Assuming the fluid has reached a certain state with pressure P, temuerature T, and vlume V, then the abstractin f dq T - T D units f heat frm the fluid delivers (- ^ dq) units f wrk frm the Garnt engine perating at this temperature T - T level. The quantity ( ^ ^ dq), termed "the mtivity" by Kelvin, is always greater than zer because the terms (T Q - T) and dq are always f the same sign; fr instance, dq is psitive when heat is received by the fluid and (T n - T), r -(T - T n ), is psitive. The reverse case is als true when the heat is given up by the fluid. Other than the wrk btained frm the exchange f energy between the fluid and surrundings, wrk may be btained further if a pressure difference exists, i.e. if P / Pp. Hence the maximum wrk which is btainable in the step is

36 35 du max = ^T-^l- (*-.*D>«(50) Prm the First Law, we have dq = du + PdV (5D and fr a reversible prcess, we have d3 = M) (52) v rev. T ' Slving equatins (50), (5D and (52), we get dw = - du - P n dv + T n ds (53) max D D Integrating frm state (I) t state (D) gives "max " < U I " V " P d' V I " V " T D (S I 7 V r W max " (U I * P D V I " Vl> " (U D + P D V D " T D S D ) <^> The value f the difference f equatin (5*0 is called the available energy at state (I). Fr any tw states, say (I) and (II), the difference f available energy with respect t the surrunding temperature and pressure f T^ and P Q is (13) given by K J ' AAE = (U IX P D V XI - TjjSjj) - (U x + PqVj - T D 3 Z ) (55) Keenan* ' expresses, the maximum wrk btainable as represented by the difference in the availability t prduce wrk between the initial state and dead state, designated as the decrease f availability (-AB) in the fllwing expressin. W = -AB = B (5&) max The available part f flw wrk is added t equatin

37 36 (5*0 resulting in U - T 3 D + P D V + (P I "? V D> I D U - T D 3 + P D V + (P - *H U - T n 3 + PV -l h - T D S (57) Accrdingly, the change f availability between any tw states, (I) and (II), in a steady flw prcess can be evaluated by Ab = b IX - bj = (h I;[ - T S D IX ) - (hj - TqSj) (58) In general, changes f kinetic energy and ptential energy terms shuld be cnsidered; hwever, fr analyzing refrigeratin systems, these terms are all small cmpared with the ttal energy at each sectin and are reasnably cnsidered t be negligible. As multiple streams enter and leave an apparatus, such as the absrber, the generatr, the heat exchanger, r the rectifier, in an absrptin refrigeratin system, equatin (58) has the mre general frm as fllws, n m AB = 2 M b - T 2 MB (59) i X 11=1 1=1 in which M dentes mass; I and II dente inlet and utlet cnditins respectively; m and n dente the number f inlet

38 37 and utlet streams, respectively. Frm equatin (56) it can be seen that fr any reversible prcess, the decrease f availability equals the maximum amunt f wrk dne by the system while the maximum increment f availability equals the wrk added t the system. Fr any irreversible prcess W\ < W irr. max therefre W. < -A3 (60) irr. Hence, it is pssible t express the irreversibility f any wrk prducing prcess by the difference between the decrease f availability and the actual wrk btained. equatin The irreversibility (I) can then be evaluated by the T - T 1 = 1 t -^ d ^ ~ W s "* 3 (61) T - T where / ~ dq is the available part f the heat added during the prcess, W is the rtary shaft wrk utput during the prcess and AB is the change in availability f the system during the prcess. Furthermre, by the Clausius inequality / ds > ; ^ r / T Q d3 > t ; f Fr each prcess the irreversibility can als be expressed

39 38 by I = / T Q d3 - T Q / $& = Z(T Q A3) - T Q / &. Fr any clsed cycle 2(T Q A3) = Therefre, the irreversibility fr the whle cycle can als be expressed by I = - T Q zf (62)

