Table 4-3

Molecular wt. 96.
Critical pressure (atm) 34.3
Critical temperature CK 567.0
Density (at 298°K) 0.851
Boiling point (1 atm) 377.6
Heat of Combustion (cal/gm) 10249.

4.12 The Method of Solution

The temperature of each gaseous zone is determined by integrating
the energy equations (4-3la) through (4-3lc). Since the liquid fuel temperature
is frozen at the initial wet-bulb temperature, the energy equations (4-2) and
(4-3) can be used to determine the energy transfer, for phase transition during
both the fuel vaporization and the combustion periods. The internal energy is
determined from the temperature, pressure and equivalence ratio. The initial
temperature of a buming zone is calculated using the Newton-Ralphson method,
based on the known internal energies of fuel and "air" before ignition, instan-
taneous heat losses and pressure.

The rate of heat transfer is described by Eqns (4-32) and (4-33). The
mass transfer between zones is described by Eqns. (4-35). (4-42, (4-43), (4-48) and
(4-49). The total mass of the individual zones is calculated by integrating Eqns
(4~14) through (4-18). The instantaneous cylinder Pressure is then determined
from over-all equations of state. The over-all energy balance equation (4-27) and
mass balance equation (4-29) are used to check the accuracy of the computational
procedures at the end of each numerical integration step.

The pollutant zonal mass fractions are obtained by integrating the species

conservation Eqns. (4-95) and (4-96) for NO concentration and by integrating

4-44


Table C-3. Comparison of the Influence of Exhaust
Emission Levels for Series 2 and 3

1500 rpm g=0.6 -20 ATC

Series 3

Low Swirl Medium Swirl High Swirl

No, Oo, NO, oO, NO,
1805 8.8 2431 8.7 2534
1780 8.8 2435 8.6 2200
1555 8.8 2383 8.7 2200
1717 8.8 2396 8.8 2190
1670 8.6 2300 8.8 2100
1685 8.3 2460 8.7 2450
1830 9.0 24ll 8.3

Series 2
2230 8.8 1340 7.0 2800
2290 7.5 1430 7.8 2830
2470 8.1 1200 7.6 2670

1460 8.0 2880


1

-1
R( PTO) = ES (+ 1,9) + exp (rg +149 aan In P)?
°
-1 cal) (4-26)
+ (tg +178 +r, In P)] (om - OK

The polynomial coefficients ay

particularly specified fuel composition by nonlinear least-square curve fitting

, be d and Fr, can be obtained, fora
:

of the calculated results from the NASA equilibrium program (Gordon and
McBride!!3)) . The fuel consists of 50 percent n-heptane and 50 percent
toluene and has a H/C ratio of approximately 1.7 and the coefficients which
have been obtained are tabulated in Tables B-1 and B-2 in Appendix B for the
range:

300 <T < 3500°K
0.7SP ¢ 100 atm
0.0$% <3.5

The fit is within 2 percent for lean mixtures, however there is a larger error of
approximately 5 percent for very rich mixtures. Tables B-1 and B-2 must be
modified for fuels of H/C ratio which differ significantly from 1.7


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling
Time

oO

722
-12
-7

- 2

3

8

13

28

38

360
800
856
1010
1113
1200
1223
1190

Exhaust Concentrations

1500 rpm No,

“30. $9

Low oBe

6 2
Og

Sample Vavle Location

R = 2.7 cms
6= 30° from jet axis
Zz 0 depth (cms)

co UHC
a pen
0.05 540
1.05 1400
1.00 900
0.85 900
0.30 700
0.10 440
0.11 450
0.11 350
0.10 -0

1830 ppm

0.1 percent

0)

8.6

9.0

co, Oy
we %e
0.45 20
3.20 16
4.30 13
4.40 13
4.40 14
4.00 15
3.90 15
4.00 15
3.90 1s

nortinaoaunnooa


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling

Exhaust Concentrations

1500 rpm NO

x
ar
m UHC
High
6 co,
2

Sample Value Location
R = 3.9 cms

@ = 15° from jet axis
Z = 0 depth (cms)

Time NO, co UHC
pom % ppm

-22 265 0.14 190
-12 227 0.36 450
-7 1968 2.2 1700
- 2 1852 1.2 500
3 1936 8.6 400

8 3637 2.0 380
13 3419 2.3 280
23 2324 1.3 230
33 1800 1.0 170
43 1385 0.8 150

2200 ppm

0.25 percent
0
8.6 percent

8.6 percent

Qa
ie)
iS

fe

ArYOVNANANHKO
COrF YO BH HO @

Or ADK HF OM © BS

Oo orIaann


EPA-460/3-76-008-a

STUDY
ON OXIDES OF NITROGEN
AND CARBON FORMATION
IN DIESEL ENGINES -
FINAL REPORT

by
C.J. Kau, PJ. Tyson, and MP. Heap
Ultrasystems, Ene.

2400 Mi son Drive
talifornia 92664

Irvine,
Contract No. 68-01-0436

EPA Project Officers: J... Baseunana and G.D. Kittredge

Prepared for

COORDINATING RESEARCH COUNCIL, INC.
30 Rockefeller Plaza
New York, N. Y. 10020

APRAC CAPE 20-71
and
ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
Office of Mobile Source Air Pollution Control
Emission Control Technology Division

Ann Arbor, Michigan 48105

March 1976


An impression of the differences in the results obtained from the various test
series can be gained from the curves of NO, versus sampling valve opening
time presented in Figure C-4. In Series 1 all the sample valve NO, values
dropped below the exhaust value. Although local values must not necessarily
agree with the exhaust level at 40 ATDC it was thought that the sample valve
values should show some distribution about the final level. Examination of
the sample train indicated that NO was being converted to NO, in the sample
line with subsequent loss of NO, in the condensate. Sample line lengths were
reduced, a chemical drier was eliminated from the train and a water trap fitted
close to the outlet of the sample valve. After these modifications, results
typified by those shown in Figure C-4 for Series 2 were obtained. Unfortun-
ately, before the second test series could be completed, an engine failure
occured and after repair the pollutant emissions for the same nominal engine
conditions were different.

In the third series of tests a complete test matrix was carried out
and the curves presented in Figure C-4 give an impression of their characteris-
tics in comparison with earlier results for the same engine condition. Table
C-1 lists the test matrix which was carried out in the third series of tests, and
a complete listing of experimental data is included in Appendix D.

Three problems are apparent upon examination of this data:

e Variation in exhaust levels for what are nominally the
same engine conditions.

e Differences in the influence of swirl on exhaust emissions from
test to test.

e Errors in the measurement of NO, concentrations.

An impression of the reproducibility of the exhaust NO levels can be gained
from the results presented in Table C-2. Even discounting the obvious rogue
values, the results exhibit a considerable degree of scatter. This scatter may
be associated with slight changes in engine parameters such as ignition timing.
Whatever their cause, they indicate that the in-cylinder sampling results could
have a greater level of uncertainty.


P (atm)

90

80

70

60

——| Calculdtea
——--]}| Measured

50

40

30

A,

20

Ty

10

-50

oOk~-~-+--F +

Qa

10 20 30 40 50 60
~

-40 -30 -20 -10

3

Figure 5-1 Calculated and Measured Pressure-Crank Angle History for Baseline Case
¢= 0.6 Speed = 1500 rpm Cer = 20° and Medium Swirl)


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling
Time

on)

-22
-12
-7
-2
3

8
13
23
33
43

NO

67
72
190
470
1206
2025
2140
1902
2045
1925

fo)

Exhaust Concentrations

1500 rpm NO
0.6 x
-20. co
Medium UHC
4 co,
O2

Q
Oo

pe

SCOFWaAwWwH HHO

ARAN OCDH AND
Onooaoaaoaao kw

Sample Valve Location
R = 5.6 cms

0° from jet axis
0 depth (cms)

UHC

120
150
7500
3000
600
400
390
300
260
200

re)
{e)
.

© O00 0 ABA NYN WOO

2190 ppm

0.05 percent

0
8.9 percent

9.0 percent

ak

RAMON OWN Ow

ONnORh BOON NWN


It was apparent from the calculations conceming NO formation in
lean versus rich zones that the major "valve" on calculated NO is the equiva-
lence ratio of each zone. Thus, it is not surprising that the constants which
influence mixing, strongly affect the NO calculations. It is, however, sur-
prising that the strongest influence is provided by Crix which is associated
with the mass transfer processes which occur after ignition, rather than Cse¢
which controls entrainment by the fuel jet. This can be attributed to the fact
that the calculated peak temperatures for lean mixtures occur close to TDC and
the mass transfer rates between the air zone and burning zones are higher,
thus producing more lean burning zones.

Thu has a stronger influence on soot emissions than on NO. Also,
the relative influence of Coer and Caix on soot production is different from that
on NO. Increased mixing after ignition tends to decrease soot emissions.

Table $-5 lists predicted peak pressures and the crank angle at
which it occurs for the range of constant variables once more illustrating the
significance of the mixing parameters.

Table 5-5. Effect of Empirical Constants on the Prediction of Peak
Pressure (Baseline is P = 78.83 atm at 3° CA)

max
. Percent Changes Predicted Peak Pressure
Variables in Value Pmax Timing °CA
Coot +100 82.42 +3 TDC
- 50 76.49 +3 TDC
Coix +100 88.49 +4 TDC
- 50 72.55 +1 TDC
Coad +100 79.44 +3 TDC
-100 78.22 +3 TDC
Thu + 50 80.64 +4 TDC
- 50 76.75 +3 TDC



Once NO has been formed in lean zones, it could be reduced in rich zones by

such reactions ast?)

NO + CH ——+HCO +N
which would allow the formation of nitrogen by

N + NO ——~N, +0

2
Although NO, has been observed both in flat flames and turbulent diffusion
flames, no attempt has been made to allow for the formation of NO, within the
cylinder. This might occur by the reaction of NO with HO, and its presence
in the exhaust would depend upon the quench rate since the high temperatures
would favor its conversion to NO.

The model allows for the formation of NO both in the homogeneous
burned gas zones and during droplet combustion. The spherical droplet diffusion
flames were originally included because it was believed that diffusion zones
of this type were characteristic of the regions of pollutant formation in diesel
engines, Also, mathematical analyses were available for single droplets con-
tained in an infinite environment. Initial calculations indicated that these
analyses gave the "improbable" situation that the flame volume was greater
than the avilable cylinder volume. Consequently, the diffusion flame analysis
was modified to include a bounded environment "filling up" with combustion
products.

The model for soot formation is similar to that used earlier by other
workers. The only difference is in the definition of zonal equivalence ratio
to include both reacted and unreacted oxygen. Oxidation of soot is also
included.

3-9


NITROGEN OXIDE (NO,), PPM

4000 - Speed: [500 rpm
P p © -20°
Load: =.5 a -15°
Swirf: Medium .
a -10°
Valve
Insertion: Flush
3000 |
e
2000 |
”
2
aos
>
3
2
<
ww
1000 -
s
1 1 L L 1 ;
7150 -100 50 te) so 100 150

Crank Angle, Degrees

Figure C-7. Dependence of Sample Valve Measurement
on Injection Timing

C-15


SAMPLE EQUIVALENCE RATIO

Swi rf Level

Speed: 1500 rpm

o=.5 4 High
ant _ 30° © Medium
ming: Gin = 3 Low
Valve [nsertion: Flush
Lor
7S F
650 Lb
25 1
i) L , 1 4
750 0 +50 +100 +150
Crank Angie, Degrees
Figure C-9. Dependence of Sample Equivalence Ratio

on Swirl - Flush Valve Position

c-21


Input Conditions

Speed

1500 rpm NO

Exhaust Concentrations

2253 ppm

. . ; x
nia ibae tone aad (nominal) oe co 0.05 percent
Swirl Level Medium co 3.9 percent
Fuel Injector 4 2
Oo 8.9 percent
Sample Valve Location
R = 2.7 cms
@= 0° from jet axis
Z = 0 depth (cms)
Sine NO, co UHC CO» 2
(2) pom % ppm % %
-22 183 -06 250 1.0 19,
-12 130 -40 600 0.8 19.
-7 300 -65 1000 1.3 19.
- 2 1080 +10 4000 3.5 16.
3 1640 .20 1700 4.3 1s.
8 2100 +93 150 6.0 ll.
13 2340 85 150 6.4 ll.
23 2411 225 120 5.7 12.
33 2600 04 100 5.9 12.
43 2722 +20 95 7.2 ll.

D-53

anaonoarwon


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO, 1718 ppm

Equivalence Ratio (nominal) +35 0.1 t

Timing (ATDC) =20.0 co +10 percent

Swirl Level Medium UHC 0

Fuel Injector 6 co, $.2 percent
0, 12.7 percent

Sample Valve Location

R= 3.9 cms
6 = 15° from jet axis
Zs 0 depth (cms)

Sampling NO co UHC co. °

Time x 2 2
(o) ppm % pom % %
-22 180 0.05 170 0.25 19.6
-12 139 5.40 240 2.30 11.2
- 7 $19 7.60 6800 4.60 7.0
- 2 475 2.00 1100 3.60 13.0
3 895 1.00 $70 4.00 15.1
8 1304 0.50 450 3.60 14.7
13 1347 0.30 370 3.40 18.7
23 911 0.15 120 3.00 16.0
33 1160 0.16 100 2.40 17.5
43 1048 0.15 100 3.20 16.5

D-42


10,000

(NO) ppm

8,000

6,000

4,000

2,000

2.4 343,000
Fuel Rich Zone (No. 21) :
- —-—- Fuel Lean Zone (No. 24) 42.2 42,500
L 2.0 42,000
1.8 41,500
1.6. 41,000
1.44
LL 1.2
1.0
!
I
LF Fool} 40.8
2 >
', o—-
id N
‘ ~
! N 40.6
! ae
~
! TS ae NO
L f L —— te 04
-10 0) 10: 20 30 40 50 60
Figure 5-6. Instantaneous Zonal Temperatures, Equilvalence Ratios

and NO Mole Fraction for a Typical Fuel Rich anda
Typical Fuel Lean Zone

$-13

T(°kK)


4.3 Air Soray Entrainment and Droolet Vaporization

The analytical representation of the phenomena associated with the
fuel spray dispersion is perhaps the single most important component of any
model of diesel engine combustion. The complexity of the actual situation,
which involves a heterogeneous, confined unsteady jet subjected to cross
flow defies rigorous mathematical description at present. Consequently,
simplifying assumptions and empirical relationships must be included to allow
the rate of fuel-air mixing and droplet vaporization to be quantified. The
analysis developed for inclusion in the overall model has the following
objectives:

e To describe the gross fuel-air distribution within the fuel jet;
e To track the trajectory of fuel elements of known "age";
e To define the state of a fuel-air parcel at the onset of ignition,

i.e., the fuel-air vapor ratio, the liquid vapor fuel ratio and
the dropsize distribution.

The gross oversimplification is made in the analysis of the fuel
soray dispersion that the fuel jet can be considered as a steady unconfined
wall jet of air and vaporizing fuel droplets, shown schematically in Figure 4-2.
The similar transverse velocity profiles are based upon constant injection
conditions throughout the injection period. The steady state properties of the
jet are determined in Eulerian coordinates. Each element of fuel is labeled
upon injection, both with respect to its age (i.e., crank angle at injection) and
its radial location within the jet. Both the location and the conditions of each
fuel-air parcel are determined in Lagrangian coordinates by integrating the
Lagrangian Eulerian (time space) relationship. The rate of droplet vaporization
is determined by the properties of the surrounding air which will vary, both
in space and time. This approach, which may be termed a “pseudo-steady”
spray model,neglects:

- the effect of piston motion upon the spray geometry;
- relative motion between the droplets and the air;


NOMENCLATURE (Cont'd)

Subscripts and Superscripts

a,a
apb

bm

char

crit
coz

el,e2

fg

fld
fb
fdb
fpb

gj

H20
HET
HOM
hu

ig
inj

max

mix

Air (instantaneous)

Air available for air/product mixing process
Air in premixed burning process

Burning process, or backward reaction
Combustion products (nstantaneous)
Convecture heat transfer or clearance

Characteristic properties

Critical conditions

Carbon Dioxide

Dilution process (cumulated)

Vaporization process

Equilibrium

Fuel vaporized (cumulated)

Fuel vapor (Instantaneous)

Liquid fuel ignited (cumulated)

Liquid fuel in buming process (instantaneous)
Liquid fuel burned in diffusion flame process (cumulated)
Fuel vapor bummed in premixed process (cumulated)
Liquid fuel in vaporizing process (instantaneous)
Fuel injection process (cumulated), or free jet
Fuel, or forward reaction

Water

Heterogeneous process

Homogeneous process

Heat-up process

Zonal identification, i= a, fg, (om,1)

Ignition

Fuel injection

I'th buming zone

Shell index

Liquid phase or droplet surface

Maximum

Mixing process

8-3


4.6 Combustion

Combustion may take place within the cylinder in several modes.
Fuel can exist in either the vapor state, or liquid droplets, the air can be
mixed with the fuel prior to reaction or a flame can separate the reactants and
diffusion of both reactants will, therefore, dictate the rate of heat release.

The rate and timing of the heat release will control both engine performance
and pollutant formation. In reality this complex process will involve droplets
burning as clouds, combustion close to solid surfaces, fuel impingement on the
piston bowl vaporization and subsequent combustion. However, the simplified
approach included in this model only takes account of:

e Homogeneous premixed, fuel vapor mixed with the air prior to
ignition

e Heterogeneous, fuel burns as single droplets surrounded by a
diffusion flame in a fuel lean zone.

e Homogeneous diffusion, diffusion flames cannot be supported around
droplets existing in fuel rich zones; immediately upon vaporization
this fuel reacts with its surroundings giving equilibrium products for
the composition and conditions of that zone.

4.6.1 Homogeneous (Premixed) Combustion

Equation 4-45 determines the point of ignition for the premixed
fuel vapor-air produced in each parcel during the preparation to bum period.
The temperature of the mixture after combustion of the fuel vapor is assumed to
be the equilibrium temperature at the equivalence ratio, pressure and specific
internal energy pertaining to that parcel. This assumption will only be valid
when the residence time is greater than 1074 seconds since certain radicals
will not have equilibrated before that time. This time scale ts slightly less
than one degree C.A. for an engine operating at 1500 rpm.


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling
Time

9)
712
-7
- 2

3

8

13

23

33

43

NO

197
201
852
2160
1880
1470
1150
976
912

Sample Valve Location

R
8
Zz

1500 rpm
0.6
-12.
Medium

= 3.9 cms

= 30° from jet axis
= 0 depth (cms)
co UHC
cn bpm
0.05 200
0.15 220
4.60 300
2.80 250
2.50 200
1.70 190
0.28 190
0.15 160
0.15 110

Exhaust Concentrations

NO,

co
UHC

co

D-28

1395 ppm

0.1 percent

3.0 percent

8.8 percent

co, O,
= a
0.54 19.5
0.60 19.4
7.40 5.2
8.50 a)
7.70 +0
7.00 AS
5.00 12.9
4.40 13.9
4.40 13.9


Those empirical constants which have been termed adjustable are those which:

e have a high level of uncertainty associated with them, and are
considered to have a significant effect upon the prediction of
pollutant formation and engine performance.

e are peculiar to the present model.

The value of these constants will depend, to some degree, upon the characteris-
tics of the engine being simulated. However, their value can be ascertained
within limits from single cylinder experiments and exploratory model calcula-
tions. Seven constants have been placed in the second group which includes:

C oof Coat (Equation 4-42) allows the rate of air entrainment by the jet
to be modified to take account of cross flow effects. This parameter has a
significant influence on the early stages of combustion, which is mainly
premixed, and is therefore, responsible for the rapid pressure rise immedia-
tely following ignition.

Cnix The parameter Cix accounts for the "random mixing" process that
is assumed to occur between burned zones, which will contain varying amounts
of liquid and gaseous fuel, and the "air" zone. Thus, Onn ix Wi have a strong
influence on the processes occurring during the later stages of heat release.
Variations in Ca x Primarily affect the predicted cylinder pressure after ignition,
and the value of co xis chosen primarily to give a fit to the measured pressure

curve and secondarily, to match observed exhaust NO levels.

Rig Aig allows the ignition delay to be predicted correctly. Values for
Aig can be found in the literature, but these cannot be considered universal
since the ignition delay depends upon several operational parameters such as
nozzle type, chamber configuration, etc. Therefore, it is considered desirable

to tune Aig for a particular engine configuration.

Ast The model does not attempt to include the detailed kinetics of soot
formation, and it is considered that there is a large degree of uncertainty
attached to the parameter Ast which is obtained by matching the predicted and

measured soot concentration levels.

5-3


Input Conditions

Speed

Equivalence Ratio (nominal

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling
Time

~22
-12
-7
-2
3

8
13
23
33
43

NO.

264

330
1518
1354
2360
4300
3234
3340
2900
2248

1500 rpm
0.6
-20.0
High

Exhaust Concentrations

NO,

co
UHC
CO,

O2

2534 ppm

0.25 percent
0
8.0 percent

8.4 percent

Sample Valve Location

R
8
Z

= 3.9 cms

= 0° from jet axis

= 0 depth (cms)

co UHC SO» 2
az 2pm * %
0.08 160 0.8 18
0.17 180 1.5 17.
0.46 180 5.1 12.
3.8 180 6.1 8.
4.3 150 6.9 7.
1.7 130 9.0 6.
1.8 130 9.3 4
1.4 130 10.5 3.
1.0 -0 11.0 3.
1.0 60 11.0 3.

Aan nr Oh Rh HD


droplet vaporization. The ratio of the vaporization rate, thee to the
vaporization rate without swirl (my, is given by:

my = 1.04+C. _ Rel’? pp 17? (4-43)

(mn) 5 evap

where the Reynolds number is based upon both the droplet diameter and the
swirl velocity and it is assumed that Pr=1. The empirical constants

Coven is set at 0.276.

The vaporization rate without swirl is given by

(a), s4np Dry In 1+} C_(T, - T)

P (4-44)

Under high pressure high temperature conditions the heat of vaporization is a
function of droplet temperature Tt

b= bea ( Ti. > 29

Tout 7 Th 0.38
eri 8

where L938 and Tort are the latent heat at 298°K and the critical temperature

of the fuel respectively. The droplet temperature is assumed to have a uniform
value equal to the stable’ wet-bulb temperature based upon the conditions of
the surroundings at the beginning of the fuel injection. Methods for evaluating
the stable wet-bulb temperature of a vaporizing droplet are discussed in the
recent work of Rosner and Chang !20) .
account for the time taken for the droplet to attain the stable wet bulb
temperature.

A mean heat-up time Thu 1S used to


The values of the adjustable constants used in later calculations
were determined by fitting the predictions to measurements obtained when the
engine was operated under the following conditions (baseline case):

Speed 1500 mm

Load equivalence ratio 0.6
Compression ratio 17:1

Swirl Medium

Fuel injection timing 20° BTDC

Injection duration 17° CA

Air pressure 30 in. Hg. absolute

Mean Wall temperature 500° K

Initially the model was tuned using the baseline case to give an
acceptable fit of the measured and calculated cylinder pressure as a function
of crank angle. The computed pressure curve for these engine conditions is
presented in Figure 5-1, together with the measured pressure curve. In order
to establish confidence in both the model and the values chosen for the
empirical constants, further computations were made with injection times of
-25° and -12°. These computations were made without subsequent adjustment
of any of the constants. The resulting calculations can be compared with mea-
surement in Figure 5-2 and it can be seen that there is excellent agreement
instantaneous cylinder averaged NO concentrations for all three injection
timings. Included on Figure 5-3 are the measured exhaust NO, values for
these conditions. The calculated averaged instantaneous soot concentration
(in gm/gm-of-fuel) for all three cases are shown in Figure 5-4 and the calculated
engine performance parameters are listed in Table 5-3.

