Turbulent Combustion: Modelling and Applications

Turbulent Combustion:Modelling and Applications

Princeton Summer School 2021

E. Mastorakos

Engineering Department

University of Cambridge

[email protected]

1

Day 3: Modelling for turbulent flames

Non-premixed

Premixed

Stratified

Spray

General comments

2

Turbulent non-premixed combustion: modelling

• No model

• Presumed PDF

• Eddy Break-up, Eddy Dissipation Concepts

• Mixture fraction approaches (flamelet, Conditional Moment Closure)

• Transported PDF

3

No model

Neglect turbulent fluctuations, hence evaluate mean reaction rate at the mean species mass fractions and mean T (“mean”=“ensemble averaged” in the case of RANS, or “resolved” in the case of LES)

4

)~

,...,~

,~

(

~

)()

~~()~

(

21 TYYfw

wx

YDD

xx

Yu

t

Y

i

t

ii

i

=

+

+

=

+

Presumed PDF

5

A. Model P(Y1,Y2,…T) as a series of delta functions evaluated at the mean Y1, Y2, …T. This corresponds to “laminar chemistry”.

B. Presume a shape for the joint PDF, determined by the mean Ys (coming from transport eqtn), possibly also by Y_rms (also coming from modelled governing equation for variance). Shape could be beta-pdf or Gaussian.

Used currently for supersonic combustion, mostly because people pay attention to the CFD, shock waves etc, and not to the turbulence effects on the reaction (Baurle and Girimaji, Comb. Flame, 134 (2003)).

dTdYYdTYYPTYYfw

TYYfw

...)(,...,,(),...,,(

),...,,(

212121...

21

=

=

Eddy break up (EBU)

If chemistry is infinitely fast, then overall reaction rate is determined by the rate of turbulent mixing. Rate of mixing determined by Tturb (=k/e). Given first by Spalding (early 70s):

6

)~

1(~

, 22

fufufufufu YYYk

YAw −−=e

After tuning with

experiment From k-e model Infinitely fast no probability

of intermediate

Developed for premixed, but also used for non-premixed (see next slide)

Eddy dissipation (Magnussen)Magnussen (16th Symp on Combustion) modified

Spalding’s EBU for non-premixed flames:

7

))Prod(1OxFu(, 1

~

,~

,~

min 2

SSS

YBYY

kYAw

prod

oxfufufu +==+

+−=e

After tuning with experiment

From k-e model

Widely used, quick to run, often reasonable results (for furnaces, diesel

engines in diffusion flame phase). Not good for flames close to walls

(similar to EBU). Not good for finite-rate chemistry (no pollution, no

extinction, no autoignition).

Eddy dissipation concept (EDC)

Reaction assumed to occur inside Kolmogorov vortices, each of them treated as a well-stirred reactor. Rate of reaction given by volumetric reaction rate inside vortices and volume fraction of vortices (“reactors”)

8

1

~

,~

,~

min 2

4/1

+

−=

S

YBYY

kY

kCw

prod

oxfufufu

e

e

After calculating volume fraction of

Kolmogorov vortices (Byggstoyl &

Magnussen, 1984)

Many variants. Used in RANS and in LES (Duwig, Chomiak, etc).

Reasonable for some problems, finite-rate chemistry can be included

with some new concepts treating Kolmogorov vortices as well-stirred

reactors.

Infinitely-fast

chemistry

version

9

Mixture fraction approaches: the PDF of the mixture fraction P(x)

• Solve equations for mean and variance of mixture fraction

• Presume P(x) (e.g. b-PDF given below).

• Then integrate over P(x).

=1

0

),,(~

),,(),(~

dtxPtxQtxY

Various options!

9

10

Mixture fraction approaches: the options for Q

=1

0

),,(~

),,(),(~

dtxPtxQtxY

Infinitely fast chemistry

(“flame sheet” or

“mixed is burnt”)

Finite rate chemistry; Q from pre-calculated

laminar flame (one version of the flamelet model)

Another version of flamelet model: solve for Qa online; function of time

and space (some rough modelling used for the latter)

CMC: solve for Qa online; function of time and space (more rigorous)

10

11

Turbulent diffusion flames: fast and slow chemistry

Q(,x,t) comes from:

(i) flame sheet model (infinitely fast chemistry). Good for big furnaces,

slow flows, flame lengths, first approximation to many problems.

(ii) Equilibrium. For every (mixture fraction), assume thermodynamic

equilibrium. Not very good, gives too much H2 and CO on the rich side.