40 39 SECTION 3 Cmputatin f a Typical Ammnia-Absrptin Refrigeratin System 3.1. Principal Determining Factrs The cmplete cycle f peratin f the absrptin refrigerating machine is illustrated with the aid f diagram in the previus sectins. Befre prceeding with the numerical prblem fr a cmplete cycle, it is well t nte what are the determining factrs which are assumeable befre wrking the particular prblem. The cndenser perates in the same manner as in the cmpressin system. The temperature f the cling water, in the mst part, determines the cndenser pressure. Hwever, the quantity f water and amunt f cndenser surface must be f sufficient magnitude t realize a desirable cndenser pressure. The temperature f the water rises a few degrees in passing thrugh the cndenser, and there is a small temperature difference between the water, leaving the cndenser and the temperature f the cndensing refrigerant in the saturated prtin f the cndenser. The temperature f the evaprating fluid in the evapratr is determined by the temperature desired in the cld strage rm. The difference in the temperature f the cld strage rm and the evaprating fluid is als affected by the amunt f heat transfer surface which is used. The temperature f the evapratr must always be a few degrees belw the temperature f the

41 JU-0 cld strage rm. The pressures, f curse, crrespnd t the varius biling temperatures f the fluid in the evapratr. In a like manner, the temperature f the water available fr cling the absrber affects the cnditins in the absrber. It is evident that the absrber must be. supplied with cling water, since the changes f states, such as cndensatin, are accmpanied by a liberatin f heat. With cnsideratin t the relative amunt f heat transmitting surface in the absrber, it is evident that the temperature f the cling water will determine the temperature f the mixed slutin in it. The temperature f the slutin must always be a few degrees abve the water temperature s that the heat f cndensatin and absrptin f the refrigerant vapr will flw int the cling water. Thus, since the pressure is apprximately the same as that f the evapratr, the exact cnditin f the slutin may be determined at nce. Knwing the temperature and pressure f the chsen refrigerant, the maximum cncentratin can be determined by the experimental frmula r by related tables. In a similar manner, the pressure in the generatr and the rectifier is determined by the cndenser pressure, which in turn depends upn the cndenser water temperature. Als it is bvius that heat must be supplied t the generatr t remve the refrigerant vapr frm the mixed slutin in the generatr. This is generally supplied by saturated steam, and the temperature f the steam must be a few degrees abve the temperature f the slutin in rder t cause the heat t flw int the slutin, thereby

42 41 distilling ff the refrigerant vapr and sme absrbent vapr. Hence, since the pressure and temperature are easily determined, the maximum cncentratin can be fund readily. Prm the abve discussins, it will be nted that the temperature f the cling water and the temperature that is desired in the cld strage rm are principal determining factrs. In accrdance with these principal determining factrs, and reasnably made assumptins, a typical example fr cmputing the perfrmance f an ammnia absrptin system is given in the fllwing sectin Example f a Typical Ammnia-Absrptin Refrigeratin System The fllwing assumptins are made: The pressures in the generatr, the rectifier, the cndenser, and the heat exchanger are identical and are equal t psia The temperature f the atmsphere is 5^0 H The temperature in the evapratr is ^70 R it The vapr leaving the rectifier (1) is pure NH-, and is at the saturatin temperature crrespnding t its pressure. There is sufficient turbulence in the generatr during the mixing f strng and weak slutins; the cncentratin existing * The numbers in parentheses refer t the sectins crrespndingly labeled in Pig. 5.

43 42 in the mixed slutin is in a cmplete unifrm cnditin s that each f the streams at sectins (8) and (9) has the maximum cncentratin f ammnia cmpatible with the pressure and temperature in the generatr. Cnsequently, the weak slutin leaving the rectifier, (10), is in equilibrium with the vapr entering it and is therefre f the same cncentratin and is the same state as the slutin leaving the generatr (8). The liquid leaving the cndenser (2) is saturated liquid at the pressure f the cndenser. The vapr leaving the evapratr (3) is saturated vapr at the pressure f the evapratr. The weak slutin enters the absrber (4a) at 560 R and leaves (5) at 540 R as a strng slutin. The maximum, r equilibrium cncentratin at (5) can be apprximately evaluated by the Mllier equatin^ ' x- = (^ ) 5 T a T where T and T are average temperatures at the evapratr and the absrber, respectively. Therefre x = (t! ) 5 = Nte that this maximum value can als be checked by Pig. 3, r by Fig. 19. Aqua-ammnia Chart f reference (9) (by Smswiller and Schwartz*, McGraw-Hill Bk C.), r by Table- Prperties f Slutins f Ammnia and Water (page 346 f reference (5) by K.

