Heywood J.B. Internal Combustion Engines Fundamentals

Подождите немного. Документ загружается.

670

INTERNAL

COMBU~ON

ENGME

FUNDAMENTALS

the walls of the intake system, combustion chamber, and exhaust system, and

the coolant is of obvious importance to the engine designer.

122 MODES OF HEAT TRANSFER

The following modes of heat transfer are important.

12.2.1 Conduction

Heat is transferred by molecular motion, through solids and through fluids at

rest, due to a temperature gradient. The heat transfer by conduction, per unit

area per unit time, q, in a steady situation is given by Fourier's law:

-kVT

where

is the thermal conductivity. For a steady one-dimensional temperature

variation

q,=-=

-k-

Heat is transferred by conduction through the cylinder head, cylinder walls, and

piston; through the piston rings to the cylinder wall; through the engine block

and manifolds.

122.2 Convection

Heat is transferred through fluids in motion and between a fluid and solid su

in relative motion. When the motion is produced by forces other than gravity, th

term forced convection is used. In engines the fluid motions are turbulent

(

Chap. 8).

Heat is transferred by forced convection between the in-cylinder gases an

the cylinder head, valves, cylinder walls, and piston during induction, compres

sion, expansion, and exhaust processes. Heat is transferred by forced convectio

from the cylinder walls and head to the coolant (which may

liquid or gas),

from the piston to the lubricant or other piston coolant. Substantial convectiv

heat transfer occurs to the exhaust valve, exhaust port, and exhaust manifol

during the exhaust process. Heat transfer by convection in the inlet system

used to raise the temperature of the incoming charge. Heat is also

transferr

from the engine to the environment by convection.

In steady-flow forced-convection heat-transfer problems, the heat flux

transferred to

solid surface at temperature

from a flowing fluid stream

temperature

is determined from the relation

h,(T

T,)

where

is called the heat-transfer coefficient. For many flow geometries (such as

flow through pipes or over a plate),

is given by relations of the form

("1")'(E$y

(y)

constant

where

and

are a characteristic length and velocity. The terms in brackets

from left to right are the Nusselt, Reynolds, and Prandtl dimensionless numbers,

respectively. For gases, the Prandtl number (c,p/k) varies little and is about 0.7

(see

Sec. 4.8).

When boiling occurs at the surface (i.e., vapor is formed in the liquid), as

may be the case in high heat flux areas on the coolant side in water-cooled

engines, then different relationships for

must be used.

12.23 Radiation

Heat exchange by radiation occurs through the emission and absorption of elec-

tromagnetic waves. The wavelengths at which energy is transformed into thermal

energy are the visible range (0.4 to 0.7 pm) and the infrared (0.7 to 40 pm). Heat

transfer by radiation occurs from the high-temperature combustion gases and the

flame region to the combustion chamber walls (although the magnitude of this

radiation heat transfer relative to convective heat transfer

only significant in

diesel engines). Heat transfer by radiation to the environment occurs from all the

hot external surfaces of the engine.

The theory of radiant heat transfer starts from the concept of a "black

body,"

i.e., a body that has a surface that emits or absorbs equally well radiation

of all wavelengths and that reflects none of the radiation falling on it. The heat

flux from one plane black body at temperature

to another at temperature T2

parallel to it across a space containing no absorbing material is given by

where

is the Stefan-Boltzmann constant

5.67

lo-'

W/m2

.K4.

Real surfaces

are not "black" but reflect radiation to an extent which depends on wavelength.

Gases are far from this black-body idealization. They absorb and emit radiation

almost exclusively within certain wavelength bands characteristic of each species.

These departures from black-body behavior are usually dealt with by applying a

multiplying factor (an

emissivity,

to Eq. (12.4). Similarly, a "shape factor" is

applied to account for the fact that the angle of incidence of the radiation usually

varies over any actual surface. These factors can be calculated for simple cases.

12.2.4 Overall Heat-Transfer Process

Figure 12-1 shows, schematically, the overall heat-transfer process from the gases

within the cylinder through the combustion chamber wall to the coolant flow.

