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Combustione turbolenta edemissioni

Alessio FrassoldatiDip. CMIC – Politecnico di Milano

Corso di Dottorato congiunto Polimi-Federico II Chimica e fluidodinamica della combustione

Anacapri: 5-9 Ottobre 2009

Combustione turbolenta ed emissioni 2

Outline

1. Introduction: interactions between turbulence and chemistry

2. Numerical modeling of nitrogen oxides formation in turbulent flames: Kinetic Post Processor

4. Numerical modeling of soot formation in turbulent non premixed flames

5. Conclusions

3. Application examples


Emissions regulations

Increasingly stringent regulations for Pollutant emissions

in furnaces, power plants, gas turbines, burners etc.

Global NOx levels - SCIAMACHY satellite in 2004.


NOx regulations and targets for 2020


C 2H6

C 2H5

C 2H4

C 2H3

C 2H2

Aromatics

Soot

Pyrolysis

O2

CH i

O2

OH

Oxidation

CH 3OOH

CH 3OH

CH 2OH

CH 3OO

CH 3

CH 3O

CH 2O

HCO

CO

CO 2

CH 4

CH4 + 2O2 →→→→ CO2 + 2 H2O

NOx

O2 + N2

Combustion: a complex chemical process

Huge number of reactions and different timescales

time [s]

norm

aliz

ed m

ass

fra

ctio

n


SOxSOx

......

nC7-iC8nC7-iC8

C6C6

C3C3

C2C2

CH4CH4

COCO

H2-O2H2-O2

NOxNOx

SootSoot

PAHPAH

Chlorinatedspecies

Chlorinatedspecies

Kinetic mechanism includes hydrocarbons up to Diesel

and jet fuels as well as several pollutants

- Hierachy

- Modularity

- Generality

Detailed kinetic mechanism of combustion

~ 400 species

~ 12000 reactions

http://www.chem.polimi.it/CRECKModeling/


NOx formation chemically controlled

NOx in a laminar premixed flame H2

(Warnatz, 1981)

10

100

1000

0.25 0.35xH2

pp

m N

Ox

Equilibrium


NON2H OH O2O

O N NO N

N O NO O

N OH NO H

+ → ++ → ++ → +

2

2

Thermal NO

High T High ττττ λλλλ > 1

HCN NCO NH N

CH

CH2

O H

H

OH

O2

CH N HCN N

CH N HCN NH

C N CN N

+ → ++ → +

+ → +

2

2 2

2

Prompt NO

Low T Low ττττ λλλλ < 1

NH2 OHH

OH HNH3

Fuel N

OHO2

CNH2

NO

NO

Reduction Mechanism:Reburning

N2O

O OH

N2O MechanismN2 + O → N2O

High P λλλλ>>1

NOx Formation kinetics


Reduction Mechanism:Reburning

Reburning mechanism

HCN

NO

O NO

NO

NO

H

H O

H

O

H

HCCO

HCCO

NO

N2

HCNO HNCO

NCO N2O

NH

N

NH2

CH3

OOH

H

CH3CN CH2CN CN


• Flame temperature

• Air excess

• Amount of nitrogen chemically bound in the fuel (FUEL NOX)

• Residence times (at high temperatures)

NOx Formation controlled by


Air excess (1/Φ)

NO

x

T

1

Rich Conditions

Lean conditions

Lawconstraints

T and ΦΦΦΦ effect on NOx formation


Fuel andPrimary Air

SecondaryAir

heightFuel andPrimary Air

SecondaryAir

Oxidizing zone (OFA)

Rich flame

Air staging technique


height

Primary Fueland Air

SecondaryAir

Secondary Fuel

Primary Fueland Air

SecondaryAir Secondary

Fuel

Oxidizing zone (OFA)

Reducing zone

Stoichiometric flame

Reburning technique


Pollutant formation in turbulent flames

Chemistry

Slow chemistry

Finite-ratechemistry

Fast chemistry

Fluid-dynamics

Kolmogorovlenght

Meanresidence time

ττττ (s)

103

100

102

101

10-1

10-4

10-2

10-3

10-5

10-8

10-6

10-7

10-9

NOx

SootPAH

CO

Mixed -Burned

Perfectmixing

Adapted from: R. Fox , “Computational models for turbulent reacting flows”, Cambridge University Press

(2002)

For PAH and soot the decoupling between chemistry and fluid

dynamics is not possible

time [s]

norm

aliz

ed m

ass

frac

tion

Turbulence-kinetics interactions


Accurate predictions of pollutant emissions from turbulent flames require simplified approaches, specifically conceived for each class of pollutant species, according to

the characteristic times of its chemistry

Combustion model

Finite rate chemistry: PAH and soot

Fast chemistry: CO Slow chemistry: NOx

Mixed-burned approach

Eddy-Dissipation (EDC)

Steady Laminar Flamelet Model

(SLFM)

The numerical modeling of PAH and soot formation

requires very detailed kinetic schemes

Soot has a strong influence on the thermal field in a flame

and must be correctly predicted

The interactions between turbulence and chemistry appear stronger than for other pollutant species

Kinetic Post-Processing

procedure (KinPP): decoupling between fluid-dynamics and

chemistry

Numerical modeling of pollutant formation


C2H4 Air

Products

Perfectly stirred reactor

Fast chemistry: CO

T

t

T

t'T T T= +

T

t

T

t'T T T= +T T T '= +

temperature [K]equivalence ratio

CO

mol

e fr

actio

n

cycle number

mol

e fr

actio

n

Steady value

Effects of fluctuations: CO



soot

vol

ume

frac

tion

[ppm

]


NO

mol

e fr

actio

n

Slow chemistry:NO

cycle number

mol

e fr

actio

n

Finite-rate chemistry: Soot

cycle number

volu

me

frac

tion

Steady value

Steady value

Effects of fluctuations: NO and Soot



mean temperature [K]

volu

me

frac

tion

Fast chemistry: CO


mol

e fr

actio

nSlow chemistry:NO


mol

e fr

actio

n

0 0.5 1 1.5 2 2.5 30.0E+000

5.0E-008

1.0E-007

1.5E-007

2.0E-007

2.5E-007

3.0E-007

cycle number

volu

me

frac

tion

quasi-stationary

100 Hz

10 Hz

cycle number

volu

me

frac

tion


Effects of fluctuations: NO and Soot


Pollutants emissions (NOx): modeling review

Different levels of detail are possible:

There are currently several techniques used in practice to predict the emissions from real combustors.

