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Energy Conversion and Management 48 (2007) 1683–1690

Comparison of performances of air standard Atkinson and Ottocycles with heat transfer considerations

Shuhn-Shyurng Hou *

Department of Mechanical Engineering, Clean Energy Center, Kun Shan University, Tainan 71003, Taiwan, ROC

Received 21 October 2005; received in revised form 3 May 2006; accepted 12 November 2006Available online 22 December 2006

Abstract

In this paper, the effects of heat transfer on the net output work and the indicated thermal efficiency of an air standard Atkinson cycleare analyzed. Comparisons of the performances of air standard Atkinson and Otto cycles with heat transfer considerations are also dis-cussed. We assume that the compression and power processes are adiabatic and reversible and that any convective, conductive or radi-ative heat transfer to the cylinder wall during the heat rejection process may be ignored. The heat loss through the cylinder wall isassumed to occur only during combustion and is further assumed to be proportional to the average temperature of both the workingfluid and cylinder wall. It is found that the net output work versus efficiency characteristics, the maximum net work output and the cor-responding efficiency bound are significantly influenced by the magnitude of the heat transfer. An increase in heat transfer to the com-bustion chamber walls decreases the peak temperature and pressure and, consequently, reduces the work per cycle and efficiency. Theeffects of other parameters, in conjunction with heat transfer, including combustion constants, compression ratio and intake air temper-ature are also reported. An Atkinson cycle has a greater work output and a higher thermal efficiency than the Otto cycle at the sameoperating condition. The compression ratios that maximize the work of the Otto cycle are always found to be higher than those forthe Atkinson cycle at the same operating conditions. The results are of importance to provide good guidance for performance evaluationand improvement of practical Atkinson engines.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Thermodynamics; Atkinson cycle; Otto cycle; Heat transfer

1. Introduction

The Atkinson cycle engine is a type of internal combus-tion engine, which was designed and built by James Atkin-son in 1882 [1]. The four stroke Atkinson cycle allows theintake, compression, power and exhaust strokes to occurin a single turn of the crankshaft. By the use of clevermechanical linkages, the expansion ratio is greater thanthe compression ratio, resulting in greater efficiency thanwith engines using the alternative Otto cycle [2–4].

For a conventional four stroke Otto cycle engine, inthe expansion stroke, the gas pressure within the cylinderat exhaust valve opening is still on the order of three to

0196-8904/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.enconman.2006.11.001

* Tel.: +886 6 2050496; fax: +886 6 2050509.E-mail address: sshou@mail.ksu.edu.tw.

five atmospheres and is greater than the exhaust pressure.Therefore, a potential for doing additional work duringthe power stroke is lost when the exhaust valve is openedand the pressure is reduced to atmospheric. However, ifthe exhaust valve is not opened until the gas in thecylinder is allowed to expand down to atmosphericpressure, the additional expansion would increase theamount of power in the expansion stroke, leading toan increase of engine thermal efficiency [3,4]. The idealcycle representing the operation of this engine is calledan Atkinson cycle or complete expansion cycle that con-sists of an isentropic compression, an isochoric (constantvolume) heat addition with internal combustion, an isen-tropic expansion all the way to the lowest cycle pressureand an isobaric heat rejection processes (as shown inFig. 1).

Nomenclature

a1 constant defined in Eq. (17)a2 constant defined in Eq. (18)a3 constant defined in Eq. (19)CP constant pressure specific heatCV constant volume specific heatk k = CP/CV

P pressure

2Q3 heat added to gas during process 2–3 as result ofcombustion per cycle

Qin heat added to working fluid during constantvolume combustion process per cycle

rc compression ratiorcm compression ratio at maximum workS entropyTi temperature at state i

V volume

W net work output per unit mass of working fluidper cycle

Wmax maximum work output per unit mass of work-ing fluid per cycle

Greek

a constant related to combustionb constant related to heat transferg efficiency of cyclegm corresponding thermal efficiency at maximum

work output

Subscripts

max maximum1, 2, 3, 4 state points

1684 S.-S. Hou / Energy Conversion and Management 48 (2007) 1683–1690

It is noteworthy that an Atkinson cycle engine is moreefficient than a conventional four stroke Otto cycle engine.An increase in thermal efficiency is achieved by controllingthe pumping losses and optimizing the expansion ratiowhile maintaining a fixed compression ratio. Starting since1885, a number of crank and valve mechanisms were triedto achieve this cycle in which the combustion chamber vol-ume is adapted to keep a constant compression ratio foreach load level while varying the expansion ratio to opti-mize efficiency. At the start of the 20th century, engineerstried to achieve strokes of different lengths with complexlinkages that were hopelessly impractical, but as variablevalve timing emerged, it can all be accomplished by com-puter control. Therefore, some modern engines (e.g. Fordand Toyota) have been built and marketed [2].

