AES-Vof. 25/HTD-Vol. 191. Second Law Analysis - Industrial and Environmental Applications ASME 1991

UNDERSTANDING COMBUSTION IRREVERSIBILITY

William R. Dunbar and Noam Liar Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia, Pennsylvania

AIISTRACT mole fraction vpcr ox tnate Iy l/:l of the useful cne r ev of the is subscripts destroyed durin~ the combustion process used in electri­ i mass stream index cal power ~eneration. This Is an attempt to clarify species index and ca t.eeor i ze the rnasons for the exc rzy destruction t ak t ne place dur lnz uncontrolled f ue I oxldat lon . The superscripts entropy production is separated into three subprocesses: rate (per unit time) (ll a combined u if'Fus i onz f'ucI ox Iua t i on . (:l) an "internal per kl1;lllole thermal enerzy nxchanec" (), and (3) the product cons t l tuent mixin( process, Four plausible process pn t hs are proposed and analyzed. Hydrogen and [NTRODUCTION methane are considered as the . The results dlsclose that the majority (about :1/4) of the e xe r zy de s t ruc t lon Past studies have revealed the combustion process. of the occurs dur lnz the internal thermal enerzy exchanae . The many processes occurr tne in the typical c lcctr i c i ty­ producin~ fuel oxidation. itself. is relatively e rrtc tcnt , hav i nz power plant. as the sinJ:'le larJ:'est contributor an exerJ:'etic efficiency of typically 94~ to 97%. of excrgy losses (cf. Ga(gioli ct al.. 19751. Wlth present technoloro'. fuel oxidation by uncontrolled . (conventional) combustion at atmospheric pressure NOKENCI.ATURE consumes about 1/3 of the fuel's utilizable enerro'. The objectlve of this work ls to investi~ate the sources of aCH specific chemical exerltY. kJ/kgmole this irreversibILIty and its underlyln( reasons. al specific flow exergy. kJ/k~ole kJ/k~ole Specifically, the approach taken in this study is to (i) aTll specific thermal mechanical exergy. c. molar specific heat. kJ/kgmole-OK descrIbe and quantify the overall (global) entropy E convective rate. kJ/s production takin( place during; combustion. and (Ll ] h specific enthalpy. kJ/kgmole separate and quantify the amount of entropy production ~ molar flow rate. kgmole/s associated with the subprocesses of combustion. namely ~. sum of total number of moles of mixture at reactor constituent mixing. oxidation. and internal thermal exit energy exchanll;e. along four conceivable representative S. molar productlon rate. k(Mole/s paths of the global combustion process. This computation P pressure. kPa along prescribed process paths is an alternative to the Po atmospheric pressure. kPa practIcally intractable rigorous solution of the full field and state equations (Navier-Stokes. energy. entropy Q heat transfer rate. kJ/s i R universal gas constant. kJ/kgmole-OK generation. and thermodynamic properties. cf. Gaggiol k~ole/s 1~61 1962) combined in a combustion process with mass Rl fuel consumption rate. s specific entropy. kJ/kgmole-OK tran~fer and reaction kinetics equatlons. a l I ti(htly Sp entropy production. kJ/oK coupled. Rigorous analysis of combustion can be performed T , OK (cf. Buckmaster and Ludford. 1982. Arai et al .. 1986) but To reference temperature. OK due to the many simplifications that are introduced,to A exergy rate. kJ/s ease the mathematical problem. and the many uncertaLn­ A~ exergy destructIon rate. kJ/s ties. especially in the reaction kinetics. the results are not accurate anyway. i chemical affinity. kJ/k~ole I' electrochemical potential. kJ/kgmole . 'f . applYL'n'" such formal analysis \ particular d i l icultY i n .. (k~ole IJ(~ stoichiometric coe rf l c i cn t , kl,'lIlolel f I ) to the determination ot' ent ropv production (exerJ.:Y

