NOX PDF

Sam Cutlan
Malcolm McDonald
Powertrain and Sustainability
Combustion Emissions, Calculations and Mapping for
Efficiency
BEng (Hons) Automotive Engineering

Sam Cutlan P134357
COMBUSTION EMISSIONS, CALCULATIONS AND MAPPING FOR EFFICIENCY
1 | P a g e
Table of Contents
1.0 Introduction ................................................................................................................................2
2.0 𝑁𝑂𝑥 Concentration Levels..........................................................................................................2
2.1 Calculation of the Net Enthalpy’s for each Fuel Equivalence Ratio........................................2
2.2 Production of Temperature (K) vs ℎ𝑜𝑇 − ℎ𝑜𝑓298 (kJ/kmol) Graph and Determination of
Initial Burning Temperatures..............................................................................................................3
2.3 Determining all Burning Temperatures with an increasing Pressure .....................................4
2.4 Determining 𝑁𝑂𝑥 concentration levels as a function of Fuel Equivalence Ratio...................6
3.0 The Effect of Adding E.G.R on NOx Concentration Levels ..........................................................8
3.1 Determining the Coefficients of the Products ........................................................................8
3.2 Determining the Initial Burning Temperatures and all Burning Temperatures......................8
3.3 Determining NOx Concentration Levels..................................................................................9
4.0 Analysis of NOx Model..............................................................................................................10
4.1 Assumptions Made ...............................................................................................................10
4.2 Effectiveness of Calculations.................................................................................................12
4.3 Mechanisms Responsible for NOx Formation.......................................................................12
5.0 References ......................................................................................................................................13
6.0 Appendices......................................................................................................................................14
6.1 Appendix 1 ..................................................................................................................................14
6.2 Appendix 2 ..................................................................................................................................14
6.3 Appendix 3 ..................................................................................................................................15
6.4 Appendix 4 ..................................................................................................................................16
6.5 Appendix 5 ..................................................................................................................................16
6.6 Appendix 6 ..................................................................................................................................17
6.7 Appendix 7 ..................................................................................................................................18
6.8 Appendix 8 ..................................................................................................................................18
6.9 Appendix 9 ..................................................................................................................................19
6.1.1 Appendix 10 .............................................................................................................................21
6.1.2 Appendix 11 .............................................................................................................................21

Sam Cutlan P134357
2 | P a g e
1.0 Introduction
The aim of this report is to successfully develop a fully working 𝑁𝑂𝑥 model for Iso-octane running on
the lean side of stoichiometric. Prior to creating the 𝑁𝑂𝑥 model, there are a number of assumptions
that have to be considered; 1) the rise in pressure at the start of combustion (SOC) is linear and
increases in 2 bar/degree increments from 10 bar (SOC) to 50 bar, 2) the engine is a 1600cc four
cylinder naturally aspirated (N/A) and 3) the engine speed is considered a constant 1800 RPM.
From knowing these critical pieces of data, a model to predict the 𝑁𝑂𝑥 Parts per Million (PPM) VS
Fuel Equivalence Ratio and the effect of adding Exhaust Gas Recirculation (EGR) VS 𝑁𝑂𝑥
concentration levels will be created within Excel. Further to the initial assumptions made, there are a
number of assumptions made later on in the 𝑁𝑂𝑥 model which are later discussed.
2.0 𝑁𝑂𝑥 Concentration Levels
2.1 Calculation of the Net Enthalpy’s for each Fuel Equivalence Ratio
To obtain the initial flame temperatures required to calculate the rising adiabatic flame
temperatures up to peak pressure, it is critical to calculate the net enthalpy released for each fuel
equivalence ratio. To do this, the standard enthalpy of formation and molecular weight of species
table was needed to calculate the net enthalpy’s released. Refer to Equation 1 below as a reference
for a fuel equivalence ratio of 0.6;
Equation 1
0.6 × 𝐶8 𝐻18 + 12.5(𝑂2 + 3.76𝑁2) = 4.8𝐶𝑂2 + 5.4𝐻2 𝑂 + 5𝑂2 + 47𝑁2
(McDonald, 2015)
As can be seen from the above equation, the enthalpy required to get the reactants to the zero level
will change due to the fuel equivalence ratio changing. As well as this, the coefficients of the
products will also change as a result of the fuel equivalence ratio changing and hence the enthalpy
released will change too. Once performed, the net enthalpy released is shared between the products
by forms of the following equation;
Equation 2
𝑁𝑒𝑡 𝐸𝑛𝑡ℎ𝑎𝑙𝑝𝑦 𝑅𝑒𝑙𝑒𝑎𝑠𝑒𝑑 = 4.8 × 𝐸𝑞𝑛(𝐶𝑂2) + 5.4 × 𝐸𝑞𝑛(𝐻2 𝑂) + 5 × 𝐸𝑞𝑛(𝑂2) + 47 × 𝐸𝑞𝑛(𝑁2)
(McDonald, 2015)
Once the above equation has been set up with all net enthalpy’s and coefficients calculated for each
fuel equivalence ratio, it is required that the ‘Eqn’ be determined. The ‘Eqn’ is a quadratic equation
determined by producing a graph through the use of Excel of Temperature (K) VS ℎ̅ 𝑜(𝑇) − ℎ̅ 𝑜 𝑓(298)
(kJ/kmol). From this graph, the equations of each line of 𝐶𝑂2, 𝐻2 𝑂, 𝑂2 𝑎𝑛𝑑 𝑁2 can be found and
inserted into Equation 2 to find the initial temperatures (T) for each fuel equivalence ratio.

Sam Cutlan P134357
3 | P a g e
2.2 Production of Temperature (K) vs ℎ̅ 𝑜( 𝑇) − ℎ̅ 𝑜 𝑓(298) (kJ/kmol) Graph and
Determination of Initial Burning Temperatures
From directly inserting the Temperature (K) and ℎ̅ 𝑜(𝑇) − ℎ̅ 𝑜 𝑓(298) (kJ/kmol) results from
𝐶𝑂2, 𝐻2 𝑂, 𝑂2 𝑎𝑛𝑑 𝑁2 obtained from the Thermodynamic Properties of Ideal Fuels Tables; a graph
could be produced to find the equations of each line required to calculate the initial temperatures;
Figure 1
Figure 1 - Enthalpy required from 298K vs Temperature.
The equations representing each line can be seen below;
Table 1
Equations of each line
CO2 0.0033408353x2
+ 46.4931007649x - 15,563.7522326659
H20 0.0044468568x2
+ 32.6521535886x - 10,643.8864074281
O2 0.0016322369x2
+ 31.1507970936x - 9,827.6586302809
N2 0.0015490125x2
+ 29.4904374322x - 9,267.6068460288
Table 1 - Equations of each line for CO2, H20, O2 and N2 respectively.
As can be seen from Table 1, each equation is in the form 𝑎𝑇2
+ 𝑏𝑇2
+ 𝑐, where 𝑥 in the above
equations represents the initial temperature (T). From inserting these equations into Equation 2, the
entire equation was summated in Excel such that an online quadratic equation calculator could be
used to find (T) (Math.com, 2005). The initial temperatures could then be found for each fuel
equivalence ratio, see Table 2.
y = 0.003x2 + 46.493x - 15,563.752
y = 0.004x2 + 32.652x - 10,643.886
y = 0.002x2 + 31.151x - 9,827.659
y = 0.002x2 + 29.490x - 9,267.607
-20000
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
0 500 1000 1500 2000 2500 3000 3500
HT-H298(KJ/Kmol)
Temperature (K)
Enthalpy Required from 298K VS Temperature
CO2 H2O O2 N2
Poly. (CO2) Poly. (H2O) Poly. (O2) Poly. (N2)