To make the analysis of an engine cycle much moremanageable, the air standard cycles are used to describethe major processes occurring in internal combustionengines. In ideal air standard cycles, air is assumed tobehave as an ideal gas, and all processes are consideredtotally reversible [3,4]. In practice, air standard analysis isquite useful for illustrating the thermodynamic aspects ofan engine operation cycle. Additionally, it can provideapproximate estimates of trends as major engine operatingvariables change. For an ideal Atkinson cycle, all processesare considered reversible. However, it is recognized thatthere are heat losses during the cycle of a real engine, butthey are neglected in an ideal air standard analysis. Inour recent paper [5], we have studied the effect of heattransfer through a cylinder wall on the work output of adual cycle assuming the heat transfer to the cylinder wallsto be a linear function of the difference between the averagegas and cylinder wall temperatures [6–9].

Although much attention has been paid to analyzing theperformances of internal combustion engines for Otto, Die-

sel and dual cycles [1,2,5–17], however, no performanceanalysis with emphasis on the internally reversible Atkin-son cycle driven by external irreversibility of heat transferis available in the literature. Therefore, the objective of thispaper is to study the effect of heat transfer on the net out-put work and the indicated thermal efficiency of an airstandard Atkinson cycle. In the present study, we relaxthe assumption that there are no heat losses during com-bustion. In other words, heat transfer between the workingfluid and the environment through the cylinder wall is con-sidered. The results obtained in this work will help us tounderstand how the net work output and efficiency areinfluenced by heat transfer during combustion, or the con-stant volume heat addition process.

2. Thermodynamic analysis of the air standard Atkinson

cycle

Internal combustion engines combust fuel with air innearly stoichiometric proportions. The maximum tempera-ture in the cycle is far below the adiabatic combustion tem-perature due to a number of factors such as heat loss,friction and so on. Particular concern for this study isplaced on heat loss. Heat transfer from the unburned mix-ture to the cylinder walls has a negligible effect on the per-formance for the compression process. However, heattransfer from the burned gases is much more important.In particular, the heat transfer rates to the cylinder wallsduring combustion are highest and extremely important[4]. Therefore, we assume that the compression and power(or expansion) processes are adiabatic and reversible, andthat any convective, conductive or radiative heat transferto the cylinder wall during the exhaust process (heat rejec-tion process) is ignored. In other words, compressionstrokes and expansion strokes are approximated by isen-

Fig. 1. (a) P–V diagram (b) T–S diagram for air standard Atkinson (1–2–3–4A) and Otto (1–2–3–4O) cycles.

S.-S. Hou / Energy Conversion and Management 48 (2007) 1683–1690 1685

tropic processes. To be truly isentropic, these strokes haveto be reversible and adiabatic. There is some frictionbetween the piston and cylinder walls, but because the sur-faces are highly polished and lubricated, this friction ismaintained at a minimum, and the processes are close tofrictionless and reversible. Therefore, heat transfer forany one of these two strokes will not be considered herein[3].

The peak burned gas temperature in the cylinder of aninternal combustion engine is of order 2500 K and up.Because of the material safety point of view, maximummetal temperatures for the inside of the combustion cham-ber space are limited to much lower values by a number ofconsiderations, and cooling for the cylinder head, cylinderand piston must be, therefore, provided. These consider-ations lead to heat fluxes to the chamber walls that canreach as high as 10 MW/m2 during the combustion period[4]. However, during other processes of the operating cycle,

the heat flux is essentially quite small. In the present study,we, therefore, assume that the heat loss through the cylin-der wall only occurs during combustion. The heat loss isfurther assumed to be proportional to the average temper-ature of both the working fluid and cylinder wall [6].