Table 5-3
Calculated Engine Performance Parameters
a inj -12 -20 -28
Indicated Mean Effective Pressure (psi) 83.3 | 82.2 | 74.25
Indicated Horsepower (hp) 22.5 | 22.1 | 20.05

Indicated Specific Fuel Consumption (lb/hp-hr) 0.441 10.446 | 0.494

wo
1
a


Input Conditions

Exhaust Concentrations

Speed 1 inal 3°00 rpm No, 2450 ppm
Fea teeceie amined 0.8 co 0.05 percent
Fuel Injector pee Co, 8.5 percent
Oo, 8.4 percent
Sample Valve Location
R = 2.7 cms
6 = 54° from jet axis
Z = 0 depth (cms)
Sampling No co fo)
Time x co UHC 2
(0) opm % ppm % %
-22 131 0.05 125 0.6 19.9
-12 402 0.80 150 4.0 15.0
-7 1500 2.50 300 7.0 +0
- 2 1600 5.00 900 7.0 0
3 1000 4.00 1000 4.8 8
8 1566 0.60 200 3.0 15.0
13 1840 0.20 150 4.9 13.2
23 2692 0.20 120 7.1 11.0
33 3500 0.30 100 8.1 9.5
43 3250 9.20 75 8.1 8.9

D-54


NOMENCLATURE (Cont'd)

N2 Nitrogen
NO Nitric Oxide
02 Oxygen

° Initial condition

os Stoichiometry

r Radiation

s Soot: Swirl

sf Soot formation process

so Soot oxidation process

turb Turbulence

v Vitiation process (cumulated)
w Wall

wi Wall jet

€ Centerline

(+) Rate in crank angle (i.e. d/dé)
(~) Averaged value

@

Ambient conditions

Note: Where other symbols are used, they are defined in the text.


Input Conditions Exhaust Concentrations

Speed 1800 rpm NO 1209 ppm
Equivalence Ratio (nominal) 0.6 x

Timing (ATDC) -12. co 0.1 percent
Swirl Level Medium UHC 0
Fuel Injector 6 CO, 8.2 percent
Oy 9.2 percent
Sample Valve Location
R = 5.6 cms
@ = 30° from jet axis
Z = 0 depth (cms)
Stime NO, co UHC CO,

(2) ppm % em se <a
-12 72 0.09 560 0.35 19.
-7 70 0.09 $40 0.30 19.
- 2 230 0.65 560 1.80 17.

3 199 10.00 460 3.80
8 735 6.80 900 $.40

13 1330 3.80 800 6.10

23 1130 1.15 420 5.80 10.

33 957 0.50 370 4.60 13.

43 730 0.40 240 4.00 16.

D-31

wo YON © © © © ©


Swirl Level
Speed: 1500 4 Hi
4oool pe rpm High
Load: os. © Medium
a, =~ 990
Timing: 9 inj 20) a Low
3000 | 3 a
3
z i
a >
= 3
fo} 3
= 5
w uw
o-
x 2000, . .
3 $745
=z
8
fe
5
Zz
1000 | }oy=3
1 1 L L 1 :
-150 100 -50 ts) +50 +600 +1.50

Crank Angle, Degrees

Figure C-5. Dependence of Sample Valve Measurement
on Swirl Level - 11/16" Valve Insertion


Flame Radius

The location of flame surface can be identified by defining 3 22, - Zoe
and making use of boundary conditions at i and Tee thus,

TE. te “ ts «x -1 (4-70)
Ty BoA Boy
where
Y
lie. . 98 ;
BD = Le p(t)
Y
a= at!
a> T= ¥p
x fn (1 + Bo)

£n(1+B,)

j = Stoichiometric Oxygen-fuel Mass Ratio

q = Heat of Combustion

lam. mperature

In a similar manner, the temperature at the flame surface is obtained
from

te 2 Fone! ~ %p (4-71)
f Ter ,
1+ ft
( Yogs 4 )

Additional information, such as major species and temperature distributions
around a fuel droplet, are also required when it becomes necessary to evaluate

the production of nitric oxide in these diffusion flames. These relations,

4-30


exhaust smoke is detected when the timing is retarded. Approximately 12 percent
reduction in peak pressure is observed for every 8° CA injection timing delay.

Effect of Load

The effect of overall equivalence ratio, %, on NO and soot emission
is shown in Figure 6-2. It has generally been observed that both NO and soot
emissions decrease with load. The calculations were made with a constant
injection rate and the load was varied by reducing the injection duration. The
explanation for the increased soot emission at the lowest load ($= 0.3) is
uncertain, and this is contrary to all the other experimental observations, but
it could reflect a decrease in the rate of soot oxidation because of the lower
temperatures.

Effect of Speed

Calculations were made for two engine speeds while the overall
equivalence ratios and injection rates were maintained constant, thus the
duration of fuel injection was increased from 17° to 23° corresponding to an
engine speed increase of 1500 rpm to 2100 rpm. The comparison between the
calculated and measured data is shown in Figure 6-3. The effect of residence
time in a high temperature and pressure environment which is inversely propor-
tional to the engine speed, is the dominating factor. The other effects of higher
speed in the real engine such as higher injection pressure, higher valve overlap
are not reflected by the calculations, however, compared to the residence time
effect these are of minimum significance.

Effect of Comoression Ratio

Decreasing the compression ratio will cause a decrease in both the
cylinder temperature and pressure, both of which will tend to reduce the rate
of NO formation. However, there are other important influential factors such
as the effects of heat transfer and ignition delay.

The overall effects of the compression ratio on emission level are
shown in Figure 6-4. The model predicts the trends; however, the comparisons
of absolute magnitudes are very poor. The exaggerated influence of compression

6-3


The NREC (Norther Research and Engineering Corporation) Model
{Bastress, Chang and Dix
This model includes a prescribed heat release schedule which has

two stages:
- an initial premixed triangular distribution;

- a secondary Gaussian distribution.

In both of these stages the fuel-air ratios over which heat release takes place
are specified. Random mixing is assumed to account for subsequent dilution

of the combustion products and Zeldovich kinetics are used to describe NO
production. The model requires the arbitrary specification of six parameters:

a fuel vaporization rate, fuel burning rate, dilution rate, an overall heat transfer
coefficient, a mean air-fuel ratio for heat release, and an air-fuel ratio excursion

parameter for the premixed heat release schedule. One major disadvantage of

the NREC approach is that there is no link between the value of these parameters

and the actual physical processes. Such a link will be necessary if the model

ts to be used to assess the effect of design changes which influence the details
of the combustion process.

)

e@ The CAV Model [Khan, Greeves, and Probert ‘ , and Khan and

Greeves

The CAV Model represents an advance from the ptevious model in
that it includes a fuel spray model. The spray is modeled by a conical free jet
which impinges upon a plane wall, thus simulating the impact of the fuel jet on
the piston bowl. Experimentally determined ignition delays are input as isa
triangular premixed heat release distribution. The pre-exponential constant in
the modified Zeldovich NO formation mechanism was increased by a factor of
S.37 over the literature value in order to match experimental exhaust data. This
model also includes an Arrhenius type expression to allow soot formation to be

predicted.

e The Cummins Model (Shahed, Chiu and Yumlu 5 ) and Shahed,
Chiu and Lyn (8) ]

(s

A preliminary version of Cummins Model (Shahed et al ) ) cor-

rectly represented the cycle thermodynamics, but ignored mixing and spray


4.0

6.0

7.0

8.0
9.0

TABLE OF CONTENTS

Page No.
Summary l-1
Introduction 2-1
The Methodology of Diesel Engine Modeling 3-1
3.1 The Objectives of Modeling 3-1
3.2 Review of Existing Models 3-2
3.3 A Qualitative Description of the Ultrasystems 3-4
Model
Detailed Description of a Model to Predict Pollutant 4-1
Formation in Diesel Engines
4.1 Cycle Thermodynamics and Heat Transfer 4-1
4.2 Fuel Injection and Spray Characterization 4-16
4.3 Air Spray Entrainment and Droplet Vaporization 4-17
4.4 Ignition Delay 4-21
4.5 Air Product Mixing 4-21
4.6 Nitric Oxide Formation 4-33
4.7 Soot Formation and Oxidation 4-38
4.8 Nitric Oxide and Soot Conservation Equations 4-39
4.9 Equilibrium Compositions 4-40
4,10 Fuel Representation 4-41
4.11 Method of Solution 4-42
4.12 Indicated Engine Performance and Engine Emission 4-43
The Empirical Nature of the Model 5-1
5.1 The Nature of the Empirical Constants 5-1
5.2 Experimental Engine and Exploratory Computations 5-6
5.3 Sensitivity Analysis 5-13
5.4 The Role of Droplet in NO Formation 5-17
Comparisons Between Engine Emission Levels and Model 6-1
Predictions
6.1 Effect of Engine Operational Parameters 6-1
6.2 Effect of Charge Intake Parameters 6-7
6.3 Effect of Fuel Injection Parameters 6-11
Limitations of the Model and Recommendations for 7-1
Future Work
Nomenclature 8-1
References 9-1
Appendix A - Simplified Representation of Fuel Spray A-1
Appendix B - Coefficients for Equations (4-25 and (4-26) B-1
Appendix C - Characterization of Diesel Combustion by C-1
Direct In-Cylinder Sampling
Appendix D - Sampling Valve Data Test Series 2 D-1]

ii


Input Conditions Exhaust Concentrations

Speed 1500 rpm No, 2200 ppm
Equivalence Ratio (nominal) 0.6 t
Timing (ATDC) -20. ogc 7° Pereen
Swirl Level High co 8.4 percent
Fuel Injector 6 2 .

fe} 2 8.6 percent

Sample Valve Location

R = 3.9 cms
a= 45° from jet axis
Z = 0 depth (cms)

Ee NO, co UHC CO,

pom % ppm %
-22 152 0.08 58 1.3 19.5
-12 350 0.60 78 3.4 15.2
-7 410 1.00 120 3.2 15.2
-2 1085 5.20 240 5.2 8.8
3 2130 1.20 95 5.8 11.2
8 1745 2.20 86 7.0 8.6
13 1530 1.40 80 6.8 9.4
23 1490 1.20 90 7.2 9.6
33 1470 0.85 80 7.2 9.5
43 1140 0.45 60 6.8 10.4


(i) at the droplet surface (r= r,)

TT, (4-54)

Yor = 0 (4-55)
ay,

~ ppDma je = [OVO Yi] (458)

ph], - ow, (4-87)

Condition (4-56) is derived from species continuity at the liquid-gas interface.
Condition (4-57) is deduced from an energy balance assuming a constant
liquid phase temperature.

(ii) at the flame surface (r = r,)

Yoo = 0 (4-58)
Ye = 0 (4-59)
dy ay,
l o2) _ f
-F7 (ed ar ds = (PD a do (4-60)
ay
- —f) . aT oT 4-61
qep(—t) = ag), + (AB) (4-61)

Condition (5-60) states that the deliveries of fuel vapor and oxidant to the flame
surface are in stoichiometric proportion. Condition (5-61) prescribes that the
heat of combustion is. equal to the sum of the heat transferred inward to the
droplet and the heat transfer outward to its surroundings.

4-27


Input Conditions

Speed

Equivalence Ratio (nominal)

Exhaust Concentrations

1s00 rpm NO
0.6 x

1300 ppm

Timing (TDC) -12 oc 9.08 percent
Swirl Level Medium co 8.4 percent
Fuel Injector 6 2
04 8.6 percent
Sample Valve Location
R = 2.7 cms
6= 30° from jet axis
Z = 0 depth (cms)
sete NO, co UHC CO, 7)
(0) ppm % ppm % %
-22 56 0.05 420 0.7 20.0
-17 94 0.25 480 1.2 19.5
-12 155 1.50 500 2.5 18.2
-7 280 2.00 1800 3.4 14.2
- 2 820 5.00 2300 8.0 4.8
3 890 4.20 3000 7.2 6.0
8 990 6.50 7100 7.0 6.0
13 850 2.50 1200 6.0 9.8
28 1160 0.35 580 5.4 13.0
38 1250 0.20 400 $.3 13.5


Z1-S

Mass Fraction

0.2

1.0F | slice eee Ko =
/ A - ATW A
/ aw
/ “Xx
0.8F / x 7 --- (im gy/me}) Overall Fuel Injection
/ / —o— (im g/m) Unburned Liquid Fuel
/ 4 —o— (mg/m gy) Burning Liquid Fuel

(mg/m) Unburned Fuel Vapor

/
/ A -zn— (ig, /m5)) Overall Fuel Burned

o 8 .
fj
Oey

-20 -10 TDC 10 20 30 40 50

Figure 5-5. Distribution of Fuel in Different States (Baseline Operation)

60


The relatively minor influence of the heterogeneous phase on the
total production of NO as shown by the model can be explained by:
e The majority of the droplets are burned in fuel rich zones where
diffusion flames cannot be established because of the lack of
oxygen. Less than 20 percent of the droplets have sufficient

oxygen (assumed to be 2 percent in these calculations) to
allow the formation of diffusion flames.

e Most of the droplets react in atmospheres containing NO which

may actually result in the destruction of NO, if not, it will certainly
reduce the rate of production.

Figures 5-11 and 5-12 present the results of calculation demonstrating
the influence of the droplet environment on the production of NO. The calcula-
tions were carried out with a droplet radius ry of 1Su and a constant ambient
pressure and temperature of 50 atm and 2000°K respectively, and the major
ambient species were assumed to be in equilibrium. The effect of ambient NO
concentration (for 6, = 0.4) is shown in Figure 5-11, the NO formation rate
decreases linearly with increasing ambient NO concentration, and when the
environment contains NO concentrations in excess of the equilibrium value
the rate becomes negative. Figure 5-12 shows the influence of ambient
oxygen concentration for both zero ambient NO and equilibrium ambient NO.

The NO formation rate increases rapidly with increasing ambient oxygen
concentration.


EPA-460/3-76-008-a
March 1976

STUDY

ON OXIDES OF NITROGEN
AND CARBON FORMATION
IN DIESEL ENGINES -
FINAL REPORT

U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
Office of Mobile Source Air Pollution Control

Emission Control Technology Division
Ann Arbor, Michigan 48105


APPENDIX A

Simplified Representation of Fuel Spray

The basic fuel spray model assumes a two-phase round jet in a quiescent
ambient atmosphere which impinges on a flat wall in a finite distance. A schematic

representation of the jet is shown in Figure 4.2 . The jet is characterized by four
distinct flow regions:

e The initial region: extends from the orifice exit plane to the apex of
constant velocity core x,

e The main region: includes that part of the jet from the end
of the potential core to the wall. This region is characterized by the
decay of centerline velocity and self-preserving transverse profiles

e The transient region: the region where the jet is deflected and trasnformed
from a free jet to a wall jet

e The wall region: includes that portion of the jet where it spreads
three-dimensionally and axisymmatically with respect to axis
of injection.

(i) Initial Region

The growth law inthis region ts calculated by

Pa ) (A-1)
eGo

db = 0,135 (1+
ax

(34)
where constant on = 0.135 was used by Newman and Brzustowski .

(ii) Main Region

Self-preserving velocity and fuel concentration profiles (abramovich'!®))

are assumed.
vo
Vv

g

=(1- 6795)?


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO, 2200 ppm
Equivalence Ratio (nominal) .35
. it
Timing (ATDC) -20.0 co 0.09 percen
Swirl Level Medium UHC 0
Fuel Injector 6 co, 6.0 percent
o, 12.2 percent

Sample Valve Location

R = $.6 cms
3 = 30° from jet axis
Z = 0 depth (cms)
‘Time NO, co UHC CO, °,
(9) ppm % _ppm_ % %
-22 160 0.11 250 0.32 20.0
-12 132 0.15 400 0.32 20.1
- 7 887 4.00 360 6.60 8.1
-2 570 10.00 1000 4.60 4.1
3 1200 $.20 310 6.60 6.5
8 1694 1.05 280 6.50 11.4
13 1860 0.65 240 §.80 12.5
23 1840 0.30 160 4.60 13.8
33 880 0.20 70 3.40 17.2
43 928 0.20 90 4.40 17.0

D-46



The possible presence of carbon in the prove and its effect on NO
reduction remains an open question. Sample lines must be kept short to reduce
NO to NO, conversion; this effect must be significant with typically 10 percent
conversion even with short sample lines.

In the results presented in Figures C-4 to C=7 the probe was located
well out near the bowl edge and somewhat downstream of the jet impingement
point. It seems reasonable to hypothesize that samples collected at this point
will be lean and will, therefore, be representative of regions of high rates of
NO formation. As time proceeds it can be assumed that gases in the vicinity of
the sample valve will eventually show a decrease in NO concentration for several
possible reasons:

- as time proceeds work extracted by the piston will cool the zones

and reduce the NO production rate.

- as the temperature drops further mixing with available air will serve

to dilute the NO concentration faster than production can compensate

- as time proceeds the sampling point will begin to experience zones

containing "younger" fuel; that is, fuel which entered the system
after ignition. Such zones are likely to have been initially richer
in composition before reaching the sampling point because their
fuel was not consumed in the intial stages of heat release. Hence
such zones would never experience high NO levels even though at
the time of sampling these may have reached a lean (but cool) con-
dition. .

Indeed all of the test conditions exhibited this rapid rise to high NO values

followed by decay to quite low values.

In all cases the NO concentration at the time of exhaust valve
opening was below the exhaust emission measurements by typically 1000 ppm.
An obvious and easy explanation for this would be that there is a significant
loss of NO in the sampling system by some unspecified mechanism. While
not ruling this out completely it appears not to be the explanation. Although
the sampling system has never been calibrated under complete simulation of
diesel conditions it has been satisfactorily checked against high pressure cal-
ibration gases. However, the possibility of carbon contamination of the valve
remains an open question.


Input Conditions

Exhaust Concentrations

Speed 1500 rpm NO 1670 ppm
Equivalence Ratio (nominal) 0.6 x
Timing (ATDC) -20. co 0.1 percent
Swirl Level Low UHC 0)
Fuel Injector 6 co, 8.5 percent
oO, 8.6 percent
Sample Valve Location
R = $.6 cms
@= 30° from jet axis
Z = 0 depth (cms)
srine NO, co UHC CO, 4
(2) ppm % ppm % %
-22 120 0.20 $000 0.61 19.5
-12 109 0.17 7300 0.52 19.8
-7 200 0.46 9500 1.50 18.5
- 2 47) 4.50 8100 2.60 13.2
3 1011 7.20 6700 $.40 6.7
8 17390 3.80 5700 6.60 7.8
13 1690 2.50 4700 6.20 9.3
23 1580 1.60 4100 6.20 10.5
33 1100 1.10 3100 5.60 12.0
43 1100 0.50 2600 4.80 12.8

D-23


ACKNOWLEDGEMENTS

This report presents the outcome of almost four year’s work and many
individuals have contributed to the final product. The authors would like to
express their thanks to several present and former Ultrasystems staff members,
G. P. Carver, C. McComis, K. Maloney, L. J. Muzio, C. H. Waldman and
R. P. Wilson, Jr., for their efforts in the early stages of the model's develop-
ment and in the conduct of the experimental investigations.

The CAPE 20-71 Steering Committee of the Coordinating Research Council
and the EPA originally defined the project and guided the work to it's final
outcome. The ultimate value of this project is largely due to the Committee,
without whose help and criticism it would have been difficult to complete. The
authors sincerely acknowledge their gratitude to the following individuals who
have served on the Steering Committee during the lifetime of the project:

F, J. Hills, Committee Chairman Mobil Research & Development

Corporation
J. L. Bascunana Environmental Protection Agency
N. G. Beck International Harvester
T. C. Belian Coordinating Research Council
J. E. Bennethum General Motors Research Laboretory
G. L. Borman University of Wisconsin
W. L. Brown Caterpillar Tractor
J. C. Hoelzer International Harvester
G. D. Kittredge Environmental Protection Agency
G. A. Lavoie Ford Motor Company
D. F. Merrion General Motors-Detroit Diesel Allison
P, C. Meurer International Harvester
J. M. Perez Caterpillar Tractor
S. M. Shahed Cummins Engine
A. D. Tuteja General Motors-Detroit Diesel Allison
A. V. Wilson Cummins Engine
A. E. Zengel Coordinating Research Council


Input Conditions

Speed

Equivalence Ratio (nominal)

Exhaust Concentrations

1500 rpm NO
0.6 x

2100 ppm

Timing (ATDC) ~20. co 0.07 percent
Swirl Level Medium con 3.3 percent
Fuel Injector 4 2
0, 8.6 percent
Sample Valve Location
R = 3.9 cms
9 = 0° from jet axis
Z = 0 depth (cms)
seine NO, co UHC CO, oP)
(2) opm % ppm % %
-22 106 0.04 200 0.4 20.3
-12 gl 0.38 7530 0.5 20.0
-7 124 0.S5 850 0.7 19.5
- 2 1333 0.15 300 3.5 18.9
3 2240 1.20 280 5.4 12.0
8 2258 0.75 250 6.6 11.0
13 2440 0.60 210 6.0 11.9
23 2140 0.55 210 6.5 11.0
33 1519 0.30 160 5.4 12.5
43 1360 0.20 140 5.0 13.5


(°¢/ Pa) =r - ¢15)
("Pale

(A-3)
where é= + and the constant growth law is assumed:

(A~4)
ab = C, = constant
dx fj
where C,, = 0.175 corresponds approximately to 10 degree half spray angle.
Utilizing the law of conservation of momentum, the decay of centerline velocity
in main region can be derived as:

v4
“Tel Tt 1
1 | ees ( Es \ ( m ) (assy
eijtes =, (ts \ _, (a
42 iz Tea leg AB Tegleg PP*Teg

Similarility from the law of conservation of fuel mass, the decay of fuel concentration
in the main region can be obtained as:

Pe J
(x) _ of (a8)
a /% cA Vg ba,
The values of the integrations
1
1.5,
I, =2rfo (1-§ "") ed
fn f beg (a-7)

Q

are listed in Table (A-1) for various n.

Tr and Jon appearing in the above equations are the flux fuel mass and the
flux of momentum, respectively.


K is a mean attenuation coefficient which will depend upon the concentration

of radiating species (gases and particles), the number of particles, the particle
cross section and the optical properties of those particles. McAuley!!5) gives
a value of Kas 5.7x 102 em3/gm x the zonal fuel concentration. Ly and Ay

are the characteristic length and surface area of the zone respectively.

Similar expressions are also used for evaluation of the rate of radiative
heat transfer from fuel vapor and “air" zones to the cylinder wall. However,

they are negligible because of the very low zonal temperatures or the very low
fuel concentration.

4.2 Fuel Injection and Soray Characterization

For the purposes of this work, the fuel jet is treated as an
incompressible jet with a constant flow rate and the injection velocity is
derived by:

fo gs / (Ors oezieCp) (4-34)
where Tg the modified fuel flow rate is defined as

= mass of fuel injected ver power stroke Ae
, = Ae N (4-35)
J ing “nozzle

Me


1.5

inc], (Soot) ,

Line

Calculated 2077 ppm 139 mg/m°
Measured 2050 ppm 10% opacity ----
SS
SS
SS
=~
SS
NS
~

1500 1800 2100

tm

Figure 6-3 Effect of Engine Speed

6-5

1.5

1,25
Soot)
Soot),

1.0

275

0.S


10

1079 ——_——

10 — =0.0
Po peer
_—- —
tae
Pots

\

3
N“
S ‘\ \
& 107 \ io}
° \ <
e \ Byo |
\ ol. n
\ \
\
-8 <2
10 . lo
Le
\
\
\
-9 3
10 . 10
\
\
-10 -4
10 or 0.2 ope o.6 oe) T.0°
?

Figure 5-12

2

Effect of Ambient Oxygen Concentration on Rate

of NO Formation Around a Burning Droplet

5-23


During the entrainment stage, the fuel droplets are treated as a single
component hydrocarbon compound which will begin to vaporize when a stable
wet bulb temperature is obtained. The rate of evaporation is influenced by the
swirl velocity of the air sweeping through the jet, thus as the fuel element
passes along the jet, its vaporization rate is increased, both by virtue of the
increase in temperature of its environment, and also because of the increased
angular velocity. The fuel that is vaporized remains in the parent shell. Thus,
immediately before ignition the fuel jet consists of parcels of fuel, all mixing
with air, which contain droplets in various stages of vaporization. The multi-
orifice fuel injector is handled by dividing the total available air equally between
the separate jets and assuming all jets are exactly similar.

Quite obviously, this is a very simple picture of a complex process
which ignores all three dimensional effects, non-steady phenomena and influ-
ence of confinement. Several omissions should be enumerated:

e Cross flow — the swirl introduced with the air charge increases
entrainment, but the jet remains axisymmetric. With sufficiently
high swirl velocities the cross flow effects will deflect the jet
axis and distort the circular section into a kidney shape (see
Figure 3-3). Air entrainment will be different on the upwind and
downwind sides. There is the possibility that vapor and small
droplets will migrate in the direction of the cross flow.

e Non-steady jet —no attempt is made to include the transient
effects of an intermittent jet, i.e., the nature of the leading and
the trailing edges.

e@ Three dimensional effects — the jets exist in a finite and continu-
ously changing space. The jet impact upon the piston bowl is
not normal to a plane surface.

e Jet interaction — at no time are the fuel jets considered to
interact.


and the two-point boundary conditions are specified by

a (4-89)
-(pD ar )* (° “q+ = pv Yo. at r= or
Yy0 = Yyo,« atr= n (4-90)

In the above equations, Yue and Yog and T are already known explicitly from the

relationships described in Section 4.5.2. The solution to the above two point
boundary value problem can be achieved by following a standard "trial and error"
procedure

- guessing the initial condition, i.e., Yno pat the droplet surface

- integrating Equation (4-87) numerically throughout the entire flow
field from r, to r, based on known Ye Yo2 and T distributions.