(iii) Laminar flamelet (either pre-calculation, or on-the-fly)

(iv) Conditional Moment Closure (Q is function of time and space)

=1

0

),,(~

),,(),(~

dtxPtxQtxY

11

12

Turbulent diffusion flames: a result of historical significance and great insight

• Bilger (1976) derived a closed-form result for the mean reaction rate.

• Direct connection between reaction rate and scalar dissipation

demonstrated for the first time. Necessary for understanding flamelet

and CMC models.

• If Yi=f(x), then:

12

(from Bilger,1976)

13

Turbulent diffusion flames: flamelet model

Flamelet model variants:

(i) Steady flamelet (i.e. laminar flame solution). Very common; already in FLUENT etc.

(ii) Transient flamelet, “Representative Interactive Flamelet” (Peters 2000)

(iii) Some issues:

- flamelet depends on N; how do we select N from flow field?

- how many flamelet solutions do we use? Over how many N’s?

=1

0

),,(~

),,(),(~

dtxPtxQtxY

13

14

Conditional Moment Closure

x

T

T

xx

xst

T

xst

•Relating the reacting scalar, Q, to

the non-reacting scalar (mixture

fraction).

•What happens if Q is very different

in space or time, as in a lifted flame?

•CMC solves PDE for Q.

=1

0

),,(~

),,(),(~

dtxPtxQtxY

14

Final (modelled) CMC equations for sprays:Mortensen & Bilger (2009)

15

+

=

||2

2

wQ

Nt

Q ( )

xx

x

−−−+

+

−

−−

QSQSS

x

QDP

xP

x

Q

xDu

jt

j

jjtj

|)1(||

)(~

)(~1

~~

''

1~2

Transient flamelet model

Terms responsible for flame propagation,

heat losses to walls, stabilization etc.

Droplet interactions. Model

for <S|> needed.

Steady flamelet model

𝑁|𝜂Conditional scalar

dissipation. Model needed.

Scalar dissipation rate (for LES)

CN=42.0

Droplet evaporation and the mixture fraction

=

=

s

sS

x

x

if finite

if 0|

0~S

0=S

r

Yfu,x

Computational cell

Yfu,s , xs

Yfu, , xcell

Yfu,s(Td)

Td

Droplet in

cell

Yfu,s= f(Td) from Clausius-

Clapeyron eqtn

16

Final (modelled) mixture fraction equations:Demoulin & Borghi (2002) + new model for <S|>

)(~

/)(~

ss PSS xx −=

17

18

Turbulent diffusion flames• Large Eddy Simulation – Conditional Moment Closure

Garmory and Mastorakos,

LES-CMC calculations in

Sandia F, PROCI 33, 2010. 18

=1

0

),,(~

),,(),(~

dtxPtxQtxY

Capturing “holes” in flame sheet

19

CMC literature

• Klimenko and Bilger, 1999, PECS

• Kronenburg and Mastorakos, 2011, In “Turbulent Combustion

Modelling”, Springer 2011.

• Journal papers by Kronenburg, Mastorakos, Huh, Bilger, Devaud and

others for applications in RANS and LES

• Typically, CMC provides very good results for finite-rate chemistry

effects in turbulent combustion and has been used for very difficult

problems such as ignition and extinction.

• Currently, used a lot for diesel engines, gas turbines, furnaces, fires…

19

20

The pdf method

• Transport equation:

- Conservation of pdf in real and scalar space

- Advection, turbulent diffusion, micro-mixing, chemistry.

- Various additional joint PDF equations can be derived (joint scalar;

joint scalar-velocity; scalar-velocity-frequency)

- Pope, Dopazo, Jones, Roekaerts, etc etc

- Fundamental derivations vs. applications

- Method now present in FLUENT & STAR-CD

- See Haworth, 2010, PECS; Haworth and Pope chapter in Echekki &

Mastorakos 2011.

20

21

The pdf method

(1) Random walk of “virtual particles”, as a solution method of the PDF

equation

(2) Compile statistics over these particles

21

22

The pdf method: Lagrangian approach

• Physical understanding:

- “decompose” fluid into virtual “particles”

- Develop random walks for these “particles” that mimic turbulent

dispersion, molecular mixing.