The pressure–volume (P–V) and temperature–entropy(T–S) diagrams for the thermodynamic processes of anair standard Atkinson cycle are shown by the cycle of 1–2–3–4A in Fig. 1(a) and (b), respectively. Following theassumptions described above, process 1–2 is an isentropiccompression from bottom dead center (BDC) to top deadcenter (TDC). The heat addition takes place in process 2–3, which is isochoric. The isentropic expansion process,3–4A, is the power or expansion stroke. The cycle is com-pleted by an isobaric heat rejection process, 4A-1. The heatadded to the working fluid per unit mass is due to combus-tion. The temperature at the completion of constant vol-ume combustion (T3) depends on the heat input due tocombustion and heat transfer through the cylinder wall.

Assuming constant specific heats, the net work outputper unit mass of the working fluid is given by the followingequation:

W ¼ CVðT 3 � T 2Þ � CPðT 4A � T 1Þ ð1Þwhere CP and CV are the constant pressure and constantvolume specific heats, respectively; and T1, T2, T3 andT4A are the absolute temperatures at states 1, 2, 3 and4A, respectively. For the isentropic processes 1–2 and 3–4A, we have

T 2 ¼ T 1rk�1c ð2Þ

T 4A

T 3

¼ V 3

V 4A

� �k�1

¼ V 3

V 1

� �k�1 V 1

V 4A

� �k�1

¼ V 2

V 1

� �k�1 V 1

V 4A

� �k�1

¼ r1�kc

V 1

V 4A

� �k�1

ð3Þ

where k is the specific heat ratio (CP/CV), while rc is thecompression ratio (V1/V2). Additionally, since process4A-1 is isobaric, we have

V 1

V 4A

¼ T 1

T 4A

: ð4Þ

Substitution of Eqs. (2) and (4) into Eq. (3) yields

T 4A ¼ T 1

T 3

T 2

� �1k

ð5Þ

The heat added per unit mass of the working fluid dur-ing the constant volume process 2–3 (2Q3) per cycle is rep-resented by the following equation:

2Q3 ¼ CVðT 3 � T 2Þ ð6ÞAs aforementioned, for an ideal air standard Atkinson

cycle, all the processes are considered reversible and heatlosses do not occur. However, in the cycle of a real engine,the combustion process is not adiabatic. Obviously, thereare heat losses. The occurrence of heat transfer betweenthe working fluid and the cylinder wall is of importance

1686 S.-S. Hou / Energy Conversion and Management 48 (2007) 1683–1690

and will be considered in the present study. The actual heattransfer processes occurring within the cylinder are quitecomplicated [6]. As an approximation, the heat lossthrough the cylinder wall is assumed to be proportionalto the average temperature of both the working fluid andcylinder wall [6]. The wall temperature is further assumedto be constant as in Mozurkewich and Berry [11] andHoffman et al. [9]. Accordingly, the heat added to theworking fluid during the constant volume combustion pro-cess can be given in the following linear expressions [6–9]:

2Q3 ¼ a� bðT 3 þ T 2Þ ð7Þwhere a is a constant related to combustion and b is a con-stant related to heat transfer. In other words, Qin can berepresented by the following equation:

Qin ¼ 2Q3 ¼ a� bðT 2 þ T 3Þ: ð8ÞCombining Eqs. (7) and (8) yields

T 3 ¼aþ ðCV � bÞT 2

CV þ b: ð9Þ

Substituting Eq. (2) into Eq. (9) gives

T 3 ¼½aþ ðCV � bÞT 1rk�1

c �CV þ b

: ð10Þ

Substitution of Eqs. (2) and (10) into Eq. (5) gives T4A as afunction of T1

T 4A ¼½aT�1

1 r1�kc þ ðCV � bÞ�ðCV þ bÞ

� �1k

T 1 ð11Þ

By combining the results obtained from Eqs. (2), (10)and (11) into Eq. (1), the net work output per unit massof the working fluid can be expressed in terms of T1 as

W ¼ CV

aþ ðCV � bÞT 1rk�1c

CV þ b� rk�1

c T 1

� �

� CPT 1

aT�11 r1�k

c þ ðCV � bÞðCV þ bÞ

� �1k

� 1

( ): ð12Þ

Similarly, substituting Eqs. (2), (10) and (11), into Eq.(8) yields

Qin ¼ a� b rk�1c T 1 þ

aþ ðCV � bÞrk�1c T 1

CV þ b

� �� �: ð13Þ

Eq. (12) divided by Eq. (13) gives the indicated thermalefficiency,

g¼ WQin

¼CV

aþðCV�bÞT 1rk�1c

CVþb � rk�1c T 1

h i�CPT 1

aT�11

r1�kc þðCV�bÞðCVþbÞ

h i1k�1

� �

a�b rk�1c T 1þ aþðCV�bÞrk�1

c T 1

CVþb

h ið14Þ

Then, differentiating with respect to rc and seeking amaximum work output, Wmax, by setting

