Applied Energy 114 (2014) 155–163

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Applied Energy

journal homepage: www.elsevier .com/locate /apenergy

Understanding optimal engine operating strategies for gasoline-fueledHCCI engines using crank-angle resolved exergy analysis

0306-2619/$ - see front matter Published by Elsevier Ltd.http://dx.doi.org/10.1016/j.apenergy.2013.09.056

⇑ Corresponding author.E-mail address: samveg@berkeley.edu (S. Saxena).

Samveg Saxena a,⇑, Nihar Shah a, Ivan Bedoya b, Amol Phadke a

a Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory, United Statesb Grupo de Ciencia y Tecnología del Gas y Uso Racional de la Energía, Department of Mechanical Engineering, University of Antioquia, Colombia

h i g h l i g h t s

� A crank-angle resolved exergy analysis method is developed for HCCI engines.� In-cylinder loss mechanisms are quantified for a wide range of operating conditions.� Loss mechanisms include: combustion, heat loss, unburned species and exhaust.� Optimal combustion timing governed by balance of unburned species and heat losses.� With higher power output conditions, later combustion timing should be used.

a r t i c l e i n f o

Article history:Received 24 June 2013Received in revised form 23 September2013Accepted 25 September 2013Available online 17 October 2013

Keywords:ExergyHCCIGasolineSecond lawLoss mechanismsEngines

a b s t r a c t

This study couples a crank-angle resolved exergy analysis methodology with a multi-zone chemicalkinetic model of a gasoline-fueled HCCI engine to quantify exergy loss mechanisms and understandhow the losses change with different HCCI engine operating conditions. The in-cylinder exergy lossmechanisms are identified as losses to combustion, heat loss, unburned species, and physical exergy lostto exhaust gases. These loss mechanisms and their effect on overall operating efficiency are studied over arange of engine intake pressures, equivalence ratios, engine speeds and for different engine sizes.

Prior studies have demonstrated that optimal efficiency is achieved in HCCI engines at intermediatecombustion timings, with this optimal combustion timing being later for higher load conditions. Thisexergy analysis study provides a quantitative explanation for this experimental observation by demon-strating that exergy losses to heat loss decrease with delayed combustion timing, and exergy losses tounburned species increase sharply at later combustion timings. The optimal exergy efficiency combustiontiming typically occurs at the combustion timing when unburned species losses surpass heat losses, andwith higher load conditions these unburned species losses take effect at later combustion timings. Theinsights from this study also provide guidance towards an optimal efficiency operating strategy to controlload in an HCCI engine. From the perspective of in-cylinder exergy losses, the results suggest that equiv-alence ratio should be maintained at relatively high values across most operating conditions while intakepressure is used to vary engine load. Only at lower load conditions should equivalence ratio begin to bechanged for load control, and combustion timing should always be maintained at a value just earlier thanthe sharp increase of unburned species losses.

Published by Elsevier Ltd.

1. Introduction to achieve low emissions of NO and particulate matter while

The homogeneous charge compression ignition (HCCI) engine isan emerging engine technology that combines characteristics ofspark-ignited and diesel engines. Similar to spark-ignited enginesthe fuel–air charge is premixed in HCCI, and similar to diesel en-gines the mixture is ignited through compression ignition. Thesecharacteristics, combined with the use of lean mixtures allow HCCI

x

maintaining high operating efficiency.Although operating efficiencies in HCCI can offer significant

improvement over spark-ignited engines, further opportunitiesmay exist to improve HCCI operating efficiency. This study appliesa newly developed crank-angle resolved exergy analysis procedureto visualize and understand the exergy efficiency loss mechanismson a crank-angle resolved basis in a gasoline-fueled HCCI engine.The relative contribution of different exergy loss mechanisms isstudied over a wide range of engine operating conditions to guideengine design and the development of engine operating strategiesto achieve maximum exergy efficiency.

