Review of II Law

8/10/2019 Review of II Law

1/17

400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-5760

SAE TECHNICALPAPER SERIES 2000011081

A Review of Investigations Using the Second Law

of Thermodynamics to Study Internal-Combustion Engines

Jerald A. Caton

Texas A&M University

Reprinted From: SI Combustion(SP1517)

SAE 2000 World CongressDetroit, MichiganMarch 69, 2000


2/17

The appearance of this ISSN code at the bottom of this page indicates SAEs consent that copies of thepaper may be made for personal or internal use of specific clients. This consent is given on the condition,however, that the copier pay a $7.00 per article copy fee through the Copyright Clearance Center, Inc.Operations Center, 222 Rosewood Drive, Danvers, MA 01923 for copying beyond that permitted by Sec-tions 107 or 108 of the U.S. Copyright Law. This consent does not extend to other kinds of copying such ascopying for general distribution, for advertising or promotional purposes, for creating new collective works,

or for resale.

SAE routinely stocks printed papers for a period of three years following date of publication. Direct yourorders to SAE Customer Sales and Satisfaction Department.

Quantity reprint rates can be obtained from the Customer Sales and Satisfaction Department.

To request permission to reprint a technical paper or permission to use copyrighted SAE publications inother works, contact the SAE Publications Group.

No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written

permission of the publisher.

ISSN 0148-7191Copyright 2000 Society of Automotive Engineers, Inc.

Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solely

responsible for the content of the paper. A process is available by which discussions will be printed with the paper if it is published inSAE Transactions. For permission to publish this paper in full or in par t, contact the SAE Publications Group.

Persons wishing to submit papers to be considered for presentation or publication through SAE should send the manuscript or a 300word abstract of a proposed manuscript to: Secretary, Engineering Meetings Board, SAE.

Printed in USA

All SAE papers, standards, and selectedbooks are abstracted and indexed in theGlobal Mobility Database


3/171

2000011081

A Review of Investigations Using the Second Law of

Thermodynamics 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 the

second 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 powerful

statement 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 analyticaresults. 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 o

availability which is also known as essergy (essence oenergy) and exergy [14]. 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 thaa 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 thermalmechanical and chemical processes. An example of the

thermal 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 istherefore, 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 ideaturbine), the energy of the system could be converted towork until the system pressure equaled theenvironmental pressure.

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

1. The chemical aspect of availability by convention refers to

the concentration differences between the species in the

system and in the environment [810]. 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.


4/17


5/173

(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 to

do 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 gastemperature for an environment temperatureof 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 combustionDuring 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 transfeand 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 a

greater portion of the energy is available to produce workOnce the energy is deposited at the wall at a lowertemperature, the energys 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 processfrom the gas temperature to the walltemperature for an environment temperatureof 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 heatransfer process is

=

gas

o

totalT

TQW 1

max

==

gas

o

total

Q

total T

T

Q

A

Q

W1

max

GAS TEMPERATURE (K)

500 1000 1500 2000 2500 3000 350

AVAILABLEENERGY(%)

0

10

20

30

40

50

60

70

80

90

100

AVAILABLE ENERGY

UNAVAILABLE ENERGY

To= 300 K

=

gas

o

totalgasT

TQA 1

=

wall

o

totalwallT

TQA 1

GAS TEMPERATURE (K)

1000 1500 2000 2500 3000

DESTROYE

DAVAILABILITY(%)

0

10

20

30

40

50

60

70

80

90

100

110

Tw= 300 K

To= 300 K

Tw= 450 K

Tw= 600 K


6/174

(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 thecombustion process for a constant volume,adiabatic system (adapted from Caton [6]).

Finally, this sub-section will end with comments onanother process which destroys available energycombustion. The chemical energy of the fuel representsthe potential to yield a maximum amount of work(available energy). As this energy is converted to thermaenergy 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, adiabatic

system. This system was selected to isolate thecombustion destruction of available energy from the otheprocesses. Results were obtained for a variety oconditions for octane and air mixtures. As an examplefigure 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 o500 kPa. This pressure, 500 kPa, is representative of thepressure at the start of combustion for a range of internacombustion engines [4]. This range of maximumtemperatures was obtained by varying the initiatemperature 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 otemperature [6].