Sam Cutlan P134357
4 | P a g e
Table 2
Fuel Equivalence Ratio (ɸ) Initial Temperatures 𝑇𝐵1
(K)
0.6 1711.482252
0.65 1807.515705
0.7 1900.877098
0.75 1991.664636
0.8 2079.972673
0.85 2165.891804
0.9 2249.508968
0.95 2330.907571
0.96 2346.928159
0.97 2362.863842
0.98 2378.715234
0.99 2394.482948
Table 2 - Fuel Equivalence Ratio against Initial Temperature.
2.3 Determining all Burning Temperatures with an increasing Pressure
The initial flame temperatures at each fuel equivalence ratio are the burning temperatures produced
at SOC where the crank angle is 0° and the pressure is 10 bar. It is then essential that the flame
temperatures be calculated for an increasing crank angle (from 0° to 20°) and an increasing pressure
(from 10 bar to 50 bar). To do this, if;
𝑃𝑉 𝑛
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
(1) 𝑃1 𝑉1
𝑛
= 𝑃2 𝑉2
𝑛
From the Ideal Gas Law;
𝑃1 𝑉1 = 𝑚𝑅𝑇1
And;
𝑃2 𝑉2 = 𝑚𝑅𝑇2
Rearrange to make 𝑉1 and 𝑉2 the subject of the equation;
𝑉1 =
𝑚𝑅𝑇1
𝑃1
And;
𝑉2 =
𝑚𝑅𝑇2
𝑃2
Therefore equation (1) becomes;
𝑃1 × (
𝑚𝑅𝑇1
𝑃1
)
𝑛
= 𝑃2 × (
𝑚𝑅𝑇2
𝑃2
)
𝑛

Sam Cutlan P134357
5 | P a g e
m x R will cancel out, therefore the equation becomes;
𝑃1 × (
𝑇1
𝑃1
)
𝑛
= 𝑃2 × (
𝑇2
𝑃2
)
𝑛
By multiplying out the brackets the equation becomes;
𝑃1 × 𝑇1
𝑛
𝑃1
𝑛 =
𝑃2 × 𝑇2
𝑛
𝑃2
𝑛
And by applying the following rule;
𝑃
𝑃 𝑛
=
1
𝑃 𝑛−1
The equation will become;
𝑇1
𝑛
𝑃1
𝑛−1 =
𝑇2
𝑛
𝑃2
𝑛−1
Then from cross multiplying the brackets the equation becomes;
𝑇2
𝑛
𝑇1
𝑛 =
𝑃2
𝑛−1
𝑃1
𝑛−1 = (
𝑃2
𝑃1
)
𝑛−1
Hence;
(
𝑇2
𝑇1
)
𝑛
= (
𝑃2
𝑃1
)
𝑛−1
From taking n over the equals sign the equation will become;
𝑇2
𝑇1
= (
𝑃2
𝑃1
)
𝑛−1
𝑛
And finally the equation will be;
Equation 3
𝑇2 = 𝑇1 × (
𝑃2
𝑃1
)
𝑛−1
𝑛
Since the initial flame temperature is represented by (𝑇1 = 𝑇𝐵1
)then (𝑇2 = 𝑇𝐵2
) can be calculated
by using Equation 3 above (See appendix 1).

Sam Cutlan P134357
6 | P a g e
2.4 Determining 𝑁𝑂𝑥 concentration levels as a function of Fuel Equivalence
Ratio
Throughout the following calculations the fuel equivalence ratio is taken as 0.6 to show workings
out. The calculations consider that an alternate fuel equivalence ratio will change the value of the
coefficients of the reactants; therefore changing the PPM of NOx. It is assumed that the engine has a
volumetric efficiency of 40% and since each cylinder has 400cc of displacement, the volume sucked
in is; 0.4*400=160ccs, hence each cylinder has 160*10^-6 m^3 of displacement. As well as this, it is
also assumed that the injection mixture comes in at 293k = 20°C.
From using the Ideal gas law;
𝑃𝑉 = 𝑛𝑅𝑢𝑇
The number of kmols of mixture in the cylinder is (n) = PV/RuT
Since the pressure (bar) of a N/A engine mixture comes in at 1 atmosphere = 10^5 N/m^2, the
equation can be solved for n.
n = 6.57 × 10−6
Therefore, since;
𝑛 = ∝× (𝜑 × 1 + 12.5 × (1 + 3.76)) = 6.57 × 10−6
Where φ=0.6, the equation can be solve to find the ∝ multiplier;
∝× 60.1 = 6.57 × 10−6
∝=
6.57 × 10−6
60.1
= 1.09287 × 10−7
∝ was solved for all fuel equivalence ratios by performing the same procedure above. To find the
Kmols of N2 and O2 in each cylinder, ∝ would then be multiplied by the coefficients of the products
of N2 and O2 for that specific fuel equivalence ratio. At a fuel equivalence ratio of 0.6;
kmols of N2 in each cylinder= ∝× 47 = 5.14 × 10−6
kmols of O2 in each cylinder= ∝× 0.625 = 5.46 × 10−8
Therefore the kmols/m^3 of N2 and O2 in each cylinder is;
N2 = 0.128412037
O2 = 0.013660855
Once this is performed the Exponential^(-67837/TB), d(NO)/dt and [NOx]/degree can be calculated.
By firstly knowing the burnt temperatures, the Exponential^(-67837)/TB) can be calculated; where
TB represents the burnt temperatures. The Zeldovich Model which is donated by d⌊NO⌋/dt is
calculated by means of the following equation;
Equation 4
𝑑⌊𝑁𝑂⌋
𝑑𝑡
= 4.7 × 1013
× ⌊𝑁2⌋ × ⌊𝑂2⌋0.5
× 𝐸𝑋𝑃(−67837
𝑇𝐵⁄ )
(McDonald, 2015)

Sam Cutlan P134357
7 | P a g e
And the ⌊NOx⌋/degree can be calculated by using the following equation;
Equation 5
⌊𝑁𝑂⌋
𝑑𝑒𝑔𝑟𝑒𝑒
=
𝑑⌊𝑁𝑂⌋
𝑑𝑡
× 𝑡𝑖𝑚𝑒 𝑓𝑜𝑟 1° =
𝑑⌊𝑁𝑂⌋
𝑑𝑡
×
1
6 × 𝑅𝑃𝑀
(McDonald, 2015)
These calculations for the fuel equivalence ratio = 0.6 can be seen in appendix 2.
From calculating the ⌊NOx⌋/degree, the total NOx during combustion can be found;
The total NOx during combustion/m^3 for fuel equivalence ratio 0.6 = 2.07191× 10−5
To find the kmols in the exhaust, ∝× (4.8 + 5.4 + 5 + 47) is calculated and is = 6.79764× 10−6
The kmols of NOx made is = ∝× 40 × 10−6
= 1.13532× 10−6
Finally, the Parts Per Million (PPM) of NOx produced =
𝑘𝑚𝑜𝑙𝑠 𝑜𝑓 𝑁𝑂𝑥 𝑚𝑎𝑑𝑒
𝑘𝑚𝑜𝑙𝑠 𝑜𝑓 𝑒𝑥ℎ𝑎𝑢𝑠𝑡
× 106
= 121.9194269
The NOx concentration levels were calculated for all fuel equivalence ratios and a table of values, as
well as a graphical representation of how the NOx PPM changes can be seen below respectively:
Table 3
Fuel Equivalence Ratio NO PPM
0.6 121.9194
0.65 590.8381
0.7 2311.211
0.75 7533.467
0.8 20904.44
0.85 49883.94
0.9 101449.5
0.95 163840
0.96 171257.1
0.97 172822.1
0.98 163962.7
0.99 134346.4

Sam Cutlan P134357
8 | P a g e
Figure 2
Figure 2 - NOx concentration level as a function of fuel equivalence ratio.
3.0 The Effect of Adding E.G.R on NOx Concentration Levels
3.1 Determining the Coefficients of the Products
When adding Exhaust Gas Recirculation (EGR) back into the cylinder, it as a result increases the mass
burned. Therefore, the coefficients of the products burned will increase (more mass will need to be
burned). Hence, each product was multiplied by the percentage of EGR added, and added on to the
original amount of product. An example of how this was performed is seen below;
Effect on Exhaust Mixtures by adding 1% EGR:
CO2 7.6
H2O 8.55
O2 0.625
N2 47
CO2 + (CO2 X 0.01) = 7.676
H20 + (H2O X 0.01) = 8.6355
O2 + (O2 X 0.01) = 0.63125
N2 + (N2 X 0.01) = 47.47,
As stated above the amount burned will increase, this is proven by the coefficients of the products
increasing with an increasing EGR. All coefficients of the products burned were calculated (see
Appendix 3).
3.2 Determining the Initial Burning Temperatures and all Burning
Temperatures
As there is now a greater number of kmols of products being burned in each cylinder as a result of
adding EGR, this means that the flame temperatures will subsequently decrease. To find the initial
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
NOxPPM
Fuel Equivalence Ratio
NOx Concentration Level as a Function of Fuel
Equivalence Ratio