- matching (Y, y,

NO,2 calculated) to NO,- ) (specified)
- repeating the procedure until agreement is reached

The contribution of the NO formed in the droplet diffusion flame to the overall zonal

production rate is calculated by integrating the NO production rate, Wo!

over the diffusion flame zone, i.e.

. 2 pt
(*no)wer 7 ann) vo (3) a(=) (4-91)


Input Conditions

Exhaust Concentrations

Speed 1800 rpm NO 3245 ppm
Equivalence Ratio (nominal) 0.6 x
Timing (ATDC) -28. co 0.1 percent
Swirl Level Medium UHC 9
Fuel Injector 6 CO, 8.2 percent
oO, 8.8 percent
Sample Valve Location
R = 3.9 cms
e= 15° from jet axis
Z = 0 depth (cms)
Sampling
Time NO, co UHC CO, 92
(2) pom % ppm % %
-27 325 0.23 190 0.7 19.2
-17 221 3.50 270 2.6 12.3
-12 644 5.20 3000 4.8 75
-7 1322 4.60 1000 5.5 6
- 2 1681 5.50 570 6.5 7
3 2317 3.20 460 6.0 +2
8 2731 1.30 420 6.6 10.0
13 3521 1.20 360 7.0 9.0
23 3571 0.60 250 6.4 10.6
33 2490 0.45 200 $.8 11.3
43 2360 0.40 180 5.0 13.0


1.4

1.0

0.8

0.6

8.0

2.0

~
~
~
~
~~
Data (nol, (soot), Line
Calculated (@=0.6) 2077(ppm) 139 mg/m
Measured (@=0.45) 1781(ppm) 6.2%. opacity —-O=-—
Measured (§=0.76) 1934(ppm) 11.6% opacity --T#—
/
7
L
7
7
7
aa
-
-
- -
- -
-_-- 7 -_ - o-oo oa
ia _ if =
0.0254 0.0305 0.0356
Fozzie (cm)
Figure 6-8 Effect of Orifice Diameter

1.0


Input Conditions Exhaust Concentrations

Speed : 1500 rpm NO 1463 ppm
Equivalence Ratio (nominal) 235 co. 0
Timing (ATDC) *20. +01 percent
Swirl Level Low UHC Q
Fuel Injecto!
erin r 6 co, S.1 percent
° 13.4 percent

2

Sample Valve Location

R = 3.9 cms
§= 18° from jet axis
Z = 0 depth (cms)

Sampuing NO, co UHC CO, 7)
(0) pom % ppm %. %
-22 163 0.06 200 0.31 20.1
12 138 5.40 240 2.80 11.5
- 7 462 10.00 7600 §.00 3.8
-2 1120 §.20 1800 6.20 7.3

3 1203 1.30 $40 $.20 11.5
8 1153 0.70 420 4.40 13.5
13 1178 0.28 320 4.20 14.7
23 950 0.20 250 4.00 15.2
33 960 0.18 150 4.00 15.1
43 1110 0.20 110 3.80 15.5

D-49


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO, 3710 ppm

Equivalence Ratio (nominal) 0.6

Timing (ATDC) -28. oS §° 15 Percent

Swirl Level Medium

Fuel Injector 6 co, 8.0 percent
oO, 8.6 percent

Sample Valve Location

R = 3.9 cms
6= 0° from jet axis
Z = 0 depth (cms)
Sime NO co UHC oO, »
—O) ppm * 2pm 4 i
27 440 0.06 96 0.8 18.6
-17 460 0.30 400 1.3 17.5
-7 2940 0.60 170 $.5 ll.1
-2 2490 0.45 160 5.8 12.9
3 2670 0.60 170 6.0 11.9
8 3400 0.45 160 6.0 11.9
13 3988 0.28 -0 6.7 11.1
23 4720 0.23 -0 8.0 9.0
33 $485 0.18 -0 8.4 8.5
43 $120 0.12 -0 7.9 9.0


However, it can be seen that there is a very rapid rate of production of NO in
the fuel lean zone. Figure 5-7 presents similar comparisons for the instantane-
ous zonal mass of liquid fuel and soot for the same two zones. In contrast to
the NO production, soot is hardly formed in the lean zone, emphasizing that
which is well known, i.e., conditions which reduce NO formation tend to

enhance soot formation.

5.3 Sensitivity Analysis

A sensitivity analysis has been carried out to assess the influence
of the adjustable constants on the calculated emission levels. The range
covered in this analysis for each constant is given in Table 5~4 and the results
of the computations are presented graphically in Figures 5-8 and 5-9 for nitric
oxide and soot, respectively. Both the calculated emissions and the empirical
constants have been normalized by the baseline values.

Table 5-4. Values of Empirical Constants for Sensitivity Analysis

Case Variable Baseline 1 2
Ll Cee 4.3 2.15 8.6
2 Cmte 7.8E-3 3.9E-3 1.56E-2
3 Cnor 5.37 1.0 8.0
4 Coat 0.1 0.0 0.2
5 Thu 2.0x 1074 1.0 x 1074 3.0x 1074



4.4 Ignition Delay

The objective of the ignition delay model is to provide a relationship
whereby the time of ignition of each fuel/air parcel can be evaluated. The

ignition delay time is calculated using the expression from work of Shipinski@ YN

Tig Aig (NQ,) ig (Pp) ig exp (E,/8D) (4-45)

where *,_, the time of ignition in seconds, and the pressure and temperature

ig
are the average values calculated over the delay period, in atmospheres and
OK respectively. The ignition delay model includes four empirical constants

1,224 x 1074

Aug
Big = -0.69
Cig = -0.386
Eig = 9290 cal/mole

representing the best fit to the experimental data.

4.5 Air Product Mixing

High speed photographic records were made during Phase I of the
present program (Wilson et al) which tended to suggest that after the initial
vapor phase heat release, the contents of the cylinder approach well-stirred
conditions on the macroscale. To accommodate these observations the model
allows mass transfer to take place between “air” and "burning" zones ina
random manner. After ignition of the vapor/air mixture in a fuel/air parcel the
combustion product-droplet~air mixture continues to mix with the air zones, but
not with other fuel/air parcels. Thus, the air zone is being continuously vitiated
and vitiated air is being mixed with the vaporizing droplets. In the light of
recent in-cylinder sampling investigations (see Appendix C) it appears that the
concept of random mixing may not be representative of actual conditions. The
mixing process used in the model does not retain any memory of the jet structure
once ignition has occurred. However, although only preliminary results are
available, sampling valve data suggest that mixing process may be dependent
upon jet properties some time after ignition has taken place.

The air product mixing is modeled as a completely random process,
i.e., the well-ordered jet is considered to have broken down and the mass

4-21


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling
Time
—o)
22
12
-7
-~ 2
3
8
13
23
33
43

Exhaust Concentrations

1500 rpm NO. 2156 ppm
3S x
-20.0 co 0.15 percent
Medium UHC 0
6
co, 5.3 percent
° 12.0 percent

2

Sample Valve Location

R= 3.6 cms
= 0° from jet axis

Zs 0 depth (cms)
co UHC co, o
% ppm % %
0.20 $0 0.65 19.5
1.00 125 1.40 17.8
2.00 $50 2.60 15.8
1.20 200 2.00 17.1
2.70 150 4.80 11.2
4,00 95 7.80 $.$
2.20 80 7.70 7.0
0.55 0 8.00 8.2
0.30 0 7.00 9.0
0.25 0 6.60 9.4

D-45


Combining Eqn (4-69) and (4-71) and assuming an ideal gas Eqn (4-76)
can be rewritten as:

( aM’, . as, 2 dr

=3 po
r = = =
max te le M/t, -e M/t + Te (

To (4-80)

as . ae M/ta )

In the above equation, T; is readily determined from Eqn (4-70) and t is an
implicit function of r_, thus Eqn (4-80) must be solved for r, by graphic or trial
and error methods.

A schematic of a droplet diffusion flame in a confined space is shown in
Figure 4-3,

4-33


¥-D

DC Power
Supply

Sampling
Valve
Electronics

Capacitor Charging

Voltage (Input)

Capacitor
Discharge
Trigger Delay

Spring Tension

Adjustment
| (Input)
Sample Sample Valve
U
= Rotometer
= e
@ Sample Crank
Valve Open Angle
(Input) Signal
H,0 Trap Filter
- [ l
O, Analyzer NO, NO,
l 2 Analyzer
(Paramagnetic) (Chemiluminescent)

Figure C-2.

Schedule of Sampling System


which has been discounted from the homogeneous formation process shown in
Equation (4-85). The summation in above equation is made over all droplets
involved in this zone.

The nitrogen ‘bound in the fuel which will be responsible for a very
small amount of NO has not been considered in this analysis.

4.7.2 Heterogeneous Formation

The nature of the heat release process in a diesel engine dictates
that the majority of fuel droplets will burn in vitiated air which also contains
nitric oxide. At high NO concentrations the net rate of NO production is
strongly dependent upon the concentration. Consequently, it is important
that the concentration profile surrounding the burning droplet is known. The
analytical solution described in Section 4.5.2 is used to define both the
temperature and concentration field around the droplet and the NO kinetics
discussed earlier are assumed to be valid, thus a local rate of NO formation
can be defined. Consequently, only the following NO mass conservation
equations must be solved, provided that it can be assumed the formation of
NO has no influence on the flow field surrounding the droplet

v *yo. = 4+ a PD 2 “xo w
p dr r dr dr + NO (4-87)

The local NO production rate can be conveniently expressed in terms of
species mass fraction by:

; 4 P) 3/2 1/2
w = TT
no 7 $:098x 10° (KK 3) (44) n2 *o2
, 2
(4 sosdg =) “no
Sa Kee / na oe | ig
ca Y. nor)
1+ 1.142887 (@) ye
Xo] Yon (4-88)

4-38


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling
Time

722
-12
-7
- 2

3

8
13
23
33
43

1500 rpm

0.6
-20.

Medium

6

Exhaust Concentrations

NO.
x

co
UHC
co,

Sample Valve Location
2.7 cms
0° from jet axis
0 depth (cms)

Now w

NO

137
90
600
1560
2146
2688
2937
3650
4240
4070

co

-003
+080
- 430
«500
«450
-900
-400
- 180
.150
-360

2460 ppm

0.005 percent
0
8.6 percent

8.7 percent

[xy

co, ie)
a _
0.50 19,
0.50 19.
2.95 15.
3.90 12,
3.70 8
7.20 10.
7.50 8
8.10 8
8.00 8
9.00 6

7arFONDBHOwaw


4-34


(soot)/(soot) 4

2.0

Variables Sy or Line
1.8 >
Coe 4.3 —_ - —.
Cus 7.8 E-3 —_—_—-

0.1 _—--—

1.6 vidi

Thu 2.0 E-3 —_---—
(soot), = 139 mg/m?

1.4

0.4

0.2

0.0 1.0 2.0

C/C, or T/ T%

Figure $-9 Effect of Empirical Constants on Soot Prediction

5-17


ee

2.5

1.0

[oe
_T
-_-

0.5

0.0

Ono],

Calculated 2077 ppm

(soot). Line

139 mg/m*

2.0

1,5
Soot,
(Soot) °

1.0

0.5

Measured 2050 ppm 10% apacity —-—O— —
oF
om ~ a
~ -
~~ -
Gi -
0.3 0.45 0.6
@
Figure 6-2 Effects of Load

0.0


(iii) at a large distance from droplet (r =r,)

T =T, (4-63)
Yo2 = 02,0 (4-64)
Y, 70 (4-65)
‘ya 7Yy2,2 (4-66)
Yyo 7*yo,# (4-87)

Analytical Solutions

Analytical integration of the governing differential will be described in

this section.

If we let

and

ct
ay = GTA Wa
T ¢ 7 e) We

where q is the heat of combustion (in cal/gm) and y's are the stoichiometric
coefficients for a single stem chemical reaction

Dv, y tL," x
i? 1 it 1
Equations (4-51) and (4-52) become

Si. 0p a (272), ,
dr ra dr

= oD (2 B)- .

=o
r

Rio.

4-28


location the final sample yielded NO, levels lower than the exhaust value.
Some idea of the unmixedness existing in the cylinder can be gained from the
results showing the influence of valve insertion depth shown in Figure C-4.
Peak NO levels are considerably greater than the exhaust value. Also, the
peak value does not increase monotonously with increasing insertion depth.

Increasing swirl increases exhaust NO levels which is reflected
in the peak NO levels recorded by the sample for two insertion depths (see
Figures C-5 and 6). It should be noted that peak levels tend to occur later
in the cycle for lower swirl levels. The dip in the NO, level close to TDC
with the lowest swirl level when the valve was in the flush position appear
to be real as the results could be repeated.

Variation of the injection timing produces a radical change in the
character of the NO, versus crank angle curves when the valve is flush with
the cylinder head. The rise in NO, is delayed in agreement with the delay in
fuel injection.

C-4, DISCUSSION

Two issues must be addressed relating to the correspondence be-
tween the measured concentrations and those actually existing in the cylinder
before discussing the implications of the results, these are:

1. Is the sample ingested into the valve representative of the con-
centration at the probe position and sampling time in the absence
of the probe?

2. Does the sample undergo chemical transformation in the probe?
Complete answers to these questions are not available although it is possible
to define possible effects and construct plausable arguments as to their
magnitude. Regarding the first question posed above, the following effects
can perturb the sample:

- influence of the inserted probe tip on local gasdynamics and com-

bustion;


APPENDIX B

Coetficients for Equations (4-25) and (4-26)

These polynomial coefficients are obtained from least-square curve fitting
of computed results from NASA Equilibrium Program'!3) , Particularly for H/C
equals 1.7. For fuel having different H/C, these coefficients have to be
reevaluated.

Table B-l. @< 1.0

i a by dq ry

1 ~5.S5492E+01 7 .346SE+02 1.3700E+01 6.8789E-02
2 7 .8374E-02 3.7817E-02 -1,1-17E+00 4.3293E-03
3 1.6734E-04 -1,0774E-04 -5.715SE-01 -9.8361E-01
4 -1.1376E-07 6.1112E-08 -2.6780E+01 6 .6435E+00
$ 4,0737E-11 -1.443S5E-11 7. 2448E+00 1.1172E-01
6 -5.4383E-15 9,9489E-16 1,3090E+00 2.30SS5E+00
7 5.0189E-01 -2.5753E+01
8 -5.2147E-01 -4.0113E-01
9 $.3444E-02

10 -2.6396E+00

11 1,6069E+00

Table B-2. 3.5>@>1.0

i ay b, qa,

1 -8.5550E+02 -1.1796E+02 9.7714E+00 4.3246E-02
2 2.5318E-01 6 .5986E-01 4.3547E+00 1, 2509E-02
3 -1.6176E-05 -1.1693E-03 -7 .2560E-02 2.3144E-01
4 -1.0564E-07 7.1490E-07 ~9,6828E+00 -3.8400E-01
$ 7.2508E-11 -1.8777E~10 -1.5763E+01 -3.38S0E-03
6 1,2100E-14 1.7905E-14 2.3124E-01 -4.0000E+00
7 -6.4446E+00 2.9256E-01
8 7 .2392E+00 -1.7973E-02
9 5.2083E-03

10 2.2071E+01

il -2.S775E+01


Table C-2. NO, Exhaust Emission Levels Measured For
Different Sample Valve Locations (Series 3)

inj

-20° -28° -12°
2431 3210 1284
2333 3100 940
2435 3245 1412
2382 3540 1395
2360 3600 1085
2669 3823 1230
2840 4440 1209
2300 3640 1300
2460 1300

Swirl Medium

Load@ 0.6

RPM 1500

As discussed earlier, between the second and third test series there
was an unexplained jump in the baseline emission levels. What is perhaps
more disquieting, is that there was also a change in the behavior of the engine.
Data presented in Section 6 shows that the measured influence of swirl level
on No, emissions was not reproduced from Phase I to Phase II. The emission
levels tabulated in Table C-3 indicate that the “influence of swirl" also varied
between the second and -third sampling valve test series.


NITROGEN OXIDE (NO,), PPM

SwirlLevet

4000 5 Speed 1500 rpm & High
Load = 4=.5 © Medium
Timing 9 ,)=- 20° oO Low

3000 |
2000 + J

dj
1000. +

L 1 n 1 1 my

100 -50 i) 5O 100 150

Crank Angle, Degrees

Figure C-6. Dependence of Sample Valve Measurements
on Swirl Level - Flush Valve Position

C14


Input Conditions

Speed

Exhaust Concentrations

1500 rpm NO 2190 ppm
Equivalence Ratio (nominal) 0.6 x
Timing (ATDC) -20. co 9.3 percent
Swirl Level High GES
Fuel Injector 6 2 8.7 percent
0, 9.0 percent
Sample Valve Location
R = $.6cms
@ = 30° from jet axis
Z = 0 depth (cms)
Sampling
Time NO, co UHC CO, 2
(2) ppm % ppm % %
-22 170 0.20 900. 0.69 19.
-12 256 0.50 1250 2.10 17.
- 344 0.70 1600 2.60 16.
- 660 7.00 1250 4.60 8
1750 5.40 1000 7.70 6
1705 2.60 800 6.50 9
13 1650 1.50 740 5.90 ll.
23 1414 0.73 470 6.00 12.
33 1036 0.45 0 4.90 13.
43 650 0.15 ie) 2.30 14.

OnNnHONUMON OU NH


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO 1805 ppm

Equivalence Ratio (nominal) 0.6 co.

Timing (ATDC) =20.0 UEC 0.15 percent

Swirl Level Low oO 9

Fuel Injector 6 c 2 8.5 percent
O, 8.8 percent

Sample Valve Location

R = 3.9 cms
@ = 0° from jet axis
Z = 0 depth (cms)

“me NO, co UHC C02 2
(2) ppm % ppm %. we
-22 130 0.1 210 156 19.5
-12 172 3.4 2000 2.3 14.3
-7 663 6.0 2500 5.2 .0
-2 767 4.4 1500 5.0 9

3 1460 2.6 400 6.0 9.5
8 1800 1.5 300 6.3 10.1
13 1817 0.95 250 8.7 10.5
23 1830 0.50 200 6.2 11.0
33 1590 0.30 200 5.9 11.8
43 1370 0.25 200 4.3 14.0


This report is issued by the Environmental Protection Agency to report technical
data of interest to a limited number of readers. Copies are available free of ;
charge to Federal employees, current contractors and grantees, and nonprofit
organizations - as supplies permit - from the Air Pollution Technical Information
Center, Environmental Protection Agency. Research Triangle Park, North ,
Carolina 27711; or, for a fee, from the National Technical Information Service,
5285 Port Royal Road, Springfield, Virginia 22161.

This report was furnished to the Environmental Protection Agency by Ultrasystems,
Inc., Irvine, California, in fulfillment of Contract No. 68-01-0436. The

contents of this report are reproduced herein as received from Ultrasystems,

Inc. The opinions, findings, and conclusions expressed are those of the

author and not necessarily those of the Environmental Protection Agency.

Mention of company or product names is not to be considered as an endorsement

by the Environmental Protection Agency.

Publication No. EPA-460/3-76-008-a


Input Conditions

Exhaust Concentrations

Speed 1 pati nal as rpm NO, 2300 ppm
sauivolence Qetio (nominal) 0,5 co. 0.15 percent
Swirl Level Medium co 8.8 percent
Fuel Injector 6 2
Oo, 8.8 percent
Sample Valve Location
R = 5.6 cms
6= 30° from jet axis
Z = 0 depth (cms)
serine NO, co UHC CO, °
(2) ppm % pom % %
-22 92 0.005 100 0.67 19.4
-12 75 0.35 100 0.65 19.1
-7 821 10.00 100 6.50 1.3
- 2 370 10.00 120 4.00 0.4
3 1160 10.00 ie) 6.40 1.2
8 2140 9.00 0 7.40 1.9
13 2170 $.00 0 8.00 4.0
23 2733 1.80 Q 8.40 6.1
33 2800 1.30 0 9.60 5.0
43 3050 1.20 0 9.90 4.7


15

16

17

18 °

19

20

2.

22

23

24

25

26

27

28

29

McAulay, K.J., etal, "Development and Evaluation of Simulation of
Compression-Ignition Engine", SAE Paper No. 650451, 1965

Borman, G., "Mathematical Simulation of Internal Combustion Engine,"
Ph,D Thesis, University of Wisconsin, 1964

Lee, D. W., "The Effect of Nozzle Design and Operating Conditions
on the Atomization and Distribution of Fuel Sprays", NASA Rept...
425, 1932

Abramovich, G.N., "The Theory of Turbulent Jets", M.I.T. Press, 1963

Wise, H. and Agoston, G.A., “Burning of Liquid Droplet", Literature
of Combustion of Petroleum, American Chemical Society, Washington,
D.C., p. 116-135, 1958

Rosner, D.E. and Chang, W.S., "Transient Evaporation and Combustion
of Fuel Droplet Near Its Critical Temperature". Combustion Science and
Technology, Vol. 7, p. 145-158, 1973

Shipinski, J., Myers, P.S. nd Uyehara, D.A., "A Spray-Droplet Model
for Diesel Combustion", Proc. Instn. Mech. Engrs., Vol. 184, PE 3J,
p. 28-35, 1969

Williams, A., "Combustion of Droplets of Liquid Fuels: A Review",
Combustion and Flame, Vol. 21, p..1-31, 1973

Williams, F.A., "Combustion Theory", Addsion-Wesley Publishing Co.,
1965

Zeldovich, J., “The Oxidation of Nitrogen in Combustion and Explosion",
Acta Physicochimica USSR 21, 557, 1946

Baulch, D.L., Drysdale, D.D., and Lloyd, A.C., “High-Temperature
Reaction Rate Data No. 1", Dept. of Physical Chemistry, The University;
Leeds, England, May 1968

Wray, K.L. and Teare, J.D., “Shock Tube Study of Kinetics of Nitric
Oxide at High Temperatures", J. Chemical Phys. 36, 2582, 1962

Caretto, L.S., Sawyer, R.F. and Starkman, E.S., “The Formation of
Nitric Oxide in Combustion Processes", University of Califomia Rpt.
TS-68-1, 1968

Lee, K.B., Thring, M.W., and Beer, J.M., “On the Rate of Combustion
of Soot in a Laminar Soot Flame," Combustion and Flame 6 p. 137-145,
1962

Field, M.A. etal, "Combustion of Pulverized Coal" BCURA, Cheney
& Son Ltd., Banbury, England, 1967

9-2


Table 5-2. Adjustable Empirical Constants

Suggested
Constants | Equations Value Remarks
Coe 4-42 4.3 Correlate to pressure-crank angle data
in initial stage (premixed) combustion
Coix 4-47 7,8E-3 Correlate to pressure-crank angle
data in the final stage of combustion
Cror 4-85 $.37 Match the measured exhaust NO value.
4-88 Same value has been used by Khan
and Greeves(4
A, 4-45 1,47E-4: Match the measured ignition delay
g di
lata
Ase 4-92 3.52 Match the measured exhaust soot
concentration
Coat 4-49 O.1 --
T ho -- 0.2 ms Droplet heat up time, assumed to be
equal to typical physical delay time
5.2 Exploratory Computations

Engine performance data and exhaust pollution levels obtained from

a series of single cylinder experiments were used to evaluate the values of the

constants listed in Table 5-2,

had the following characteristics:

Displacement

Bore
Stroke

Connecting rod

Piston bowl/bore
Fuel nozzle type
Nominal orifice size

Cone angle

The direct injection single cylinder engine

2340 cm?