81 destruction) is the fact that irreversible thermodynamic processes are path-dependent. Wlthout exact knowied~e of the sequence of processes and reactions in the lIere for all chemical species j in ~as stream the coaous t Ion process. the solut ion of the full field. enthalpies are thus expressed as state. and kinetic equations will provide results which are .uch harder to obtain and probablY no more accurate (7) than those obtained from the below-described analysis along prescr ibed paths. I t is noteworthy that the "rIgorous" analysis has so far only been applied to the and the entropies are expressed as s Iap Ies t heat/mass transfer problems. such as flow in ~PJ (8 ) two- dimensional channels without any chemical reactions §j S §]" + I (dT/Tl - Rln(Pj / Po) . (Be jan , 1:;)79. San et a1.. 1:;)87). and even that required '0 the use of a number of simplifications and empirical correlations. The exergy destruction rate can also be expressed as and it was computed in this study in two ways: by using GLOBAL ANAL.YSIS (9 ) General Descrjpti on We consider steady combustion in a well-insUlated combustion chamber. The term "zIobul " refers here to Eq , (I) and then by us Ing Eq . (91. to doub Ie-check the consideration of the combustor as a sin~le "hlack-box" correctness of the results. control volume. with conditions known or determined only at the control-volume Inlet and outlet. The global The entropy for Eq . (~) was calculated from tbe balance combined First and Second Luw analysis is performed here first. and the equillbrium state of the combustor ( 10) products. the ex t en t of reaction (defined :]S the molar amount of fuel reacted per mole of fuel Inputl. and the effects of excess air are determined. Two analyses are From conservat Ion of ctrcm i ca I spcc i es performed: one with hydro~en and one with methane as the t». N;,~' ( 11 ) fuels. They are assumed to be pure. at the ambient ..., + conditions of 25°C. I atm. The oxidant Is atmospheric air wit h an assumed composI t Ion 0 f :! I'; oxygen and 79'; ru t roeen . The amount of excess air is varied. r anz i nz wnere the equation of reaction equilibrium Is from O~;-100%. Dissociation of nydroaen and oxygen Is deemed neel Ig Ib Ie (Wark. In71 at the adiabatic flame L V,~; - L V,~, ~ O. (12) ~rod t ••c of these reactions. which cnn be reduced to an expression for the equilibrium ~atbemarjcJJ ~orlpl In~ cons tan t . K, Due to the adiabatic boundary restriction and the fact that no work Is produced durln~ conventional combustion. II .v;' the exer~ balance is EE!!....- (2).10. (13) Il y? s; EAj [A~ + Ad' (t) r ••c in ~ut

With no heat or work transfer across the combustor i.e .. the useful cne rgy associated with the enrer ine boundaries. the equation is matter Is equal to the available enerlO' of the exltin~ matter pius the irreversible destruction of exerlO' (14 ) associated with the combustion. llere , the total flow exerlO' of stream i is Enthalpies of formation. absolute entropies. chemical cxergies. and ideal ~as coefficients were (2 ) obtained from Reynolds and Perkins (1!l7'i). Rodriguez (1980). Sonntag and Van Wylen (1982). and Gurvich and where the total specific exerlO' of a given flow stream veyts (1989). (e.g.. stream l ) is Boundarv Conditions (3 ) The boundary condltions for the global reactor are: (1) the fuel and air entrance temperatures are at the assumed The specific flow exergIes are evaluated by enp Loyi ng reference. ambient temperature of 25°C. (2) lncoal na fuel calcuiat Iona l procedures found in the I I terature (cf. and air compositions. (3) the product zas stream exits Rodr l zuez , 1980). by first separat l ng them into their the reactor under chemical equilibrium conditions. (4) thermomechanical and chemicai components all gas streams are at atmospheric pressure. and (5) the combustion chamber (reactor) walls are adiabatic. (4) Results Of the Global Analysis Where the specific flow excrgy , af' is composed of two Results of the global analysis of hydrogen combustlon are exerlO' contributions: (1) the specifIc thermomechanlcal contained in Fig. 1. Based on the equ i Llbr lua reaction exergy , aN' and (2) the specific chemical exergy , aCH' cquat ions (12) and (13). the ex tent of react ion bas Ical Iy Assumin~ ideal gas behavior for all components. becomes 1.00 (implying complete oxidation of fuel) above 50\ excess air. The equilibrium. adiabatic. product gas (5 ) temperature ran~es from 1646°K to 2433°K. decreasing with .in Increase in the amount of excess air. The exerzy .'dic[cncv is defined. :IS arc all efficiencies in this

82 a energy conversion systems in our . such IlO '0 40 .0 '00 100 1.00 '" 1.00 2.00 as residential and commercial space heating furnaces. E>!lenl or ReocMon industrial furnaces for materials processing, internal g and external combustion engines, and combustion chambers ..~1' Z a.11 2JOO

