Using the Ideal Gas Law and Heat Release Models to Demonstrate Timing in Spark and Compression Ignition Engines

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, [email protected]

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


2/18

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



3/18

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.


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)


4/18


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)


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)


5/18



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


6/18


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


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)


7/18



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


8/18


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


9/18



{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}


10/18


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)



11/18



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


12/18

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


13/18

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


14/18



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.


15/18


Fig. 3. Pressure distribution for an Oldsmobile 3.1 l V6. s = 50.




16/18



Fig. 6. Power versus the start of heat release for a Ford 2.5 l DI Diesel.



17/18



Fig. 7. Pressure distribution for a Ford 2.5 l DI Diesel. s = 20.



18/18




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.

Documents

Using the Ideal Gas Law and Heat Release Models to Demonstrate Timing in Spark and Compression Ignition Engines