Heywood J.B. Internal Combustion Engines Fundamentals

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define the exhaust gas composition and equivalence ratio under these conditions.

The notation

jti

denotes the wet mole fraction of species

and

denotes the dry

mole fraction of species

Equations (4.57) to (4.62), with Eq. (4.63) to relate CO,,

CO, H,O, and H, concentrations and the assumption that

b/a

m/n, were used

to derive these results. The equations apply for

fuel of composition C,H,O,

The fuellair equivalence ratio is given by

where the wet and dry mole fractions are related by

jti

ZHZO)q'

and

Note that

X,,,,,

is the measured (wet) HC concentration as a mole fraction C,

@pm C,

ZCHb,,

aZCaHb. Figure 4-23 shows wet exhaust gas concentra-

tions, based on the

MIT

measured dry concentrations of CO,

CO,

shown in

Fig. 4-20, and wet HC concentration, as well as Eqs. (4.68).

For lean mixtures, varying the value of

between 1.5 and 5.5 had a neglgi-

ble effect on the value of

computed from Eq. (4.67). For stoichiometric mix-

tures, varying

K from 2.5 to 4.5 varied the computed

by 2 to

percent. For

1.2, varying K from 2.5 to 4.5 varied the computed

to 4 percent. The

error in

involved in omitting NO, is 0.2 percent for an NO, level of 1000 ppm,

increasing to 1 percent for an NO, level of 5000 ppm. The sensitivity of the

computed

to errors in the measurements of CO,

CO, and

is modest within

the normal range of

used.

2 percent error in CO, or CO or

gives about a 0.1 percent error in computed

For leaner and richer mixtures,

the error in

9 increases for errors in measured CO, concentration, and CO

1) and

concentrations, but is still significantly less than the mea-

surement error in fuel and air flow.

4.93 Effects

Fuel/

Air

Ratio

Nonuniforrnity

Neither the masses of air inducted into the different cylinders of a multicylinder

engine per cycle nor the masses of fuel which enter the different cylinders Per

Fuellair

equivalence

ratio

FIGURE

4-23

Wet

exhaust gas species concentrations as a function

fuel/air equivalence ratio,

based on

the

dry

exhaust gas composition data in Fig.

4-20

and Eqs.

(4.68).

cycle are exactly equal. In addition, mixing of fuel and air within each cylinder is

not necessarily completely uniform. Thus the exhaust gas composition may corre-

spond to a distribution in the fuellair ratio in the unburned mixture about the

mean value. For example, if the mean

fuellair ratio is stoichiometric, extra

oxygen will be contributed by any cylinders operating lean of the average and

extra carbon monoxide by any cylinders rich of the average, so that the exhaust

gas will have higher levels of

and CO (and a lower level of CO,) relative to an

engine operating with identical fuellair ratios in each cylinder.

Eltinge has developed a method for defining this nonuniformity in the fuel/

air ratio distribution for spark-ignition engines which operate close to

stoichio-

metric.29

function

f(x)

for theafuel/air ratio distribution

F/A) was

assumed, with standard deviation

S,.

For each value of

(i.e., FIA), complete

utilization of the available bxygen was assumed (i.e., no exhaust HC) and the

CO,, H,O, CO, H, concentrations were related by Eq. (4.63) (with

3.5). The

concentrations of each species for each (FIA) were weighted by the distribution

function

(x)

and summed to produce the average exhaust concentration.

cor-

rection to allow for the presence of unburned HC in the exhaust was also devel-

oped.) Figure 4-24 shows one set of results, for a fuel H/C ratio of 1.8 (typical of

gasoline), for a normal distribution in the fuellair ratio. For each mean (FIA) and

maldistribution parameter

(the standard deviation of the FIA distribution) the

corresponding dry concentrations of CO,, CO, and

are shown. This

type

information can

used to define the fuel-air mixture nonuniformities

spark-

ignition engines operating relatively close to stoichiometric. For diesel engines

'he variations of major exhaust gas species concentrations with fuellair equiva-

154

INTERNAL

COMBUSTION

ENGINE

FUNDAMENTALS

Assumptions:

Fuel

HIC

atom

ratio

1.80

Water

gas

constant

3.5

unburned

fuel

Stoichiometric

airlfuel

ratio

14.5

FIGURE

4-24

Computed relationship between dry

exhaust gas composition (CO,, CO, and

O,), airjfuel ratio, and maldistribution

parameter

S,.

Fuel: (CH,.,),

The correc-

tion to

added to the burned gar

(FIA)

which allows for the measured

un-

burned hvdrocarbon concentration is

4.7

lo-;

HC (ppm

C,)

(From

~Itinge.'')

lence ratio are linear, so the effects

any nonuniformities are not apparent in

this manner (see Fig. 4-22).