>­ 0 w wl t hIn power pLan t boilers. It is thus important to o >= 0:: Z ~ w o E'8fgetlc eMCl8I'eY 2 improve our understanding of the phenomena contributing ~o.•• iJ I·· 2100 ~ a: to entropy generation in combustion. and we approach it 0." w i:: 1ll a. w ...0 ::! in the following by a breakdown and quantification of the w o ~o.14 .... subprocesses taking place during combustion. 0.14 '.00 .... e<:J u ::J ffiu 8 Cl The initial condition before fuel combustion (state I) 0 0 0.12 0:: o.n 1700 a. includes a fuel stream and an air stream, both at ambient PrOdUct femperature / temperature and pressure. The final condi t ion. r.hat after fuel combustion (state 2). is characterized by (i) IlO 0.• 0 1 0 i 0.80 a ;0 '0 ,a 1500 the presence of a number of new chemical species (e.g., .0 lao '00 EXCESS AIR (e) water. carbon d t oxide ) , (iiI a higher temperature, and Fig. 1 Exergetic efficiency, extent of reaction and (iii) all constituents being mixed. The processes which product temperature, vs. excess air, for global analysis cause these phys icaI changes. fue i oxidat ion. heat of hydrogen combustion. transfer. and product mixing produce the aforementioned amounts of irreversible entropy production, The immedi­ work. as the rat~o of exer~ outputs to exergy inputs. ate objective is to conceptualiy separate and quantify The exergetlc efficiency of hydrogen combustion ranges the amounts of entropy production associated with these from 66.5% ~o 77.3%, decreasing with increasin~ amount various physicochemical subprocesses of combustion. of excess aIr. In conclusion, such conventional combus­ tion destroys npprux tnn to tv 23'. to :1 ..•• of t he usn t'ul cner-zy of hydrolren t'ue l for the invest il!ated rance or BREAKDOQ OF FJITROI'Y ('RODUCTION IN COJllRUSTTON excess a i r , Ilirsclifeider, Curtiss and Bird (I~S") present an expres­ ~esults of the ~iobai analysis of methane combustion arc sion for the local rate or entropy production, [ntegrat­ contained in ri\!o 2. for the range of excess air amount ing their equation over the volume of the system results studied. the extent of reaction for water format ion in a reiatlon for the ~lobal rate of entropy production: ranges from 0.~81 to l.00, basically becoming 1.00 (~mplYinl! compiete formation of water) above 40% excess Sp • {gdV a i r , The extent of reaction for carbon dioxide formation :anges from 0.~09 to 1.00. basically becoming 1.00 above .. {(liT> {-(oom - (t':Vv) (15 ) ;)0% excess air. -E(j1'V(l/ol - 1/o.,)J + D'jRj + E(j1·g1))dV. a '0 '0 1 J! IlO '.00 H10Mol'" Amoun. Oer MOlOr .Amounr otter The first term on the right-hand-slde is the contribution Como•• ,. ComOUSl1Qn .- ZO.'I 0." 1200 g to entropy production due to heat transfer. the second ~'.>- W u s 0:: term is that due to momentum transfer (fluid friction), Z o ::J w ~o the third and fifth terms are those due to diffusion. and .•• '000 ~ Q -a... w tlll ... a. the fourth term is due to chemical reactions, The volume w 0 ::! integrals in equation (15) are process-dependent and o ~ !Z0." 0.'4 \loa ~ hence, path-dependent ln the thermodynamic sense. To e<:J evaluate these volume integrals. the approach taken here e..eroetlc E~encv O.n ffi85 8 cO':!MOIQIAmoun' oer 1.. j is to assume hypot he t i ca l sequences of subprocesses. >< D.n w MOlar AmOunr an., 00 Compte'. ComousftOn wherein these volume integrals may then be evaiuated by surface integrals. 110 0.10 a 0.10 1400 20 40 50 sa 100 100 EXCESS AIR (e) In this study, it is assumed that three physicochemical subprocesses are the primary contributors to the global Fig. 2 Exer'get Ic efficiency, extent of reaction and rate of entropy production: (i) reactant diffusion and product temperature. vs. excess air, for global analysis fuel oxidat ion. ( i I) internal exchange ( I . of methane combustion. e .• heat transfer between gas constituents within the reactor), and (iii) product mixing, Because the magni­ tudes of the various contributions to entropy production The equilibrium. adiabatic. product gas temperature are path-dependent, four conceivable process-paths are ranges from 14800K to 2249°K, decreasing with an increase studied and the results thereof are compared. Two of in the amount of excess air. The exergetic efficiency these paths assume incremental stages of fuei oxidation: of methane combus t ion ranges from 60.4% to 71. 6%, two assume instantaneous fuel oxidation, The equations decreasing with increasing amount of excess air. In used are those described in the Mathematical Analysis other words, conventional combustion destroys approxi­ section above. mately 28% to 40% of the usefUl energy of methane fuel for the investigated range of excess air. The combustion process is envisioned here to proceed in the follOWing manner. As the air and fuel enter the The significant degradation of the potential to produce reactor, the oxygen and fuel molecule "sense" each useful work, during combustion. computed above to be 23% other's presence. They have an intrinsic affinity for to 40% with hydrogen and methane as fuels, was also each other -- yearning to react due to the greater observed for other types of hydrocarbon fuei combustion che.ical stability of the oxidation product(s) in (cf. Hedman e t a l , t sso i , This irreversibility has comparrson to that of the reactants. Thus. the oxveen significant dc t r iment a I impact in all combustion-based and fuei molecules are "drawn" t oze t her in a dI ffusion

83 process which consumes useful power. used to "pull" them In chamber 2. heat transfer (but no mass transfer) ls fro. the .ixed gas stream. allowed to take place between the gas particles in the separated compartments of th is chamber. Al~ gas tempera­ H~ving approached the fuel. and with the possibilitY,of tures exiting chamber 2 arc the same ( t .c.• thermal a nusoer of series/parallel steps. the oxygen re~cts wlth equilibrium Is assumed). Thus. the additional boundary the fuel, formin" product molecules. DUr,lng this conditions for chamber 2 are: (I) heat transfer (but no ocess there is a concomitant energy converslon: net mixing) allowed between the compartments within the P~anges'of energy in the forms of (1) "internal-chemical reactor (but no heat transfer to ambient sur-round tnes r, ~nergy" -- energy associated wi th intramo~ecuiar forces. and (2) thermal equilibrium between all constituents at (21 radiation energy (in the case of chemlcal reactions. the exit of chamber 2. most likely. x-ray radiation) and (3) "Internal-thermo­ " -- assoclated with particle motions Finally, the reaction products and the unreacted air and Intermolecular forces between system constituents components mix in chamber 3. The boundary conditions for (Hlrschfelder et a1.. 1~54). Havl ng stabilized (react­ chamber 3 are: (1) uniform mixture of all reaction ed). ~he participants have added to the system entropy. products and oxygen-depleted air stream at exit, and (21 destroying useful power. adiabatic boundaries.