Sam Cutlan P134357
9 | P a g e
flame temperatures, the same process as section 2.2 was undertaken. By a process of summating
the quadratic equation through the use of Excel from all the equations of each line (Figure 1), the
quadratic equation could be inputted into the online quadratic equation calculator to find the initial
temperature. It is important to note that the enthalpy released stays the same, as adding EGR does
the exact same on each side of the equation. For example, at ɸ=0.9 adding EGR=20%;
0.9𝐶8 𝐻18 + 12.5(𝑂2 + 3.76𝑁2) + 0.2(7.2𝐶𝑂2 + 8.1𝐻2 𝑂 + 1.25𝑂2 + 47𝑁2)
→ 1.2((7.2𝐶𝑂2 + 8.1𝐻2 𝑂 + 1.25𝑂2 + 47𝑁2)
From using the equations in Table 1 and taking into consideration that the coefficients of products
are increasing, each initial flame temperature was found for each EGR percentage from 0% to 20% in
1% intervals. The initial flame temperatures can be seen in Appendix 4.
To find all of the burning temperatures, the same process was undertaken by using Equation 3. The
flame temperatures can be seen Appendix 5.
3.3 Determining NOx Concentration Levels
It is important to note that adding EGR back into the cylinder will change the alpha multiplier
required to determine the number of kmols/m^3 of N2 and O2. To find alpha, the coefficients of the
reactants for a fuel equivalence ratio of 0.95 will increase as the EGR increases. For example;
Adding 1% EGR to a fuel equivalence ratio of 0.95 is:
0.95𝐶8 𝐻18 + 12.5(𝑂2 + 3.76𝑁2) + 0.01(7.6𝐶𝑂2 + 8.55𝐻2 𝑂 + 0.625𝑂2 + 47𝑁2)
0.95 × 1 + 12.5(4.76) + (0.01 × 63.775)
60.45 + 0.63775 = 61.08775
As can be seen with an increasing EGR, the air/fuel mass will increase. This was completed for all
EGR percentages; see Appendix 6.
To then find the alpha multiplier to find the correct trapped number of kmols/cycle, the number of
kmols of mixture in the cylinder is divided by 60.45 + [𝐸𝐺𝑅(%) × 63.775]. The alpha multiplier in
relation to an increasing EGR(%) can be seen in Appendix 7.
To find the kmols of N2 and O2, the alpha multiplier is multiplied by the coefficients of the products
of N2 and O2 for a fuel equivalence ratio of 0.95 (see appendix 8). Once found, the kmols/m^3 of N2
and O2 that are burned during combustion in the head volume of 40*10^-6m^3 can be found (also
seen in appendix 8).
Once this is calculated the Exponential^(-67837/TB) was found and then d(NO)/dt and [NOx]/degree
can be calculated by using the same process as before (in section 2.4) but taking into account that
the kmols/m^3 of N2 and O2 will be changing with an increasing EGR (%) (see Appendix 9).
Finally, the last procedure is to find the NOx PPM with a changing EGR (%). To perform this, the total
NOx during combustion/m^3 is summed up from the NOx (kmol/m^3) for each degree. Then it is
essential to multiply this summed value by 40*10^-6 to obtain the total NOx during combustion in
kmols. Then from there, the kmols in the exhaust is equal to the kmols in the exhaust multiplied by
(1+EGR(%)) from 0% to 20% EGR. To finish, the NOx PPM was calculated for all EGR percentages by
using the following equation;

Sam Cutlan P134357
10 | P a g e
𝑁𝑂𝑥 𝑃𝑃𝑀 =
𝑘𝑚𝑜𝑙𝑠 𝑜𝑓 𝑁𝑂𝑥 𝑚𝑎𝑑𝑒
𝑘𝑚𝑜𝑙𝑠 𝑜𝑓 𝑒𝑥ℎ𝑎𝑢𝑠𝑡
× 106
The values of the calculations can be seen in Appendix 10.
Once calculated, a graph the effect of adding EGR on NOx concentration levels can be plotted (see
Figure 3).
Figure 3
Figure 3 - Effect of Adding EGR on NOx Concentration Levels.
4.0 Analysis of NOx Model
4.1 Assumptions Made
When creating the NOx model there were a number of assumptions that were made, these included;
1) Rise in pressure after SOC is linear (in 2 bar/degree intervals)
2) Assuming the same volumetric efficiency of 40%
3) Pressure in the cylinder after inlet valve is closing is 1 bar
4) Temperature of air and fuel coming in is 20°C
5) Assume a Universal Gas Constant of 8316JKMOL^-1K^-1
6) Assume a Polytropic Index of 1.2
7) Assume the combustion volume in the head = 40cc’s
8) N2 and O2 concentrations are constant during combustion
When considering bullet point 1), the pressure rise after SOC is considered constant in 2 bar intervals
up to a pressure of 50bar. This is untrue to assume a constant rise in pressure; as firstly the NOx
0.000
20000.000
40000.000
60000.000
80000.000
100000.000
120000.000
140000.000
160000.000
180000.000
0 0.05 0.1 0.15 0.2 0.25
NOxPPM
EGR (%)
NOx Concentration Levels VS EGR Percentage

Sam Cutlan P134357
11 | P a g e
model uses an increasing fuel equivalence ratio (from 0.6 to 0.99), therefore meaning that there will
be more kmols of mixture burned inside the cylinder. As more mass is burned it is expected that the
pressure rise accordingly, and the model does not take this into account.
Bullet point 2) considers that the volumetric efficiency stays constant at 40% throughout
combustion. However, this does not take into account that some constants in the NOx model change
the percentage of volumetric efficiency. These include;
 Mixture temperature (which is influenced by heat transfer)
 Ratio of exhaust to inlet manifold pressures
 Compression ratio
 Intake and manifold port design
 Intake and exhaust valve geometry, size, lift and timings.
(Heywood, 1988).
Bullet point 3) considers that when the inlet valve closes the pressure will be 1 bar (atmospheric
pressure). This however does not concern that there will be reverse flow of gas when drawn into the
cylinder. Before the intake valve closes there is a pressure drop inside the cylinder as the piston
reaches BDC (drawing in air). The air will be drawn into the cylinder even when the piston passes
BDC; this inward movement of air combined with the upward movement of the piston on the
following stroke causes a pressure rise (so will not be exactly atmospheric); also stopping the inward
flow of gas. This is the point at which the intake valve should close (Hillier & Coombes, 2004).
Plenum size will also alter the intake pressure. The NOx model does not take these factors into
account.
Concerning bullet point 4) the temperature of the fuel and air mixture coming into the cylinder is
considered to be 20°C. However the NOx model doesn’t take into account the radiated heat (heat
transfer) from the surroundings. It is therefore likely that the temperature of the air and fuel coming
in be higher than 20°C. It is suggested that an increase in fuel temperature coming into the cylinder
can reduce NOx levels (Chen, 2008).
Bullet point 5): The Universal Gas Constant (UGC) comes from the Ideal Gas Law and has been
discovered through past physical experiments undertaken. The UGC is a constant of proportionality
that relates between the energy scale in physics and the temperature scale. This value of the UGC
will not change due to it being a set value, however it is suggested that there is a slight uncertainty
in the value of 9.1*10^-7Jmol^-1K^-1 (Winterbone, 2015). This can therefore alter the NOx PPM if
there is uncertainty!
Bullet Point 6): A polytropic Index can vary from 1 – 1.4 (Engineering Toolbox, 2015), which as tested
on the NOx model at a fuel equivalence ratio of 0.95 can vary the temperature by 34 kelvin. Hence it
was calculated that this change in the polytropic index could vary the NOx PPM produced by a total
of 51,671.52 (between the values of 1 – 1.4). This is a 31.53% change in NOx PPM produced when
compared to the NOx PPM at a fuel equivalence ratio of 0.95.
Bullet point 7) assumes that the combustion volume in the head is 40cc’s. However, this may not be
the exact value for the engine in question. A change in this volume will also change the volumetric
efficiency of the engine as a result of the compression ratio changing. This will therefore result in the
amount of NOx produced changing; a higher volume will decrease the amount of NOx PPM
produced whereas a lower volume will increase the amount of NOx PPM (Hill, 2006).