156 S. Saxena et al. / Applied Energy 114 (2014) 155–163

Exergy analysis has been applied to spark ignited and diesel en-gines in several prior studies [1–3] to explore the interaction of lossmechanisms with different engine design and operating parame-ters. In an HCCI context, exergy analysis has been applied in priorstudies [3–5] as well, however many of these prior studies signifi-cantly simplify the in-cylinder processes and approximate them asideal thermodynamic cycles. This simplification ignores the com-plex dynamics that govern combustion timing in HCCI engines,and thus the present study uses detailed chemical kinetics in HCCIengine simulations to provide a more accurate account of the lossmechanisms and how they are influenced by different engine oper-ating parameters. One study [6], used a more detailed single-zonemodel with detailed chemical kinetics to perform exergy analysisof a dual-fueled HCCI engine. Most recently, a study [7] by theauthors of the present study combined crank-angle resolved exer-gy analysis with a detailed chemical kinetic model for an ethanolfueled HCCI engine. The present study applies a similar crank-angleresolved exergy analysis methodology with a detailed chemical ki-netic model for a gasoline-fueled HCCI engine, and improves uponprior studies by modeling in-cylinder processes in much greaterdetail, and explores a much wider range of plausible gasoline-fueled engine operating conditions.

1 Misfire is defined in these simulations as the inability to achieve hot ignition,resulting in a pressure trace which resembles a motoring pressure trace.

2. Specific objectives

By combining a crank-angle resolved exergy analysis procedurewith a detailed chemical kinetic HCCI model for a gasoline-fueledengine, this study accomplishes the following objectives:

1. Quantifies exergy loss mechanisms in HCCI engines.2. Explores how the loss mechanisms change with different

engine operating conditions, particularly by changing oper-ating parameters that govern HCCI engine load.

3. Provides an explanation of the causes behind prior experi-mental observations [8,9] that show that optimal combus-tion timing for an HCCI engine occurs at intermediatecombustion timing (i.e. CA50 � 5-10 CAD ATDC), with theoptimal combustion timing being later for higher poweroutput conditions.

3. Simulation and exergy analysis methodology

3.1. HCCI engine simulation methodology and simulated operatingconditions

The HCCI simulations are run using a well-accepted and vali-dated multi-zone chemical kinetic HCCI modeling approach [13–16], where each zone is treated as a homogeneous reactor. Massinteractions between zones are not considered, while heat transferto the walls is modeled using the Woschni correlation [17,18]. Onlythe closed portion of the cycle is considered. A well validated re-duced chemical kinetic mechanism for gasoline is used [19,20].The model is used to simulate engine conditions representing theHCCI experimental setup used in previous studies by the authors[8,9,21–24]. A detailed validation of the HCCI engine simulationmethodology is given in prior publications [7,14].

The 10-zone chemical kinetic model is used to perform simula-tions spanning a wide range of engine operating conditions, includ-ing sweeps of intake pressure, equivalence ratio, engine speed andengine size. These parameter sweeps are chosen because they areparameters that can most directly influence power output in anHCCI engine. A list of parameter sweeps is shown in Table 1. Foreach engine operating condition (i.e. each intake pressure, equiva-lence ratio, engine speed and engine displacement condition) 12simulation points were recorded to capture data for combustion

timings sweeping from before TDC to near misfire conditions.1

Combustion timing is changed by varying the intake charge temper-ature, with hotter temperatures leading to earlier combustion tim-ing. As a result, a total of 300 engine simulations were run for thisstudy.

3.2. Exergy post-processing analysis methodology

3.2.1. Crank-angle resolved exergy analysisThe chemical kinetic HCCI engine model calculates values for

in-cylinder pressure, temperature, composition, and many otherparameters at each time step of engine operation. Results are out-put from the engine model in time steps of 0.25 crank-angle de-grees. These 10-zone averaged crank-angle resolved pressure,temperature and composition profiles are used as inputs for theexergy analysis post-processing step which is described in thissection.

The purpose of the exergy analysis step is to determine thesources of exergy loss from the in-cylinder gases. As a first step,the physical and chemical exergy are calculated using Eqs. (1 and2), respectively:

aphys ¼ ðu� u�Þ þ P0ðv � v�Þ � T0ðs� s�Þ ð1Þ

achem ¼ l� � l0 ð2Þ

In Eq. (1), u is specific internal energy, P is pressure, v is specific vol-ume, T is temperature (in Kelvin), and s is specific entropy for thein-cylinder gas mixture at a given time step. Terms that have nosubscript correspond to the properties of the in-cylinder mixtureat a given time step. Terms with a 0 subscript (i.e. P0) correspondto the properties of a mixture that is at dead state conditions, de-fined in Table 2.