The heat flux into the wall has in general both a convective and a radiation

component. The heat flux is conducted through the wall and then convected from

672

INTERNAL COMBUSTION

ENGINE

FUNDAMENTALS

ENGINE

HEAT

TRANSFER

673

FIGURE

Schematic

121

of temperature distribution

and heat

flc

Distance,

across the combustion chamber

wall.

the wall to the coolant.

schematic temperature profile, and mean gas and

coolant temperatures,

and

Tc,

are shown.

In internal combustion engines, throughout each engine operating cycle, the

heat transfer takes place under conditions of varying gas pressure and tem-

perature, and with local velocities which vary more or less rapidly depending on

intake port and combustion chamber configuration (see Chap. 8). In addition, the

surface area of the combustion chamber varies through the cycle. The heat

flux

into the containing walls changes continuously from a small negative value

during the intake process to a positive value of order several megawatts per

square meter early in the expansion process. The flux variation lags behind the

change in gas temperature. This lag between heat flux and driving temperature

difference is clearly perceptible1 but the precision of measurements to date suffice

only for a rough estimate of its magnitude. Generally, investigators have con-

cluded that the assumption that the heat-transfer process is

quasi

steady

is sufi-

ciently accurate for most calculation purposes. However, gas temperature and gas

velocities vary significantly across the combustion chamber. The heat flux dis-

tribution over the combustion chamber walls is, therefore,

nonuniform.

For a steady one-dimensional heat flow through a wall as indicated in Fig.

12-1, the following equations relate the heat flux

and the temperatures

indicated

where

is the emissivity. The radiation term is generally negligible for SI engines.

Wall:

Coolant side

9cv

hC,,(Tw,

Tc)

(12.7)

If he, and

h,,

are known, the temperatures re, TW,#, Tw,c, and

can

to each other.

FIGURE

122

Ratio of coolant heat flow rate to brake power

a function of engine

speed.

Diffemt

size

and

types of engines:

(a)

small

automotive diesels;

(b)

larger automotive diesels;

(c)

various diesels;

(a)

spark-ignition engines.

(Developed

from

Euginc

speed,

dmin

Howmth.')

123

HEAT TRANSFER AND ENGINE

ENERGY

BALANCE

Figure 12-2 shows the magnitude of the heat-rejection rate to the coolant relative

to the brake power for a range of engine types and sizes at maximum power. This

ratio decreases with increasing engine speed and with increasing engine size. The

smaller diesel engine designs use higher gas velocities to achieve the desired

fuel-

air

mixing rates and have less favorable surface/volume ratios (see Sec. 10.2).

An overall first law energy balance for an engine provides useful informa-

tion on the disposition of the initial fuel energy. For a control volume which

surrounds the engine

(see

Fig. 3-8), the steady-flow energy-conservation equation

where

is the brake power,

e,,

is the heat-transfer rate to the cooling medium,

&,,

is the heat rejected to the oil

(if

separately cooled) plus convection and

radiation from the engine's external surface. It proves convenient to divide the

exhaust enthalpy he into a sensible part

he,,

hdT)

hd298

K),

plus the exhaust

reference state enthalpy

(see

Sec.

4.5).

Then

Eq.

(12.8) can be written:

where

fie,ic

represents the exhaust enthalpy loss due to incomplete combustion.

Typical values of each of these terms relative to the fuel flow

heating value are

given in Table 12.1.

The energy balance within an engine is more complicated and is illustrated

TABLE

121

Energy balance for automotive engines at

maximum power

Q-

H..k

"'4,

(Pereenupe

of fd

beating

vdw)

SI engine

25-28

17-26

3-10

2-5

34-45

Diesel

34-38 16-35 26 1-2 22-35

Sowces:

From

Khovakh,'

Sitkei,*

and

Burke

al?

in the energy flow diagram in Fig. 12-3. The indicated power is the sum of the

brake power and the friction power.

substantial part of the friction power

(about half) is dissipated between the piston and piston rings and cylinder wall

and is transferred

thermal energy to the cooling medium. The remainder of the

friction power is dissipated in the bearings, valve mechanism, or drives auxiliary

devices, and is transferred as thermal energy to the oil or surrounding

environment (in

&,,,,).

