Second Law Analysis if IC Engines

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SAE TECHNICALPAPER SERIES 2000–01–1081

A Review of Investigations Using the Second Lawof Thermodynamics to Study Internal-

Combustion Engines

Jerald A. CatonTexas A&M University

Reprinted From: SI Combustion(SP–1517)

SAE 2000 World CongressDetroit, MichiganMarch 6–9, 2000

1

2000–01–1081

A Review of Investigations Using the Second Law ofThermodynamics to Study Internal-Combustion Engines

Jerald A. CatonTexas A&M University

Copyright © 2000 Society of Automotive Engineers, Inc.

ABSTRACT

Investigations that have used the second law ofthermodynamics to study internal-combustion engines ina detailed manner date back to the late 1950s. Over twodozen previous investigations which have used thesecond law of thermodynamics or availability analyseswere identified. About two-thirds of these have beencompleted for diesel engines, and the other one-thirdhave been completed for spark-ignition engines. Themajority of these investigations have been completedsince the 1980s. A brief description of each of theseinvestigations is provided.

In addition, representative results are presented for bothcompression-ignition (diesel) and spark-ignition enginesto illustrate the type of information obtained by the use ofsecond law analyses. Both instantaneous values for theengine availability, and the overall values for energy andavailability are described.

INTRODUCTION

Reports on the detailed use of the second law ofthermodynamics to study internal combustion engineshave been published for over 40 years. While the use of asecond law analysis is not necessary for generalperformance computations, the insight provided by asecond law analysis is invaluable in understanding thedetails of the overall thermodynamics of engineoperation.

The second law of thermodynamics is a rich and powerfulstatement of related physical observations that has awide range of implications with respect to engineeringdesign and operation of thermal systems. For example,the second law can be used to determine the direction ofprocesses, to establish the conditions of equilibrium, tospecify the maximum possible performance of thermalsystems, and to identify those aspects of processes thatare detrimental to overall performance.

The objective of the current work was to provide acomprehensive listing and description of all the knownwork in this area, and to compare and contrast the more

significant findings. The next subsections will review theconcept of availability, and provide basic analyticalresults. This will be followed by major sections onprevious work, example results, and summary.

AVAILABILITY – Related to the analysis based on thesecond law of thermodynamics is the concept ofavailability which is also known as essergy (essence ofenergy) and exergy [1–4]. Availability, a thermodynamicproperty of a system and its surroundings, is a measureof the maximum useful work that a given system mayattain as the system is allowed to reversibly transition to athermodynamic state which is in equilibrium with itsenvironment. One key aspect of availability is the fact thata portion of a given amount of energy is “available” toproduce useful work, while the remaining portion of theoriginal energy is “unavailable” for producing useful work.

In general, the processes of interest are the thermal,mechanical and chemical processes. An example of thethermal aspect of availability is a case where the systemtemperature is above the environmental temperature. Byutilizing an ideal heat engine (such as a Carnot engine),the availability from the system could be converted towork until the system temperature equaled theenvironmental temperature (the remaining energy is,therefore, the unavailable portion of the energy). Anexample of the mechanical aspect of availability is asystem which is at a pressure above the environment. Byutilizing an ideal expansion device (such as an idealturbine), the energy of the system could be converted towork until the system pressure equaled theenvironmental pressure.

A final consideration is the chemical aspect1 ofavailability. This aspect considers the potential tocomplete work by exploiting the concentration differencesof the various species relative to the relatedconcentrations in the environment. The consideration of

1. The chemical aspect of availability by convention refers to the concentration differences between the species in the system and in the environment [8–10]. In contrast, the (chemical) fuel energy is included in the availability terms since the total (chemical and sensible) energy is used for the internal energy and for the enthalpy.

2

the species concentration component of availability isoften neglected (particularly when considering mobileengine applications) due to the practical difficulties ofimplementing such a system and the relatively smallamounts of work produced [4, 5].

DETERMINATION OF AVAILABILITY – Thedetermination of availability is based on the values ofother thermodynamic properties. In this development, thekinetic and potential energies are neglected (and can beshown to be negligible). Since the overall engineoperation includes both closed system and open systemportions, two forms of availability are needed. At all times,for the complete system:

(1)

where a is thespecific availability (or exergy), u is the specific internalenergy, uo, vo and so are the specific internal energy,

specific volume and specific entropy for the dead state1,respectively, po and To are the pressure and temperatureof the dead state, respectively, v is the specific volume,and s is the specific entropy. The dead state is defined asthe conditions of the environment at a temperature of Toand a pressure of po. The term, po(v–vo), representsthe work completed against the atmosphere at po andhence is not useful.

For the flow periods (open system), the flow availability

(or exergy for flows), , is given by:

(2)

where h is the specific enthalpy, ho and so are thespecific enthalpy and specific entropy of the dead state,respectively, and s is the specific entropy of the flowingmatter. For flows out of the system, the flowing matter isthe cylinder contents, and for flows into the system, theflowing matter must be specified.

With the above relations (eqs. 1 and 2) and aspecification of the reference (or dead) state, theavailability of the cylinder contents may be determinedthroughout the cycle. The total availability is obtained by

(3)

where m is the system mass and a is the specificavailability.

Availability is not a conserved property, but in fact, maybe destroyed by irreversible processes such as heattransfer through a finite temperature difference,combustion, friction, and mixing processes. Between anyend states, therefore, the change in the availability maybe related to the relevant processes:

(4)

where is the change of the total system availability fora process, Aend is the total availability at the end of theperiod, Astart is the total availability at the start of theperiod, Ain is the total availability transferred into thesystem accompanying flow into the system, Aout is theavailability transferred out of the system accompanyingflow out of the system, AQ is the availability transferredaccompanying the heat transfer, AW is the availabilitytransfer due to work, and Adest is the availability which isdestroyed by irreversible processes. This relation may beused to ascertain the destruction of availability by solvingeq. 4 to find Adest. That is,

(5)

For work interactions, the availability is equal to theamount of the work:

(6)

For heat transfer, the availability which is transferred outof the system is equal to the “available” portion of theheat transfer:

(7)

where AQ is the available portion of the heat transfer, is the differential heat transfer which is transferred at asystem (boundary) temperature of T. The availability thattransfers into the system (Ain) and out of the system(Aout) due to flows are given as follows:

(8)

where the subscript “ i ” refers to each individual flow (forthis study, intake or exhaust).

The fuel availability of the fuel is needed. this is foundfrom standard relationships, and is often only a fewpercent higher than the lower heating value of the fuel [4].

ANALYTICAL RESULTS – In this sub-section, results arepresented which illustrate the general characteristics ofavailability. These results are general, and notnecessarily related only to engines. First, the portion ofenergy that is available to do work is described. Second,the amount of available energy that is destroyed due to aheat transfer process from a high temperature to a lowertemperature is presented. Finally, the amount of availableenergy which is lost due to combustion processes isdescribed.

