Multiphysics Model of Diesel Injector Deposit Formation.

Richard H. WestAmrit JalanWilliam H. GreenRiccardo Rausa

Massachusetts Institute of Technology

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Deposits form on diesel fuel injectors, blocking the nozzles

More efficient engines and less pollution → smaller nozzles

Smaller nozzles → deposit more problematic

Leedham et al. (Infineum UK) SAE 2004-01-2935

Fuel additives is big busine$$!

Nobody understands the deposit-forming process.

Current development is based on expensive engine tests.

bp.combp.com

Dirty and clean injector nozzles, from BP Ultimate Diesel advertisement

We want a predictive model of deposit formation.

Aim to gain insight into the effect of

•different conditions

•different fuels and fuel blends

•different detergents

Model system of interest:a thin film of fuel, evaporating.

evaporating film

vapor diffusion

Oxygen diffuses into the fuel from the air.

O2 diffusion

evaporating film

vapor diffusion

Free-radical autoxidation reactions gradually oxidize the fuel.

chemical reaction

O2 diffusion

evaporating film

vapor diffusion

Over time the reaction continues; the diesel becomes more oxidized.

chemical reaction

O2 diffusion

evaporating film

vapor diffusion

Heavily oxidized reaction products are insoluble in non-polar diesel & phase separate.

chemical reaction

O2 diffusion

evaporating film

vapor diffusion

insolubleoxygenates

This polar oxygenate phase forms the deposit.

chemical reaction

O2 diffusion

evaporating film

vapor diffusion

insolubleoxygenates

deposit

Fuel injections wash the walls

speciesdiffusion

fresh diesel

insoluble oxygenates

Model overview: React & evaporate, equilibrate, wash, replenish...

chemical reaction

O2 diffusion

evaporating film

vapor diffusion

partially oxidizeddiesel

diesel

partially washeddiesel

insoluble oxygenates

phase equilibrationand separation

washing with clean dieseladd fresh diesel toreplace evaporated

Chemistry depends on starting species

Diesel contains thousands of species.

Choose simple mixture to represent surrogate diesel.

chemical reaction

Oxidation is driven by free-radical chain reactions

O OH

O OHO OO O

Oxidation is driven by free-radical chain reactions

O OH

O OHO O

O OOO O

OOO

Oxidation is driven by free-radical chain reactions

O OH

O OHO O

O OOO O

O

OO

OOH

HOO

HOO

O O

Oxidation is driven by free-radical chain reactions

O O HO OH

O O

O OOO O

O

OO

OOH

HOO

HOOO O

OH

O

OO

OH

OOO

OH

OOO

O O

Oxidation is driven by free-radical chain reactions

O O HO OH

O O

O OOO O

O

OO

OOH

HOO

O OHOO

OH

O

OO

OH

OOO

OH

OOO

OH

O

OO H

O

OHO

OHOH

H

O O

Oxidation is driven by free-radical chain reactions

HO O

O OOO O

O

OO

OOH

HOO

O OHOO

OH

O

OO

OH

OOO

OH

OOO

OH

O

OO H

O

OHO

OH

OH OH H2O

Detailed kinetic modeling is complex

Estimating all the reactions is tedious and error prone.

Detailed kinetic modeling is complex

Estimating all the reactions is tedious and error prone.

Teach the chemistry to a computer!

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Reaction Mechanism Generator

•free and open source software

•version 3.3 released in February

Reaction families propose all possible reactions with given chemical species

bond breaking and hydrogen abstraction

intramolecularH-abstraction

Reaction families propose all possible reactions with given chemical species

Octane autoxidation has many pathways

Detailed kinetic modeling is complex

For each chemical reaction

we need:

•forward rate coefficient

•equilibrium constant

k f = A exp�−EaRT

�

∆G = ∆H − T∆S

k f

kr= Keq = exp

�−∆G

RT

�

A + B � C + D

r = k f [A][B]

We can estimate thermochemistry of solvation from the molecular structure of the solute

Molecular structure

Platts’ group contributions

Solute parameters

Solvent parameters

Abraham’s method

Partition coefficient,K K=exp(-∆G/RT) ∆G

solvation

Mintz modelfor alkanes ∆H

solvation

∆G=∆H-T∆S∆S solvation

RMG group contributions

gas phase H(T), S(T)

See (551d) “Progress towards Capturing Solvent Effects In Automatic Mechanism Generation”Amrit Jalan, Richard H. West and William H. Green. Reaction Path Analysis II, Wednesday, 1:30pm

RMG with solution-phase corrections was used to study autoxidation of surrogate diesel

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Current model contains 252 species and 5185 reactions.

•n-decylbenzene is most reactive componentand dominates kinetics

22/02/2009 5:23PM_rp_svg2.html

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chemical reaction

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Model overview: React & evaporate, equilibrate, wash, replenish...

chemical reaction

O2 diffusion

evaporating film

vapor diffusion

partially oxidizeddiesel

diesel

partially washeddiesel

insoluble oxygenates

phase equilibrationand separation

washing with clean dieseladd fresh diesel toreplace evaporated

Evaporation

•Abraham model gives gas/solvent concentration ratio

•Diffusivity estimated from molecular structure

O2 diffusion

evaporating film

vapor diffusion

Fuller, Schettler, Giddings. I&EC, 58, 1966.