44 k3 J. Mac in tire, Jhn Wiley & C.). In an ideal case, if we assume that there is a sufficiently large vessel fr the absrber with a design mechanism which will cause a cmplete mixing cnditin in the absrber, then the cncentratin f the fluid at the utlet stream f the absrber can reach the abve value. Hwever, in an actual design prblem, the cncentratin f the utlet stream f the absrber is always less than this value. Accrdingly, assume x = x = s (1) Mass Rate f Flw at Each Sectin Let M-, = M = n = M, = 1 lb f NH, 1 2 2a 3 ni 3 M = punds f strng slutin circulated per pund f ammnia cndensed Mg = punds f weak slutin circulated per pund f ammnia cndensed x«= weight cncentratin f strng slutin = The weak slutin leaving the generatr (8), Xn = 0.13 by weight which is the maximum cncentratin f ammnia cmpatible with the pressure and temperature in the generatr. Fr steady state cnditins, M? - Mg = 1. (63) and M? X? - MgXg 1. (64) Slving equatins (63) and (64), we get

45 ^ 7 r x? - x " ^ lb /lb NH cndensed m m 3 J and M 8 = 5.^38-1 = kaj8 lb /lb NH cndensed m m 3 Equating mass flws int and ut f the rectifier, M 9 - M 1Q = 1 (65) By assumptin Xg = x, Q = The cncentratin x Q, n the ther hand, is that f vapr which is in equilibrium with a 13 per cent slutin f ammnia at the pressure existing in the generatr. Emplying the chart f the enthalpy-cncentratin diagram v ' fr the system NH--H 2 0, we get x = Fr the ammnia alne, we have X M 9 9 " X M = 1 (66) Slving equatins (65) and (66), we get 1 " x 10 ri 9 x 9 " x " and = 1.8*13 lb /lb NH~ cndensed m m 3

46 ^5 M 10 = M - M x = = 0.8^3 lb m /lb m NH 3 c ndensed (2) Energy Balance Befre emplying the equatins which have been derived in the previus sectins t calculate the energy balance, the surce data fr the calculatin will be nted here. Values f availabilities at each sectin are taken frm Warburtn (see page 305 f reference (6)) where the prperties f ammnia are frm Jennings and Shannn. In rder t check Warburtn 1 s values f availability, ammnia tables frm the United States Bureau f Standards^' were used. As the base fr the ammnia tables f Jennings and Shannn is different than that fr the United States 3ureau f Standards Tables, a crrectin fr bth the enthalpy and entrpy terms was necessary, which was dne in the fllwing manner: In a ftnte t Table IV, page 25^ f reference (6), it is stated that the values f enthalpy taken frm the United States Bureau f Standards Tables were reduced by 77.Q BTU/lb m. Prm Warburtn' s values f availability at the inlet t the cndenser, the inlet and utlet f the expansin valve, and the utlet frm the evapratr, the values fr entrpy were calculated. These entrpy values were then cmpared with thse f the United States Bureau f * T. Warburtn, master's thesis, M.I.T., 1938.

47 Q r = h l + M 10 h 10 - M 9 h Standards Tables. In each case it was fund that Warburtn*s values f entrpy were less by BTU/lb R m than thse fund In the United States Bureau f Standards Tables. By means f equatins (10), (11), (12), (13), (14), (15), and (16) we set % = M 8 h 8 + M 9 h 9 " M 7 h? " M 10 h 10 = x x x x239 = BTU/lb^ NH 3 cndensed = x x890 = BTU/lb NH, cndensed Q c = h 2 - h x = = BTU/lb m NH., cndensed ^e = h 3 - h 2a = = BTU/lb m NH g cndensed