- Each “particle” carries its own chemistry

- Example:

homogeneous (in the mean),

“Interaction by Exchange with the Mean” mixing model

=

=−

−=pN

n

n

mix

nn

n

YYT

YYw

dt

dY

1

,

Chemistry

Molecular mixing

22

23

The pdf method: Eulerian approach

• Physical understanding:

- “decompose” fluid into virtual “fields”

- Develop random walks for these “fields” that mimic turbulent

dispersion, molecular mixing.

- Each “field” carries its own chemistry, convection, diffusion

- Jones et al. (and others now): for applications in LES for a variety of

flames

- Applications also to urban pollution (Garmory and Mastorakos).

- See original papers for the mathematics and applications (Valino,

Jones etc)

23

24

The pdf method: Eulerian approach

24

Modelled PDF

conservation equation

Stochastic PDE for

every field; solve this for

N fields (N: large for

RANS, not too large for

LES).

Careful with solver!

(must be consistent with

stochastic PDE)

Random walk term

(Wiener)

Micromixing (here, modelled by

“Interaction by Exchange with the Mean”

Chemistry

Turb. diffusionConvection

25

Premixed flame modelling

• Flamelet

• Flame surface density

• PDF (discussed already)

• CMC (discussed already; some sub-models different)

25

26


26

Flame surface density modelling: turb. flame locally is (almost) like laminar

one; turbulence makes itself known through FSD & I0.

Mean reaction rate

Reactant density

Unstrained

laminar flame

speed

Factor to

account for

strain and

curvature

Flame surface

density (algebraic

model, transport

equation

FSD is active area of research (transport equation, I0, etc). See Cant and

Mastorakos 2007 for an introduction. See Driscoll’s review paper (2008)

for more info on how we measure flame area and how to define flame

speed.

27


• Flamelet model:

• We need Y(c) (and w(c), T(c), etc) and P(c).

• Calculate laminar premixed flame, store results in terms of c (Bradley,

“FGM”, etc): they are all the same model.

• Definition of c varies, could be based on Yfuel or T, 0 in reactants, 1 in

products. Different definition needed if NOx is the target.

• Can be extended for equivalence ratio inhomogeneities.

• Driscoll’s 2008 review paper: how far does flamelet structure go?

27

𝜑 = න

𝑐=0

𝑐=1

𝜙 𝑐 𝑃 𝑐 𝑑𝑐

𝑤(𝑐)

𝑌(𝑐), 𝑇(𝑐)

𝜙

28


28

How about P(c)?

If flame thin relative to the turbulence scales, Bray-Libby-Moss concept

seems applicable: “Double Delta Function” model for the PDF of c.

BLM go further and close mean reaction rate, turbulent flux etc (see Cant

& Mastorakos, Ch 4)

29


29

Mean and variance of c, scalar dissipation of c: (eqtns below are for RANS

or LES, from Farace et al, Comb. Theory and Modelling, 2018):

Progress variable dissipation (new models by Swaminathan, given below

for LES) – unlike passive scalar dissipation, it now depends on chemistry!

Fundamentals of stratified / partially-premixed turbulent

combustion

• Very difficult and topical research area

• “Stratified” : a derivative of premixed flame concepts

• “Edge flames” (e.g. after ignition): a derivative of non-premixed concepts

• “Partially premixed”: this term is vague and should be avoided; better to say “imperfectly premixed”, or “edge”, or “stratified”; described by P(x).

30

0.3ms 0.7ms 1.9ms

7.1ms 16.5ms

Turbulent edge flames: definitions

31

U: far-field fluid velocity

Ut: fluid velocity at triple point

Vf: absolute flame speed

Vf

Ut

U

SE=Vf-U: edge flame speed relative to the far field

SE=(u/b)1/2SL for laminar flame (Ruetch et al, 1996; analytical result)

S=Vf-Ut : edge flame displacement speed

Turbulent edge flames: DNS & experiments

32

Vabs

AVf

Vrθ0.5 ms

0.9 ms

1.8 ms

2.3 ms

3.3 ms

4.2 ms

6.5 ms

9.3 ms

CH4 (Le0.9)

S/SL

P(S

/SL)

<S> = 0.5-0.8 SL,0

<SE>(u/b)1/2SL,0

Must examine

for spraysExp: Heeger et al., 32nd Symp.

DNS: Hesse et al., 32nd Symp.

Fuel

Air

OH-PLIF PIV

Turbulent gaseous edge flames: DNS & experiments

• Absolute, relative edge flame speed, displacement speed

• Dependence on local scalar dissipation, strain etc.