Only a certain portion of a given amount of energy can beconverted to work. The maximum portion would beobtained if the original energy was used in a Carnot heatengine:

1. This is actually a “restricted” dead state since composition equilibrium with the environment is not considered [1].

a u u p v v T s so o o o o= − − − − − −( ) ( ( )) ( )

af

a h h T s sf o o o= − − −( ) ( )

A m a=

∆∆

A A A

A A A A A Aend start

in out Q W dest

= −= − + − −

∆A

A A A A A A Adest start end in out Q W= − + − + −

A WW =

∫

−= Q

T

TA o

Q δ1

δQ

( )∫= dtamA ifii ,�

3

(9)

where Wmax is the maximum work that could beobtained from the original energy, Qtotal is the totaloriginal energy, To is the environment temperature, andTgas is the constant temperature of the original energy.Therefore, the percentage which is available is

(10)

Figure 1 shows the percentage of the energy which isavailable (or unavailable) as a function of gastemperature for an environment temperature of 300 K. Asshown, the percentage of available energy increases asthe gas temperature increases. Conversely, for lowtemperatures, a smaller percentage of the original energyis available to produce work. Energy at the ambienttemperature (300 K for these results) has no potential todo work, and hence, the available energy is 0% of theoriginal energy. On the other hand, energy at 3500 K isover 91% available.

Figure 1. Percentage of the energy which is available (and unavailable) as a function of gas temperature for an environment temperature of 300 K.

As mentioned above, available energy may be used toproduce useful work, may be transferred via heat transferor mass flows, and may be destroyed by irreversibleprocesses. One such irreversible process is the heattransfer across finite temperature differences described

above. Another irreversible process is combustion.During combustion, the fuel availability is converted froma chemical form to a thermal form, and in the process thepotential to do work is reduced. In the following fewparagraphs, the destruction of availability by heat transferand by combustion are examined.

For heat transfer processes across finite temperaturedifferences, a portion of the availability is destroyed. Thisis due to the fact that at the higher gas temperature agreater portion of the energy is available to produce work.Once the energy is deposited at the wall at a lowertemperature, the energy’s capability to produce work isdiminished. This may be determined from the following

(11)

(12)

Figure 2. Percentage of the availability which is destroyed during the heat transfer process from the gas temperature to the wall temperature for an environment temperature of 300 K.

where Agas and Awall are the available energy of the gasand wall, respectively, and Tgas and Twall are thetemperatures of the gas and wall, respectively. Thepercentage of the availability destroyed due to the heattransfer process is

−=

gas

ototal T

TQW 1max

−==

gas

o

total

Q

total T

T

Q

A

Q

W1max

GAS TEMPERATURE (K)

500 1000 1500 2000 2500 3000 3500

AV

AIL

AB

LE E

NE

RG

Y (

%)

0

10

20

30

40

50

60

70

80

90

100

AVAILABLE ENERGY

UNAVAILABLE ENERGY

To = 300 K

−=

gas

ototalgas T

TQA 1

−=

wall

ototalwall T

TQA 1

GAS TEMPERATURE (K)

1000 1500 2000 2500 3000

DE

ST

RO

YE

D A

VA

ILA

BIL

ITY

(%

)

0

10

20

30

40

50

60

70

80

90

100

110

Tw = 300 K

To = 300 K

Tw = 450 K

Tw = 600 K

4

(13)

Combining eqs. 11, 12 and 13 yields

(14)

Figure 2 shows the percentage of the availability which isdestroyed due to the heat transfer process from the gastemperature to the wall temperature for an environmenttemperature of 300 K. First, for the case with a walltemperature of 300 K, 100% of the availability isdestroyed since all the energy is at the environmenttemperature and can not produce work. For the other twocases (wall temperatures of 450 and 600 K), thepercentage destroyed increases with gas temperature.This is because the availability at the wall temperatureremains the same, but the initial availability of the gas ishigher for the higher temperatures. Therefore, moreavailability is destroyed for higher gas temperatures. Inother words, the larger the temperature difference, thelarger the destruction of availability. Finally, for the higherwall temperatures, the percentage destroyed decreasessince the higher wall temperatures retain more of theoriginal availability.

Figure 3. Percentage of the availability destroyed by the combustion process for a constant volume, adiabatic system (adapted from Caton [6]).

Finally, this sub-section will end with comments onanother process which destroys available energy,combustion. The chemical energy of the fuel representsthe potential to yield a maximum amount of work(available energy). As this energy is converted to thermalenergy at a specific temperature, some portion of thatavailable energy is destroyed. Caton [6] has presentedresults from an analytical study which examinedcombustion processes in a constant volume, adiabaticsystem. This system was selected to isolate thecombustion destruction of available energy from the otherprocesses. Results were obtained for a variety ofconditions for octane and air mixtures. As an example,figure 3 shows the destroyed availability as a percentageof the original available energy as a function of themaximum (adiabatic flame) temperature for anequivalence ratio of 1.0 for an initial reactant pressure of500 kPa. This pressure, 500 kPa, is representative of thepressure at the start of combustion for a range of internalcombustion engines [4]. This range of maximumtemperatures was obtained by varying the initialtemperature from 500 to 2500 K.

The results in figure 3 show that the percentage of thetotal reactant availability destroyed by combustiondecreases monotonically from about 20 to 7.5% as themaximum temperature increases from about 2800 to3400 K for these conditions. In other words, thedestruction of the original availability decreases as thetemperature of the combustion process increases. Thisresult was shown to be a direct consequence of thecharacteristics of the specific availability as a function oftemperature [6].

In general, these results suggest that as the combustiontemperature increases, the destruction of availabilitydecreases. For the assumptions of this study, however,the destruction of availability does not attain zero even forunrealistically high temperatures. In any case, these hightemperatures and pressures are beyond the practicallimits of today’s designs and materials for combustiondevices.

Although higher gas temperatures may minimize thedestruction of available energy by combustion [5, 6],these higher temperatures may lead to other losses ofavailable energy in practical (actual) engineeringsystems. In particular, the higher temperatures mayresult in higher heat transfer which will remove theavailable energy. Also, if not utilized, the higheravailability will be expelled with the exhaust gases.Another consideration would be the potential for highernitric oxide (NO) formation rates at these highertemperatures.

In summary, the above analytical results are intended toillustrate the general characteristics of availabilityanalyses. Specifically, the above discussion has shownthat energy has an available and an unavailable portion.Also, two modes of availability destruction, due to heattransfer, and combustion, were described.

−=

−=

∆

gas

wall

gas

wallgas

gas

dest

A

A

A

AA

A

A1

−

−−=

∆

gas

o

wall

o

gas

dest

T

TT

T

A

A

1

1

1

MAXIMUM TEMPERATURE (K)

2800 3000 3200 3400

DE

ST

RO

YE

D A

VA

ILA

BIL

ITY

(%

)

8

10

12

14

16

18

20Constant Volume,

Adiabatic CombustionpR = 500 kPa

φ = 1.0Octane-air

5

PREVIOUS STUDIES

Over two dozen previous studies employing the secondlaw of thermodynamics or availability analyses withrespect to internal combustion engines were identified.The majority of these have been completed for dieselengines. The following is a chronological presentation ofdescriptions of these studies. This presentation is dividedinto two subsections: (1) early work (1957–1989), and (2)recent work (1990–2000).

EARLY WORK: 1957 to 1989 – One of the earliestdocumented studies was a brief report presented byTraupel [7] in 1957. Although there were few details, heapparently completed calculations to determine theavailability values based on measurements of theprincipal energy terms. He compared a naturallyaspirated diesel engine and a turbocharged dieselengine. He stated that the combustion processaccounted for a destruction of about 22.5% and 21.9% ofthe fuel’s availability for natural aspirated andturbocharged diesel engines, respectively. He alsoreported on the losses related to cooling, exhaust,mechanical, and aerodynamic processes.