In Eqs. (1) and (2), terms with an asterisk subscript (i.e. u⁄) cor-respond to the properties of a mixture that is at restricted deadstate conditions. The difference between restricted dead stateand actual dead state is that mixtures at restricted dead state con-ditions would simply be at a temperature of T0 and pressure of P0

but with a chemical composition of the in-cylinder gases at a giventime step, while a mixture at actual dead state will not only be at T0

and P0, but with a composition equal to air (defined in Table 2).In Eq. (2), l is the chemical potential which is calculated using

the definition in Eq. (3). The specific application of Eq. (3) to calcu-late the restricted dead state and actual dead state chemical poten-tials in Eq. (2) are shown in Eqs. (3a and 3b):

l ¼ h� T0s ð3Þ

l� ¼ h� � T0s� ð3aÞ

l0 ¼ h0 � T0s0 ð3bÞ

Each of the thermodynamic property terms in Eqs. (1)–(3) can becalculated for a single species using NASA polynomials as in Eqs.(4)–(6) by assuming that gases are thermally ‘‘perfect’’ (meaningthat standard-state thermodynamic properties of all species arefunctions of temperature only).

DH� ðTÞ

RT¼ a1 þ

a2

2T þ a3

3T2 þ a4

4T3 þ a5

5T4 þ a6

Tð4Þ

DS�ðTÞ

R¼ a1 lnðTÞ þ a2T þ a3

2T2 þ a4

3T3 þ a5

4T4 þ a7 ð5Þ

U� ¼ H

� � RT ð6Þ

Table 1List of engine parameter sweeps explored in this study.

Sweep name Intake pressure (bar) Equivalence ratio Combustion timing Engine speed (RPM) Engine displacement (cm3)

Intake pressure 1.0, 1.4, 1.8, 2.2, 2.6 0.40 Before TDC to misfire 1800 475Equivalence ratio 1.8 0.20, 0.30, 0.40, 0.50 Before TDC to misfire 1800 475Engine speed 1.8 0.40 Before TDC to misfire 1500, 1800, 2100, 2400, 2700, 3000 475Engine size 1.80 0.40 Before TDC to misfire 1800 475, 625, 750, 875, 1000

Table 2Properties of the dead state.

Temperature, T0 298.15 KPressure, P0 1.01325 barComposition (mole fractions) N2 0.7565

O2 0.2029H2O 0.0313Ar 0.0090CO2 0.0003

Fig. 1. Cumulative crank-angle resolved total, physical, and chemical exergy of thein-cylinder gas mixture for an operating condition with Pin = 1.8 bar, / = 0.40,engine speed = 1800 RPM, displacement = 475 cc.

S. Saxena et al. / Applied Energy 114 (2014) 155–163 157

The in-cylinder mixture at any given time step will include several(perhaps thousands) of individual species, and thus thermodynamicproperties of gas mixtures are calculated from individual speciesquantities using Eqs. (7)–(9), where k denotes individual speciesproperties and X is the mass fraction of each species:

H�¼XK

k¼1

HkXk ð7Þ

U�¼XK

k¼1

UkXk ð8Þ

S�¼XK

k¼1

S�

k � R ln Xk � R lnðP=PatmÞ� �

Xk ð9Þ

In addition to calculating the physical and chemical exergies of thein-cylinder mixture at every time step, exergy loss quantities arealso calculated. Combustion irreversibilities are calculated by con-sidering the state of the mixture in the control volume (i.e. theworking fluid) before and after combustion. Exergy destruction bythe combustion process is calculated by applying the Guoy-Stodalalaw [10] during the combustion process (between the timings of0.05% and 99.95% of heat release), as in Eq. (10):

xdest;combustion ¼ T0sgen ð10Þ

The entropy generation term, sgen, is taken as the difference in mix-ture entropy during each time step during the combustion process.

Exergy loss to heat transfer is calculated using Eq. (11)[10–12]:

Xloss;HL ¼ Q outT � Twalls

T � Twalls

� �T0 ð11Þ

The heat loss term, Qout, in Eq. (11) is determined from the enginemodel by applying the Woschni model for heat loss [13]. T is theaverage in-cylinder gas temperature at a given time step.

3.2.2. Additional exergy calculationsIn addition to the crank-angle resolved exergy analysis equa-

tions applied above (Eqs. (1)–(11)), a few additional exergy calcu-lations are performed for each simulation data point (i.e. once perengine cycle).