13.97 cm

15.24 cm

30.48 cm

0.59

Roosa pencil injector
0.0254 cm

160°



K, is equal to 0.22078 K

1 Seq 3

Ky is equal to (Ki Kyo/Keg Seq)

K, is equal to Ki Key

Table 4-1 Literature Values of NO Rate Constants

Rate ‘

Constants Values Units Reference
Rey 1.36 x 10%4 exp (-75,400/RT) om?/mole-sec Bauicn'25)
Re 3.12 x 1013 exp (-400/RT) em?/mole-sec Bauich?®)

10 3
Ke 1,33 x 10°" T exp (-7,080/RT)| cm~/mole~sec | Wray & Teare
(26)
Kua 3.2x 109 T exp (-39,100/RT) om?/mole-sec wey & Teare
26
7
Keg g | 5-0 exp (-88,300/RT) fase" Carette!?7)

*R = 1,986 cal/mole-°K

T = Temperature in °K

The mass involved in the NO formation process in diffusion flames

surrounding the burning droplets is evaluated by mass integration over flame zone:

= 2
Mae “ren fl predr (4-86)

5

4-37


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sample Valve Location

Exhaust Concentrations

1500 rpm NO,
“is. 9
Medium Be
6 2
O

R = 3.9 ppm
@= 45° from jet axis
Z = 0 depth (cms)
sme NO co
) ppm %
-27 21s 0.06
-17 322 1.10
-7 2336 1.15
- 2 2340 1.00
3 2360 0.40
8 2188 0.25
13 2525 0.40
23 2804 0.25
33 2560 0.20
43 2020 0.15

D-37

UHC

ppm
70
100
100
30
90
80
70
60
60
60

3600 ppm

0.1 percent

0

8.7 percent
8.5 percent
co, [@)
2 %
0.66 19
0.71 19
5.80 il
5.50 12
5.20 12
4.80 13
5.60 12
5.70 ll
§.90 iL
§.00 13

FP OnOHNWAUN BAH


8.0 NOMENCLATURE

Area (cm?) or pre-exponential factors.

Jet half width (cm)

Constants

Constant pressure specific heat (cal/gm-*K)
Constant volume specific heat (cal/gm-°X)
Diffusion coefficient (cm?/sec)

Engine bore (cm)

Droptet diameter (cm)

Maximum droplet diameter (cm)

Activation engine in Arrhenius rate expression
ert Error function

£,F/A Fuel/air ratio by mass

G Mass fraction of a drop size group

aeo0d0aAaAaaAT

ma
R

h Enthalpy (cal/gm)

I Integral function

J Heat equivalent of work

j Stoichiometric oxygen - fuel mass ratio

K Reaction rate constants, or absorption coefficient in measure of density
of radiating particle per unit path length

L Latent heat or characteristic length

m Mass (gm)

m Mass flow rate (gm/CA)

M Molecular weight

M Nondimensional droplet burning rate

Noe Cetane Number

P Pressure (atm)

B Pressure derivative (atm/CA)

Q Rate of convective heat transfer (Cal/CA)

Qe Overall ratio of radiative heat transfer (Cal/CA)

Zonal rate of heat transfer (Cal/CA)
Heat of Combustion (Cal/gm)

Gas constant

Connecting rod length (cm)

waa


Over-all Conservation Equations

The overall energy conservation equation is obtained by summing up
equations (4-1) through (4-5), i.e.,

+ + + + (4-27)

Mota Mata Bap Yeip Migtég T bn, 1 “bm, 1

where Q. is the overall radiation loss from all zones, i.e.,

O, = Seg * Bec] +h Tom 1 (4-28)

The over-all mass conservation equation is obtained by summing

equations from (4-14) through (4-18), thus:

+<Om = (4-29)
I

mh, +m, +m ta bm, 1 fj

tg

The equation of state can be written as

pv =i m,RT,
T roid (4-30)
where
i=a, fg, (bm,1)

and J is the mechanical equivalent of heat.


Mass Conservation Equation

The law of conservation of mass in each zone is described by

the following mass rate balance equations:

“Aire

= - - (4-14)
m= TM, 7 TM), 7 Mapb

Liquid Fuel (Vaporizing)

~ on oh ea (4-15)
me Me 7 Mey 7 Mag

Liquid Fuel (Burning

. . . (4-16)
May ~TMaq ~ Midd
Fuel Vapor
ee = me - ioe (4-17)
Buming System
Bm tpt ep, t * Bepe,t * ®aph,t 7 Be,1 (4-18)


10

ll

12

13

14

9.0 REFERENCES

Wilson, R. P. Jr., Waldman, C.H. and Muzio, L.J., "Foundation for
Modeling NO, and Smoke Formation in Diesel Flames", Final Report
for Phase I, EPA-460/3-74-002a, January, 1974

Bastress, E.K. et al, "Model of Combustion and Nitrogen Oxide Formation
in Direct and Indirect Injection Compression-Ignition Engines" SAE
No. 719053, 1971

Khan, I.M., Greeves, G. and Probert, D.M., “Prediction of Soot and
Nitric Oxide Concentrations in Diesel Engine Exhaust," Inst. Mech.
Engr., Paper C142/71, 1971

Khan, I.M. and Greeves, G., "A Method of Calculating Emissions of
Soot and Nitric Oxide from Diesel Engines," SAE Paper No. 730169,
January, 1973

Shahed, S.M., Chiu, W.S. and Yumla, V.S., “A Preliminary Model for
the Formation of Nitric Oxide in Direct Injection Diesel Engines and Its
Application in Parametric Studies," SAE Paper 730083, 1973

Shahed, S.M., Chiu, W.S. and Lyn, W.T. "A Mathematical Model of
Diesel Combustion", Institution of Mechanical Engineers (1975).

Lyn, W. T., "Study of Burning Rate and Nature of Combustion in Diesel
Engines," IX Symposium (International) on Combustion, 1963

Lyn, W. J., and Valdmanis, E., "The Effects of Physical Factors on
Igntion Delay” SAE Paper 680102, 1968

Lyn, W. T. and Valdmanis, E., "The Effect of Physical Factors on Ignition
Delay," Proceedings of Inst. of Mech. Engrs., Vol. 181, 2A, No. 1, 1966

Bowman, C. T., The Fourteenth Symposium (International) on Combustion,
p. 729, The Combustion Institute, 1973

Fenimore, C. P., “Formation of Nitric Oxide in Premixed Hydrocarbon
Flames", Thirteenth Symposium on Combustion, The Combustion
Institute, p. 373, 1971

Myerson, A. L., Fifteenth Symposium (International) on Combustion,
p. 1085, The Combustion Institute, 1975

Gordon, S. and McBride, B.J., "Computer Program for Calculation of
Complex Chemical Equilibrium Compositions, Rocket Performance,
Incident and Reflected Shocks, and Chapman-Jouguet Detonation",
NASA, SP-273, NASA Lewis Research Center, 1971

Annand, W.J.D., "Heat Transfer in Cylinders of Reciprocating Internal
Combustion Engines”, Institution of Mech. Engrs. 1962


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling
Time
(o

-12
-7
- 2
3
8
13
23
33
43

NO
x

102
$8

70°

238
984
1094
1394
1350
1290

Sample Valve Location

R

6
v4

Exhaust Concentrations

1500 rpm NO
0.6 *

~12.
Medium

6

u

co
UHC
co,

92

3.9 cms

0° from jet axis
0 depth (cms)

~30
+20
«1S
+23

UHC

175
250
700
400
150
150

D-26

1254 ppm

0.1 percent
7.9 percent
8.6 percent
co, °
4 4
0.35 19
0.36 19
0.60 18
1.20 17
3.40 14
3.60 1s
4.50 13
6.00 12
6.40 ll

CONF NUN OON


Input Conditions Exhaust Concentrations

Speed 1800 rpm NO 1085 ppm
Equivalence Ratio (nominal) 0.6 co. 0.01
Timing (ATDC) -12. UHC 5 percent
Swirl Level Medium co 8.5 t
Fuel Injector 6 2 +9 percen'
O, 8.6 percent
Sample Valve Location
R = 3.9 cms
9= 45° from jet axis
Z = 0 depth (cms)
Sampling
Time NO, co UHC C0,
a) pom % ppm %
-22 83 0.05 94 0.7 19.
-12 $6 0.05 100 0.7 19.
-7 56 0.05 120 0.8 19.
- 2 72 0.05 130 1.2 19.
3 1055 0.50 110 4.8 13.
8 1730 0.40 100 5.4 13.
13 1328 0.40 100 $.0 13.
23 1015 0.20 88 5.5 12.
33 785 0.10 $5 4.4 14,
43 560 0 $2 0 0

D-29

aunonnn oan


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling
Time
—
-22
-17
-12
-7
- 2
3
3°
13
28
38

NO

240
250
580
905
1750
2460
3800
4000
4150
4200

Exhaust Concentrations
1500 rpm No,

3640 ppm

oe cee 5° percent
Medium co, 8.3 percent
0, 8.9 percent

Sample Valve Location
R = 2.7 cms
ied 30° from jet axis
Z = 0 depth (cms)
co UHC SO, 2
% ppm % %
0.15 500 0.6 20.0
1.50 580 2.2 16.2
6.20 1400 6.2 2
7.00 4000 6.2 5.0
1.00 700 5.2 11.7
0.35 640 5.8 12.0
0.40 $20 6.5 11.2
0.40 440 7.4 8
0.28 280 8.0 -8
0.35 240 8.1 a)

D-33


- the transition zone from a free to a wall jet;
- the fuel volume;
- the curvature of the piston bowl;

- preferential fuel vapor transfer, all vapor remains associated
with the parent fuel parcel;

- the influence of confinement both by the piston and cylinder
walls and the adjacent fuel jets.

However, the following phenomena are included in the analysis:

- droplet heat-up and vaporization;
- jet entrainment due to impingement upon the wall;
- the influence of swirl on the jet entrainment rate.

The relationships governing the behavior of an unconfined jet impinging upon
a plane wall in a quiescent atmosphere can be drived from fundamental
turbulent jet theory (see Abramovich !8)) and the detailed formulations have
been included in Appendix A. The influence of air swirl induced by the
masked inlet valve on the fuel-air mixing rate is approximated by

jTM.). 7 1.0 + C Set (vo/¥_ ) (4-42)

jO'
where Coot is an adjustable constant obtained by matching experimental data.

(19)

tion rate to account for liquid droplets in crossflow. A similar expression

Wise and Agoston proposed a correction to the normal vaporiza-

has been used to account for the influence of the swirling air motion on


Input Conditions Engine Concentration

Speed 1500 rpm NO 1880 ppm

Equivalence Ratio (nominal) 0.35 x

Timing (ATDC) -20. co 0.05 percent

Swirl Level Medium GHC 3

Fuel Injector 6 2 -4 percent
Oy 13.2 percent

Sample Valve Location
R = 2.7 cms

6 = 0° from jet axis
Z = 0 depth (cms)
Sampli

Tee NO, co UHG CO, On
) ppm % ppm % %
22 72 0.01 250 0.05 20.
-12 75 0.05 2000 o.15 20.
-7 500 1.70 2600 3.80 14.
- 2 1190 1.15 900 6.00 ll.
3 1285S 0.65 550 $.30 12.
8 1070 0.20 500 4.40 1s.
13 1370 0.07 400 5.00 14.
28 2280 0.03 250 6.00 13.
38 2420 0.03 -0 5.80 13.

D-39

HPN a HnOnNONnNN


construction and operation has been given by Nightingale(?) . Details of the
sampling valve tip used in this investigation are given in Figure C-l1. Valve
lift and open times are dependent upon spring strength, which acts to close

the valve, and the magnitude and duration of the current pulse passing through
the electromagnet. Since cylinder pressure acts to open the valve, adjustments
must be made to provide constant sampling conditions for different loads and
crank angles. The actual valve opening time represents a compromise between
that necessary to provide sufficient sample for analysis and a desire to maintain
a high temporal resolution. Figure C-2 provides a schematic of the sampling
system. In the final series of tests the triggering delay electronics for acti-
vating the electromagnet which allowed an accurate adjustment of the triggering
crank angle were supplied by AiResearch.

Experience with the sample valve indicated that the titanium valve
tip and seat could not maintain satisfactory operation under conditions of high
load and insertion. In the initial series of tests an insertion of 1/4 in. was
only possible at part load. Leakage occurred after a short period of time due
to the forging action of the valve stem. This problem was overcome in the
final test series by using Waspolloy (0.50 Nc; 0.19 CN, 0.14 CO, 0.04 MO
and 0.03 Tc) for the valve seat and titanium carbide for the stem tip. These
design modifications allowed operation under high engine load conditions with
full insertion without leakage. Included in Figure C-1 is an alternate valve
tip design which utilizes a sphere as the tip, rather than a conical section.
The sphere is a press fit into the end of the stem and the seat is coined rather
than machined thus allowing rapid inexpensive renewal of the valve component
not subject to failure.

The sampling probe could be located in three different ports in the
cylinder head. Rotation of the fuel injector then allowed samples to be
obtained on these three radii at any distance from the fuel fet axis. Figure
C-3 shows the radial location of the three sampling ports.


TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)

eh °9803-76-008-a 2 3. RECIPIENT'S ACCESSIONNO,

7

TLE ANO SUBTITLE IS, REPORT OATE

Issued May 1976
‘study of the Oxides of Nitrogen and Carbon Formation G- SSHESaMING SAGANIZATION SOOT
in Diesel Engines

7 AUTHOAIS) Is. PERFORMING ORGANIZATION REPORT NO.

C. J. Kau, T. J. Tyson, M. P. Heap

I9. PERFORMING OAG ANIZATION NAME ANO ACORESS 10. PROGRAM ELEMENT NO.
Ultrasystems, Inc.
2400 Michelson Drive 71, CONTRACTIGAANT NO.

Irvine, California 92715

68-01-0436
12, SRONSORING AGENCY NAME ANDO ADDRESS. 13, TYPE OF REPORT AND PERIOD COVERED
U.S. Environmental Protection Agency Final Report June '73-June '/6
Office of Air and Waste Management 74, SPONSORING AGENCY COOE

Office of Mobile Source Air Pollution Control
Ann Arbor, Michigan 48105

15, SUPPLEMENTAAY NOTES

Co-sponsor: Coordinating Research Council, 30 Rockefeller Plaza, New York,
New York, 10020

16, ABSTRACT

A mathematical model describing heat release and pollutant formation in direct injec- |
tion diesel engines has been developed and tested. The model includes several empiri
cal constants which can be tuned to fit the requirements of a particular engine. Sen-:
sitivity studies indicate that the model is most responsive to those constants which
control fuel/air mixing. Numerical experiments strongly suggest that diffusion flames,
modelled by spherical droplet flames are unsuitable for this type of system. The i
model has been tested against results obtained with a single cylinder diesel engine.
Reasonable predictions of the influence of engine design and operation parameters on |
NO. emissions were obtained. However, predictions of smoke emissions were not satis-
fattory. .

17. KEY WORDS ANO DOCUMENT ANALYSIS.

a. DESCRIPTORS D.IDENTIFIERS/OPEN ENDED TERMS |c. COSAT! Field/Group
Diffusion Flames Mathematical Modeling /MobiTe Sources J T-07 (Recipro=
Air Pollution Soot Exhaust Gas Recirculation] cating Engines)
Diesel Engines Computer Program Divided Chamber Engine 21-02 (Combus -
Combustion Fuel Sprays , tion)

Emission Internal Combustion En

Nitric Oxide (NO) Fuel Comsumption
Nitrogen Oxides
Smoke

a SSTSUTION STATEMENT 19. SECURITY CLASS (This Report) Zi, NO, OF PAGES

20. SECURITY CLASS (This page) 22, PRICE

Release Unlimited

EPA Form 2220-1 (9-73)


REFERENCES

1.

Wilson, R.P. Jr., Waldman, C.H., and Muzio, L.J., “Foundation for
Modelling NO, and Smoke Formation in Diesel Flames," Ultrasystems
Final Report, APRAC Project CAPE 20-17, (1974).

Nightingale, D.R., "A Fundamental Investigation into the Problem of NO

Formation in Diesel Engines," Paper presented at the SAE Off. Highway
Vehicle Meeting Milwaukee, Sept. 8-11 (1975), SAE 750848.

C-23


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO, 1840 ppm

Equivalence Ratio (nominal) 35

Timing (ATDC) -20.0 Sec 0.10 percent

Swirl Level Medium

Fuel Injector 6 CO, 5.5 percent
0, 12.3 percent

Sample Valve Location
R =3.9 cms
@= 0° from jet axis

Z = 0 depth (cms)

Sampling NO, co UHC co fe}

Time 2 2
(0) ppm % _ppm_ _% _%
-22 154 0.06 1400 0.03 19.
-12 163 0.15 1500 0.40 19.
-7 234 0.50 1300 1.40 17.
-2 1715 0.65 840 4.60 13.

3 1730 1.00 900 5.40 12.

8 1830 0.60 780 5.40 12.
13 1570 0.17 760 4.50 14,
23 1630 0.10 600 4.20 14,
33 2012 0.10 400 4.70 13.
43 2250 0.60 300 5.10 13.

D-41

nanonnrowon


4.11 Fuel Representation

The laboratory report on the diesel fuel used in this study gave the
following properties:

Table 4-2

H/C (by mole, approx) 1.7
Gravity, CAPT 34.5
Total sulfur, wt % 0.3
Flash point, °F 170
Pour point, °p 20
Cloud point, °F 24
Cetane number 46.7
Viscosity, CS @ 100°F 2.5
Aromatics, % 37.6
Distillation

Initial boiling (°F) 386

50% point (°F) 514

End point — (°F) 658

Residue 1%
Total nitrogen, wt % <0.05

The model representation of this diesel fuelis a mixture of 50% (by volume)
n-heptane (CH) 6) and 50% toluene (C,H) . The sulfur and nitrogen content of
the fuel are neglected. This fuel model is used in the parametric calculation of
the equilibrium thermodynamic properties and species distribution of the combustion
products.

The extended properties of the fuel mixture based upon the properties

of the fuel model constituents are listed in the table.

4-43


The velocity decay, derived from conservation of momentum flux, is

~ 33+ [8 2 mo
; Tt VE 1) +4 (r+b) be IT, ate

8 2(r+b ov! p,t

4

where initial jet momentum flux is

a gt 2 a (A-17)
Tig! = PyyPo’ wo [aly * Creo Ig]
Similar to Eqn (A-9) the Trajectories of fuel elements in the wall region are
computed from
4-2
1 8 3 gi+ 3 52-5 -g5 1-3 4], ana
3.5 j 2.5 ; Onpiy +b be Aq
5.5 j 4% j 2m Pav (r+b))

Table A-1 Numerical Values of I &1

“tn

a qh Ten

1 3.7699 1.3446
2 2.8274 0.8105
3 2.3122 0.5592
4 1,9854 0.4209
5 1.7487 0.3311
6 1.5738 0.2709
7 1.4730 0.2276



1x 107+

Lx 107?

Mass gm

1x10?

1x1074

c 31073
r n —---4
1074
L. ~-—-- Fuel Lean Zone (No. 24)
L ——— Fuel Rich Zone (No. 21)
“5
Dect lo
L
n 1078
~10 () 10 20 30 40 $0 60
Figure 5-7. Instantaneous Zonal Masses, Masses of Burning Fuel

and Soot Concentrations. for Typical Fuel Rich and
Fuel Lean Zones

$-15

Yg Soot Mass Fraction


1_i\x
B. =|
om,. om

OR OU : : .
- bm 1 bm, 1 -
Mom t (Fons t 8 * 30. ) Pom tt Mg Pam D (m1 * Mapp?
Pom 1 bm,I

* Meg > Pot) Baer * Meg - Bom t) Binet 7 (Yom, t 2c * Sebmyt * Sen, 2

and

U. R,
c =m Pom 1 +T Rom +R
bm,I “bm,I | oy bm, oy ‘bm, I
bm,I bm,t
Similarly for fuel vapor we have
t = > (4=31c)
Tig Ag P+ Beg
where
Real eg
4eg =
cc. +
P ( vig Reg)
_ (he, = neg) me, ~ ( PegQe + Freq)
fg m, (¢, + R,)

fg © vig fg

If Eqns (4-27) &(4-29) are introduced into the differentiated over-all equation of

state, Pp can be written by

; . aR oR,
p +
- ; V+ 2 RT m, + Eats? + rm, (Ri +T, sty) Bi
P=
Vv ‘
AR; OR
[F - Lat se 7 Lyla se aT ' ‘|

(4-31d)


as
fe}

Loe ele eS
_—_— ~

-_— 7 =~
NO, (Soot) Line
Calculated 2077 ppm 139 mg/m? ~=_ 14
Measured 2950 ppm 10% opacity -——_—— —
1.2
Soot)
a Soot) ,
fee -— S“
- N
-_ = R 1.0

\| 0.8

0.6
a) 1.0 1.2 1.4 1.6 1.8 2.0

P (atm)

Figure 9-7 Effect of Turbocharge

5-19


(7)

empirical ignition delay correlation based on data of Lyn and Valdmanis

and an
(8,9)

combustion. An empirical burning law based on the work of Lyn

were used and it was assumed that heat release took place under stoichiometric
conditions and the subsequent mixing between stoichiometric packages of com-
bustion products and excess air was not included. The NO model is also based
upon the Zeldovich mechanism with adjusted rate constants to correctly predict
experimental data.

The latest version of the Cummins model contains considerable improve-
ments over the preliminary model, particularly in the areas of mixing and fuel
spray combustion. The formulae describing unsteady jet mixing were obtained
via curve fitting experimental data obtained for various engine operating con-
ditions and geometry (e.g., various chamber pressures, temperatures, swirl
levels, injection pressures and hole sizes). The stoichiometric burning and
non-dilution mixing assumptions were totally discarded. Thus, a more precise
mathematical representation of the NO formation processes, which is capable
of reflecting the important effects of local oxygen concentration history on NO
formation has been included.

3.2 A Qualitative Description of the Ultrasystems' Model

The Ultrasystems' model of pollutant formation in diesel engines has
(1)

there are important differences in the details of the various model components.

been develoved along the guidelines set down by Wilson et al However,
The model was developed recognizing that the complexity of the process will
not allow the total elimination of all empirical constants from the analytical
expressions. The initial concept of eliminating all arbitrarily assigned con-
stants has not been achieved. Certain adjustable constants have been included
and these are discussed in detail in a later section. The aim of this section

is to describe the model in qualitative terms before the mathematical formula-

tion is presented in Section 4.

Figure 3-1 presents a general view of the various components of the
model which has been constructed in such a way that any of these components
can be modified as additional information becomes available. The model

simulates conditions occurring in the cylinder of a four stroke direct injection


2.0

1.8

1.6

1.4

0.8

0.4

0.2

0.0

Variables Cc 9 OF TS Line

-— Cet 4.3 -
Crux 7.8 E-3 ——————
Coor 5.37 -r-rCro
Cytat O.1 _ooo
Tuy 2.0 E-3 =e

= 2077 ppm
%x0,

A
-
Le
“|
eee eee start
SE es
| --- —.
—a
7
4
2
7
7
0.0 1.0 3.0

C/G, oF 1%

Figure 5-8 iffect of Empirical Constzats on °C Prediction

S-

16



10 T
P = 50
,, = 0.4
TTM = 2000
o
8.
oO
o
a
E PD]
BD 0
a o
1 oO
n a
rN
x PD.
oO -
S 8.
“¢ i
-10 Ss
2000°K equil 2500°K equil 2750°K
0 ! { | equi}
0.0 4.0 8.0 12. 16. 20. 4.
3
XNO , @o* 10
Figure 5-11 Effect of Ambient NO Concentration Formation

Around a Burning Droplet



- the ignition model can be extended to more adequately reflect
the fuel history; and

- mixing between burning zones can be included.

Four areas have been identified in which the model is deficient and which
require more extensive work to include in the model:

- fuel injection schedules can rarely be approximated by a constant
injection rate. The present model is limited to a constant fuel

injection rate;

- the model considers that the jet behaves throughout its lifetime
as a steady state jet, the influence of the transient nature of
the jet is neglected;

- fuel/air mixing dictate pollutant emission levels and a more
realistic mixing model which reflects the three dimensionality
of the process and which includes fuel vapor segregation should
be included. An effort must be made to ascertain the degree to
which the well-ordered jet structure is maintained throughout the
cycle; and

- as other components in the model are improved, the deficiencies
in the equilibrium heat release model will become more apparent
and some kinetic overlay will be called for.

In conclusion, it should be recognized that the model has only been compared
against one set of single cylinder engine data. Before further improvements are
made to the model, more extensive tests will be required to fully uncover both
the weaknesses and the strong points in the model. Modifications should also
be made to the basic model to allow prechamber engines to be accommodated.


are evaluated and listed in Table (A-1). It should be noted that the energy
dissipation and entrainment during the transition from the jet to the wall jet are
not considered.

(iv) Wall Region
Self-preserving velocity and fuel concentration profiles are assumed i.e.