They fall into three general categories:

• Empirical and semi-empirical models

• Simplified physics-based models

• Detailed models

Each method has strengths and weaknesses and will be briefly discussed


Empirical models are very simple and the least computationally intensive.

Require empirically determined constants and are useful for correlating known historical NOx emissions for a specific combustor.

1-Empirical models

Since empirical models are generated from fitting a certain number of constants using historical data, they cannot be expected to perform well when the combustor undergoes a design change.

[D.L. Allaire – Thesis, MIT, 2006]


2-Simplified Physics-based models

D.L. Allaire - MIT

Primary zone modeled using 16 parallel PSRs

PFR for other zones



D.L. Allaire - MIT

Problem: it is necessary to define parameters: Primary zone Unmixedness, Temperature and dimensions of the PFRs

It represent the level of mixing between fuel and air in the primary zone

Sensitivity of the results to this parameter -> tuned using experimental data obtained in some operating conditions

Only CO and NO



A similar approach is used by Visser and Kluiters at NLR to model gas turbine performances and emissions. Multi reactor 1D model (typically 3 reactors for conventional combustors)

Visser and Kluiters NLR-TP-98629

• Mixing is assumed to occur instantaneously (PSR)

• Air flow split between zones (reactors)( based on estimates or CFD modeling)

• Semi-empirical models for kinetics. Use of “Temperature tuning factors”

=>Need to improve the model for CO, UHC, Soot and remove 1D model limitations such as the effects of film cooling


3-Detailed models

• CFD model but simplified kinetics

• Only Thermal NOx formation

• NOx emission index as a function of inlet air temperature

• NOx underestimated due to the exclusion of the N2O and prompt NOx mechanism


Chemistry

Slow chemistry


Fast chemistry

Fluid-dynamics

Kolmogorovscale

Meanresidence

time

ττττ(s)

103

100

102

101

10-1

10-4

10-2

10-3

10-5

10-8

10-6

10-7

10-9

NOx

Soot

CO

Mixed - Burned

Perfect mixing

It is still unfeasible to directly couple fluid dynamics and detailed kinetic

Pollutant species (such as NOx) affect only marginally

the main combustion process and consequently do not influence the overall temperature and flow field

The prediction of pollutant species (NOx) can be decoupled from the

CFD simulation

Kinetic Post Processor (KinPP)

NOx => Kinetic Post Processor


The problem:CPU time in CFD ∝ N 2Species or N 3Species

Memory used in CFD ∝ N Species

⇒ Kinetic mechanisms adopted in CFD simulations of industrial interest (3D) refer to a few chemical species

But:Chemical kinetics is absolutely necessary to predict pollutant formation (ppm or ppb)

⇒ Detailed mechanisms have to be adopted

Good news: Pollutants are present in traces and (generally) do not influence the velocity and temperature fields

⇒ Emission predictions (NOx) can be de-coupled from CFD computation

⇒ Kinetic Post Processor (KPP)

Faravelli, T., Frassoldati, A., Ranzi, E., Comb Flame, 135:97 (2003)

3-Detailed models: KPP


Kinetic Post Processor: advantages

The Kinetic Post-processor:�assumes the temperature and flow fields as predicted by the CFD.

�solves mass balances in the cells with detailed chemistry at fixed temperature. Each cell is a PSR reactor.

Advantages over direct coupling of CFD and Detailed Kinetics

� possibility to group several cells. Clustering equivalent cells reduces the dimensions of the problem.

� fix the temperature inside the cells. This reduces the high non linearity of the system, mainly related to the reaction rates and to the coupling between mass and energy balances.


µ= − ⋅ ∇ωr

ti i

t

JSc

Diffusion flux due to concentration gradientsand velocity fluctuations of the turbulent flow

ConvectionChemicalreactionsDiffusion

Turbulentdiffusion

ConvectiveTransport

1 1

0ω ω ν= =

⋅ − ⋅ + + ⋅ ⋅ + = ∑ ∑*,

Ns Nrin outi i i n n i ij j i

n j

W W J S V M r S

Mass balance for a single reactor

Non linear system of equations

Number of equations: Nspecies x Nreactors

1 4

22 13λ λ

νεγ γ = ⋅ =

/

* .V Vk

The effective volume V* available for chemical reactions is evaluated according

to the EDC model

Reactor network

EvaporationDevolatilization


T

t

T

t'T T T= +

T

t

T

t'T T T= +T T T '= +

Expanding the mean reaction rate as a Taylor series(8th order) and assuming sinusoidal fluctuations:

The correction coefficient is significantly > 1 for high activation energies (Thermal NOx )

22 2 2 1 2 2

2

2 11

4

( ) '( ) ...