4.9.4

Combustion Inefficiency

Internal combustion engine exhaust contains combustible species: CO, Hz,

unburned hydrocarbons, and particulates. When their concentrations are known,

the combustion efficiency

rt,

given by Eq. (3.27) can

calculated. The chemical

energy carried out of the engine in these combustibles represents the combustion

inefficiency,

where the

are the mass fractions

CO,

HC, and particulates, respectively,

the

Q,,,

are the lower heating values of these species, and the subscripts

and

denote fuel and air. The heating values for CO (10.1. MJ/kg) and Hz(120 MJFg)

are well defined. The composition of the unburned HC is not usually known.

However, the heating values of hydrocarbons are closely comparable, so the fuel

heating value (typically 42 to

MJ/kg) is used. The particulates (only present in

diesels) are soot with some adsorbed hydrocarbons; usually the mass fraction is

low enough for their contribution to be small, and

heating value for solid

carbon (32.8 MJ/kg) can

used. Combustion efficiency data as a function

equivalence ratio have already been presented in Fig. 3-9.

PROPERTIES

WORKING

FLUIDS

155

PROBLEMS

(a) Calculate the low-temperature burned gas composition resulting from the com-

bustion of

g/s air with 0.48 g/s ethane (C,H,). Assume

3.5 in

Eq.

(4.6).

(b)

Calculate the low-temperature burned gas composition for the combustion of

7 g/s air with 0.48 g/s ethanol (C,H,O). Assume

3.5

in Eq. (4.6). (Note the

large difference in burned gas composition due to this difference in fuel.)

4.2.

evaluate the accuracy of the simple analytic ideal gas model, use the results of

Example 4.1 and Eqs. (4.23) (constant-volume adiabatic combustion) and (4.24)

(constant-pressure adiabatic combustion) to calculate

for a stoichiometric

isooctane-air mixture. Compare this result with that obtained using Figs. 4-3 and

4-8. Assume the following unburned mixture conditions:

700

0.125 m3/

air,

15 atm, and

0.1.

43.

(a) In Fig. 4-1, why does

decrease as

increases?

(b) In Fig. 4-14, why does

decrease as

increases?

(c)

In Fig. 4-14, why does

decrease as

increases?

4.4.

Show how, for an ideal gas with fixed composition, the molecular weight

related to the specific heats

and c,, and

J?.

Use Figs. 4-15 and 4-16 to calculate

for

1750, 2250, and 2750

and

1.0. Compare these results with values of

obtained from Fig. 4-14 and explain any differences.

45.

EGR,

exhaust gas recirculation, is often used to reduce NO, by acting

diluent in

the intake mixture.

(a) For low-temperature isooctane-air combustion products at

1.0, determine

the percentage of the burned gases' average specific heat at constant pressure

which comes from each component in the burned gas mixture.

(b) Compare the specific heat at constant pressure of isooctane-air combustion pro-

ducts at

1.0 to that of air, both at 1750

This difference is one reason why

EGR

instead of leaner fuel-air mixture is used to control NO, emissions.

4.6.

Explain qualitatively the causes of the trends in the curves in Fig. 4-23

increased from 1.0 and decreased from 1.0.

4.7.

Compare the

CO,

and CO data in Fig. 4-22 with the predictions of the elemen-

tal balance in Table 4.3. Explain any differences. Assume diesel fuel is a hydrocarbon

with H/C ratio of 2.

4.8.

The following exhaust data were obtained from a four-stroke cycle spark-ignition

engine. CO, CO,, and

NO,

molar concentrations are all measured fully dry; HC is

measured fully wet as ppm C,. Determine the fuellair equivalence ratio

for the

following three sets of data. Make the following assumptions: (1) the constant

Eq. (4.63) equals 3.5; (2) the fuel composition is C,H,,,,,; (3) the unburned hydro-

carbon H/C ratio is the same as that of the fuel; and (4) N0,is entirely NO.

(a) CO, 14.0%, CO OH%,

0.7%, NO, 3690ppm, HC 3200ppm.

(b)

CO, 13.8%, CO 3.05%,

Ox, NO, 1600ppm, HC 34% ppm.

4.0%, NO, 4600ppm, HC 2100 ppm.

4.9.

The exhaust from a spark-ignition engine has the following composition (in mole

fractions):

The

fuel is isooctane, C,H,,; as shown above, a small fraction of the fuel escapes

156

INTERNAL

COMBUSTION ENGINE

FUNDAMENTALS

from the cylinder unburned. The lower heating value of isooctane is 44.4 MJ/kg, of

carbon monoxide is 10.1 MJ/kg, and of hydrogen is 120 MJ/kg. The atomic weights

of the elements are: C

12.0

16, H

14.

(a) Calculate the combustion inenlciency in the engine; i.e., the percentage of the

entering fuel enthalpy which is not fully released in the combustion process and

leaves the engine in the exhaust gases (for this problem, the exhaust can

assumed to be at room temperature).