At the Instant following the exothermic reaction. the Followin~ the first Incrementai extent of reaction. the pr~duct molecules leave the reaction site with a kinetic gas components flow into chamber 4. repeating .these steps energy which Is much higher than the statistical average of combustion for the second (and subsequent) tncreacntat of the neighboring particles. 'tomentum ,~xtent(sl of reaction. This procedure is repeated untii (and associated kinetic energy) transfers therefore take the ~as constituents reach the fuel Ignition temperature, place. bringing the reaction product temperature down to whereupon the fuel oxidation is assumed to be instanta­ an equt t tbr tun value consistent with that of the sur­ neous (i.e .• all the remaining fuel is oxidized immedi­ rounding medium. This process. which is here called an .i t e Iy at the fuel ignition temperature). The assumed "Internal thermal ennrey exchange", also consumes useful fue 1 lzn i t ion tempera turcs are 5i12"C for hydroucn and power by increasing the entropy of the system. Finally. ii90"C for methane Illabcock and Wi l cox, 197R). The fi na t in a process which occurs simultaneously with the products of combustion then ~xi~ the r~a~tor under [he t internal-thermal ene rzy exchanzo , but snpara od here for required ~lobal system equlllbrium condItions. the sake of l ns Lah t , the product molecules mix with the remaining global system constituents. further reducing Effects Of incrcmcnt size. ~n analysis was first the system exergy. Honce, the above description provides performed to determine the sensitivity of the res~lts.to a cateeorrz at ion Ibreakdown) of subprocesses that occur the number of Increments In the process descrlhed In Flg. within the global combustion process. To summarize. the 3. These results are displayed in Figures 4 and 5 for processes are theoretically separated as follows: the cases of O~ and 50~ excess air amount.

(1) a combined diffusion process (where the oxygen and .\s shown. a t a number of Increments of about 100 the fuel molecules arc drawn together) and a chemical results approach a value which does not change with the reaction (oxidation of the fuel). increase of the number of Increments. This is because the reactants' condl t l ons have smaller changes. for given (2) an internal-thermal energy exchange. where the overall process be~innlng and end states. as the number product molecule "shares" its kinetic energy with its of Increments becomes iarger. For example. the Increase neighbors. and in temperature in each increment. for an excess air value of 100~ and at 500 Increments is only about 1 to 2 K. (3) a mixing process whereby system constituents mix uniformly. The exe rzy destruction due to oxidation decreases with Increas t nz number of Increments because larger perccntae­ es of the fuei oxidation are evaluated under more The contributions to exergy destruction arc calculated c tf Ic Ient conditions; i.e.. at n t ener temperatures and below for four process paths. The paths were chosen to therefore closer to equilibrium (hence more reversible represent somewhat limiting conditions in the determina­ see fi~. 6). five hundred increments were chosen for the tion of subprocess irreverslbllitles. and to be physico­ followin~ chemically plausible. combustion irreversibility breakdown analysis, thus assuring the determinatlon of Increment-size­ eat.h-l. independent exergy destruction values for the assumed In this process path the breakdown of combustion irre­ sequence of subprocesses in this path. verslbillty is investigated by assuming that (i) fuel OXidation occurs In stages of reaction (i.e.. not Breakdown Of aYera 11 FICrO' ConSllmpt I00. The InstantaneOUsly). and (ii) fuel combustion takes place relevant results of the breakdown of exergy losses In In the subprocess order of (a) reactant diffusion and hydrogen combustion are given in fig. 7. The significant fuel ox Idat Ion. (b) Internal thermal energy exchange. and result Is that the lar~cst subprocess exergetlc consump­ (c) product mixing. Thus. with this scheme. the global tion takes place during the Internal thermal energy combustion process Is envisioned to proceed as follows. exchan~e (chambers 2.5. etc. in fl~. 3). The exer~etic efficiency of thIs subprocess Is 73% to 83%. decreasing fig. 3 displays schematically the technique of analysis. wIth Increasing amounts of excess air. l .e . approximately for example. in chamber 1. the oxygen (on Iy the incremen­ i2-77% of the overall exergy loss of the coabus t l on tal stoichiometric amount which will react in this process is associated with it. The reaction (oxidation. chamber) enters a compartment where it reacts with the in chambers 1. 4, etc .• In fig. 3) has a 94% to 95% Incremental amount of fuel consumed. Upon reaction. the exergetic efficIency and destroys about 15% to 18% of the products exit Into chamber 2 at the temperature charac­ total exergy ioss. and gas constituent mixing (In terized by a completed reaction in an adlabatlc chamber. chambers 3. 6. e tc .• In fig. 3) has an exergetlc effi­ flowIng In a separate compartment. Isolated from the ciency of 96.5% to ~7.4'0. destroying the remainin~ 8% to reaction momentarily. Is the amount of unreacted fuel and 10% of the total exergy loss. the oxygen-depleted air/product streams.