The enthalpy initially in the exhaust gases can

sub-

divided into the following components: a sensible enthalpy

(60

percent), an

exhaust kinetic energy

percent), an incomplete combustion term (20 percent),

and a heat transfer to the exhaust system (12 percent) (part of which is radiated

FIGURE

123

Energy flow diagram for

engine.

(rir/Q,)

fuel Bow rate

lower heating value,

heat-transfer

rate

to combustion chamber wall,

exhaust gas enthalpy flux,

brake power,

total friction power,

indicated power,

P,,

piston friction power,

e,,

heat-rejection

rate to coolant,

heat-transfer rate to coolant in exhaust ports, k,,, =exhaust sensible

enthalpy flux entering atmosphere,

k,,

=exhaust chemical enthalpy flux due to incomplete

corn-

bustion,

heat flux radiated from exhaust system,

&+,

exhaust kinetic energy flux,

&i,

sum of remaining energy fluxea and transfers.

Radiation,

incomplete

combustion

Exhaust

enthalpy

Coolant

load

FIGURE

124

1100

1500

1800

2200

mlmia

Brake power, coolant load, sensible exhaust

128

160

245

h,$,

enthalpy, and miscellaneous energy transfers as

percent of fuel flow

heating value for spark-

ignition engine at road-load operating condi-

Vehicle

speed,

kmlh

ti on^.^

to the environment and the remainder ends up in the cooling medium).? Thus the

heat carried away by the coolant medium consists of heat transferred to the

combustion chamber walls from the gases in the cylinder, heat transferred to the

exhaust valve and port in the exhaust process, and a substantial fraction of the

At part-load, a greater fraction of the fuel heating value is absorbed into the

coolant. Figure 12-4 shows data for a six-cylinder

engine operated at road-

load over a range of vehicle speeds. At low speeds and loads, the coolant heat-

transfer rate is 2 to

times the brake power.

Although the heat losses are such a substantial part of the fuel energy input,

elimination of heat losses would only allow a fraction of the heat transferred to

the combustion chamber walls to be converted to useful work. The remainder

would leave the engine as sensible exhaust enthalpy. Consider this example for an

automotive high-speed naturally aspirated

engine with a compression ratio of

15. The indicated efficiency is 45 percent, and 25 percent of the fuel energy is

camed away by the cooling water. Of this 25 percent, about

percent is due to

friction. Of the remaining 23 percent, about

percent is heat loss during com-

bustion,

percent heat loss during expansion, and

percent heat loss during

exhaust.

the

percent lost during combustion about half (or 4 percent of the

fuel energy) could

converted into useful work on the piston

(see

Fig.

5-9).

the

percent heat loss during expansion, about one-third (or 2 percent) could

The

percentages are approximate.

678

INTERNAL

COMBUSTION ENGINE FUNDAMENTALS

average effective gas temperature

T,,

such that

over

heat

the

keat

-tral

engi

was

nsfer

,ne cy

remo

data

cle.

lved

vlc

T,,

is the temperature at which the

from outside.

T,,

was obtained by

~tted versus gas-side combustion

(

wall woi

extrapol

:hamber

Jld

ati

~erature back to the-zero heat-transfer axis. The Nusselt number, dehed as

plotted against Reynolds number, dehed as

where

is the charge mass flow rate, is shown in Fig. 12-5. Taylor and Toong

proposed a power law of 0.75. Annand8 suggests three separate lines for the three

different types of engines covered, with slope 0.7. The diesel line is about

percent higher than the spark-ignition engine line (which corresponds in part to

the radiative heat flux component present in diesels). The air-cooled engine

lower than the

liquid-cooled line, presumably because surface temperatures

are

higher. The average gas temperature values developed by Taylor and Toong are

shown in the insert in Fig. 12-5.

12.43

Correlations

for

Instantaneous Spatial

Average Coefficients

Annands developed the following convective heat-transfer correlation to match

previously published experimental data on instantaneous heat fluxes to selected

cvlinder head locations:

The value of

varied with intensity of charge motion and engine design.

With

normal combustion, 0.35

0.8 with

0.7, and

increases with increasing

intensity of charge motion. Gas properties are evaluated at the cylinder-average

charge temperature

T,:

The same temperature is used in

Eq.

(12.2) to obtain the convective heat flux.

Note that in developing this correlation, the effects of differences

geometry and flow pattern between engines [the ratios y,,

ym and u,,

...,

Eq.

