Dimension Reduction of Combustion Chemistry

Zhuyin (Laniu) RenS. B. Pope

Mar. 29th, 2005

Outline

Motivation

Advantage of dimension reduction combined with ISAT in CFD simulation

Dimension reduction of combustion chemistry

Pre-image curve method

Motivation

Knowledge of detailed mechanismContinually increasing in accuracy and scope

50 – 1000 species in detailed description

Use in computations of combustionDNS, LES, PDF and other approaches

Need general methodology toReduce the computational costRetain accuracy and adequate detail

Reduce the computational cost by using dimensionreduction combined with ISAT

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)

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!

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 reductionError in dimension reduction (in species reconstruction part) is crucial

to this methodology.Develop more accurate method to do the dimension reduction!!

Represent combustion chemistry in terms of reduced composition r (nr) (e.g. major species ) instead of the full composition φ(nφ) (e.g. full species)

Dimension Reduction of combustion chemistry

1: Unimportant species and reactions in the detailed mechanism2: Large range of chemical time scales

)(S

dt

d

Dimension Reduction of combustion chemistry

PRF: Primary Reference Fuel; mixture of Heptanes and Octane ---1034 species; 4236 reactionsGreat potential for dimension reduction

--1d-5 sec--1d-6 sec--1d-7 sec

Existing Dimension Reduction methods

Skeletal mechanism 1Quasi-steady state assumptions (QSSA) 2Intrinsic low-dimensional manifolds (ILDM) 2Rate-controlled constrained equilibrium (RCCE) 2Trajectory-generated low-dimensional manifold 2

Flamelet generated manifolds (FGM) 2Roussel & Fraser algorithm (RF) 2Pre-Image Curves 2

General procedure of dimension reduction of combustion chemistry:

Step 1: Detailed mechanism => Skeletal mechanism (Small detailed mechanism) Step 2: Further reduction based on time scale analysis

Evaluation of existing methods

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

Accuracy (very important)Easy to generate and use

Dimension Reduction (Geometric Picture)

Represent combustion chemistry in terms of reduced composition r (nr) instead of the full composition φ(nφ)

Impose nu= nφ-nr conditions which determine the manifold φm; ----i.e., given a reduced composition r, provide a procedure to determine the corresponding full composition on the manifold φm (Species reconstruction)

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)

Pre-Image Curves

Sketch of reaction trajectories in the pre-image manifold MP.

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”

How to generate the Pre-Image Curves?

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

Dimension reduction by Pre-Image Curves method

Trajectories colored by dimension Reconstructed 1-dimension manifold (blue dashed line)

Pre-image Curves Performance- Comparison with QSSA and RCCE

QSSA: Q10, Q12

RCCE: R4, R6

Pre-image curve: B4, B6

Normalized errors in Pre-Image Curve are less than those in RCCE and QSSA

Normalized error in reconstructed species at different temperatures during autoignition.

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