dWdrc

¼ 0 ð15Þ

we finally get

a1r2kc þ a2r1þk

c � a3 ¼ 0 ð16Þwhere

a1 ¼CV � bCV þ b

ð17Þ

a2 ¼a

ðCV þ bÞT 1

ð18Þ

a3 ¼1� a1

a2

� � 11�k

ð19Þ

Note that rcm can be found by solving Eq. (16) numerically.Hence, Wmax occurs at rcm (the corresponding compressionratio at maximum work output condition). In other words,Wmax can be obtained by substituting rc = rcm into Eq.(12). Furthermore, the corresponding thermal efficiencyat maximum work output, gm, can be obtained by substi-tuting rcm into Eq. (14).

3. Thermodynamic analysis of an air-standard Otto cycle

Comparisons of the performances of the air standardAtkinson and Otto cycles with heat transfer considerationsare also discussed herein. Therefore, thermodynamicanalysis of an air standard Otto cycle is summarized asfollows.

The air standard Otto cycle incorporates an isentropiccompression, an isochoric heat addition, an isentropicexpansion and an isochoric heat rejection processes,sequentially. The pressure–volume (P–V) and tempera-ture–entropy (T–S) diagrams for the thermodynamic pro-cesses of an air standard Otto cycle (1–2–3–4O) areshown by the cycle of 1–2–3–4O in Fig. 1(a) and (b),respectively. Considering heat transfer to the cylinder wallsfor the Otto cycle with the same heat transfer model usedfor the Atkinson cycle,

Qin ¼ 2Q3 ¼ CVðT 3 � T 2Þ ¼ a� bðT 2 þ T 3Þ ð20Þ

the work and thermal efficiency are given in the followingexpressions [7]:

W ¼ CVðT 3 � T 2Þ � CVðT 4O � T 1Þ

¼ CV T 1ð1� rk�1c Þ þ

½aþ ðCV � bÞT 1rk�1c �ð1� rk�1

c ÞðCV þ bÞ

� �ð21Þ

and

g ¼ WQin

¼ 1� ðar1�kc � 2bT 1Þ

ða� 2bT 1rk�1c Þ

ð22Þ

A simple analytical expression for the compression ratio atmaximum net work that does not involve T3 is apparent asfollows:

S.-S. Hou / Energy Conversion and Management 48 (2007) 1683–1690 1687

rcm ¼a

2T 1b

� �1=ð2K�2Þ

ð23Þ

Additionally, the maximum work output, Wmax, and thecorresponding thermal efficiency at maximum work out-put, gm, can be obtained by the following equations:

W max ¼aCV½1� 2bT 1ð Þ1=2�2

CV þ bð24Þ

and

gm ¼ 1� 2bT 1

a

� �1=2

ð25Þ

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1η

0

200

400

600

800

1000

1200

W(k

J/kg

)

β=0.5 kJ/kg-K, T1=350K

α=3500(kJ/kg)

.

Atkinson

Otto

α=3000(kJ/kg)

α=3250(kJ/kg)

Fig. 3. Effect of a on the W versus g characteristics.

4. Results and discussion

The net work output versus efficiency characteristics andthe efficiency bound gm at maximum work depend on a, band T1. The ranges for a, b and T1 are 3000–3500 kJ/kg,0.3–1.5 kJ/kg K and 300–400 K, respectively. Additionally,CP = 1.003 kJ/kg K, CV = 0.716 kJ/kg K and k = CP/CV = 1.4. Numerical examples are shown in the following.

The effect of b on the W–g characteristic curves for theAtkinson and Otto cycles at a = 3000 kJ/kg, andT1 = 350 K is indicated in Fig. 2. Increasing b correspondsto enlarging the heat loss and, thus, decreasing the amountof heat added to the engine. Accordingly, the maximumwork and efficiency decrease with increasing b. For a givenb, it is found that the maximum net work of the Atkinsoncycle is greater than that of the Otto cycle and that the cor-responding thermal efficiency at the maximum net work ofthe former is slightly higher than the latter by about 1%.The question as to why the corresponding thermal effi-ciency at the maximum work output of the Atkinson cycle

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1η

0

200

400

600

800

1000

1200

1400

W(k

J/kg

)

α=3000 kJ/Kg, T1=350K

β=0.3(kJ/kg-K)

.