In general, these results suggest that as the combustiontemperature increases, the destruction of availability

decreases. For the assumptions of this study, howeverthe destruction of availability does not attain zero even founrealistically high temperatures. In any case, these hightemperatures and pressures are beyond the practicalimits of todays 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 the

available energy. Also, if not utilized, the higheavailability will be expelled with the exhaust gasesAnother consideration would be the potential for highenitric oxide (NO) formation rates at these highetemperatures.

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 portionAlso, two modes of availability destruction, due to heatransfer, and combustion, were described.

=

=

gas

wall

gas

wallgas

gas

dest

A

A

A

AA

A

A1

=

gas

o

wall

o

gas

dest

TT

T

T

A

A

1

1

1

MAXIMUM TEMPERATURE (K)

2800 3000 3200 3400

D

ESTROYEDAVAILABILITY(%)

8

10

12

14

16

18

20Constant Volume,

Adiabatic CombustionpR= 500 kPa

= 1.0Octane-air


7/175

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 (19571989), and (2)

recent work (19902000).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 fuels 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 at

top 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 the

possibilities 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 ratioand showed the various transfers and destruction of thefuel availability.

Beginning in the mid1980s, a number of more detailedinvestigations were reported on the use of availabilityPerhaps 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-cylinderdiesel engine operating at 300 kW at 2100 rpm. Inparticular, they used the second law analysis to evaluatelow heat rejection (LHR) engine concepts and secondary

heat 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 cylinderthat of the original fuel availability about 46% wasdelivered as useful indicated work, 26% was destroyed10% 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 leanerAlso, as the equivalence ratio becomes leaner, the

destruction 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 decreasesThe 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]. Furthedetails from this study [5] are presented in a subsequentsection of this paper.

Primus [11] reported on a second law analysis of exhaussystems for a turbocharged, intercooled diesel engineThis was a companion study to the one reported by Flynn

et al. [5]. Primus reported on the influence of the exhaustmanifold cross-sectional area upon a number ocharacteristics such as frictional losses for a 14-litediesel 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 coolingturbocompounding, the implementation of a bottomingcycle, and the use of insulating techniques. The baseline


8/176

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 study

which 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, they

demonstrated 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 dieseengine. 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). This

study [15] was based on a diesel engine and used a deadstate based on standard saturated air (with trace CO2H2O, 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 abou15% 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 (fuelenergy. In other words, for the rich cases, the presence ofCO and H2 and other such species have unused fueenergy which means that the availability would bedominated by the chemical component. At least to someextent, the results for the rich cases are not unexpectedFrom 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, dieseengine 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 cylinderSecond, 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 was

responsible for the greatest availability transfer, and thatthe combustion destruction of availability was the nexmost important mechanism of availability removal. Fothe cases he studied, the combustion destruction was

1. The chemical component, as mentioned earlier, refers tothe 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 chemicalenergy of the fuel. [4].


9/177

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 fuelsavailability 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 the

second 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 the

performance 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 chemicaavailability 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 o0.56. 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 delayaspiration, turbocharger speed, and other parametersThey also examined transient operation with particular

emphasis 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 timingsThey examined the effects of ignition timing, duration ocombustion, 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 ethanothan for gasoline.

Al-Najem and Diab [25] presented a short technical notewhich described brief results for turbocharged dieseengine operated at 243 kW with an air-fuel ratio of 20They 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 engineThe major parameters studied were the compressionratio, fuel-air ratio, and ignition advance. The authorsmodel 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


10/178

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 fraction

for 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 law

quantities 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 othe 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 onmeasurements; few

details

1964 Pattersonand van

Wylen [8]

SI Compression andexpansion strokes;simple treatment ofintake and exhaust

1976 Clarke [9] SI/CI Otto, Joule and

Atkinson air-standardcycles

1984 Edo andFoster [10]

SI= Simple Otto air-standard cycle model

with equilibriumproducts (no flows)

1984 Flynn et al.[5]

CI Comprehensive modelof all processes

1984 Primus [11] CI Comprehensive modelof all processes;

focused on exhaustsystem optimization

1984 Primus et al.[12]


1985 Primus andFlynn [13]


1986 Primus andFlynn [14]


1987

(&1990)

van Gerpenand Shapiro

[15]

CI Compression andexpansion strokes; no

intake or exhauststrokes; included

chemical availability

1988

(&

1989)

Alkidas [16,17]

CI Experimentalmeasurements of

energy terms;calculated availability

1988 McKinleyand Primus

[18]

CI Comprehensive modelof all processes;

evaluation ofturbocharging systems

1989 Kumar et al.[19]


including manifold flowdynamics; included

chemical availability;only preliminary results

1989 Lipkea andDeJoode

[20]


included chemicalavailability; included

experimentalmeasurements

1989 Shapiro andvan Gerpen

[22]

SI & CI Compression andexpansion strokes; no


chemical availability

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


11/179

*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 Millecycle.