= ( ) ( )C k

R R ERT E T Tk k T

TR

k T C k T

β β β− − − + ⋅ − + = ⋅ + ⋅ + =

⋅ =

Rate constant is highly non linear function oftemperature

( ) exp attEk T A T

RTβ = ⋅ ⋅ −

The kinetic correction coefficient

fluctuation amplitude

corr

ectio

n co

effic

ient

Cc

corr

ectio

n co

effic

ient

Cc



corr

ectio

n co

effic

ient

Cc


corr

ectio

n co

effic

ient

Cc

Comparison with β-PDF

A. Cuoci, A. Frassoldati, G. Buzzi Ferraris, T. Fara velli, E. Ranzi, “The ignition, combustion and flame structure of carbon monoxide/hydrogen mixtures. Note 2: Fluid dynamics and kinetic aspects of syngascombustion”, International Journal of Hydrogen Energy, 32 (2007), pp. 3486-3500


The fluctuations of concentration have a small effect on the mean reaction rate if compared to the temperature fluctuations, especially for reactions with large activation energy

= −

n 2aER AT exp c

RT

Second-order reaction

Concentration fluctuations


The numerical problem

See Manca, Buzzi-Ferraris, Frassoldati, Cuoci, “The solution of very large non-linearalgebraic systems”, Computers and Chemical Engineering, 2009

Boolean structure of the Jacobian matrixof the NLS for a simple structured 2D

computational mesh (2500 cells);

zoom of the single diagonal block element describing the chemical species presence.

block dimension:Nspecies x Nspecies(106 x 106)


CFD Results ⇒ First guess solution

Newton’s method

OK

YesNo

Time integration (ODE)

Low residuals in all equationsYes

No

Global Newton’s method

OK

Yes NoTime integration (ODE)

Solution Low pollutant concentrations (ppm)Need of very low residuals (Newton’s method)

KPP: numerical solution of a large NLS

Local solution in each “reactor”

Global solution for all “reactors”


Convergence of the numerical method

Convergence behavior during the iterative solution and effect of the global Newton’s method.


CO / H2 / N2 Jet Flames 1

Unconfined turbulent jet flame in low-velocity coflow

Fuel composition:

40% CO, 30% H2, 30% N2

Fuel inlet velocity: ~ 45-76 m/s

Air Fuel

Computational domain

Non uniform, structured mesh

About 42000 cells (320x130)

High resolution in the region close to the inlets

Com

bust

ion

cham

ber

CFD Simulation details

CFD Code FLUENT 6.3.2

Space 2D Axial-Symmetric

Time Steady

Turbulence modeling Standard κ-ε turbulence model

Wall treatment Standard wall functions

Radiation Discrete Ordinate Model

Solver Segregated implicit solver

Spatial resolution Second-Order Upwind scheme

Pressure Interpolation PRESTO!

Combustion model

Eddy Dissipation (ED)

Steady Laminar Flamelets (SLF)

Eddy Dissipation Concept (EDC)

1 Barlow, R.S., et al., Sandia/ETH-Zurich CO/H2/N2 Flame Data - Release 1.1.

www.ca.sandia.gov/TNF, Sandia National Laboratories, 2002

Experimental flames


The best agreement with experimental measurements is obtained for the EDC model

CFD simulations: comparison with exp data (Sandia Syngas jet flame)

temperature CO2 mass fraction

SLFM

EDEDC

SLFM

EDEDC

temperatureaxial velocityturbulent kinetic energy

Temperature[K]

axial coordinate [mm]

tem

pera

ture

[K]

radial coordinate [mm]

turb

ulen

t kin

etic

ene

rgy

[m2/

s]


velo

city

[m/s

]


tem

pera

ture

[K]


mas

s fr

actio

n


KPP: NOx predictions

NO mass fraction Axial profiles


NO

mas

s fr

actio

n


NO

mas

s fr

actio

nradial coordinate [mm]

NO

mas

s fr

actio

n

radial coordinate [mm]N

O m

ass

frac

tion

Radial profiles

Barlow, R.S., et al. , Sandia/ETH-Zurich CO/H2/N2

Flame Data - Release 1.1. www.ca.sandia.gov/TNF, Sandia National Laboratories, 2002


NOx scatter plots

NO mass fraction

OH mass fraction

the effect is less relevant than for NO as a consequence of the lower apparent activation energy of OH radicals formation process

the predicted NO profile obtained when suppressing the effect of temperature fluctuations lies at the lower boundary of the scatter plot, especially close to the fuel inlet

mixture fraction

NO

mas

s fr

actio

n

mixture fraction

NO

mas

s fr

actio

n

mixture fraction

OH

mas

s fr

actio

n

mixture fraction

OH

mas

s fr

actio

n


Parente et al., European Combustion Meeting 2009 14-17 April 2009 - Vienna, Austria

rad

ian

t tu

be

flam

e tu

be

fuel inlet

air inlet

window

FA [s] T [K] |V| [m/s]

20 30 40 50 60 70 8020

30

40

50

60

70

80

NO [ppm] - Exp.

NO

[ppm

] - N

um.

CFD simulation

(FLUENT 6.3.26)

Case 2.

Mesh 9500 cells

NOx prediction (KPP)

Application example: FLOX® Burner


Numerical efficiency

Different techniques are used to reduce the CPU time

1) Fluid Age : The idea is to take into account the relevant physical phenomena, i.e. solving the individual reactors according to their f luid age (FA).The age on an element of fluid is the time elapsed since it entered the computational domain. This has an impact on the iterative solution which is accelerated because of the higher convergence speed. FA can be easily calculated by CFD codes and describes how the fluid flows inside the domain.

2) Analytical Jacobian Matrix : the numerical solution of large NLS involves computing Jacobian matrices several times, making the computation of derivatives a central and time-consuming partof the solution process. =>the derivatives of kinetic rate equations are evaluated analytically rather than numerically. The MATLAB differentiation toolbox was used to calculate the analytical derivatives , which are then directly included and compiled in the C++ routines of the KPP code . This calculation is needed only one time for each mechanism and takes less than 1 h on a PC.

3) Parallel computing : work in progress….

Speed ×××× 8

Speed ×××× 1.3


Ethylene Furnaces (Technip BV): S. Barendregt, M. van Goethem, I. Risseeuw, A. Frassoldati, T. Faravelli, A. Cuoci, X. J. Li, The Design Of Ultra-Low NOxCritical Furnaces, Proceedings of the 8th european conference on industrial furnaces and boilers, Vilamoura Portugal, 25-28 March 2008.

