Development of Surrogates for Aviation Jet Fuels by Seyed Ali Nasseri A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Aerospace Studies University of Toronto Copyright c 2013 by Seyed Ali Nasseri
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Development of Surrogates for Aviation Jet Fuels
by
Seyed Ali Nasseri
A thesis submitted in conformity with the requirementsfor the degree of Master of Applied ScienceGraduate Department of Aerospace Studies
In which ncoefficients is the number of coefficients in the model, npredictors is the number of
predictor parameters used and nhidden is the number of hidden neurons used in the model.
ncoefficients is important in assessing the model, as it should not exceed the number of
experimental data points available in the training set. The number of maximum hidden
neurons was calculated using equation 3.1 and the regressions were developed starting
with 1 hidden neuron and reaching the maximum number of hidden neurons. Due to
the random nature of breaking down the data set into three sets and the optimization
procedure, the results of consecutive regression analysis are different. The algorithm was
run many times (at least 20 times for each number of hidden neurons), so that the best
reliable results were achieved. The outputs of the regression analysis using the MATLAB
ANN fitting tool have the following mathematical form (using matrix notation):
f(Xk×1) = W1×n tanh(wn×kXk×1 + bn×1) +B (3.2)
Where k is the number of predictor parameters (inputs), n is the number of neurons
used by the ANN, w is the input layer weight, b is the input bias, W is the hidden
Chapter 3. Regression Analysis Procedure 20
layer weight and B is the hidden layer bias. The ANN fitting tool in MATLAB requires
the number of hidden neurons to be input by the operator. In the IBM SPSS package
[52], this parameter is automatically tuned. Moreover, this software package uses other
transfer functions such as hyperbolic sine for both the hidden and output layers. Using
different transfer functions (as tested with the software packages STATISTICA [53] and
IBM SPSS) proved no major improvements in the results compared to the MATLAB
standard model. As a result, only the results from the standard model in MATLAB are
reported in Chapter 4.
3.3 Regression Diagnostics
There are no generic criteria for assessing regression results as such criteria generally
depend on the specific algorithm. The main criteria for choosing regression models in
this work were the highest R2 value and the lowest Root Mean Square Error (RMSE).
Regression equations developed using ANNs might over fit the data, as mentioned earlier.
Although precautionary measures were taken to prevent this, there was no way to make
sure over fitting did not occur. Some of the diagnostic measures used in this project are
summarized in the next subsections. There are also many other statistical parameters for
assessing regression models; however, as such measures are not common among engineers,
they were not used in this work.
3.3.1 Coefficient of Determination (R2 Value)
This regression diagnostic parameter is mainly used in assessing least squares results as
they focus on minimizing the errors used in calculating this parameter. It can also be
used to compare results obtained using ANNs, but should be used with caution when
comparing different methods (linear models to artificial neural networks). As the R or
R2 increases towards one, the regression results become more reliable. However, there
is no specific threshold that marks an acceptable regression result. In most cases, an R
value of 0.9 and higher is considered acceptable for ANN analysis and an R2 value of
more than 0.9 for linear regression analysis. The results reported here have the highest
attainable R2 values. The R2 values attained are compared to values published in the
literature to ease assessing the regression results.
Chapter 3. Regression Analysis Procedure 21
3.3.2 Residuals
The least squares method requires that the residuals (difference between the predicted
values and actual values) form a normal distribution around zero. As a result, the average
of the residuals should be near zero and the standard deviation of the residuals should
be preferably within the error range of the experimental method. This requirement is
generally accepted for other regression methods as well. The histogram of the residuals
or a Normal Quartile Quartile plot (qqplot) can be used to check for normality.
The residuals should also be independent of the predicted and predictor values. To
check this, residuals can be plotted against the predictor, expected and predicted values.
The plot should show no special geometric feature. All the MLR results presented in
this report were checked for these requirements. For the ANNs, more than 50% of the
residuals were normal, the rest being at the lower range of the spectrum (helping reduce
the total RMSE value). As ANN regression does not require that residuals be normally
distributed, this aspect will not affect the result. In this case, only the mean and standard
deviations were checked.
3.3.3 Predicted Results
The mean and standard deviation of predicted values and the actual sample should be
the same. This is equivalent to the mean of the residuals being negligible. The plot of
predicted versus actual results was also used to assess the regression results, as it is the
best method of assessing the fitness of the regression model.
3.3.4 Root Mean Square Error
The root mean square error shows the general level of error seen when using a regression
equation. If the regression results met all other requirements, the most accurate regres-
sion model (the one with the lowest RMSE) was chosen. It should be noted that ANNs
all had lower RMSE values compared to their linear counterparts.
RMSE values depend on the units used. It is common practice to normalize these values
by the average experimental value of the parameter being predicted in the data set or
the difference between the maximum and minimum values in the data set. In this work,
normalization with respect to the latter will be used.
Chapter 4
Correlation Development for Fuel
Parameters
4.1 Chemical Structure and Nuclear Magnetic Res-
onance (NMR) Spectroscopy
4.1.1 Chemical Structure
Physical and chemical properties of a compound arise due to its chemical structure. Many
different parameters can be used to account for the chemical structure of a compound or
mixture, including:
• The type of atoms the molecule is made of and their relative numbers such as
carbon to hydrogen or oxygen to nitrogen ratios.
• Bonding and bond strength.
• Composition of mixtures as reported through mass percentage, volume percentage
or molar percentage.
Many methods have been used to quantify the chemical structure of compounds and mix-
tures. These include gas chromatography-mass spectrometry (GC-MS), nuclear magnetic
resonance (NMR) spectroscopy, liquid chromatography (LC) and infrared (IR) spec-
troscopy. Each of these methods reveals pieces of information about the chemical struc-
ture and environment of the compound or mixture. In this work, proton nuclear magnetic
resonance(NMR) spectroscopy is used as a measure of the chemical structure of the fuel.
This method reveals many details about the chemical structure and environment of a
22
Chapter 4. Correlation Development for Fuel Parameters 23
mixture. Moreover, facilities for measuring the NMR spectra of compounds are available
at the University of Toronto.
4.1.2 Nuclear Magnetic Resonance (NMR) Spectroscopy
One of the most powerful methods for predicting the structure of hydrocarbons is nuclear
magnetic resonance (NMR) spectroscopy [54]. NMR spectroscopy is based on the inher-
ent magnetic properties of the nucleus of different atoms. Magnetic nuclei are stimulated
by a magnetic field and their response in terms of the resonance frequency of the emitted
electromagnetic radiation is measured. Usually the frequency is Fourier transformed and
reported as a shift relative to a standard (tetramethylsilane (TMS) is usually assigned a
chemical shift of zero as the standard). A solvent is usually used in preparing mixtures
for the analysis and it slightly affects the chemical shifts observed. All isotopes that
contain an odd number of protons and neutrons have a nonzero spin and are possible
targets for NMR spectroscopy. In hydrocarbons, H-1 (proton) and C-13 can be used.
Specific ranges of chemical shifts have been correlated with specific functional groups in
chemical compounds. The spectrum output of NMR spectroscopy reveals the following
information about a compound:
• The different types of chemical environments present in the molecule as identified
by the different shift values.
• The relative numbers of the nuclei in each environment as identified by the area
under each shift.
• The electronic environment of the different types of nuclei as identified by the
location of the shift (up field or down field) in the shift range.
• The number of neighbors each nuclei has as identified by the splitting of the shifts.