Rakopoulos and Giakoumis [29] in 1997 reported on theuse of a computer analysis to assess the performance ofa turbo-charged, aftercooled, indirect-injected, sixcylinder marine-duty, diesel engine operated over a rangeof engine speeds, loads and compression ratios. Anumber of the engine sub-assemblies were studiedThese 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, naturallyaspirated diesel engine operating under steady-state and

transient 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 a1500 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 fuelengine and load torques, and maximum cylindepressures 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 cylinderspark-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, heatransfer 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 experimentalmeasurements

1992 Gallo andMilanez [24]

SII Comprehensive modelof all processes

1992 Al-Najemand Diab

[25]

CI Brief results for aturbocharged diesel

engine

1993 Rakopoulos[26]

SI Compression andexpansion strokes; no


transient operation

1993 Rakopoulosand

Andritsakis[27]

CI Calculated availability;experimental

measurements ofenergy terms;

considered only valveclosed period; related

combustionirreversibility to fuel

reacted fraction

1993 Rakopouloset al.[28]

CI Experimentalmeasurements of

energy terms;calculated availability;considered only valve

closed period

1997 Rakopoulosand

Giakoumis[29]


included experimentalmeasurements

1997 Rakopoulosand

Giakoumis[30]


included experimentalmeasurements;

included transientoperation

1997 Alasfour [31] SI= Experimentalmeasurements of

energy terms;calculated availability

1997 Rakopoulosand

Giakoumis[32]


included experimentalmeasurements;

1998 Anderson etal.[33]

SI Comprehensive quasi-dimensional model of

all processes

1999,2000

Caton [3437]

SI Comprehensive modelof all processes

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


12/17


13/1711

the flows past the intake and exhaust valves accountedfor about 5.3% of the fuels availability.

Figure 4. Useful system availability and availabilitytransfers as a function of crank angle for thespark ignition engine [36].

Figure 5. Percentage of the fuels energy andavailability 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 entropyavailability, irreversibilities, and the related entropy andavailability balances. From the balances, destruction oavailability 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 V8 configuration with a compression ratio o8.1:1, 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 neresult of the transfer of availability through heat transferflows 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 usefuwork is shown as the top (dashed) curve. Duringcompression, availability is transferred into the systemdue to the compression work. After top dead cente

(0CA), 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 (at584aTDC). 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 continues

until 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, thereforeis 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 othe total fuel energy and total fuel availability that each othe major processes uses. The left-hand bar is for thefirst law (energy) analyses, and the right-hand bar is fothe 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

USEFULSYSTEMAVAILABILITY(kJ)

AVAILABILITYTRANSFERS

(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

ENERGYorAVAILABILITY(%)

0

20

40

60

80

100

(47.6%)*

(12.6%)*

(41.4%)*Destruction

due to

Combustion(21.0%)

Energy Availability

(9.7%)

(18.3%)

(45.8%)

ValveLosses(5.3%)

TotalIndicated

Work

HeatTransfer

Net TransferOut Dueto Flows


14/1712

Figure 6. Percentage of the fuels energy andavailability 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 is

available 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 quantitative

measure 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 oEngineering Thermodynamics, John Wiley & SonsInc., New York, New York, third edition, 1995.

3. Wark, K., Jr., and Richards, D. E., Thermodynamicssixth edition, McGraw-Hill Company, New York, NY1999.

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 PrimusR. J., A New Perspective on Diesel EngineEvaluation Based on Second Law Analysis, Societyof Automotive Engineers, SAE Paper no. 8400321984.

6. Caton, J. A., On the Destruction of Availability(Exergy) Due to Combustion Processes with

Specific Application to Internal-CombustionEngines, submitted to Energy, 04 August 1999.