(b) What fraction of this inefficiency is due to the unburned fuel emissions?

4.10. A %liter displacement four-cylinder engine, operating at 2000 rev/min and 30

percent of its maximum power at that speed, has the following exhaust composition

(in percent by volume or mole percent):

C02, 11%; H20, 11.5%; CO, 0.5%;

Hz,

0%; O,, 2%; unburned hydrocarbons

(expressed as CH,, i.e., with a molecular weight of 14), 0.5%; N2,74.5%

The fuel is (CH,), with a heating value of

MJ/kg. The atomic weights of the

elements are

12,

1,0

16,

14. The heating values of CO and

are

10 and

MJ/kg, respectively.

(a) Is the engine a diesel or spark-ignition engine? Is there enough oxygen in the

exhaust to burn the fuel completely? Briefly explain.

(b) Calculate the fraction of the input fuel energy

(m,Q,,)

which exits the engine

unburned as (1) CO and (2) unburned HC.

(c)

An inventor claims a combustion efficiency of 100 percent

can

achieved. What

percentage improvement in engine specific fuel consumption would result?

4.11. A gasoline engine operates steadily on a mixture of isooctane and air. The air and

fuel enter the engine at 25OC. The fuel consumption is 3.0 as. The output of the

engine is 50 kW. The temperature of the combustion products in the exhaust mani-

fold is

660

K. At this temperature, an analysis of the combustion products yields the

following values (on a dry volumetric basis):

CO,, 11.4%;

02,

1.6%; CO, 2.9%; N2, 84.1%

(a) Find the composition in moles (number of moles per mole of isooctane) of the

. .

reactants and the reaction products.

(b) Determine the heat-transfer rate from the working fluid as the working fluid

passes through the engine.

Constants for the calculations:

Enthalpy of formation,

Sensible

enthalpy at

660

kJ/kmol kJ/kmol

4.12 A direct-injection four-stroke cycle diesel engine is used to provide power for

pumping water. The engine operates at its maximum rated power at 2000 rev@&

PROPERTIES

WORKING

FLUIDS

157

with an equivalence ratio of 0.8 and an air flow of 0.5 kas. The gross indicated fuel

conversion efficiency is 45 percent, and the heat losses from the working fluid to the

engine coolant and elsewhere within the engine are 280

kW.

Diesel fuel has a heating

value of 42 MJ/kg and stoichiometric fuel/air ratio of 0.067. Fuel and air enter the

engine at ambient conditions. The mechanical efficiency of the diesel engine is 85

percent.

(a)

Calculate the rated brake power of the engine, the average sensible enthalpy of

the exhaust gases as they leave the engine, and the average exhaust gas tem-

perature.

(b) Since the exhaust gas temperature is significantly above ambient, the advantages

of using the diesel exhaust gas stream to heat the boiler of a

Rankine cycle (see

sketch) and generate additional power are to be explored. If the exhaust gases

leave

the Rankine-cycle system boiler at 400

and 30 percent of the heat trans-

ferred from the exhaust gas stream in the boiler is converted to power at the

Rankine-cycle power plant drive shaft, calculate the additional power obtained

and the brake fuel conversion efficiency of the combined cycle system (diesel plus

Rankine cycle).

4.13.

diesel engine has a compression ratio of 22

1. The conditions in the cylinder at

the start of compression are

101.3 kPa and

325

Calculate the pressure

and temperature at the end of compression, assuming the compression process is

isentropic:

Diesel

engine

(a) ~ssume the cylinder contains an ideal gas with

1.4 and

287

J/kg

Hot

Rankine cycle boiler cooled

diesel diesel

exhaust exhaust

400

K-

(b)

Assume the cylinder contains air which may

regarded as a semiperfect gas (use

the gas tables).

(c)

Compare the work of compression in (a) and (b) above.

In practice, heat losses reduce the final compression temperature by 100 K. For a

diesel engine operating at

equivalence ratio_ of 0.75 (full load):

(6)

Calculate the ratio of heat loss during compression to the fuel energy added per

cycle.

Rankine (liquid)

cycle fluid

(vapor)

FIGURE

P4-12

4.14.

While the geometric compression ratio of an engine is

VJV,,,,

the actual compres-

sion process starts somewhere between bottom-center and when the inlet valve

closes, and it is conditions at time of spark (for an SI engine) or fuel injection (for a

CI engine) that determine ignition. At low engine speed, compression starts about

the time when the inlet valve closes. With this

assuplption, for the diesel engine of

Prob. 4.13, calculate the air pressure and temperature at the start of injection. The

inlet valve closes at

30' after BC; injection commences 15" before TC. Use the gas

tables. Compare your answers with those of Prob. 4.13(b).