Technip developed a parallel versionof the KPP code based on MPI

KPP used to evaluate effect on NOx of different burnerdesign , possible burner-burnerinteraction etc

Application example: Ethylene Furnace

NOx0 Max

Technip GK6 Furnace


Temperature [800÷2500 K]

NO2 [0÷160 ppm]NO [0÷2300 ppm]

[min ÷ max]

Main(LPP)

Pilot


NO2 [0÷160 ppm]NO [0÷2300 ppm]

[min ÷ max][min ÷ max]

Main(LPP)

Pilot

experimental analysis:

CLEAN and NEWAC combustors studied at Karlsruhe University, ONERA

modeling activity

CFD CodeAVIO BODY 3D

Kinetic Post Processor

Application example: Gas Turbines

Gas Turbine for Aero-engines (Frassoldati, Cuoci, F aravelli, Ranzi, Colantuoni, Di Martino, Cinque, Comb Sci Tech,181:483, 2009)


CLEAN combustor

Pilot Run Stage Burning Full Running

Main Stage (LPP)

Pilot

ICAO 7% ICAO 30% ICAO 85-100%

Outerliner

Innerliner

Dilutionholes


Main Stage (LPP)

Pilot



Main Stage (LPP)

Pilot


Outerliner

Innerliner

Dilutionholes

CLEAN is an axially staged combustor equipped with

• 18 LPP injectors (Lean Premixed Prevaporised

technology)

• 18 conventional pilot injectors

Good agreement with experimental measurements of

Radial and Overall Temperature Distribution Factors at

the outlet.

0.0

0.2

0.4

0.6

0.8

1.0

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8

Temperature Distribution Factor

Nor

mal

ized

Rad

ialP

ositi

on

CFD predictions

Measured data

RTDFOTDF

RTDFOTDF

0.0

0.2

0.4

0.6

0.8

1.0

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8

Temperature Distribution Factor

Nor

mal

ized

Rad

ialP

ositi

on

CFD predictions

Measured data

RTDFOTDF

RTDFOTDF


CLEAN combustor: KPP simulation

[min ÷ max]


NO2 [0÷160 ppm]NO [0÷2300 ppm]

Main(LPP)

Pilot

Formation of NO2 in the low temperature region (film cooling)

Different amounts of NOx formed in the conventional (pilot) and LPP injectors

0

100

200

300

400

500

600

0 20 40 60 80 100 120 140 160 180 200 220 240Angular position [deg]

NO

x E

mis

sion

s [p

pm]

NO

NO2Possible NO→NO2conversion in the probe


NEWAC combustor

Fuel

(Pilot line)

Fuel

(Main line)

Studied the performance of the PERM injection system in a simple tubular combustor

(Partial Evaporation & Rapid Mixing). Exp Data from UNI Karlsrhue

15%Pilot Fuel/Total Fuel

18÷32Air/Fuel Ratio (AFR)

506÷522Combustor Inlet Temperature [K]

8Combustor Inlet Pressure [bar]

Operating Conditions

(Frassoldati, Cuoci, Faravelli, Ranzi, Colantuoni, Di Martino, Cinque, Kern, Marinov, Zarzalis, Medite rranean Combustion Symposium 2009)


NEWAC combustor: effect of pressure

Good agreement with measured emissions: higher pressure and air preheat significantly increases emissions (∼2 orders of magnitude)

P = 8 Bar, Tair inlet=500 K

1.1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

10 15 20 25 30 35

AFR (Air/Fuel Ratio)

Non

dim

ensi

onal

NO

Experimental data

BODY3D+KPP

0

2

4

6

8

10

12

20 22 24 26 28 30

AFR (Air/Fuel Ratio)N

on d

imen

sion

al N

O

Experimental data

BODY3D+KPP

P = 22 Bar, Tair inlet=800 K


SOxSOx

......

nC7-iC8nC7-iC8

C6C6

C3C3

C2C2

CH4CH4

COCO

H2-O2H2-O2

NOxNOx

SootSoot

PAHPAH

Chlorinatedspecies

Chlorinatedspecies

Kinetic mechanism includes hydrocarbons up to Diesel

and jet fuels as well as several pollutants

- Hierachy

- Modularity

- Generality

Detailed kinetic mechanism of combustion

~ 400 species

~ 12000 reactions

http://www.chem.polimi.it/CRECKModeling/


CH CH3

CH2CH2

CHCH

CH2

CH

CH2CH

O2

COCO2

CH2

CH2

0 ms

1 ms

10 ms

100 msParticleSize range1-1000nm

MolecularSize range0.1-1nm

The first BIN is equal to coronene (C24H12).C atoms increase exponentially, doubling

moving from one BIN to the next:

Large PAH and soot particles are divided in a finite number of sections or lumped components (BINs) which represent groups of species. The number of

conservation equations is just reduced to the number of sections.

Soot formation is described in the form of usual gas phase kinetics.

The discrete sectional method

BIN1: C24H12

PM = 300

BIN20: C12972032H1622016

PM > 150. E+6Dp ~ 30 nm

Soot formation: detailed mechanism 48 / 30

Adapted from: Bockhorn, H. , Soot Formation in Combustion:

Mechanisms and Models, Springer, Berlin (1994)


• Soot emissions from combustion devices have negative effects on human health

• Increasingly stringent limitations on soot emissions

=> need of reliable computational tools to predict soot formation in turbulent flames (inside CFD codes)

•Problems:

• two-way coupling between soot formation and thermal radiation

• complex chemistry to describe soot formation/oxidation

• importance of turbulence-chemistry interactions

Motivation: soot

PM: 40 µµµµg/m3PM: 40 µµµµg/m3PM: 8 µµµµg/m3PM: 8 µµµµg/m3


Soot formation in laminar flames can be successfully modeled using large detailed kinetic mechanism –> useful to understand the mechanism and develop/validate kinetic schemes.

• This analysis can help identifying the conditions that reduce soot formation

……in turbulent flames:

• The direct coupling of CFD codes and large kinetic mechanism is unfeasible due to the limited computational resources, especially considering the large grid used for complex geometries and industrial applications

• A complete decoupling (Pollutants Post-Processing, NOx) is not easily possible due to the effect of soot on thermal radiation.