First, overall exergy efficiency of each engine operating point iscalculated using Eq. (12), where the numerator represents the totalindicated work against the surroundings, and the denominator isthe total exergy in the fuel.

gex ¼P540

�

h¼180� ðP � P0ÞdV

afuel �mfuelð12Þ

The fuel exergy is calculated using Gibb’s free energies using Eq.(13) by assuming complete combustion for gasoline fuel at thesimulated equivalence ratios (i.e. the only products are CO2, H2O,O2, and N2).

afuel ¼ �grxn;complete ¼ �ðgproducts � greactantsÞ ð13Þ

Finally, two additional exergy loss quantities are calculated for eachengine operating point. The first is the physical exergy lost to ex-haust gases which is calculated as the value of physical exergy atthe timing of exhaust valve open, as in Eq. (14). The second is theinaccessible chemical exergy that was not released as a result ofincomplete combustion (related to combustion inefficiencies), cal-culated as Eq. (15).

xloss;exhaust ¼ aphysðh ¼ EVOÞ ð14Þ

xloss;unburned ¼ �ðgrxn;actual � grxn;completeÞ ð15Þ

In Eq. (15), grxn,actual, is the difference between Gibb’s free energy ofthe products and reactants of the actual reaction that occurred (i.e.calculated in the chemical kinetic HCCI engine model) and will in-clude contributions from unburned species (like unburned hydro-carbons and CO). grxn,complete is the difference between Gibb’s freeenergy of the products and reactants of a hypothetical completereaction that would occur at the same operating conditions suchthat only CO2, H2O, O2, and N2 will remain in the products.

4. Results

4.1. Crank-angle resolved exergy analysis results

Using the exergy analysis methodology described in Section 3.2,the physical, chemical and total exergy of the in-cylinder gases arecalculated on a crank angle resolved basis. Fig. 1 shows a sample ofthis crank-angle resolved exergy result for a single engine operat-ing condition (results are displayed on a cumulative basis).

Fig. 2. Cumulative crank-angle resolved exergy loss and useful PdV work outputfrom in-cylinder gas mixture for an operating condition with Pin = 1.8 bar, / = 0.40,engine speed = 1800 RPM, displacement = 475 cc.

158 S. Saxena et al. / Applied Energy 114 (2014) 155–163

Additionally, the exergy losses to combustion and heat loss arecalculated on a crank-angle resolved basis using equations pre-sented in Section 3.2. Sample results of these exergy loss mecha-nisms and the useful PdV work output from the engine at asingle operating point are shown on a cumulative basis in Fig. 2on a crank-angle resolved basis.

The plot for exergy destruction by combustion (blue2 line inFig. 2) shows that losses caused by this mechanism decrease beforecombustion has begun and after combustion has completed. This istechnically not possible, however the reader is reminded that weare only utilizing the results between the crank angle timing of0.05% and 99.95% heat release.

The results in Figs. 1 and 2 correspond to a single engine oper-ating point; however the main purpose of this study is to explorehow exergy loss mechanisms change over a wide range of engineoperating points (300 operating points for this study). Summaryinformation about the cumulative useful work output and totalexergy loss to the four loss mechanisms (combustion, exhaust, un-burned species, and heat loss) are extracted from the crank-angleresolved exergy analysis to allow comparisons across a wide rangeof engine operating conditions. In the following four sub-sections,trends in the exergy loss mechanisms are explored while engineoperating parameters are varied.

4.2. Sensitivity of exergy loss mechanisms to intake pressure

The impact of changes in intake pressure and combustion tim-ing are presented in Fig. 3.3 Perhaps the most important result thatis apparent from Fig. 3 (by focusing on the black data points) is thathigher exergy efficiency operation is achieved with increasing intakepressure.

The values plotted in Fig. 3 are in terms of exergy efficiency,meaning that the absolute value of each exergy quantity (i.e.indicated work, combustion, heat loss, exhaust and unburnedspecies) is divided by the total fuel availability. From Fig. 4 it isapparent that the absolute fuel availability increases with higherintake pressures and with delayed combustion timing.4 The abso-lute quantity of most exergy loss mechanisms also increase withhigher intake pressures, and so the results must be analyzed on anexergy efficiency basis (as in Fig. 3) to determine the relative impactof each of these loss mechanisms as operating conditions arechanged.