(12.10)] have been incorporated in the proportionality constant

and

the

engines, water-coo1ed (10)

engines, water-cooled (8)

engine, air-cooled

(1)

Equivalence ratio

4th

~PZB

FIGURE

124

Overall engine heat-transfer correlation: gas-side Nusselt number versus Reynolds number for

differ-

ent types of

engines.

See

text for dehition of symbols. Insert gives effective gas temperature (wall

temperature for adiabatic operation),

gas

viscosity

and thermal conductivity

k,.

Lines

have slope

0.7.8.

effect of chemical energy release is omitted. While only data from cylinder head

thermocouple locations were used as a basis for this correlation, it has often been

used to estimate instantaneous spatial average heat fluxes for the entire com-

bustion chamber.

Woschni" assumed a correlation of the form

cylinder bore

taken as the characteristic length, with

as a local

average gas velocity in the cylinder, and assuming

and

pRT,

the above correlation can

written

During intake, compression, and exhaust, Woschni argued that the average

gas velocity should

proportional to the mean piston speed. During com-

L.....

~d expansion, he attempted to account directly for the gas velocities

the change in density that results from combustion

10 m/s), which

rable to mean piston speeds. Thus a term proportional to the pressure

ENGINE

HEAT

TRANSFER

681

680

INTERNAL

COMBUSTTON

ENGINE

FUNDAMENTALS

lations for Instantaneous

Local

rise due to combustion

p,,,) was added

(p,

is the motored cylinder pressure).

The coefficients relating the local average gas velocity

to the mean piston speed

and

pJ were determined by fitting the correlation, integrated over the ~eFeuvre

a1.lS and Dent and Sulaimant6 have proposed the use of the flat-

engine cycle, to time-averaged measurements of heat transfer to the coolant for a plate forced convection heat-transfer correlation formula

wide range of engine operating conditions for a direct-injection four-valve diesel

without swirl.

in Eq. (12.17) is the mean cylinder gas temperature defined by

(

0.036($)0'8(7r'333

(12.20)

Eq. (12.15); the same temperature is used to obtain the heat flux from the heat-

transfer coefficient

h,.

Thus this correlation represents spatially averaged

corn-

where

is the length of the plate and

the flow velocity over the plate. This

bustion chamber heat fluxes.

n applied to

diesel engines with swirl, with

and

evaluated

The average cylinder gas velocity

(meters per second) determined for a

four-stroke, water-cooled, four-valve direct-injection

engine without swirl

was

2sr

expressed as follows

[

GT,

being the solid-body angular velocity of the charge. The heat flux at any radius

Cl~p+C2-@-p~]

r (with Pr

0.73) is then given by

wr2 0.8

where

is the displaced volume, p is the instantaneous cylinder pressure, pr,

@(r)

0.023

(-;-)

[Fa(r)

Tw(r)]

(12.21)

are the working-fluid pressure, volume, and temperature at some reference

state (say inlet valve closing or start of combustion), and p, is the motored

This equation can

used if the swirl variation with crank angle is known (see

cylinder pressure at the same crank angle as p.

Sec.

8.3) and an appropriate local gas temperature can be determined. It would

For the gas exchange period:

6.18,

not

consistent to use the cylinder average gas temperature given by Eq. (12.15)

For the compression period

2.28,

because during combustion substantial temperature nonuniformities exist

For the combustion and expansion period:

2.28,

3.24

between burned gases and air or mixture which has yet to bum or mix with

already burned gas.

Subsequent studies in higher-speed engines with swirl indicated higher heat

An alternative approach is zonal modeling, where the combustion

chamber

transfer than these velocities predicted. For engines with swirl, cylinder averaged

is divided into a relatively

small

number of zones each with its own temperature,

gas velocities were given by Eq. (12.18) with:

heat-transfer coefficient, and heat-transfer surface area history. This approach has

been applied to spark-ignition engines (e.g., Ref. 17), where the division of the

For the gas exchange period

6.18

0.41 7

in-cylinder gases during combustion into a higher-temperature burned gas region

behind the flame and lower-temperature unburned gas region ahead of the flame

For the rest of cycle:

2.28

0.308

is clear (see Fig. 9-4). The heat transfer to the combustion chamber surfaces in

contact with the unburned and burned gas zones [analagous to Eq.