158

INTERNAL

COMBUSTION

ENGINE

FUNDAMENTALS

4.15. Use an equilibrium computer code (which calculates the composition and properties

of chemically reacting gas mixtures in equilibrium) to calculate the data you need for

the following graphs:

(a) Values of c,,

molecular weight, and

gas

composition (mole fractions of

N,,

CO,, H20. CO, Hz, O,, OH, 0, H, and NO)

a function of the equivalence

ratio (4

0.2 to 1.4) for products of combustion of isooctane (C,H,,) with air at

atm and

2500

Put all species concentrations on the same graph.

Use a log scale for the composition axis.

(b)

Unburned mixture consisting of isooctane vapor and

air

at 700 K and 20 atm is

burned fist at constant pressure and then at constant volume.

(1) Calculate the enthalpy and internal energy of isooctane vapor at

700

cal/gmol; also calculate the volume per unit mass of mixture (cm3/g) for

0.2,0.4,0.6,0.8,

1.0,

1.2, 1.4.

(2) Use these data and the equilibrium program to calculate the temperature

attained after combustion at constant pressure, and temperature and pressure

attained after combustion at constant volume. Plot these temperatures and

pressures against the equivalence ratio

Thermodynamic

data

for

isooctane vapor

Z,,

cal/mol-

&,,

kd/mol

&-;,

kd/mol

298 45.14

0.00

53.57

700 85.66

27.02

62.79

4.16.

heavy wall bomb with a volume of 1000 cm3 contains a mixture of isooctane with

the stoichiometric air requirement at

101.3 kPa and

25•‹C. The mixture is

then ignited with a spark. Find the pressure and temperature of the equilibrium

combustion products just after combustion is complete

(i.e., before heat losses to the

wall are significant).

Assume the burned gases are uniform.

4.17.

gas engine, running on a gaseous mixture of butane,

C,H,,,

and air has the

following conditions in the cylinder prior to constant-volume adiabatic combustion:

pressure, 6.48

loS

N/m2; temperature,

600

The charge composition is air plus

50 percent of the stoichiometric quantity of butane fuel. Calculate the pressure and

temperature at the end of combustion using the data given below.

For

air

Jlpof

For

butane

JIgmol

PROPERTIES

WORKING

FLUIDS

159

Internal energy of combustion of butane at 298

Air

-2.659 MJ/gmol.

Extract from gas tables for products of combustion for 50 percent stoichiometric

fuel

REFERENCES

Komiyama, K., and Heywood,

B.: "Predicting NO, Emissions and the Effects of Exhaust

Gas

Recirculation in Spark-Ignition Engines;" SAE paper 730475,

SAE

Trans.,

vol. 82, 1973.

Danleli,

G.,

Ferguson, C., Heywood, J., and Keck, J. "Predicting the Emissions and Performance

Characteristics of a Wankel Engine," SAE paper 740186,

SAE

Trans.,

vol. 83,1974.

Hottel,

C., Williams,

C., and Satterfield, C. N.:

Thermodynamic Charts for Combustion

Processes,

John Wiey, 1949.

See

also charts in C. F. Taylor,

The Internal Combustion Engine in

Theory

and

Practice.

vol. 1, MIT Press, 1960.

Newhall, H.

K..

and Starkman, E. S.: "Thermodynamic Properties of Octane and Air for Engine

Performance Calculations," in

Digital Calculations of Engine Cycles, Progress in Technology,

vol.

TP-7, pp. 38-48, SAE, 1964.

Starkman, E. S., and Newhall,

H. K.:

"Thamodynamic Properties of Methane and Air, and

Propane and Air for Engine Performance Calculations," SAE paper 670466,

SAE

Trans.,

vol. 76,

1967.

Keenan, J. H., Chao, J., and Kaye, J.:

Gas

Tables,

2d ed., John Wiey, 1983.

7. Reynolds,

C.:

ThermodynMlie Properties

SI; Graphs, Tables, and Computational Equations

/or Forty Substances,

Department of Mechanical Engineering, Stanford University, 1979.

JANAF

Thmnochemical Tables,

ad.,

NSRDS-NB537, U.S. National Bureau

Standards,

June 1971.

9. Gordon, S., and McBride, B. J.: "Computer Program for the Calculation of Complex Chemical

Equilibrium Composition, Rocket Pcrformanoe, Incident and Reflected Shocks, and Chapman-

Jouguet Detonations;" NASA publication SP-273,1971 (NTH number N71-37775).

10.

Svehla,

A., and McBride, B.

J.:

"Fortran

Computer Program for Calculation of Thermody-

namic and Transport Properties of Complex Chemical Systems," NASA technical note TND-

7056.1973 (NTIS number N73-15954).

Fremont,

A.,

et al.: Properties of Combustion Gases,

General Electric Company, Cincinnati,

Ohio, 1955.

