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

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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, [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

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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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    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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    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.