(12.211 is

where

Bod2 and w, is the rotation speed of the paddle wheel used to

measure the swirl velocity (see Sec. 8.3.1).12 Spark-ignition engine tests showed

that the above velocities gave acceptable predictions for this type of engine

An,,

h~,

~(x

Tw)

A,,

b(G

T,)

(12.21u,b)

also.13

respectively. Since

depends on local gas properties and velocities,

. and

Woschni's correlation, with the exponent in Eq. (12.17) equal to 0.8, can be

are not necessarily the same. Examples of how the burned gas wetted areas on

summarized as

the piston, cylinder head, and liner vary during the combustion process are given

h,(wIm2

3.26~(m)-~.~~(k~a)~.~~(~)-~.~~w(m/~)~'~

(12.19)

in Fig. 14.8. Since the burned gas temperature

is much larger than the

burned

gas temperature, the heat flux from the burned gas zone dominates.

with

defined above.

One useful development of this two-zone approach is the division of the

~~h~~be~~~~ examined Woschni's formula and made changes to give better

burned gas zone into an adiabatic core and a thermal boundary layer. The

predictions of time-averaged heat fluxes measured with probes in a direct-

advantages are: (1) this corresponds more closely to the actual temperature dis-

injection diesel engine with swirl. The modifications include use of a length based

tribution (see

Set.

12.6.5); (2) a model for the boundary-layer flow provides a

on instantaneous cylinder volume instead of bore, changes in the &ective gas

more fundamental basis for evaluating the heat-transfer coefficient. The local heat

velocity, and in the exponent of the temperature term.

682

INTERNAL COMBUSITON ENGINE FUNDAMENTALS

ENGINE

HEAT

TRANSFER

683

flux is then given byl8

was developed. Here

ipDdv,

where

iip

is the time-averaged exhaust port

kdT,

Tw)

gas velocity and

is the port diameter. For straight sections of exhaust pipe

downstream of the port, an empirical correlation based on measurements of

average heat-transfer rates to the pipe has been deri~ed:~'

where

is the effective thermal conductivity in the boundary layer,

T,,

is the

0.0483

adiabatic core temperature, and

the boundary-layer thickness. In the laminar

(12.25)

regime

would grow as t1I2; in the turbulent regime

would grow as to.'. Both

The ~eynolds number is based on pipe diameter and velocity. Heat-transfer cor-

growth regimes are observed.

relations for steady developing turbulent flow in pipes predict values about half

Zonal models have also been used to describe DI diesel engine heat trans-

that given by Eq. (12.25).

fer.lg A bowl-in-piston chamber was divided into three flow regions and two

gas-temperature zones during combustion. An effective velocity

12.5

RADIATIVE HEAT TRANSFER

(U2

2k)'lZ

There are two sources of radiative heat transfer within the cylinder: the high-

was used to obtain the heat-transfer coefficient, where

and

are the two

temperature burned gases and the soot particles in the diesel engine flame. In a

velocity components parallel to the surface outside the boundary layer and

spark-ignition engine, the flame propagates across the combustion chamber from

the turbulent kinetic energy. Zonal models would be expected to be more accu-

the point of ignition through previously mixed fuel and air. Although the flame

rate than global models. However, only limited validation has been carried out. front is slightly luminous

(see

color plate, Fig.

9-l),

all the chemical intermediaries

in the reaction process are gaseous. Combustion is essentially complete early in

the expansion stroke. In the compression-ignition engine (and in fuel-injected

12.45

Intake and Exhaust System

Heat

~ransfer

stratified-charge engines), most of the fuel burns in a turbulent diffusion flame as

fuel and air mix together. There can be many ignition locations, and the flame

Convective heat transfer in the intake and exhaust systems is driven by much

conforms to the shape of the fuel spray until dispersed by air motion (see color

higher flow velocities than in-cylinder heat transfer. Intake system heat transfer is