One key objective of this paper is to explain why efficiencyshows a parabolic trend with combustion timing (as shown inthe black data points in Fig. 3), with the highest exergy efficiencyobserved at intermediate combustion timings, and more delayedcombustion being advantageous for higher power operating condi-tions. By inspecting the exergy loss mechanisms in Fig. 3, it is clear

2 For interpretation of color in Fig. 2, the reader is referred to the web version ofthis article.

3 Given that the plot style of Fig. 3 is used extensively throughout this paper, a briefexplanation is given of how to interpret these plots: The indicated exergy efficiency ofeach simulated engine operating point is shown as black data points on the top of thegraph. Each black data point will have four corresponding data points, (1) red forlosses to the combustion process, (2) blue for physical exergy lost to exhaust gases,(3) green for exergy lost to heat loss, and 4) purple for exergy lost to unburnedspecies. The sum of values from useful indicated work, combustion, exhaust, heat lossand unburned species is 100%, within ±1.01%. Changes in exergy losses withcombustion timing can be observed by moving left- or right-wards on the graphs,while changes in the parameter of interest (i.e. intake pressure) can be observed bymoving upwards or downwards on the graph with the changing symbols.

4 As a reminder, the reader should note that the results in this study are for anengine with port fuel injection. It is assumed that the fuel has fully vaporized andmixed with air before the crank-angle timing window over which we perform theanalysis in this paper. For an engine with direct injection, the results would be slightlydifferent as there would be some exergy loss associated with vaporization andmixing.

that this parabolic shape is caused by a tradeoff between exergylosses to heat loss and exergy losses to unburned species.

Exery losses to heat loss are relatively insensitive to changes inintake pressure; only at early combustion timings is it observedthat exergy efficiency losses to heat loss decrease slightly withhigher intake pressures.5 More importantly, exergy losses to heatloss decrease almost linearly with delayed combustion timing. As aresult, for early combustion timings (CA50 < 365 CAD) the overallexergy efficiency increases with delayed combustion timings be-cause exergy losses to heat loss are decreasing. However, beyond acertain level of combustion timing delay it can be seen that lossesto unburned species begin to rise rapidly with further delayed com-bustion timing – the CA50 timing where the unburned species exer-gy losses exceed exergy loss to heat loss corresponds with thecombustion timing where maximum overall operating efficiency isachieved.

At early combustion timings, exergy losses to unburned speciesremain relatively flat. For lower intake pressures (1.0 and 1.4 bar)at early combustion timings unburned species exergy losses are5%, however the value is lower for the higher intake pres-sures (P1.8 bar). As combustion timing is delayed the unburnedspecies losses rapidly rise. With higher intake pressures the rapidrise in losses to unburned species take effect at later combustiontimings.

Exergy efficiency losses to combustion are relatively insensitiveto changes in combustion timing, they only increase slightly withdelayed combustion timing. On an absolute value basis (Fig. 4) itcan be seen that these losses increase with delayed combustiontiming, but these increases are of a similar magnitude as the in-creases in fuel availability with delayed combustion timing. FromFig. 3 it can be seen that exergy efficiency losses to combustion in-crease with higher intake pressures.

Exergy efficiency losses to the exhaust are fairly insensitive toboth combustion timing and intake pressure. These losses increaseslightly with delayed combustion timing, but no clear trend isobservable with varying intake pressure.

5 As can be seen in Fig. 4, the absolute magnitude of exergy loss to heat lossincreases with increasing intake pressure (this is no surprise as in-cylindertemperatures are higher because there is more fuel for the higher intake pressureconditions). However, Fig. 4 shows that the magnitude of fuel availability increasesmuch more than the magnitude of exergy loss to heat loss, thereby causing the lowerexergy efficiency losses to heat loss at increasing intake pressure conditions. Theweak intake pressure dependence of exergy losses to heat loss shown in Fig. 3 isvisible only at early combustion timings, likely because heat loss plays a larger role atearly combustion timings.

Fig. 3. Impact of intake pressure variations on exergy efficiency loss mechanisms for Pin = 1.0–2.6 bar, / = 0.40, engine speed = 1800 RPM, displacement = 475 cc, and for thefull range of CA50.

Fig. 4. Impact of intake pressure variations on absolute value of exergy loss mechanisms for Pin = 1.0–2.6 bar, / = 0.40, engine speed = 1800 RPM, displacement = 475 cc, andfor the full range of CA50.