A pioneering work on this topic was reported byPatterson and van Wylen [8] in 1964. They described anearly version of a thermodynamic cycle simulation forspark-ignition engines in which they includeddetermination of entropy values. With the entropy values,they then determined availability for the compression andexpansion strokes. They isolated the availabilitydestruction associated with the heat transfer andcombustion processes. Some of the simplifications of thisearly work included (1) idealized induction and exhaustprocesses with instantaneous valve events occurring attop dead and bottom dead center, (2) the induction,compression, and exhaust processes were assumedadiabatic, and (3) the cylinder pressure during theinduction and exhaust processes was assumed constantand specified. They summarized their findings by statingthat of the availability at the beginning of the compressionprocess, 1/3 was delivered as work, 1/3 was lost due tothe combustion and heat transfer processes, and 1/3 wasexpelled.

Clarke [9] examined the Otto, Joule and Atkinson air-standard cycles from the perspective of availability andthe associated availability destruction. He described thepossibilities of achieving higher thermal efficiencies byrecognizing the fundamental availability loss mechanismsfor internal combustion engines. Clarke stated that toachieve minimum destruction of availability, thecombustion process should be under conditions of nearchemical equilibrium. He suggested strategies to achieveminimum destruction of availability.

Edo and Foster [10] in 1984 reported on an availabilityanalysis for an engine which utilized dissociatedmethanol. The use of dissociated methanol wasmotivated by the potential to capture exhaust energy bydissociating liquid methanol into more readily used

gaseous species such as carbon monoxide (CO) andhydrogen (H2). The dissociated products then have thepotential to be used as a much leaner reactant mixturethus improving fuel efficiency and reducing emissions. Inthe course of this study, they completed an availabilityanalysis which used a simple adiabatic, air-standardanalysis with an instantaneous heat release for thecombustion process, but with equilibrium products. Theyreported availability as a function of equivalence ratio,and showed the various transfers and destruction of thefuel availability.

Beginning in the mid–1980s, a number of more detailedinvestigations were reported on the use of availability.Perhaps the most notable contributions were from aseries of investigations by researchers at the CumminsEngine Company. In 1984, the first of these was reportedby Flynn et al. [5]. They used a second law analysis tostudy a turbocharged, intercooled diesel engine. Theengine for this study was a 14-liter, in-line six-cylinder,diesel engine operating at 300 kW at 2100 rpm. Inparticular, they used the second law analysis to evaluatelow heat rejection (LHR) engine concepts and secondaryheat recovery devices. Essentially they used a standardthermodynamic cycle simulation to obtain thethermodynamic states for a particular engine cycle. Theythen determined entropy and availability values for thesestate points, and completed availability balances for thegiven engine cycle. They showed (for the engine cylinder)that of the original fuel availability about 46% wasdelivered as useful indicated work, 26% was destroyed,10% was transferred as heat, and 18% was exhausted.

They showed that, as expected, the work output per unitof fuel increased as the equivalence ratio became leaner.Also, as the equivalence ratio becomes leaner, thedestruction of availability becomes greater. The reasonthat the work output increases anyway is that theavailability transfers due to heat transfer and exhaust flowdecrease much faster as equivalence ratio decreases.The net result, therefore, is an increase in the workoutput per unit of fuel for the leaner mixtures. Thisobservation has also been reported by others [4]. Furtherdetails from this study [5] are presented in a subsequentsection of this paper.

Primus [11] reported on a second law analysis of exhaustsystems for a turbocharged, intercooled diesel engine.This was a companion study to the one reported by Flynnet al. [5]. Primus reported on the influence of the exhaustmanifold cross-sectional area upon a number ofcharacteristics such as frictional losses for a 14-literdiesel engine operating at 1900 rpm with an air-fuel ratioof 34.4. He was able to determine an optimum exhaustmanifold diameter which minimized the overall loses.

Primus et al. [12] described another study which was acontinuation of their earlier work (Flynn et al. [5] ). In thisstudy, they used the second law analysis to assess thebenefits of turbocharging, charge air cooling,turbocompounding, the implementation of a bottomingcycle, and the use of insulating techniques. The baseline

6

engine for this study was a 14-liter direct-injection,natural aspirated, diesel engine rated at 185 kW at 2100rpm. They showed that as the combustion becomesleaner (excess air), the availability destruction increasesdue to increased mixing and lower bulk gastemperatures. This happens because the hightemperature products of combustion are mixed with theexcess air. For mixtures closer to or at stoichiometric, thiseffect is minimized (less excess air, higher temperatures),and hence, the conversion of chemical potential to workis more effective. This finding explained the relativemerits of the various options they investigated since eachoption would have a unique stoichiometry (amount ofexcess air). For this reason, they found that forturbocharging (with a higher AF ratio) relative to naturalaspiration (with a lower AF ratio) the combustiondestruction of availability was higher.

In 1985, Primus and Flynn [13] reported on acontinuation of their earlier work. The engine they used inthis study was an inline 10-liter, six-cylinder,turbocharged and aftercooled, direct-injected dieselengine. They conducted a detailed parametric studywhich examined the effects of a number of engineparameters on the various thermodynamic processes ofthe engine operation. The parameters examined wereengine speed, load, peak cylinder pressure limit,compression ratio, intake air temperature, injection timingand apparent heat release rate shape. They presentedtheir results for the distribution of availability uses andtransfers in three forms: tables of the numerical values,graphs of the absolute availability for each mode ofavailability use or transfer, and graphs of the percentageof the fuel availability for each mode of availability use ortransfer. As an example of their results, theydemonstrated that as the combustion duration isshortened the combustion destruction of availabilitydecreases due to the increase in the cylinder pressuresand temperatures. Also, they showed that as the injectiontiming is retarded, the combustion destruction ofavailability increases due to the decrease in the cylinderpressures and temperatures. They listed the percentageof the availability destroyed by combustion as increasingfrom 21.8 to 32.5% as load (equivalence ratio)decreased.

Primus and Flynn [14] in 1986 reported on a further studywhich continued their previous work. They focused onitemizing the various loss mechanisms associated with a10-liter, six-cylinder, turbocharged and aftercooled,direct-injected diesel engine. They demonstrated how thesecond law enhanced their understanding of thethermodynamic processes. They studied in-cylinder andout-of-cylinder processes: in-cylinder heat transfer,combustion, exhaust, friction, turbine, exhaust valve,compressor, aftercooler, intake valve, and exhaustmanifold heat transfer. They provided examples ofparametric variations of key engine parameters such asintake manifold temperature, injection timing, andexhaust manifold size.

van Gerpen and Shapiro [15] also used a second lawanalysis with a standard cycle simulation for a dieselengine. In contrast to the previous investigations, this

work included the “chemical component1” of theavailability. Some simplifications of this work were (1) theinitial cylinder conditions at bottom dead center (BDC)were assumed to be the ambient conditions with noresidual gases, and (2) only compression and expansionstrokes were considered (no flows were included). Thisstudy [15] was based on a diesel engine and used a deadstate based on standard saturated air (with trace CO2,H2O, and Ar) at 298.15 K and 101.35 kPa. They foundthat the chemical contribution to the availability is highlydependent on the equivalence ratio. For the case theystudied, they reported that for lean and stoichiometricequivalence ratios the chemical availability was about15% of the total availability. For rich cases, the availabilitywas shown to be as high as 90% of the total availabilityfor an especially rich equivalence ratio of 2.0.

