Spark Ignition Internal Combustion Engine Modelling using Matlab

42 Pages·0.42 MB·English

by  Buttsworth D.R.

http://www.Drshokuhi.com

کیناکم یسدنهم شزومآ تیاس
Spark Ignition Internal Combustion Engine
Modelling using Matlab
David R Buttsworth
[email protected]
http://www.usq.edu.au/users/buttswod/
October 16, 2002
Faculty of Engineering & Surveying Technical Reports
ISSN 1446-1846
Report TR-2002-02
ISBN 1 877078 02 6
Faculty of Engineering & Surveying
University of Southern Queensland
Toowoomba Qld 4350 Australia
http://www.usq.edu.au/
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Abstract
A number of Matlab routines for combustion calculations and thermodynamic simulation of spark
ignition internal combustion engine operation are described. Functions that return the thermody-
namic curve coeÆcients for a variety of fuel, air, and combustion product species are described.
A Matlab version of the Olikara and Borman method for determining the equilibrium state of
combustion products is also presented. Additional routines speci(cid:12)cally designed for spark ignition
engine modelling are also described. Most of the routines included in this report are essentially
Matlab versions of the FORTRAN programs presented by Ferguson for spark ignition engine cal-
culations. Comparisons of results from the new Matlab routines and previous routines and data
indicate that the new Matlab routines are reliable { typical deviations from previous results are
less than 1%.
Contents
1 Introduction 4
2 Basic Thermodynamic Data 4
2.1 Air and Combustion Products Data . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Fuel Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 Fuel, Air, and Residual Gases 7
4 Equilibrium Combustion Products 9
5 Adiabatic Flame Temperature 10
6 Arbitrary Heat Release 11
6.1 Engine Speci(cid:12)cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6.2 Functions for Di(cid:11)erential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6.3 Heat Transfer Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6.4 Arbitrary Heat Release Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6.5 Analysis of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
7 Conclusions 12
A airdata.m 17
B fueldata.m 19
C farg.m 21
D ecp.m 23
E Tadiabatic.m 28
CONTENTS 3
F enginedata.m 29
G RatesComp.m & RatesComb.m & RatesExp.m 29
H ahrind.m 33
I plotresults.m 35
J calcq.m 38
K ferguson.txt 39
1 Introduction 4
1 Introduction
Matlab is popular for theoretical calculations and the analysis of experimental data. Although
many thermodynamic and combustion routines are readily available in FORTRAN, the Matlab
environment o(cid:11)ers many advantages. Given the relative simplicity of internal combustion (IC)
engine routines presented by Ferguson [1] it appeared reasonable to develop equivalent routines
using Matlab. Having the fundamental routines available in Matlab a(cid:11)ords workers that are
familiar with this environment the capacity to rapidly adapt and extend the routines as required.
The Matlab routines describedherein are based largely on the FORTRAN programs for IC engine
calculations presented by Ferguson [1]. However, extensive use is made of the matrix and array
data structures available in Matlab. In the subsequent sections of this report, the Matlab routines
are described. Where appropriate, results obtained using the Matlab routines are compared to
results obtained using established methods.
2 Basic Thermodynamic Data
2.1 Air and Combustion Products Data
Gordon and McBride [2] (cid:12)tted curves to the tabulated JANAF data [3] (and a similar approach
hasbeenadoptedfortheChemkincurves[4])to giveexpressionsforthethermodynamicproperties
of the form,
cp 2 3 4
= a1 +a2T +a3T +a4T +a5T (1)
R
h a2 a3 2 a4 3 a5 4 1
=a1+ T + T + T + T +a6 (2)
RT 2 3 4 5 T
s a3 2 a4 3 a5 4
=a1lnT +a2T + T + T + T +a7 (3)
R 2 3 4
The Matlab function airdata.m (Appendix A) returns the curve coeÆcients a1 to a7 for either the
Gordon and McBride [2] curves or the Chemkin [4] curves over two di(cid:11)erent temperature ranges:
1) 300 < T < 1000K; and 2) 1000 < T < 5000K. There are 10 rows in the returned matrix and
each row provides the seven coeÆcients (in ascending order) for a di(cid:11)erent species. The 10 species
for which data is available are (in the following order): CO2, H2O, N2, O2, CO, H2, H, O, OH,
and NO. The options for airdata.m are listed in Table 1, and the numerical values for the curve
coeÆcient can be found in the listing of airdata.m in Appendix A.