11 Banes, B., McIntyrc, R. W., and Sims, J.

Properties of Air

and

Combustion Products with

Kerosene

and

Hydrogen Fuels,

vols. I-XIII, Propulsion and Energetics Panel, Advisory Group for

Aerospace Research and Development (AGARD), NATO, published by Bristol Siddeley Engines

Ltd., Filton, Bristol, England, 1967.

13.

Hires, S. D., Ekchian, A., Heywood, J. B, Tabaczynski, R. J., and Wall, J. C.: "Performana and

NO, Emissions ModelSig of a Jet Ignition Rechamber Stratified Charge Engine," SAE paper

760161,

SAE

Trans.,

vol. 85,1976.

Id.

LoRusso, J.

"Combustion and Emissions Characteristics of Methanol, Methanol-Water, and

Gasoline-Methanol Blends

a Spark Ignition Engine," S. M. Thesis, Department of Mechanical

Engineering, MIT, May 1976.

IJ.

BY.

A.,

Kempinski, B, and Rife, J.

M.:

"Knock

in Spark-Ignition Engines," SAE paper 810147,

1981.

16.

Rossini.

D..

Pitzer, K. S., Arnett, R. L., Braun, R. M., and Primentel,

C.:

Selected Values

Physical

and

Thennodynamic Properties of Hydrocarbons and Related Compounds,

Carnegie Preq

Pittsburgh, Pa..

1953.

17.

Mansouri. S. H., and Heywood, J. B.: "Correlation for the Viscosity and Prandtl Number

Hydrocarbon-Air Combustion Products,"

Combust. Sci. Technology,

vol.

23,

pp.

251-256,1980.

18.

Osjara, C., and Borman,

L.:

"A Computer Program for Calculating Properties of Equilibrium

Combustion Products with Some Applications to LC. Engines," SAE paper

750468,1975.

19.

Krieger, R. B., and Borman, G. L.: "The Computation of Apparent Heat Release for Internal

Combustion Engines," in

Proc. Diesel Gas Power,

ASME paper

66-WA/DGP-4,1966.

20.

Martin, M.

K.,

and Heywood. J. B.: "Approximate Relationships for the Thennodynamic Proper.

ties of Hydrocarbon-Air Combustion Products,"

Combust. Sci. Technology,

vol.

15,

pp.

1-la

1977.

21.

Chapman, S., and Cowling, T.

G.:

The Mathematical Theory of Non-Uniform Gases,

Cambrid@

University Press, Cambridge,

1955.

22.

Hirschfelder,

O.,

Curtiss, C. F., and Bud, R. B.:

Molecular Theory of Gases and Liquids.

John

Wdey.

1954.

23.

Patterson,

J., and Henein, N. A.:

Etnissionsfrom Combustion Engines and Their Control,

Ann

Arbor Science Publishers,

1972

24.

D'Alleva,

A.,

and Lovell,

G.:

"Relation of Exhaust Gas Composition to Air-Fuel Ratio."

SAE

J.,

vol.

38,

no.

pp.

90-96,

March

1936.

25.

Stivender.

L.: "Development of a Fuel-Based Mass Emission Measurement Procedure," SAE

paper

710604.1971.

26.

Hamngton, J. A., and Shishu,

C.:

"A SingleCylinder Engine Study of the Effects of Fuel Type,

Fuel Stoichiometry and Hydrogen-to-Carbon Ratio on CO, NO, and HC Exhaust Emissions,-

SAE paper

730476,1973.

27.

Spindt, R. S., "Air-Fuel Ratios from Exhaust Gas Analysis," SAE paper

650507,

SAE Trans.,

vol

74. 1965.

28.

Fleming,

D.,

and Eccleston,

B.: "The Effect of Fuel Composition, Equivalence Ratio, and

Mixture Temperature on Exhaust Emissions," SAE paper

710012,1971.

29.

Eltinge,

L.:

"Fuel-Air Ratio and Distribution from Exhaust Gas Composition," SAE paper

6801 14,

SAE Trans.,

vol.

77,1968.

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Leonard,

S.: "Fuel Distribution by Exhaust Gas Analysis," SAE paper 379A,

1961.

31.

Bishop, R. P.: "Combustion Efficiency in Internal Combustion Engines," B.S. Thesis, Department

of Mechanical Engineering, MIT, February

1985.

32.

The Engine Test Code Subcommittee of the General Technical Committee,

General Motors Auto-

motive Engine Test Code for Four Cycle Spark Ignition Engines,

6th ed,

1975.