4.1.3 Identifying Chemical Characteristics of Compounds and
Mixtures Using NMR Spectra
A Jet A sample from the combustion and propulsion group was analyzed by the NMR
services at the University of Toronto. The result of this analysis is depicted in Figure
4.1. The NMR test sample was prepared at the University of Toronto NMR facilities by
mixing equal parts of Jet A and CDCl3 (400 µL of each). The sample was placed in a 5
mm × 8 inch tube for one dimensional proton NMR acquisition using a Bruker Avance
Chapter 4. Correlation Development for Fuel Parameters 24
III 400 spectrometer. The spectrum was acquired at 25 ◦C over a 6410.3 Hz (16 ppm)
spectral window with a 1 s recycle delay.
0 1 2 3 4 5 6 7 8
0
4
8
12
16
In
tens
ity
(ppm)Figure 4.1: Complete proton NMR spectrum of the Jet A fuel from the combustion andpropulsion group. The horizontal axis shows the chemical shift and the vertical axis theintensity of each peak.
To use the information from the NMR spectrum, the spectrum was discretized into
several regions, each corresponding to a specific chemical environment. These regions
are summarized in Table 4.1. These proton NMR shift ranges were developed based
consensuses on the ranges of chemical shifts that correspond to different functional groups
[55, 56, 57, 58, 59, 60] and the Jet A NMR spectrum. In the following chapters, each
chemical range shift will be denoted using the letter “P” and a number corresponding
to the number assigned to each range in Table 4.1. It should be noted that, as most
CH3 shifts had a chemical shift less than 1 and most CH and CH2 shifts above 1, the
Chapter 4. Correlation Development for Fuel Parameters 25
general chemical shift group identified in most references as 0.5-1.6 was broken into two
categories. Moreover, this corresponded well to the two shifts seen in the Jet A NMR
spectrum between 0.5-1.6.
In breaking down the shift ranges, functional groups which are not found in the Jet A
were also taken into account. This was mainly due to the fact that databases used for
correlation development might have included compounds with similar shifts. Moreover,
although these groups are not found in aviation jet fuel, other functional groups can have
similar chemical shift values. It should also be noted that the NMR shift ranges outlined
in Table 4.1 are the most detailed version used in this work. Whenever possible, ranges
with similar group functionalities (overlapping functional groups) were lumped together
to simplify the regression analysis.
As mentioned earlier, the height of each shift shows the number of hydrogens contributing
to that shift. As a result, the area under two regions of the NMR spectrum can be used
to compare the relative number of protons in the two group functionality. As the area
under the curve is arbitrary, normalization of all area calculations will lead to values that
can be compared between different spectra.
AP1 + AP2 + AP3 + ...+ APn = 1 (4.1)
Where A denotes the area under the range of chemical shifts corresponding to the sub-
script, as outlines in Table 4.1. Values normalized in this way show the percentage of
protons in each range of chemical shifts, which can be used as a measure of chemical
composition.
Chapter 4. Correlation Development for Fuel Parameters 26
Table 4.1: Ranges of chemical shifts and their corresponding functional groups [55, 56,57, 58, 59, 60].
Chapter 4. Correlation Development for Fuel Parameters 27
4.2 Cetane Number (CN)
4.2.1 Ignition Quality and the Cetane Number
As mentioned in Chapter 1, ignition quality was chosen as one of the fuel properties
modeled using the surrogate fuel. Ignition quality is determined from the ignition pro-
cess. The injected fuel in an engine is first evaporated, leading to the physical delay in
ignition. Factors affecting evaporation include fuel properties (density, viscosity, surface
tension, specific heat, enthalpy of vaporization, vapor pressure, vapor diffusivity), air
properties (temperature, density, velocity and turbulence) and spray properties (atom-
ization, penetration and shape) [61]. For ignition to occur, the fuel should be heated so
that radicals form which can initiate the oxidation process. The rate of radical formation
is responsible for the chemical delay in ignition. Ignition will only be initiated when a
specific amount of radicals have formed.
The efficiency of the complete ignition process is quantified using the cetane number.
The cetane number (CN) is a measure of the ignition quality of diesel fuels. It is used
to quantify the ignition quality of middle distillates in diesel engines by measuring their
self-ignition delay, the time between injection and combustion [62]. It takes into account
all delay effects such as spray formation, heating, vaporization, mixing and chemical
induction times [63]. Of course, ignition delay is also dependant on engine type and op-
erating conditions. In the absence of a parameter to quantify ignition quality of jet fuel,
cetane number has been used extensively with jet fuels as a measure of ignition quality
due to the the similarities between jet and diesel fuels.
Cetane number is generally dependent on the chemical composition of the fuel and can
affect engine startability, noise level and exhaust emissions [64]. Fuels with low cetane
numbers generally lead to hard starting, tough operation, more noise and higher emis-
sions of particulate matter and NOx [65]. Particulate emissions is less affected by cetane
number compared to NOx formation [51, 66, 67, 68]. Cetane number has an inverse re-
lationship with octane number (ON), meaning a compound with a higher ON typically
has a lower CN [69].
The first proposed rating scheme for ignition quality was the cetene (ketene) rating.
Since cetene was hard to prepare, the higher reference value was later replaced with n-
hexadecane (cetane, hence the name change to cetane number) with a cetane number of
100. The lower reference was changed to 2,2,4,4,6,8,8- heptamethylnonane, assigned a
cetane number of 15. It has been suggested that cetane number of a mixture has a linear
relationship with the cetane number of its components, although this is not always true
[61].
Chapter 4. Correlation Development for Fuel Parameters 28
Empirical equations used for predicting cetane number are called cetane indices (CIs)
[70, 71, 72]. For convenience, most refineries rely on ASTM approved CIs which are
“non-engine” predictive equations for cetane number. Such indices are updated based on
the crude properties and composition. They generally relate to the mid-boiling point of
the fuel and the API gravity [54]. Many of the CIs can not be used with fuels contain-
ing cetane number improvers and are not applicable to vegetable oils, diesel fuel blends
containing alcohols, synthetic fuels derived from oil sands or oil shales [70].
The cetane number of a compound depends on its molecular structure [62]. Based on
experimental data, it has been deduced that normal alkanes have higher cetane numbers
than branched alkanes. Cyclo-alkanes and aromatics generally reduce cetane number,
unless they have an n-alkane group attached [63, 67]. A linear relationship between the
chain length and CN for compounds with 8-16 carbon atoms has been proposed for dif-
ferent classes of hydrocarbons [68, 73]. This shows that one of the primary factors in CN
determination is carbon chain length. Another suggested factor is the ratio of primary
to secondary C-H bonds in a molecule [73].
4.2.2 Cetane Number Measurement
The most accepted methods for measuring CN are the ASTM D613 (engine test) [74]
and the ASTM D6890 (IQT measurements) [75]. Overall, it has been suggested in the
literature that due to the simplicity of IQT tests and its higher accuracy and reproducibil-
ity, this test should replace the engine test. Unfortunately, only a few pure compounds
have been tested using the IQT procedure which reduces the usefulness of these data.
Of course, there have also been many alternative experimental methods developed for
measuring CN or ignition delay, such as the combustion bomb experiment [76]. Such
methods have not been widely used.
ASTM D613
ASTM D613 is the more prominent standard for CN measurement. It is based on the
measurement of the ignition delay in a standard CFR test engine built by the Waukesha
company [61]. Other standardization agencies have similar tests with engines manufac-
tured by the country of origin of the standard. This method has several limitations. It
requires a large volume of fuel sample of high purity (about 1 L), takes typically long to
test (approximately a few hours) and has a high reproducibility error (3-5 CN numbers)
[63, 61, 77] (Note that the ASTM standard cites a reproducibility error of 0.8 [78].).
Despite all its flaws, ASTM D613 measurements and test facilities are widely available.