Sam Cutlan P134357
12 | P a g e
Bullet point 8) assumes that N2 and O2 concentrations are constant during combustion. This is due
to the fact that the quantity produced during combustion is very small and change would not be
great enough to effect the NOx PPM much (McDonald, 2015).
4.2 Effectiveness of Calculations
Taking into consideration the assumptions made, the calculations have been very effective as they
have shown that NOx concentration levels as a result of fuel equivalence ratio and the introduction
of EGR on NOx concentration levels can be predicted. At the choice of the user, Excel can calculate
results to a large number of decimal places for each calculation performed. This then makes sure
that the end result (as the model performs many calculations) is accurate. A large part of the NOx
model was calculating the initial flame temperatures for each fuel equivalence ratio and for each
EGR percentage. To obtain the flame temperatures, a quadratic formula for each line of
𝐶𝑂2, 𝐻2 𝑂, 𝑂2 𝑎𝑛𝑑 𝑁2 was gathered from Figure 1. The number of decimal places outputted by the
formula trend line label could also be chosen by the user (see Figure 4), this would ensure that the
initial temperatures were very accurate. It was essential that this initial stage be accurate as it
greatly affects the NOx PPM at the end of the NOx model.
Figure 4
Figure 4 - Trend line decimal places.
4.3 Mechanisms Responsible for NOx Formation
There are a number of factors responsible for the NOx PPM being so high. These factors are;
1) There are a lot of free O2’s
2) Increasing Fuel Equivalence Ratio
3) The burning temperatures are too high because the polytropic index is too high
4) The pressure is too high
(McDonald, 2015).
Considering bullet point 2), the increasing fuel equivalence ratio increases the amount of NOx PPM
produced as there is more Iso-octane being burned in the cylinder. As discussed before, the
polytropic index in bullet point 3) can range between 1 – 1.4, it is a direct cause of calculating the
temperatures after finding the initial temperature so will increase the NOx PPM produced
considerably (as previously mentioned in section 4.1). Since the EXP^(67837/TB) is very sensitive to
alterations in TB, this will alter the NOx PPM greatly. When concerning bullet point 4), the pressure
maybe too high for lower fuel equivalence ratio’s but more suited to higher equivalence ratio’s. This
is due to the fact that there is more mass in the cylinder being burned so the pressure in the cylinder
will increase. A factor that has to also be taken into account is that the combustion process will last
for greater than 20° of crank angle. It would be interesting to be able to produce a NOx model from

Sam Cutlan P134357
13 | P a g e
SOC to when the flame eventually dissipates (sometimes up to a maximum of 90° crank angle)
(Heywood, 1988).
5.0 References
Chen, G., 2008. Gas Turbines Power. Study of Fuel Temperature Effects on Fuel Injection,
Combustion, and Emissions of Direct-Injection Diesel Engines, 131(2), p. 8.
Engineering Toolbox, 2015. Compression and Expansion of Gases. [Online]
Available at: http://www.engineeringtoolbox.com/compression-expansion-gases-d_605.html
[Accessed 15 December 2015].
Heywood, J., 1988. Combustion in Spark-Ignition Engines. In: J. Holman, ed. Internal Combustion
Engine Fundamentals. New York: McGraw-Hill, p. 374.
Heywood, J., 1988. Volumetric Efficiency. In: J. Holman, ed. Internal Combustion Engine
Fundamentals . New York: McGraw-Hill Book Company, p. 209.
Hillier, V. & Coombes, P., 2004. Hillier's Fundamentals of Motor Vehicle Technology. 5th ed.
Cheltnham: Nelson Thornes.
Hill, V., 2006. Cylinder Head Volumes - CCing Your Heads. [Online]
Available at: http://www.hotrod.com/how-to/engine/ctrp-0611-cylinder-head-volumes/
[Accessed 5 January 2015].
Math.com, 2005. Quadratic Equation. [Online]
Available at: http://www.math.com/students/calculators/source/quadratic.htm
[Accessed 12 December 2015].
McDonald, M 2015, NOx Model When Lean, lecture notes, Powertrain & Sustainability, University of
Wales Trinity Saint David Swansea, delivered 24 November 2015.
McDonald, M 2015, Tailpipe Emissions, lecture notes, Powertrain & Sustainability, University of
Wales Trinity Saint David Swansea, delivered 3 November 2015.
Winterbone, D., 2015. Thermodynamic Properties of Ideal Gases and Ideal Gas Mixtures of Constant
Composition. Volume 2, pp. 177-205.

Sam Cutlan P134357
14 | P a g e
6.0 Appendices
6.1 Appendix 1
6.2 Appendix 2
Cranks Angle (degrees) Pressure (bar)
SOC 0 10 1711.482 1807.516 1900.877 1991.665 2079.973 2165.892 2249.509 2330.908 2346.928 2362.864 2378.715 2394.483
1 12 1764.394 1863.397 1959.645 2053.239 2144.277 2232.852 2319.055 2402.97 2419.486 2435.914 2452.256 2468.511
2 14 1810.405 1911.989 2010.747 2106.782 2200.194 2291.079 2379.53 2465.633 2482.58 2499.436 2516.204 2532.883
3 16 1851.23 1955.105 2056.09 2154.29 2249.809 2342.744 2433.189 2521.234 2538.562 2555.799 2572.945 2590
4 18 1888.004 1993.942 2096.933 2197.084 2294.5 2389.281 2481.523 2571.317 2588.99 2606.569 2624.055 2641.449
5 20 1921.518 2029.337 2134.155 2236.085 2335.23 2431.693 2525.572 2616.96 2634.947 2652.838 2670.635 2688.337
6 22 1952.347 2061.896 2168.396 2271.961 2372.697 2470.708 2566.093 2658.947 2677.222 2695.4 2713.483 2731.469
7 24 1980.923 2092.076 2200.135 2305.215 2407.426 2506.871 2603.652 2697.866 2716.408 2734.853 2753.2 2771.45
8 26 2007.58 2120.228 2229.742 2336.236 2439.822 2540.606 2638.689 2734.171 2752.963 2771.655 2790.249 2808.745
9 28 2032.581 2146.631 2257.509 2365.329 2470.205 2572.244 2671.549 2768.219 2787.245 2806.171 2824.996 2843.722
10 30 2056.135 2171.507 2283.67 2392.74 2498.831 2602.052 2702.508 2800.298 2819.545 2838.69 2857.733 2876.676
11 32 2078.416 2195.038 2308.416 2418.668 2525.909 2630.249 2731.793 2830.643 2850.098 2869.451 2888.7 2907.849
12 34 2099.565 2217.375 2331.906 2443.28 2551.612 2657.013 2759.591 2859.447 2879.1 2898.649 2918.095 2937.438
13 36 2119.703 2238.642 2354.272 2466.714 2576.085 2682.497 2786.059 2886.872 2906.714 2926.451 2946.083 2965.612
14 38 2138.928 2258.946 2375.625 2489.087 2599.45 2706.828 2811.328 2913.057 2933.078 2952.994 2972.804 2992.51
15 40 2157.329 2278.38 2396.062 2510.5 2621.813 2730.114 2835.514 2938.117 2958.311 2978.398 2998.379 3018.254
16 42 2174.979 2297.02 2415.665 2531.039 2643.262 2752.45 2858.712 2962.154 2982.514 3002.765 3022.909 3042.947
17 44 2191.942 2314.934 2434.505 2550.779 2663.877 2773.916 2881.007 2985.256 3005.774 3026.184 3046.485 3066.679
18 46 2208.274 2332.183 2452.644 2569.785 2683.726 2794.585 2902.474 3007.5 3028.171 3048.732 3069.185 3089.529
19 48 2224.025 2348.818 2470.139 2588.115 2702.868 2814.518 2923.176 3028.952 3049.77 3070.478 3091.076 3111.566
EOC 20 50 2239.239 2364.885 2487.036 2605.819 2721.358 2833.771 2943.173 3049.671 3070.632 3091.482 3112.221 3132.851
Fuel Equivalence Ratio (ɸ) 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 0.96 0.97 0.98 0.99
Burned Flame Temperatures (K)
Pressure (Bar) Flame Temperature B (K) Exponential^(-67837/TB) d(NO)/dt NO/degree
10 2330.907571 2.29412E-13 0.056719352 5.25179E-06
12 2402.969843 5.49107E-13 0.135759954 1.25704E-05
14 2465.633002 1.12525E-12 0.27820428 2.57597E-05
16 2521.233619 2.06421E-12 0.51035093 4.72547E-05
18 2571.316643 3.48622E-12 0.861924476 7.98078E-05
20 2616.959863 5.5232E-12 1.365543729 0.000126439
22 2658.946752 8.31688E-12 2.056247529 0.000190393
24 2697.86572 1.20171E-11 2.971079166 0.0002751
26 2734.170553 1.67803E-11 4.14872558 0.000384141
28 2768.218991 2.27684E-11 5.629205701 0.000521223
30 2800.298334 3.01475E-11 7.453601945 0.000690148
32 2830.642995 3.90872E-11 9.663829161 0.000894799
34 2859.446871 4.97595E-11 12.30243591 0.001139114
36 2886.872278 6.23385E-11 15.41243356 0.001427077
38 2913.056534 7.69994E-11 19.0371493 0.001762699
40 2938.116899 9.39181E-11 23.22009965 0.002150009
42 2962.154345 1.13271E-10 28.0048817 0.002593045
44 2985.256478 1.35235E-10 33.43507959 0.003095841
46 3007.499822 1.59984E-10 39.554184 0.003662424
48 3028.951638 1.87696E-10 46.40552314 0.004296808
50 3049.671374 2.18543E-10 54.03220342 0.005002982