CHAPTER

IDEAL

MODELS

ENGINE

CYCLES

5.1

INTRODUCTION

The operating cycle of an internal combustion engine can be broken down into a

sequence of separate processes: intake, compression, combustion, expansion, and

exhaust. With models for each of these processes, a simulation of a complete

engine cycle can

built up which can

analysed to provide information on

engine performance. Models of individual engine processes at various levels of

approximation have been developed. In this chapter we consider the simplest set

models which provide useful insights into the performance and efficiency of

engines. The cycles analysed are commonly called the constant-volume, constant-

pressure, and limited-pressure cycles; each title describes the approximation

made for the engine combustion

process.t The description of more accurate

Simulations of engine processes is deferred until Chap.

14.

For each engine cycle, a choice of models for working fluid thermodynamic

Properties must

made. These models have been reviewed in Chap.

Ideal

These

cycles are also referred to by the titles Otto cycle, Diesel cycle, and dual cycle, respectively,

for historical reasons. The more descriptive titles

used

above are preferred

~CC~UK

they avoid the

ohmade assumption that the SI or Otto engine is best approximated by the constant-volume cycle.

the

or diesel engine is best approximated by the constant-pressure cycle. These assumptions

not necessarily

wmct.

162

INTERNAL COMBUSTION ENGINE FUNDAMENTALS

engine cycle models combined with a simple ideal gas model (specific heats con-

stant throughout the engine cycle-model

in Table 4.2) provide analytic results

and are useful for illustrative purposes; we will call these cycles

ideal gas standard

cycles.

Ideal engine cycles combined with more realistic models of working fluid

properties (a frozen mixture of ideal gases for the unburned mixture and an equi.

librium mixture for the burned mixture--model

in Table 4.2) are called

fuel-air

cycles

and provide more quantitative information on engine operation.

An internal combustion engine is not a heat engine in the thepodynamic

definition of the term. It is not a closed system. The working fluid does not

execute a thermodynamic cycle. The temperature changes which occur around

minimum and maximum cylinder volumes are not primarily a result of heat-

transfer interactions. An engine can best be analyzed as an open system which

exchanges heat and work with its surrounding environment (the atmosphere).

Reactants (fuel and air) flow into the system; products (exhaust gases) flow out.

(An overall second law analysis of the engine from this point of view has already

been presented in

Sec. 3.6.) Thus, the cycles discussed in this chapter are not

thermodynamic cycles. Rather, each is a consecutive sequence of processes

through which we can follow the state of the working fluid as the engine executes

a complete operating cycle.

5.2

IDEAL MODELS

ENGINE PROCESSES

The sequence of processes which make up a typical SI and CI engine operating

cycle has been described in Sec. 1.3. To illustrate these processes, cylinder pres-

sure

(p)

and volume

(V)

data from a throttled four-stroke cycle

engine are

plotted as a

p-V

diagram in Fig. 5-1. The cycle can be divided into compression,

Cylinder volumelV,,

FIGURE

5-1

Pmsure-volume diagram of firing spark-ignition engine.

8.4, 3330 rev/min,

0.4

atm,

atm, imep,

2.9 atm.

TABLE

5.1

ldcal

models

engine

processes

Rarss

kssumptiom

compression (1-2)

1. Adiabatic and reversible (hence isentropic)

combustion (2-3)

Adiabatic

2. Combustion occurs at

(a) Constant volume

(b)

Constant pressure

(c)

Part

at constant volume and part at constant

pressure (dled limited pressure)

3. Combustion

complete (q,

~xpansion (3-4) 1. Adiabatic and reversible (hence isentropic)

Exhaust

(4-5-6)

Adiabatic

and

Valveevents occur at top and bottomcenter

intake

(6-7-1)

3. NO change in cylinder volume

pressure

differences across open valves drop to mo

Inlet and exhaust pressures constant

Velocity effects negligible

prasure-volume diagrams of ideal cycles. Unthrottled operation: (a) constant-volume combustion;

(b)

constant-pressure combustion;

(c)

limited-pr&urc combustion.

Throttled constant-volume

We;

(e)

supercharged constant-volume cycle.

combustion, expansion, exhaust, and intake processes. Sets of assumptions which

simplify each of these processes to a form convenient for analysis are given in

Table 5.1.

Pressure-volume diagrams for the constant-volume, constant-pressure, and

limited-pressure cycles for unthrottled engine operation are illustrated in Fig.

5-2a to

Throttled engine operation

(pi

and supercharged engine operation

(p,

are shown in Fig. 5-2d and

each cycle 1-2 is the compression

process, 2-3 is the combustion process,

3-4

(or 2-4 in the constant-pressure cycle)

is the expansion process, 4-5-6 is the exhaust process, and 6-7-1 is the intake

process.

The most critical assumption in determining how useful these ideal cycles

are as indicators of engine performance is the form assumed for the combustion

process. The real engine combustion process occupies a finite crank angle period

(between about 20 and 70 crank angle degrees), and the spark or fuel-injection

timing may be retarded from its optimum advance to closer to

TC.

