Auto Ignition, Premixed

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Auto Ignition, Premixed Diffusive Combustion in
CI Engines

• P M V Subbarao
• Professor
• Mechanical Engineering Department

Prediction of Combustion Zones.
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Four Stages of Combustion in CI Engines
10
30
-10
TC
-20
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Auto-Ignition

• One of the main issues in design of combustion
  systems for CI engine is to estimate the location
  and timing of auto-ignition that should take
  place in stratified-mixture conditions.
• A detailed chemistry-based auto-ignition analysis
  including low temperature phenomena is to be used
  to compute a local reaction rate of fuel.
• The premixed combustion mode is to be analyzed
  assuming that the reaction mechanism, which
  controls premixed combustion.

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Auto Ignition Premixed Combustion

• In DI Diesel engines, an equivalence ratio
  gradient exists across the spray volume.
• There exist a non-linear dependency for the
  reaction rate of fuel on equivalence ratio.
• The equivalence ratio distribution, which
  develops in the surrounding gas, must be
  considered to correctly estimate the rate of heat
  release by premixed combustion.
• The mean reaction rate of fuel is evaluated by an
  approach based on the determination of the
  Probability Density Function of the mixture
  fraction, Z? 0,1.

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Combustion Model

• A phenomenological diesel combustion model is
  composed of several sub models for fuel spray and
  combustion.
• Fuel spray model Spray penetration,
  Air-entrainment model, and Droplet evaporation
  model.

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Multi Zone Model for Spray at Ith Time Step
where p and T represent thpressure in MPa and the
temperature in K in the cylinder. The
equivalence ratio, ?j, is for the given element,
i. The constants are chosen to be Cr0.015
0.025, n -2.0 -- -3.0 and m -1.02 -- -1.06.
The activation temperature, Ea/R, is 3500K --
4500K.

• The ignition delay for the j-th element of the
  spray is expressed in seconds as

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Occurrence of Ignition delay

• It is assumed that ignition occurs when the
  following condition is satisfied.

The integral expression accounts for the
variation of pressure and temperature during the
ignition delay. The suffix, inj and ig, denote
the timing of fuel injection and ignition,
respectively.
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Premixed combustion

• It is assumed that the rate of premixed
  combustion is proportional to the mass of the
  fuel-air mixture prepared during the ignition
  delay period and given as

where ? is the Taylor microscale and Sl is the
laminar flame speed. Mmix,j is the mass of the
fuel-air mixture in the given element. Cp is an
arbitrary tuning constant determined to (0.002
to 0.005) to match the test bed data.
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The Taylor microscale

• The Taylor microscale is given as

where u' is the rmms value of turbulent
fluctuation velocity, L is the integral length
scale, and ? is the kinematic viscosity. The
constant, A, is set to be close to unity. The
integral length scale is given as
where the constant, Cv, is in the range of 0.06
0.12.
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Diffusion combustion

• Fuel-air mixing is the dominant mechanism to
  determine the rate of combustion during the
  diffusion combustion period.

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• The turbulent mixing time scale is introduced to
  represent the rate of fuel-air mixing as,

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• where mb and me are the masses of burned fuel
  and entrained air in the element.
• The time scales, ?c and ?ca, denote the mixing
  time and the time corresponding to one degree
  crank angle.
• The arbitrary tuning constant, Ce, is chosen here
  to be 3.0 -- 5.0 X 10-5 to match the test bed
  data.

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Post Injection Combustion

• The models during the fuel injection period may
  not be applicable after the end of fuel injection
  for the spray detached from the nozzle and moving
  downstream.
• The in-cylinder flow effects need to be
  considered to predict the combustion after the
  end of fuel injection.
• This is described as a mixing process with the
  available air at a rate controlled by turbulence
  in the fuel jet as,

where mea is the total mass of unused air in the
cylinder. The constant, Ce,a, is determined from
the continuity of the combustion rate at the end
of fuel injection.
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Fuel Energy Distribution

• Around 35 of the total chemical energy that
  enters an engine is converted to useful
  crankshaft work.
• About 30 of the fuel energy is carried away from
  the engine in the exhaust flow in the form of
  enthalpy and chemical energy.
• About one-third of the total energy is dissipated
  to the surroundings by some mode of heat
  transfer.

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Distribution of Fuel Power
Speed, RPM