Sam Cutlan P134357
15 | P a g e
6.3 Appendix 3EGR(%)00.010.020.030.040.050.060.070.080.090.10.110.120.130.140.150.160.170.180.190.2
CO27.67.6767.7527.8287.9047.988.0568.1328.2088.2848.368.4368.5128.5888.6648.748.8168.8928.9689.0449.12
H2O8.558.63558.7218.80658.8928.97759.0639.14859.2349.31959.4059.49059.5769.66159.7479.83259.91810.003510.08910.174510.26
O20.6250.631250.63750.643750.650.656250.66250.668750.6750.681250.68750.693750.70.706250.71250.718750.7250.731250.73750.743750.75
N24747.4747.9448.4148.8849.3549.8250.2950.7651.2351.752.1752.6453.1153.5854.0554.5254.9955.4655.9356.4

Sam Cutlan P134357
16 | P a g e
6.4 Appendix 4
6.5 Appendix 5
EGR(%) 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
InitialFlameTemperatures(K) 2330.908 2312.977 2295.365 2278.065 2261.067 2244.364 2227.948 2211.812 2195.948 2180.35 2165.011
EGR (%) 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Flame Temps (K) 2330.908 2312.977 2295.365 2278.065 2261.067 2244.364 2227.948 2211.812 2195.948 2180.35 2165.011
2402.97 2384.485 2366.329 2348.493 2330.97 2313.751 2296.827 2280.192 2263.838 2247.757 2231.944
2465.633 2446.666 2428.036 2409.736 2391.756 2374.087 2356.723 2339.654 2322.873 2306.373 2290.147
2521.234 2501.839 2482.789 2464.076 2445.69 2427.624 2409.867 2392.413 2375.254 2358.382 2341.791
2571.317 2551.536 2532.109 2513.024 2494.273 2475.847 2457.738 2439.937 2422.437 2405.23 2388.309
2616.96 2596.829 2577.056 2557.632 2538.548 2519.796 2501.365 2483.249 2465.438 2447.925 2430.704
2658.947 2638.492 2618.402 2598.667 2579.277 2560.224 2541.497 2523.09 2504.994 2487.2 2469.702
2697.866 2677.112 2656.728 2636.704 2617.03 2597.698 2578.697 2560.021 2541.659 2523.605 2505.851
2734.171 2713.138 2692.479 2672.186 2652.247 2632.654 2613.398 2594.47 2575.862 2557.565 2539.572
2768.219 2746.924 2726.009 2705.462 2685.275 2665.439 2645.943 2626.779 2607.939 2589.414 2571.197
2800.298 2778.757 2757.599 2736.814 2716.394 2696.327 2676.605 2657.219 2638.161 2619.422 2600.993
2830.643 2808.868 2787.481 2766.471 2745.829 2725.545 2705.61 2686.014 2666.749 2647.806 2629.178
2859.447 2837.45 2815.845 2794.622 2773.77 2753.279 2733.141 2713.346 2693.885 2674.75 2655.932
2886.872 2864.665 2842.853 2821.426 2800.374 2779.687 2759.355 2739.37 2719.722 2700.404 2681.406
2913.057 2890.647 2868.638 2847.016 2825.773 2804.899 2784.383 2764.216 2744.391 2724.897 2705.726
2938.117 2915.515 2893.316 2871.509 2850.083 2829.029 2808.336 2787.996 2768 2748.338 2729.003
2962.154 2939.368 2916.987 2895.001 2873.4 2852.174 2831.312 2810.806 2790.646 2770.823 2751.33
2985.256 2962.292 2939.737 2917.579 2895.81 2874.418 2853.394 2832.727 2812.41 2792.433 2772.788
3007.5 2984.364 2961.641 2939.318 2917.387 2895.835 2874.654 2853.834 2833.366 2813.24 2793.448
3028.952 3005.651 2982.765 2960.284 2938.196 2916.491 2895.159 2874.19 2853.575 2833.306 2813.373
3049.671 3026.211 3003.169 2980.534 2958.295 2936.441 2914.963 2893.851 2873.095 2852.687 2832.618
EGR (%) 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2
Flame Temps (K) 2149.924 2135.083 2120.483 2106.117 2091.979 2078.065 2064.369 2050.886 2037.611 2024.539
2216.391 2201.091 2186.04 2171.229 2156.655 2142.311 2128.191 2114.291 2100.605 2087.129
2274.188 2258.49 2243.046 2227.849 2212.895 2198.177 2183.689 2169.426 2155.384 2141.556
2325.472 2309.419 2293.627 2278.088 2262.796 2247.746 2232.932 2218.348 2203.988 2189.849
2371.666 2355.295 2339.189 2323.341 2307.746 2292.396 2277.288 2262.414 2247.769 2233.349
2413.765 2397.104 2380.711 2364.582 2348.71 2333.089 2317.712 2302.574 2287.669 2272.993
2452.492 2435.563 2418.908 2402.52 2386.393 2370.521 2354.897 2339.517 2324.373 2309.461
2488.389 2471.212 2454.313 2437.686 2421.323 2405.218 2389.366 2373.76 2358.395 2343.265
2521.875 2504.467 2487.341 2470.489 2453.906 2437.585 2421.519 2405.703 2390.131 2374.798
2553.28 2535.655 2518.315 2501.254 2484.465 2467.94 2451.674 2435.662 2419.896 2404.371
2582.869 2565.039 2547.499 2530.24 2513.256 2496.54 2480.085 2463.887 2447.938 2432.234
2610.857 2592.835 2575.104 2557.658 2540.49 2523.593 2506.96 2490.586 2474.465 2458.59
2637.424 2619.219 2601.308 2583.684 2566.341 2549.272 2532.47 2515.93 2499.644 2483.608
2662.72 2644.34 2626.257 2608.465 2590.955 2573.723 2556.76 2540.061 2523.619 2507.429
2686.872 2668.325 2650.078 2632.124 2614.456 2597.067 2579.95 2563.099 2546.508 2530.171
2709.986 2691.28 2672.876 2654.767 2636.947 2619.409 2602.145 2585.149 2568.415 2551.938
2732.157 2713.298 2694.743 2676.487 2658.521 2640.839 2623.433 2606.299 2589.428 2572.816
2753.466 2734.459 2715.76 2697.361 2679.255 2661.435 2643.894 2626.625 2609.623 2592.881
2773.982 2754.833 2735.995 2717.459 2699.218 2681.265 2663.594 2646.197 2629.068 2612.201
2793.768 2774.483 2755.51 2736.842 2718.471 2700.39 2682.592 2665.071 2647.82 2630.833
2812.879 2793.462 2774.359 2755.564 2737.067 2718.862 2700.943 2683.302 2665.933 2648.83
0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2
2149.924 2135.083 2120.483 2106.117 2091.979 2078.065 2064.369 2050.886 2037.611 2024.539