Chapter 4. Correlation Development for Fuel Parameters 29
Ignition Quality Tester (IQT)
IQT is an alternative method developed by Southwest Research Institute (SwRI). It
requires a Constant Volume Combustion Apparatus (CVCA) which is developed by Ad-
vanced Engine Technology Ltd. This method measures the ignition delay which is corre-
lated with the cetane number. Details of this method are available in references [79, 80].
CN measured using this method is called the derived cetane cumber (DCN). IQT mea-
surements require a smaller sample volume (less than 50 mL [77], although 100 ml has
also been cited as the sample size [62].) and a much shorter time (less than 10 min).
This testing method operates based on the ASTM D6890 standard [75] and has a repro-
ductivity error of 1 to 2 cetane numbers [77]. It has been mainly used for measurements
of CN of middle distillates and alternative fuels. Despite the availability of test facilities,
reported values of IQT measurements are rare compared to the ASTM D613 method.
4.2.3 Sources of Cetane Number Data
In order to develop correlations between CN and fuel chemistry, a CN database was
developed. Most CN data for this database were acquired from reference [61]. These
data were measured or calculated using the following methods:
• Cetene rating.
As previously mentioned, cetene ratings had been used before the CN rating was
established. Cetene ratings can be transformed to CNs using a correlation [61].
• ASTM D613.
• Blend CN.
In some cases, measurements were not available for pure compounds and instead
blends of compounds with a specific composition were tested. In such cases, the
CN of the pure compound was wstimated from the blend cetane number. Such
data are of high uncertainty and are based on the assumption that the CN of the
blended mixture has a linear relationship with the CNs of its components. It is
suggested that large errors might exist for blend CNs [61].
• Cetane numbers based on ignition delay correlations.
These are cetane numbers which were calculated based on the ignition delay calcu-
lated for a special fuel using correlations developed between CN and ignition delay.
IQT measurements were considered separately, due to their higher accuracy and
reproducibility.
Chapter 4. Correlation Development for Fuel Parameters 30
• Derived CNs based on IQT measurement.
• CNs based on Octane Number correlations.
Various sources were used in the creation of the CN database [61, 62, 68, 69, 70, 81, 82,
83, 84, 85, 86, 87, 88]. There were a lot of overlap between data in these sources and
several issues existed with the numbers acquired including:
• In many cases, duplicate data did not agree. Fluctuations of 5 to 10 cetane num-
bers (and even higher) were noticed. When small fluctuations existed in the data,
average values were used.
• There was not enough information on the purity of the compounds used in the
measurements, specially in older sets of data.
• There is no standard for extending the Cetane Rating to below zero and over 100
[61].
• In some cases, the method used to measure CN was not stated by the source.
4.2.4 Correlations Development for Cetane Number
Correlations between the CN and other properties of fuels have been developed in order
to make CN prediction simpler. These correlations are either based on thermophysical
properties or the chemical structure of the fuel.
Physical properties are a good indicator of chemical structure for many hydrocarbon
compounds. As a result, they may be used for correlating a chemical phenomenon (igni-
tion) with a compound. Physical properties typically correlated with CN include aniline
point, density, mid-boiling point, viscosity, heat of vaporization and heat of combustion.
Density and aniline point are somehow indicators of the composition of the mixture,
while boiling point and viscosity are indicators of molecular size and mass [70].
Obviously, thermophysical properties stem from fuel chemistry. As a result, there has
been an increased interest in correlating different fuel characteristics directly with the
fuel chemical structure. It has been suggested that due to the changes in most cetane
indices, an index based on compositional analysis might be better predictor of CN com-
pared to indices based on physical properties [89]. This requires the characterization of
different classes of hydrocarbons available in the fuel. Different spectroscopic methods
may be used for such correlation development, creating a field called chemometrics [63].
Such models have been proposed based on NMR and IR spectra, liquid chromatography
Chapter 4. Correlation Development for Fuel Parameters 31
and gas chromatography-mass spectrometry (GC-MS) [51, 77]. They have reached ac-
ceptable results but extrapolation of these models is not reasonable since most of them
are based on linear assumptions and special functional forms. Moreover, such models
are application specific, focusing on special fuels and need to be updated. Another prob-
lem with such methods is that an overlap between the spectra of different hydrocarbon
species might exist which causes confusion in interpretation [89]. It should be noted that
analytical methods based on topological indices have also been used to develop prediction
models for cetane number [90, 91].
A review of quantitative structure-property relationships (QSPRs) for cetane number
shows that most CN QSPRs have an R2 value in the range 0.79 to 0.97 [92]. Reviewing
previous QSPRs developed for CN also reveals that as the range of CN values to which the
correlations is applicable increases, the R2 value decreases and the RMSE increases [93].
The statistical properties of some of the correlations developed for CN are summarized
in Table 4.2. As evident from this table, several simple linear and nonlinear correlations
for CN have been published with correlation coefficients of 0.9 to 0.99. However, in most
cases the correlation equations were solved and tested by the same data set which, with
a limited and insufficiently diverse data set, may lead to an overly optimistic assessment
of the correlation. Moreover, they mainly focus on special fuels or classes of compounds,
helping them achieve better regression statistics at the expense of generality. The R2
and RMSE values in Table 4.2 will be used as references in assessing the suitability of
CN correlations developed in this work.
4.2.5 Correlation of Cetane Number with NMR Spectrum
As previously mentioned, a database of CN data and NMR spectra of compounds was
created. Initial regression studies using all the CN data revealed that the difference in
experimental methods used to acquire the data created large errors for regression anal-
ysis. The best regression results were achieved when only the ASTM D613 data were
used. This was reasonable, since the ASTM D613 is the standard method of testing
and many of the pure compound properties were measured using this method. It should
also be noted that only hydrocarbons were used in regression analysis, since our focus
is on the aviation jet fuel which is primarily composed of carbon and hydrogen. The
properties of the data set used in the regression analysis along with the statistics of the
results obtained using high precision MLR and ANNs are summarized in Table 4.3.
All linear regression models met the requirements for the normality of residuals and their
independence from predicted and predictor values. They also had R2 values higher than
Chapter 4. Correlation Development for Fuel Parameters 32
Table 4.2: Statistical properties of some of the correlations proposed for CN (MLRdenotes Multiple Linear Regression, MNR denotes Multiple Nonlinear Regression andANN denotes Artificial Neural Network).
Predictor Range Data Set Size R2 RMSE Method Source1 Proton NMR 20-75 67 fuel mixtures diesel 0.992 1.11 MNR [94]
Normalized RMSE (%) 6.70 6.12 6.03 5.08Mean of Residuals 0.77 1.21 0.72 -0.63SD of Residuals 8.63 8.83 7.99 6.72
Range of Residuals -25.8 to 18.7 -19.1 to 26.6 -18.9 to 28.9 -25.7 to 14.2Training Set R 0.98 0.97 0.97 0.98
Validation Set R 0.91 0.95 1.00 0.98Test Set R 0.99 0.98 0.97 0.98
Chapter 4. Correlation Development for Fuel Parameters 34
-20 0 20 40 60 80 100 120
-20
0
20
40
60
80
100
120 Perfect fit MLR 1 ANN 1 training set ANN 1 validation set ANN 1 testing set
Pred
icte
d ce
tane
num
ber
Actual cetane number
(a) Predicted vs. actual values for MLR 1 and ANN 1.
-20 0 20 40 60 80 100 120
-20
0
20
40
60
80
100
120 Perfect fit MLR 2 ANN 2 training set ANN 2 validation set ANN 2 testing set
Pred
icte
d ce
tane
num
ber
Actual cetane number
(b) Predicted vs. actual values for MLR 2 and ANN 2.
-20 0 20 40 60 80 100 120
-20
0
20
40
60
80
100
120 Perfect fit MLR 3 ANN 3 training set ANN 3 validation set ANN 3 testing set
Pred
icte
d ce
tane
num
ber
Actual cetane number
(c) Predicted vs. actual values for MLR 3 and ANN 3.