48 1*7 ^a n 5 h 5 ~ M ^a h 4a - h 3 = 5.^38x(-^0.5) - ^.^38x = BTU/lb m NH cndensed Q P M 5 (h 6 - h 5 ) = 5.^38 (-^0.1 + ^0.5) = 2.18 BTU/lb NH~ cndensed m 3 Or by equatin 1 15) Q P 1^ G V S (P R - P L ) 778 = 1^(4 x 5.^375 x ^( ) 778 = BTU/lb NH, cndensed m 3 in which the value f V q, which is a functin f temperature and weight cncentratin, is taken by interplatin frm the table f "Specific Vlume f Aqua Ammnia Slutin"^) by Jennings and Shannn. Substituting these values int equatin (17), we have Q g + Q e + Q p = 22^+3.91 and Q a + Q c + Q r = -22^3.72 The right hand side f equatin (17) must be zer. The trivial discrepancy ccurs frm the cncerned values f weak and strng slutins which are carried t finite decimal places.

49 ^ 1*8 (3) Steam Cnsumptin The steam cnsumptin at the generatr per hur per tn f refrigeratin can be evaluated by equatin (18), i.e. Steam Cnsumptin. ^.. 1$$.,^00, = ^9.73 lb f -steam/hr tn. (*0 Perfrmance Rati 10 ^ Accrding t the equatins derived in 3ec. 2.3, Q T PP T^T^Sp : 65?j) 5lH) * 2 ' 18 " 7 ' 380 BTU/lb NH- cndensed n 3 *a " Q + Q n " " u -^ ^ (GP) rev = T T A - T e = 5^ = 6,?1 ^3 T_ " - («) _ T T, p: _ 7^-1 - ^ _ k 29^ ; ( rev T ~ u.^y<+<+ S ^nax = (GP)( V = 6.71^-3 x 0.29^- = i. fc -. - ^«.max _SL- _ _- u.xjm- ^ x ' ' M- = 1- e = ^ = In cmparisn with a crrespnding cmpressin refrigeratin system, assuming the thermal efficiency, tj f a pwer installatin, including pwer transmissin lsses, is It = a 5-

50 49 Then, by equatin (48), (CP) = tsl _ _ -, v ;?686 a» t 0.15 " 1 *' 0Q0 This states that an absrptin refrigeratin cycle, which has a value f $^ > , can cmpete with a cmpressin refrigeratin cycle with a cefficient f perfrmance, (CP) k = I Figure 6 shws a diagram fr the ideal, r reversible, absrptin refrigeratin cycle which perates at the same temperature levels and the refrigerating lad, Q = BTU/lb m NH^ cndensed, as the numerical prblem discussed in this sectin. Area (D+S) represents the refrigerating lad, Q e. The ideal wrk required fr perating the refrigeratr is T - T T - T w _ -a is -2. ideal ~ y = g T % T S e which is represented by the area A, r (B+C). Area (A+B+D) represents the ideal amunt f heat supplied, Q. The ideal S cefficient f perfrmance is thus evaluated by (CP), je ^e T g " T p jj. 7 i. U ideal Q g - T g T Q - T e = (5) Entrpy Change in Each Apparatus The amunt f entrpy change in each apparatus, in the actual case, can be calculated by use f the fllwing frmula fr the difference in entrpies f the exit and in-

51 50 A h Fig. 6. Diagram fr an Idee! absrptin refrigeratr, cycle

52 51 let fluid streams, AS act = < M3 >ut " - (MS >in Referring t equatins derived in Sec. 2.3, we can calculate the entrpy change in each apparatus. Furthermre, the creatin f entrpy f the ammnia, due t frictin, is zer in the rectifier cndenser, the main cndenser and the evapratr, as these prcesses were assumed t be reversible. Likewise the creatin f the entrpy f the cling water, due t frictin, is zer in the rectifier cndenser, the main cndenser and the absrber. Hwever, in the rectifier cndenser and the main cndenser heat is transferred frm the ammnia at 550 R t the cling water at 5^0 R. These heat transfers thrugh a finite temperature difference f 10 F cause creatins f entrpy as fllws: AS,. a = M C S- - M,, S,, - S- act, a a 4-a 3 = 5-^38x0.05^8-4.^38x = BTU/r ib m NH 3 cndensed Q 3 AS created, a act " T«..U371. ( ) = BTU/ R lb^ NH cndensed