Sam Cutlan P134357
17 | P a g e
6.6 Appendix 6
EGR Mass Burned
0 60.45
0.01 61.08775
0.02 61.7255
0.03 62.36325
0.04 63.001
0.05 63.63875
0.06 64.2765
0.07 64.91425
0.08 65.552
0.09 66.18975
0.1 66.8275
0.11 67.46525
0.12 68.103
0.13 68.74075
0.14 69.3785
0.15 70.01625
0.16 70.654
0.17 71.29175
0.18 71.9295
0.19 72.56725
0.2 73.205

Sam Cutlan P134357
18 | P a g e
6.7 Appendix 7
6.8 Appendix 8
EGR Alpha
0 1.08654E-07
0.01 1.0752E-07
0.02 1.06409E-07
0.03 1.05321E-07
0.04 1.04255E-07
0.05 1.0321E-07
0.06 1.02186E-07
0.07 1.01182E-07
0.08 1.00197E-07
0.09 9.9232E-08
0.1 9.8285E-08
0.11 9.73559E-08
0.12 9.64442E-08
0.13 9.55494E-08
0.14 9.46711E-08
0.15 9.38088E-08
0.16 9.2962E-08
0.17 9.21304E-08
0.18 9.13136E-08
0.19 9.05111E-08
0.2 8.97225E-08
EGR Alpha Kmols of N2 in Cylinder Kmols/m^3 of N2 Kmols of O2 in Cylinder Kmols/m^3 of O2
0 1.08654E-07 5.10674E-06 0.127668543 6.79088E-08 0.00169772
0.01 1.0752E-07 5.05343E-06 0.126335697 6.71998E-08 0.001679996
0.02 1.06409E-07 5.00122E-06 0.125030392 6.65055E-08 0.001662638
0.03 1.05321E-07 4.95007E-06 0.123751784 6.58254E-08 0.001645635
0.04 1.04255E-07 4.89996E-06 0.122499063 6.51591E-08 0.001628977
0.05 1.0321E-07 4.85086E-06 0.121271449 6.45061E-08 0.001612652
0.06 1.02186E-07 4.80273E-06 0.120068197 6.38661E-08 0.001596652
0.07 1.01182E-07 4.75554E-06 0.118888587 6.32386E-08 0.001580965
0.08 1.00197E-07 4.70928E-06 0.11773193 6.26234E-08 0.001565584
0.09 9.9232E-08 4.6639E-06 0.116597562 6.202E-08 0.001550499
0.1 9.8285E-08 4.61939E-06 0.115484845 6.14281E-08 0.001535703
0.11 9.73559E-08 4.57573E-06 0.114393165 6.08474E-08 0.001521186
0.12 9.64442E-08 4.53288E-06 0.113321931 6.02776E-08 0.001506941
0.13 9.55494E-08 4.49082E-06 0.112270574 5.97184E-08 0.00149296
0.14 9.46711E-08 4.44954E-06 0.111238546 5.91694E-08 0.001479236
0.15 9.38088E-08 4.40901E-06 0.110225318 5.86305E-08 0.001465762
0.16 9.2962E-08 4.36922E-06 0.109230383 5.81013E-08 0.001452532
0.17 9.21304E-08 4.33013E-06 0.108253247 5.75815E-08 0.001439538
0.18 9.13136E-08 4.29174E-06 0.107293439 5.7071E-08 0.001426774
0.19 9.05111E-08 4.25402E-06 0.106350502 5.65694E-08 0.001414235
0.2 8.97225E-08 4.21696E-06 0.105423994 5.60766E-08 0.001401915

Sam Cutlan P134357
19 | P a g e
6.9 Appendix 9
EGR (%) 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
N2 (kmols/m^3) 0 0.076 0.152 0.228 0.304 0.38 0.456 0.532 0.608 0.684
O2 (kmols/m^3) 0 0.171 0.342 0.513 0.684 0.855 1.026 1.197 1.368 1.539
Exponential^(-67837/TB) 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25
0 0.47 0.94 1.41 1.88 2.35 2.82 3.29 3.76 4.23
7.6 7.676 7.752 7.828 7.904 7.98 8.056 8.132 8.208 8.284
8.55 8.6355 8.721 8.8065 8.892 8.9775 9.063 9.1485 9.234 9.3195
0.625 0.63125 0.6375 0.64375 0.65 0.65625 0.6625 0.66875 0.675 0.68125
47 47.47 47.94 48.41 48.88 49.35 49.82 50.29 50.76 51.23
2330.908 2312.977 2295.365 2278.065 2261.067 2244.364 2227.948 2211.812 2195.948 2180.35
2402.97 2384.485 2366.329 2348.493 2330.97 2313.751 2296.827 2280.192 2263.838 2247.757
2465.633 2446.666 2428.036 2409.736 2391.756 2374.087 2356.723 2339.654 2322.873 2306.373
2521.234 2501.839 2482.789 2464.076 2445.69 2427.624 2409.867 2392.413 2375.254 2358.382
2571.317 2551.536 2532.109 2513.024 2494.273 2475.847 2457.738 2439.937 2422.437 2405.23
2616.96 2596.829 2577.056 2557.632 2538.548 2519.796 2501.365 2483.249 2465.438 2447.925
2658.947 2638.492 2618.402 2598.667 2579.277 2560.224 2541.497 2523.09 2504.994 2487.2
2697.866 2677.112 2656.728 2636.704 2617.03 2597.698 2578.697 2560.021 2541.659 2523.605
2734.171 2713.138 2692.479 2672.186 2652.247 2632.654 2613.398 2594.47 2575.862 2557.565
2768.219 2746.924 2726.009 2705.462 2685.275 2665.439 2645.943 2626.779 2607.939 2589.414
2800.298 2778.757 2757.599 2736.814 2716.394 2696.327 2676.605 2657.219 2638.161 2619.422
2830.643 2808.868 2787.481 2766.471 2745.829 2725.545 2705.61 2686.014 2666.749 2647.806
2859.447 2837.45 2815.845 2794.622 2773.77 2753.279 2733.141 2713.346 2693.885 2674.75
2886.872 2864.665 2842.853 2821.426 2800.374 2779.687 2759.355 2739.37 2719.722 2700.404
2913.057 2890.647 2868.638 2847.016 2825.773 2804.899 2784.383 2764.216 2744.391 2724.897
d(NO)/dt 2938.117 2915.515 2893.316 2871.509 2850.083 2829.029 2808.336 2787.996 2768 2748.338
2962.154 2939.368 2916.987 2895.001 2873.4 2852.174 2831.312 2810.806 2790.646 2770.823
2985.256 2962.292 2939.737 2917.579 2895.81 2874.418 2853.394 2832.727 2812.41 2792.433
3007.5 2984.364 2961.641 2939.318 2917.387 2895.835 2874.654 2853.834 2833.366 2813.24
3028.952 3005.651 2982.765 2960.284 2938.196 2916.491 2895.159 2874.19 2853.575 2833.306
3049.671 3026.211 3003.169 2980.534 2958.295 2936.441 2914.963 2893.851 2873.095 2852.687
2.29E-13 1.83E-13 1.46E-13 1.17E-13 9.34E-14 7.47E-14 5.98E-14 4.79E-14 3.84E-14 3.07E-14
5.49E-13 4.41E-13 3.55E-13 2.85E-13 2.3E-13 1.85E-13 1.49E-13 1.2E-13 9.69E-14 7.82E-14
1.13E-12 9.09E-13 7.35E-13 5.94E-13 4.81E-13 3.89E-13 3.16E-13 2.56E-13 2.07E-13 1.68E-13
2.06E-12 1.68E-12 1.36E-12 1.11E-12 8.99E-13 7.31E-13 5.95E-13 4.85E-13 3.95E-13 3.22E-13
3.49E-12 2.84E-12 2.32E-12 1.89E-12 1.54E-12 1.26E-12 1.03E-12 8.42E-13 6.89E-13 5.64E-13
5.52E-12 4.52E-12 3.7E-12 3.03E-12 2.48E-12 2.03E-12 1.67E-12 1.37E-12 1.12E-12 9.22E-13
8.32E-12 6.82E-12 5.6E-12 4.6E-12 3.78E-12 3.11E-12 2.56E-12 2.11E-12 1.73E-12 1.43E-12
1.2E-11 9.89E-12 8.14E-12 6.71E-12 5.53E-12 4.56E-12 3.76E-12 3.1E-12 2.56E-12 2.12E-12
1.68E-11 1.38E-11 1.14E-11 9.44E-12 7.8E-12 6.45E-12 5.33E-12 4.41E-12 3.65E-12 3.03E-12
2.28E-11 1.88E-11 1.56E-11 1.29E-11 1.07E-11 8.85E-12 7.34E-12 6.09E-12 5.05E-12 4.19E-12
3.01E-11 2.5E-11 2.07E-11 1.72E-11 1.43E-11 1.18E-11 9.84E-12 8.18E-12 6.8E-12 5.66E-12
3.91E-11 3.25E-11 2.7E-11 2.24E-11 1.86E-11 1.55E-11 1.29E-11 1.08E-11 8.96E-12 7.47E-12
4.98E-11 4.14E-11 3.45E-11 2.87E-11 2.39E-11 1.99E-11 1.66E-11 1.39E-11 1.16E-11 9.67E-12
6.23E-11 5.2E-11 4.33E-11 3.61E-11 3.02E-11 2.52E-11 2.1E-11 1.76E-11 1.47E-11 1.23E-11
7.7E-11 6.43E-11 5.37E-11 4.49E-11 3.75E-11 3.14E-11 2.62E-11 2.2E-11 1.84E-11 1.54E-11
NO kmol/m3 9.39E-11 7.85E-11 6.57E-11 5.5E-11 4.6E-11 3.86E-11 3.23E-11 2.71E-11 2.27E-11 1.91E-11
1.13E-10 9.48E-11 7.95E-11 6.66E-11 5.58E-11 4.68E-11 3.93E-11 3.3E-11 2.77E-11 2.33E-11
1.35E-10 1.13E-10 9.51E-11 7.98E-11 6.7E-11 5.63E-11 4.73E-11 3.98E-11 3.35E-11 2.82E-11
1.6E-10 1.34E-10 1.13E-10 9.48E-11 7.97E-11 6.7E-11 5.64E-11 4.75E-11 4E-11 3.37E-11
1.88E-10 1.58E-10 1.33E-10 1.12E-10 9.4E-11 7.91E-11 6.67E-11 5.62E-11 4.74E-11 4E-11
2.19E-10 1.84E-10 1.55E-10 1.3E-10 1.1E-10 9.27E-11 7.82E-11 6.6E-11 5.57E-11 4.7E-11
0.056719 0.044556 0.035028 0.027558 0.021697 0.017095 0.013479 0.010635 0.008397 0.006635
0.13576 0.107372 0.084982 0.06731 0.053351 0.042318 0.03359 0.02668 0.021207 0.016869
0.278204 0.221257 0.176093 0.140249 0.111779 0.089151 0.071153 0.056828 0.045418 0.036323
0.510351 0.407798 0.326083 0.260925 0.208932 0.167415 0.134239 0.10771 0.086482 0.069484
0.861924 0.691528 0.555204 0.446062 0.358621 0.288516 0.232272 0.187117 0.15084 0.121675
1.365544 1.0995 0.885897 0.714278 0.576295 0.465278 0.375896 0.303885 0.245829 0.198993
2.056248 1.660898 1.342473 1.085827 0.878831 0.711766 0.576837 0.46779 0.379602 0.308236
2.971079 2.406694 1.950831 1.582367 1.284344 1.043132 0.847771 0.68944 0.561037 0.456835
4.148726 3.369345 2.738201 2.226749 1.81201 1.475473 1.202209 0.980178 0.799656 0.652789
5.629206 4.582531 3.73293 3.042831 2.481914 2.025695 1.654387 1.35199 1.105556 0.9046
7.453602 6.080924 4.964286 4.055319 3.31491 2.711405 2.219169 1.817428 1.489337 1.221222
9.663829 7.899998 6.462286 5.289617 4.332499 3.550801 2.91196 2.389534 1.962038 1.612002
12.30244 10.07585 8.257555 6.771705 5.556723 4.562585 3.748628 3.081771 2.535086 2.086637
15.41243 12.64505 10.38119 8.528028 7.010067 5.765877 4.745432 3.907966 3.220241 2.655131
19.03715 15.64452 12.86466 10.5854 8.715379 7.180145 5.918962 4.882259 4.029551 3.327751