Motivation: soot


Chemistry

Slow chemistry


Fast chemistry

Fluiddynamics

Kolmogorov scale

Meanresidence time

ττττ(s)

103

100

102

101

10-1

10-4

10-2

10-3

10-5

10-8

10-6

10-7

10-9

NOx

Soot

Combustionprocess

The soot characteristic time is of the same order

of the fluid dynamics times.

Combustion process: Thermal field and species

can be successfully modeled using the flamelets

approach

Soot: strong interactions between fluid mixing and

chemical reactions

=>Specific approaches need to be used to model soot in turbulent flames.

Soot modeling in turbulent flames


• turbulent flames are successfully modeled using the flamelets approach and a presumed pdf of the mixture fraction (degree of mixing between fuel and air).

This allows to pre-process the kinetic calculations and store them in a library… computationally efficient but not possible for soot.

=> the approach used in this work

1) turbulent combustion is modeled using the flamelets approach (=> provides detailed temperature and composition fields T, CO, C2H2, CO2,OH… using detailed chemistry)

2) two additional balance equations are solved for soot number density and volume fraction:

semi-empirical (global) kinetic models for

nucleation, growth, aggregation, oxidation



Two additional transport equations are solved in the CFD code

(Density-weighted variables for numerical convenience)

1. Soot particle number density equation

2. Soot volume fraction

± ° ±( ) ±²

ff fr r

æ ö¶ ×¶ ¶¶ ÷ç ÷+ = G +ç ÷ç ÷÷ç¶ ¶ ¶ ¶è ø 0

1i NN Nt m

i i i AV

uS

t x x x N

± ° ±( ) ±±i MM M

t Mi i i

uS

t x x x

ff fr r

æ ö¶ ×¶ ¶¶ ÷ç ÷+ = G +ç ÷ç ÷ç¶ ¶ ¶ ¶è ø

±±

fr

= 0N

AV

mN

±°r

fr

= soot VM

f

nucleation aggregation

nucleation growth oxidation

Hp: particles number density non affected by oxidation (Syed et al., 1990)

semi-empirical models for nucleation, growth, aggregation, oxidation



Liu(2006)

- Flame: methane-air diffusion flames in laminar conditions; pressures 5 ÷ 40 atm

- Growth: square root of soot surface

Liu(2003)

- Flame: ethylene-air diffusion flames in laminar conditions and atmospheric pressure

- Growth: proportional soot surface

Liu (2003)

Liu (2006)

Brookes (1999)

Wen (2003)

0.004857 2.857 54 54 = E/R 7548 16103 21100 21100

8400 8400 144 1200 2.40 2.40 0.65 1.20

Reference (Liu et al.

2003) (Liu et

al. 2006) (Brookes and Moss 1999b)

(Wen et al. 2003)

Some global mechanisms

A. Cuoci, A. Frassoldati, T. Faravelli, E. Ranzi,Kinetic modeling of soot formation in turbulent nonpremixed flamesEnvironmental Engineering Science, 25 (10), pp. 1407-1422, (2008).


Additional source term in in the energy equation

( )s ¥= - × × -4 44rad SQ a T T

( )( )1 2000soot soot va B f C Tr= × + -

2

1232.4m

Bkg

=

4 14.8 10C K- -= ×2 2 2 2S H O H O CO CO CO CO soota a p a p a p a= + + +

Ambient temperature ~300K

Absorption coefficient

Soot absorption coefficient

Sazhin1 (1994)

[1] S. S. Sazhin. An Approximation for the AbsorptionCoefficient of Soot in a Radiating Gas. Manuscript, FluentEurope, Ltd., 1994.

http://www.ca.sandia.gov/TNF/radiation.html

Soot radiation: asoot


The coupling between the flamelets library and radiation in a turbulent flame is achieved introducing a parameter called enthalpy defect1:

[1] Bray, K. N. C., and Peters, N. (1994). Turbulent Reacting Flows, P. A. Libby and F. A. Williams, eds., Academic Press, London, 78-84

( )f xé ù= - = - + -ë ûH AD OX FUEL OXH H H H H H

Using the laminar flamelet model the thermochemical state of a turbulent flame is completely determined by the mixture fraction ξ, the scalar dissipation rate χ and the enthalpy defect,

through the joint PDF P(ξ, χR, ΦΦΦΦH) :

° ( ) ( )1

0 0

, , , ,R H R H R HP d d dy y x c f x c f x c f+ ¥ + ¥

- ¥

= × × × ×ò ò ò

The single PDF’s are assumed to be statistically independent:

Scalar dissipation rate Log Normal

Distribution

Enthalpy defect Dirac

Delta

( ) ( ) ( ) ( )x c f x c f= × ×, ,R H R HP P P P

Mixture fraction β PDF

Sooting flames: non-adiabatic library



The mean enthalpy, used to obtain the enthalpy defect, is calculated from its conservation equation:

° ° °( ) °r r

æ ö¶ ×¶ ¶ ¶ ÷ç ÷+ = G +ç ÷ç ÷ç¶ ¶ ¶ ¶è ø

i

t radi i i

u HH HQ

t x x x

FlameletLibrary

FlameletLibrary

Enthalpy Defect 1 (adiabatic)

Enthalpy Defect 1 (adiabatic)

Enthalpy Defect 2

Enthalpy Defect 2

Enthalpy Defect N

Enthalpy Defect N

Equilibrium Flamelet

Strain Rate 1

Strain Rate 2

Extinction Flamelet

Non-reacting Flamelet

The Flamelets library is pre-calculated and organized in shelves, each for a different value of Enthalpy Defect.