plate, Figs. 10-4 and

10-5). The flame is highly luminous, and soot particles

usually described by steady, turbulent pipe flow

correlation^.^

With liquid fuel

(which are mostly carbon) are formed at an intermediate step in the combustion

present in the intake, the heat-transfer phenomena become especially complicated

(see

Sec. 7.6). Exhaust flow heat-transfer rates are the largest

the entire cycle

The radiation from soot particles in the diesel engine flame is about five

due to the very high gas velocities developed during the exhaust blowdown

times the radiation from the gaseous combustion products. Radiative heat trans-

process and the high gas temperature

(see

Sec. 6.5). Exhaust system heat transfer

fer in conventional spark-ignition engines is small in comparison with convective

is important since it affects emissions burnup in the exhaust system, catalyst, or

heat transfer. However, radiative heat transfer in diesel engines is not negligible;

particulate trap, it influences turbocharger performance, and it contributes sig-

it contributes 20 to 35 percent of the total heat transfer and a higher fraction of

nificantly to the engine cooling requirements.

the maximum heat-transfer rate.

The highest heat-transfer rates occur during blowdown, to the exhaust

valve

and port. Detailed exhaust port convective heat-transfer correlations have

been developed and tested. These are based on Nusselt-Reynolds number correla-

125.1

Radiation from Gases

tions. For the valve open period, relations of the form

Gases absorb and emit radiation in narrow wavelength bands rather than in a

Re;

continuous sPectrum as do solid surfaces. The simpler gas molecules such as H,,

02,

and

are essentially transparent to radiation. Of the gases important in

have been proposed and evaluated." For

LJD,

0.2, the flow exits the valve

combustion, CO, CO2, and Hz0 emit suflicient energy to warrant consideration.

a jet, and Rej

vJDJv,

where

is the valve diameter,

the velocity of the

In gases, emission and absorption will occur throughout the gas volume. These

exhaust gases through the valve opening, and

the kinematic velocity. For

Processes will be governed by the number of molecules along the radiation path.

LJD,

0.2, the port is the limiting area and a pipe flow model with Re

Ddv

For each species, this will be proportional to the product of the species partial

is more appropriate.

is the velocity in the port and

is the port diameter. For

Pressure p, and the path length

In addition the radiative capacity depends on

the valve closed period, the correlation

gas te~~erature

T'hus the emissivity of the gas

can be expressed as

0.022

&e=f(q3

PIL

...,

P,I)

(12.26)

684

INTERNAL COMBUSTION ENGINE FUNDAMENTALS

The mean path length for a volume

with surface area

is given with sufficie

accuracy by

0.9

4V/A

is the mean path length for a hemispherical enclosure.

Standard methods have been developed for estimating

for mixtures of

CO, and

H,O

by Hottel and others (see Ref. 22). Charts based on experimental

data give

eCO2

and

E,,,

as functions of

and

T,.

Correction factors are applied

for total pressures above one atmosphere and for the overlapping of spectral

bands of CO, and

H,O.

Estimates for engine combustion gases at peak con&

0.2

Variation in monochromatic emissive power

and

emissivity, with wavelength, at

three

different

tions give

rz 0.1 and peak heat fluxes due to gas radiation of order 0.2

MW/

crank angles.

diesel engine with

114

bore,

rn2.

This amounts to

-5

percent of the peak convective heat transfer. Since gas

1995

rcv/min, overall equivalence ratio

0.46.

Radi-

radiation is proportional to

Ti,

this radiative flux falls off more rapidly from

ation from piston bowl measured through cutout

peak values than convective heat flux and, when integrated over the cycle, can

Wavelength,

in piston crown.23

neglected.

125.2

Flame

Radiation

matic emissivity. Equation (12.28), combined with Planck's equation for black-

body monochromatic emissive power

Flame radiation is a much more complex process because the detailed geometry

and chemical of the radiating region are not well known. Since the

2xK1

radiation from the optically transparent or nonluminous flames of spark-ignition

eb.