53 ' 52 act,c 2 1 = = BTU/ R lb m NH- cndensed created, c, AT ~ Q c *Tn " T ' C - M8-5 (550 " 53» = BTU/OR lb NH, cndensed m 3 * S act,r = S l * M M 9 S 9 = x x = BTU/OR 1^ NH^ cndensed Q r g _ a s - created, r act,r T ' = -I = BTU/ R lb m NH 3 cndensed The entrpy creatin, due t the finite temperature in the rectifier, is created, r, AT " *r v T n T' 1 = (Jjjr 54"0 " - ^r) 550' = BTU/OR lb m NH, cndensed Therefre, the ttal creatin f entrpy in the rectifier is BTU/r lbm NH cndensed.

54 A 3 act,e " 3 3 " S 2a = "W " ' 16^ = ^ 53 BTU/ Rlb m NH 3 AS act,g " M 8 S 8 + M 9 S 9 " V? " M 10 S 10 = 4.438x x x x = BTU/QR lb m NH cndensed s s - 5a _ 2 364? - U22+n S created,g ~ 4S =3. S act,g T ~ d '> W( e> = BTU/OR lb NR~ cndensed, = M,(3-3,) + act, ex created, ex 6 Mi,(S k - S) X 7 * ** = 5.438( ) ( ) s BTU/OR lb NH~ cndensed * S act,vs = S created,vs = M 4 (3 4a " S 4 } = ( ) = BTU/ R lb NH~ cndensed act.ve created, ve 2a 2 = = BTU/ R lb m NH cndensed ^3 = S. act,p created,, =

55 5^ 2S created = S created,a + S created,r, at + created, + S created,c, at * S created,ex + created, vs + created, ve = BTU/OR lb ffl NH, cndensed ^atmsphere = (3 e + S g ) + 2S created = = BTU/OR ib m NH~ cndensed (6) Changes f Availabilities and Irreversibilities By equatins (59) and (61), changes f availability and irreversibility fr each prcess can be evaluated as fllws AB a = M 5 b 5 - M^b 4a - b 3 = 5.i+38x(-70.1) x(-43.1) - (-95.6) = BTU/lb NH~ cndensed I = - a ab a _ BTU/lb NH~ cndensed Further AB s b - b, C 2 1 = (-7.7) = -8.5 BTU/lb NH- cndensed

56 - 55 AB C = b 2 - b x = (h 2 - T Q S 2 ) - ( hl - T Sl ) Q _ h c - T ^c T - T T c Therefre, 1=0 fr ammnia nly. This can be seen by referring t equatin (6l). Hwever, due t the finite temperature difference when heat is transferred frm the ammnia t the cling water, the available energy degraded is *c = TK (tt-th C = 540 (488.5 (3^- 3^)] = 8.86 BTU/lb m NH 3 cndensed AB r = b l + M 10 b 10 - M 9 b 9 = x x119.3 = BTU/lb m NH 3 cndensed T - T I r = ^ -Ztt-1 - ** r r = (-884.8) 55 " ^ - ( ) 5 5Q = BTU/lb m NH- cndensed The irreversibility created by heat transfer thrugh a finite temperature difference can be evaluated by

57 56 Z v - T [ V< T " f> ] = 5il [ 88 ^ (3^0-530)] - l6-9 BTU/lb m NH- cndensed. AB e = b 3 - b 2 = (-24.8) = BTU/lb m NH cndensed X e = AB g = M b + M b E h 9 9 " M b = 4.438x x x(-49.3) x1.5 = BTU/lb NH m cndensed 3 T - T it n I = Q^ -&= V- -AB S g T g g = ?65 7^ 3 5;40 " ^ BTU/lb m NBL cndensed = BTU/lb NH~ cndensed * B ex - V b 8 - V * V b 4 " V = 5.438( ) ( ) = BTU/lb m NH cndensed 3 I = - AB ex ex = BTU/lb m MHk cndensed