HOO

HOO

HO

O

Model overview: React & evaporate, equilibrate, wash, replenish...

chemical reaction

O2 diffusion

evaporating film

vapor diffusion

partially oxidizeddiesel

diesel

partially washeddiesel

insoluble oxygenates

phase equilibrationand separation

washing with clean dieseladd fresh diesel toreplace evaporated

Abraham’s Method predicts partition coefficients for different solutes and solvents

Solute parameters

Solvent parameters

Abraham’s method

Partition coefficient, K

log K= c + eE + sS + aA + bB +log K= c + eE + sS + aA + bB +

/solvent partitioning

lL

gas /solvent partitioning

Abraham’s Method predicts partition coefficients for different solutes and solvents

Solute parameters

Solvent parameters

Abraham’s method

Partition coefficient, K

log K= c + eE + sS + aA + bB +

log K= c + eE + sS + aA + bB +

/solvent partitioning

vV

lL

gas

/solvent partitioningsolvent

Model overview: React & evaporate, equilibrate, wash, replenish...

chemical reaction

O2 diffusion

evaporating film

vapor diffusion

partially oxidizeddiesel

diesel

partially washeddiesel

insoluble oxygenates

phase equilibrationand separation

washing with clean dieseladd fresh diesel toreplace evaporated

Washing is mass transfer problem

Look up a correlation in Perry’s Handbook:

TABLE 5-19 Mass-Transfer Correlations for Flow in Pipes and Ducts—Transfer Is from Wall to Fluid. W: Tubes, turbulent, smooth tubes, constant surface concentration

NSh,avg =k�avgdt

DNSc =

µ

ρD NRe =ρubulk dt

µ

NSh,avg =0.0097N9/10

Re N1/2Sc

�1.10 + 0.44N−1/3

Sc − 0.70N−1/6Sc

�

1 + 0.064N1/2Sc

�1.10 + 0.44N−1/3

Sc − 0.70N−1/6Sc

�

Current model overview:React, equilibrate, wash, replenish...

chemical reaction

O2 diffusion

evaporating film

vapor diffusion

partially oxidizeddiesel

diesel

partially washeddiesel

insoluble oxygenates

phase equilibrationand separation

washing with clean dieseladd fresh diesel toreplace evaporated

Implementation

•Python: chosen for speed of development.

•PyDAS: Python interface to Fortran DAE solver DASSL.

•Cython: gives orders of magnitude reduction in CPU time.

•Parallel computing: simple use of array jobs.

Python chosen for speed of development.

•General-purpose, high-level programming language.

•Free, open-source, extensible.

•Easy to learn.

•Fast (and fun) to develop in.

•Multi-paradigm programming language,but this project mostly object-oriented.

PyDAS created to access specialized ODE solvers from Python code.

•Chemical reactions → very stiff systems of differential equations → require specialized ODE solvers.

•VODE (provided by SciPy) is not always robust enough.

•Fortran-based DASSL (Petzold, 1982) is a stiff DAE solver widely used in kinetic modeling.

•Python interface to DASSL developed and released:

https://github.com/jwallen/PyDAS

Cython used to speed up the slow partsby orders of magnitude.

•Develop your code in Python

•Identify the slow parts by profiling (right hand side of ODE)

•Add some static type declarations (“cdef double x”)

•Compile to C using Cython

•50x speed up in overall computation time!

Parameters:

•Reaction T

•Phase separation T

•Nozzle diameter

•Nozzle length

•Film thickness

•Injection velocity

•Injection duration

•Reaction time

Running simulations with different parameters gives a variety of results.

chemical reaction

Parallel computing is easy and useful for parameter studies and sensitivity analysis.

Head Server

Compute nodes

submit jobs 1-1000 run job 3

run job 4...

•Use cluster’s queuing system for “array” jobs.

•Your code translates job number into set of parameters:

•Random (Uniform Distribution)

•Global Sensitivity Analysis (Modified Morris Method)

run job 1

run job 2

Simulate with parameter

set 1Simulate

with parameter set 2

Simulate with parameter

set 3

Global Sensitivity Analysis identifies most significant model parameters.

•Identifies sub-models needing refinement.

•Guides laboratory experiments.

•Gives insight to underlying processes.

Acknowledgements

•Project collaborators at MIT:

Amrit Jalan and Prof. William Green (ChE)Yinchun Wang and Prof. Wai Cheng (MechE)

•RMG developers:

•Industrial sponsors:

Eni S.p.A.

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Multiscale, multiphysics model gives insight into

•chemical reactions

•evaporation

•phase separation

•washing

Computational experiments reveal important parameters

•guide model development

•guide experiments

Contributions to industrial problem of deposit formation in diesel fuel injectors:

chemical reaction

OH

O

OO H

Suggestions for multi-scale modeling ofother chemical engineering systems.

•Build detailed kinetic model to capture complicated T,P-dependence of real chemistry (RMG).

•Write software in Python: easy, fast, pleasant to write.

•Use specialized DAE solvers when necessary (PyDAS).

•Use Cython to speed up the slow parts.

•Use parallel computing environment for Global Sensitivity Analysis (eg. modified Morris method)

•Identify sensitive parameters, then refine models and experiments accordingly.

Massachusetts Institute of Technology

Any questions?r.west@northeastern.edu