The large contribution of the chemical component to theavailability for the rich cases was a direct result of therelatively high concentrations of species such as H2 andCO which possess significant amounts of chemical (fuel)energy. In other words, for the rich cases, the presence ofCO and H2 and other such species have unused fuelenergy which means that the availability would bedominated by the chemical component. At least to someextent, the results for the rich cases are not unexpected.From an energy perspective, for these rich cases, the

combustion inefficiency2 would be high. Thequantification of these losses by the availability analysisis an alternative way to view these inefficiencies.

Alkidas [16, 17], in 1988 and 1989, reported on a studywhich examined the application of a second law analysisfor a diesel engine. The engine he used was a 2.0-litersingle-cylinder, direct-injection, open-chamber, dieselengine operated at 1200 and 1800 rpm with variousloads. This work was different than many of the otherinvestigations in two major ways. First, he defined thethermodynamic system as outside the engine cylinder.Second, he used experimental measurements of theenergy rejected to the coolant and lubricating oil, of thebrake work, and of the air and fuel flow rates. He thencalculated availability values from the thermodynamicstates based on the measured values.

Alkidas [16, 17] showed that the heat transfer wasresponsible for the greatest availability transfer, and thatthe combustion destruction of availability was the nextmost important mechanism of availability removal. Forthe cases he studied, the combustion destruction was

1. The “chemical component,” as mentioned earlier, refers to the potential to do work due to the species concentrations relative to the concentrations in the surroundings. This does not refer to the chemical energy of the fuel.

2. Combustion inefficiency is defined as the ratio of the chemical energy carried out of the engine (due primarily to the presence of combustible species) and the chemical energy of the fuel. [4].

7

between 25 and 43% of the original fuel availability.Alkidas stated that preheating the intake air decreasesthe combustion irreversibilities due to the fact that thecombustion temperatures increased.

In the second paper [17], Alkidas also studied a low-heat-rejection diesel engine. This engine used air-gap-insulated piston, liner, fire deck and exhaust port. Theengine was tested for 10 operating conditions at 1200and 1800 rpm. Alkidas showed that the low-heat-rejection engine more effectively utilized the fuel’savailability largely due to the reduced heat losses and thehigher combustion temperatures.

McKinley and Primus [18] described an assessment of anumber of turbocharging systems from both a first lawand a second law perspective. They studied a 10-liter, in-line six-cylinder, diesel engine operating at 224 kW at2100 rpm. They examined variable geometryturbocharging, wastegating, and resonant intakesystems. The baseline turbocharging system used fixedgeometry with no wastegate. Air-to-air aftercooling wasemployed for all systems. In general, the results of thesecond law analysis were dominated by the associatedchanges in the air-fuel ratio used with each of theturbocharging systems.

Kumar et al. [19] reported on a second law analysis of asingle-cylinder, direct-injected, diesel engine using acomprehensive simulation. This report included onlypreliminary results for an operating condition of 2000 rpmwith an equivalence ratio of 0.7. For the one conditionexamined, they reported that 16.1% of the fuel availabilitywas destroyed during the combustion process.

Lipkea and DeJoode [20] reported on the use of bothexperimental and simulation results to assess theperformance of two direct-injection, 7.6-liter, six-cylinder,heavy-duty, turbocharged, intercooled diesel enginesfrom a second law perspective. Details concerning thisengine are provided by Whiting et al. [21]. They includedchemical availability in their analysis. For the dead state,they selected standard air at 101.34 kPa and 298.15 Kwith trace amounts of H2O, CO2, and other species. Oneobjective of their work was to determine the effect ofmajor engine parameters on the fuel consumption. Theyused an availability analysis to identify the sources ofirreversibilities and availability losses during the enginecycle.

Lipkea and DeJoode [20] completed an availabilityanalysis for each of the various engine components(such as the turbocharger, intercooler, ports/manifolds,and cylinder). They showed that the exhaust and the heattransfer accounted for about 60% of the fuel energy, butonly about 20% of this energy could be used potentiallyto produce additional work. About 40% of the fuelavailability was lost due to internal irreversibilities such ascombustion, friction, mixing and heat transfer.

Shapiro and van Gerpen [22] extended their earlier work[15] to include a two-zone combustion model and appliedthis model to both a compression-ignition and a spark-

ignition engine. As before, this study included chemicalavailability considerations. Their work considered onlythe compression and expansion strokes, and included noconsideration of intake or exhaust flows. They presentedthe time-resolved values of the availability for cases withdifferent equivalence ratios, residual fractions, and burndurations. They showed, for example, that thecombustion irreversibility increases with increasing burnduration.

RECENT WORK: 1990 to 2000 – In 1991, Bozza et al.[23] described a second law analysis of an indirect-injected, four-cylinder turbocharged, diesel engine. Theyused experimental measurements to obtain informationfor the heat release and flow expressions in theirsimulation. As an example, one operating conditionstudied was at 4500 rpm and an equivalence ratio of0.56. They found that for steady-state operation thepercentage of the fuel availability destroyed bycombustion ranged between about 22 and 26%depending on the values used for the ignition delay,aspiration, turbocharger speed, and other parameters.They also examined transient operation with particularemphasis to the turbocharger performance.

Gallo and Milanez [24] reported in 1992 on the use of acycle simulation to determine the instantaneousirreversibilities, and other second law considerations for aspark-ignition engine using ethanol and gasoline. Theyfocused on the combustion process and valve timings.They examined the effects of ignition timing, duration ofcombustion, combustion shape factor, and equivalenceratio on second law efficiencies. They found that the useof ethanol (at a compression ratio of 12 compared to acompression ratio of 8 for gasoline) relative to gasolineprovided a more effective use of the fuel energy. Further,the combustion irreversibilities were less with ethanolthan for gasoline.

Al-Najem and Diab [25] presented a short technical notewhich described brief results for turbocharged dieselengine operated at 243 kW with an air-fuel ratio of 20.They stated that about 50% of the fuel availability isdestroyed due to unaccounted factors such ascombustion, 15% is removed via exhaust and coolingwater, and about 1% is destroyed in the turbocharger.

Rakopoulos [26] in 1993 described a first and second lawanalysis of a spark ignition engine using a cyclesimulation and experiment. The engine studied was avariable compression Ricardo E-6 spark ignition engine.The major parameters studied were the compressionratio, fuel-air ratio, and ignition advance. The author’smodel included the development of a spherical flamefront. Only the valve closed period was studied. Theauthor discusses possible ways for improving cycleperformance by reducing availability losses due tocombustion through improvements in combustionchamber design, fuel-air mixing, and ignition processes.

Rakopoulos and Andritsakis [27] in 1993 presentedresults for the irreversibility rates of two four-stroke cycle

8

diesel engines. The first engine was a high-speed, directinjection (DI), naturally aspirated, single-cylinder, dieselengine, and the second engine was a medium-speed,indirect-injection (IDI), turbocharged six-cylinder dieselengine. They used experimental information to determinethe fuel burning rate, and then used the second law ofthermodynamics to deduce the irreversibility rates foreach engine. They showed that the accumulatedirreversibility was proportional to the fuel burned fractionfor a wide range of engine loads, speeds, and injectiontimings. For the DI engine, the destroyed availability wasbetween about 21 and 31% of the original fuel availability.For the IDI engine, the destroyed availability (for the caseof both combustion chambers) was between about 24and 29% of the original fuel availability. Also, for the IDIengine, the irreversibility of the flow between theprechamber and main chamber was identified.

