1. Heat Release Modeling
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Transcript of 1. Heat Release Modeling
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1. Heat Release Modeling
Differentiate the Ideal Gas Law With Respect to Crank-Angle
Rearrange To Find Instantaneous Change in Pressure, Numerically Integrate To Find Pressure
First Law Of Thermodynamics
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Rearrange to Find Instantaneous Change In Temperature, Integrate To Find Temperature
Change In Net Heat Transfer As A Function Of Crank-Angle
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• The engine volume (as a function of crank angle) can be calculated using engine geometry
=clearance volume=bore=connecting rod length=crank radius (1/2 of stroke)=instantaneous distance between piston pin and crank axis
2. Cylinder Volume Modeling
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3. Mass Fraction Burned Modeling
Weibe function is used to predict the combustion burn profile
=fraction of fuel mass burned at specific crank angle=Spark advance=Burn duration, = constants fit to a specific engine (approximately 5,2)
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4. Heat Transfer Modeling
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5. Two-Zone Model (For Burned-Zone Temperature)
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burned mass→mb (i )=mb (i −1 )+d X b (i )d θ
mc
unburned mass→mu (i )=mu (i−1 )−d Xb (i )dθ
mc
unburned volume→V u (i)=( (mu ( i )V u (i −1 ) )mu (i −1 ) )( P (i )
P (i −1 ) )− 1γ u
TotalVolume→V ( i )=V b (i )+V u (i )
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burned − zone temperature→Tb (i )=P ( i )V b (i)mb ( i ) R (i )
unburned −zone temperature→T u (i )=P ( i )V u (i )mu (i )R (i )
R (i )=instantaneous , fluid specific gas constant
This is found using the specific heat ratios model
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ε= 44+ y
6. Atom Balancing
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Species
0
0
0
Total:
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KWGS=nH 2OnCO
nCO2nH 2
Water−Gas Shift Reaction→CO 2+H 2↔CO+H 2O
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zeldovichmechanism→ d [NO ]dt
=2 k1f [N 2 ] e [O ]e
[N2 ]e=equilibrium concentration of N2
[O ]e=equilibrium concentration of O
k 1f=forward reaction rate coefficient
7. NO Formation Model
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k 1f ( c m3
gmol− s )= (1.82∗1014 ) exp(− 38370T b )
[O ]e=kO [O2 ]e
12
(RuT b )12
Ru=UniversalGasConstant (8315[ Jkmol− K ])
K o(Pa
12 )=3.6 x 103 exp(− 31090
T b ) x (101325 )12
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The equilibrium concentration of is found using the following equilibrium equation:
𝐂𝐎𝟐=𝐂𝐎+(𝟏𝟐 )𝐎𝟐
The equilibrium constant can be calculated as a function of the burned zone temperature using the JANAF tables:
𝐥𝐨𝐠𝟏𝟎𝐊𝐩=𝐊 𝐩𝐂𝐎𝟐−𝐊 𝐩𝐂𝐎 .
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Use the following equation to calculate the percentage of dissociation of :
𝟏−𝛂
𝛂 (𝛂𝟐 )𝟏𝟐(𝐧𝐩
𝐏𝐩 )𝟏𝟐=𝐊𝐩
𝐧𝐩
𝐏𝐩= 𝟏 .𝟓𝐏𝐄𝐗𝐇 ( 𝐓𝐛
𝐓𝐁𝐃𝐂 )
Assume that the equilibrium mole fraction of nitrogen is equal to that provided by the atom balance equations. Assume that the composition is frozen at 90% of the peak burned-zone temperature.
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8. Hydrocarbon Emissions Model (flame-quenching)
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This is total crevice emissions index. A further explanation of HC formation mechanisms can be found on the Mindworks website.
The peak cylinder pressure and IMEP can be found from the single-zone model. The coolant temperature can be estimated as 350 [K]. The crevice volume can be measured.
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mass of oil film→moil=ρoil π δ oil BS
ρoil=oil density 900[ kgm3 ]δ oil=oil layer thickness 3 [ μm ]
mass of HC→mHC=Pest( 1A Fmol )(
M W air
M W HC)( M W HC
M W oil H )moil
M W i=constituent molecular weights
H=Henr y ′ sConstant
8. Hydrocarbon Emissions Model (Oil Layer Absorption and Desorption
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The pressure term used in predicting the mass of hydrocarbons can be estimated as an average between the inlet and peak combustion temperatures.
Pinlet (atm )=0.09875+0.00986 IMEP (kPa)
S Fwall=63024( 1IMEP ( kPa ) )( 1
A Fmol (100.0082 Toil (K ) ) B (m ) )Pest