1.5, 2

% =a - 5) (a-12)

&

(2,/ p.)' (a-13)
aff fl 2 (1 - gfe)

(0,70, Ye

The boundary layer in the vicinity of the wall is not considered here. The
growth law of the wall jet is:

db. = t -
Bmezac constan' (A=14)
dr wi

where Cwy = 0.204 is taken from the work by Gauntner, et al (35),

The fuel concentration nearest to the wall, derived from mass conservation relationship
is

/ st « 1s
( a. . ?,%% (r + bw) bT

3
(A-15)


3000
2000
¢
a
2
2
x
1000

G@ysr-ail NO Concentration
—— -—— Homogeneous Contribution to NO Concentratieg
Only
—--— — Heterogeneots (Diffusion Flame) Concentration]
to NC Concentration Cnly
(>
weoct 22-74
°
:
ea
,
:
7
7
c
‘
‘
,
oe
ZZ
7s =20 -10 TDC 10 20 30

@

Figure 5-10 Instantaneous Diffusion Flame and Homogeneous
Contributions to NO Concentration (Baseline)

3000

2000

1000


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling
Time
—)
~22
~12
- 7
-2
3
8
13
23
33
43

NO,

133

680
1457
1366
1740
1370
1560
3080
3500
4020

Exhaust Concentrations

2100 rpm No, 2440 ppm
-60
0.35

40.0 co percent

Medium UHC 0

8 CO, 8.5 percent

O, 8.3 percent
Sample Valve Location

R=5.6 cms

g= 0° from jet axis

Z = 0 depth (cms)
co UHC co, °,
% ppm % %
0.006 $00 0.40 20.2
0.200 500 1.20 19.0
2.300 1700 7.90 7.4
5.700 550 8.70 3.9

10.000 450 7.50 0.4
5.000 300 8.50 5.0
0.800 0 9.00 7.0
1.070 0 11.00 4.2
0.760 0 11.50 3.8
0.500 0 11.3 4.2


30

31

32

33
34

35

Sitkei, G. and Ramanaiah, G. V., "A Rational Approach for Calculations
of Heat Transfer in Diesel Engines”, SAE Paper No. 720027, 1972

Bracco, F.V., “Nitric Oxide Formation in Droplet Diffusion Flames",
14th International Symposium on Combustion, p. 831-842, 1972

Ranz, W.D., Marshall, W.R., Chem. Eng. Prog. Vol. 48, p. 141-173,
1952

Frossling, N., Gerlands Beitr. Geophysics, Vol. 52, p. 170, 1938

Newman, J.A. and Brzustowski, T.A., "Behavior of a Liquid Jer Near
the Thermodynamic Critical Region”, AIAA, Vol. 9, No. 8, 1971

Gauntner, J.W., Livingood, J.N.B. and Hrycak, "Survey of Literature

on Flow Characteristics of Single Turbulent Jet Impinging on a Flat
Plate", NASA TN D-5652, Lewis Research Center, 1970

9-3


1.6
1.2
{xo} d
0.8 ew
SS
S .
0.4
- ~
~
{vo}, (Soot), Line ~~ < z
Calculated 2077 ppm .139 mg/m?
0.0 -— 4.0
Measured 2050 ppm 10% opacity —-O- —
= 3.0
- -
- 7 Soot)
a Soot,
a °
- 2.0
7
7
a
a“
a 1.0
0.0
0.0 10 20 30
(m.g-/" TM otal) ®

Figure 6-5 Effect of Exhaust Gas Recirculation

6-8


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

1500 rpm

+35

-20.0
Medium

6

R=3.9 cms

Exhaust Concentrations

No
x
co
UHC
co,
9%

Sample Valve Location

g= 45° from jet axis
Z = 0 depth (cms)

Sampling NO, co
(o) pom %
-22 147 0.05
-12 148 0.70
- 7 825 0.60
- 2 2145 1.00
3 2268 2.00

8 1600 1.00
13 1300 0.30
23 1430 0.10
33 1400 0.08
43 1275 0.07

D-44

1824 ppm

0.07 percent

)

5.0 percent

13.2 percent

UHC CO, O,

ppm % %
100 0.30 19.8
120 0.33 19.8
125 3.80 14,5
105 7.00 9.7
98 7.40 8.3
95 5.60 11.5
80 4.00 14.0
70 4.10 14.5
70 4.00 15.0
70 3.70 15.2


Input Conditions

Speed

Equivalence Ratio (nominal)
Timing (ATDC)

Swirl Level

Fuel Injector

1500 rpm

+35
-20.0
Low

6

Exhaust Concentrations

No,
co
UHC
co,
or)

Sample Valve Location
= 2.7 cms

= 30° from jet axis
Z = 0 depth (cms)

1570 ppm

0.10 percent

800 ppm
5.4 percent

13.0 percent

Sampling NO, co UHC CO, °
Time

©) oom % ppm % %
-22 115 0.00 310 0.60 20.3
-17 90 0.00 480 0.30 20.0
-12 96 0.60 1700 1.00 18.5
-7 410 1.70 2500 4.40 13.5
- 2 745 1.00 900 4.60 13.5
3 708 0.30 640 4.00 15.2
8 690 0.15 500 3.80 16.0
13 710 0.15 460 3.30 16.2
18 720 0.15 380 3.20 16.2
28 760 0.10 300 3.00 16.5
38 840 0.15 240 3.20 16.7

D-47


Eqns (4-98) and (4-99) for soot.

The governing differential equations in the analytical model of
diesel engine combustion are all first order differential equations and can be
represented symbolically as:

ay 5
sr TE) (4-100)

The symbolic variables Yi are functions of crank angle 6. Numerically
this first order system could be integrated by various finite difference techniques.
For accuracy and computational efficiency, the modified iterative, second order
Runge-Kutta method has been employed. The recurrence formula for the finite

difference equivalence of eqn (4-100) can be written as:

+1
¥, 97" (9440) = ¥, (8) +
(4-101)
ae fY,.9) +ey,e (0+ 40),6 +46]
where n is the index of integration and the initial (n=0) approximations are
evaluated by
v,° (6+ 48) =¥, (6) + a8 + £C2,°,8) (4-102)

At each integration step the iteration is continued until a stable pressure and

mass averaged temperature is obtained.

4.13 Indicated Engine Performance and Engine Emission

The engine performance parameters, including indicated mean effective
pressure, indicated horsepower and indicated specific fuel consumption are

calculated by the following relationship:

4-45


Where P is in atm, and Aso has a value of 6.51 x 104, The averaged soot density
Ps: and particulate diameter, d,, are assumed to be 2.0 gm/em? and lu respec-

tively. The activation energy Eso is set equal to 39.3 Kcal/mole (also see
Field et a9),

4.9 Nitric Oxide and Soot Formation Equations

The total zonal NO production rate is the algebric sum of the homogeneous and
heterogeneous contribution:

Wg = som * Lo wer (4-94)

The summation in above equation is made over all droplets,

The species conservation equations for NO in the “air" and buming zones are
written as:

“ie
: = a | () ~(Y_.) m + (w ) (4-35)
xo), om NO’bm,1 ‘NO al v,t Noa
a
Burming Zone
. yo - Yo) (yt Bap pl
(wo [ve ~ “No | TMp,1* app,
NO nm ,1 Bm, t NO, bm,I

) + (wo)

- Yo) NO

. as
NO (May 1 Epp,

bm,1 om.1|

4-41


- the thermodynamic properties and species concentration
(except those of nitric oxides and soot) of the "air" and
burning zones are assumed to be in their equilibrium state
based upon the zonal temperature, equivalence ratio and
the pressure.

It should be stressed that the zones above are conceptual and
although their total volume at any instant is that of the cylinder volume, their
physical shape is irrelevant. The mass transfer between each of the zones
is calculated by other relevant model components. Thus, the rate of liquid
fuel vaporization is controlled by the fuel vaporization model, which relates
to the physical process. However, for thermodynamic purposes, once
vaporized all of that fuel is assumed to exist in one hypothetical zone. Fig-
ure 4-1 presents a pictorial representation of the cylinder contents showing
the mass transfer between the various zones. The basic mathematical formula
describing the thermodynamic state of these zones can be expressed by the
following set of conservation equations.

Basic Energy Conservation Equations

Following the first law of thermodynamics, the basic energy con-
servation equations can be written as:

"Rip

P 84V

~ =e . _ * > .
mus hy TMD that, op! * ob Ey T

-(4Q, + 44 + da) + thy - Ug) my, (4-1)

el j

The last term represents the pumping work and kinetic energy dissipation
associated with the injection of the fuel into the air which is generally negli-
ble and is included only for self-consistency.

4-3


and the nitrogen mass fraction at the droplet surface can be calculated by

- (4-78)
- 1 Ye 1
N2,1 1+xX

where
la [wee (22 al" [ Xx + wea) (e)
Xn z=

x=
28 [w + = el
\ ‘02
it is assumed that the only species present at the droplet surface are fuel

Y,

vapor and the products of complete combustion, W represents the number of
carbon atoms in a fuel molecule and x is the number of hydrogen atoms.

Determination of r,, _in the Finite-Space Formulation

The solution for the bounded single droplet burning model requires the
determination of a distance r,, for which the boundary conditions specified
in equation 4-63 though 4-67 are applicable. This distance is evaluated by

invoking the zonal oxygen concentration relation

is
3 max
4 = f 2 (4-79)
3 TMnax 2, Younes Pp Yo. (4 dr)

where Tmax is a function of equivalent droplet center-to-center spacing. It is
assumed that the volume of each zone is apportioned equally between all the
droplets and Tax is evaluated by

1/3

Vom I
Tax” 0.23873 “e4)

where Ny is the total number of droplets in "I" th zone or more precisely:
Tmax = 0.62 Da
where Dg is droplet center-to-center spacing
4-32


4.7.1 Homogeneous NO Formation

The calculation of the rate of homogeneous NO formation is based upon

the Zeldovich mechanism* 4) ‘and assumes complete combustion of the reactants
before NO formation begins and also that oxygen atoms are equilibrated with

exygen molecules. The governing kinetic equations are:

nw
rn

(1) i No + N

t

(4-82)

ge

tal
fe
i)

No + 0 (4-83)

th

x

4-84)
(3) fol/ to,1 7? = x (area
eq 3

The literature values of the forward and backward rate constants for these reactions
are tabulated in Table 4-1. The instantaneous NO production rate (gm/em? - sec)

in any zone can be determined by

30 2 1/2
(Ww) -( ) K, (m -m,j(—2-\ x
VHom “\Moe / St emt Tae (a roy RAT}

ae yo 7 XyaXoe)
Cnor)

®yo Koa) (4-85)

1+k,

Where Man I is the averaged zonal molecular weight and


5.4 Droplet Diffusion Flames as a Source of Nitric Oxide

The model of pollutant formation in diesel engines grew from a belief
that spherical droplet diffusion flames characterized the total class of high
temperature diffusion flames which were responsible for pollutant formation.

No claim was made that such a belief would improve heat release predictions
nor that it actually described the burning process. However, it did dictate

the development of the model. Since a spherical diffusion flame was assumed
the influence of droplet interaction, and the relative velocity between the droplets
and their surroundings was ignored. In the early stages, droplets are confined
by the jet and even without violent mixing it is difficult to believe that single
droplets existing in an infinite environment will actually simulate the process.
It is more real to consider that the droplets exist as a cloud and act as a source
of fuel which is transported to the boundary of the cloud. More serious is the
tacit assumption of a quiescent atmosphere, droplet velocity lag would produce
wake flames which are dissimilar in structure to spherical diffusion flames or
even produce blow-off. Fuel vapor can be stripped from the parent droplet, it
may partially mix with oxident before combustion, and is therefore, unlikely

to remain associated with the parent droplets.

Calculations have been made in an attempt to ascertain the contri-
bution to the total NO production of the two modes of NO formation included
in the model. This was done by separately suppressing the homogeneous and
heterogeneous NO formation mechanisms. The calculated instantaneous NO
concentration history for the baseline case for these computations and the
normal predictions are shown in Figure 5-10. The NO formation from the droplet
diffusion flame appears to be only significant during the early stages of NO
formation. It can be seen that contributions of NO from the homogeneous and
heterogeneous phases are not additive and NO formed in homogeneous zones
appears to suppress NO formation in the heterogeneous phase,


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO, 2383 ppm
Equivalence Ratio (nominal) 0.6
Timing (ATDC) -20. osc a percent
Swirl Level Medium
. it
Fuel Injector 6 CO, 8.1 percen
Oo 8.7 percent

Sample Valve Location

R = 3.9 cms
@ = 30° from jet axis
Z = 0 depth (cms)

ee NO, co UHC CO, 2
(2) pom_ % pom % %
-22 315 0.12 130 0.9 18.9
-12 327 Ll 400 3.6 18.0
-7 680 2.6 1600 4.2 11.8
-2 2546 4.5 1000 7.0 7.0

3 3440 4.2 220 9.0 5.5
8 2360 6.6 200 8.1 3.5
13 3570 2.0 160 9.1 5.5
23 2940 1.4 130 9.5 5.3
33 2750 0.6 110 9.0 6.6
43 2027 0.9 90 8.1 9.5


C-S. CONCLUSIONS

Experience gained from in cylinder sampling suggests, that if

properly applied, this technique could provide valuable information which
would aid in the development of improved mathematical models. However,

certain questions regarding sample integrity remain to be answered. The

tentative conclusions suggested by the data are:

Significant unmixedness persists throughout the cycle

It does appear that the mixing process cannot be described by a
random homogeneous turbulence field with variations of species
concentration occurring in a random fashion in space and time.

The mixing process appears well ordered and repeatable, that has
its origins in the well-ordered jet mixing patterns occurring only

in the cycle.

There is considerable need to generate much more data, particularly
with the sample valve inserted to cover the total free volume. Data
obtained with the valve flush with the cylinder head is of limited
value because of the significant vertical gradients.

C-22


Real Injection Schedule

Swirl \ Direction

8
Migration of vapor
Injection _ and small droplets
Nozzle ~

——— Swirl

Jet Cross Section

Figure 3-3. Schematic Showing Simplified Cross Flow Effects

Heat Release

The complex chemistry of ignition is not included in the model. A
shell containing air and fuel vapor will ignite when an empirical ignition
criterion has been satisfied. This criterion depends upon the properties of the
fuel and the average pressure and temperature over the period of time before
ignition takes place. Once ignited the vapor reacts with the air oroducing
equilibrium combustion products. Initial heat release rates were too slow
when a turbulent flame speed model was used to ignite other shells. An
improved simulation has been achieved by allowing successive ignition in
other shells when they also satisfy the ignition criteria.


APPENDIX D
SAMPLING VALVE DATA TEST SERIES 3

Sampling value data test series 3 are presented in this appendix under the
following order.

No. of Speed Load Timing Swirl Fuel

points (rpm) g (ATDC) Level Injector
8 1500 0.6 -20 Medium 6
7 1500 0.6 -20 High 6
7 1500 0.6 -20 Low 6
8 1500 0.6 -12 Medium 6
7 1500 0.6 -28 Medium 6
8 1500 0.35 ~20 Medium 6
4 1500 0.35 -20 Low 6
1 1500 0.75 -20 Medium 6
1 2100 0.6 -20 Medium 6
4 1500 0.6 -20 Medium 4


4.8 Soot Formation and Oxidation

Little is known concerning the detailed mechanism of soot formation
and the model of soot formation is based upon empirical relationships derived
from experimental observations. It is believed that the following processes
are involved in the formation of soot:

- dehydrogeneration: breakdown of hydrocarbon molecules to form
molecules with a higher C/H ratio

- polymerization: formation of higher molecular weight molecules

- agglomeration: formation of solid particules

The most favorable conditions for soot production in diesel engines
are those high temperature zones deficient in oxygen. These conditions are
produced during the ignition delay period or during the early stages of combustion.
An Arrhenias type equation for the rate of soot formation has been suggested

by Khan and Greeves (4)

which is based upon the local unburnt equivalence
ratio, partial pressure, temperature and includes several empirically determined
coefficients. The Khan and Greeves relationship is not directly applicable
to this study due to the singularities in defining the zonal unburmt equivalence
ratio (when it is based solely upon unreacted oxygen) fora fuel rich zone.

A modified rate equation based upon local equivalence ratio of the

burned products their pressure and temperature has been used in this study is

Vv -
. T 4-92
Wot Ace (Aa G) e exp (-E¢/RT) as

The activation energy Est is taken to be 40 kcal/mole. P is pressure in atm.

T is averaged temperature of cylinder contents and the pre-constant A t is fitted
s

to exhaust soot data,

The mass rate of oxidation used is the expression proposed by Lee

28
et al. | ,

2 |
Ge exp - (E,,/RT)

(4-93)

4-40


1.0 SUMMARY

A modular model describing the processes of energy release and
pollutant formation in direct injection diesel engines has been developed and
tested. The model consists of separate modules describing the following

processes:
e Cylinder thermodynamics and heat transfer;
e Fuel injection and spray characterization;
e Air spray entrainment and droplet vaporization;
e@ Ignition delay:
e Air product mixing;

Heat release;

° Nitric oxide formation;
e@ Soot formation and oxidation.

It was recognized at an early stage of development that a model of this type must
be able to evolve with time. Consequently, the total package was constructed to
ensure that any of the modules listed above could be readily updated as more
definitive information becomes available. In essence, the present model pro-
vides a framework which can be readily used by other workers, after simple
modification, for their own specific purposes.

The model contains a considerable number of empirical constants
which have been divided into two groups:

e Those constants whose values are perhaps not universal, but
which remain unaffected by gross changes in engine design, or
do not strongly influence predictions of pollutant formation.

° Those constants which require adjustment to allow accurate pre-
dictions and which will require a certain degree of readjustment if
the model is used outside its original frame of reference.

A sensitivity study has been carried out to ascertain the influence coefficients
of these adjustable constants on nitrogen oxide and soot formation.

1-1


Input Conditions Exhaust Concentrations

Speed 1 , rie rpm NO, 3823 ppm
Tining AIDC) a. SO 0.1 percent
oO, 8.8 percent
Sample Valve Location
R = 5.6 cms
6= 30° from jet axis
Z = 0 depth (cms)
senme NO, co UHC SO,
ppm * Bem 4
-27 180 0.21 240 0.65
-17 260 0.25 360 0.65
-12 1635 5.20 450 6.80
-7 1600 9.00 $40 6.00
-2 1555 6.20 $70 6.60
3 2500 2.30 490 6.70
8 3507 0.90 440 6.70
13 3499 0.60 370 6.40
23 2590 0.50 240 §.60
33 1711 0.40 180 4.70
43 1430 0.25 180 2.40

fe)
nN

® pe

nn
roy
AOnNOrF OH AAONHN

HP On A

e


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Exhaust Concentrations

1500 rpm NO
0.6 *

-12 co

Medium ae

6 2
2

Sample Valve Location
= 3.9 cms

R
6 = 15° from jet axis
Z = 0 depth (cms)

sonme NO, co UHC
(2) ppm. % ppm
-12 200 0.10 300
-7 108 4.00 4500
-2 236 7.60 8000
3 280 5.20 7000

8 370 3.70 3900
13 1014 1.20 1100
23 923 0.40 500
33 718 0.28 320
43 737 0.19 210

D-27

1412 ppm

0.15 percent
0
8.0 percent

8.4 percent

Q
ce)
i)

[:

Bow wr SDS
oR YY DOH OD A

Ww wow

fe)
iy

fe

NOKF UHH OON


The engine performance is, of course, strongly linked to the rate
of fuel~air mixing and the state of the fuel, i.e., liquid or vapor. Figure 5-5
presents the distribution of fuel between these states from the onset of injec-
tion (-20°) to almost complete combustion (+60°). Fuel can exist as:

- unburned liquid fuel, i.e., that liquid fuel which is heating up
but not vaporizing or which is vaporizing;

- unburned fuel in the vapor state which is composed mainly of fuel
vaporized before the onset of ignition;

- burning liquid fuel, i.e., those droplets contained in burning zones.

Figure 5-5 shows that initially the mass of unburned liquid fuel is equal to the
mass of fuel injected. During this period the droplets are being heated, but
are not vaporizing. Before ignition the mass of fuel vapor increases, but it

is rapidly bummed out once ignition is initiated (at 9 = -13°). From this time
on the mass of unbumed liquid fuel also decreases. The plateau in the liquid
fuel curve represents the constant droplet heat-up time. After all the premixed
vapor has burned, the conditions are such that fuel can only exist as a droplet
in a burning zones or as unburned liquid fuel.

Elements of fuel are tagged by two indexes upon injection, reflecting
their crank angle at birth, and their location with respect to the fuel spray axis.
After ignition only a single index is used, reflecting age since the location is
irrelevant in the random mixing process. The history of two such zones is given
in Figure 5-6. The calculation of equivalence ratio ¢ does not include fuel in
the liquid state, only vapor and products are considered. Thus, as fuel either
evaporates or burns, the equivalence ratio increases and then decreases by
dilution. The temperature of the lean zone increases from the onset of ignition
because fuel is able to burn; however, the temperature of the rich zone hardly
varies because of the heat requirements associated with vaporization. In the
extremely rich zone virtually no NO is produced because temperatures are too
low by the time oxygen becomes available, and the NO that is found in this
zone is due mainly to dilution. This highlights one of the weaknesses of the

model which does not allow for NO formation by Fenimore type mechanisms‘! y .


Working Energy Conservation Equations

Internal energy and mass conservation relationships are expressed
by polynomials, thus the energy conservation equations for the “air” and
burning zones can be solved for the following temperate rate equations:

= 4-3
T, ALP + BL (4=31a)
where
(m RTs _O%a_ 7 ORa )
a 2s ta_P oP a OP
a Cc
a
. aR, — . Sed ea)
By =yrm, (T, 30, * %,) 8, + 2 (be By) By p> (YaQe tra * Fer
+ (he; - Uey) me; /C,
ou ORa
=m Zea
Cy a! at +RU+T, OT )
a a
and
Thm,1 = Aum, I P+ Baal (4-3 1b)
where
(Fomatomat , _2¥bmt Rom 1
_ “emT\ Pe oP bm, 1 ap
Aam c
‘bm ,I

4-12


4000
! aust
[NO] ppm I Concentration
| (Pha se II)
! inj = -28°CA
! eee ben wooed a
T 2
' /
yf
\
3000 f-
pod
fs
/ !
‘ ; Experimental Data Spread Between
/ 1 Phasaq I and Phase II
7 T
/ | 2387
! !
| | inj = -20°CA
H ! 2050
2000 i t
1
q 1
| !
! {
L |
/ ! 9iny = -12°Ca
i —_ rs a 1233 —_—
| | 7
! I
i | f
1000 T 1 /
H
n I
) /
/
t 1
/ 7 —T
H "
j /\
‘ a |
WA, vA 1
-30 =20 -10 TDC 19 20 30 40

6

Figure 5-3 Comparison of Calculated Instantaneous NO with
Measured Exhaust Levels for Various Injection Timing

S-9


Speed

Equivalence Ratio (nominal!)

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling
Time
—O_
~22
-12
- 7
- 2

3
8
13
23
33
43

Input Conditions

NO

115

143
1560
3400
3419
2280
1312
1581
2233
2355

Sample Valve Location

ov

Exhaust Concentrations

1500 rpm NO
x

0.

6

-20.
High

6

co
UHC
co,

Oy

2100 ppm

0.005 percent
0
8.5 percent

8.6 percent

= 2.7 cms

= 0° from jet axis

= 0 depth (cms)

co UHG CO, O2
% ppm % %
0.002 320 0.40 19.8
0.45 1200 1.85 17.0
0.75 1500 5.50 12.3
2.20 400 8.60 6.0
8.80 0 8.40 1.0
10.00 0 8.40 0.1
10.00 0 8.50 0.0
7.00 0 10.10 0.0
3.80 0 11.60 0.3
2.00 0 11.80 1.3


we

i

Table 5-1

Nonadjustable Empirical Constants

Constant

reaction, Eqn (4-93)

Field et a29)

Description Literature References Remark
Value
c Pre-constant In Annand type of convective 0.17 Mcaulay et all!S) | riterature value
‘a
heat loss expression Eqn (4-32) : used
co Power for Reynolds number dependent 0.7 sitket 9 Literature value
in Annand type of convective heat Mehulay et atl!5) [used
less expression, Eqn (4- 32)
eb Product of density and masa diffusion 3.0% 10741 Bracco!) Literature value
coeffictent used as a constant In g-cm/sec used
droplet diffusion flame model
Cove Convective conrection on droplet wisel!9) Literature value
vap | vaporization, Ban (4-43) 0.276 Ranz ot al(32) used
Frossling
Cha See Eqn (4-37) 37.5 teo!!7) Value obtained via
* curve fit toLee’s data
é See Eqn (4-36) 0.85 Lee(!7) Value obtained via
curve fit to Lee's data
CH laltial free Jet spread 0.135 Newman?) Literature value used
coefficient, Eqn (A-1) :
Cy Free Jet main region, spread 0.175 Newman (34) Literature value used
coefficient, Eqn (A-4 )
c Wall Jet spread coeffictent 0.204 Gauntner et a5) | Derived from Gauntner’s
wi tan (A-14 ) resulta
(21)
g Activation energy for Ignition 9290, cal/ |. Shipinskt et a! , Literature value used
9 reaction, Eqn (4-45 ) g-mole
B, Centane number dependence for -0.69 Shipinsk! et ai (2) Literature value used
'9 ignition delay, Eqn (4-45)
Cc, Preasure dependence for ignition -0,386 Shipinski et ai? » Literature value used
‘a delay, Eqn (4-45)
E£ Activation anergy for soot 40 kcal/ Khan & Creeves') Literature value used
bd formation reaction, Eqn (4-92) g-mole
Ang Pre-constant for soot oxidation 6.5x 104 Lee et a(28) Literature value used



Liquid Fuel (Vaporizing

ww oy ne - +4 4-2
afl Bey Mey He Mey 8a Mag * [el (4-2)

Liquid Fuel (Buming)

m u = n - r 4 (4-3)
flb “fb Ta Bag 7 Peg Migy * 402
Fuel Vapor
. . . . . . (4-4)
m, u = - - v - 7a.
tg fg beyMe, [hey Menp! P Beg ( Vgc q rig!