Fig. 5. Impact of equivalence ratio variations on exergy efficiency loss mechanisms for Pin = 1.8 bar, / = 0.20–0.50, engine speed = 1800 RPM, displacement = 475 cc, and forthe full range of CA50.

S. Saxena et al. / Applied Energy 114 (2014) 155–163 159

Summarizing the results in this section, Figs. 3 and 4 show thathigher intake pressures enable higher exergy efficiency operation.With higher intake pressures, exergy efficiency losses to unburnedspecies decrease significantly and to heat loss decrease slightly.These decreases outweigh the increase in exergy efficiency lossesto combustion with increasing intake pressure. Later combustiontiming allows higher efficiency operation up to the point wherelosses to unburned species begin rapidly rising. With higher intake

pressures, the combustion timing delay threshold where unburnedspecies losses begin rising rapidly occurs later.

4.3. Sensitivity of exergy loss mechanisms to equivalence ratio

The impact of varying equivalence ratio and combustion timingis shown in Fig. 5 in terms of exergy efficiency (which is normal-ized by total fuel availability) and in terms of absolute values of

Fig. 6. Impact of equivalence ratio variations on absolute value of exergy loss mechanisms for Pin = 1.8 bar, / = 0.20–0.50, engine speed = 1800 RPM, displacement = 475 cc,and for the full range of CA50.

Fig. 7. Impact of engine speed variations on exergy efficiency loss mechanisms for Pin = 1.8 bar, / = 0.40, engine speed = 1800–3000 RPM, displacement = 475 cc, and for thefull range of CA50.

Fig. 8. Impact of energy speed variations on absolute value of exergy loss mechanisms for Pin = 1.8 bar, / = 0.40, engine speed = 1800–3000 RPM, displacement = 475 cc, andfor the full range of CA50.

160 S. Saxena et al. / Applied Energy 114 (2014) 155–163

exergy in Fig. 6. The results in Fig. 5 show that HCCI engine exergyefficiency generally improves with higher equivalence ratios, withthe optimal combustion timing occurring later for higher equiva-lence ratios.

From Fig. 5 it is clear that exergy losses to combustion decreasewith higher equivalence ratios in terms of exergy efficiency(however from Fig. 6, the combustion losses increase in terms of

absolute values of exergy loss). In general, exergy losses tocombustion increase with delayed combustion timing, particularlyat higher equivalence ratios. However, a decrease in exergy lossesto combustion is observed at the latest combustion timingsbecause exergy losses to unburned species dominate causinglosses to combustion to decrease because there is less fuelcombusting.

Fig. 9. Impact of engine size variations on exergy efficiency loss mechanisms for Pin = 1.8 bar, / = 0.40, engine speed = 1800 RPM, displacement = 475–1000 cc, and for the fullrange of CA50.

S. Saxena et al. / Applied Energy 114 (2014) 155–163 161

Physical exergy losses to the exhaust increase with higherequivalence ratios, both in terms of exergy efficiency and absolutevalues of exergy loss. The impact of combustion timing delay onexhaust losses changes depending on equivalence ratio; at higherequivalence ratios exergy losses to the exhaust increase at latercombustion timings, while at lower equivalence ratios exergylosses to the exhaust decrease at later combustion timings.

Exergy losses to heat loss decrease almost linearly with delayedcombustion timing, and increase with higher equivalence ratio.

Exergy losses to unburned species play the most important rolein determining the overall operating efficiency as there is a signif-icant sensitivity to both combustion timing and equivalence ratio.Exergy losses to unburned species increase significantly at lowerequivalence ratios. At these lower equivalence ratios the losses tounburned species increase rapidly with delayed combustion tim-ing. At higher equivalence ratios, greater levels of combustion tim-ing delay can be tolerated before the losses to unburned speciesplay a significant role.

Summarizing the results in this section, it is clear that overallexergy efficiency is highly sensitive to equivalence ratio – lowequivalence ratios should be avoided in order to maintain anacceptable operating efficiency. Exergy efficiency losses to combus-tion and unburned species decrease with higher equivalence ratio.Exergy efficiency losses to exhaust and heat loss increase with high-er equivalence ratio. Given that losses to unburned species are sosensitive to combustion timing, the optimal exergy efficiencycombustion timing is largely determined by the combustion timing

Fig. 10. Impact of engine size variations on absolute value of exergy loss mechanisms fofor the full range of CA50.

delay when losses to unburned species take effect. These losses takeeffect at later combustion timing for higher equivalence ratio.