For each enthalpy defects several values of strain rate (represents the effect of turbulent flow on the flame)

(linear interpolation between the shelves)

Non-adiabatic Flamelets library


Soot nucleation is described by the acetylene-route, which is modeled with a simple one-step reaction:

1. Soot Nucleation1

soot particle number density soot volume fraction

2. Soot Growth1

The surface growth rate is a modified Arrhenius form and depends on the soot specific soot area Asoot:

¾ ¾® +2 2 22 sootC H C H

æ ö÷ç= × - ×÷ç ÷÷çè ø0 2 2expnucl nucl

m nucl C H

TS A C

T=

0

nucl nuclM soot mS M S

( )æ ö÷ç ÷= × - × ×ç ÷ç ÷çè ø 2 2

exp growthgrowthM growth C H soot

TS A C f A

T

[1] F. Liu , K.A. Thomson, H. Guo, G. J.Smallwood, Numerical and experimental study of an axisymmetric coflow laminarmethane–air diffusion flame at pressures between 5 and 40 atmospheres, Combustion and Flame 146 (2006) 456–471

Global Soot models


The rate of oxidation is proportional to the soot surface area:

Soot oxidation is a one-step reaction:

3. Soot Oxidation1

4. Soot Aggregation2

The aggregation rate depends on soot particles density; assuming a monodisperseddistribution of spherical particles:

+ ¾ ¾®2

12sootC O CO

2exp Oox oxM ox soot

pTS A A

T T

æ ö÷ç= - ×÷ç ÷çè ø

0

202

aggraggrm

AV

AS T m

N= ×

[1] Lee K.B., Thring M.W., Beer J.M., On the rate of combustion of soot in a laminar soot flame, Combustion And Flame 6 (1962) 137–145

[2] Brookes S.J., Moss J.B., Predictions of soot and thermal radiation properties in confined turbulent jet diffusion flames, Combustion and Flame 116, 486-503 (1999)

Global Soot models


This closure entirely ignores the effect of turbulence and formulates mean sourceterms from mean values alone.

=>In this case the joint-PDF simply becomes a combination of Dirac delta function centered on the mean value of each property:

( ) ( ) ±( ) ±( ) ±( ) °( )%x c f d x x d c c d f f d d= - × - × - × - × -0 0 0, , , ,R H V R R H H V VP m f m m f f

(I) Mean Properties Closure

This is the simplest approach and it has been largely used by many authors1,2,3,4.

[3] F. Liu, H. Guo, G. J.Smallwood, Gulder O., Numerical modelling of soot formation and oxidation in laminar coflow non-smoking and smoking ethylene diffusion flames, Combustion Theory and Modelling 7 (2003) 301–315

[1] Brookes S.J., Moss J.B., Predictions of soot and thermal radiationproperties in confined turbulent jet diffusion flames, Combustion and Flame 116, 486-503 (1999)

[2] Wen, Z., Yun, S., Thomson, M. J., and Lightstone, M. F. (2003). "Modeling soot formation in turbulent kerosene/air jet diffusion flames." Combustion and Flame, 135, 323-340

[4] Zucca, A., Marchisio, D. L., Barresi, A. A., and Fox, R. O. (2006). "Implementation of the population balance equation in CFD codes for modelling soot formation in turbulent flames." Chemical Engineering Science, 61, 87-95

Closure of the soot source term


(II) Uncorrelated Closure

The soot properties are assumed to be totally uncorrelated with the mixture fraction and the radiative heat loss and each other1,2.

Therefore the joint PDF has this form (Statistical Independence):

Unfortunately the individual PDFs for the soot particle number density and the soot fraction are unknown; therefore the PDF is further simplified:

( ) ( ) ±( ) °( )x c f x c f d d= × - × -0 0 0, , , , , ,R H V R H V VP m f P m m f f

( ) ( ) ( ) ( )x c f x c f= × ×0 0, , , , , ,R H V R H VP m f P P m P f

[1] Brookes S.J., Moss J.B. , Predictions of soot and thermalradiation properties in confined turbulent jet diffusion flames, Combustion and Flame 116, 486-503 (1999)

[2] Roditcheva, O. V., and Bai, X. S. (2001). "Pressure effect on soot formation in turbulent diffusion flames." Chemosphere, 42, 811-821



(III) Correlated Closure

The soot properties are assumed to be perfectly correlated with mixture fraction, which is acceptable only in regions of vigorous (fast) soot formation.

⇒the soot is directly pre-calculated in the non-adiabatic flamelets library

⇒joint PDF P(ξ, χR, φH , m0, fV) is replaced by joint PDF P(ξ, χR, φH) .

The laminar flamelets library is solved using two additional equations equations:

Flameresidence

time



Air

Ethylene

Air

Flame A: Ethylene turbulent jet flame (Kent & Honnery, 1987)

-Nozzle diameter = 3.00 mm

-Fuel velocity = 52 m/s

-Jet Reynolds number = 14660

-Turbulence: k-e model with correction for axisymmetric jets

-Radiative heat transfer: optically thin approximation (CO, CO2, H2O, Soot)

-Flamelets Model (POLIMI KINETIC SCHEME)

-Computational grid: axial-symmetric structured, non uniform, 120 x 60 cells

CFD Simulation (FLUENT 6.2)

Kent, Honnery , Soot and mixture fraction in turbulent diffusion flames, Combustion Science and Technology 54, 383-397 (1987)

Experimental data: jet flames


Flame B: Methane turbulent jet flame (Brookes & Moss, 1999)

-Nozzle diameter = 4.07 mm

-Fuel velocity = 20.3 m/s

-Jet Reynolds number = 5000

- Computational grid: structured, non uniform, 150 x 80 cells

CFD Simulation (FLUENT 6.2)

Brookes S.J., Moss J.B. , Predictions of soot and thermal radiation properties in confined turbulentjet diffusion flames, Combustion and Flame 116, 486-503 (1999)

Air

Methane

Air

Experimental data: jet flames


Temperature [K]

The CFD results refer to the simulation performed using the uncorrelated approach (II) for soot predictions.

Very similar results were obtained using the other closures.