The constant-

volume cycle is the limiting case of infinitely fast combustion at TC; the constant-

pressure cycle would correspond to slow and late combustion; the limited-

pressure cycle lies in between.

THERMODYNAMIC RELATIONS

FOR ENGINE PROCESSES

The overall engine operating parameters of greatest interest which can be deter-

mined from a thermodynamic analysis of the engine operating cycle are:

The indicated fuel conversion efficiency

v,,~:

(which, since the combustion efficiency is unity, is equal to the indicated thermal

conversion efficiency

v,,~;

see Sec. 3.6.2)

The indicated mean effective pressure (imep):

W,,,

the indicated work per cycle, is the sum of the compression stroke work and

the expansion stroke work:

Using the notation of Fig. 5-2 to define the endpoints of each engine process, the

following relationships are obtained by applying the fist and second laws of

thermodynamics to the cylinder contents:

compression stroke:

Since the process is adiabatic

and

reversible

The compression work is

Combustion process:

For the constant-volume cycle,

For the constant-pressure cycle,

For the limited-pressure cycle,

and

Expansion stroke:

For the constant-volume cycle,

and the expansion work is

m(u3

14,)

For the constant-pressure cycle,

rc s4

and the expansion work is

166

INTERNAL COMBUSTION ENGINE FUNDAMENTALS

For the limited-pressure cycle,

vdu3a

P3b

P3a S4

S3b

and the expansion work is

u3b

~3(~3b

v33

mC(u3b

~4)

~3(~3b

v3lr)I

mC(h3b

h4)

P4 v4

P3 03al

The indicated fuel conversion efficiency is found by substitution into

Eqs.

(5.3)

and

(5.1):

FIGURE

5-3

Enthalpyzntropy diagram of gas state during

exhaust process.

See

text for explanation.

For the constant-volume cycle:

mC(u3

(~2

u1)1

gas to leave have the same stat-5. There is, therefore, a gradient in temperature

41.1

within the exhausted gas. The temperature of the first element exhausted,

T,,

QLHV

slightly less than

T,;

the temperature of the last element exhausted is

For the constant-pressure cycle:

displacement of gas out of the cylinder follows the blowdown process as

the piston moves from

to TC.

heat-transfer and kinetic energy dissipation

mC(:(h3

h4)

(u2

~1)

~4 v4

v21

ekts are neglected, no change in thermodynamic state of the gas occurs. In this

4f.i

QLHV

displacement

process, the mass of gas within the cylinder at the end of the blow-

down process is further decreased by the ratio

&/&.

For the limited-pressure cycle:

The mass of residual gas

the cylinder at point

in the cycle is

rnC(h3b

~1)

P4 04

P3 u3aI

obtained by first determining the state of the gas

(T,,

us)

at the end of the blow-

41.i

down process following an isentropic expansion from

and then by

QLHV

reducing the cylinder volume to the clearance volume

V,.

The residual mass

The state of the mixture at point

in the cycle depends on the intake

fraction is thus given by

mixture properties and the residual gas properties at the end of the exhaust

stroke.

vdvs

-=x,=---

(5.17)

When the exhaust valve opens at point 4, the cylinder pressure is above the

exhaust manifold pressure and a

blowdown

process occurs. In the ideal exhaust

The average state of the exhausted gas can

determined by considering

process model, this blowdown occurs with the piston stationary at BC. During

the

Open system defined by the piston face, cylinder walls, and cylinder head,

this blowdown process, the gas which remains inside the cylinder expands isen-

shown in Fig. 5-4. Applying the first law of thermodynamics for an open system

tropically. The gases escaping from the cylinder undergo an unrestrained expan-

gives

sion or throttling process which is irreversible. It is assumed that the kinetic

energy acquired by each gas element as it is accelerated through the

exhaust

p&V4

V,)

(5.18~)

valve is dissipated in a turbulent mixing process in the exhaust port into internal

energy and flow work. Since it is also assumed that no heat transfer occurs, the

where

is the enthalpy of the mass of gas exhausted from the cylinder. The

s~ecific exhaust enthalpy is, therefore,

enthalpy of each element of gas after it leaves the cylinder remains constant.

These processes are illustrated on an

h-s

diagram

Fig. 5-3.

gas

m4"4-m6u6+~e6

remaining in the cylinder expands isentropically along the line 4-5. The

fint

(5.18b)

"'4

element of gas which leaves the cylinder at point 4 enters the exhaust manifold

state

on the pressure

line. An element that leaves the cylinder at an inter-

which, with

pe,

defines the average exhausted-gas state.

mediate state

on the expansion line 4-5 would enter the exhaust manifold

The

mixture temperature at the end of the intake stroke and at the start of

state

At the end of the blowdown process the gas in the cylinder and the last

Ihe

stroke (point

in Fig. 5-2) can now be determind, again using

Exhaust

Definition of system boundary for thermodynamic

analysis of ideal cycle processes.

the open system in Fig.