-20 0 20 40 60 80 100 120
-20
0
20
40
60
80
100
120 Perfect fit MLR 4 ANN 4 training set ANN 4 validation set ANN 4 testing set
Pred
icte
d ce
tane
num
ber
Actual cetane number
(d) Predicted vs. actual values for MLR 4 and ANN 4.
Figure 4.2: Cetane number regression results.
-20 0 20 40 60 80 100 120
-20
0
20
40
60
80
100
120 Perfect fit Paraffins, Creton et al. 2010 [59] Naphtenes, Creton et al. 2010 [59] Aromatics, Creton et al. 2010 [59] Olefins, Creton et al. 2010 [59] Gulder et al. 1989 [44] MLR 1 MLR 4 ANN 1 ANN 4
Pred
icte
d ce
tane
num
ber
Actual cetane number
Figure 4.3: Cetane number regression results compared to several proposed correlations.
Chapter 4. Correlation Development for Fuel Parameters 35
4.3 Sooting Tendency
4.3.1 Introduction
Soot particles are carbon particulate matter formed during combustion. In the combus-
tion literature, distinctions are made between two types of soot. The first type is in-flame
soot which is measured within the combustor. Affecting combustor durability, in-flame
soot relates more directly to the chemical composition of the fuel. Soot particles that
stick to combustor walls affect the flow field, combustion properties and heat transfer
rates of the combustor, usually leading to higher maintenance costs. In jet engines, soot
can cause erosion, if it sticks to turbine blades and stators. Moreover, it could turn into
carbon deposits which clog filters and plug the holes in the combustor wall that supply
dilution air to the combustion subsection. This in turn can disrupt flow in the combus-
tion chamber [35, 100].
The second class of soot particles are exhaust soot emissions, soot particles that exit the
engine. Obviously, part of the soot formed in the combustor either stays there or oxidizes
on its way towards the exhaust. As a result, exhaust soot emissions are generally lower
than soot formed in the combustor. Soot represents a significant component of the par-
ticulate matter (PM) emitted by engines [101]. PM emissions from soot have been linked
to lung and heart disease and cancer [102, 103, 104, 105, 106]. In addition, PM emissions
contribute to smog and reduced visibility, affect local climate, and play a significant role
in the global climate [107, 108, 109, 110]. Soot formation increases the exhaust emissions
of aircraft engines, an important factor in a military aircraft’s stealth capabilities. They
also reduce visibility on the ground when large quantities are formed by ground vehi-
cles [111]. Soot is also the main contributor to fire radiation [112, 113, 114, 115, 116].
Furthermore, soot is involved in the formation of the most common fire toxicant, carbon
monoxide [117, 118].
Due to all these detrimental effects of soot on human health and the environment, we
chose sooting tendency of aviation jet fuel as one of the properties the surrogate fuel has
to mimic. This will enable future researchers to conduct more detailed analysis on soot
formation using such surrogate fuels.
4.3.2 Effect of Chemical Structure on Sooting Tendency
It has been revealed that the fuel molecular structure has a significant effect on its sooting
tendency [119, 120, 121, 122]. Sooting has been correlated with the chemical structure
of the fuel [123, 124, 125, 126, 127, 128] alongside other fuel properties [123, 129]. There
Chapter 4. Correlation Development for Fuel Parameters 36
is still controversy on the effect of different functional groups on sooting tendency and
different sources have proposed different trends. Some sources cite the following general
trend between the sooting tendency of different classes of hydrocarbons of same chain
length in both laminar and diffusion flames [130, 131]:
Where f(Xk×1) is the predicted value, c is a matrix of coefficients of linear regression
and X is a matrix of predictor parameters. As is evident, there is no intercept for this
equation, meaning the results are a linear combination of the predictor parameters. Table
A.1 shows the coefficients used for each correlation presented in Chapter 4. Detailed
statistical properties of these correlations are also highlighted in Chapter 4.
Neural Network Models
The neural network models have the following mathematical form:
f(Xk×1) = W1×n tanh(wn×kXk×1 + bn×1) +B (7.2)
where X is a matrix of predictor parameters, k is the number of predictor parameters
(inputs), n is the number of neurons used by the ANN, w is the input layer weight, b
is the input bias, W is the hidden layer weight and B is the hidden layer bias. Figure
A.1 shows how the MATLAB documentation depicts this function [49]. First, a linear
transformation is applied to the predictor parameters and then the hyperbolic tangent of
the results is taken. The final predicted value is a linear combination of these hyperbolic
tangent transformations, plus an intercept.
Figure A.1: The artificial neural network model as depicted by the MATLAB documen-tation [49].
APPENDIX 75
Tab
leA
.1:
Coeffi
cien
tsfo
rlinea
rco
rrel
atio
ns
pre
sente
din
Chap
ter
4.
Nam
eA
P1
AP2
AP3
AP4
AP5
AP6
AP7
AP8
AP9
AP10
AP11
AP12
AP13
H/C
MW
(mol
/g)
Cet
ane
num
ber
ML
R1
-16.
6510
9.24
-11
.65
-3.
36-
3.36
-3.
3610
.20
10.2
010
.20
43.6
243
.62
11.0
911
.09
--
ML
R2
76.9
819
2.14
51.6
050
.38
80.6
436
.84
-10
.91
-10
.91
-10
.91
118.
7511
8.75
53.4
153
.41
-39
.08
-M
LR
3-3
0.24
66.3
5-
27.0
1-
33.5
5-
39.7
3-
36.9
3-
1.34
-1.
34-
1.34
27.0
027
.00
-22
.14
-22
.14
-0.
185
ML
R4
14.1
710
8.23
4.03
4.29
-1.
66-
15.3
5-
13.3
9-
13.3
9-
13.3
961
.05
61.0
50.
590.
59-
18.0
50.
169
Sm
oke
poi
nt
(mm
)M
LR
113
8.69
84.2
46.
74-
115.
92-
13.7
0-
5.43
17.2
617
.26
17.2
665
.30
65.3
05.
375.
37-
-M
LR
2-
98.3
3-
110.
34-
143.
75-
224.
15-
143.
00-
134.
2745
.79
45.7
945
.79
-12
2.16
-12
2.16
-97
.01
-97
.01
95.0
5-
ML
R3
153.
8111
5.21
31.0
6-
94.4
56.
8124
.32
29.5
529
.55
29.5
586
.03
86.0
330
.68
30.6
8-
-0.
203
ML
R4
-82
.34
-79
.04
-11
9.18
-20
2.58
-12
2.26
-10
4.49
57.6
857
.68
57.6
8-
100.
93-
100.
93-
71.7
2-
71.7
294
.57
-0.
198
Thre
shol
dso
otin
dex
(TSI)
indiff
usi
onflam
esM
LR
1-
1.42
12.9
112
.58
42.6
123
.71
31.9
0-
17.7
5-
17.7
5-
17.7
51.
0090
.33
74.6
374
.63
--
ML
R2
63.6
865
.93
49.8
269
.08
57.3
879
.10
-26
.86
-26
.86
-26
.86
54.0
310
5.22
102.
5010
2.50
-25
.67
-M
LR
3-
7.44
-4.
284.
7532
.31
13.4
48.
23-
23.3
1-
23.3
1-
23.3
1-
8.14
89.6
460
.77
60.7
7-
0.11
0M
LR
455
.66
47.7
741
.08
58.3
846
.48
55.0
3-
31.8
0-
31.8
0-
31.8
043
.49
104.
0488
.40
88.4
0-
24.7
60.