The speci(cid:12)c heat curves for the 10 species using the Gordon and McBride [2] and the Chemkin [4]
coeÆcients are presented in Fig. 1 and Fig. 2. These (cid:12)gures indicate that di(cid:11)erences between the
two sets of coeÆcients are relatively insigni(cid:12)cant. For example, with the O2 curve, the maximum
di(cid:11)erence between the values of cp for the two di(cid:11)erent schemes is only 0.3% at around 3500K.
By itself, this is a relatively small di(cid:11)erence in engineering terms. When it is recognised that
2.1 Air and Combustion Products Data 5
scheme switch meaning
’GMcB_low’ Gordon and McBride [2], 300 <T <1000K
’GMcB_hi’ Gordon and McBride [2], 1000 <T <5000K
’Chemkin_low’ Chemkin [4], 300 <T <1000K
’Chemkin_hi’ Chemkin [4], 1000 <T <5000K
Table 1: Options available in airdata.m
Gordon and McBride [2] Chemkin [4] JANAF [3]
0 0 0 0 0 0
species hf s hf s hf s
(kJ/kmol) (kJ/kmolK) (kJ/kmol) (kJ/kmolK) (kJ/kmol) (kJ/kmolK)
CO2 -393 500. 213.697 -393 543. 213.735 -393 520. 213.69
H2O -241 817. 188.708 -241 843. 188.713 -241 810. 188.72
N2 -0.3 191.502 1.4 191.509 0. 191.50
O2 -0.4 205.037 -0.8 205.042 0. 205.04
CO -110 526. 197.533 -110 540. 197.546 -110 530. 197.54
H2 3.0 130.580 2.4 130.594 0. 130.57
H 217 977. 114.604 217 977. 114.604 218 000. 114.61
O 249 195. 160.944 249 195. 160.944 249 170. 160.95
OH 39 463. 183.594 38 986. 183.603 38 987. 183.60
NO 90 285. 210.639 90 297. 210.651 90 291. 210.65
0 0
Table 2: Values of hf and s using the Gordon and McBride [2] and the Chemkin [4] coeÆcients
compared with JANAF [3] values.
1.5
CO
CO 2
1.4
O
1.3
)
K
NO
g
k
/1.2
J
k
(p O2
c
1.1
1
N
2
0.9
0 1000 2000 3000 4000 5000
T (K)
Figure 1: Comparison of speci(cid:12)c heat curves for CO2, N2, O2, CO, O, and NO using coeÆcients
from Gordon and McBride [2] (solid lines) and Chemkin [4] (broken lines).
2.2 Fuel Data 6
3.5
H O
2
3
K)2.5
g
k OH
/
J
k H/10
(
p 2
c
H /10
1.5 2
1
0 1000 2000 3000 4000 5000
T (K)
Figure 2: Comparison of speci(cid:12)c heat curves for H2O, H2, H, and OH using coeÆcients from
Gordon and McBride [2] (solid lines) and Chemkin[4] (broken lines). (The speci(cid:12)c heat values for
H2 and H have been reduced by a factor of 10 for this (cid:12)gure.)
most of the O2 will have dissociated by this temperature anyway, the equilibriumthermodynamic
properties calculated by the two di(cid:11)erent schemes will be practically the same.
Reference values of enthalpy and entropy at T = 298:15K (and p = 101:325kPa) calculated
using the Gordon and McBride [2] and Chemkin [4] coeÆcients are presented in Table 2 where
comparisons can also be made with the tabulated JANAF [3] values. Apart from the reference
enthalpies for N2, O2, and H2 (which should be zero), the maximum relative di(cid:11)erence between
curvevaluesandJANAF valuesisabout1%inthecase oftheGordonandMcBride [2]coeÆcients
0
for (cid:16)hf(cid:17) . All of the other reference values (apart from zero reference enthalpies) typically
OH
deviate from the JANAF values by around 0.01% only.
Through comparison of the Gordon and McBride [2] and Chemkin [4] curves, it was found that
the coeÆcient a1 reported by Ferguson [1] p129 for O in the high temperature range is incorrect.
The correct value is a1 =2:5420596, and this value is used inairdata.m (see AppendixA) whereas
the value reported by Ferguson is a1 =5:5420596 (which is incorrect).