Burning Systems

mn u m i + (hin +h, m (4-5)
om, ttbm,t = Mapp * Bega r 7 MaTMape,1 * Meg epb, 2
L ; . -
“Py yr P Bom 7 %om,1 20 * tebm,t* Fe2,7

Here dot represents the time rate of change in crank angles (i.e., d/d4).
The relative zonal volumes of gaseous systems to the total cylinder

volume under uniform pressure, are defined by

_ Ta Ra Ta

= By (4-6)

4-5


rate of dilution and vitiation is derived with the following provisions:
- only the "air" and burning zones are involved;
- turbulence is unsteady but homogeneous throughout the engine cylinder;

- the overall dilution rate decreases as the mass of available air
decreases;

- overall dilution rate vanishes with the total mass of combustion
products;

- the zonal dilution rate depends upon the zonal surface area in contact
with "air" zone, This area is assumed to be proportional to the
zonal volume

Thus, a rate of dilution can be expressed by

dm, = 1 MaaTMbm

d0 0 Tmix mi, +m, (4-46)

bm

where Ma is the mass of the "air" available for mixing, and is equal to the mass

of unburnt “air" lessthe mass of "air" mixed with unburmnt fuel vapor. An

expression similar to Eqn (4-46) has been used by Bastress et al! 2) where

T mix Was input as a arbitrary adjustable constant. Physically,

Tix in Eqn (4-46) is the characteristic mixing time (measured in crank angles) and
is related to the characteristic turbulent length scale f and the turbulent diffusivity

D by:

the turbulent diffusivity is in tum related both to the scale of turbulence,

# , and the scale of turbulent velocity Meare by:

«fh:
Pp “turb


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling

Exhaust Concentrations

1500 rpm NO
0.6 x

co
-20.
Low cae
6 2
92

Sample Valve Location
= 3.9 cms

R
e= 30° from jet axis
Z = 0 depth (cms)

Time NO co UHC
ppm % ppm

-22 173 0.08 200
-12 198 0.25 260
-7 1681 3.4 400
-2 2008 3.8 350
3 2390 2.4 240

8 2160 1.4 200
3 2142 - 0.7 200
23 1867 0.2 170
33 1493 0.14 110
43 1380 0.13 100

D-21

1555 ppm

0.1 percent
0
8.6 percent

8.8 percent

Ra aAanarnrnnrroae
wow OrFrARAAAN &N

10.
ll.
13.
13.
14,

nw Owe Ou Bb & MN ©


The net rate of soot formation is
. ° .
We = oe 7 Woo (4-97)
The species conservation equations for soot in the “air" and the burning zone
are:
Jair

-+12 [es - %) i + we) (4-98)
m. v,I

Burning Zones

. 1 . .
Yom 1 7 TMom,I [a 7 Som, 1] ("D,1 *TMapb,?

(4-99)

Ws)omit Mab, * TMeppid * 5) om,t

4,10 Equilibrium Compositions

The equilibrium species distributions (in mole fractions) of combustion
products are computed by means of a computer program developed by the NASA
Lewis Research Laboratory. For fuel-lean mixtures, eleven species including

CO,, CO, H,0, Hy, NO, OH, Ny. O,. H, N and O are considered and CH, is
added for fuel-rich mixtures. The Argon content of the air is neglected.

For a given fuel, the species distribution are calculated as functions
of three parameters: pressure, temperature and equivalence ratio. For com-
putational efficiency, a set of species distribution tables, covering the pressure,
temperature and equivalence ratio ranges of normal engine operation, are cal-
culated and stored in magnetic tape. Consequently, a 3-D table look-up is the
only operation needed whenever equilibrium composition, for specified pressure,
temperature and equivalence ratio, is required.

4-42


Equivalence Ratio

In order to determine the composition and theromodynamic properties
of each zone, instantaneous equivalence ratios must be calculated. This can be
achieved by maintaining separate accounts for the mass of pure air and the mass
of fuel in each zone. The equivalence ratio of the."air" zone is governed by

5 8 ae : .2
Ba pga a tt oma/ os” paa (4-19)

where the total flux of fuel and pure air due to the .various rate processes, i.e.

vitiation, dilution and combustion can be expressed by:

Mea mm, “Na (my * Mob) (4-20)

. . “oad
Moga =D yr 7a Mp * Mapp) (4-21)
Similarly, the equivalance ratio of the burning zone is govermed by:

. +2
> = m.,-m, ,m Yt_m
Pom 1 (moat f,1 f,1 vet fos pa,l (4-22)

where

_. . *
me = Began * eps 1” Ta Mut

: : xf , (4-23)

Moa, %aTMpD,I “rT wl

de
1
w


Input Conditions

Speed

Equivalence Ratio (nominal)
Timing (ATDC)

Swirl Level

Fuel Injector

Exhaust Concentrations

1500 rpm NO,
0.6

-20. co

Medium GHC

6 2
%

Sample Valve Location
R = 3.9 cms

e= 45° from jet axis
Z = 0 depth (cms)

Sete NO co UHC
°) ppm % ‘ppm
-22 280 0.15 820
-12 300 0.28 920
7 2220 2.35 660
-2 2980 3.80 600
3 3015 3.40 0

8 3007 2.00 0
1B 3800 1.35 0
23 4118 0.80 0
33 3700 0.45 0
43 3590 0.60 0

2396 ppm

0.006 percent
0
8.5 percent

8.8 percent


(NO)
(NOY,

1.0

0.6

0.2

G80), (Soot) °

Calculated 2077 ppm 139 gm/m?

—-— — Measured 2050 ppm 10% opacity

1.0
(Soot)
Soot),
0.8
0.6
0.4
14 15 16 17 18
CR
Figure 6-4 ‘ffect of Compression Ratio


Input Conditions

Speed

Equivalence Ratio (nominal) 0.6

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling

Exhaust Concentrations

1500 rpm NO,
co

28.

Medium gBe

6 2
2

Sample Valve Location
= 3.9 cms

30° from jet axis
0 depth (cms)

R
8
Zz

Time No, co
(2) ppm %
-32 560 0.15
-12 1830 3.20
-7 2370 3.40
- 2 2760 2.00

3 2440 0.76
8 3070 0.70
13 3840 0.46
23 3645 0.30
33 3300 0.34
43 2820 0.26

D-36

UHC

100
300
350
240
200
160
140
130

90

80

3540 ppm

0.1 percent

0

8.0 percent

8.6 percent

co, oO,
a a
1.0 18.3
7.4 7.0
7.8 6.6
7.3 9
6.0 10.0
6.6 10.6
7.0 10.2
6.7 9.8
7.4 10.0
6.4 10.8


where w is defined by wi = wy," - vi Wy. If we further specify that

a22,- 2,
or
B52, + 2p
we have
M dg _ 1 d/2dg
SE =f;
a r re = ( 2)
where
M .2u
2 =)

Integrating the above equation once, with respect tor, we have

dg 2 SL Mt
dr re

Further integration gives the general solution as

Cc .
- 21 .-M/

3 me + CO, (4-68)
here GC, and Cy are the constants of integration, to be determined by imposing
appropriate conditions in accordance with the assigned definition of 8. The
important relations deduced from the above general solution are explained
briefly in the following.

Mass Burning Rate

The expression for mass burning rate, which is obtained by defining
3: Zp + 2059 and utilizing the boundary conditions at the droplet surface and
the far field,can be written as

r
. = a
m= 47 eDr ( T c) £a(1+B,) (4-69)


6.0 COMPARISONS BETWEEN ENGINE EMISSION
LEVELS AND MODEL PREDICTIONS

The tuned model predictions have been compared to the engine
performance data reported by Wilson et all t am The characteristics of the
single cylinder experimental diesel engine were described in Section 5.2 as
were the engine conditions used for the baseline data. The response of the
model to the following parameters has been investigated:

e Engine operational parameters - timing, load and speed and
compression ratio;

e Charge intake parameters - air swirl, turbocharging and exhaust gas
recycle;

e Fuel injection parameters - diameter and number of orifices.

Calculations of both scot and NO formation are carried only as far as 30° after
top dead center since initial calculations indicated formation and distribution
rates were negligible beyond this point because of the low zonal temperatures.
Calculated NO levels are given in ppm and soot in mg/m3,

6.1 Effect of Engine Operating Parameters.

Effect of Timing
The effect of fuel injection timing on exhaust NO level is well known.
Timing retardation significantly reduces the emission of NO due to:

- reduction of ignition delay;

- heat release in the expansion stroke where bulk temperatures
and pressure are declining

- reduction of the total residence time.

These effects are more pronounced at high load, that is, when the duration of
fuel injection is longer. The comparisons of calculated and measured exhaust
NO concentration are shown in Figure 6-1. For @= 0.6, a delay 8° CA injection
reduces the NO by 35 percent, conversely a 70 percent increase in NO is
observed by 8° CA timing advancement over baseline case. The effect of

timing on the level of soot in the exhaust is shown in Figure 6-1. Higher

6-1


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO, 2000 ppm

Equivalence Ratio (nominal) +35 t

Timing (ATDC) -20.0 Bee aso aia

Swirl Level Medium

Fuel Injector 6 co, 5.2 percent
° 13.1 percent

2

Sample Valve Location
R=2.7 cms
a= 30° from jet axis
Z = 0 depth (cms)

Sampling NO, co UHC CO, oO,
(9) pom % ppm % %
-22 108 0.08 280 0.30 19.8
-17 80 0.10 700 0.40 19.8
12 98 1.50 2800 1.80 17.0
-7 $80 8.00 6000 6.20 5.0
-2 715 2.00 1100 $.00 13.0
3 908 0.38 600 3.60 18.0
8 1350 0.20 500 4.50 14.5
13 1472 0.18 450 4.50 14.0
18 1810 0.10 0 4.50 14.0
23 2100 0.18 0 4.60 13.7
28 2030 0.18 280 5.80 12.5
38 2420 0.15 250 5.20 13.0

D-40


§.0 THE EMPIRICAL NATURE OF THE MODEL

One of the major objectives of this program was to develop a model
describing the formation of pollutants in a compression ignition engine which
contained the minimum number of arbitrarily assigned empirical constants.

The previous section indicated that limitations in the fundamental knowledge of
many of the physical processes described in the model necessitated that several
empirical constants be included. Although the physical significance of the
empirical constants included in the Ultrasystems' model has been discussed

in the previous section, it is necessary to summarize the empirical constants
used in the model and to ascertain the sensitivity of predicted engine per-
formance to the value of those constants.

S.1 The Nature of the Empirical Constants

The empirical constants included in the model have been divided into
two groups and the basis for this division is:

- the level of uncertainty associated with their numerical value;
- their importance with respect to the prediction of engine performance;

- the availability of experimental data to allow re-evaluation.

The first group of constants are considered to have nonadjustable values for

the purpose of this study and are listed in Table 5-1. Although it is recog-
nized that several of the constants listed in Table 5-1 cannot be considered

as well established (e.g., E, activation energy for soot formation), some
bounds must be placed on the number of “adjustable” constants. Consequently,
those constants included in Table 5-1 were selected because:

- they had values which were generally recognized and had been
established from acceptable experimental evidence (e.g., C

Cy Cray: o Eig: B., Cig and Coyap)!

a’

ig

- they had been used previously and no new data was available
to necessitate re-evaluation (e.g., oD, Aso! ES: Cay and Coyy) i

- they were considered to have a minor influence on the calcula-
tion of engine performance (e.g., Ce) .


NO.

1.5

1.0

0.5

0.0

(Yo
VA

T

Inc], (soot),
Calculated 2077 (ppm) 139 gm/m

oo

——O-—— Measured 2387 (ppm) 10% opacity

1.5
Soot)
Soot)

1.0

(Phase II)
a
a SS
=
|~
/'|
fe
-28 -20 -12
inj
Figure 6-1 Effect of Timing

6-2


8-5

Table C-1.

Experimental Condition for In-Cylinder Investigations

No. of Orifices No. of
Series R.P.M. Load in Injector Timing Swirl Valve Locations Remarks
A 1500 0.6 6 -20 Low 8
Medium 7
High 6
B 1500 0.6 4 -20 Medium 6
Cc 1500 0.6 6 -28 Medium 8
D 1500 0.6 6 -12 Medium 8
E 2100 0.6 6 -20 Medium 4
F 1500 0.35 6 -20 Low 2 *
Medium 2 *
G 1500 0.35 6 -28 Medium 2 *
H 1500 0.35 6 -12 Medium 2 *
I 1500 0.3 6 -20 Low 6
Medium 8

*
Series with sample valve

inserted 0.25 in,



The dead volume in the sampling system was reduced as much as
possible. However, the sample analyzed always contained a significant
fraction of NO,, and it is hot known whether all of this is due to oxidation in
the sample line or whether NO, is actually formed in the cylinder. Conse-
quently, the concentration of interest is that of the total nitrogen oxides since
the NO level will not be sufficient to characterize the pollutant content of the
sample. NO, levels were determined by passing the sample through a conver-
ter which normally converts the nitrogen dioxide to nitric oxide, thus allowing
the total nitrogen oxides to be measured by the chemiluminescent analyzer.
However, when the sample contains fuel gases such as hydrocarbons and carbon
monoxide (the sample would probably also include hydrogen, but this was not
measured) NO, levels lower than NO levels can be recorded. Typical results
are presented in Table C-4 where it can be seen that for samples withdrawn
around TDC the NO, levels are obviously in error. Thus, the results will mis-
Tepresent actual NO, levels when fuel gases are present tending to give lower
tates of NO, increase since these are the samples normally containing fuel
gases.

The modified valve design allowed measurements to be made during
the fourth test series with much deeper valve insertion distances. Several of
the results obtained with this design are presented in Figure C-l. Time restric-
ted the extent of the test matrix which was limitted to one sample valve posi-
tion (No. 2) with the fuel nozzle rotated such that the sample valve was located
30° downstream from the initial jet orientation. Probe insertion was varied
between the flush condition and 11/16 inch penetration. Swirl and injection
times were varied, while load and speed were held constant at ¢=0.5 and
1500 rpm. Considerable care was taken to ensure that exhaust levels were
reproducible and that actual sample valve data was repeatable.

In the fourth series of tests the sample valve was operated over a
wider cycle range since it was expected that at sample times greater than +100°
the sample valve concentration would approach the exhaust values. As shown
in Figures C-4, 5, 6 and 7, this was not the case for this one sample valve


It is assumed that the fuel spray breaks into droplets immediately upon
injection and that the droplets have a specified size distribution. The drop-
size distribution is described by an upper-limit distribution function, the
fraction of the total fuel mass, having a dropsize within the interval d,_,sdsd,
being given by

4m d d
1 1 i (—__—icl
G, = =— = Flerf | 6ln (=———- - erf|6ln = (4-36)
1 Mot 2 | ez ~ i) | Come a)|

The maximum droplet size, duax’ is directly proportional to the
nozzle diameter, and is inversely proportional to the product of the Weber and
Reynolds numbers to the 1/4 power, and to the pressure of the cylinder air
charge at the time of injection to the 1/5 power, i.e.,

3/8 .-1/8 1/4 .-1/5

= 1/2 1/4 ,-
d = Cod ay’ Ap Py Wy” Pa (4-37)

max max nozzle
where
Ap is the pressure difference across the injector orifice in (dyne/cm?)
oy is the liquid surface tension in (gm/sec*)
My is the fuel viscosity in (gm/cm-sec)

d ‘is the nozzle diameter in (cm)

nozzle

The two empirical parameters in the above expressions 6and Coa
have values of 0.85 and 37.5, respectively, which represent the best fit
to experimental data by Lee(t7) .

x!


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO, 1780 ppm

Equivalence Ratio (nominal) 0.6

Timing (ATDC) -20. oe oT Percent

Swirl Level Low

Fuel Injector 6 co, 8.6 percent
04 8.8 percent

Sample Valve Location
R = 3.9 cms

@ = 15° from jet axis
Z = 0 depth (cms)

a rd NO co UHC oO, O2
ppm =a ppm =n =a

-22 135 0.13 350 0.43 20.1
-12 224 8.5 4000 4.6 7.0
-7 760 10.0 8000 6.5 2.0
-2 1245 7.0 3000 7.2 4.5
3 1295 3.6 1200 7.5 7.2

8 1935 Ll 750 6.8 11.0
1B 1880 0.8 650 6.0 11.3
23 1790 0.4 450 6.0 12.5
33 1750 0.36 400 6.0 12.5
43 1684 0.4 210 6.0 13.0


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO
Equivalence Ratio (nominal) +35 Cc o.
Timing (ATDC) -20.0
Swirl Level Medium UHC
Fuel Injector 6 co
2
2

Sample Valve Location
R= 3.9 cms
a= 30° from jet axis
Z = 0 depth (cms)

Sampling NO co UHC
Time x
—o) pom 4 ppm
22 150 0.06 170
-12 158 1.10 240
-7 1700 4.20 500
- 2 2020 4.80 600
3 1373 1.40 300
8 1017 0.53 280
13 970 0.24 240
23 1140 0.18 210
33 1045 0.18 150
43 1000 0.16 140

D-43

1765 ppm
0.06 percent
ie)

5.1 percent

13.2 percent

co, °,
4% %
0.40 “19.8
2.40 16.0
8.00 5.5
7.80 5.0
7.10 8.8
4.40 13.5
3.80 14.5
3.40 15.2
3.70 15.2
3.40 18.6


3.0 THE METHODOLOGY OF DIESEL ENGINE MCDELING

Diesel engines are a fact, they operate satisfactorily in all manner
of equipment. A significant reason for attempting to develop an analytical model
describing the processes occurring within a diesel engine can be that such a
model lies on the critical path to the construction of a more efficient, cleaner
engine. As a design tool the analytical model is at present in its infancy. The
complex interaction of physical and chemical processes occurring in a diesel
engine involve phenomena which are not completely understood at present.
However, each small advance in the state-of-the-art of modeling helps to
build what can be a powerful tool in the hands of engine designers.

The mathematical simulation along will not enable improved diesel
engines to be built. Development and prototype testing, rejection and redesign
are mandatory. However, the availability of an analytical model which will
guide this iterative process could greatly reduce development costs. This is
particularly applicable to attempts to reduce pollutant emissions through engine
redesign without incurring the penalty of increased fuel consumption. Pollutant
formation in diesel engines is controlled by several interrelated parameters
which mades complete redesign based upon intuition difficult. An accurate
analytical model which has been tested and the range of applicability established,
will help to guide this intuition, thus saving valuable experimental test resources.

Before presenting the detailed mathematica! formulation, a qualita-
tive description of the model developed during this orogram will be given and
contrasted with other models.

3.1 Review of Existing Models

Wilson et al! 4)

reviewed, in considerable detail, the characteristics
of the various models which predate the present model. However, a concise
description of their salient features will be presented to allow an adequate

comparison to be made with the new Ultrasystems' model.


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO 2411 ppm

Equivalence Ratio (nominal) 0.6 x

Timing (ATDC) -20. co 0.006 percent

Swirl Level Medium UEC 0)

Fuel Injector 6 CO, 7.8 percent
oO, 8.3 percent

Sample Valve Location
R = 2.7 cms

@ = 30° from jet axis
Z = 0 depth (cms)

aoa NO, co UHC co,

an ) ppm = ppm a
-22 139 0.001 360 0.30 19,
-12 123 0.003 $400 0.58 14

-7 660 5.10 9500 6.70

-2 820 5.50 12500 6.40

3 1489 4.50 2500 6.10

8 2090 0.70 950 7.00

13 2188 0.65 850 8.00

23 3150 0.66 650 7.70

33 3800 0.60 0 7.20

43 4120 0.50 0 7.10

annwowowonrn s
AOnwnuwonnoruanr


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO, 2450 ppm
Equivalence Ratio (nominal) 0.6 oO
Timing (ATDC) -20. osc 0.2 percent
Swirl Level High es 36
Fuel Injector 6 2 +6 percent
O02 8.9 percent
Sample Valve Location
R = 2.7 cms
@ = 30° from jet axis
Z = 0 depth (cms)
Sampling
Time NO, co UHC SO, ir)
ppm % ppm % %,
22 112 0.05 1600 0.6 20.5
-17 40 0.40 4500 0.8 19.0
-12 180 5.40 9200 $.0 9.2
-7 860 9.00 10200 7.8 2.6
- 2 2010 10.00 14000 6.6 1.2
3 3000 4.40 2600 9.9 2.7
8 3220 6.50 1100 10.0 0.8
13 2210 8.00 1000 9.9 0.2
28: 2250 4.00 1000 12.0 0.6
38 950 2.40 770 12.0 1.2


Input Conditions Exhaust Concentrations

Speed 1800 rpm NO 1685 ppm
Equivalence Ratio (nominal) 0.6 co.
Timing (ATDC) -20. T 0.1 percent
Swirl Level Low HC 9
Fuel Injector 6 CO, 8.2 percent
ie) 8.3
2
Sample Valve Location
R = 2.7 cms
@ = 0° from jet axis
Z = 0 depth (cms)
Sampling
Time NO, co UHC CO, 7)
(°) ppm % ppm % %
-22 135 0.05 300 0.50 19.3
-12 70 0.80 2500 1.02 17.9
-7 188 1.80 4000 2.80 14.1
- 2 432 1.70 4000 3.30 13.5
3 718 0.60 800 4.30 13.4
8 770 0.23 500 3.60 14.8
13 916 0.15 0 3.70 15.0
23 917 0.10 0 3.80 14.7
33 1038 0.08 0 3.90 14.5
43 980 0.09 0 4.20 14.2


which can be obtained from methods similar to those described above, are

listed as follows without further explanation.

Temperature Distribution

(r, _ Tt) (e -M/r -e M/ty
T=T+ -M/r, -M/r
(e l-e f) roe<t
, -T, ) (e -M/r _ a Mey
T=T + — = ror
0 Ce M/t, -e M/t,, ) f£
Fuel Distribution
_ Yq oMe -< "9 P<
f (eA Mt
and
vy. 2 17 (Yona
f,1 T+ Bo
Oxygen Distribution
“Nv -M/r;
y= You, 2 Ce Mite £) ro> fs
02 (e/g _ ay

Nitrogen Distribution

where nondimensional burning rate is defined by
m
f£
47PD

Me=

(4-72)

(4-73)

(4-74)

(4-76)

(4-77)


2.0 INTRODUCTION

This report presents the culmination of three years effort to provide
diesel engine designers with an analytical tool to aid in the development of
clean, efficient diesel engines. The initial phase of this program was concemed
with the construction and operation of a single cylinder engine to provide data
on pollutant formation and to give some insight into the mechanism of pollutant
formation. Experimental information was generated with which to test the
analytical model to be developed in a later phase. The successful completion
of this work has been adequately described by Wilson et ay) . The second
phase of the work, namely the construction, modification and exercise of a
mathematical model to predict pollutant formation in a diesel engine is des-

cribed in this report.

The general objective of the total study was to provide industry with
a working computerized tool to aid engine development. This tool was to be
developed in an iterative manner in conjunction with diagnostic experiments
planned to provide information on the phenomena occurring within the cylinder
during combustion. The model development included in this report is confined
to direct injection engines, although the experimental investigations described by
Wilson et al) include data on prechamber configurations. At the initiation of
the project is was hoped that the model development would include both con-
figurations. However, the realities of modeling such a complex process as
intermittent combustion in a compression ignition engine dictated otherwise.
The progress of combustion and, therefore, energy release and pollutant for-
mation is dominated by the fuel/air mixing process. Since the mixing processes
are entirely different in the two configurations, this would necessitate two
separate models. Constraints imposed by time and budget precluded the develop-
ment of two models and it was decided to concentrate the modeling effort on
direct injection engines. The constraints stated above also prevented applica-
tion of the model to other engine geometries and multi-cylinder engines.


4.6.2 Heterogeneous (Droplet) Combustion

When fuel droplets exist in an environment containing oxygen, reactions
can occur in a narrow zone surrounding the droplet-the diffusion flame envelope.

In recent years numerous theoretical and experimental studies have been carried

out to establish the mechanism of combustion of single droplets in an infinite
atmosphere (williams(22+49)), Due to the complexity of the process, none

of this work can be directly applied to heterogeneous combustion in diesel engines.
The droplets do not exist in an infinite environment and interaction will take pl2ce
between droplets. The atmosphere is not quiescent thus allowing the formation

of wake flames or producing complete flame blow-off. Calculations indicate
that droplet combustion does not take place as though single droplets existed

in an unbounded environment since the volume necessary to accommodate such
flames was found to be many times the engine displacement. The ultimate
solution will involve some form of unsteady combustion coupled with effects

due to relative motion between the droplet and its surroundings. As a very small
first step, the classical droplet theories have been modified to provide flame
confinement and to allow continuous vitiation of the atmosphere surrounding the

droplets.

The basic assumption involved in the analytical solution for con-
fined pseudo-steady state droplet combustion which has been included in the

model are:
- combustion takes place under quasi-steady state conditions;
- the rate of chemical reaction involved in heat release are infinity
fast
- the pressure throughout the system is uniform
- the system is spherically symmetric
- average values are used for the specific heat and thermal conductivity
of the gas and liquid phases
- Lewis number is unity (i.e., PD = 2 = constant)
is}

- liquid temperatures are constant, the droplet temperature is given
by the stable wet-bulb temperature of vaporization thus temperature
transients in the liquid phase are neglected

4-25


NITROGEN OXIDE (NO,), PPM

Vafve Depth
Speed: — rpm © Flush
4oook Load: =.5 ° a V8
Timing: Bij = ~ 20 a 1/4
Swirl: Medium ° V2
v U/I6
3000)
e@ Exhaust
Vatue.
2000+
| eae
Sx 8,33
1900 | Zz Psy
1 L L 1 1
100 [) 109.
Crank Angle, Degrees
Figure C-4. Dependence of Sample Valve Measurement

on Valve Insertion Depth

C-7


@ "fb"
%,
%
o

Figure 4-1 Conceptual Zones of Cylinder Contants


Once ignition has occurred, the location of that shell is no longer
tracked in space, but only in time. Mass transfer between air and zones
containing combustion products and vaporizing fuel droplets is no longer
considered to be controlled by the turbulent jet mixing model. All the air
is assumed to be equally available to all the parcels of fuel and the mixing
rate is dependent upon the mass of air available and the mass of each package
of burned products. Air is vitiated with combustion products, but no provision
is made for mixing to take place between packages of products. This random
mixing process is related to the turbulence properties of the air charge, but
it still includes an empirical constant.

The mechanism of heat release depends upon the state of the fuel
and oxygen availability. The chemistry of hydrocarbon combustion is not
included. Ignited fuel vapor, or fuel vaporizing in a rich zone is immediately
transformed into equilibrium products. Droplets vaporizing in oxygen rich
atmospheres can support spherical diffusion flames. No criterion is included
for flame blow-off or the production of wake flames.

Pollutant Formation

The model does not consider that the pollutant species, nitric oxide
and soot are in chemical equilibrium. The rates of formation and destruction
of these species are calculated from simple kinetic considerations assuming
that the species involved in their production and oxidation are in equilibrium.
Extens ive reviews of the kinetic mechanism of NO formation in combustion
processes are available in the literature (!) | The model includes the following

reactions:

N, +0 => NO+N

2
N + 0, — NO +0

which ts usually referred to as the Zeldovich mechanism. This approach does
not include any coupling of the hydrocarbon chemistry with the nitric oxide
formation, either in terms of superequilibrium atom concentrations, or Fenimore

type reactions (1) 1 O.de,

3-8


Experience gained during the development of the model and during
subsequent application has highlighted two areas of major importance:

e  Macromixing. The results of the sensitivity study indicated that

the most sensitive parts of the model are those parameters related
to fuel/air mixing.

e Spherical droplet diffusion flames. The model suggests that non-
premixed heat release regions can not be adequately described by
single droplet diffusion flames.

Chemistry inherently sets the lower limit on pollutant formation in diesel engines,
however, it is not the governing mechanism. Macromixing, fuel and air con-
tacting on the macroscale is the limiting mechanism. Consequently, it is not
surprising that those parameters included in the model which influence fuel/

air mixing have the strongest influence on pollutant formation.

Two regions are identified in the model which appear to be of major
importance from the aspect of NO formation:

e Those regions where combustion products are well mixed on a
scale which is small compared to the total volume of that region,
and therefore, local gradients can be neglected. The NO forma-

tion rate is calculated by a non-equilibrium homogeneous model
based upon extended Zeldovich kinetics.

e Those regions in the vicinity of fuel droplets which allow the
formation of spherical diffusion flames. These regions are typified
by steep gradients, and molecular diffusion plays a strong role.

Calculations indicate that the total exhaust NO level is dominated by NO pro-
duced in the former regions. In the model as it now stands, droplet diffusion

flames do not contribute a significant fraction of the total NO production under
normal diesel operating conditions. This can be attributed to:

e A large fraction of the droplets are contained within rich zones
which cannot support spherical diffusion flames;

1-2


Without obtaining further data at different probe locations it is
impossible to be definitive in providing an explanation for the observed be-
havior. However, it is possible to construct a variety of plausible explana-
tions which could represent the actual situation. For example, as suggested
above it may be that late in the cycle the probe is sampling relatively “young”
zones where the fuel came into the system late in the injection period. As
a consequence such a zone would experience rather rich combustion early
in its history with attendant low NO levels. Subsequently such a zone ex-
periences dilution by air entrainment to lean conditions but the temperatures
are too low at that time to produce significant NO. A necessary condition
for this or any other mechanistic explanation to be valid is that there exists
considerable unmixdeness late into the expansion stroke. Otherwise the
late sample measurements would have to reflect the entire cylinder content
and hence the exhaust value. Now the measured fuel/air ratios (deduced from
the excess oxygen) confirm that this unmixedness does indeed exist. Sample
equivalence ratios at the exhaust valve opening point are presented in
Figures C-4, 5, 6, and C-7. The mass average of these values must be
0.5 (the exhaust value).

The distribution of equivalence ratio with crank angle is presented
in Figures C-8 and C-9 for several swirl levels and at two valve insertions.
An interesting peculiarity is the dip in equivalence ratio after the initial spike
followed by a period of growing richer and then a final dilution period. A
possible explanation again rests on the concept of "younger" and previously
richer zones appearing in the neighborhood of the valve later in the cycle.
Another explanation might be that this behavior reflects a jet interaction
phenomenon where at approximately 25° ca the sample position begins to
experience the presence of a neighboring jet. Figure C-7 provides additional
evidence that unmixedness persists late into the cycle. Data is presented
there for different valve insertion depths. Substantial gradients exist at
6= 150° in both NO and equivalence ratios.


The locus of the mass element in '"j" shell is expressed by

§
U- 201, = 20 b f } peveds (a-8)

(iii) Transient Region

The initial conditions of the wall jet are obtained from conversation of mass
and mechanical energy during the transition. The initial width and velocity of

3-D wall jet are expressed as;

' Teo B's,
n= 12 [Se ws
eae ancl

l
(¥ Ty fPs Teg * raw ted

=] v

& (A-10)
© [Tez Cale * (Pa ')lev1 |

The initial fuel density of the wall jet at the location nearest to the wall is
obtained from conservation of fuel mass:

ly

p_\=
( 2); ay (A-11)
ar Ew Teo i)

Where subscript "o" represents the values at r = > and the numerical values

of the integrations
1.59
1, =2r (l-¢€ ) dé

A-3


uw

P (atm)

90

BO

70

60

$0

40

30

20

10

I
_ ;
N = -28°
in| N Ginj 28°CA

Calculated
Measured

K-
2

>

y

“7

SS

oke--4 ee He ee he Ke eH KH Ke He
a

7 N
h
o
-60 -50 -40 -30 -20 -10 10 20 30 40 50 60
8
Figure 5-2 Calculated and Measured Pressure Crank Angle Histories of Cases

(Ci -28° and -12°, g=0.6, speed = 1500 ppm)


and 7 and « are defined by:

f

7= “T+90
1
“(1 + £)

Caloric Equations of State

The combustion products are assumed to be in thermodynamic and
chemical equilibrium and the properties of the “air” and burning zones can be

calculated based upon the pressure, the local temperature and the local

(4-24)

equivalence ratio. Consequently, it is possible to express the internal energy
and the gas constant of the combustion products and the “air" by the following

general forms, i.e.,

where

T

1000

and f is the stoichiometric air-fuel ratio based on the fuel used, and
os

4-9


Input Conditions

Exhaust Concentrations

Speed 1500 rpm NO 2426 ppm
Equivalence Ratio (nominal) 0.6 co 0.1 percent
Timing (TDC) -20. UHC 0
Swirl Level Medium co 8.5
Fuel Injector 6 2 +5 percent
Oo, 8.8 percent
Sample Valve Location
R = 3.9 cms
6 = 30° from jet axis
Z = 0 depth (cms)
Sampling
Time NO, co UHC C02 2
(°) ppm % ppm % %
22 133 0.2 600 0.61 19.5
-12 123 1.9 1050 1.55 16.5
-7 890 10.0 5750 6.50 2.7
- 2 1112 6.6 3000 7.00 4.9
3 2100 5.4 2000 7.00 $.5
8 2950 2.2 1050 8.60 6.4
13 3300 1.4 900 8.80 6.8
23 3800 0.8 700 9.10 6.9
33 4018 0.8 0 9.50 6.0
43 3700 0.8 0 9.20 6.0


t-€

Engine Description —e| Fuel Spray Dispersion
Operational Conditions
Fuel Fuel Jet
Injection Vapori- Entrain-
zation ment
Heat Release
i] Premixed
|}_-—___________-»-|
Engine Thermodynamic
Performance Cycle Analysis & Heat
Transfer <

geneous
Diffusion

geneous
Diffusion,

Pollutant Formation
NO Soot
Pollutant
Emtssion Homo- Hetero-
Formation } {Oxidation
geneous f \ geneous
Fig. 3-1

Elements of the Ultrasystems Model


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sample Valve Location

1500 rpm
0.6

~20.
Medium
6

R = 3.9 cms
@ = 15° from jet axis
Z = 0 depth (cms)
te NO, co UHC
Oy ppm % ppm
22 77 0.005 1500
-12 84 0.65 6500
- 7 350 0.65 8000
- 2 1480 1.6 4000
3 2190 1.7 1700
8 2730 1.55 1200
13 2880 1.5 1200
23 3170 1.15 1050
33 3840 0.86 0
43 3890 0.8 0

Exhaust Concentrations

NO
x

co
UHC
CO,

Q2

2435 ppm

0.01 percent

0

8.5 percent

8.6 percent

co, oO,

_% %

0.47 20.0
0.8 16.5
1.0 13.5
2.1 10.3
4.6 7.8
6.0 7.1
7.4 6.9
8.1 6.5
8.9 6.2
9.3 5.6


Input Conditions

Speed 1500 rpm NO,

Equivalence Ratio (nominal) .35 co

Timing (ATDC) -20.0 UHC

Swirl Level Low

Fuel Injector 6 CO,
O2

Sampling
Time

2
-22

Sample Valve Location
R =3.9cms

@= 0° from jet axis
Z =0 depth (cms)

Exhaust Concentrations
1539 ppm

0.10 percent
0

S.6 percent
12.8 percent

NO, co UHC co, °,

ppm A ppm % %
76 0.06 500 0.35 19.9
155 3.00 5000 2.10 15.0
622 7.00 5500 6.00 6.0
930 4.40 1700 6.70 8.5
1489 1.80 770 6.10 11.1
1618 0.75 660 5.40 13.1
1537 0.30 610 $.10 13.8
1623 0,18 $00 §.00 14.2
1540 0.10 0 4.40 14.2
1255 0,12 0 4.00 14.8

D-48


where i=a, fg, (bm,I) and the volume rate is expressed by:

y= Zp2 ow cos 8
v= 7D. Ry sin é tt

2
R,
1 - () sin? 9
1
Equations (4-31la) through 4-3lc) are the working form of energy conversation
equations.

Convective Heat Transfer

The gross convective heat transfer to the cylinder walls is expressed
in a similar method to that used by Annand‘t4) .

B
\ = ae c TF . at 32)
Qo (a. D, R, AT 2] de (4-32)
where
x is the mean thermal conductivity of cylinder gas

R is the Reynolds number based on the mean piston velocity and
cylinder bore

is the average gas temperature

o

oe |

T, is the average cylinder wall temperature

cs

A is the surface area of the cylinder chamber

D, is the bore

It should be noted that two empirical constants, A, and Bo have been intro-
duced whose accepted values range from 0.17 to 0.49 for Ag: and Bo = 0. 7(tS. 18)

Radiative Heat Transfer

The rate of radiative heat transfer from each zone to the cylinder wall
is expressed by

~KL
. elnaah.- 1 4. 4) | at
Frm 1 = [>, o ( ° ) o(Tom,t 4) de (4-33)


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO, 1230 ppm
Equivalence Ratio (nominal) 0.6
Timing (ATDC) -12. co 0.008 percent
Swirl Level Medium coe 8.2 percent
Fuel Injector 6 2 .

0, 9.2 percent

Sample Valve Location

R = 5.6 cms

@= 0° from jet axis
Z = 0 depth (ems)
ore No, co UHC co,
—2) pom s ppm a
-12 88 0.005 30 0.3
-7 77 0.15 100 0.3
-2 231 4,80 4000 4.2
3 430 4.30 850 5.2
8 980 3.40 180 7.7
13 1440 7.80 60 8.0
23 2080 3.60 9.5
33 1900 1.90 8.5
43 1830 0.70 0 8.0

pra?

EN
Nnrnuwr nA wMwwWodsa

OND DDE HUAN NH


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO, 1620 ppm
Equivalence Ratio (nominal) .35
. t
-Timing (ATDC) -20.0 co 0.06 percen
Swirl Level Low UHC 0
Fuel Injector 6 co, 5.1 percent
ie} 2 13.2 percent

Sample Valve Location
R = 3.9 cms

@= 30° from jet axis
Z = 0 depth (cms)

Sampling NO, co UHC CO,
(o) pom % ppm_ %
-22 242 0.04 200 0.45 19,
-12 255 0.20 250 0.66 19,
- 7 1455 1.40 310 6.60 10.
- 2 1620 1.60 330 7.20 9.
3 1550 1.00 280 6.80 9.
8 1292 0.27 240 $.00 “12.
13 1250 0.10 200 4.60 14,
23 1100 0.07 180 4.20 14,
33 1080 0.08 140 3.60 15.
43 1100 0.08 130 3.60 1s.

ae

An 1 OC wvH ON HH SF wo


Table 7-1. Summary of Model Predictive Capability

Variables Exhaust NO Exhaust Soot
Fuel Injection Timing good good
Load . good fair
Engine Speed good good
Compression Ratio poor fair
Exhaust Gas Recirculation good poor
Swirl good poor
Turbocharge poor fair
Nozzle No. and Diameter good fair

Initial concepts concerning the formation of pollutants in compression
ignition engines directed the model towards the consideration of droplet com-
bustion. It was believed that spherical diffusion flames formed around droplets
were typical of the "diffusion flame" nature of the combustion process. Experi-
ence with the model tends to refute this hypothesis. Undoubtedly, diffusion
flames exist within the heat release zone, however their scale is apparently
very different from those modeled by a spherical diffusion flame surrounding
a single droplet. In order to include this type of heat release zone, a pseudo
steady state confined droplet model has been formulated. Model calculations
indicate that droplet contribution to the total production of NO is only signifi-
cant in the early stages of heat release, and has a negligible influence on the
final exhaust value. The results of these calculations can be attributed to:

e A large fraction (approximately 80 percent) of the droplets are
contained within rich zones which cannot support spherical

diffusion flames.

e The droplet lifetime is restricted to the time period close to
top dead center where the available volume is small and
therefore, the volume available for each separate spherical flame
is small, thus minimizing the total flame surface area.

e The droplet environment contains NO produced during premixed
combustion which will reduce the net rate of NO formation.


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO, 2431 ppm

Equivalence Ratio (nominal) 0.6

Timing (ATDC) ~20.0 tac yo” percent

Swirl Level Medium

Fuel Injector 6 CO, 9.1 percent
° 8.7 percent

2

Sample Valve Location
R = 3,9 cms

6 = 0° from jet axis
Z = 0 depth (cms)

sere NO co UHC CO, Og
a (oo ppm a ppm % %
-22 140 0.005 500 0.7 19.5
-12 143 0.004 1250 0.4 20.0
-7 1370 0.4 650 4.9 14.0
-2 3542 2.7 500 8.4 7.0

3 3280 2.5 0 8.9 6.3

8 3980 1.9 0 9.3 5.8

13 3950 1.6 0 9.1 6.5

23 4035 0.86 0 9.4 7.1

33 4039 0.94 0 9.8 6.1

43 3300 0.6 0 9.4 6.5


ratio can be attributed, in part, to Cnor which had been fitted fora higher
compression ratio,

6.2 Effect of Charge Intake Parameters
Effect of Exhaust Gas Recirculation (EGR)

The effect of EGR was computed assuming a constant mass flow of
intake charge (i.e., mass of fresh air intake plus mass of recirculated exhaust
gas) and maintaining both the overall fuel/air ratio (i.e., pooportionally reducing
the fresh air intake and the mass of fuel) and the fuel injection rate constant.
Figure 6-5 shows that excellent agreement is obtained between predicted and
calculated NO emission from the measured values. However, there is complete
disagreement with the measured soot values which probably reflects the model's
lack of real understanding of the density of soot formation and does not take
adequate account of the influence of temperature.

Effect of Air Swirl

The influence of the level of air swirl on NO formation can be seen
in Figure 6-6, the NO concentration increases with increasing swirl. This
effect is caused by the improved fuel-air mixing which leads to earlier heat
release, thus the higher local temperatures and the increased oxygen availability
promote NO formation. The experimental data from Phase I and that obtained
during experiments with the sampling valve are scattered. Data reported
by cav"4) is also plotted for comparison and to give an indication of the normal

trend.

The comparison of measured and calculated exhaust soot level is
poor, particularly.at higher swirl levels. This error is probably caused by an
over-estimate of the influence of temperature on soot formation which is used
in the present study. Thus, the higher dilution due to the higher swirl does not
significantly lower soot emission in the calculated results.

ffect of Turbochargin:

The effects of turbocharging on NO are plotted in Figure 6-7 and are
compared with the experimental data obtained during Phase I. Poor agreement
is shown between the predictions and measurements at low levels of super-
charging. Computations at higher manifold pressure and higher loads were

6-7


Input Conditions

Exhaust Concentrations

Speed lence Ratio ( 1 1500 rpm NO, 2364 ppm
Toning ‘ATDC). 40 (nominal) 30. Gc g.t percent
Swirl Level Medium co 8.6 percent
Fuel Injector 4 2
O, 8.5 percent
Sample Valve Location
R = 5.6 cms
a= 45° from jet axis
Z = 0 depth (cms)
ane NO co UHC CO, °,
(2) ppm % ppm % %
22 197 0.9 110 0.9 18.8
-12 357 3.0 160 3.8 13.5
-7 362 10.0 380 4.4 1.8
-2 477 10.0 1600 3.8 1.2
3 1040 10.0 5000 5.2 2.1
8 1450 4.8 1000 6.8 7.1
13 1640 1.3 360 5.8 11.2
23 2620 1.4 300 7.8 8.2
33 2734 1.0 120 8.4 8.1
43 2380 lel 100 8.5 8.5


diesel engine from the crank angle degree of intake valve closure to the angle
at which the exhaust valve opens. The model is built around the thermodynamic
cycle and heat transfer analysis components which both receives and supplies
information to and from the other components of the model. The interaction of
the separate modules can be seen in Figure 3-1.

Fuel Spray Dispersion

In the fuel spray dispersion module the fuel jet is modeled as though
it were a steady axisymmetric unconfined wall jet. Figure 3-2 shows a pictorial
representation of the initial stages of the jet before impact. The fuel injection
schedule is considered to be uniform and the fuel forms droplets of a specified
size distribution immediately upon injection. In order to ascertain the subse-
quent history of all the fuel elements in 1° crank angle intervals it is considered
to be distributed equally between four shells. Thus, each element of fuel can be
denoted, both by its age and by its initial location in the jet. The fuel jet
entrains air in the manner prescribed by well-established theories of turbulent
jet mixing. Thus, the total mass in each shell will increase and those shells
on the periphery of jet will have fuel air ratios lower than those shells on the
jet axis.

Fuel Injection Schedule

Swirl \. Direction

m
Air
\ \ Locii of
= x?
Bo a
Injection Ty = - Bis Fuel droplets
Nozzle Fuel vapor

Air

Locii of
9 = (xt1)°

Shells defined by
equal fuel mass Jet Boundary
and @ = !° intervals :

Figure 3-2. Pictorial Representation of the Fuel Jet

3-5


7.0 LIMITATIONS OF THE MODEL AND RECOMMENDATIONS
FOR FUTURE WORK:

While it is unlikely that a diesel engine will be designed solely on
the basis of a mathematical model, such a model can provide insight which
will allow more rapid development of engines. The preceding sections have
described the development of an analytical model which simulates the mechanisms
of heat release and pollutant formation occurring within a direct injection diesel
engine. Several simplifying assumptions have been made during the development
process to allow the complex phenomena, which occur in practice, to be treated
mathematically. Thus, the ultimate goal, that of building a model based entirely
upon physical and chemical laws and free from empiricism has not been achieved.
What has been accomplished is the construction of a modular model which will
predict, after tuning, most of the pollutant emission characteristics of a single
cylinder diesel engine. Its modular nature will enable the rapid update of any
of the model's components as improved fundamental and experimental informa-
tion becomes available.

Recognizing that gaps in fundamental knowledge make the inclusion
of several empirical constants mandatory, the success of the model must be
judged from predictions after adjustment of these constants fora particular
class of engine. To date, the model has only been compared to single cylinder
engine data. On the basis of these comparisons it can be concluded that the
overall predictive capability of the model with respect to pressure history and
exhaust NO levels is good while its ability to predict exhaust soot emissions
can only be considered as fair. The model's predictive performance has been
summarized qualitatively in Table 7-1.

7-1


Input Conditions Exhaust Concentrations

Speed 1500 rpm NO

Equivalence Ratio (nominal) .75 x 2420 pem

Timing (ATDC) -20.0 co 0.35 percent

Swirl Level Medium UHC 0

Fuel Injector 6 co, 10.8 percent
fe) 2 4,5 percent

Sample Valve Location
R = 5.6 cms

] 0° from jet axis

Z = 0 depth (cms)
Sampling NO, co UHC co, °,
Time
—o)_ _ ppm. as pom % _%
-22 300 0.46 35 1.2 19.5
-12 260 7.10 1250 4.5 7.2
-7 711 10.0 1000 6.2 1.2
-2 1080 10.0 800 6.6 0.1
3 1570 10.0 250 7.0 0.3
8 1870 7.0 140 8.5 2.5
13 1950 4.7 0 9.3 4.0
23 2640 2.5 0 10.5 3.2
33 2884 2.2 0 11.4 2.3
43 2920 2.6 0 11.6 1.3

D-51


NOMENCLATURE (Cont'd)

Crank radius or half stroke length (cm)
Reynolds number

Radial coordinate (cm)

Temperature (K)

Time (sec)

Internal energy (cal/gm)

Vv Volume and clearance volume (cm?)

o” <

seen

a

v Velocity (cm/sec)

WwW Production rate gm/cm’-sec)

(w) Production rate(gm/sec)

w Number of carbon atoms in a fuel molecule

X, (] Mole fraction

x Axial or downstream coordinate (cm), or number of hydrogen atoms ina

fuel molecule
Mass fraction
y Radial or cross-stream coordinate (cm)

Greek Symbols

Stephen Baltzman constant

Absorptance or g = 1/(1+f)

Volume ratio

Fraction factor of convecture heat transfer
Crank angle

Equivalence ratio defined as 4 = (F/A)/(F/A)
Density (gm/cm)

Nondimensional radial coordinate, y/b
Thermal conductivity (cal/cm-sec-°K)
Absolute viscosity (gm/cm-sec)

Parameter for drop size distribution
Characteristic time

Defined by 7 = £/(1+£)

Stoich.

x mo 8 @ YX WR Q

3a rAQWE


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sample Valve Location

R

@ = 33° from jet axis

Exhaust Concentrations

1500 rpm = NO,

0.6 co

-20.

Medium Cae

4 2
2

= 3.9 cms

Z = 0 depth (cms)

rime NO, co UHC
©) ppm % ‘ppm
22 80 0.1 260
-12 156 3.0 900
-7 435 8.0 2200
-2 350 6.0 2800
3 290 3.8 700

8 1008 0.6 380
13 1540 0.5 240
23 2000 0.6 200
33 1730 0.7 120
43 1670 0.7 120

2120 ppm
0.05 percent

8.7 percent
8.8 percent

CO,

ae

oor Pe eB Ow HE
Anan kb FB wWwHNO


R/R Bowl
LA

0,95 ——__

re
u

2
CYLINDER HEAD}

aa
y>

ISTON

R, = 1.62 p 72-75

Figure C-3. Location of Sample Valve Ports

C-3. RESULTS

Four test series, all of which were not completed, have been carried
out using the sampling valve:

Series 1 — All exhaust values were higner than the local values
at 40° after TDC.

Series 2 — Problems with the sampling train were corrected, but
engine failure occurred before the test matrix was
completed.

Series 3 — Complete test matrix, but discrepancies apparent in
results.

Series 4 — Partial test series with new valve tip and seat after

the engine had been rebuilt.


Coat The parameter Coit has been included to provide some vitiation

Of the air prior to mixing with the burning zones during the air/product mixing
processes. The value of C4; influences both the droplet burning rate and

the early stages of NO formation. The suggested value is somewhat arbitrary.
However, its influence on the prediction of performance and pollutant formation

is concluded to be minimal.

Thu The droplet heat up time is a function of droplet size, convective
transfer and the surrounding temperature. Detailed modeling of transient heat
transfer effects within each individual droplet is considered to be outside the
scope of this study and must be justified before consideration is given to its
inclusion. A uniform value, which is approximately equal to the physical
ignition delay (0.2 ms), has been chosen for all droplet sizes. It has been
assumed that vaporization of liquid fuel does not occur during the heat up time.

Cror It has been well established that it is not possible to decouple the
kinetics of NO formation from those of hydrocarbon combustion. Super-
equilibrium radical concentrations are known to occur in reacting regions

and elementary reactions other than those described by Equations 4-83
through 4-84 take part in NO formation. Consequently, it is reasonable to
expect that any NO prediction which is based solely upon the Zeldovich model
would be an underprediction in those zones where combustion is taking place.
A value of Cror = 5.37 has been used previously by Kahn and Greeves! 4) to

allow exhaust NO levels to be calculated using the Zeldovich mechanism.

Table S-2 lists the seven empirical constants which are considered to be
adjustable, together with their suggested values and the method used to
determine this value.

ow
’
cs


10

3

Soot (gm/gm of fuel)

10

40

—a
Z- Se
eee oe emma, —-——--
“x “
ma
/ /
‘
i /
L L U =
tef—# % 4
4 mar = -12°CA 4
ay a “ 4
1 —_—_ = ro}
r f 8,4) = ~20°CA =
=s- 9, “
! / nm 8) = 28° CA
t iT
i IL
! |
! '
i J
T T
{ j
!
|
4
T il
T T
T 1
H i
| T
! i
H t
| 1
|
| 1
T
i I
I fl |
103 ! !
-30 29 19 TDC 10 - 20
4
Figure 5-4 Calculated Instantaneous ‘Value of Soot (in sm/gm of

total fuel :njection)

5-19


4.0 DETAILED DESCRIPTION OF A MODEL TO PREDICT POLLUTANT

FORMATION IN DIESEL ENGINES

The physical and chemical processes controlling heat release and
pollutant formation in diesel engines are extremely complex. The model, des-
cribed in detail in this section, has been developed upon the premise that
many of these processes can be decoupled from each other and, therefore, the
total process can be subdivided into several tractable components. Although
each of these components contains certain simplifying assumptions to make
them mathematically amenable, every effort has been made to ensure that they
retain their physical significance. Thus, a modular model has been developed
which reflects the present state-of-the-art but which will allow any of its
components to be updated independently as an improved understanding of the
controlling phenomena is achieved. The separate components of the model
are:
The cycle thermodynamics and heat transfer
Fuel injection and spray characterization
Air spray entrainment and droplet vaporization
Ignition delay
Air product mixing
Combustion

Nitric oxide formation

@ Soot formation and oxidation
A complete description of symbols, superscripts and subscripts included in these
various components is given in Section 8, Nomenclature.

Cycle Thermodynamics and Heat Transfer

The cycle thermodynamic analysis serves as the skeleton upon which
the separate components of the whole model are assembled and it describes the
thermodynamic state of the cylinder contents during the compression and expan-
sion processes for that period of the cycle when both the intake and the exhaust
valves are closed.

At any instant the cylinder contents, which may be either gaseous or
liquid, are considered to exist in separate zones:

Air zone: the mixture of fresh air, recirculated exhaust gas (if any)

and residual gas, Subsequent to ignition the “air" zone is vitiated

and mixed with the burning gas zone. The properties related to this
zone are identified by subscript "a".

4-1


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling
Time

©)
-12
-7
- 2
3
8
13
23
33
43

NO

of,

90
280
800

1195
1330
1760
2074
1948

Exhaust Concentrations

1500 rpm NO

x
ti. 69
Medium cee
6 2
%

Sample Valve Location
R = 2.7 cms

@ = 0° from jet axis
Z = 0 depth (cms)

co UHC
am ppm
0.04 300
0.06 $00
0.84 1300
0.80 2000
0.83 600
1.00 350
0.46 0
0.47 0
0.30 0

1300 ppm

0.06 percent

3.0 percent

8.4 percent

co, oO,
a B
0.48 19.1
0.40 19.1
2.30 16.2
4.10 13.3
4.60 12.5
4.90 12.0
6.20 10.9
6.80 9.5
7.00 8.9


Exercise of the model has highlighted several deficiencies and
omissions which can be easily modified in the near term; these include:

e Modifications to extend the equilibrium species tables to higher
pressures and richer mixtures.

e Limits can be imposed upon the equilibrium assumption to enable
carbon monoxide and hydrocarbon levels to be predicted.

e The model contains a very simple ignition criteria and it should
be modified to take account of the equivalence ratio and
temperature history of the fuel parcel.

e Mixing between burning zones should be included.

Four general areas of ignorance have been identified which require
considerable effort to allow improvements to be made to the model; these include
a transient fuel spray model, non-uniform fuel injection rate, an improved fuel
spray dispersion model, and an improved energy release model. Both physical
and numerical experiments will be necessary to allow improvements to be made
in these components.

Transient Fuel Spray

The present model considers that the fuel spray behaves as though it
were a steady state jet. No attempt has been made either to model the leading
or the trailing edge of the jet. More experimental information is required before
a realistic approach can be included in the model which will describe these
transient phenomena.

Fuel Air Mixin

In view of the conclusions conceming fuel droplets, it is suggested
that numerical and physical experiments be conducted to establish the importance
of droplets. The phenomena of ignition may well be strongly linked to droplet
properties. However, it appears that the major portion of the jet could be
treated as a gaseous fuel. This would simplify certain aspects of the model
and allow a more rigorous treatment of the fuel/air mixing process to take
account of the following.


a Mig Reg Teg
fg Py (4-7)
a. a emt Som,t "bmi (4-8)
bm, PV

The instantaneous total volume of the engine cylinder is computed by

2., 2
Vv =V_ + ud pd? R l= cos 9+ * *L Aw ) a3)
(@)=Vo* | e ( R
Ww
The fraction factors for zonal convective heat transfer rate are evaluated by
y= (T, - Ty) By
a B (4-10)
2/3
y (tts Tw So (4-19
fg B
4-12)
(r B 2/3 (
y = bm,I_ 1, bm,I
bm,I B
where normalizations were made by B, which is
_ 2/3, . ae 2/3 (4-13)
BT) -T,) By (Ty 7 T) 8 EL -TY Bont

temoerature TY. 18 usec in above equations.

de
1
oO


4.7 Nitric Oxide Formation

The rate of the chemical reactions involved in the formation and
destruction of nitric oxide are extremely temperature sensitive. Under con-
ditions typical of normal diesel engine operation, characteristic residence
times are small compared to the times necessary to achieve equilibrium.
Consequently, the amount of nitric oxide formed will depend upon the time-
temperature-pressure history of the reactants. If heat release took place in
one homogeneous zone, temperatures would be too low to allow the formation
of significant quantities of NO because of the extremely lean overall opera-
ting conditions. Thus, it becomes apparent that nitric oxide is formed in
zones whose characteristic size is much less than the characteristic cylinder
size and that local homogenity will exist on various scales within those
zones.

Two zones of NO formation are identified in the model depending
upon the scale of local homogenity:

° Reactants can be well mixed on a scale which is small compared
to the total reacting volume and local gradients can be neglected.
These well mixed zones will have a wide distribution of equiva-
lence ratio. The rate of NO formation in regions of this type are
calculated by the homogeneous NO equations.

e Reactants are separate and the reaction zone is characterized by
steep gradients and molecular diffusion plays a strong role in
NO formation in these regions. Reaction zones of this type can
typically exist around a single droplet, a cluster of droplets or
at the boundary of a fuel and air zone. In this model NO produced
in diffusion flames is assumed to form around single fuel droplets
and is calculated by the heterogeneous NO equations.

4-35


limited by equilibrium species tables and thermodynamic property expressions;
however, in future work this could easily be remedied.

6.3 Effect of Fuel Injection Parameters

Injector Orifice Diameter

The diameter of the fuel injection orifice affects béth the fuel dis-
persion rate and the drop size distribution. Calculated exhaust pollutants for
various fuel orifice diameters are plotted in Figure 6-8, along with the experi-
mental data. The computations are based on constant total orifice area anda
constant total fuel mass. The emission of an engine with larger and therefore
fewer orifices showed substantial reductions in NO. The phenomena is mainly
caused by a smaller total surface-to-volume ratio of vaporizing and burning
fuel droplets in association with an increased mean droplet diameter which, in
tum, reduces rates of vaporization, mixing and thus energy release rates.


y
1
b °

J)

Ew

rm

transient

N —_ region
initial main ~\

——~| region [*——— _ region

wall
regio:

Note: I is equivalent to [(i-1) X (No. of shells) + j]

Figure 4-2 Schematic of Fuel Spray


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling
Time
—__
-32
-22
-12
-7
- 2

3
8
13
23
33
43

NO

291

201

322
1880
2722
3580
4400
4785
5400
5664
$500

Sample Valve Location

R

@ = 0° from jet axis

Z

1500 rpm

0.

6

-28.
Medium

6

eo0 0 FGA OF roo

2.7 cms

Exhaust Concentrations

NO
x

co
UHC

Cc
fe)

2

2

0 depth (cms)

UHC
ppm
200
600

2500
600
300
300
250
225

4440 ppm

0.06 percent
7.9 percent

8.1 percent
co, °
4 a
0.4 19.
0.5 19.
3.2 14,
5.9 ll
6.5 10.
6.6 10
7.0 10
8.0 8
8.8 7.
8.9 7
8.7 7

Qeunnornunaonooua


07-5

SAMPLE EQUIVALENCE RATIO, @

Speed: 1500 rpm
1.0, Load: $=.5

. o *
Timing: Sinj= - 20 . a High
Vatve Insertion: 11/16 ° Medium
275 E
50 +
.e5L
0 n 1 }
“50 0 50 100

Crank Angle , Degrees

Figure C-8. Dependence of Sample Equivalence Ratio on Swirl
~ 11/16" Valve Insertion


Vaporizing liquid fuel zone: for thermodynamic purposes, all the
pre-ignition liquid fuel is considered to exist in one single zone.
This zone is identified by subscript "fl".

Burning liquid fuel zone: all the post-ignition liquid fuel, which
is either engulfed by combustion products or diffusion flame
envelopes is considered to exist in one single zone which is
identified by the subscript "flb".

Fuel vapor zone: thermodynamically, all the vaporized fuel
(either mixed or unmixed with air) is considered to exist ina
single zone prior to ignition, designated by the subscript "fv".
This approach might well introduce errors into the calculation

of the thermodynamic properties during the ignition delay. How-
ever, it is considered that these errors will have little influence
on overall pollutant predictions.

Buming zones: the zones which contain the combustion products
are identified by subscripts which indicate both the time of
ignition and the proximity to the fuel spray axis at the time of
ignition (see Figure 3-2). Each burning zone is subsequently fed
either by the combustion products generated by diffusion flames or
by fuel vapor (when conditions do not allow diffusion flames to be
established) from the fuel droplets engulfed by the zone itself.
Although mass transfer between burning zones and the air zone,
i.e., dilution and vitiation, is taken into consideration, the mass
transfer between burning zones is not considered. Burning zones
are signified by double subscript “bm,I".

The basic assumptions contained in the cycle thermodynamics model are:
- pressure is uniform throughout the cylinder;

- each zone is considered to be thermodynamically
homogeneous;

- each zone radiates independently to the cylinder wall (i.e.,
radiative exchange between zones is not considered);

- the kinetic energy of the fluid within the cylinder is
neglected except when it is required to characterize the
velocity of the cylinder contents;

- the sole source of heat necessary for fuel vaporization ts
provided by the “air" zone;

- the specific heat of both the vapor and liquid fuel is constant:
- a "mixed burned" assumption is used to account for the com-
bustion of the premixed air and vaporized fuel and equili-

brium combustion products are formed immediately following
ignition;

4-2


Indicated Mean Effective Pressure (IMEP)

2 ¢ dv © dv
IMEP = DIR f P a6 do + P 46 do
® =180 c
v0 180
dv dy (4-104
+ f P36 de f P36 dé
° vo

where %e and 946 are the intake valve closing angle and exhaust valve opening
angle respectively. The sum of the first term and last term on right hand side
of Eqn (4-103) ts small and can be ignored when comparing engines of similar

manifold pressures and valve timings.

Indicated Horsepower (IHP)

The total horsepower developed in the engine is calculated by:

(IMEP) Ways) (RPM)

THP = 396000 x N, (ap)

(4-104)

Indicated Specific Fuel Consumption (ISFC)

The indicated specific fuel consumption given by:

(60) (m,,) (RPM)

ISFC = N, (HP)

(gm/np-hy (4-105)

is a comparative parameter that is indicative of the efficiency of an engine
in converting chemical energy into work and N, = 2 for four stroke engine, N.
= 1 for two stroke engine.


- ingestion of the quench layer adjacent to the probe tip;

- influence on the local gasdynamics of the sink strength during the
sample period;

- size and duration of the sample as they affect spatial and temporal
resolutions

Simple fluid mechanical arguments suggest that the quench layer
and injector trapped mass do not represent a significant effect at the sample
rates under consideration. This conclusion has been bore out by varying
the sample rate and the duration of the valve opening time. The presence of
the probe itself undoubtedly outweighs the sink and sample size effects. For-
tunately the flow is predominantly across the.probe and hence the largest
perturbation to the flow lies in the wake, downstream of the probe. All of
these items taken together probably mean that the sample should be considered
as representative of a zone whose scale is that of several probe diameters.
The long valve open time (© 1 msec) is probably the single most severe effect
with regard to both temporal and spatial resolutions due to high swirl velo-
cities which can convect material from 30° upwind during this period.

With regard to chemical transformation within the probe, the fol-

lowing effects may be of concern:

- lack of adequate quenching within the probe;

- catalytic wall reactions;

- presence of carbon in the probe;

- presence of condensate in the sample line
Analysis of the first point requires the recognition that the probe's internal
gasdynamics is an unsteady filling and emptying process. The stem fills
over a period of 0.5-1.0 msec and empties over a period of 80 msec. During
this process the sample at first expands very rapidly and then undergoes a re-
heating through shock compression and boundary layer stagnation. Although
the required quench rates are severe, an analysis of this process indicates
that the favorably lower pressures in the probe combined with the cool walls
is adequate to terminate the nitrogen oxide production. This conclusion seems
to be validated by the independence of measured NO, with sample rates for
rates greater than 300 SCCM. However, conditions may not be adequate to
insure complete quenching of all reactions concerning carbon monoxide burnout.

C-17


APPENDIX ©

CHARACTERIZATION OF DIESEL COMBUSTION
BY DIRECT IN-CYLINDER SAMPLING

C-1. INTRODUCTION

The model of diesel engine combustion described in the body of this
report includes several arbitrarily adjusted constants and is based upon a
healthy dose of conjecture. In an attempt to provide experimental evidence to
support the model development, an effort has been made to characterize the
cylinder contents during the period of heat release. Wilson et ai! 1) reported
earlier unsuccessful efforts to utilize ultraviolet emission and absorption
spectroscopy for this purpose. A sampling valve,which was designed by the
Ricardo Company and provided to Ultrasystems by the General Motors Research
Laboratories, has been used in an attempt to provide data to aid further model
development.

In addition to the overall objectives stated above, one important
feature of the project was to establish the validity of the results from
in-cylinder direct sampling. The project could not be concluded in the pre-
sent study, but answers to the following questions were sought:

e What kind of spatial and temporal resolutions are possible?

e On what scale is it possible to characterize gradients and
unmixedness in the system?

e To what degree is the sample analyzed, representative of
the system being measured?

C-2. EXPERIMENTAL EQUIPMENT

The characteristics of the single cylinder diesel engine used in
these experiments have been given elsewhere'!), The sampling valve was
designed around a powerful electromagnet and armature originally intended
to operate a Societe Francaise d'Etudes et de Development de 1, Injection
(S.O.F.R.E.D.I.) diesel fuel injector. A detailed description of the development,


£-D

RICARDO SAMPLING VALVE

SEAL
«K ‘i ']
SAMPLE LINE
9/64 mW) RN
COOLING WATER — 48 DIA
. _— a ' on ~~
CYLINDER a
HEAD a
Z, Allie V/8 DIA oi
yi TITANIUM
4 Z , 096 0.D. x
' .06B 1.D.
STAINLESS
i STAINLESS
TIP
90°
t
3/66 DIA. —) — 2
0.28

Figure C-1.

ALTERNATE TIP DESIGN

0625 DIA
TUNGSTEN CARBIDE
SPHERE 1

WASPALLOY

Details of Sampling Valve Tip

STAINLESS
VALVE STEM

Ve

COINED
SEAT


e The droplet lifetime is restricted to the time period close to top
dead center where the available volume is small and, therefore,
the volume available for the single flame is small, thus minimizing
the total flame surface area;

e The droplet environment contains NO which will reduce the net
rate of NO formation.

Model predictions have been compared with experimental data
generated in a single cylinder diesel engine for the following operation and
engine parameters:

Load (or overall air/fuel ratio)
Fuel injection timing

Engine speed

Compression ratio

Exhaust gas recirculation

Air swirl

Fuel nozzle diameter
Turbocharge.

Based upon comparison with single cylinder test data, it is concluded
that the overall predictive capability of the model with respect to pressure history
and exhaust NO level is adequate. However, its ability to predict exhaust soot
emissions can only be considered fair. The model includes an arbitrary
empirical relationship describing carbon formation in fuel rich regions since a
more fundamental understanding of the chemistry of carbon formation is not
presently available.

Experience with the model indicates that several minor modifications
are possible which will improve and extend the model; these include:

- modifications to the equilibrium species tables to allow fuels of
different hydrogen/carbon ratios to be easily treated and to
extend these tables to higher pressures and richer mixtures;

- limits can be imposed on the equilibrium assumptions to enable
carbon monoxide and hydrocarbon emissions to be included;

1-3


[No]

1.6

| | 4
of
Calculation [vo], = 2077 pom /
1:4 = ——-O — Phase I data {wo}, = 2050 ppm 7
— << — Phase II sample valve data /
(NO], = 2387 ppm /
— + — CAV data (Khan & Greeves, 1973) |/ va
W2R re
as
fon ee:
~ ef LA
7 RFS ae ae!
1.0 =
se
=
0.8
Calculated (@ = 0.6) (soot) , = 139 mg/m
o.6 1.6
— ~O — Phase I data 3 = 0.45 (soot), = 6.2% opacity
1.2
4 (Soot)
| Soot)
LT 2 N 3°
7
0.8
4 N
7 “N
7 N
7 N
7 0.4
4 NX
/
if 0.0
1.0 2.0 3.0
Relative Swirl Magnitude
Figure 6-6 Effect of Swirl

6-9


Finally, ¢ and Yeurb Fe scaled by the volume surface area ratio and mean flow
velocity.

gel

tt
Fis

Yeurb =U = Yohar

The characteristic charge velocity is defined by:

1/2
0/2 , <2 2
y . me (vo + %) + My Vio
char 3
ms + Mey

where Yp is instantaneous piston velocity and v5 is the swirl velocity based
upon swirl angular velocity and half bowl radius assuming solid body rotation.

“£0 is the fuel injecting velocity.

or

RPM x L
"mix ~ UT (4-47)
Coix U
Here empirical constant Cnix is introduced. The zonal dilution rate for each

burning zone is estimated by

4
amy Bom st EMD (4-48)

dé de
Lat

The vitiation rate from each burning zone is assumed to be directly proportional

to the dilution rate and therefore can be evaluated by

dm. dm
SE = Cyigi DL (4-49)

dé

4-23


Input Conditions

Speed

Equivalence Ratio (nominal)

Timing (ATDC)
Swirl Level
Fuel Injector

Sampling
Time

-22
-12
-7
- 2

3

8
13
23
33
43

NO

150
185
350
290
1136
1410
1220
1250
1040
755

Exhaust Concentrations

1500 rpm No, 1717 ppm

a6 . co 0.15 percent

Low. UHC 0

6 co, 8.6 percent
oO, 8.8 percent

Sample Valve Location
= 3.9 cms

R
@= 45° from jet axis
Z = 0 depth (cms)

co UHC CO, On

% ppm % %

0.08 240 0.66 19.7
0.26 400 0.9 19.3
1.2 550 3.2 18.5
3.6 460 5.5 8.5
4.0 360 7.2 6.5
2.0 310 7.5 7.5
L.S 160 6.8 8.5
0.4 110 4.3 5.2
0.2 48 4.0 6.0
0.2 40 3.6 6.1

D-22


Table C-4. Examples of Erroneous NO,
Concentrations Due to Converter Errors

Sample Measured Measured Calculated Measured
Time NO, ppm NO ppm NO, ppm O02 %
732 291 166 125 19.5
722 201 113 88 19.0
-12 126 322 -196 14.2

-7 1880 1600 280 11.0
=2 2722 2300 422 10.5
3 3580 28Ll 769 10.7
-22 152 140 12 19.8
712 255 350 -95 9.8
-7 245 410 -165 8.5
-2 1085 960 125 12.0
3 2130 1820 310 13.2


- air swirl;
- jets in cross flow; and
- jet interaction and three dimensional effects

An essential prerequisite for an improvement in the fuel/air mixing
model is more detail of the mixing processes occurring in the cylinder under
fired conditions. This is particularly true of conditions after ignition. A major
unanswered question concerns the lifetime of the well-ordered jet structure.

Non-Uniform Fuel Injection Schedule

The fuel injection schedule is assumed to be constant. As a first
simple step towards taking account of a non-uniform injection schedule the
model could be modified to calculate the entrainment into a series of steady
jets with different injection rates.

Heat Release Model

Improvement in the heat release model will be necessary if a more
real approach to-pollutant formation is required. This could occur if engines
with low pollutant potential were being considered or fuels containing signifi-
cant quantities of bound nitrogen were to be utilized. Under these conditions
it will be necessary to treat the hydrocarbon oxidation process in more detail
than the present equilibrium assumption.

In view of the fact that the model has only been tested against one
set of experimental data, a necessary first set in deciding where the model
needs the most refinement is it's application to other engine geometries and
multicylinder engines.

7-4


- radiant heat transfer is negligible

- single component fuel composition
- body forces and internal motion within the droplet are negligible

the droplets exist in a large but finite space which is continuously
vitiated during the entire droplet lifetime.

convective effects are neglected, the diffusion flame limit depends
solely on ambient oxygen concentration.

The governing differential equations of mass, species and energy conservation
are written as (Williams (23) )

Continuity (4-50)
d 2
oa pwn
Species
(4-51)
d 2 ay, .
pv i
qo awe (Pea)
Energy
aT lo d,2A 2 dt 1
pv = Oo.
dr ogee! “ge STL wy (4-52)
P Pp
The equation of state is
PT = Constant (4-53)
The boundary conditions at the droplet surface n , the flame surface Tee and the

assumed radius of influence r, are presented below.