Atkinson

Otto

β=0.5(kJ/kg-K)

β=0.4(kJ/kg-K)

Fig. 2. Effect of b on the W versus g characteristics.

is only about 1% higher than that of the Otto cycle can notbe answered satisfactorily by this approach. The Atkinsoncycle engine can be up to 10% more efficient than a conven-tional four stroke petrol Otto engine because of controllingthe pumping losses and optimizing the expansion ratiowhile maintaining a fixed compression ratio.

The effect of a on the W–g characteristic curves for theAtkinson and Otto cycles at b = 0.5 kJ/kg K, andT1 = 350 K is depicted in Fig. 3. Increasing a increasesthe amount of heat added to the engine due to combustion.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1η

0

200

400

600

800

1000

1200

1400

W(k

J/kg

)

α=3500 kJ/kg, β=0.5 kJ/kg-K

.

Atkinson

Otto

T1(K)=300

350 400

Τ1(K)=300

350 400

Fig. 4. Effect of T1 on the W versus g characteristics.

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

β(kJ/kg-K)

0

200

400

600

800

1000

1200

1400

1600

Wm

ax(k

J/kg

)

T1=350K

α(kJ/kg)3000

3250 3500

.

α(kJ/kg)3000

3250 3500

Atkinson

Otto

Fig. 6. Effect of a and b on W .

1688 S.-S. Hou / Energy Conversion and Management 48 (2007) 1683–1690

Therefore, a has an opposite effect on the W–g characteris-tic curves to that of b.That is, the maximum work and effi-ciency increase with increasing a. For a given a, Fig. 3further shows that the Atkinson cycle yields larger maxi-mum net work than the Otto cycle. Also, the correspondingthermal efficiency at maximum work of the former is onlyslightly higher than that of the latter. The reason as to whya dramatic increase in the corresponding thermal efficiencyat the maximum work output of the Atkinson cycle can notbe achieved is the same as the explanations in the discus-sion of Fig. 2.

Fig. 4 shows the effect of intake temperature, T1, on theW–g characteristic curves for a = 3500 kJ/kg, andb = 0.5 kJ/kg K. The results show that the maximum workand efficiency decrease as T1 increases, and for a given T1,the maximum net work of the Atkinson cycle is higher thanthat for the Otto cycle.

The compression ratios (rcm) that result in maximumwork as a function of a and b for the Atkinson cycle areplotted in Fig. 5. The values of b for each value of a aresuch that the maximum gas temperature lies in the rangeof 1500–3000 K, as observed in actual engines. It is foundthat for a given a, an increase in b leads to a decrease ofrcm. However, for a fixed b, rcm increases as a increases.Note that the compression ratios that maximize the workof the Otto cycle are always higher than those for theAtkinson cycle at the same operating conditions. Thisimportant characteristic is very desirable for good fueleconomy because of the limitation of the compression ratioin a spark ignition engine owing to the octane rating of thefuel used, while a high expansion ratio delivers a longerpower stroke and decreases the heat wasted in the exhaust.These factors make an Atkinson engine more efficient.

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

β(kJ/kg-K)

0

5

10

15

20

r cm

, Com

pres

sion

Rat

io a

t Wm

ax

T1=350K

α(kJ/kg)3000

3250 3500

.

α(kJ/kg)

3000 3250 3500

Atkinson

Otto

Fig. 5. Compression ratios at maximum net work for various values of aand b at T1 = 300 K.

The effects of a and b on the maximum work output,Wmax, and the corresponding efficiency at Wmax, gm, aredemonstrated in Figs. 6 and 7, respectively. Fig. 6(Fig. 7) shows that an increase in b results in a decreaseof Wmax (gm). The maximum work of the Atkinson cycleis always found to be higher than that for the Otto cycleat the same operating condition.

The effects of b and T1 on the maximum work outputand the corresponding efficiency at maximum work outputare shown in Figs. 8 and 9, respectively. It is seen that the

max

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

β(kJ/kg-K)

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

η m

T1=350K

α(kJ/kg)3000

3250 3500

.

α(kJ/kg)3000

3250 3500

Atkinson

Otto

Fig. 7. Effect of a and b on gm.