104
Den
sity
(kg
m3)
ML
R1
0.60
0.78
0.71
0.74
0.74
0.74
0.74
0.74
0.74
0.69
0.69
1.01
1.01
--
ML
R2
1.30
1.37
1.15
1.08
1.14
1.23
0.51
0.87
0.87
1.25
0.70
1.31
1.31
-0.
282
-M
LR
30.
570.
690.
670.
710.
700.
790.
780.
830.
830.
660.
470.
920.
92-
0.00
05M
LR
41.
221.
241.
091.
081.
081.
080.
600.
720.
721.
131.
131.
201.
20-
0.27
0.00
05B
oiling
poi
nt
(K)
ML
R1
285.
5251
0.78
344.
2533
1.80
409.
9752
6.11
354.
5572
3.57
852
2.65
329.
6216
9.66
534.
9393
1.35
--
ML
R2
528.
6170
6.41
492.
9445
8.37
561.
1861
9.62
363.
2272
1.48
561.
2550
4.74
260.
1062
4.86
958.
70-
95.2
7-
ML
R3
177.
5421
1.51
224.
1125
2.41
240.
0225
5.09
337.
7241
5.04
210.
2119
6.82
157.
2527
0.92
448.
02-
1.60
8M
LR
431
2.41
324.
7330
8.06
323.
5032
3.50
323.
5034
0.26
327.
5929
0.13
290.
1329
0.13
326.
3447
2.70
-51
.90
1.57
3F
reez
ing
poi
nt
(K)
ML
R1
156.
0323
2.96
235.
3917
7.89
242.
5133
2.16
395.
3879
8.76
853.
2816
6.31
160.
9029
2.18
883.
07-
-M
LR
242
7.50
451.
4340
1.44
319.
2441
1.37
436.
5840
5.07
796.
4289
6.39
361.
8826
1.90
392.
6191
3.61
-10
6.39
-M
LR
399
.41
76.0
517
2.40
136.
2615
3.40
190.
0638
6.56
636.
9868
9.46
96.6
815
4.39
153.
7562
9.64
-0.
843
ML
R4
322.
1226
2.85
310.
5525
3.04
295.
5928
3.91
394.
9764
6.11
735.
3625
9.08
236.
2624
4.14
671.
51-
85.7
70.
786
Dynam
icvis
cosi
ty(c
P)
ML
R1
-0.
361.
570.
88-
1.22
0.72
3.89
7.90
7.90
7.90
0.42
-0.
310.
620.
62-
-M
LR
23.
294.
383.
04-
0.08
3.03
5.98
7.98
7.98
7.98
3.08
0.72
2.01
2.01
-1.
36-
ML
R3
-0.
86-
0.97
-0.
14-
1.41
-1.
320.
654.
184.
184.
18-
1.31
0.39
-0.
79-
0.79
-0.
015
ML
R4
-0.
63-
0.78
0.00
3-
1.34
-1.
170.
794.
214.
214.
21-
1.13
0.44
-0.
69-
0.69
-0.
080.
01
APPENDIX 76
Tab
leA
.2:
Coeffi
cien
tsfo
rar
tifici
alneu
ral
net
wor
km
odel
spre
sente
din
Chap
ter
4.
wH
/CM
W(m
ol/g
)b
WB
AP1
AP2
AP3
AP4
AP5
AP6
AP7
AP8
AP9
AP10
AP11
AP12
AP13
Cet
ane
num
ber
AN
N1
-9.7
8-2
.39
1.64
9.88
9.88
9.88
-3.5
1-3
.51
-3.5
1-7
.97
-7.9
7-1
.12
-1.1
23.
320.
273.
474.
450.
02-2
.38
-3.6
6-3
.66
-3.6
60.
250.
250.
250.
250.
910.
91-2
.99
1.33
0.38
0.26
-1.3
41.
23-0
.80
-0.8
0-0
.80
0.71
0.71
0.71
-0.4
3-0
.43
-0.7
4-0
.74
2.45
-4.2
1
AN
N2
0.57
-0.3
9-1
.74
0.22
-1.2
52.
02-0
.47
-0.4
7-0
.47
0.84
0.84
2.62
2.62
0.84
0.68
-0.8
5-0
.47
-0.4
10.
41-2
.16
1.65
-2.2
4-0
.57
0.27
0.27
0.27
0.09
0.09
0.48
0.48
-2.7
9-1
.30
0.67
AN
N3
0.68
-0.2
9-1
.07
-0.6
81.
14-0
.29
-0.6
5-0
.65
-0.6
50.
970.
97-0
.10
-0.1
0-0
.06
-1.4
4-2
.16
-0.5
9-1
.20
-1.1
2-0
.23
0.16
-1.2
11.
190.
200.
200.
20-1
.02
-1.0
2-0
.79
-0.7
9-0
.19
-1.0
6-2
.17
AN
N4
-3.3
5-5
.79
-4.6
2-2
.00
6.12
1.65
-0.5
9-0
.59
-0.5
90.
770.
772.
952.
9510
.43
2.41
0.18
-0.4
80.
08-1
.41
-2.3
31.
47-1
.10
-1.2
42.
683.
443.
443.
44-0
.68
-0.6
8-4
.13
-4.1
3-2
.53
-1.3
72.
79-0
.66
Sm
oke
poi
nt
(mm
)
AN
N1
-0.9
6-2
.88
-2.4
62.
472.
472.
47-1
.91
-1.9
1-1
.91
1.28
1.28
-0.2
9-0
.29
3.19
-6.2
8
-0.8
7-1
3.47
9.62
-2.8
0-4
.03
-4.0
3-4
.03
-4.4
3-4
.43
-4.4
3-3
.34
-3.3
4-2
.60
-2.6
04.
366.
52-1
.33
0.96
3.33
-1.0
4-1
.04
-1.0
4-0
.21
-0.2
1-0
.21
1.64
1.64
-1.7
4-1
.74
-0.0
1-0
.70
3.77
0.78
-0.8
4-2
.65
-2.6
5-2
.65
-0.1
4-0
.14
-0.1
41.
851.
85-3
.09
-3.0
9-0
.55
0.83
4.33
-17.
873.
975.
355.
355.
352.
312.
312.
3116
.93
16.9
31.
401.
40-3
.08
0.21
AN
N2
-6.4
5-2
3.88
40.6
530
.99
30.9
930
.99
1.59
1.59
1.59
-5.5
2-5
.52
-0.1
8-0
.18
82.1
7-1
.27
0.23
-0.2
52.
51-2
.79
-1.8
4-1
0.23
-10.
23-1
0.23
-3.6
6-3
.66
-3.6
60.
730.
73-0
.03
-0.0
3-2
2.31
2.71
-0.6
9-0
.35
-1.8
84.
428.
318.
318.
312.
902.
902.
909.
119.
11-1
.80
-1.8
01.
89-1
.97
-0.1
9
AN
N3
0.79
0.73
0.76
-0.2
1-0
.21
-0.2
10.
350.
350.
35-0
.29
-0.2
9-0
.20
-0.2
0-1
.88
-2.4
03.
22
2.09
-1.7
00.
630.
840.
230.
230.
23-1
.25
-1.2
5-1
.25
-0.9
9-0
.99
0.39
0.39
-1.6
31.
083.
79-1
.00
-1.0
3-0
.05
1.40
1.40
1.40
-1.1
9-1
.19
-1.1
9-0
.98
-0.9
80.
550.
55-0
.58
0.69
-3.2
45.
09-1
.03
-2.9
4-0
.91
-0.9
1-0
.91
0.49
0.49
0.49
1.35
1.35
-1.2
8-1
.28
-2.3
5-1
.78
0.39
AN
N4
-14.
7414
.94
2.56
27.5
69.
658.
8810
.60
10.6
010
.60
-5.7
1-5
.71
12.3
012
.30
99.2
0-5
.34
-10.