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

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

9. Clarke, J. M., The Thermodynamic Cyclerequirements for Very High Rational Efficiencies,proceedings of the Sixth Thermodynamics and Fluid

Convention, University of Durham, paper no. C53/76Institute of Mechanical Engineers, London, England68 April 1976.

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

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

12. Primus, R. J., Hoag, K. L., Flynn, P. F., and BrandsM. C., An Appraisal of Advanced Engine ConceptsUsing Second Law Analysis Techniques, Society o

Automotive Engineers, SAE Paper no. 841287, alsoInternational Conference on Fuel Efficient PoweTrains and Vehicles, the Institution of MechanicaEngineers, paper no. C440/84, pp. 7387, 1984.

13. Primus, R. J., and Flynn, P. F., Diagnosing the ReaPerformance 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. 529538, 1985.

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

1 2

ENERGYorAVAILABILITY(%)

0

20

40

60

80

100

(30.6%)

(28.7%)

(40.0%)

Destructiondue to

Combustion(20.6%)

Energy Availability

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


15/1713

Systems, ed. by R. A. Gaggioli, the American Societyof Mechanical Engineers, Advanced Energy SystemsDivision, AES-Vol. 23, 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. 129137, 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 of

Mechanical Engineers, Advanced Energy SystemsDivision, AES-Vol. 33, 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. 462469, 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. 335346, 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-Exergy

Analysis of a Diesel Engine, Heat RecoverySystems & CHP, vol. 12, No. 6, pp. 525529, 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. 12991314, 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. 1732, New Orleans, LA,1993.

28. Rakopoulos, C. D., Andritsakis, E. C., and Kyritsis, DK., Availability Accumulation and Destruction in a DDiesel Engine with Special Reference to the LimitedCooled Case, Heat Recovery Systems & CHP, vol13, pp. 261276, 1993.

29. Rakopoulos, C. D., and Giakoumis, E. G., Speedand Load Effects on the Availability Balance andIrreversibilities Production in a Multi-CylindeTurbocharged Diesel Engine, Applied ThermaEngineering, vol. 17, no. 3, pp. 299313, 1997.

30. Rakopoulos, C. D., and Giakoumis, E. G., Simulationand Exergy Analysis of Transient Diesel-EngineOperation, Energy, vol. 22, no. 9, pp. 8758851997.

31. Alasfour, F. N., Butanol A Single-Cylinder EngineStudy: Availability Analysis, Applied ThermaEngineering, vol. 17, no. 6, pp. 537549, 1997.

32. Rakopoulos, C. D., and Giakoumis, E. G.Development of Cumulative and Availability RateBalances in a Multi-Cylinder, Turbocharged, IndirecInjection Diesel Engine, Energy Conversion andManagement, vol. 38, no. 4, pp. 347369, 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 EngineersSAE Paper No. 980889, 1998.

34. Caton, J. A., Incorporation and Use of an AnalysisBased on the Second Law of Thermodynamics foSpark-Ignition Engines (Using a ComprehensiveCycle Simulation), Report No. ERL9901, EngineResearch Laboratory, Texas A&M UniversityDepartment of Mechanical Engineering, Version 2.015 February 1999.

35. Caton, J. A., Performance, Energy and AvailabilityCharacteristics as Functions of Speed and Load for a

Spark-Ignition Engine Using a Thermodynamic CycleSimulation, Report No. ERL9902, EngineResearch Laboratory, Texas A&M UniversityDepartment of Mechanical Engineering, Version 1.012 April 1999.

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

37. Caton, J. A., Operation Characteristics of a SparkIgnition Engine Using the Second Law of

Thermodynamics: Effects of Speed and Load, theSociety of Automotive Engineers, 2000 SAEInternational Congress & Exposition, Cobo CenterDetroit, MI, 69 March 2000.

CONTACT INFORMATION

Dr. Jerald A. Caton is a professor in the Department ofMechanical Engineering at Texas A&M UniversityCollege Station, Texas, 778433123. He has beenworking on topics associated with internal combustion


16/1714

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 for

compression-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.

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

Table 01List of CI Engines Reviewed

First Author Ref.No.

Vd

(L)

Type No. of

Cyls

BrakePower

(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 1 333 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


17/17

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

Table 02List of SI Engines Reviewed

First Author Ref.

No.

Vd

(L)

Type No. of

Cyls

BrakePower

(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 3437 5.7 NA 8 21.9 1400

Review of II Law

Documents

Transcript of Review of II Law