Rakopoulos et al. [28] in 1993 reported on the availabilityaccumulation and destruction in a high-speed, direct-injection, naturally aspirated diesel engine. Theycompleted experiments to determine the fuel reactionrates, and then computed the associated second lawquantities including the irreversibility production rate.They limited their considerations to the valve closedperiod. They completed this work for a range of speedsand loads. They also studied limited cooling conditions todetermine the implications from a second law perspectiveon improving efficiency. They considered the use ofexhaust heat recovery devices to utilize the extraavailability present in the exhaust gases for the limitedcooling cases.

*SI: spark ignition engine; CI: compression ignition(diesel) engine.

=SI engine using dissociated methanol.

Rakopoulos et al. [28] stated that their results indicatedthat the irreversibilities decrease and the availability ofthe exhaust gas increases with increasing fuel-air ratio(or increasing equivalence ratio). On the other hand, theyreported that both the irreversibility and the availability ofthe exhaust gas increased with engine speed, andslightly decreased with increasing injection timing.

Table 1. Summary of Previous Investigations (Part 1) (1957 – 1989)

Date Investigators Engine*

Comments

1957 Traupel [7] CI Values based on measurements; few

details

1964 Patterson and van

Wylen [8]

SI Compression and expansion strokes; simple treatment of intake and exhaust

1976 Clarke [9] SI/CI Otto, Joule and Atkinson air-standard

cycles

1984 Edo and Foster [10]

SI= Simple Otto air-standard cycle model

with equilibrium products (no flows)

1984 Flynn et al. [5]

CI Comprehensive model of all processes

1984 Primus [11] CI Comprehensive model of all processes;

focused on exhaust system optimization

1984 Primus et al. [12]


1985 Primus and Flynn [13]


1986 Primus and Flynn [14]


1987

(& 1990)

van Gerpen and Shapiro

[15]

CI Compression and expansion strokes; no

intake or exhaust strokes; included

chemical availability

1988

(& 1989)

Alkidas [16, 17]

CI Experimental measurements of

energy terms; calculated availability

1988 McKinley and Primus

[18]

CI Comprehensive model of all processes;

evaluation of turbocharging systems

1989 Kumar et al. [19]


including manifold flow dynamics; included

chemical availability; only preliminary results

1989 Lipkea and DeJoode

[20]


included chemical availability; included

experimental measurements

1989 Shapiro and van Gerpen

[22]

SI & CI Compression and expansion strokes; no


chemical availability

Table 1. Summary of Previous Investigations (Part 1) (1957 – 1989)

9

*SI: spark ignition engine; CI: compression ignition(diesel) engine.

=Used gasoline and a 30% butanol-gasoline blend.

IUsed ethanol and gasoline.

¨Completed for both a conventional cycle and a Millercycle.

Rakopoulos and Giakoumis [29] in 1997 reported on theuse of a computer analysis to assess the performance ofa turbo-charged, aftercooled, indirect-injected, six-cylinder marine-duty, diesel engine operated over a rangeof engine speeds, loads and compression ratios. Anumber of the engine sub-assemblies were studied.These included the compressor, turbine, inlet andexhaust systems, and in-cylinder processes. Theyshowed that the combustion irreversibilities decreasedwith increasing compression ratio. This observation wasdue to the fact that the equivalence ratio increased ascompression ratio increased due to the correspondingdecrease in the compressor pressure ratio.

Rakopoulos and Giakoumis [30] in 1997 reported on theuse of a computer analysis to study the energy andexergy performance of an indirect-injection, naturally-aspirated diesel engine operating under steady-state andtransient conditions. The engine was a Ricardo E-6research diesel engine with about a 21:1 compressionratio. As an example of their transient results, theyconsidered an acceleration which started at 15% load at1500 rpm and accelerated to 100% of full load at 1500rpm in 0.2 seconds. They presented the engine responseto the imposed acceleration for speed, injected fuel,engine and load torques, and maximum cylinderpressures as a function of time (or engine cycles). Theyreported that the combustion irreversibility decreasedduring acceleration due to slightly higher fueling ratesassociated with this transient event.

Alasfour [31] in 1997 described the results of anavailability analysis completed for a single cylinder,spark-ignition fuel-injected Hydra engine using bothgasoline and a 30% butanol-gasoline blend. The majorityof this work was an experimental study during which heobtained general engine performance results as afunction of equivalence ratio. Once he had obtainedengine performance, he was able to report the results interms of energy quantities: brake work, friction work, heattransfer to the coolant, energy out the exhaust, andunaccounted energy losses. He then used these resultsto determine the related second law quantities. He found

Table 2. Table I. Summary of Previous Investigations (Part 2)(1990 – 2000)

Date Investigators Engine*

Comments

1991 Bozza et al. [23]


included experimental measurements

1992 Gallo and Milanez [24]

SII Comprehensive model of all processes

1992 Al-Najem and Diab

[25]

CI Brief results for a turbocharged diesel

engine

1993 Rakopoulos [26]

SI Compression and expansion strokes; no


transient operation

1993 Rakopoulos and

Andritsakis [27]

CI Calculated availability; experimental

measurements of energy terms;

considered only valve closed period; related

combustion irreversibility to fuel

reacted fraction

1993 Rakopoulos et al. [28]

CI Experimental measurements of

energy terms; calculated availability; considered only valve

closed period

1997 Rakopoulos and

Giakoumis [29]


included experimental measurements

1997 Rakopoulos and

Giakoumis [30]


included experimental measurements;

included transient operation

1997 Alasfour [31] SI= Experimental measurements of

energy terms; calculated availability

1997 Rakopoulos and

Giakoumis [32]


included experimental measurements;

1998 Anderson et al. [33]

SI¨ Comprehensive quasi-dimensional model of

all processes

1999, 2000

Caton [34–37]

SI Comprehensive model of all processes

Table 2. Table I. Summary of Previous Investigations (Part 2)(1990 – 2000)

10

for an equivalence ratio of 0.9 for the butanol-gasolineblend that 49.4% of the fuel’s availability was not used toproduce useful work. In addition, he found that both thefirst and second law efficiencies increased for leanoperation.

Rakopoulos and Giakoumis [32] in 1997 described theiruse of a computer analysis to assess the cumulative andavailability rate balances of a multi-cylinder diesel engine.They studied a six-cylinder, turbocharged andaftercooled, indirect-injection diesel engine at full loadand 1500 rpm. They neglected chemical dissociation.They included all individual components fromcompressor through the cylinder to the turbine. Theyincluded all processes for both the closed valve and openvalve portion of the cycle. They showed that 21.4% of thefuel’s availability left the cylinder with the exhaust, butafter the turbine, the exhaust only contained 13.5%. Thecombustion irreversibility was responsible for destroying21.9% of the fuel’s availability.