300 310 320 330 340 350 360T1(K)

200

300

400

500

600

700

Wm

ax(k

J/kg

)

β=1.0 kJ/kg-K, T1=350 K

.

α(kJ/kg)=3500

Atkinson

Otto

3250

3000

Fig. 10. Effect of a and T1 on Wmax.

300 310 320 330 340 350 360T1(K)

0.45

0.5

0.55

0.6

0.65

ηm

.

α(kJ/kg) 3500 3250

3000

Atkinson

Otto

α(kJ/kg) 3500 3250

3000

β =1.0 kJ/kg-K, T1=350 K

Fig. 11. Effect of a and T1 on gm.

300 310 320 330 340 350 360

T1(K)

0

200

400

600

800

1000

1200

1400

Wm

ax(k

J/kg

)

β(kJ/kg-K)=0.5

.

α=3500 kJ/kg

Atkinson

Otto

1.0

1.5

Fig. 8. Effect of b and T1 on Wmax.

300 310 320 330 340 350 360T1(K)

0.3

0.4

0.5

0.6

0.7

0.8

ηm

β(kJ/kg-K)=0.5

.

α=3500 kJ/kgAtkinson

Otto

1.0

1.5

Fig. 9. Effect of b and T1 on gm.

S.-S. Hou / Energy Conversion and Management 48 (2007) 1683–1690 1689

heat loss parameter has a strong effect on the performanceof the cycle. Both Wmax and gm decrease as b or T1

increases.The effects of a and T1 on Wmax and gm are shown in

Figs. 10 and 11, respectively. It is found that both Wmax

and gm increase as the constant a increases. Figs. 8–11 alsoshow that the maximum work and the corresponding effi-ciency at maximum work output of the Atkinson cycleare always found to be higher than those for the Otto cycleat the same operating conditions.

5. Conclusions

The effects of heat transfer through the cylinder wall onthe performance of an Atkinson cycle are investigated inthis study. The relation between net work output and ther-mal efficiency is derived. Furthermore, the maximum workoutput and the corresponding thermal efficiency at maxi-mum work output are also derived. In the analyses, theinfluence of four significant parameters, namely the heattransfer and combustion constants, compression ratio

1690 S.-S. Hou / Energy Conversion and Management 48 (2007) 1683–1690

and intake air temperature on the net work output versusefficiency characteristics, and the maximum work and thecorresponding efficiency at maximum work are examined.Comparisons of the performances of air standard Atkinsonand Otto cycles with heat transfer considerations are alsodiscussed. The general conclusions drawn from the resultsof this work are as follows:

1. The maximum work output and the corresponding effi-ciency at maximum work output decrease as the heattransfer constant b increases. In other words, higherheat transfer to the combustion chamber walls will lowerthe peak temperature and pressure and reduce the workper cycle and efficiency.

2. The maximum work output and the corresponding effi-ciency at maximum work output increase as the combus-tion constant a increases.

3. The maximum work output and the corresponding effi-ciency at maximum work output decrease as the intaketemperature (T1) increases.

4. For a given value of heat release during combustion (a),an increase in heat loss (b) leads to a decrease of thecompression ratio (rcm) that maximizes the work of theAtkinson cycle.

5. The Atkinson cycle has a greater work output and ahigher thermal efficiency than the Otto cycle at the sameoperating conditions.

6. The compression ratios that maximize the work of theOtto cycle are always found to be higher than thosefor the Atkinson cycle at the same operating conditions.

The analysis helps us understand the strong effect ofheat loss through the cylinder wall during combustion. Itis also verified that for the Atkinson cycle, the expansionratio is greater than the compression ratio, resulting ingreater efficiency and work output than with engines usingthe alternative Otto cycle. The results are of great signifi-cance to provide good guidance for the performance eval-uation and improvement of real Atkinson engines.

In this study, particular concern is placed on heat loss.There is a significant contribution in the paper, namelythe Atkinson cycle analysis and its comparison with theOtto cycle. In view of the results from this work, we realizethat the understanding of the characteristic, i.e. the corre-sponding thermal efficiency at maximum work of theAtkinson cycle is higher than that of the Otto cycle byabout 1%, should be further explored by considering amore advanced model with a new type of cycle analysis.Additionally, the combined effects of heat loss and friction

on the performance of engine cycles are worthy of furtherstudy [17].

Acknowledgement

The author would like to thank the reviewers and Dr.Denton for their valuable comments and helpfulsuggestions.

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