84 First lucremcnuu SI.:l:lOlIllllinelllClllal Elltelll uf Rcacuou lixtcnt ut I{cal.:!lllil

Uurcuctcrl Flid I) Fuel Unreaeted - [0....,1 - Fucl Q f I I -- t­ .. tllll ": _ 1120 -t- - - - ~ \) Ciluual I{cal.:lur .. I 112 - (Suuch. CUIIIUllSlIUli I ~ /\1I11. ) Products Oz Q Uuder ChCllli,aJ Air (Stoich. I:ljlliliul iuiu FfOr'r1 AIIIl.) Couduions

Chambee

1 lJlrfllsillll/l{eacllIlIl \112 ~ 1/2 ()2 _. 112U) 2 hucrnal Thcuual i:llcrl-\Y 1::\I.:II;lIII,;C J I'vlill (1'1(~llICIS/I)cplcICd '\11') 4 nur USiUI'/({C;ll:III'" 5 lnternnl Thcnual ElIl:rl,;Y E:\l.:Ilalll:C (I)Il~llIl:Is/Uqllcted <> Mix Air) Flg. 3 Hypothet IcaI combustion chamber for Process Path 1.

'00 zoo '00 "'0 '00 zoo <00 .00 .00 1000 'zoo '·00 '600 zo 100 '00 ~ IGloOalI /0...... >- U '5 Zt5 ~t5 \oJ U EneIQy :z r:n'ernatll'l""""bcn0n08 ~ o "- \oJ s: '0 II ,o .0 ~ u II) E3 ... <.:I I­ o a: >­ ~i'u"OllCallOl1 \oJ u ~., o X s \oJ ...x '-.:.....:.. MI.OlCI 0 00 10 0 '00 zoo JOo 400 ZOO +00 600 600 ,ODO 'ZOO 1600 NUloIIlER OF' INCREMENTS ,­(K) """ REACTANT(S) TEMPERATURE Flg. 4 Ellergy destruction YS. number of process incre­ of hydrogen oxidation YS. ments. for 0% eAcess air. Fig. 6 Ellergetic efflclency temperature of reactants. '00 100 '00 .0 - 20 ­ M1."'O ~c.eraI (GloOaII ~r'-~ 90 en..v. UcnonQ8 ..

5 '0 ~ '0 '0 111 ... c..011 (GloOCII o ~Fu8l0lddalI0I1 L ~ ~ <, M1mo o •o I go lOG JOG 400 .0 ..0 60 NUlil8ER OF' INCRElilEHTS """ EXCESS AlR (II) Flg. 5 Exer~ destruction YS. number of process incre- Fig. 1 Exergetic effIciency of the hydrogen combustion ments. for 50~ excess air. process. Path 1. vs. excess air.

85 reactor under the r equ i r en glooal system equillbr The overall (global) exerze t ic eff ic iency r-anees from conditions. 66.5% to 77.3%. decreasing with increasing amounts of excess air. As in the Path 1 study. an analysis was first perforr to determine the sensitivity of the results to the cno­ eA.t.b-.2. number of increments. The results of this analysis w. In this process path. described in rig. 8. we study the simllar to those shown In Figs. 4 and 6 describ. breakdown of combustion irreversibility assuming that (i) results of the Path 1 analysis. Two hundred incre.en all the fuel and air mixed in the first step. before were chosen for the Path 2 analysis. ampiy adequate reaction. (ii) fuel oxidation occurs progressively in a ensure results independent of increlllent nUlllber. nuaber of dIscrete stages of rcac t Ion , and (iii) f'ue I combustion takes piace in a repeating series of two-step Qualitatively similar to the results of the Path subprocesses: (a) f'ue l oxidation. and (b) internal thermal enerlO' exchange. These subprocesses are repeated analysis. the largest exergy destruction. 66% to 73\ until the required exit equilibrium product gas state is the total. takes place dur Ine the internal thcraa l ener attained. The boundary conditions for chamber L in which exchanze (chambers :1. o , etc.. Fig. 8). The fu oxidation Ichambers 2. -to etc .. rig. 8) is rcspons ib mixing takes p lace (Fig. 8) are: (L) the incomIng matter for i8~; to 25% of the e.,ergy destruction. The mixi rate. composition. and temperature for both the fuei and process consumes about 8% to [0% of the t otaI exer air. (2) adiabatic boundaries. (:Jl no chemical reactions. des t ruc t ion. The co r r-e spond i ng subprocess exerzet and (4) the gas constituents exit as a uniform mixture. efficiencies. which reflect these results. are display The boundary conditions for the fuel oxidation chambers (2.4. etc .. Fig. 8) arc: (ll adiabatic boundaries. (2) in Fig. 9. the gas constituents exit as a uniform mixture. (:J) the oxidation product gas constitUents (their quantity 10 '0 ••I computed from the increment in extent of reactlonl exit under complete adiabatic reaction conditions. and (4) the gas constituents not Involved in the oxidation exit with ~ the same temperature IlS that when entering the chamber. .. nt.rnot lhetrT'IOI :nelQ'(uCI>OnQe e FtnaILy, to I Low t na the f'ueI oxidation. the In t e rna I __ ~.50 thermal enerlO' exchange subprocess occurs (In chambers 3. 5. etC .. Fig. 81. The boundary conditIons for these chambers arc: (1) ad Labat Ic boundaries. 12) uniform '. mixture of gas constituents. (.1) thermal equilibrium .-Ovelo'