Anderson et al. [33] in 1998 reported on an investigationof a naturally-aspirated, Miller cycle spark-ignition engineusing late intake valve closure. Using a comprehensivequasi-dimensional engine cycle simulation, theycompared the Miller cycle strategy with a conventionalspark-ignition engine. The advantage of the Miller cycle isthat it can use late intake valve closure to control loaddown to 35% of full load with the use of a throttle. Belowthis load, the Miller cycle would use supplementalthrottling. First law considerations showed that the Millercycle increased the indicated thermal efficiency at lightloads by as much as 6.8%. The second law analysisshowed that the conventional throttle destroys up to 3%of the availability.

Caton [34–37] reported on the use of the second law ofthermodynamics to study a spark-ignition engine. Thiswork was based on the use of a comprehensivethermodynamic cycle simulation. In one portion of thisstudy, he examined the effects of engine load and speedon a number of performance, energy and availabilityterms [37]. A commercial, V-8, spark-ignition engine wasselected for this study. Engine loads corresponding tobrake mean effective pressures (bmep) of 163, 325, and655 kPa, and engine speeds of 700, 1400, and 2800 rpmwere examined.

For these conditions, the availability displaced to thecylinder wall via heat transfer (as a percentage of the fuelavailability) ranged between 15.9 and 31.5%. The netavailability expelled with the exhaust gases rangedbetween 21.0 and 28.1%, and the availability destroyedby the combustion process ranged between 20.3 and21.4%. In addition, this study showed that the mixing ofthe inlet charge with existing cylinder gases was anadditional (but small) mechanism for the destruction ofavailable energy [34–37].

Table I is a chronological summary of these previousinvestigations which used a second law analysis forengine evaluations. The table lists the year of the report,

the investigator(s), the type of engine (SI or CI), andcomments. In addition, appendix A contains two tableswhich provide some additional details about the enginesused in the above studies.

In summary, over two dozen previous studies have beenidentified which have used the second law ofthermodynamics and the concept of availability toexamine engine operation in some detail. Most of thesestudies have use some type of engine simulation,although several based their results on measurements ofthe principal energy terms. The majority of this previouswork has been completed for diesel engines. Althoughmost of the previous work has considered conventionalengines, at least four (4) studies included some non-conventional characteristics. These non-conventionalcharacteristics included the use of alternative fuels (suchas butanol, ethanol and methanol), and a Miller cycleengine.

EXAMPLE RESULTS

In this section, representative results derived from use ofthe second law are presented for both a compression-ignition and a spark-ignition engine. The presentation ofthese results is intended to provide a general overview ofsecond law analyses. For detailed results, the referencedworks should be consulted.

Direct comparisons between the results from the twoengines are not possible since the two engines areoperating at different conditions and with differentoutputs. Furthermore, each study has chosen a differentthermodynamic system. The following results, therefore,are meant to be illustrative of the nature of second lawanalyses.

COMPRESSION-IGNITION ENGINE – Forrepresentative results for a compression-ignition (diesel)engine, sample results from the work of Flynn et al. [5]will be presented. In one of their investigations, theystudied a 14-liter (with a bore of 140 mm and a stroke of152mm) turbocharged and intercooled, direct injectiondiesel engine. The engine was operated at 2100 rpmproducing 300 kW of brake power with a 16:1compression ratio.

Figure 4 shows the percentages of the fuel’s energy andavailability for the indicated work, heat transfer, and netexhaust flow. In addition, for the availability, this figureshows the percentage destroyed by combustion andvalve throttling irreversibilities. As shown, the indicatedwork is 47.6% of the energy and 45.8% of the availability(the slight difference is because the availability of the fuelis 1.0317 times the fuel’s heating value). The heattransfer accounts for 12.6% of the fuel energy, but only9.7% of the fuel availability. This is because not all theenergy of the heat transfer is available to do work. Also,the net exhaust flow consists of 41.4% of the fuel energy,but only 18.3% of the fuel availability. Finally, thecombustion irreversibilities are significant: 21.0% of theavailable energy is destroyed. The throttling losses due to

11

the flows past the intake and exhaust valves accountedfor about 5.3% of the fuel’s availability.

Figure 4. Useful system availability and availability transfers as a function of crank angle for the spark ignition engine [36].

Figure 5. Percentage of the fuel’s energy and availability for a compression-ignition engine. (*Note: energy values do not add to 100% because of a reported imbalance of –1.6%). Adapted from Flynn et al. [5].

SPARK-IGNITION ENGINE – The representative resultsfor a spark-ignition engine are based on recent work byCaton [36]. A thermodynamic engine cycle simulationwas extended to include an analysis based on thesecond law of thermodynamics and the associatedcomputation of availability. The major augmentations to

this simulation included the computation of entropy,availability, irreversibilities, and the related entropy andavailability balances. From the balances, destruction ofavailability was determined.

This simulation was used to complete first and secondlaw analyses for a commercial, spark-ignition engineoperating at a part load condition. The selected enginewas a V–8 configuration with a compression ratio of8.1:1, and with a bore and stroke of 101.6 and 88.4 mm,respectively. A part load operating condition at 1400 rpmwith an equivalence ratio of 1.0 was selected.

The instantaneous availability of the system was the netresult of the transfer of availability through heat transfer,flows and work, and the destruction of availability due tocombustion. Figure 5 shows the system availability andthe availability transfers as a function of crank angle. Theavailability transfers are exhibited as accumulative valueswhich lead to the final system availability. First, the usefulwork is shown as the top (dashed) curve. Duringcompression, availability is transferred into the systemdue to the compression work. After top dead center(0×CA), the availability transfer is out as the systemdelivers work. The net indicated useful work is equal tothe final value (0.286 kJ) at the end of the cycle (at584×aTDC). The next curve down is for the availabilitydestroyed during the combustion process. Oncecombustion ends, the difference between the two topcurves remains constant.

The next curve down (in fig. 5) represents the transfer ofavailability due to heat transfer, and the final curveaccounts for the availability transfer due to flows. Whenthe exhaust valve opens (EVO), the availability decreasessharply. This decrease due to exhaust flow continuesuntil fresh charge enters and availability is thentransferred into the system. Near the end of the intakeprocess, the flow reverses and flows out of the systeminto the intake manifold. Eventually, at the end of thecycle, the system availability of the system has returnedto the original value. The final (darkest) curve, therefore,is the instantaneous total system availability.

In addition to the instantaneous values of availability, thedistribution of the total energy and availability values forthe cycle is of interest. Figure 6 shows the percentage ofthe total fuel energy and total fuel availability that each ofthe major processes uses. The left-hand bar is for thefirst law (energy) analyses, and the right-hand bar is forthe second law (availability) analyses. First, with respectto the net indicated work, the values using energy unitsare the same since the indicated work is 100% availableenergy. The percentages are slightly different due to theslightly higher availability of the fuel relative to its energyvalue [36].

CRANK ANGLE

-180 0 180 360 540

US

EF

UL

SY

ST

EM

AV

AIL

AB

ILIT

Y (

kJ)

AV

AIL

AB

ILIT

Y T

RA

NS

FE

RS

(kJ)

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

Net UsefulIndicatedWork Out

Availability Transferdue to Heat Loss

AvailabilityTransfer

due to Flows

AvailabilityDestruction dueto Combustion

CompressionWork

Final SystemAvailability

CombustionEnds

CombustionStarts

EVO

FreshChargeEnters

1 2

EN

ER

GY

or

AV

AIL

AB

ILIT

Y (

%)

0

20

40

60

80

100

(47.6%)*

(12.6%)*

(41.4%)*Destruction

due toCombustion

(21.0%)

Energy Availability

(9.7%)

(18.3%)

(45.8%)

ValveLosses(5.3%)

TotalIndicated

Work

HeatTransfer

Net TransferOut Dueto Flows

12

Figure 6. Percentage of the fuel’s energy and availability for a spark-ignition engine [36].