5-4.

Application of the first law between points

and 1

gives

-pi(Vl

V6)

(ml

m6)hi

(5.19~)

where

is the specific enthalpy of the inlet mixture and

pi.

Note that when

pe,

part of the residual gas in the cylinder at the end of

the exhaust stroke will flow into the intake system when the intake valve opens.

This flow will cease when the cylinder pressure equals

pi.

However, provided

heat transfer occurs, this backflow will not affect Eqs.

(5.19)

above, since the flow

of residual through the intake valve is a constant enthalpy process.

In many engines, the closing of the exhaust valve and the opening of the

intake valve overlap. Flow of exhausted gases from the exhaust system through

the cylinder into the intake system can then occur. Equations

(5.18)

and

(5.19)

would have to

modified to account for valve overlap.

In the four-stroke engine cycle, work is done on the piston during the

intake and the exhaust processes. The work done by the cylinder gases on the

piston during exhaust is

The work done by the cylinder gases on the piston during intake is

PXVI

V2)

(5.21)

The net work to the piston over the exhaust and intake strokes, the

pumping

work,

(Pi

P~XVI

V2)

(5.22)

which, for the cylinder gas system, is negative for

and positive for

PI-

fie ~umping mean effective pressure (pmep) is usually defined as a positive

Thus:

For

Pe:

For

pe:

The net and gross indicated mean effective pressures are related by

The net indicated fuel conversion efficie;cy is related to the gross indicated fuel

conversion efficiency by

5.4

CYCLE ANALYSIS WITH

IDEAL

GAS

WORKING

FLUID

WITH

AND

CONSTANT

the working fluid in these ideal cycles is assumed to

an ideal gas, with

and

constant throughout the engine operating cycle, the equations developed in the

previous section which describe engine performance and efficiency can be further

simplified. We will use the notation of Fig.

5-2.

5.4.1

Constant-Volume Cycle

The compression work (Eq.

5.6)

becomes

mc,,(Tl

T2)

The expansion work (Eq.

5.9)

becomes

mc,,(T3

T,)

The denominator in Eq.

(5.14),

QLHv, can be related to the temperature

rise during combustion. For the working fluid model under consideration, the

U(T)

lines for the reactants and products on a

U-T

diagram such as Fig.

3-5

are

parallel and have equal slopes, of magnitude

c,.

Hence, for a constant-volume

adiabatic combustion process

Note that

insutficient air is available for complete combustion of the fuel,

Eq.

(5.28)

must

modified. The right-hand side of the equation should then

m,QLHv.

where

is the combustion

dtiency given by

Eq.

(3.27).

Note that the heating values at constant volume and constant pressure are the

same for this working fluid. For convenience we will define

Q* is the specific internal energy (and enthalpy) decrease, during isothermal com.

bustion, per unit mass of working fluid.

The relation for indicated fuel conversion efficiency (Eq. 5.14) becomes

Since 1-2 and

3-4

are isentropic processes between the same volumes,

and

V2,

where

c Jc, . Hence:

and Eq. (5.30) can be rearranged as

Values of q,,, for different values of

are shown in Fig. 5-5. The indicated

fuel conversion efficiency increases with increasing compression ratio and

decreases as

decreases.

FIGURE

5-5

Ideal gas constant-volume cycle

fuel

con-

version dficiency

a function of

corn-

pression ratio;

E#,.

The indicated mean effective pressure, using Eqs. (5.2) and (5.31), becomes

The dimensionless numbers

r,,

and Q*/(c,T,) are sufficient to describe

[he characteristics of the constant-volume ideal gas standard cycle, relative to its

initial conditions pl, TI.

is useful to compare the imep-a measure of the effectiveness with which

[he displaced volume of the engine is used to produce work-and the maximum

pressure in the cycle, p3. The ratio p31pl can be determined from the ideal gas

applied at points

and 3, and the relation

obtained from Eq. (5.28). Equations (5.32) and (5.33) then give

high value of imeplp, is desirable. Engine weight will increase with increasing

to withstand the increasing stresses in components.

The indicated fuel conversion efficiency and the ratios imeplp, and imep/p3

for this ideal cycle model do not depend on whether the cycle is throttled or

supercharged. However, the relationships between the working fluid properties at

points 1 and

do depend on the degree of throttling or supercharging. For throt-

tled engine operation, the residual gas mass fraction

can be determined as

follows. From Eq. (5.17), since state 5 corresponds to an isentropic expansion

from

state

to p

p,,

is given by

follows

that

The residual mass fraction increases as pi decreases below pe, decreases as

increases, and decreases as Q*/(c,

T,)

increases.

Through a similar analysis, the temperature of the residual gas T, can be

determined: