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8/2/2019 Using the Ideal Gas Law and Heat Release Models to Demonstrate Timing in Spark and Compression Ignition Engines
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Using the ideal gas law andheat release models todemonstrate timing in sparkand compression ignition
enginesG. DAVID HUFFMAN, School of Engineering Technology,University of Southern Mississippi, Hattiesburg, MS 39402, USA.huffman@netdoor.com
International Journal of Mechanical Engineering Education Vol 28 No 4
Received 5th January 1999
Analysis techniques of internal combustion engines range from thermodynamic methods tocomplex engine design programs. Thermodynamic analyses preclude engine timing while thedetails of engine design programs are beyond the level of undergraduate courses. Thisarticle combines the ideal gas law with heat release models and an engineering equation
solver to demonstrate timing in spark and compression ignition internal combustion enginesin a manner that can be used in undergraduate courses.
Key words: spark and compression ignition engines, engine timing, combustion models.
NOTATION
m
a area, m2
b bore, m
C mass loss parameter, m mL
Cp specific heat at constant pressure, kJkg-KCv specific heat at constant volume, kJkg-K
f1,f2 fractional heat release functions for compression ignition engines
F fuelair ratio
H heat loss parameter, b ht p v2 1 1 12
h heat transfer coefficient, kWm2-K
k ratio of specific heats
K1, K2, K3, K4 fractional heat release parameters for compression ignition enginesl connecting rod length, m
m mass, kg
mass flow rate, kgs
M mass ratio, mm1n fractional heat release parameter for spark ignition engines
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280 G. David Huffman
N engine rotational speed, revmin
Nc number of cylinders
p pressure, kPa
P pressure ratio, pp1q heat, kJ
Q heat ratio, qp1v1rc compression ratio
R gas constant, kJkg-Ks stroke, m
t temperature, KT temperature ratio, tt1v volume, m3
V volume ratio, vv1
w work, kJkgpower, hp
W work ratio, wp1v1x fractional heat release
Subscripts
c clearance
d displacement
in input
L loss
s stoichiometric
w wall
1 bottom dead center
1. INTRODUCTION
Analyses of spark and compression ignition internal combustion engines, range from an
elementary thermodynamic approach, to complicated fuel system approaches, which may
include flow analysis of the intake and exhaust systems, analysis of friction and heat losses
and other factors to numerous to mention. Programs of this type are normally beyond the
Greek
pre-mixed-diffusion combustion parameter for compression ignition
engines
shape-compression ratio parameter, (sb) (2rc(rc 1))
1,
2fractional heat release parameters for spark ignition engines
b heat release duration, degrees geometric parameter, s2l
crank angle, degreess start of heat release, degrees
angular ratio, ( ) s bid ignition delay time, msec equivalence ratio rotational speed, radsec
w
International Journal of Mechanical Engineering Education Vol 28 No 4
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Using the ideal gas law and heat release models 281
level of junior and/or senior undergraduate students in mechanical engineering technology.
The basic thermodynamic approach illustrates the cyclic nature of the engine and the com-
pression, heat addition and expansion processes, but provides no information on the effect of
timing on the heat release process. This article presents an analysis of the effects of timing,i.e., the initiation and duration of heat release, on spark and compression ignition engines.
The method used in this article combines the geometric relationship between the combus-
tion chamber surface area and volume and the crank angle with a differential form of the
ideal gas law and the first law of thermodynamics. The method also includes empirical data
on heat and mass loss, although, these factors are not essential to demonstrate timing.
The system of differential equations is evaluated using the Engineering Equation Solver
[1]. This is a software package designed to solve algebraic and initial value differential
equations.
2. ENGINE GEOMETRY
Fig. 1. Piston-cylinder schematic drawing.
International Journal of Mechanical Engineering Education Vol 28 No 4
As noted above, the approach employed in this article uses the ideal gas law and first law of
thermodynamics in differential form. The solution to the equations is driven by the combus-
tion chamber volumecrank angle relationship and the rate and time of heat release. The
engine geometry is shown in Fig. 1. The relationship between the volume ratio and the crank
angle is
Vr
rc
c= + +
1
11
21
11
11 2 2( ) cos sin
(1)
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282 G. David Huffman
where the various parameters are defined in the Nomenclature. Fig. 1 and equation (1) have
been adopted from Heywood [2]. Equation (1) can be differentiated with regard to the crank
angle and
If both the piston and cylinder head have flat surfaces, then
ab
V=
+
2
2 1( ) (4)
International Journal of Mechanical Engineering Education Vol 28 No 4
3. IDEAL GAS, ENERGY AND CONSERVATION OF MASS EQUATIONS
The ideal gas equation is
p mRt v = (5)
This equation can be written in logarithmic form and differentiated yielding
1 1 1 1
p
p
m
m
t
td
d
d
d
d
d
d
d + = +
v
v(6)
The first law of thermodynamics in differential form for an open system is given by
Ferguson [3] as
C mt
tm q
pm C tp
v
vd
d
d
d
d
d
d
d
L
+
=
(7)
Equations (6) and (7) can be combined yielding
d
d
d
d
d
d
L p k q kp
kpm
m =
1
v v
v
v
(8)
Since this model considers migration of mass from the combustion chamber, conserva-
tion of mass can be used to provide an equation for m
d
d
Lm m
=
(9)
The heat term consists of both heat added through heat release and heat loss through heat
transfer
q = qinx qL (10)
where qin denotes the total and x the fraction of heat released. The heat loss term takes the
form
d
d
c
c
V r
r
=
+
( )sin cos
sin
1
21
1 2 2(2)
The combustion chamber surface, i.e., heat transfer, area can be linked to the volume and
a ab
= + c c4
( )v v (3)
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International Journal of Mechanical Engineering Education Vol 28 No 4
Using the ideal gas law and heat release models 283
d
d
Lw
q hat t
= ( ) (11)
The heat addition/loss term can finally be written as
d
d
d
din w
qq
x b hV t t
= +
2
21( ) ( ) (12)
The work takes the form of
d
d
d
d
wp
=
v
(13)
Equations (8), (10), (11), (12) and (13) can be written in dimensionless form as
dd
dd
dd
dd
inLP k
VQ x Q k P
VV kCP
=
1 (14)
d
d
Lw
QH V
PV
MT
= +
( )1 (15)
d
d
MCM
= (16)
d
d
d
d
WP
V
= (17)
The temperature ratio can be determined from equation (5)
TPV
M= (18)
4. HEAT ADDITION
The heat addition can be estimated using data from Pulkrabek [4] and equations from
Ferguson [3], i.e.,
qF
Fin
s
s
=+
1
11 (19)
qF
Fin
s
s
=+
[ ] >
11 11 2 ( ) (20)
where Fs = 0.68, 1 = 43 000 and 2 = 3751 for spark ignition engines and 0.69, 42 500 and
3708 for compression ignition engines.
5. HEAT RELEASE FRACTION
Experimental studies have shown that the fraction of heat released varies with crank angle
and differs for spark and compression ignition engines. For spark ignition engines, Heywood
[2] and Ferguson [3] suggest
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284 G. David Huffman
x an ( )1 exp (21)
where Heywood recommends a = 5 and n = 3 and Ferguson uses a = 1 and n = 4. Since the
heat release varies with the crank angle
d
d
xan
xn
b
=
1 1 (22)
The compression ignition heat release model is considerably more complicated than the
spark ignition model. Most compression ignition models use two functions. Stone [5]
suggests
x f f = + 1 21( ) ( ) ( ) (23)
where f1() represents the pre-mixed and f2() the diffusion burning phase. The two func-tions are combined with a weighing factor which is defined as
= 1 0 875
0 350
..
id0.375
(24)
The numerical factors can take on a range of values. The values in equation (24) are at the
mid-point of the respective ranges [5].
The ignition delay time can be estimated with many different formulae, i.e., references
[2], [3] and [5]. The most straight-forward to apply is offered by Stone [5] and
International Journal of Mechanical Engineering Education Vol 28 No 4
d
d
fK K f
K23 4
12
4 1
= ( ) (33)
d
d
fK K
K K K11 2
1 11 1 21
= ( )
(32)
Equations (27) and (28) are differentiated yielding
K K4 30 25
0 79= . . (31)
K3 0 64414 2
=.
.(30)
K2 5000= (29)
K N18 2 42 1 25 10= + . ( ) .id (28)
The Kvalues are defined as
fK K
1 1 11
2( ) = ( ) (26)
where t t rk
id c=
11
and p p r k
id c= 1 .The pre-mixed and diffusion functions, i.e., references [2] and [4], are
idid
id
=( )
( )
3 52 2100
1001 022
. exp
.
t
p(25)
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International Journal of Mechanical Engineering Education Vol 28 No 4
Using the ideal gas law and heat release models 285
d
d
d
d
d
d
x f f
b b
=
+
1 21 (34)
6. ENGINE POWER
Since the primary thrust of this article is an assessment of engine timing, power values are
not strictly necessary and values ofWcan be used. Comparing values of power will, how-
ever, have more impact on the students than dimensionless units. Power can be derived from
the computed values using conventional techniques [6] and
vv
11
=
r
r N
c
c
d
c
(35)
m p
Rt1
1 1
1
= v (36)
mN
m N1 1120
= c (37)
.
wm
mp W=
1 341 1
11v1 (38)
7. SOLUTION OF THE GOVERNING EQUATIONS
The equations of Sections 2 through 6 must be solved numerically. A computer program can
be written for this purpose or EES32 [1] can be employed. EES32 can be used to solve a set
of simultaneous algebraic equations and/or initial value differential equations. EES32 differs
from numerical equation solving programs in three ways: EES32 automatically groups
equations which must be solved simultaneously, it provides built-in mathematical and
thermophysical functions and built-in input and output including spreadsheets and graphs.
As noted earlier, the objective of this article is to demonstrate timing effects. The model
developed herein contains many simplifications and omissions. At the same time, the model
utilizes many characteristics of real engines, i.e., the piston-cylinder geometry, the enginecompression ratio, the engine rotational speed and the equivalence ratio. As a result, the
characteristics of existing engines were employed in the example cases. The engine
parameters are given in Table 1. All factors are from the manufacturers with the following
exceptions. The connecting rod length has been determined using bore and stroke and stand-
ard design practice. The equivalence ratio was chosen as 1.0 for the spark ignition engines
and as 0.52 for the compression ignition engine. Stone [5] states that equivalence ratios
range from 0.14 to 0.90 for compression ignition engines and a mid-point value of 0.52 was
chosen. Standard sea-level conditions of 101.35 kPa and 333K were selected for the condi-tions at bottom dead centre. The values for Cand Tw were taken from Ferguson [3]. The
combustion duration was set at 40. This is a typical value and is discussed in references [2]through [6]. The heat loss coefficient, i.e., H, was set so that the engine produced rated
power at the rated rotational speed. This has the effect of lumping all the losses in the heat
loss coefficient.
The EES32 program used to evaluate and integrate the equations of Sections 2 through 6
is shown in Table 2. Note that this version of the program is for the Chrysler 2.2 litre spark
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286 G. David Huffman
Table 1. Spark and combustion ignition engines used in the examples
Manufacturer
TypeCharacteristics
Chrysler
Spark ignitionCarburettored I4
Oldsmobile
Spark ignitionSequential fuel injected V6
Ford
Compression ignitionDirect injection I4
vd (litres)
b (mm)
s (mm)
l (mm)
rcsb
NcN(revmin)
p1 (kPa)
t1 (K)
H
C
Twb (degrees)
2.213
87.5
92.0
145.6
8.9
1.0514
0.3159
45200
96.6
101.35
333
1.00
0.919
0.004
1.2
40
3.132
88.9
84.1
140.3
9.6
0.9460
0.2997
64800
150.0
101.35
333
1.00
0.350
0.004
1.2
40
2.496
93.7
90.5
149.4
19.0
0.9658
0.3029
44000
69.7
101.35
333
0.52
1.150
0.004
1.2
40
w (hp)
Table 2. EES32 Computer program for the analysis of engine timing
{Engine Timing EES_32 Program }{Heat Input}
Procedure Heatlnput(1sc$:Q,q_in)$Common Theta_s,DELTA Theta_b,Phi,Pwr,t1,p1,k,R,r_c,NIf(lsc$=Cl) Then{Compression Ignition Model}
F_s:=0.069Gamma_1:=42500Gamma_2:=3708
Else{Spark Ignition Model}
F_s:0.068Gamma_1:=4300Gamma_2:=3751
EndifIf(Phi
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International Journal of Mechanical Engineering Education Vol 28 No 4
Using the ideal gas law and heat release models 287
{Heat Release Fraction}
Procedure HeatReleaseFraction(Theta,Isc$:x,dxdTheta,DELTATheta_id)$Common Theta_s,DELTATheta_b,Phi,Pwr,t1,p1,K,R,r_c,N
If(Isc$=Cl) Then{Compression Ignition Model}
t_id:=t1*r_c^(k-1)p_id:=p1*r_c^kTau_id:=3.52*Exp(2100/t_id)/(p_id/100)^1.022\DELTA Theta_id:=6*N*(Tau_id/1000)If(Theta=Theta_s+DELTA Theta_b) Then
x:=0dxdTheta:=0
Else
Lambda:=(Theta-Theta_s)/DeltaTheta_bAlpha:=1-0.875*Phi^0.35/Tau_id^0.375If(Alpha=1) Then Alpha:=1K_1:=2+1.25E-08*(Tau_id*N)^2.4K_2:=5000K_3:=14.2*Phi^0.64444K_4:=0.79*K_3^0.25f_1:=1-(1-Lambda^K_1)^K_2f_2:=1-Exp(-K_3*Lambda^K_4)
x:=Alpha*f_1+(1-Alpha)*f_2df2dLambda:=(K_1*K_2*Lambda^(K_1-1))*((1-Lambda^K_1)^(K_2-1))df2dLambda:=(1-f_2)*(K_3*K_4*Lambda^(K_4-1))dxdTheta:=(alpha*dF1dLambda+(1-Alpha)*df2dLambda)/(Pi*DELTATheta_b/180)
EndifElse{Spark Ignition Model}
Tau_id:=-1DELTA Theta_id:=-1
If(Theta=Theta_s+DELTATHETA_b) Then
x:=0dxdTheta:=0
ElseLambda:=(Theta-Theta_s)/DELTATheta_be:=1-exp(-(Lambda)^Pwr)dxdTheta:=((1-x)*pwr*(Lambda)^(Pwr-1))/(Pi*DELTATheta_b/180)
EndifEndifEnd
{Main Program}Isc$=Sl{Cl--Compression Ignition and Sl--Spark Ignition}Engine$= Chrysler 2.2Liter 14{Gas Constants and Inlet Conditions}
k=1.336R=0.287{kJ/kg-Deg K}
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288 G. David Huffman
t1=333{Deg K}p1=101.35{kPa}{Combustion Parameters}
Phi=1Pwr=4DELTATheta_b=40{Degrees}Theta_3=-30{Degrees}{Engine Geometry}
r_c=8.9v_d=0.002213{m^3}N_c=4N=5200{rev/min}b=0.0875{m}
s=0.0920{m}l=0.1456{m}Epsilon=2/(2*l){Mass and Mass Flow Rate at Condition1}v1=(r_r/(r_c-1))*(v_d/N_c)m1=p1*v1/(R*t1)m_dot_1=m1*N*N_c/120{Heat Loss Parameters}H=0.919T_w=1.2
Beta=2*(s/b)*(r_c)/(r_c-1){Mass Loss Parameter}
C=0.004{Heat Input Parameter}Call Heatlnput(Isc$:Q,q_in){Dimensionless Volume}
Va=(1/Epsilon)+1-cos(Theta)-(1/Epsilon)*Sqrt(1-(Epsilon*sin(Theta))^2)Vb=(r_c-1)*Va/2V=(1+Vb)/r_c
{Differential Equations}
Theta=180*ThetaRadTmp/PidVdThetat=1+Epsilon*cos(Theta)/Sqrt(1-(Epsilon*sin(Theta))^2)dVdTheta=(r_c-1)*sin(Theta)*dVdThetat/(2*r_c)Call HeatReleaseFraction(Theta,Isc$:x,dxdTheta,DELTATheta_id)dPdTheta=-k*P*dVdTheta/V+(k-1)*(Q*dxdTheta-dQLdTheta)/V-k*C*PdWdTheta=P*dVdThetadQLdTheta=H*(1+Beta*V)*(P*V/M-T_w)dMdTheta=-C*M{Integration of Differential Equations}P=P_i+Integral(dPdTheta,ThetaRadTmp,ThetaRad_i,ThetaRad)
W=W_i+Integral(dWdTheta,thetaRadTmp,ThetaRad_i,ThetaRad)QL=QL_i+Integral(dQLdTheta,ThetaRadTmp,TehtaRad_i,ThetaRad)M=M_i+Integral(dMdTheta,ThetaRadTmp,ThetaRad_i,ThetaRad)P_i=TableValue(Row-1,#P)W_i=TableValue(Row-1,#W)QL_i=TableValue(Row-1,#QL)
International Journal of Mechanical Engineering Education Vol 28 No 4
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International Journal of Mechanical Engineering Education Vol 28 No 4
Using the ideal gas law and heat release models 289
M_i=TableValue (Row-1,#M)ThetaRad_i=TableValue(Row-1,#ThetaRad)T=P*V/M
{Power}w_dot=1.341*(m_dot_1/m1)*p1*v1*W
ignition engine. Procedures are used for the heat release fraction and the heat input. The
procedures are similar to those employed in a programming language. Note the use of
Common and the passage of variables through the calling statement. An IfThenElse con-
struct is used and the equations come directly from Sections 4 and 5.
The various input parameters comprise the first portion of the main program followed by
the volume equations of Section 2 and the differential equations of Section 3. The built in
integral function is used to integrate the differential equations. EES32 uses an automatic step-
size adjustment algorithm to minimize error. The user specifies the step-size in the paramet-
ric table. A parametric table for the Chrysler engine is shown in Table 4. The integration
proceeds from 180 to 180 with 0 denoting top dead centre. The initial values are dis-
played in the first row of the parametric table, ie. P = 1, Q1 = 0, M= 1 and W= 0 at
= 180. The integration begins with the second table row. EES32 also provides a solutionwindow, Table 3, which includes all variables appearing or referenced in the main program.
Graphs can be generated from any combination of variables in the parametric table. Note
that units can be displayed for all variables.
Table 3. EES
32
Solution window
b = 0.0875 [m]b = 40 [Degrees]dPdTheta = -0.2446dVdThetat = 0.6841Engine$ = Chrysler
2.2Liter 14ISC$ = SlM = 0.975
Mi = 0.976P = 1.393Pwr = 4QL = 12.900R = 0.287b [kJ/kg-Deg K]s = 0.0920 [m] = 180 [Degrees]ThetaRadi = 2.9671
[Radians]V = 1.000
Vb = 7.9w = 96.6 [hp]
= 2.369
id = -1.00 [Degrees]
dQLdTheta = 0.7058dWdTheta = 0.0000
= 0.3159
k = 1.336
m1 = 6.610E-04 [kg]
N = 5200 [rev/min]p1 = 101.4 [kPa]
Pi = 1.448
QLi = 12.764
Row = 47
T = 1.428
ThetaRad = 3.1416[Radians]
s = -30 [Degrees]V1 = 6.233E-04 [m3]
vd = 2.213E-03 [m
3
]Wi = 6.575
C = 0.004
dMdTheta = -0.0039
dVdTheta = 0.0000dxdTheta = 0.000E+00
H = 0.919
I = 0.1456 [m]m1 = 0.1146 [kg/sec]
Nc = 4 = 1.00
Q = 28.647
qin = 2737.8 [kJ/kg]
rc = 8.9
t1 = 333 [Deg K]
ThetaRadTmp = 3.1416[Radians]
Tw = 1.2
Va = 2
W = 6.582x = 0.000
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Table4.
EES32
parametrictable
Row
ThetaRad
[radians]
[degr
ees]
P
QL
M
W
V
T
w[hp]
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
3.1
416
2.9
671
2.7
925
2.6
180
2.4
435
2.2
689
2.0
944
1.9
199
1.7
453
1.5
708
1.3
963
1.2
217
1.0
472
0.8
727
0.7
854
0.6
981
0.6
109
0.5
236
0.4
363
0.3
491
0.2
618
0.1
745
0.0
873
0.0
000
0.0
873
0.1
745
180
170
160
150
140
130
120
110
100
90
80
70
60
50
45
40
35
30
25
20
14
10
5
0
5
10
1.0
00
1.0
39
1.0
85
1.1
41
1.2
11
1.3
00
1.4
14
1.5
63
1.7
62
2.0
32
2.4
05
2.9
35
3.7
04
4.8
42
5.6
07
6.5
42
7.6
75
9.0
25
10.6
02
12.5
61
15.4
66
20.3
41
28.2
68
39.3
31
51.5
17
61.0
13
0.0
00
0.0
99
0.1
79
0.2
42
0.2
88
0.3
19
0.3
36
0.3
38
0.3
25
0.2
99
0.2
58
0.2
03
0.1
34
0.0
50
0.0
02
0.0
49
0.1
05
0.1
64
0.2
27
0.2
96
0.3
77
0.4
87
0.6
56
0.9
25
1.3
33
1.9
02
1.0
00
0.9
99
0.9
99
0.9
98
0.9
97
0.9
97
0.9
96
0.9
95
0.9
94
0.9
94
0993
0.9
92
0.9
92
0.9
91
0.9
91
0.9
90
0.9
90
0.9
90
0.9
89
0.9
89
0.9
89
0.9
88
0.9
88
0.9
88
0.9
87
0.9
87
0.0
00
0.0
05
0.0
20
0.0
46
0.0
84
0.1
37
0.2
07
0.2
97
0.4
10
0.5
52
0.7
27
0.9
42
1.2
05
1.5
23
1.7
04
1.9
00
2.1
10
2.3
30
2.5
54
2.7
74
2.9
84
3.1
76
3.3
33
3.4
03
3.2
89
2.9
10
1.0
00
0.9
95
0.9
81
0.9
58
0.9
25
0.8
83
0.8
32
0.7
71
0.7
03
0.6
28
0.5
49
0.4
68
0.3
88
0.3
13
0.2
78
0.2
45
0.2
16
0.1
89
0.1
67
0.1
47
0.1
32
0.1
21
0.1
15
0.1
12
0.1
15
0.1
21
1.0
00
1.0
34
1.0
66
1.0
96
1.1
24
1.1
52
1.1
81
1.2
12
1.2
46
1.2
84
1.3
29
1.3
83
1.4
49
1.5
28
1.5
73
1.6
22
1.6
74
1.7
28
1.7
85
1.8
72
2.0
68
2.4
95
3.2
79
4.4
75
5.9
80
7.4
95
0.
0
0.1
0.3
0.7
1.2
2.0
3.0
4.4
6.0
8.1
10.7
13.8
17.7
22.4
25.0
27.9
31.0
34.2
37.5
40.7
43.8
46.6
48.9
50.0
48.3
42.7
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Table4.
Contin
ued
Row
ThetaRad
[radians]
[degr
ees]
P
QL
M
W
V
T
w[hp]
Run27
Run28
Run29
Run30
Run31
Run32
Run33
Run34
Run35
Run36
Run37
Run38
Run39
Run40
Run41
Run42
Run43
Run44
Run45
Run46
Run47
26
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
0.2
618
0.3
491
0.4
363
0.5
236
0.6
109
0.6
981
0.7
854
0.8
727
1.0
472
1.2
217
1.3
963
1.5
708
1.7
453
1.9
199
2.0
944
2.2
689
2.4
435
2.6
180
2.7
925
2.9
671
3.1
416
15
20
25
30
35
40
45
50
60
70
80
90
100
110
120
130
140
150
160
170
180
59.5
72
49.9
45
41.0
94
33.4
85
27.2
10
22.1
56
18.1
33
14.9
46
10.4
08
7.5
07
5.6
06
4.3
27
3.4
45
2.8
25
2.3
82
2.0
61
1.8
27
1.6
57
1.5
34
1.4
48
1.3
93
2.58
4
3.27
9
3.93
9
4.56
4
5.15
7
5.72
0
6.25
4
6.76
2
7.70
4
8.55
2
9.31
0
9.98
0
10.56
4
11.06
7
11.49
4
11.85
3
12.15
1
12.39
7
12.59
9
12.76
4
12.90
0
0.9
86
0.9
86
0.9
86
0.9
85
0.9
85
0.9
85
0.9
84
0.9
84
0.9
83
0.9
83
0.9
82
0.9
81
0.9
81
0.9
80
0.9
79
0.9
79
0.9
78
0.9
77
0.9
77
0.9
76
0.9
75
2.2
48
1.4
21
0.5
53
0.2
97
1.0
95
1.8
21
2.4
70
3.0
43
3.9
81
4.6
87
5.2
14
5.6
05
5.8
94
6.1
07
6.2
64
6.3
78
6.4
60
6.5
17
6.5
55
6.5
75
6.5
82
0.1
32
0.1
47
0.1
67
0.1
89
0.2
16
0.2
45
0.2
78
0.3
13
0.3
88
0.4
68
0.5
49
0.6
28
0.7
03
0.7
71
0.8
32
0.8
83
0.9
25
0.9
58
0.9
81
0.9
95
1.0
00
7.9
83
7.4
63
6.9
42
6.4
38
5.9
63
5.5
23
5.1
18
4.7
48
4.1
05
3.5
73
3.1
33
2.7
69
2.4
70
2.2
24
2.0
23
1.8
60
1.7
29
1.6
24
1.5
42
1.4
77
1.4
28
33.0
20.9
8.1
4.4
16.1
26.7
36.3
44.7
58.5
68.8
76.6
82.3
86.5
89.7
92.0
93.7
94.9
95.7
96.2
96.5
96.6
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International Journal of Mechanical Engineering Education Vol 28 No 4
292 G. David Huffman
8. SPARK AND COMPRESSION ENGINE TIMING EXAMPLES
The impact of engine timing, i.e., the start of the release process, can be demonstrated by
varying s
for fixed values of all other parameters. All parameters used in these examples are
give in Table 1. An Oldsmobile 3.1 litre V6 spark ignition engine and a Ford 2.5 litre direct
injection naturally aspirated compression ignition engine are used in the examples. The
performance of both engines was calculated for a series ofs values and the engine power at
180 determined. The power was then plotted against s and an optimum value determined,i.e., the value of s for which the maximum power is produced. The results for the spark
ignition engine are shown in Fig. 2. The optimum value in this case is approximately 30 or30 before top dead centre. Figs 3, 4 and 5 show pressure distributions for s values of 50,30 and 10. The compression ignition engine results are shown in Figs 6, 7, 8 and 9. Inthis case, the optimum s value is approximately 0 and pressure plots for s values of 0,
10 and 20 are included. Note that the 10 case is used for optimization purposes only.An engine would never operate with heat release beginning after top dead centre.
Fig. 2. Power versus the start of heat release for an Oldsmobile 3.1 l V6.
9. CONCLUSIONS
The use of the ideal gas equations and a heat release model coupled with an engineering
equation solver provides a method of demonstrating engine timing effects to undergraduate
students in mechanical engineering technology.
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Using the ideal gas law and heat release models 293
Fig. 3. Pressure distribution for an Oldsmobile 3.1 l V6. s = 50.
International Journal of Mechanical Engineering Education Vol 28 No 4
Fig. 4. Pressure distribution for an Oldsmobile 3.1 l V6. s = 30.
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International Journal of Mechanical Engineering Education Vol 28 No 4
Fig. 5. Pressure distribution for an Oldsmobile 3.1 l V6. s = 10.
Fig. 6. Power versus the start of heat release for a Ford 2.5 l DI Diesel.
294 G. David Huffman
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Using the ideal gas law and heat release models 295
International Journal of Mechanical Engineering Education Vol 28 No 4
Fig. 7. Pressure distribution for a Ford 2.5 l DI Diesel. s = 20.
Fig. 8. Pressure distribution for a Ford 2.5 l DI Diesel. s = 10.
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International Journal of Mechanical Engineering Education Vol 28 No 4
296 G. David Huffman
Fig. 8. Pressure distribution for a Ford 2.5 l DI Diesel. s = 10.
REFERENCES
[1] EES32 Engineering Equation Solver, F-Chart Software, Madison, WI, 1997.[2] Heywood, John B., Internal Combustion Engine Fundamentals, McGraw Hill, Inc., New York,
1988.[3] Ferguson, Colin R., Internal Combustion EnginesApplied Thermosciences, John Wiley & Sons,
New York, 1986.[4] Pulkrabek, Willard, W., Engineering Fundamentals of the Internal Combustion Engine, Prentice
Hall, Upper Saddle River, NJ, 1997.
[5] Stone, Richard, Introduction to Internal Combustion EnginesSecond Edition, Society ofAutomotive Engineers, Inc., Warrendale, PA, 1994.
[6] Ganesan, V.,Internal Combustion Engines, McGraw Hill, New York, 1996.
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