For the heat loss, although 0.268 kJ of energy istransferred out of the system, only 0.221 kJ of this isavailable energy. Hence the percentages are different.Similarly, for the net flow out, only 24.7% of the availableenergy is expelled, but 40.0% of the actual energy isexpelled. The next two categories apply only to theavailability accounting, and not to the first law (energy)aspect. These two categories quantify the availabilitydestruction due to combustion and inlet mixing. Theavailability destroyed was 20.6 and 1.3%, respectively, forthese two processes. Finally, for the parameters selected[36], about 0.7% of the availability and energy of the fuelwere not used.

SUMMARY

This paper has reviewed investigations that have usedthe second law of thermodynamics in studying internal-combustion engines. Over 40 years of efforts and over 28technical papers have been identified. About two-thirds ofthese have been completed for diesel engines, and theother one-third has been completed for spark-ignitionengines. Almost all of these investigations have beencompleted since the 1980s. The second law ofthermodynamics was shown to provide a frameworkwhich leads to a more thorough understanding of theenergy conversion process, provides a quantitativemeasure of the capability to produce useful work, andidentifies those processes that are destructive to thegoals of high performance and high efficiency engines.

Representative results were presented for bothcompression-ignition (diesel) and spark-ignition enginesto illustrate the type of information obtained by the use ofsecond law analyses. Both instantaneous values for theengine availability, and the overall values for energy andavailability were presented.

REFERENCES

1. Moran, M. J., Availability Analysis – A Guide toEfficient Energy Use (Corrected Edition), TheAmerican Society of Mechanical Engineers, NewYork, NY, 1989.

2. Moran, M. J., and Shapiro, H. N., Fundamentals ofEngineering Thermodynamics, John Wiley & Sons,Inc., New York, New York, third edition, 1995.

3. Wark, K., Jr., and Richards, D. E., Thermodynamics,sixth edition, McGraw-Hill Company, New York, NY,1999.

4. Heywood, J. B., Internal Combustion EngineFundamentals, McGraw-Hill Book Company, NewYork, New York, 1988.

5. Flynn, P. F., Hoag, K. L., Kamel, M. M., and Primus,R. J., “A New Perspective on Diesel EngineEvaluation Based on Second Law Analysis,” Societyof Automotive Engineers, SAE Paper no. 840032,1984.

6. Caton, J. A., “On the Destruction of Availability(Exergy) Due to Combustion Processes –– withSpecific Application to Internal-CombustionEngines,” submitted to Energy, 04 August 1999.

7. Traupel, W., “Reciprocating Engine and Turbine inInternal Combustion Engineering,” in proceedings ofthe International Congress of Combustion Engines(CIMAC), Zurich, Switzerland, 1957.

8. Patterson, D. J. and van Wylen, G., “A DigitalComputer Simulation for Spark-Ignited EngineCycles,” in SAE Progress in Technology, “DigitalCalculations of Engine Cycles,” vol. 7, 1964.

9. Clarke, J. M., “The Thermodynamic Cyclerequirements for Very High Rational Efficiencies,”proceedings of the Sixth Thermodynamics and FluidConvention, University of Durham, paper no. C53/76,Institute of Mechanical Engineers, London, England,6–8 April 1976.

10. Edo, T., and Foster, D., “A Computer Simulation of adissociated Methanol Engine,” proceedings of the IVInternational Symposium on Alcohol FuelTechnology, Ottawa, Canada, May 1984.

11. Primus, R. J., “A Second Law Approach to ExhaustSystem Optimization,” Society of AutomotiveEngineers, SAE Paper no. 840033, 1984.

12. Primus, R. J., Hoag, K. L., Flynn, P. F., and Brands,M. C., “An Appraisal of Advanced Engine ConceptsUsing Second Law Analysis Techniques,” Society ofAutomotive Engineers, SAE Paper no. 841287, also,International Conference on Fuel Efficient PowerTrains and Vehicles, the Institution of MechanicalEngineers, paper no. C440/84, pp. 73–87, 1984.

13. Primus, R. J., and Flynn, P. F., “Diagnosing the RealPerformance Impact of Diesel Engine DesignParameter Variation (a Primer in the Use of SecondLaw Analysis),” in International Symposium onDiagnostics and Modelling of Combustion inReciprocating Engines, pp. 529–538, 1985.

14. Primus, R. J., and Flynn, P. F., “The Assessment ofLosses in Diesel Engines Using Second LawAnalysis,” in Computer-Aided Engineering of Energy

1 2

EN

ER

GY

or

AV

AIL

AB

ILIT

Y (

%)

0

20

40

60

80

100

(30.6%)

(28.7%)

(40.0%)

Destructiondue to

Combustion(20.6%)

Energy Availabilit y

UnusedFuel

(0.7%)

(24.7%)

(23.0%)

(29.7%)

UnusedFuel

(0.7%)

Destructiondue to

Inlet Mixing(1.3%)

TotalIndicated

Work

HeatTransfer

Net TransferOut Dueto Flows

13

Systems, ed. by R. A. Gaggioli, the American Societyof Mechanical Engineers, Advanced Energy SystemsDivision, AES-Vol. 2–3, December 1986.

15. van Gerpen, J. H., and Shapiro, H. N., “Second-LawAnalysis of Diesel Engine Combustion,” Journal ofEngineering for Gas Turbines and Power, Vol. 112,pp. 129–137, 1990, also in Analysis and Design ofAdvanced Energy Systems: Computer-AidedAnalysis and Design, ed. by M. J. Moran, R. A.Bajura, and G. Tsatsaronis, the American Society ofMechanical Engineers, Advanced Energy SystemsDivision, AES-Vol. 3–3, December 1987.

16. Alkidas, A. C., “The Application of Availability andEnergy Balances to a Diesel Engine,” Transactions ofthe ASME, Journal of Engineering for Gas Turbinesand Power, vol. 110, pp. 462–469, July 1988.

17. Alkidas, A. C., “The Use of Availability and EnergyBalances in Diesel Engines,” Society of AutomotiveEngineers, SAE paper no. 890822, 1989.

18. McKinley, T. L., and Primus, R. J., “An Assessment ofTurbocharging Systems for Diesel Engines from Firstand Second Law Perspectives,” Society ofAutomotive Engineers, SAE Paper no. 880598, 1988.

19. Kumar, S. V., Minkowycz, W. J., and Patel, K. S.,“Thermodynamic Cycle Simulation of the DieselCycle: Exergy as a Second Law Analysis Parameter,”International Communications in Heat and MassTransfer, vol. 16, pp. 335–346, 1989.

20. Lipkea, W. H., and DeJoode, A. D., “A Comparison ofthe Performance of Two Direct Injection DieselEngines from a Second Law Perspective,” Society ofAutomotive Engineers, SAE paper no. 890824, 1989.