Sam Cutlan P134357
20 | P a g e
EGR (%) 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2
N2 (kmols/m^3) 0.76 0.836 0.912 0.988 1.064 1.14 1.216 1.292 1.368 1.444 1.52
O2 (kmols/m^3) 1.71 1.881 2.052 2.223 2.394 2.565 2.736 2.907 3.078 3.249 3.42
Exponential^(-67837/TB) 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 4.75 5
4.7 5.17 5.64 6.11 6.58 7.05 7.52 7.99 8.46 8.93 9.4
8.36 8.436 8.512 8.588 8.664 8.74 8.816 8.892 8.968 9.044 9.12
9.405 9.4905 9.576 9.6615 9.747 9.8325 9.918 10.0035 10.089 10.1745 10.26
0.6875 0.69375 0.7 0.70625 0.7125 0.71875 0.725 0.73125 0.7375 0.74375 0.75
51.7 52.17 52.64 53.11 53.58 54.05 54.52 54.99 55.46 55.93 56.4
2165.011 2149.924 2135.083 2120.483 2106.117 2091.979 2078.065 2064.369 2050.886 2037.611 2024.539
2231.944 2216.391 2201.091 2186.04 2171.229 2156.655 2142.311 2128.191 2114.291 2100.605 2087.129
2290.147 2274.188 2258.49 2243.046 2227.849 2212.895 2198.177 2183.689 2169.426 2155.384 2141.556
2341.791 2325.472 2309.419 2293.627 2278.088 2262.796 2247.746 2232.932 2218.348 2203.988 2189.849
2388.309 2371.666 2355.295 2339.189 2323.341 2307.746 2292.396 2277.288 2262.414 2247.769 2233.349
2430.704 2413.765 2397.104 2380.711 2364.582 2348.71 2333.089 2317.712 2302.574 2287.669 2272.993
2469.702 2452.492 2435.563 2418.908 2402.52 2386.393 2370.521 2354.897 2339.517 2324.373 2309.461
2505.851 2488.389 2471.212 2454.313 2437.686 2421.323 2405.218 2389.366 2373.76 2358.395 2343.265
2539.572 2521.875 2504.467 2487.341 2470.489 2453.906 2437.585 2421.519 2405.703 2390.131 2374.798
2571.197 2553.28 2535.655 2518.315 2501.254 2484.465 2467.94 2451.674 2435.662 2419.896 2404.371
2600.993 2582.869 2565.039 2547.499 2530.24 2513.256 2496.54 2480.085 2463.887 2447.938 2432.234
2629.178 2610.857 2592.835 2575.104 2557.658 2540.49 2523.593 2506.96 2490.586 2474.465 2458.59
2655.932 2637.424 2619.219 2601.308 2583.684 2566.341 2549.272 2532.47 2515.93 2499.644 2483.608
2681.406 2662.72 2644.34 2626.257 2608.465 2590.955 2573.723 2556.76 2540.061 2523.619 2507.429
2705.726 2686.872 2668.325 2650.078 2632.124 2614.456 2597.067 2579.95 2563.099 2546.508 2530.171
d(NO)/dt 2729.003 2709.986 2691.28 2672.876 2654.767 2636.947 2619.409 2602.145 2585.149 2568.415 2551.938
2751.33 2732.157 2713.298 2694.743 2676.487 2658.521 2640.839 2623.433 2606.299 2589.428 2572.816
2772.788 2753.466 2734.459 2715.76 2697.361 2679.255 2661.435 2643.894 2626.625 2609.623 2592.881
2793.448 2773.982 2754.833 2735.995 2717.459 2699.218 2681.265 2663.594 2646.197 2629.068 2612.201
2813.373 2793.768 2774.483 2755.51 2736.842 2718.471 2700.39 2682.592 2665.071 2647.82 2630.833
2832.618 2812.879 2793.462 2774.359 2755.564 2737.067 2718.862 2700.943 2683.302 2665.933 2648.83
2.47E-14 1.98E-14 1.59E-14 1.28E-14 1.03E-14 8.26E-15 6.65E-15 5.35E-15 4.31E-15 3.48E-15 2.8E-15
6.31E-14 5.1E-14 4.12E-14 3.33E-14 2.7E-14 2.18E-14 1.77E-14 1.43E-14 1.16E-14 9.44E-15 7.66E-15
1.37E-13 1.11E-13 9.02E-14 7.34E-14 5.97E-14 4.86E-14 3.96E-14 3.22E-14 2.63E-14 2.14E-14 1.75E-14
2.63E-13 2.14E-13 1.75E-13 1.43E-13 1.17E-13 9.55E-14 7.82E-14 6.4E-14 5.24E-14 4.29E-14 3.52E-14
4.62E-13 3.78E-13 3.1E-13 2.54E-13 2.09E-13 1.71E-13 1.41E-13 1.16E-13 9.51E-14 7.82E-14 6.43E-14
7.58E-13 6.23E-13 5.12E-13 4.22E-13 3.47E-13 2.86E-13 2.36E-13 1.94E-13 1.6E-13 1.32E-13 1.09E-13
1.18E-12 9.71E-13 8.01E-13 6.61E-13 5.46E-13 4.51E-13 3.73E-13 3.09E-13 2.55E-13 2.11E-13 1.75E-13
1.75E-12 1.45E-12 1.2E-12 9.91E-13 8.21E-13 6.8E-13 5.64E-13 4.68E-13 3.88E-13 3.22E-13 2.67E-13
2.51E-12 2.08E-12 1.72E-12 1.43E-12 1.19E-12 9.87E-13 8.2E-13 6.82E-13 5.67E-13 4.72E-13 3.93E-13
3.48E-12 2.89E-12 2.41E-12 2E-12 1.67E-12 1.39E-12 1.15E-12 9.62E-13 8.02E-13 6.69E-13 5.58E-13
4.71E-12 3.92E-12 3.27E-12 2.72E-12 2.27E-12 1.9E-12 1.58E-12 1.32E-12 1.1E-12 9.22E-13 7.71E-13
6.23E-12 5.2E-12 4.34E-12 3.62E-12 3.03E-12 2.53E-12 2.12E-12 1.77E-12 1.48E-12 1.24E-12 1.04E-12
8.08E-12 6.75E-12 5.65E-12 4.73E-12 3.96E-12 3.31E-12 2.78E-12 2.33E-12 1.95E-12 1.64E-12 1.37E-12
1.03E-11 8.62E-12 7.22E-12 6.05E-12 5.08E-12 4.26E-12 3.57E-12 3E-12 2.52E-12 2.12E-12 1.78E-12
1.29E-11 1.08E-11 9.1E-12 7.64E-12 6.41E-12 5.39E-12 4.53E-12 3.81E-12 3.2E-12 2.7E-12 2.27E-12
NO kmol/m3 1.6E-11 1.34E-11 1.13E-11 9.5E-12 7.99E-12 6.72E-12 5.66E-12 4.77E-12 4.01E-12 3.38E-12 2.85E-12
1.96E-11 1.65E-11 1.39E-11 1.17E-11 9.83E-12 8.28E-12 6.98E-12 5.89E-12 4.97E-12 4.19E-12 3.54E-12
2.37E-11 2E-11 1.68E-11 1.42E-11 1.2E-11 1.01E-11 8.52E-12 7.19E-12 6.08E-12 5.14E-12 4.34E-12
2.84E-11 2.4E-11 2.02E-11 1.71E-11 1.44E-11 1.22E-11 1.03E-11 8.7E-12 7.35E-12 6.22E-12 5.27E-12
3.37E-11 2.85E-11 2.41E-11 2.03E-11 1.72E-11 1.45E-11 1.23E-11 1.04E-11 8.82E-12 7.47E-12 6.33E-12
3.97E-11 3.36E-11 2.84E-11 2.4E-11 2.03E-11 1.72E-11 1.46E-11 1.24E-11 1.05E-11 8.89E-12 7.54E-12
0.005247 0.004151 0.003287 0.002605 0.002065 0.001639 0.001301 0.001034 0.000822 0.000654 0.00052
0.013427 0.010694 0.008524 0.006798 0.005426 0.004333 0.003463 0.002769 0.002216 0.001774 0.001421
0.029069 0.02328 0.018655 0.014959 0.012003 0.009638 0.007743 0.006225 0.005008 0.004031 0.003247
0.055864 0.044943 0.03618 0.029145 0.023493 0.018949 0.015293 0.01235 0.00998 0.00807 0.006529
0.098214 0.079327 0.064113 0.05185 0.041959 0.033976 0.027529 0.022319 0.018106 0.014697 0.011937
0.161184 0.130641 0.105953 0.085984 0.069822 0.056732 0.046125 0.037524 0.030545 0.024878 0.020275
0.250445 0.203617 0.165648 0.134843 0.109833 0.089517 0.073002 0.05957 0.048638 0.039736 0.032482
0.37222 0.303465 0.247563 0.202082 0.165056 0.134896 0.110312 0.090262 0.073899 0.060538 0.049621
0.533226 0.435829 0.356439 0.291687 0.238841 0.195686 0.160422 0.131591 0.108003 0.088695 0.07288
0.740626 0.606744 0.497363 0.407945 0.334801 0.274934 0.225903 0.185725 0.15278 0.12575 0.103562
1.001983 0.822598 0.675732 0.555417 0.456792 0.3759 0.309511 0.254994 0.210199 0.173371 0.143076
1.325213 1.090097 0.897226 0.738914 0.608891 0.502037 0.414173 0.341881 0.282366 0.233343 0.192938
1.718546 1.416226 1.167776 0.963474 0.795374 0.65698 0.542975 0.449007 0.371509 0.307558 0.254756
2.19049 1.808225 1.493541 1.234335 1.020701 0.844522 0.699148 0.579123 0.47997 0.398012 0.33023
2.7498 2.273554 1.88088 1.556921 1.289495 1.068608 0.886056 0.735098 0.610196 0.506793 0.421142