Following the fIrst lncrcmentai extent of reaction. the '0+1 ~·0 gas components flow into the downstream chambers. ., .1] 6~ IDa repeating these steps of combustion for the subsequent EXCESS AIR (II) incremental extent (s ) of reaction. This procedure is repeated until the gas constituents reach the fuel Ignition temperature. whereupon the fuei oxidation is Fig. 9 Exere;etic effIcIency of the hydrogen combustil ~ssullled to be lnstantaneous t t .e .. all the remainine; fuel process. Path 2. YS. excess air. 1S oxidized immedl.1tely at the fuel ignition tempera­ ture). The I lnal products of combustion then edt the

Firsl 11IuclIIc1IIai SCl:Ulld luricmcmul Extent of Rcacuuu 1:~ICIlIIII IkaLl II 1/1 I

Fuel F~~ .-r' - - ~ - - hucrnal hucrnal Milting Fuel '111el111al Fuel Thermal . . Oxidation E"er~y UlIi

Chamber I Chamber 2 Cluunber J Cluunber 4 Cluuuber 5

Fi~. 8 I~pothetical combustion chamber for Prllccss Path 0

86 £.atlLJ. Finally. in chamber 4. all the constitucnts mix uniform­ In this process path. described in Fig. iO. we study the ly. Thus. the two additional boundary conditions for breakdown of combustion irreversibility assuming that l l ) this chamber are: (L) adiabatic boundaries. and (2) the fuel and air are internally preheated to the ignition uniform composition and temperature at the chamber exit. temperatur~. u r: the fuel is oxidized instantaneousiy the exiting gas leaving under the required global at the igrution temperature. and (iii) fuei combustion chemical equilibrium conditions. takes p l ace in the subprocess order of (a) internai reactant preheating. (b) reactant diffusion/fuei oxida­ Qualitatively similar to the results of the studies tion. (c) internal thermal energy exchange. and (d) performed using Paths 1 and 2. the internal thermal product mixing. Thus. with this scheme. the global energy exchange subprocess is again responsible for the combustion process is envisloned to proceed as follows. majority of the combustion irreversibility. According to tbe results of this study. this subprocess. which As the air and fuel enter the reactor. these reactants includes the effects of Internal preheating. destroys are internally preheated (via. e.g.• back radiation from approximately 74% to 80% of the total exergy de~troyed the downstream combustion products). Cpon reaching the in the process. The fuel oxidation destroys about 12~ ignition temperature. the fuel is oxidized instantaneous­ to 16% of the total exergy destroyed. and the mixing iy. The instant folloWing this exothermic reaction. the process is responsible for approximateiy 8% to 10% of the product molecules transfer energy to the neighboring combustion exergy destruction. The exergetic efficien­ consti tuents in the internal thermal energy exchange cies. reflecting also these results. are d Isp l ayed in subprocess. Fi nalIv , the ox idat ion produc ts and inert Fig. 11. gas constituents mix uniformly. The boundary conditions I (1) 0 10 .0 '0 .0 '00 for chamber are: the incoming matter rate. '00 composition. and temperature for both the fuel and air. '00 Mlxtnq (2) no chemical reactions. and (3) both the fuel and air OXlda'lon exit the chamber at the ignition temperature. ~IO ~to ,.. >c ~ (n chamber 2. the fuel and oxygen react instantaneousiy. nrernal Thermal w SO E.o The boundary conditions for this chamber arc: t l ) U :nQrgy t.xcnonQe t G: product gas exits at a temperature cnnructer Ized by a ...w completed r cac t Ion in an adiabatic chamber. (:::1 the U 70 t;O amount of unreacted f'uc l and the oxygen-depLet cd air exit E; at the same temperature as when entering chamber 2. and '-'a: E w ~60 (3) adiabatic boundaries. ?j 10 > E In chamber 3. internal heat transfer (but no mixing) is '0 '0 , :00 allowed to take place (i) between the gas particles in 20 .. . '0 the separated compartments of this chamber. and (11) EXCESS AIR (.) between the gas in this chamber and the lower temperature Fig. 11 Exergetic efficiency of the hydrogen combustion fuel and air In chamber 1. Thermai equilibrium prevails process. Path 3. vs. excess air. between all constituents at the chamber 3 exit. lnternul huernai r-uel '111el111a1 Product Preheat Oxidauon Energy MillUI!: Exchauge • t t Uureacied Fue' .> Q <, .... Fuel r:f"f"d -~r 112U ~ .... A Gleba! Reactur I Combusuon Air Products reed 02 ~Q Under Chemi cal Equilibrium ../y Conditions

---...... -.,a,. t ~ QI'II

Chamber I Chamber 2 Chamber J Chamber 4 Fig. 10 Hypothetical combustion chamber for Process Path 3.