4.4. Sensitivity of exergy loss mechanisms to engine speed

The impact of varying engine speed and combustion timing isshown in Fig. 7 in terms of exergy efficiency and in terms of abso-lute values of exergy in Fig. 8. The results in Fig. 7 show that higherexergy efficiency is achieved at higher engine speeds, though this isonly a subtle trend. Fig. 8 shows that fuel availability increaseswith lower engine speeds and delayed combustion timings, pri-marily because of decreasing intake temperatures causing greatercharge density and thus more fueling at these conditions.

Fig. 7 shows that exergy efficiency losses to combustion arefairly insensitive to changes in engine speed and combustion tim-ing – these losses only increase slightly with lower engine speeds.On an absolute value basis, in Fig. 8, it can be seen that the exergylosses to combustion increase with lower engine speeds and de-layed combustion timings, however these increases are generallycanceled by increases in fuel availability so that their impact isnot seen in the exergy efficiency plot of Fig. 7.

Exergy losses to heat loss are very sensitive to both enginespeed and combustion timing. Both on an efficiency basis (Fig. 7)and absolute value basis (Fig. 8), exergy losses to heat loss decreasealmost linearly with delayed combustion timing, and decreasewith higher engine speeds. The increase with lower engine speedscan be explained by there being more time for heat loss to occur.

r Pin = 1.8 bar, / = 0.40, engine speed = 1800 RPM, displacement = 475–1000 cc, and

162 S. Saxena et al. / Applied Energy 114 (2014) 155–163

Exergy efficiency losses to the exhaust increase with higher en-gine speeds as shown in Fig. 7. On an absolute value basis, in Fig. 8,the exergy losses to exhaust only increase slightly with higher en-gine speed. Exergy losses to the exhaust are fairly insensitive tocombustion timing. The increase in losses to the exhaust is largelydue to the decrease in heat transfer losses at higher engine speeds,causing more unutilized exergy in the cylinder gases at EVOtiming.

Exergy losses to unburned species are also fairly sensitive to en-gine speed and combustion timing. Exergy losses to unburned spe-cies increase with delayed combustion timing. At lower enginespeeds, greater levels of combustion timing delay can be sustainedbefore exergy losses to unburned species begin rising.

Summarizing the results from this section, it was observed thatoverall exergy efficiency increases slightly at higher engine speeds.Exergy efficiency losses to combustion decreases with higher en-gine speeds, to the exhaust increase with higher engine speeds,and to heat loss decrease with higher engine speeds. Exergy lossesto unburned species increase with later combustion timings, andthe threshold of combustion timing delay before these losses in-crease is later with lower engine speeds.

4.5. Sensitivity of exergy loss mechanisms to engine size

The impact of engine displacement (engine size) and combus-tion timing is shown in Fig. 9 in terms of exergy efficiency and inFig. 10 in absolute value terms. The most distinguishing featureof Fig. 9 compared to earlier plots is that the overall exergy effi-ciency and the exergy loss mechanisms are very tightly bounded,indicating that the loss mechanisms are almost completely insen-sitive to changes in engine size. Exergy losses to heat loss are theonly exception, with increased exergy efficiency loss to heat lossoccurring for the smaller engine sizes. The increase in exergy lossesto heat loss is caused by the larger surface-to-volume ratio whichincreases wall heat transfer in smaller engines.

Exergy efficiency losses to combustion and exhaust are fairlyinsensitive to combustion timing. Exergy losses to heat loss de-crease with delayed combustion timing. Exergy losses to unburnedspecies remain fairly flat at early combustion timings, then rapidlyincrease at later combustion timings. Earlier parameter sweepshave shown that greater levels of combustion timing delay canbe sustained with changes in intake pressure or equivalence ratiobefore losses to unburned species begin rising – however this trendis not apparent with changes in engine size.

5. Conclusions

This study developed and applied a detailed crank-angle re-solved exergy analysis methodology to understand exergy lossmechanisms in a gasoline-fueled HCCI engine. The crank-angleresolved analysis methodology was applied across 300 differentengine operating conditions to explore the impact upon exergy lossmechanisms from varying intake pressure, equivalence ratio,engine speed and engine size, several parameters that might bevaried in practical engines to achieve different levels of enginepower output. The main results from this study are:

5.1. Changes in exergy loss mechanisms

1. Combustion – Exergy losses to combustion are generallybounded between 19% and 23%. The efficiency losses tocombustion rise with higher intake pressures, with lowerequivalence ratio, and with higher engine speeds. Exergyefficiency losses to combustion are insensitive to enginesize and do not show a significant sensitivity to combustiontiming.