Sam Cutlan P134357
21 | P a g e
6.1.1 Appendix 10
6.1.2 Appendix 11
0
0.2
0.4
0.6
0.8
1
1.2
0
0.05
0.1
0.15
0.2
0.25
1600 1700 1800 1900 2000 2100 2200 2300 2400 2500
FuelEquivalenceRatio
EGR(%)
Initial Temperatures
Initial Temperatures for Fuel Equivalence Ratio's and EGR (%)
EGR Fuel Equivalence Ratio
EGR (%) 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
TOTAL NOX kmol/m3 0.028383 0.023387 0.019284 0.015911 0.013136 0.010852 0.008971 0.007421 0.006142 0.005087 0.004216
TOTAL NOX kmol 6.93E-06 6.86E-06 6.79E-06 6.72E-06 6.65E-06 6.58E-06 6.52E-06 6.45E-06 6.39E-06 6.33E-06 6.27E-06
Kmols Exhaust 1.14E-06 9.35E-07 7.71E-07 6.36E-07 5.25E-07 4.34E-07 3.59E-07 2.97E-07 2.46E-07 2.03E-07 1.69E-07
NOX PPM 163840 136427.2 113663.9 94750.79 79027.76 65949.47 55065.04 46001.48 38450.06 32155.11 26904.75
EGR(%) 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2
TOTALNOXkmol/m3 0.003496 0.002901 0.002408 0.002001 0.001662996 0.001383103 0.001150982 0.000958365 0.000798435 0.000666
TOTALNOXkmol 6.21E-06 6.15E-06 6.09E-06 6.04E-06 5.98266E-06 5.92865E-06 5.87562E-06 5.82352E-06 5.77234E-06 5.72E-06
KmolsExhaust 1.4E-07 1.16E-07 9.63E-08 8E-08 6.65198E-08 5.53241E-08 4.60393E-08 3.83346E-08 3.19374E-08 2.66E-08
NOXPPM 22523.31 18865.07 15809.04 13254.77 11118.78157 9331.652936 7835.649686 6582.714912 5532.829033 4652.648

NOX PDF

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (7)

Similar to NOX PDF

Similar to NOX PDF (20)

NOX PDF