970.
56-0
.13
-57.
4873
.56
-50.
76-2
2.63
-0.5
7-1
.78
-2.5
1-2
.51
-2.5
15.
625.
62-0
.39
-0.3
9-1
71.1
0-6
2.41
1.12
-0.2
7T
hre
shol
dso
otin
dex
(TSI)
indiff
usi
onflam
es
AN
N1
-0.3
3-0
.43
-0.0
5-0
.18
2.24
-0.0
9-0
.06
-0.0
6-0
.06
-0.4
80.
37-0
.46
-0.4
61.
801.
66
-1.1
2-0
.17
-1.4
31.
25-1
.38
-0.3
11.
380.
180.
180.
181.
21-0
.52
0.48
0.48
0.15
-0.4
5-3
.26
1.76
-1.8
11.
80-0
.43
-0.0
8-0
.66
-0.6
6-0
.66
0.30
0.81
2.95
2.95
0.69
0.17
1.85
0.70
-1.4
2-0
.19
3.77
-0.5
3-1
.12
-1.1
2-1
.12
-1.7
30.
28-3
.00
-3.0
01.
99-0
.89
AN
N2
0.35
-1.0
1-0
.73
-0.1
7-0
.17
-0.1
7-0
.31
-0.3
1-0
.31
-0.3
8-0
.38
1.93
1.93
0.50
1.34
3.59
-1.3
20.
54-0
.97
-0.5
9-0
.06
-0.0
6-0
.06
0.60
0.60
0.60
-0.2
5-0
.25
0.23
0.23
0.96
0.63
-2.6
6-1
.22
-1.8
61.
77-0
.04
-0.0
4-0
.04
-1.3
1-1
.31
-1.3
10.
940.
94-0
.33
-0.3
32.
771.
37-0
.56
1.21
-3.8
9-0
.16
2.18
2.18
2.18
-0.3
7-0
.37
-0.3
70.
670.
671.
321.
32-0
.01
1.45
0.03
AN
N3
-5.0
53.
31-0
.45
2.11
-3.1
01.
011.
651.
651.
653.
14-0
.000
41.
151.
153.
89-1
.74
-0.7
4-0
.89
-4.0
61.
13-0
.44
1.04
0.17
0.04
1.77
1.77
1.77
0.79
1.25
1.28
1.28
3.43
1.74
0.76
AN
N4
0.14
-0.6
00.
280.
070.
070.
07-0
.56
-0.5
6-0
.56
1.10
1.10
-0.2
2-0
.22
-0.1
81.
50-1
.63
1.24
-0.3
60.
34-0
.27
0.06
-0.3
6-0
.36
-0.3
60.
750.
750.
75-1
.31
-1.3
10.
001
0.00
10.
05-2
.23
0.66
1.46
-0.1
80.
460.
620.
790.
790.
791.
611.
611.
61-0
.36
-0.3
60.
810.
81-0
.58
0.68
-0.7
6-0
.38
-1.3
30.
004
-0.9
20.
003
0.00
30.
003
0.06
0.06
0.06
0.61
0.61
-0.1
5-0
.15
-0.9
82.
53-1
.67
1.16
APPENDIX 77
Tab
leA
.2(c
onti
nued
):C
oeffi
cien
tsfo
rar
tifici
alneu
ral
net
wor
ks
pre
sente
din
chap
ter
4.
wH
/CM
W(m
ol/g
)b
WB
AP1
AP2
AP3
AP4
AP5
AP6
AP7
AP8
AP9
AP10
AP11
AP12
AP13
Den
sity
(kg
m3)
AN
N1
3.34
-3.2
60.
160.
940.
050.
240.
901.
261.
260.
481.
36-0
.13
-0.1
3-2
.29
-0.9
2
0.29
-0.1
41.
121.
40-1
.40
0.04
0.18
0.56
0.33
0.33
0.85
0.08
-0.7
2-0
.72
-0.8
6-1
.18
-1.2
3-0
.34
1.24
-1.2
53.
230.
210.
21-0
.57
-0.5
7-0
.67
-0.1
4-0
.96
-0.9
6-0
.05
0.13
0.64
-0.7
4-0
.76
0.38
0.86
-0.2
0-0
.31
-0.1
7-0
.17
-0.3
70.
38-0
.43
-0.4
30.
97-0
.51
-0.4
8-0
.60
0.50
1.42
-0.1
90.
28-0
.77
-0.1
0-0
.10
0.43
0.67
2.31
2.31
-2.1
22.
35
AN
N2
1.70
1.89
0.81
0.39
-1.3
2-1
.32
0.67
0.67
0.67
-0.3
2-0
.32
0.69
0.69
-5.5
9-2
.90
2.83
1.31
0.39
-0.1
1-0
.13
1.27
-0.4
6-0
.46
-1.3
1-1
.31
-1.3
10.
620.
62-0
.23
-0.2
31.
12-1
.02
0.50
0.34
0.50
0.75
0.65
0.81
0.81
-0.7
6-0
.76
-0.7
6-0
.10
-0.1
0-0
.96
-0.9
6-0
.85
0.94
1.12
-0.7
90.
93-1
.23
0.92
0.50
0.50
0.65
0.65
0.65
0.75
0.75
0.46
0.46
2.03
-0.3
20.
560.
68-2
.23
1.26
-2.0
0-2
.66
-2.6
60.
210.
210.
21-0
.69
-0.6
90.
500.
50-3
.02
0.38
0.67
1.75
-0.7
51.
22-0
.64
1.16
1.16
1.42
1.42
1.42
-0.7
4-0
.74
0.53
0.53
-2.3
50.
07-0
.77
0.12
0.14
0.25
0.73
-1.4
1-1
.41
-0.3
2-0
.32
-0.3
20.
100.
10-0
.73
-0.7
30.
22-1
.27
-1.6
90.
48-1
.06
-0.7
7-0
.54
-1.2
6-1
.26
0.25
0.25
0.25
-0.3
4-0
.34
-0.5
3-0
.53
-0.4
21.
960.
28
AN
N3
-0.1
0-0
.43
-0.4
0-0
.31
-0.3
1-0
.31
-0.0
7-0
.07
-0.0
7-0
.49
-0.4
9-1
.25
-1.2
54.
322.
501.
78
1.96
-0.8
8-1
.11
0.17
0.53
0.53
0.53
-0.4
2-0
.42
-0.4
20.
030.
03-0
.66
-0.6
60.
361.
340.
36-1
.98
-2.7
01.
201.
131.
131.
130.
920.
920.
921.
791.
792.
452.
451.
92-1
.30
0.11
-1.0
0-1
.90
-1.6
5-0
.64
-0.6
4-0
.64
-1.0
3-1
.03
-1.0
3-2
.33
-2.3
3-4
.23
-4.2
311
.00
2.92
-4.4
0-0
.02
-1.5
2-2
.11
0.39
0.39
0.39
0.65
0.65
0.65
0.17
0.17
1.28
1.28
-1.1
90.
30-0
.10
0.61
-0.2
2-3
.01
-1.4
6-1
.46
-1.4
6-1
.68
-1.6
8-1
.68
1.18
1.18
0.57
0.57
3.85
0.04
0.03
-0.1
71.
09-3
.76
-0.7
0-0
.70
-0.7
00.
320.
320.
32-2
.07
-2.0
72.
692.
691.
291.
22-0
.09
-0.0
80.
091.
99-1
.89
-1.8
9-1
.89
1.99
1.99
1.99
1.85
1.85
-0.9
6-0
.96
-2.7
40.
36-0
.07
-1.0
32.