87 In chamber 3. the fuel and oxygen react instantaneously. ~s process path. described In Fi~. 12. we study the The boundary conditions for this chamber are: (1) the breakdown of combustion Irreversibillty assum ne that (il oxidation product gas molecule exit at a teapera ture the fuel and aIr are Internally preheated to the i~itlon characterized by a completed reac t Ion in an adIabatic te.perature. (i l ) the fuel Is oxIdIzed Instantaneously chamber. (2) the unreacted fuel and a i r , and the in~rt at the Ign Lt Ion temperature. and (Ill) fuel combustion gases exit at the same temperature as when entermg takes place in the subprocess order of (a) reactant chamber 3. and (3) adiabatic boundaries. mix1n~. (b) internal reactant preheat tne. (c) fuel ox tdat ron , and (d) internal thermal ene rzy exchanze , The Finally. in chamber 4. internal heat transfer occurs ~~) global combustIon process Is thus envisioned to proceed between the gas constituents in this chamber. and (11) as follows. between the gas in this chamber and the lower temperature fuel and air in chamber 2. The product ~as exits chamber As the air and fuel enter the reactor. the reactants mix 4 under thermal and chemical equIlIbrium conditions. unIformly. Althou~h Internal preheatin~ is occurrin~ at the same time. the internal preheat process Is anaiyzed \~ain qua Li t at Ive Iy simi Lar to the results of the studies separately In order to quantify the Irreversibility performed usin~ Paths 1. 2 and 3. the internai thermal associated with these two subprocesses. Thus. after the energy exchanKe subprocess is responsible for the mixln~. the reactants are Internally preheated to the I~itlon Followln~ mixIn~ majority of the combustion irreversibility. According temperature. the and Internal to the results of this study. this subprocess. which preheat Ine processes. the fuel Is oxidized Instantaneous­ includes the effects of internal preheating. destroys ly at the l~nition temperature. Finally. the Internal 74~ eXer~ thermal energy exchan~e subprocess occurs. wherein the approximately to 80% of the total destroyed products then exit the reactor under thermal and chemical in the process. The fuel oxidation destroys about 12~ equilibrium conditions. to 16% of the total exerlO' destroyed. and the mixing­ process Is responsIble for approximately 8% to 9~ of the exer~ \s shown. in chamber t , all the reactant Iras constituents combustion destruction. The exergetlc efficien­ mix uniformiy. The boundary conditions for this chamber cies. reflecting also these results. are displayed in are: II) the i ncont ne matter rate. composition. and Fig. 13. temperature for both the fuel and a I r , (2) no chem leal react ions. (:J) the zas ex i ts with a un!form composi t ion To observe the effect of fuel type on combustion subpro­ at ambient temperature and pressure. and (4) adiabatic cess irreversibility. the Path 4 combustion process was boundaries. rueva 1ua ted us i ng me thane as fue 1. Qual i t a t ive ty , the results are simIlar to those obtained from the hydro~en in chamber 2. the fuel and air are internally preheated combustion breakdown ana i ys i s . The internal thermai to the i~nitlon temperature. The sourCe of heat Is the (~nergy exchange subprocess is res pons i b Le for the hot product gas I n chamber 4. downst re aa of the fue I majority of the combustion Irreversibility. This oxidat Ion chamber. The add 1t lanai boundar-y eond I t inns subprocess. whIch includes the effects of Internal for this chamber are: (1) no chemical reactions. and (2) preheating. destroys approximately 57'. to 67!. of the both the fuel and aIr exit the chamber at the l~nItlon total exer~ destroyed In the process. The fuel oxIda­ temperature. t Ion destroys about :10% to 40% of the total exerey destroyed. and the mLxlng process is responsible for

"Hemal ReaCI:UII "Hemal l:lIcl Mixmg Thermal Preheat ( hld.ullIn linergy lixchange

I

. 01'11 QPII Fuel /.,.. F....,I "",......

Global Reac) or Combustion z, ..-/'.,.. Products Under Chemi cal "'-..... Equilibrium Conduions Qpll QPH

• Chamber I Chamber 2 Chamber 3 Chamber 4

cil:'. I:! IIypothet i cal combust lou chamber for Process Path 4.

88 0 '0 '0 .0 eo 100 chamber prior to reaction by heat transfer from hot 100 ...... 100 upstream products of reaction and the colder enter Ine fuel and air (reactants). v la radiation and possibly C._non ::!: 80 conduction in the combustor walls. o>­ Z '0 -a .0 eo 100 '!!110 !Memal Thermal ~ u Ene/gy e.cnanoe ." ...c "0 E ... E _ oyela' (GIa/)CII) u £20'" e ~ LJ ~ ~a""3ana.· ...0:: ""\ !:i ~.o ~1~ 1= ,", , U :1 :J e "Pam2' : ~Ia so! .>0 ~,o £0 tiC a'o loa ... EXCESS AIR ••l.) c >- , LJ 0:: ~. Fig. 13 Exer~etic efficiency of the hydro~en combustion ... • process. Path 4. vs. excess ai r . !:i