A~(~K~/~TR

(12.29)

engines is small, we will deal only with luminous nontransparent flames where

the radiation comes from incandescent soot particles and has a continuous spec-

where K1

0.59548

W.mZ

and

1.43879

.K,

defined an appar-

tr-. Because the particle size distribution, number density and temperature, and

ent radiation temperature

TR and optical thickness

for the radiating medium.

flame geometry in a diesel engine are not well defined, flame emissivities cannot

An apparent grey-body emissivity

was also calculated from the standard qua-

calculated from first principles. Direct measurements of flame emissivities are

required. A number of measurements of the magnitude and spectral distribution

of radiation from a diesel engine combustion chamber have been made (see ~ef.

e.4 eb,

for a summary). The most extensive of these by Flynn

al.13 in a direct-injection

.I'

eb. AdA

engine used a monochromator to measure intensity of radiation at seven wave-

Figure 12-7 shows sample results for four equivalence ratios at an engine speed of

lengths. The viewing path cut through the piston crown into the central region

2000

revbin. The radiation flux has approximately the same shape and time

the bowl-in-piston combustion chamber. Fuel was injected through a five-hole

span

the net heat-release rate curve (which was determined from the cylinder

nozde and some

air

swirl was provided. At any given crank angle, the distribu-

Pressure curve). During the period of maximum radiation, the apparent emis-

tion of energy over the seven wavelengths was

used

to reconstruct the complete

sivit~ is 0.8 to 0.9; it then decreases as the expansion process proceeds.2J

energy spectrum and to calculate the apparent radiation temperature and optical

previous experiments On the same engine, instantaneous total heat fluxes had

thickness.

been measured at various locations on the cylinder head.14

comparison

The energy distribution was skewed from that of a grey-body model (for

radiant and total heat fluxes (both peak and average) showed that the radiation

which emissivity is independent of wavelength), and the monochromatic emis-

heat flux can

a substantial fraction of the peak heat flux. The average radiant

sivity was well fitted by the equation

flux

is about 20 Percent of the average total flux: the percentage varies signifi-

cantly with load. These conclusions are supported by other experimental data

exp

($)

summarized in the next section.

The radiation or apparent flame temperatures measured in diesels by

used to describe the emissivity variation from clouds of small particles. Figure

several investigators show consistent results (see Fig. 12-8). ~l~~ included.in the

12-6 shows sample results for the monochromatic emissive power and monochro-

figure during the combustion and expansion process are typical values of: (1) the

ENGINE

HEAT

TRANSFER

687

Equvalence

rauo

------

-.-.--

Unstabll~zed

pressure

----

120 150 180

FIGURE

12-9

- Measured and calculated values of

Jc,

as a funct~on of wavelength

monochromatic absorption

coeffi-

ctent,

the

soot concentration.

(From Field

and

Greeves

and

Wavelength

Meeh~n.~~)

temperature of any air not yet mixed with fuel or burned gases;

(2)

the average

temperature of the cylinder contents; and (3) the maximum possible flame tem-

Crank

angk,

deg

perature [corresponding to combustion of a slightly rich mixture

1.1) with

air

at the temperature shown]. The measured radiation temperatures fall between

FIGURE

127

~~di~~t heat

flux

apparent radiant temperature and net heat-release rate as

function

crank

angle

the maximum flame temperatures and the bulk temperature. Such a model has

for

desel enme at

few

different loads. Enlgne and measurement det&

Fig.

12-6; 2000

been proposed, fits the available data, and has been used.27 Zonal models have

rev/rmn.Z3

been proposed (e.g., the burned

gas

region is stoichi~metric'~*

19)

to define an

appropriate flame temperature.

300-

The emissivity of an incandescent soot-burning flame

can

be calculated

2000

FIGURE

128

lm-

Apparent radiatton temperatures masur*

did eng~nes, compared to calculated

maximum

where n is the refractive index,

is the absorption term in the complex refractive

lalo-

M~.,,

gas

adiabatic

flame,

cylinder-mean and air tm-

index,

is the soot concentration

kilograms per cubic meter, and

is the

peratures, during the combustion

perid.

Adla-

density of the soot particles (x2 g/m3).28 The absorption coefficient depends on

batic

temperature

temperature attam*

500-

burning air at ur temperature

with

fuel for cquiva-

wavelength and temperature, is independent of particle size, and depends only on

lena ratio of

1.1.

(~atafrom Dent

and

sulmi6

the soot mass loading. Figure 12-9 shows several estimates of

kJc,

a function

340

360

380 400

420

440

460

Flym

d.,2=

~yn,'~ Kamimoto

et al.;16

ca*ed

The strong dependence on

shows that clouds of soot particles are mark-

crank

angle,

deg

curwsfrom Assarus and Heyw~od.~')

edly not grey. There is a considerable spread in the different estimates shown.