Results flame A: Temperature


Soot Volume fraction

Comparison with experimental measurements

Soot volume fractionmean properties closure (I)

correlated closure (III)

uncorrelated closure (II)

(I)

(II)

(III)

(I)

(II)

(III)(II)

(III)

(I)

Results flame A: soot


Particle Mean Diameter [micron]

Comparison with measurements

mean properties closure (I)

correlated closure (III)

uncorrelated closure (III)

(I)

(III)

(II)

(I)

(III)

(II)(III)

(II)

(I)

1. Nucleation zone2. Growth zone

3. Oxidation zone4. Aggregation zone


volu

me

frac

tion

radial coordinate [mm]vo

lum

e fr

actio

n


volu

me

frac

tion


volu

me

frac

tion

Results flame A: soot


Soot Volume fraction

mean properties closure (I)

correlated closure (III) uncorrelated

closure (II)

(I)

(III)

(II)

Comparison with experimental measurements

(I)

(III)

(II)

Methane forms less acetilene and thus soot formation is significantly reduced in comparison to flame A

Results flame B: Soot


Premixed CH4/O2, Φ=2.45 (Faeth et al.)

0

1e-007

3e-007

5e-007

7e-007

9e-007

0 0.5 1 1.5 2 2.5 3

Soot

volu

me fra

ctio

n

Height above the burner

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0

C2H

2m

ole

fra

ctio

n

Soot (Detailed Kinetics)

Liu 2006

Liu 2003

C2H2 (Detailed Kinetics)

Test case: Global soot mechanism in a premixed CH4 laminar flame


Soot (Detailed Kinetics)

Liu 2006

Liu 2003

C2H2 (Detailed Kinetics)Premixed Benzene/O2/N2 (Ciajolo)

Soot

conce

ntr

ation

[g/c

m3]

Height above the burner

0

2e-007

4e-007

6e-007

8e-007

1e-006

1.2e-006

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

0.002

0.004

0.006

0.008

0.010

0.012

0.014

C2H

2m

ole

fra

ctio

n

Test case: Global soot mechanism in a premixed Benzene laminar flame


T. Faravelli, A. Frassoldati and E. RanziKinetic Modeling of Mutual Interactions in NO-Hydrocarbon Low Temperature Oxidation Combustion and Flame, 132/1-2 pp 188 - 207 (2003)

A. Frassoldati, T. Faravelli and E. RanziKinetic Modeling of Mutual Interactions in NO-Hydrocarbon High Temperature OxidationCombustion and Flame 135, pp. 97-112, (2003)

A. Frassoldati, S. Frigerio, E. Colombo, F. Inzoli, T. FaravelliDetermination of NOx emissions from strong swirling confined flames with an integrated CFD-based procedureChem. Eng. Sci. 60, pp. 2851-2869, (2005).

E. Ranzi, A. Frassoldati, S. Granata, T. FaravelliWide-Range Kinetic Modeling Study of the Pyrolysis, Partial Oxidation, and Combustion of Heavy n-AlkanesInd. Eng. Chem. Res. (2005) 44(14), 5170-5183

S. Granata, A. Frassoldati, T. Faravelli, E. Ranzi, S. Humer, K. SeshadriPolycyclic Aromatic Hydrocarbons and Soot Particle Formation in Liquid Fuel CombustionChem. Engng. Transactions Vol. 10 pp. 275-280 AAAS AIDIC Milano 2006

A. Cuoci, A. Frassoldati, G. Buzzi Ferraris, T. Fara velli, E. Ranzi, Ignition, Combustion and Flame Structure of Carbon Monoxide/Hydrogen Mixtures. Note 2: fluid Dynamics and Kinetics Aspects of Syngas CombustionInt. J. of Hydrogen Energy, 32: 3486-3500 (2007)


A. Frassoldati, A. Cuoci, T. Faravelli, E. Ranzi, D . Astesiano, M. Valenza, P. Sharma,Experimental and modelling study of low-NOx industrial burnersMPT Metallurgical Plant and Technology International, 31 (6), pp. 44-46, (2008).

References


ReferencesA. Cuoci, A. Frassoldati, T. Faravelli, E. Ranzi, Frequency response of counter flow diffusion flames to strain rate harmonic oscillations,Combustion Science and Technology, 180 (2008), pp. 767-784

A. Frassoldati, A. Cuoci, T. Faravelli, E. Ranzi, S . Colantuoni, P. Di Martino, G. Cinque,Experimental and modeling study of a low NOx combustor for aero-engine turbofanCombustion Science and Technology, 181 (3), pp. 483-495, (2009).

A. Frassoldati, A. Cuoci, T. Faravelli, E. Ranzi, G . Buzzi Ferraris,Robust and efficient numerical methods for the prediction of pollutants using detailed kinetics and fluid dynamicsComputer Aided Chemical Engineering, 26, pp. 707-711 (2009).

A. Cuoci, A. Frassoldati, T. Faravelli, E. Ranzi,Formation of soot and nitrogen oxides in unsteady counterflow diffusion flamesCombustion and Flame, 156 (10), pp. 2010-2022, (2009)

D. Manca, G. Buzzi Ferraris, A. Cuoci, A. Frassoldat i,The solution of very large non-linear algebraic systemsComputers and Chemical Engineering, 33 (10), pp. 1727-1734 (2009)

A. Parente, A. Cuoci, C. Galletti, A. Frassoldati, T. Faravelli, L. Tognotti, NO formation in flameless combustion: comparison of different modeling approaches, paper number 810.144, 4th European Combustion Meeting, Vienna, Austria, 14 - 17 April 2009.

A. Frassoldati, P. Sharma, A. Cuoci, T. Faravelli, E. Ranzi, Kinetic and Fluid Dynamics Modelling of a Methane/Hydrogen Jet Flames in Diluted Coflow, paper number 810.145, 4th European Combustion Meeting, Vienna, Austria, 14 - 17 April 2009.