00-1
.23
-1.0
4-1
.04
-1.0
4-0
.01
-0.0
1-0
.01
2.03
2.03
-0.7
5-0
.75
0.88
-1.3
7-0
.05
-2.4
60.
55-1
.90
0.06
0.06
0.06
-0.4
2-0
.42
-0.4
21.
151.
152.
762.
76-0
.81
-1.3
90.
11
AN
N4
-0.2
70.
491.
15-0
.61
0.65
0.65
-0.9
9-0
.99
-0.9
9-0
.80
-0.8
0-0
.22
-0.2
2-2
.99
-0.3
9-1
.48
0.11
0.95
1.35
1.31
-0.3
00.
84-0
.66
-0.6
61.
011.
011.
010.
790.
790.
830.
83-4
.23
-1.3
8-1
.94
2.69
0.63
0.96
0.48
-1.2
40.
730.
730.
820.
820.
82-0
.77
-0.7
70.
360.
360.
14-0
.81
-0.7
20.
630.
140.
280.
170.
110.
500.
500.
810.
810.
81-0
.36
-0.3
6-0
.06
-0.0
60.
95-0
.23
0.02
-0.8
8-0
.08
0.29
-0.5
5-1
.11
0.29
0.29
-0.4
8-0
.48
-0.4
8-0
.02
-0.0
2-0
.61
-0.6
10.
36-0
.25
0.90
-0.0
8-0
.10
0.09
-0.1
3-0
.46
0.09
0.09
1.15
1.15
1.15
-0.5
1-0
.51
-0.2
2-0
.22
-0.8
0-1
.28
-1.5
2-0
.80
-0.1
40.
020.
27-0
.12
-0.3
0-0
.30
-0.8
5-0
.85
-0.8
50.
840.
840.
720.
721.
26-0
.04
-1.6
4-0
.59
Dynam
icvis
cosi
ty(c
P)
AN
N1
1.11
1.14
0.99
0.53
0.53
0.53
-1.4
7-1
.47
-1.4
71.
281.
280.
660.
660.
23-5
.22
-5.2
315
.67
-7.2
2-8
.28
1.75
1.75
1.75
-1.8
4-1
.84
-1.8
4-2
.21
-2.2
1-1
.37
-1.3
71.
75-0
.51
AN
N2
-2.9
62.
701.
452.
092.
092.
090.
270.
270.
272.
382.
38-0
.64
-0.6
4-0
.62
0.29
-2.0
3-1
.83
-5.6
12.
640.
960.
690.
690.
691.
001.
001.
001.
041.
040.
360.
36-0
.33
-1.2
31.
03
AN
N3
0.06
0.28
0.15
-0.1
9-0
.19
-0.1
90.
420.
420.
42-0
.36
-0.3
6-1
.00
-1.0
02.
00-0
.82
0.64
-0.0
8-0
.72
-4.5
3-1
.24
-0.6
7-0
.67
-0.6
76.
486.
486.
48-3
.66
-3.6
61.
551.
556.
090.
390.
26A
NN
4-0
.74
-0.8
2-0
.53
0.17
-0.1
7-0
.28
-0.1
2-0
.12
-0.1
2-0
.25
0.51
0.09
0.09
1.80
-0.9
60.
20-2
.03
1.10
APPENDIX 78
Tab
leA
.2(c
onti
nued
):C
oeffi
cien
tsfo
rar
tifici
alneu
ral
net
wor
km
odel
spre
sente
din
Chap
ter
4.
wH
/CM
Wb
WB
AP1
AP2
AP3
AP4
AP5
AP6
AP7
AP8
AP9
AP10
AP11
AP12
AP13
Boi
ling
poi
nt
(K)
AN
N1
-0.0
70.
32-2
.11
1.59
2.17
0.32
-0.3
1-0
.13
-0.0
21.
500.
770.
371.
061.
351.
48
-0.1
0
5.80
-3.6
6-6
.05
-0.1
4-2
.50
0.29
-0.3
2-0
.13
-0.4
31.
280.
341.
36-0
.37
1.47
0.72
-0.6
90.
65-2
.17
1.82
-1.2
4-3
.40
2.15
-0.5
6-0
.36
3.18
-1.1
2-4
.11
0.44
1.62
-0.7
2-0
.32
-0.5
2-0
.06
-0.7
4-0
.69
-0.3
30.
23-0
.67
-0.4
6-0
.64
-0.0
7-0
.49
-0.1
60.
450.
501.
42-2
.16
1.66
-1.3
2-0
.48
-1.0
8-0
.21
0.08
0.85
3.69
0.24
1.17
0.12
-0.4
2-0
.50
5.75
-9.4
05.
110.
23-1
.08
2.16
2.84
-0.5
6-0
.53
0.25
0.60
-2.2
6-0
.10
0.40
0.35
2.72
1.21
2.40
0.74
0.33
-0.3
50.
461.
490.
04-5
.14
0.26
2.87
-1.5
60.
45-0
.86
1.45
0.74
0.97
-0.3
6-1
.44
-4.1
13.
220.
200.
31-1
.54
-0.6
5-0
.03
0.44
-0.8
30.
75-5
.11
1.14
2.23
-1.0
7-0
.05
0.35
-1.1
80.
71-0
.29
2.13
-0.6
03.
350.
481.
490.
70
AN
N2
-1.4
0-0
.65
1.79
-0.7
40.
190.
190.
900.
900.
90-1
.45
-1.4
5-0
.50
-0.5
00.
231.
831.
01
-1.1
6
0.28
0.86
-0.1
5-0
.11
0.48
0.77
0.47
0.47
0.47
0.86
0.86
0.40
0.40
0.46
-1.2
90.
004
0.10
-0.6
40.
50-0
.27
0.47
0.15
0.13
0.13
0.13
0.95
0.95
-0.4
3-0
.43
1.04
1.25
-1.5
7-0
.02
-0.3
7-0
.02
-1.6
20.
84-0
.58
-0.2
8-0
.28
-0.2
8-0
.60
-0.6
00.
050.
052.
450.
90-0
.95
2.31
0.35
-0.2
2-0
.18
-0.7
1-0
.45
-0.4
4-0
.44
-0.4
4-1
.12
-1.1
20.
250.
250.
600.
02-1
.64
-2.5
91.
031.
051.
47-0
.17
0.48
0.13
0.13
0.13
0.22
0.22
-0.0
1-0
.01
-0.1
3-0
.37
-2.3
6-0
.98
0.35
-1.1
90.
41-0
.51
0.66
0.33
0.33
0.33
-0.9
0-0
.90
-0.0
1-0
.01
-0.0
2-0
.82
-1.0
94.
01-1
.64
-0.6
8-0
.88
0.05
-0.5
6-0
.19
-0.1
9-0
.19
-0.6
1-0
.61
0.00
40.
004
0.14
1.31
-1.0
4-1
.37
0.12
0.01
-0.2
3-0
.38
-0.1
60.
940.
940.
940.
960.
960.
230.
23-2
.54
-1.7
9-1
.32
AN
N3
1.63
1.59
-0.3
60.
920.
920.
92-0
.54
-0.5
4-0
.54
-0.5
4-0
.54
-0.2
7-0
.27
-1.5
3-2
.39
-1.6
2
-0.3
7
0.05
-0.7
4-1
.09
0.86
0.86
0.86
-0.7
1-0
.71
-0.7
11.
401.
400.
750.
751.
871.
81-0
.42
0.61
0.16
-0.3
9-0
.25
-0.2
5-0
.25
0.86
0.86
0.86
-0.3
5-0
.35
-0.0
1-0
.01
-1.5
0-1
.28
0.84
0.11
-0.1
6-0
.66
-1.7
1-1
.71
-1.7
10.
380.
380.
38-1
.99
-1.9
90.
320.