2. Exhaust – Exergy losses to the exhaust are generallybounded between 12% and 20%. Efficiency losses to theexhaust increase with higher intake pressure, higher equiv-alence ratio, higher engine speed, and can slightly increasewith delayed combustion timing. Exergy efficiency lossesto the exhaust are fairly insensitive to changes in enginesize.

3. Heat loss – Exergy losses to heat loss are generally boundedbetween 5% and 15%. Exergy efficiency losses to heat lossincrease with higher intake pressure, lower equivalenceratio, and lower engine speed, and can increase slightly atsmaller engine sizes. In all cases, exergy efficiency lossesto heat loss are very sensitive to combustion timing, show-ing a roughly linear decrease in losses with delayed com-bustion timings.

4. Unburned species – Exergy losses to unburned species canbe as low as 1%, but can rise to levels where they dominateover all other losses in worst-case operating conditions.These losses are very sensitive to combustion timing: atearly combustion timings unburned species losses are verylow (as low as 1%), but with delayed combustion timingsthe unburned species losses can rise rapidly. The combus-tion timing delay threshold where unburned species lossesbegin rising is later with higher intake pressures, higherequivalence ratios and lower engine speeds.

5.2. Applying these results to develop optimal engine operatingstrategies

1. Optimal combustion timing – The results in this study andprior experimental studies [8,9] generally show that overallexergy efficiency follows a ‘‘parabolic’’ trend with combus-tion timing, and exergy efficiency is generally highest atintermediate combustion timings. The optimal combustiontiming (i.e. the maximum of the ‘‘parabola’’) is later forhigher power output conditions. This ‘‘parabolic’’ shape iscaused by a balance between exergy losses to heat lossand unburned species. Exergy losses to heat loss decreasewith delayed combustion timing, causing the increase inoverall exergy efficiency with combustion timing delay atearly combustion timings. Exergy losses to unburned spe-cies rise sharply at late combustion timings, causing thedecrease in overall exergy efficiency at late combustiontimings. The optimal combustion timing is therefore oftendetermined by the combustion timing when exergy lossesto unburned species begin rising and surpass losses to heatloss. At higher power output conditions (i.e. with higherintake pressure or higher equivalence ratio) the losses tounburned species take effect at later combustion timingscausing the optimal efficiency operating point to occur atlater combustion timings at higher power conditions.

2. Optimal operating strategies for different levels of engine load– The understanding of exergy loss mechanisms and theirsensitivity to different engine operating conditions pro-vided in this study can be used to guide the creation ofan optimal engine operating map to achieve different levelsof load in an HCCI engine, while achieving the highest pos-sible operating efficiency. An important result of this studyis the sensitivity of exergy efficiency and losses to intakepressure and equivalence ratio. At the highest load of anHCCI engine, high intake pressures and high equivalenceratios should be used, with combustion timing set as lateas possible before unburned species losses begin rising.Given that efficiency levels rapidly decrease at lower equiv-alence ratios, for lower required loads, equivalence ratioshould be maintained at high levels, while intake pressure

S. Saxena et al. / Applied Energy 114 (2014) 155–163 163

is gradually decreased. Only near ambient intake pressuresshould equivalence ratio begin to be changed as a mecha-nism for controlling engine load.

The use of exergy analysis to guide the creation of engineoperating strategies shows promise, but requires further investiga-tion. The authors intend follow-up studies to explore the use ofexergy analysis for guiding engine design and the creation ofengine operating maps. An important planned improvement forfuture studies is to expand the engine simulations beyond simplycapturing in-cylinder phenomena. Gas exchange processes and aturbocharger model will be included for future studies.

Acknowledgements

This study is part of a research effort at Lawrence Berkeley Na-tional Laboratory that is using exergy analysis as a research portfo-lio analysis tool to quantify and compare the efficiency gains thatcan be achieved by guiding the strategic direction of researchand development funding in various technology areas. This workwas supported by the Director, Office of Science, of the US Depart-ment of Energy under Contract No. DE-AC02-05CH11231.

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