• Findings:

– effects of turbulence NOT the same as in fully-premixed flames

– Counter-gradient transport possible

– Lewis number effects

– Flame speed has large fluctuations

• Chakraborty & Mastorakos Phys. Fluids, 18 (2006), 105103; Proc. Comb. Inst. 32 (2009) 1399–1407; Flow Turbul. Comb. (2009) to appear.

• Richardson et al., Proc. Comb. Inst. 31 (2007) 1683–1690

• Heeger et al. Proc. Comb. Inst. 32 (2009) 2957–2964;

33

DN

S

Ex

p.

Turbulent spray flames

• Models usually as for non-premixed flames

• Turbulent Combustion of Sprays Workshop

• To first-order, evaporation is uncoupled from the combustion model (evaporation creates the fuel)

– BUT: mixture fraction and variance (in RANS or LES) have terms including spray effects

– Scalar dissipation modelling needs improvement when sprays are present

– If premixed flame are used for flamelet modelling, spray flames should in principle be used for tabulations: laminar flame in spray very different than in gases!

34

Laminar “premixed” spray flame

Neophytou and Mastorakos, CNF, 200935


Neophytou and Mastorakos, CNF, 2009

36

Post-flame pyrolysis

Evaporation The flame creates its fuel.

Very complex structures; not used in

turbulent combustion modelling so

far.


Neophytou and Mastorakos, CNF, 2009 37

Flame speed depends on SMD,

overall f, gaseous f.

Turbulent “premixed” spray flame

Chakraborty’s group, 201738

Model validation

39

Velocity, mixture fraction: needed as “background”; good agreement does not provide validation for the combustion model.

Mean T and major species: if good, we begin to pay attention…

RMS of major species: extra level of validation.

Mean and rms of radicals (e.g. OH): agreement provides good evidence that model works

NO & soot: difficult to predict (chemistry + experiment problematic…)

Validation must be done across a range of conditions (e.g. low velocity, high velocity etc), otherwise it means little.

Industry also needs validation at high pressure and very high Reynolds number.

DNS can be used for sub-model validation, typically based on small-scale quantities (large scale phenomena typically not converged statistically).

Target flames for model validationNon-premixed:

Sandia D-E-F: piloted CH4/air jet flames, still diffusion flame, strong local extinctionSydney swirl CH4: stabilisation by recirculation zone; local extinction

“Partially premixed”:DLR: nominally non-premixed, local liftoff causes some premixing, quick mixing

Premixed:Piloted Bunsen flame: overall shape, relatively low KaPiloted jet flames (Sydney, Michigan, Lund, USC etc): very high Ka – combustion sustained by the

hot co-flowing productsTurbulent flame speed experiments

Sprays:Sydney piloted jet (carrier air+vapour+droplets): various fuels, range of conditionsCambridge swirl spray flames: range of fuels and conditions, focus on local and global extinctionRouen, Delft, Heidelberg: spray in low co-flow (low Re)

http://swirl-flame.eng.cam.ac.uk/

40

Target flames for model validation

Autoignition:“Cabra” flame (fuel in vitiated air), Cambridge (fuel in hot air), diesel-like (Sandia, ETH)

Spark ignition:Cambridge (series of flames); Ecole Centrale (annular)

Soot:Laminar diffusion flame (Santoro), Adelaide jet flames, DLR swirl flames (1-3bar)

Pick the flame experiment whose research focus was the focus of your modelling effort.

No flame is good for everything!

No model is good for everything!

41

Combustion CFDStep 1: Decide what you want to predict well, and what is OK to be less accurate. What phenomenon are you looking to simulate well? What is the focus of your research?

Step 2: Make sure aerodynamics is OK (grid should be sufficient, validate code against simple problems, then code+grid against cold flow in complex geometry).

Step 3: Estimate how many CPU hours you have. Should they be spent on better statistical convergence? On more chemistry? On more grid nodes? On running more conditions?

Step 4: Perform the simulations, compile averages (if LES), compare against experiment.

Step 5: Draw conclusions on the suitability of your code/model for the particular phenomenon you set out to simulate.

Many papers, from well-known groups, in high-quality journals, make over-claims about their models without the appropriate validation. Examples or erroneous claims:

“Model works for blow-off” although validated for stable flame far from blow-off…“Model OK for heat loss” although not validated against radiative heat transfer data…“Model works for autoignition at 50bar” although chemistry validated at 10bar…Often, people confuse conclusions on chemistry / CFD / turbulent combustion model.

