Zhuyin Laniu Ren

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Dimension Reduction of Combustion Chemistry

• Zhuyin (Laniu) Ren
• S. B. Pope
• Mar. 29th, 2005

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Outline

• Motivation
• Advantage of dimension reduction combined with
  ISAT in CFD simulation
• Dimension reduction of combustion chemistry
• Pre-image curve method

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Motivation

• Knowledge of detailed mechanism
• Continually increasing in accuracy and scope
• 50 1000 species in detailed description
• Use in computations of combustion
• DNS, LES, PDF and other approaches
• Need general methodology to
• Reduce the computational cost
• Retain accuracy and adequate detail

Reduce the computational cost by using
dimension reduction combined with ISAT
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CFD/Full Chemistry/Direct Integration
Schematic of DI with full representation used in
the reaction fractional step of a CFD computation.
Computationally prohibitive with large detailed
mechanism (Both CPU/Memory)
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CFD/ Full Chemistry/ISAT
Schematic of ISAT with full representation used
in the reaction fractional step of a CFD
computation.

• Computationally much less expensive (100-1000
  fast than previous approach)
• Memory issue!

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CFD/Dimension Reduction (via Species
Reconstruction)/ISAT
Schematic of ISAT with dimension reduction (via
species reduction and reconstruction) used in
the reaction fractional step of a CFD computation.

• Use only the major species both in CFD and ISAT
  (Both speed up the CFD part and ISAT retrieval
  solve memory issue )
• ISAT allows more expensive procedure to do the
  dimension reduction
• Error in dimension reduction (in species
  reconstruction part) is crucial to this
  methodology.
• Develop more accurate method to do the dimension
  reduction!!

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Dimension Reduction of combustion chemistry
Represent combustion chemistry in terms of
reduced composition r (nr) (e.g. major species )
instead of the full composition f(nf) (e.g. full
species)
1 Unimportant species and reactions in the
detailed mechanism 2 Large range of chemical
time scales
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Dimension Reduction of combustion chemistry
--1d-5 sec --1d-6 sec --1d-7 sec
PRF Primary Reference Fuel mixture of Heptanes
and Octane ---1034 species 4236
reactions Great potential for dimension reduction
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Existing Dimension Reduction methods

• Skeletal mechanism
  ?1
• Quasi-steady state assumptions (QSSA)
  ?2
• Intrinsic low-dimensional manifolds (ILDM)
  ?2
• Rate-controlled constrained equilibrium (RCCE)
  ?2
• Trajectory-generated low-dimensional manifold
  ?2
• Flamelet generated manifolds (FGM)
  ?2
• Roussel Fraser algorithm (RF)
  ?2
• Pre-Image Curves
  ?2

General procedure of dimension reduction of
combustion chemistry Step 1 Detailed mechanism
gt Skeletal mechanism (Small detailed mechanism)
Step 2 Further reduction based on time scale
analysis
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Evaluation of existing methods

• Accuracy (very important)
• Easy to generate and use

• X Quasi-steady state assumptions (QSSA)
• ---difficult to choose QSSA species
  
• X Intrinsic low-dimensional manifolds (ILDM)
  
• X Rate-controlled constrained equilibrium
  (RCCE)
• ---difficult to choose constraints
• X Trajectory-generated low-dimensional
  manifold
• X Flamelet generated manifolds (FGM)
  
• X Roussel Fraser algorithm (RF)
• Pre-Image Curves
• ---Easy to choose the reduced composition
  while maintain the
• accuracy
• ---Reconstructed composition is
  independent of the reduced composition,
• fully determined by the chemical
  kinetics
  

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Dimension Reduction (Geometric Picture)

• Represent combustion chemistry in terms of
  reduced
• composition r (nr) instead of the full
  composition f(nf)
• Impose nu nf-nr conditions which determine the
  manifold fm
• ----i.e., given a reduced composition r,
  provide a procedure to
• determine the corresponding full
  composition on the
• manifold fm (Species reconstruction)
  

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Pre-Image Curves (Ideas)

• Use the fact that trajectories will be attracted
  to the low
• dimension attracting manifold
• Identify the corresponding composition point at
  the attracting
• manifold as the reconstructed composition.
  (Identify the
• attracting manifold)
• The reconstructed composition (manifold
  construction) is
• independent of the reduced composition r
• Give the reduced composition r, construct a curve
  (Pre-image
• curve) in the full composition space (the
  trajectories
• starting from this curve will have the same
  reduced composition at some positive time)

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Pre-Image Curves

• Assumption there is an attracting manifold
  (black line)
• Ideally, species reconstruction should identify
  point A
• A good approximation to point A can being
  obtained by following the reaction trajectory
  from a point such as I
• A suitable initial point I is achieved by
  generating a curve C in the pre-image manifold
  from a starting feasible point, denoted by O

Sketch of reaction trajectories in the pre-image
manifold MP.
How to generate the Pre-Image Curves?
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Pre-Image Curves (Current Status)

• Have identified the tangent space of the
  pre-image manifold
• Have formulated different ways to construct the
  pre-image curves
• Have understood the method itself to some extent
• Plan to do a PaSR simulation to solve the
  embarrassment

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Dimension reduction by Pre-Image Curves method
Trajectories colored by dimension
Reconstructed 1-dimension manifold (blue dashed
line)
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Pre-image Curves Performance- Comparison with
QSSA and RCCE
QSSA Q10, Q12 RCCE R4, R6 Pre-image curve B4,
B6
Normalized error in reconstructed species at
different temperatures during autoignition.
Normalized errors in Pre-Image Curve are less
than those in RCCE and QSSA
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Conclusion

• Dimension reduction of combustion chemistry is
  crucial
• and promising in numerical simulation of
  combustion
• process with complicated fuels.
• Developing new method with great accuracy
• Combining dimension reduction with ISAT in
  simulations