2.2 Fuel Data
Heywood [5] represents the thermodynamic properties of selected fuels using curves that di(cid:11)er
slightly in form to those of the air and combustion products species (Section 2.1). The fuel
property curves of Heywood are given by,
3 Fuel, Air, and Residual Gases 7
cp 2 3 1
=a1+a2T +a3T +a4T +a5 2 (4)
R T
h a2 a3 2 a4 3 1 1
=a1+ T + T + T (cid:0)a5 2 +a6 (5)
RT 2 3 4 T T
s a3 2 a4 3 a5 1
= a1lnT +a2T + T + T (cid:0) 2 +a7 (6)
R 2 3 2 T
whereas other workers such as Ferguson [1] have adopted simpli(cid:12)ed versions of Eq. (4) to Eq. (6)
in which a4 =a5 =0.
The Matlab function fueldata.m (listed in Appendix B) returns a vector of curve coeÆcients
corresponding to a1 to a7 for a number of di(cid:11)erent fuels. Actual numerical values for the curve
coeÆcients can be found in Appendix B.
The various di(cid:11)erent fuel options and the sources of the data used in fueldata.m are presented
in Table 3. Values of reference enthalpy and entropy for the curves at T = 298:15K (and p =
101:325kPa) are also listed in Table 3. Where di(cid:11)erent curve (cid:12)t coeÆcients are available for
nominally the same fuel, the coeÆcients of Heywood [5] have been denoted with the suÆx _h.
Values for a7 were not presented by Heywood [5], so these values have been obtained from other
0 0
sources ([6], [1], and [7]). There is some scatter in the values of hf and s reported by various
0 0
authors { the maximum di(cid:11)erences are around 0.8%. The values of hf and s from the present
curves (Table 3) typically fall within the previously reported range of values.
In the case of methane, methanol, and iso-octane, recommended curve (cid:12)ts from di(cid:11)erent sources
are available. Figure 3 provides a comparison cp over the temperature range 300 < T < 1000K.
In the case of methane, the values of cp from the two di(cid:11)erent sources di(cid:11)er by less than 2% over
the speci(cid:12)ed temperature range.
3 Fuel, Air, and Residual Gases
Due to the volumetric ineÆciency of IC engines, combustion products remain within the cylinder
when the exhaust valve closes. These combustion products (also known as residual gases) are
mixed with the fresh air-fuel mixture that enters the engine while the inlet valve remains open.
The thermodynamic properties of the mixture of fuel, air, and residual gases can be determined
using the routine farg.m which is listed inAppendix C. For details of the inputsand outputs from
this function, see Appendix C, or from the Matlab base workspace, type: help farg.
Thefuelairresidualgasroutine,farg.misessentiallyaMatlabversionoftheFORTRANsubroutine
of the same name that is presented by Ferguson [1] p111. For this subroutine, Ferguson [1] uses
the results of Hires et al. [9] to determine the low temperature combustion products. farg.m
utilizesthe lower temperature range curve coeÆcients (300 <T <1000K) from airdata.m and the
coeÆcients from fueldata.m. Hence, results from farg.m may be in error for T >1000K.
3 Fuel, Air, and Residual Gases 8
0 0
fuel switch composition source hf s
(kJ/kmol) (kJ/kmolK)
’methane’ CH4 Ferguson [1] -74 846 186.290
’methane_h’ CH4 Heywood [5] -74 870 186.271
’propane’ C3H8 Heywood [5] -103 856 270.200
’benzene’ C6H6 Ferguson [1] 82 939 269.241
’hexane’ C6H14 Heywood [5] -167 028 386.811
’toluene’ C7H8 Raine [8] 49 999 319.742
’isooctane’ C8H18 Raine [8] -224 012 422.964
’isooctane_h’ C8H18 Heywood [5] -224 109 422.960
’methanol’ CH3OH Ferguson [1] -201 161 239.720
’methanol_h’ CH3OH Heywood [5] -201 004 239.882
’ethanol’ C2H5OH Heywood [5] -236 266 280.640
’nitromethane’ CH3NO2 Ferguson [1] -74 718 275.044
’gasoline’ C7H17 Ferguson [1] -267 089 465.242
’gasoline_h1’ C8:26H15:5 Heywood [5] -112 702 |
’gasoline_h2’ C7:76H13:1 Heywood [5] -72 105 |
’diesel’ C14:4H24:9 Ferguson [1] -99 946 645.445
’diesel_h’ C10:8H18:7 Heywood [5] -180 940 |
Table 3: Fuel choices available in fueldata.m
5
Heywood
a =a =0
4.5 4 5
4
)3.5 C H
K 8 18
g
k
/ 3
J
k CH
(
p 4
c2.5
2 CH OH
3
1.5
1
300 400 500 600 700 800 900 1000
T (K)
Figure 3: Comparison of speci(cid:12)c heat curves for methane, methanol, and iso-octane from di(cid:11)erent
sources.