21. Whiting, T. M., Hewlitt, R. W., and Shea, M. H., “NewDeere 7.6L Engine,” Society of AutomotiveEngineers, SAE paper no. 881284, 1988.

22. Shapiro, H. N., and van Gerpen, J. H., “Two ZoneCombustion Models for Second Law Analysis ofInternal Combustion Engines,” Society of AutomotiveEngineers, SAE paper no. 890823, 1989.

23. Bozza, F., Nocera, R., Senatore, A., and Tuccillo, R.,“Second Law Analysis of Turbocharged EngineOperation,” Society of Automotive Engineers, SAEpaper no. 910418, 1991.

24. Gallo, W. L. R., and Milanez, L., F., “ExergeticAnalysis of Ethanol and Gasoline Fueled Engines,”Society of Automotive Engineers, SAE paper no.920809, 1992.

25. Al-Najem, N. M., and Diab, J. M., “Energy-ExergyAnalysis of a Diesel Engine,” Heat RecoverySystems & CHP, vol. 12, No. 6, pp. 525–529, 1992.

26. Rakopoulos, C. D., “Evaluation of a Spark IgnitionEngine Cycle Using First and Second Law AnalysisTechniques,” Energy Conversion and Management,vol. 34, no. 12, pp. 1299–1314, 1993.

27. Rakopoulos, C. D., and Andritsakis, E. C., “DI and IDICombustion Irreversibility Analysis,” inThermodynamics and the Design, Analysis andImprovement of Energy Systems, edited by H. J.Richter, Proceedings of ASME-WAM, AES-vol. 30,(also, HTD-vol. 266), pp. 17–32, New Orleans, LA,1993.

28. Rakopoulos, C. D., Andritsakis, E. C., and Kyritsis, D.K., “Availability Accumulation and Destruction in a DIDiesel Engine with Special Reference to the LimitedCooled Case,” Heat Recovery Systems & CHP, vol.13, pp. 261–276, 1993.

29. Rakopoulos, C. D., and Giakoumis, E. G., “Speedand Load Effects on the Availability Balance andIrreversibilities Production in a Multi-CylinderTurbocharged Diesel Engine,” Applied ThermalEngineering, vol. 17, no. 3, pp. 299–313, 1997.

30. Rakopoulos, C. D., and Giakoumis, E. G., “Simulationand Exergy Analysis of Transient Diesel-EngineOperation,” Energy, vol. 22, no. 9, pp. 875–885,1997.

31. Alasfour, F. N., “Butanol — A Single-Cylinder EngineStudy: Availability Analysis,” Applied ThermalEngineering, vol. 17, no. 6, pp. 537–549, 1997.

32. Rakopoulos, C. D., and Giakoumis, E. G.,“Development of Cumulative and Availability RateBalances in a Multi-Cylinder, Turbocharged, IndirectInjection Diesel Engine,” Energy Conversion andManagement, vol. 38, no. 4, pp. 347–369, 1997.

33. Anderson, M. K., Assanis, D. N., and Filipi, Z. S.,“First and Second Law Analyses of a Naturally-Aspirated, Miller Cycle, SI Engine with Late IntakeValve Closure,” Society of Automotive Engineers,SAE Paper No. 980889, 1998.

34. Caton, J. A., “Incorporation and Use of an AnalysisBased on the Second Law of Thermodynamics forSpark-Ignition Engines (Using a ComprehensiveCycle Simulation),” Report No. ERL–99–01, EngineResearch Laboratory, Texas A&M University,Department of Mechanical Engineering, Version 2.0,15 February 1999.

35. Caton, J. A., “Performance, Energy and AvailabilityCharacteristics as Functions of Speed and Load for aSpark-Ignition Engine Using a Thermodynamic CycleSimulation,” Report No. ERL–99–02, EngineResearch Laboratory, Texas A&M University,Department of Mechanical Engineering, Version 1.0,12 April 1999.

36. Caton, J. A., “Results From the Second-Law ofThermodynamics For a Spark-Ignition Engine Usinga Cycle Simulation,” proceedings of the 1999 FallTechnical Conference, the American Society ofMechanical Engineers, Internal Combustion EngineDivision, Ann Arbor, MI, October 1999.

37. Caton, J. A., “Operation Characteristics of a Spark-Ignition Engine Using the Second Law ofThermodynamics: Effects of Speed and Load,” theSociety of Automotive Engineers, 2000 SAEInternational Congress & Exposition, Cobo Center,Detroit, MI, 6–9 March 2000.

CONTACT INFORMATION

Dr. Jerald A. Caton is a professor in the Department ofMechanical Engineering at Texas A&M University,College Station, Texas, 77843–3123. He has beenworking on topics associated with internal combustion

14

engines since 1972. He also has worked in the areas ofgas turbines, selective noncatalytic removal (SNCR) ofnitric oxides, alternative fuels, cogeneration, fundamental

combustion topics, and boiler combustion. He may becontacted at: [email protected]

APPENDIX A – ENGINE CHARACTERISTICS

The following two tables are lists of the major enginecharacteristics for the reviewed investigations forcompression-ignition and spark-ignition engines,respectively. The brake power and speed listed are forthe stated design point or base operating condition of the

study. Where no information was available, dashes areentered.

ß NA: naturally aspirated; TC: turbo-charged; AC: aftercooled

Table 01—List of CI Engines Reviewed

First Author Ref. No.

Vd

(L)

Typeß No. of

Cyls

Brake Power

(kW)

Speed

(rpm)

Trauple 7 ---

---

NA

TC

---

---

---

---

---

---

Flynn 5 14 TC/AC 6 300 2100

Primus 11 14 TC/AC 6 268 1900

Primus 12 14 NA

TC/AC

6 185

220

2100

Primus 13 10 TC/AC 6 224 2100

Primus 14 10 TC/AC 6 224 2100

van Gerpen 15 1.17 NA 1 --- ---

Alkidas 16, 17 2.0 TC/AC 1 3–33 1200 & 1800

McKinley 18 10 NA 6 224 2100

Kumar 19 0.78 --- 1 --- 2000

Lipkea 20 7.6 TC/AC 6 ~170 ~2200

Shapiro 22 1.17 NA 1 --- ---

Bozza 23 1.37 TC 4 55.8 4500

Al-Najem 25 --- TC --- 243 ---

Rakopoulos 27 0.48

16.6

NA

TC/AC

1

6

4.0

235

2000

1500

Rakopoulos 28 0.48 NA 1 4.0 2000

Rakopoulos 29 16.6 TC/AC 6 235 1500

Rakopoulos 30 0.51 NA 1 4.0 2000

Rakopoulos 32 16.6 TC/AC 6 235 1500

15

ß NA: naturally aspirated; TC: turbo-charged; AC: aftercooled

Table 02—List of SI Engines Reviewed

First Author Ref.

No.

Vd

(L)

Typeß No. of

Cyls

Brake Power

(kW)

Speed

(rpm)

Patterson 8 --- NA 1 14.2 2800

Edo 10 --- --- --- --- ---

Shapiro 22 1.17 NA 1 --- ---

Gallo 24 0.4 NA 1 --- 5200

Rakopoulos 26 0.51 NA 1 --- 2500

Alsafour 31 0.45 NA 1 5.7 1700

Anderson 33 2.0 NA 4 6.67 2000

Caton 34–37 5.7 NA 8 21.9 1400

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