686

Fkil.2

0;to

OOO

from a knowledge of the monochromatic absorption coefficient, which is given by

n2~')'

4(n2

n2u2

I)]

36x

f(2,

(12.30)

688

INTERNAL COMBUSTION ENGINE FUNDAMENTALS

ENGINE

HEAT

TRANSFER

689

This could be the result of different soot compositions (the

C/H

ratio a

lation gave a reasonable match to Flynn's data, an example of which was shown

optical properties) and temperatures. To find a mean value for the

absorpt

coefiicient of a wide spectrum of radiation, the expression

It has been proposed that the apparent absorptivity should be proportional

eb,

to pressure.4p

The assumption is then made that the proportionality constant

~ould be a unique function of the equivalence ratio and crank angle. Although

eb+

is dependent on p for gas radiation, it is not clear that the same proportionality

must be evaluated. For example, for radiation from a black body at temperah

should apply to soot radiation.

1800

K, the mean absorption coefficient is

1300c, per meter, where c, is

kilograms per cubic meter. At higher black-body temperatures, the value of

would

higher.

Annand30 has applied this approach to a diesel engine. The apparent flam

12.6

MEASUREMENTS

emissivity was related to the apparent mean absorptivity by

INSTANTANEOUS HEAT-TRANSFER

RATES

exp (-k,l)

12.6.1

Measurement

Methods

For Flynn's data, the peak emissivity is 0.8 which gives

kal

1.6.

Values of instantaneous heat flux into the combustion chamber walls have been

0.07 m, this gives

and c,

16 g/m3 (x 1 g/m3 at NTP), wh

obtained from measurements of the instantaneous surface temperature. The tem-

a soot loading comparable with values measured in diesel engines during

perature variation at the wall is a result of the time-varying boundary condition

bustion

(see

Figs. 11-42 to 11-44).

at the gaslwall interface. It

damped out within a small distance

mm) from

the wall surface, so measurements must be made at the surface. Various types of

thermocouple or thermistor have been used.g One-dimensional unsteady heat

12.5.3

Prediction Formdas

conduction into the wall is then assumed:

Well-accepted prediction formulas for radiant heat flux in an engine are n

available. Annand has proposed a radiation term of the form

----kg)

at ax

(12.34)

pO(q

sinusoidal variation with time of heat flux into a semi-infinite solid can

where

is the Stefan-Boltzmann constant,

is the mean gas temperatu

shown to produce a sinusoidal variation of surface temperature of the same fre-

is the wall temperature. This term was coupled with a convecti

quency displaced in phase by

90".

The surface temperature

is expressed as a

term to give a correlation for predicting total heat flux. In a first evalua

Fourier series

coupled with Eq. (12.14),

0.6 was prop~sed.~ In a later study with

convective heat-transfer ~orrelation,~~

1.6 was proposed. (Note that si

[A,

cos

(not)

B, sin (not)]

temperature used is the average gas temperature and not the apparent

n=l

(12.35)

temperature,

is not an emissivity.) The limited evaluation of this a

shows that

0.6 gave approximately correct magnitude for

for one e

where

is the time-averaged value of

A, and B, are Fourier coefficients, n is

and was too low for another.32

1.6 gave radiant heat fluxes higher

a harmonic number, and w is the angular frequency (radians per second). The

experimental data.33

boundary conditions are

T,t)

0 and

(constant) at

The

nynn et al.23 developed an empirical expression for instantaneous radia

solution of

Eq.

(12.35) is1

heat flux to fit their data, of the form

T(x,

(T,,

'I;)

exp

4,x)F,(x,

e-e,

a (e-ej+l

"=I (12.36)

2bR

'I(=)

exp

[

360

]

where 8, is the crank angle at the start of the radiation pulse. Correlatio

and

in terms of engine speed, manifold pressure, crank angle at the start

cos (not

4,x)

B, sin (not

4,x)

fuel injection, and the equivalence ratio were obtained and presented. This

tor

and

(no/2a)'I2, where

is the thermal diffusivity of the wall material k/(pc).