32-0
.67
1.07
-0.9
2-0
.70
1.99
2.66
-0.9
5-0
.95
-0.9
5-0
.14
-0.1
4-0
.14
0.71
0.71
1.82
1.82
-2.3
4-0
.08
0.75
-0.3
60.
081.
620.
160.
160.
161.
011.
011.
01-0
.97
-0.9
70.
760.
761.
07-0
.03
0.33
0.65
0.40
-0.2
01.
061.
061.
06-1
.11
-1.1
1-1
.11
1.27
1.27
0.60
0.60
-0.4
40.
001
-0.4
60.
180.
160.
39-0
.37
-0.3
7-0
.37
0.59
0.59
0.59
-0.2
5-0
.25
-0.0
3-0
.03
-1.2
7-0
.02
-1.0
5-0
.02
0.47
1.30
0.44
0.44
0.44
0.67
0.67
0.67
-0.4
3-0
.43
-1.3
4-1
.34
2.28
-1.6
10.
12-0
.60
1.11
1.71
0.39
0.39
0.39
0.20
0.20
0.20
-1.6
5-1
.65
0.70
0.70
-0.9
8-1
.51
-1.1
80.
560.
450.
13-0
.46
-0.4
6-0
.46
-0.8
3-0
.83
-0.8
3-0
.49
-0.4
9-2
.23
-2.2
3-0
.29
1.82
-0.1
3-0
.93
1.43
0.98
-0.8
7-0
.87
-0.8
7-0
.02
-0.0
2-0
.02
1.18
1.18
0.58
0.58
1.09
-2.2
8-0
.11
AN
N4
-0.4
1-0
.62
7.86
5.62
1.48
-3.8
9-3
.60
-1.0
6-0
.67
-4.2
1-0
.05
-2.6
01.
04-5
.65
2.24
1.62
0.27
-2.3
3
4.53
4.35
0.76
-1.1
53.
790.
700.
914.
382.
39-0
.13
2.05
-2.8
4-0
.63
-3.5
15.
01-2
.81
1.00
2.55
-5.4
8-2
.24
-3.0
6-9
.02
-4.1
20.
63-4
.31
-0.7
15.
37-1
.01
8.73
6.62
6.97
-9.1
10.
19-0
.04
1.24
0.76
0.06
0.11
0.67
-1.1
3-1
.54
-0.0
70.
500.
781.
01-0
.10
-0.0
4-5
.06
-0.7
7-0
.76
-0.4
1-0
.14
-0.0
60.
130.
02-0
.11
0.26
0.08
0.00
3-0
.08
-0.1
0-0
.02
0.12
-0.0
61.
55-0
.36
1.13
-1.3
01.
15-1
.65
-1.6
2-1
.50
-2.0
8-0
.91
-0.8
1-0
.53
-0.8
82.
75-0
.84
-0.3
10.
35-2
.63
7.00
2.18
3.76
APPENDIX 79
Tab
leA
.2(c
onti
nued
):C
oeffi
cien
tsfo
rar
tifici
alneu
ral
net
wor
km
odel
spre
sente
din
Chap
ter
4.
wH
/CM
Wb
WB
AP1
AP2
AP3
AP4
AP5
AP6
AP7
AP8
AP9
AP10
AP11
AP12
AP13
Fre
ezin
gp
oint
(K)
AN
N1
-2.8
91.
860.
08-1
.18
-2.2
31.
43-0
.21
0.95
0.51
1.11
-0.3
50.
742.
811.
510.
22
1.18
0.69
0.74
2.77
-0.4
5-3
.88
-0.2
6-0
.11
-0.2
2-0
.03
-1.4
90.
72-1
.68
0.04
1.33
-0.2
3-1
.39
-0.9
0-0
.05
-2.4
4-3
.38
11.7
81.
29-0
.49
-1.0
8-3
.80
-1.0
0-4
.36
-2.6
01.
26-1
.54
4.42
-1.4
2-3
.25
5.73
0.97
0.69
-2.4
4-0
.36
-0.0
8-3
.83
0.69
4.37
-2.4
0-0
.53
-0.2
5-8
.12
-1.1
4-2
.31
0.74
-6.7
16.
09-2
.17
-1.3
8-1
.03
-0.5
6-0
.86
8.32
-0.4
60.
69-0
.23
0.01
-1.5
1-1
.99
0.53
-2.4
12.
690.
25-0
.42
-0.1
1-4
.57
-0.8
0-1
.22
5.75
0.18
0.38
-0.9
212
.04
-9.4
35.
28-6
.30
-1.9
1-1
.67
-0.7
40.
242.
79-0
.43
2.79
1.16
-1.4
5-0
.06
3.06
4.09
-0.0
6-3
.07
0.66
4.23
0.37
0.53
0.05
-6.8
50.
69-2
.55
-0.0
4-2
.01
-0.2
5
AN
N2
-0.3
80.
37-0
.44
-0.8
00.
330.
380.
970.
970.
970.
280.
28-0
.02
-0.0
21.
28-1
.62
1.32
-0.4
5
0.45
-1.0
9-0
.04
0.56
-0.2
81.
920.
310.
310.
31-0
.90
-0.9
0-0
.50
-0.5
00.
311.
49-0
.82
0.78
2.38
0.33
1.39
-0.8
7-0
.43
1.11
1.11
1.11
-1.2
9-1
.29
0.80
0.80
-1.2
4-1
.64
-1.7
00.
47-4
.16
-0.0
021.
05-0
.62
-0.7
80.
440.
440.
440.
610.
610.
500.
50-0
.42
-0.4
00.
35-0
.62
-0.8
4-0
.04
0.71
-1.4
70.
07-0
.18
-0.1
8-0
.18
-0.4
8-0
.48
-0.3
0-0
.30
-0.7
10.
420.
13-0
.06
1.87
1.04
-0.9
0-0
.08
-1.7
4-0
.14
-0.1
4-0
.14
-0.8
4-0
.84
-0.4
1-0
.41
-1.1
4-0
.09
-1.0
4-0
.01
-1.4
21.
240.
29-0
.19
0.58
-1.1
9-1
.19
-1.1
90.
250.
25-0
.49
-0.4
90.
890.
50-0
.60
-0.0
5-2
.51
0.66
-0.1
3-0
.55
0.02
0.33
0.33
0.33
0.72
0.72
-0.2
0-0
.20
-0.5
21.
190.
551.
511.
722.
190.
39-0
.66
-0.0
4-0
.59
-0.5
9-0
.59
-1.3
1-1
.31
-0.4
6-0
.46
-3.8
71.
170.
86-0
.98
0.04
-1.7
71.
18-0
.32
-0.3
4-0
.76
-0.7
6-0
.76
0.35
0.35
-0.7
0-0
.70
-2.7
1-1
.26
-0.1
9
AN
N3
-1.8
3-0
.50
-0.6
6-0
.64
1.74
1.72
1.13
-0.2
4-0
.32
-0.9
9-0
.47
-2.1
00.
281.
53-0
.93
0.29
1.69
0.93
-1.7
30.
080.
26-0
.40
0.08
-0.1
4-0
.16
1.12
-0.4
60.
270.
780.
510.
44-0
.40
0.69
1.51
-3.9
00.
751.
143.
75-0
.81
0.66
0.53
-0.2
50.
150.
34-0
.11
0.10
-1.8
3-0
.95
-0.7
80.
241.
10-1
.89
-1.8
8-1
.76
0.47
0.71
-2.5
6-0
.09
2.26
-0.0
31.
50-0
.74
-4.0
01.
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.33
AN
N4
-2.3
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.69
1.90
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.95
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0.36
0.36
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0.50
0.63
0.63
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0.44
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1.62
1.04
0.25
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940.
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.27
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92.
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