0 ,a '0 so lOa about 3% of the combustion exergy destruction. The EXCESS AIR ••(lO) exereet Ic ef flc1enc i cs , re f lec t In~ also these results. are displayed in ri~. 14. FIg. l5 Exe r gy destruction due to internal thermal energy exchunze in hydrnzen combustion. vs , excess air. , z~ '0 '0 00 100 100 '00 0; 1 "--~I.anQ To explain the effect of internal preheat let us consider 1 Flrst the results from Path 1 and Path 3 .•hich differ :!: ao~ <. primarilY by the fact that Path 3 has internal preheat >­ " ~ "'-l'ulll C.lOanon while Path 1 does not. Path 1 assumes the fuel is g 10 oxidized in increments until the i~nition temperature is u E attained. whereupon the r cmatn inx fuel is oxidized. With ... this scheme. nppr-ox i aatc l y [0-25% of the fuel is oxidized U 70 prior to reacn l ne the fuel ignition temperature. In this eLJ 72·;-7i~; t 0:: path. of the total combustion (!xerlO' dcs ruct Ion ... occurs due to the internal thermal encrl:Y cxchanze ~ , 10 laj OY"a' (G:"aal) subprocess. E , : So& • . I '0 Path 3. on the other hand. assumes the Identical sequence 2'0 '0 '0 eo '00 I:)(CESS AIR (.) of subprocesses. except that. prior to any oxidation. the reactants are heated to the Igni t Ion temperature. at Fig. 14 Exeree t ic efficiency of the methane combus t ion which the fuel Is then oxidized instantaneously. The process. Path 4. VS. excess air. results of this scheme disclose that the Internal thermal energy exchange and Internal preheating are responsible The main di fference between the hydrogen and methane for approximateiy 74%-80% of the total combustion combustion exer~ destruction breakdown results Is that Irreversibility. Thus. accord Ina to these results. the methane oxidation subprocess destroys a fraction of internal preheatin~ to the ignition temperature prior to the overall exer~ loss which is about 2.5-fold lar~er reaction causes the internal heat transfer irreversibili­ than that destroyed in hydrogen combustion. and the ty to increase by about 2%-3% of the total combustion destruction of exe rzy in the internal enerlO' exchanee and Irreversibility. A similar comparison between the mixing are smaller. results of Paths 2 and 4"reveals that this internal preheating raises the internal heat transfer exergy destruction by approximately 7%-8% of the total combus­ ADDITIONAL DISCUSSION tion irreversibility. These effects are also dlspiayed In Fig. 15. Comparj son of the RCSIII ts from the fOllr process Paths :\nalYZed The results of the four different hypothetical process CONCLUSIONS AND REC~DATIONS paths have revealed that the internal thermal energy exchange subprocess is responsibie for more than 2/3 of The understanding of the sources of combustion Irrevers­ the global exergy destruction. This is shown in Fig. 15. ibility and Its underiying reasons was improved by as a function of excess air. decompos ing the overall exer~ des truct ion into hypothet­ ical subprocess contr I but ions. The results obtained from The Effect of pre-mixIng the analysis indIcate that the major contribution to the Paths 1 and 3 assume that full mixing occurs after destruction of usefui energy occurring in typical gaseous reaction. whUe Paths 2 and 4 assume pre-mixing. xo hydrocarbon fuel combustion is due to the internal perceptible differences were found between these modes thermal ener~ exchange (heat transfer) between part IcIes of mixing in the exergetic efficiency of the mixing within the system. subprocess. Since these kinetic energy (or momentum I transfers are The Effect of Tnternal Preheat ineVitable. to reduce entropy production during combus­ As discussed eariier. internal preheatIng is the process tion the above conclusion points to the need to seek wherein fuel and air are preheated withIn the combustion means for reducing the amount of conversion of the reactants' "chemical encrsy" to the form of "thermal

89 energy" which causes this undesirable internal thermal lIirschfelder. J. 0., Curtiss. C. F. and Bird. R. B.• energy exchange. 1954. ~pleeular Theory oC Gases am! [Iqulds. IUiey. New York. One such way. employing fuel cells. is already being explored by the authors (cf. Dunbar 1983. Dunbar et al. Reynolds. W. C. and Perkins. f1.C .. 1977. EngIneering 1990). Described briefly, fuel oxidation performed in Thermodynamics. McGraw-Hill. New York. fuel cells produces useful work () durin~ the process. thus generating less internal thermal energy and Richter. H. J. and Knoche. K. F.• 1983. Reversibility of entropy between the process end-states. and resulting in combustion processes. EffICienCY aod Costing Second a signiflcantly more efficient process. An alternative law Aoalysls oC processes. R. A. Gaggioii ed .• ACS Sy_p. technique. using metal oxides. was proposed by Richter Ser. 235. pp. 71-75. Washington. DC. and Knoche (19831. These are good examples of how exergy analysis leading to fundamental understanding of process Rodriguez. S. J .• 1980. Calculation of available energy irreversibilities can point to the develop_ent of more quantities. Thermodynamics' Secood law Apa'ysis. Ch. 3. efficient practical processes. R. A. Gaggloli, cd .• ACS Symp. Ser., Washington. D.C.

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90