58 57 = f.^38(-^ ) = BTU/lb m NH~ cndensed X vs = - A3 vs = 1 «78 BTU/lb m NH 3 cndensed *B ve = b 2a " b (-16.2) = -8.6 BTU/lb NH~ cndensed X ve = - A \e = 8.6 BTU/lb NH, cndensed ^B n = -W P P 1=0 P = BTU/lb^ NH 3 cndensed

59 H\ Eh CQ {N- C\) c v in- H H (N- ON un ON un cv VO j± UN CM ON ON CN H ON H CM ON -ti" -cr - VO jj- rh I H H O En CQ rh cn- H v -.=}-.* ON ON C- On -d- UN v CV CM CM UN UN ON ON CM ON rh H r-1 H H ON ^ J* J* H O rh O rh O -d" U> ^}" UN c c VO c CM H \ D Eh H vo v O VT» un UN H H O ^4- UN UN 1N- UN UN O ^j- ON O ON v/n vo v ON CM CM _^- ^fr m ON ON ON VJN UN 1 1 H CM CM Ph cc G, vo VO un un vo UN UN vo VO VO VO vo O O c c O c c O O 00 ON n ON ON c c H rh H rh H H H H cc! O O c O O ON ON ON a * vo un UN UN -A. UN UN cv- IN vo VO * ON v VO VT\ UN ^ 3r UN UN un un vo c- CN- {N- S3 Xi H c ON ON (A ON ON ON n ON -3" O c O ^H-.=*.=* J* _^- cj- 00 H H H H ^3".* UN UN UN -rf- rh O Cm ko <H bo <M <M Cm CrH Cm «n M Cm O H -P cu c *^ *-H cs. ^-* Id -- *. ^^ ^-^,, O H CM CM ON ^±.* UN VO CN- ON H

60 59 -d -P cs^d B w rh O CQ E-i -d «<n O K ^Eh * d ca «en cs p\s O D asen c e_, PQ P ^ >H 5 OlEH' CQ vo CM v v j* v en vn OJ UN ON EN en 3" - ON VOI vn A 00 VO H 00 OS CM evi CM 00 vn v H - en v - H CM vn vn H H J* H O O O - ON ON.* v> - en VO en 00 H VO vn H j* CM (»> H O rh H rh CM c O CM vn H ^Jen vo C*. v H ON H ON - - v -4- J* 00 i CM rh 00 CM v CM vn en CM en c O p u <M rh d P as rh as ft P. ai OS <3f ^ Eh Eh CQ c 1 ON v H 1 H CM tn 1 ON rh rh UN v CM -3- bfl sd as.d >> ft O H P c p*-^ u d 13 P<EH C PQ M*-- O O O H CM 00 rh CM -d d CCS -p xi "^ p-i w s cd c 3- en en v> ^ en O -3- rh - 00 c - cv H ON ON H >> ft rh P sd d -p cd In as a, u u h f-i rh c u p sd H cd p t O H fit «H >H al p d w > > Oh u H O rh as cs P H C H 3 d P Q. 4d d as as cs d a as W rh> On> CM & > X K < cd H M W H rh > as EH

61 6 ^ CM O CM vo ON - ON ON O NO 00 c ON ON O O VI PQ B± M Vi. 5 + S s PQ E-i <] PQ I PQ <J <U n»? W KZ <D - f-,5 5 S3 3 c C n CM CM On O Os n ih CS- NO CM CM On NO vn O O ON CM CM O vn VO c c\: NO vn ON NO c c ON CM H On H CM *0 a) cv c H O NO c H cn; O NO CC NO -$ cn O- H H CM CN. CN? CM 3- rh CN- On ts CM O H VO On O 0) H P H H **""x H CM,Q H J-l CD l> 0) Jh (h H P tj C d) S <ḵ <D H u rl P CC H d H P H r' P (H as cd H Oh H P< as d > OS X c:< <M c: i CD bo t3 p" OS u s: X O P M w H CQ En c O -3- VO CM CM O c CN, O c cv NO rh CM VO ON -3" (1) H P cfl P as as a, a, «! < u a 0) CD H H P <d u p as u Ph as > -p as c C (D O u <r O O U h a> h a) P p > t > as <S 3H <h (D x: H as S d ffl > XW a> A M H ft Oh

