Optimisation of Fuels for Future Engine Technologies via Mixture Inhomogeneity Modelling

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Optimisation of Fuels for Future Engine
Technologies via Mixture Inhomogeneity Modelling

• Neal Morgan
• Tuesday 13th March 2007

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Outline

• The problems at hand
• Modelling approach
• Future work

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Future Engine Technologies

• Future engines - both CI and SI -are heading in
  the direction of

• Direct Injection
• Partial Premixing

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What is the problem?

• The mixture inhomogeneity can be both beneficial
  and detrimental
• Some inhomogeneity is important to the
  autoignition of resistant fuels (high RON)
• Too much inhomogeneity can lead to unacceptable
  levels of soot and NOx

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Where do we start?

• Modelling this system requires both
• An ability to simulate the turbulent mixing and
  inherent inhomogeneity.
• An ability to simulate the chemistry accurately
• A detailed mechanism able to recreate the
  ignition behaviour of real fuels

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Modelling turbulent combustion

• Various models exist to simulate closed volume
  combustion

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There is another way

• The Probability Distribution Function (PDF) based
  Stochastic Reactor Model (SRM) is a 4th way to
  simulate the turbulent mixing and combustion.
• Local quantities (xi, T) are considered as random
  variables
• Joint scalar PDF, F(?1, , ?s1t)
• PDF model

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The SRM algorithm
Initialise N particles at time t t0
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The Mechanism

• Before we can use the SRM however, we require
  accurate and relatively small chemical mechanisms
  to model real fuels.
• Detailed PRF mechanisms exist, but PRF does not
  reflect the true nature of actual fuels.
• The Toluene Reference Fuel (TRF) mechanism
  developed by Johan Andrae goes some way to
  redressing this balance.

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The big problem

• TRF mechanism contains 1500 of species and 5000
  of reactions.
• Can we make the calculations easier?
• Use a reaction flux analysis to determine
  important species.
• Reject unimportant species and all reactions that
  involve them.

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DRG Reduction
Starting detailed reaction mechanism N species,
M Reactions Initial starting list of species to
keep (Fuel species, Oxidiser) Accept/Reject
parameter, ?
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Optimising the parameters

• Chemical mechanisms are a set of ODEs which
  describe the trajectories of the concentrations
  of the chemical species.
• A reaction, i, proceeds with a rate constant ki,

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The statement (mathematically)
What we would like to find is a
physically-realistic, optimal set of rate
parameters, Popt over all reactions, J,
Such that the weighted sum of the squared errors
between the model and experimental observations,
over differing conditions, n,
Is a minimum
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Where do we go from here?

• Searching the parameter space is not a trivial
  matter
• There are 1000s of reactions
• Each reaction has up to three parameter to
  optimise
• Surely this is impossible then?
• Some reactions affect the simulations more than
  others so we focus on those
• Experimental observations place bounds on certain
  rate parameters - so we have a constrained
  optimisation problem.

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Modelling the model how very meta

• Response surface methodology (RSM) was invented
  by Box and Hunter (1951) to help with
  optimisation problems in chemical engineering
• One performs experiments in such a way to span
  sparsely the design space (the x values).
• A simple function (often a polynomial) is then
  fitted to the responses (the y values)
• The turning points of this function are then
  easily found and should be indicative of the true
  optima of the actual responses.

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Applying RSM to the TRF mechanism
Decide on variable to tune, the span of the
tuning and the number of numerical experiments to
perform
Decide on experimental data set to compare
results to
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Applying RSM to the TRF mechanism
The sensitive branching reaction C6H5CH2 O2 ?
C6H5 CH2O O Was added to the Toluene
mechanism subset in Andrae et al (2006)

• Its pre-exponential rate constant (A) tuned to a
  value of 6.32x1011 cm3mol-1s-1
• But is this its optimal value?

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Applying RSM to the TRF mechanism
Overall 343 simulations were performed resulting
in 49 error polynomials.

• Example plot
• pure Toluene
• ? 0.5,
• T 1211 K,
• P 44.4 atm.

Initial results for pure Toluene indicate a value
of 7.96x1011 cm3mol-1s-1(26 increase) would give
better results
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Future work

• Develop more automatic methods for parameter
  optimisation
• Apply method to reduced mechanisms for various
  conditions
• Use the SRM code to simulate different PCCI
  engine configurations

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Acknowledgements