Variable Property Modeling of of IC Engine Cycles

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Variable Property Modeling of of IC Engine Cycles

• P M V Subbarao
• Associate Professor
• Mechanical Engineering Department

Less Approximations will lead to better Blue
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Variable Property I.C. Engine Cycle

• Variable property analysis is more accurate
  analysis when compared to Air-standard cycle
  analysis.
• An accurate representation of constituents of
  working fluid is considered.
• More accurate models are used for properties of
  each constituents.

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SI Engine Cycle vs Thermodynamic Otto Cycle
FUEL
A I R
Ignition
Fuel/Air Mixture
Combustion Products
Actual Cycle
Intake Stroke
Compression Stroke
Power Stroke
Exhaust Stroke
Qin
Qout
Air
Otto Cycle
TC
BC
Compression Process
Const volume heat addition Process
Expansion Process
Const volume heat rejection Process
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Actual SI Engine cycle
Ignition
TC
BC
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Air-Standard Otto cycle
Process 1? 2 Isentropic compression Process 2
? 3 Constant volume heat addition Process 3 ? 4
Isentropic expansion Process 4 ? 1 Constant
volume heat rejection
Compression ratio
Qin
Qout
TC
v2 TC
v1 BC
BC
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Early CI Engine Cycle and the Thermodynamic
Diesel Cycle
Fuel injected at TC
A I R
Air
Combustion Products
Actual Cycle
Intake Stroke
Compression Stroke
Power Stroke
Exhaust Stroke
Qin
Qout
Air
Diesel Cycle
BC
Compression Process
Const pressure heat addition Process
Expansion Process
Const volume heat rejection Process
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Thermodynamic Cycles for CI engines

• In early CI engines the fuel was injected when
  the piston reached TC
• and thus combustion lasted well into the
  expansion stroke.
• In modern engines the fuel is injected before TC
  (about 15o)

Fuel injection starts
Fuel injection starts
Early CI engine
Modern CI engine

• The combustion process in the early CI engines
  is best approximated by
• a constant pressure heat addition process ?
  Diesel Cycle
• The combustion process in the modern CI engines
  is best approximated
• by a combination of constant volume and constant
  pressure ? Dual Cycle

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Air-Standard Diesel cycle
Process 1? 2 Isentropic compression Process 2
? 3 Constant pressure heat addition Process 3 ?
4 Isentropic expansion Process 4 ? 1 Constant
volume heat rejection
Cut-off ratio
Qin
Qout
v2 TC
TC
BC
v1 BC
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First Law Analysis Transient Compression of
Control Mass
Compression Process
SI Engine
CI Engine
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Compression Process
Parameters that require Process Rate model
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Isentropic Compression Process Control mass
Variable Property Single Fluid
0
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Ideal Gas Model
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Properties of Gases
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g
cp
cv
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Properties of Fuels
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Isentropic Compression Variable Property Model
T
For a small compression ratio
s
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Geometrical Details of Cylinder and Piston Motion
Compression Ratio, rc
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Cylinder Volume at any Crank Angle
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S(q)
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Isentropic Compression Variable Property Model
T
For a small compression ratio
s
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Explicit Method
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Pressure Profile During Compression
Ideal Gas Model
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Initial Conditions
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Engine Respiratory System
Pexh,cyl
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Exhaust Valve Operation Schedule
Pcyl
Patm
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Inlet Valve Operation Schedule
Pcyl
Patm
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Cylinder Pressure Diagram
Aintake
Aexhaust
Pcyl
q
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Work Required for Compression
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Global Isentropic Compression Process
The overall isentropic process between states 1
2
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Basics of Combustion
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23 Complete combustion at constant volume
0
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23 Complete combustion at constant volume
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23 Complete Finite Duration combustion
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Finite Heat Release
A typical heat release curve consists of an
initial spark ignition phase, followed by a rapid
burning phase and ends with burning completion
phase
.99
The curve asymptotically approaches 1 so the end
of combustion is defined by an arbitrary limit,
such as 90 or 99 complete combustion where xb
0.90 or 0.99 corresponding values for efficiency
factor a are 2.3 and 4.6 The rate of heat
release as a function of crank angle is
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Ideal gas model
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3 ? 4 Isentropic Expansion





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Isentropic Expansion Variable Property Model
T
For a small compression ratio
s
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Explicit Method
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Pressure Profile During Expansion
Ideal Gas Model
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Work Delivered during Expansion
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Global Isentropic Expansion Process
The overall isentropic process between states 3
4
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Constant Volume Heat Removal
0
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41 Complete Cooling at constant volume
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41 Complete Finite Duration Cooling
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Surface Area for Cooling
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The Cyclic Integral
k1for two-stroke cycle k2for four-stroke cycle