62 Cnclusins In relatin t the previus discussins, there are sme imprtant cnclusins which will be shwn as fllws: (1) Fr the cycle, the summatin f the quantities f the net heat received and the net wrk input must be zer. This can als be expressed by the equatinal frnr ' with numerical values taken frm the example in Sec Q in + W in = ^ ? = = in which 2in = Q e + Q g, W ln = Q p and Q Q = Q a + Q c + 3 r «(2) In each prcess in which there is heat flw, the available and unavailable parts f the heat flw equals the ttal heat flw. Fr the ttal f the evapratr and the generatr Q = (A3) (US) in ^m *in = and fr the ttal f the cndenser, absrber and rectifier, Q n = (AE) + (UE) Q Q = (3) The net change f entrpy fr any cycle, AS, zer. ac 1/, must be (4) Fr the wrking fluid in cycle, the summatin f the ttal increase in availability, 2A3, and the ttal decrease in + availability, 2A3_, must be zer. (5) All rtary shaft wrk, such as pump wrk, is available.

63 = 62 (6) Frm Table III, we can see that the greatest increase in the irreversibility ccurs in the rectifier. This is mainly due t the mixing f fluids f large temperature difference. (7) The next largest increase in the irreversibility ccurs in the absrber. This is principally due t the mixing f fluids f different temperatures (the temperature difference f mixing fluids in the absrber is less than thse in the rectifier) (8) Fr the cycle, A3, =2S,=43,, universe created atmsphere e g' -(3+3) = = (9) The actual amunt f wrk, which is required t perate the unit, can be evaluated by W., W,,, _ + T n AS. m,act in, ideal universe = = (10) The increase in unavailable energy, caused by the system alne as it cmpletes ne cycle f peratin can als be evaluated by -T Q 7?. The ttal increase in unavailability, due t the abve term and the increase catised by transfer f heat thrugh a finite temperature difference t the cling water in the cndenser and the rectifier, can be evaluated by T n 4 S. J universe

64 63 ACKNOWLEDGEMENT The authr wishes t express gratefully his highest appreciatin here t his majr advisr, Dr. Wilsn Tripp, fr intrducing him t the subject f "Absrptin Refrigeratin System" and fr helpful guidance thrughut the prcess f this wrk, a.nd t Dr. R. G. Nevins, Dr. A. H. Duncan, Dr. C. L. Hwang, Dr. Jhn M. Marr fr reading and criticizing the manuscript.

65 64 BIBLIOGRAPHY 1«SHARPE, Nrman, "Refrigerating Principles and Practices," First Editin, McGraw-Hill Bk Cmpany, Inc., New Yrk, Trnt, Lndn. (1944) 2. ASHRAE, "Guide and Data fr I965 and 1966," Page 11, Chapter 1, American Sciety f Heating, Refrigerating and Air Cnditining Engineers. 3. MATZ, W. H., "Principles f Refrigeratin," Third Editin, Revised, Nickersn & Cllins C., Chicag, 111. (194?) 4. BARNARD, W. N., ELLSNWOOD, F. 0. and IIIR3HFELD, C. F., "Heat Pwer Engineering," Part III, Jhn Wiley & Sns, Inc., New Yrk. (1933) 5. WOOLRICH, W. R., "Handbk f Refrigerating Engineering," Vl. 1, The AVI Publishing C., (1965) 6. KEENAN, Jseph H., "Thermdynamics," Fifteenth Printing, Jhn Wiley & Sns, Inc. (1957) 7. SPARKS, N. R., "Thery f Mechanical Refrigeratin," McGraw-Hill Bk Cmpany, Inc. (1938) 8. ULL, James, "Equilibrium Thermdynamics," Jhn Wiley & Sns, Inc., New Yrk. (1964) 9. SALI33URY, J. Kenneth, "Kent's Mechanical Engineers' Handbk," Pwer, Twelfth Editin, Jhn Wiley & Sns, Inc. (1950) 10. BOSNJAKOVIC, Fran, "Technishe Thermdynamic," Dresden and Leipzig, (I960) 11. BENT, A. Henry, "The Secnd Law," New Yrk, Oxfrd University Press. (1965) 12. RYSSELBERGHE, Pierre Van, "Thermdynamics f Irreversible Prcess," Blaisdell Publishing Cmpany, Paris. (1963) 13. BRUGES, Edward A., "Available Energy and the Secnd Law Analysis," Academic Press, Inc., Publishers, New Yrk. (1959) 14. "Tables f Thermdynamic Prperties f Ammnia," Circular f the Bureau f Standards, N (1923)