A. Frassoldati, A. Cuoci, T. Faravelli, E. Ranzi, S . Colantuoni, P. Di Martino, G. Cinque, M. Kern, S. Marinov, N. Zarzalis, Fluid dynamics and detailed kinetic modeling of pollutant emissions from lean combustion systems, Sixth Mediterranean Combustion Symposium, Porticcio – Ajaccio, Corsica, France, June 7-11, 2009


Soot in turbulent flames

Detailed description (Discrete Section method)

Method of Moments

Detailed chemistry-turbulence interactions(Closure of soot source term)

73 / 30


( )0

1i NN Nt m

i i i AV

uS

t x x x N

φφ φρ ρ∂ ⋅ ∂ ∂∂+ = Γ + ∂ ∂ ∂ ∂

Two additional transport equations are solved in the CFD code to predict soot formation and evolution: the first equation accounts for the transport of particle number density m0; the second equation describes the transport of the soot volume fraction fV.

1. Soot particle number density equation (moment 0)

2. Soot volume fraction (moment 3)

nucleation

aggregation

nucleation

growth oxidation

Soot transport equations 74 / 30

( ) 1i MM Mt M

i i i AV

uS

t x x x N

φφ φρ ρ∂ ⋅ ∂ ∂∂+ = Γ + ∂ ∂ ∂ ∂

0N

AV

mN

φρ

=⋅

soot VM

fρφρ

⋅=


Turbulence model

Scalar dissipationrate

Soot Library

Soot source term: m0 equation

Coupling between CFD and soot library 75 / 30

RANS code

mass

momentum

energy

species

Turbulent kinetic energy

Dissipation rate of turbulent kinetic energy

Soot source term: fv equation

Soot Transport Equation- m0 equation

- fv equation

A. Cuoci, A. Frassoldati, T. Faravelli, E. Ranzi, “Kinetic Modeling of Soot Formation in Turbulent Flames”, Environmental Engineering Science, 25(10):1407-1422, 2008

( )2'', ,st stχ χ κ ε ξ=


Closure of soot source term 76 / 30

Soot Library

RANS CODE

Single-PDFsP(T) - P(χR) -

P(Qrad) P(m0) -P(fV)

(I) Mean properties closure

(II) Uncorrelated closure

(III) Correlated closure

Joint-PDF: P(T, χR, Qrad , m0, fV)

mean variance

Log-Normal PDF

dummy variable

Beta-PDF

dummy variable


Additional


The application example: FLOX(R)

burner

0 2000 4000 6000 8000

0

2000

4000

6000

8000

Cell index

Cel

lind

ex

0 2000 4000 6000 8000

0

2000

4000

6000

8000

Cell index

Cel

lind

ex

Boolean structure of the Jacobian matrix

Left (CFD): bandwith reduced usingthe reverse Cuthill-McKee method: cells

are ordered so that neighboring cellsare near each other in the zone and in the computer memory. This increases

the CFD code memory accessefficiency.

Right (KPP): mesh is ordered accordingto the fluid age (FA) of each cell : the structure of the matrix becomes lessregular and the sparsity is increased, but allowed to enhance convergence

speed of ~1.3.

0 2000 4000 6000 8000

0

2000

4000

6000

8000

Cell index

Cel

lind

ex

0 2000 4000 6000 8000

0

2000

4000

6000

8000

Cell index

Cel

lind

ex

CFD KPP – reorderedaccording to FA

The analytical Jacobian matrix improved the numerical efficiency of ~8 times . The re-ordering according to the fluid age => ~1.3


Semplificazione problema

Cinetica complessa

Fluidodinamica complessa

Problema intrattabile

Cinetica semplice

-- previsione meno …accurata

-- modelli tarati sul …singolo problema

Fluidodinamica semplice

-- soluzione semplice

-- misure sperimentali di …laboratorio


Struttura delle fiamme

• Fiamme laminari diffusive contrapposte


Modello matematico( ) ( )[ ] ( )[ ] ( )txhtxngtxnv

t

txnx ;;;;;;

;; rrrrrrrrrr

r ξξξξξ =⋅⋅∇+⋅⋅∇+

∂∂

ξr

= coordinata interna

( )txn ;;rr

ξ = distribuzione dimensione particelle

vr= velocità di trasformazione coordinate esterne

gr= velocità di trasformazione coordinate interne

Modello a 2 equazioni

Quadrature Methodof Moments (QMOM)

Modelli numerici semplificati

oxidcoagcrescnucl SSSStxh +++=);;(rr

ξ

Termine Sorgente


Modello a 2 equazioni

• Ipotesi di particelle monodisperse

• 2 equazioni di trasporto:1

MΦ = frazione massiva del soot

( ) 012 =

−Φ∂∂−

∂Φ∂

MKMM SV

xx

F ρρρ

oxidM

crescM

nuclMM SSSS ++=

2

0m = numero particelle di soot per unità di volume

AN N

m

ρ0=Φ

( ) 012

0=

−Φ∂∂−

∂Φ∂

mkNN SV

xx

F ρρρ

( )A

coagm

nuclmm N

SSS1

000 ⋅+=


Quadrature Method of Moments

La distribuzione della dimensione di particelle è approssimata da una combinazione lineare di delta di Dirac

( ) ( )1 1

( ) ( )NN

ij

f w t tαα

ξ δ ξ ξ= =

≈ ⋅ −∑ ∏( )tiξ = ascisse ( )twα = pesi

x

w Original particle sizedistribution

x

wQMOM (N=2)

2N incognite:

-- N ascisse

-- N pesi

Le N ascisse e gli N pesi vengono calcolati imponendo che i momenti della distribuzione discreta siano uguali a quelli delladistribuzione continua.

1

NQMOM k

k km m wα αα

ξ=

= = ⋅∑ 0...2 1k N= −con

( ) 012 )( =

−∂∂+

∂∂ N

kkkk SVm

xx

mF ρρρ

con k=0,…, 1−N

combustione turbolenta ed emissioni - unina.itwpage.unina.it/anddanna/capri/capri...

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