66 LEWIS, G. H., and RANDALL, M., "Thermdynamics," McGravr- Hill Bk Cmpany, Inc., New Yrk. (1923) 16. TRIPP, Wilsn, "Secnd Law Analysis f Cmpressin Refrigeratin Systems," p. ^9, A3HERAS Jurnal, January I966.

67 - 66 NOMENCLATURE (AE) Available part f internal energy BTU b Availability per unit mass BTU/1 m B Available part f enthalpy BTU (CP) Cefficient f perfrmance dimensinless E Energy BTU f Liquid state dimensinless S Vapr state dimensinless G Punds f strng slutin circulated per pund f refrigerant dimensinless h Enthalpy BTU/lb. m I Irreversibility BTU I" (Quantity f available energy degrades t the cling water) + I BTU J M P q Q s Cnversin factr, 778 Mass Pressure Quantity f heat transferred per unit mass Quantity f heat transfer Entrpy ft - lb /BTU f m psia BTU/lb m BTU BTU/ R lb m T Abslute temperature OR u Internal energy per unit mass BTU/lb m (UE) Unavailable energy BTU v W x Specific vlume Wrk Weight cncentratin ftvib m ft - lb. lb /lb m m

68 6? i Perfrmance rati dit.ensinless 1 Thermal efficiency- dimensinless Subscripts a Absrber act. Actual cnditins c D e ex Cndenser Dead state Evapratr Heat exchanger f Frictin lss g H irr k L max. p Generatr High Irreversible prcess Cmpressin refrigeratin cycle Lw Maximum value Pump pp Defined as equatin (22) n page 25 r Rectifier rev Reversible prcess s Strng slutin t Thermal prperty ve vs w Expansin valve Slutin valve weak slutin

69 68 a Absrptin refrigeratin cycle Cnditins f surrundings + Increment Decrement

70 ABSORPTION REFRIGERATION SYSTEM, I965-I966 by CHUN -MING CHENG B.S., Taiwan Prvincial Cheng Kung University, 1958 AN ABSTRACT OF A MASTER'S REPORT submitted in partial fulfillment f the requirements fr the degree MASTER OP SCIENCE Department f Mechanical Engineering KANSAS STATE UNIVERSITY Manhattan, Kansas 1966

71 The field f refrigeratin is a brad subject, and invlves the applicatin f many basic studies. In this reprt the absrptin refrigeratin system has been analyzed frm the thermdynamic viewpint. The reprt cnsists f three sectins. In the first sectin general cncepts f absrptin refrigeratin systems are utlined, starting with a cmparisn with a simpler system the cmpressin refrigeratin system. In the secnd sectin the absrptin refrigeratin system is analyzed by the First-Law and Secnd -Law f thermdynamics, invlving mass balance, energy balance, steam cnsumptin, entrpy change, perfrmance rati, and the cncepts f availability and irreversibility. In the last sectin a numerical example f a typical ammnia absrptin refrigeratin system is presented, emplying the described principles and derived frmulas f previus sectins. Availabilities and irreversibilities are tabulated \>y percentages n Table III. The rectifier accunts fr apprximately ne-half f the ttal irreversibility f the system, while the absrber and the heat exchanger each accunts fr abut ne-fifth f the ttal degradatin f energy. Effective changes in the design f these three pieces f equipment wuld materially imprve the perfrmance f the system.