42

Conclusions – Day 3

Old models (EBU etc) use infinitely-fast chemistry. OK for flame length for easy problems.

Useful for initial condition of more complex simulation.

Flamelet models:

If flame does not have local extinction, flamelet model (for prem or non-prem) is OK.

Premixed flames seem more resilient to stretch effects than non-premixed, and hence

flamelet models for premixed have wider applicability.

If significant finite-rate kinetic effects, solve chemistry together with flow:

(i) CMC

(ii) PDF (Lagrangian or Eulerian)

(iii) flamelet with c-x formulation

(iv) Linear Eddy Model

(v) Thickened Flame Model

(vi) “Eddy Dissipation” versions

Must see validation for difficult lab-scale problems involving local extinction (e.g. Sandia F;

Cambridge bluff-body premixed, Cambridge swirl non-premixed and spray, Sydney, DLR

etc), before trusting results. Same for soot.

Sprays: usually derivative from non-premixed; spray flame intricacies not included yet.43

Turbulent Combustion:Modelling and Applications

Princeton Summer School 2021

E. Mastorakos

Engineering Department

University of Cambridge

[email protected]

1

Day 4 & 5: Applications to diesel engines and gas turbines

RANS of diesel-like “bomb” experiments

RANS of diesel engines

Pollutants

Gas turbine combustion

LES/CMC of swirl flame – focus on local and global extinction

LES/CMC of g.t. flame – focus on soot emission

LES/TFM of interacting burners – focus on LBO

2

Diesel engine modelling

• Some preliminary considerations:

– Is initial condition (P,T) OK?

– Is grid sufficient for good spray penetration prediction?

– Which chemistry should I use?

– Soot and NOx schemes at my conditions?

– RANS or LES?

– Models for heat losses to walls?

– How many cycles? Exhaust gas recirculation?

3

Diesel engine modelling

ETH experiment - heptane injection in constant volume chamber. Data exist for:

Autoignition time

Autoignition location

Pressure rise vs. time

Modelling: RANS with Lagrangian spray description, CMC for turbulent reaction model , reduced heptane scheme

Target of simulation: autoignition time, overall pressure rise

Wright et al., Flow Turbulence and Combustion, 2010

4

ETH diesel-like experiment

5


6


7


8

Mie scattering (spray core)

Schlieren (spray)


9

Separate autoignition visualisations at same time from injection:

- Each time, autoignition occurs at different locations, but at the same time approximately


10

No spray terms in mixture fraction variance; no spray correction in c model; no spray correction in CMC equation.


11


12

Atomisation model affects spray development; but perhaps only in the beginning (for this experiment!)


13

Natural outcome of CMC and flamelet models is Q vs. mixture fraction.In CMC, these are functions of space (not only time).

Transient flamelet calcs, constant scaldis.

Choice of chemical scheme affects ignition time.

A general comment about non-premixed autoignition

14

Autoignition time depends on scalar dissipation rate (different dependencies for each P,T condition, chemical scheme, fuel)

If engine operates in this regime,no delaying effect due to strain, hence simpler models OK

But operation at high N means strong effect of strain, hence need good turbulent combustion model.


15

Large sensitivity to chemical mechanism!Uncertainty of initial condition!

What can we really conclude about the CMC turbulent combustion model?


16

Everything in real devices has uncertainties.Significant sensitivities to CFD (injection model, initial temperature, initial turbulence in chamber), solver settings, chemical model.

Very important: be careful with comparison done against ONE set of conditions only!

Sandia diesel-like experiment

17

“Engine Combustion Network”

Sandia experiment with heptane

RANS-CMC, focus on spray models in combustion model

Borghesi et al., Comb. Theory and Modelling, 2011

Focus of simulation: see whether spray terms in CMC equation make a difference


18

<x> xrms <OH> <T>


19

What do we conclude?

- We capture flame location vs. time. This is a success of the CMC model (spatial diffusion and convection terms responsible). Analysis in paper consolidates this conclusion.

- We capture autoignition time trends with exhaust gas recirculation (more important than capturing the exact autoignition time, which is a strong function of the chemical scheme).

- Good validation case for the turbulent combustion model for a diesel-engine like configuration.

Sandia diesel-like experiment: focus on soot

20

Now focus on sooting tendency of fuels, conditions (EGR), and relative performance of two models:

- “Laminar chemistry”- Multidimensional Conditional Moment Closure

Why? Because recently people have ignored 40 years of combustion research and run CFD codes for engines with no combustion model…BUT: often the results look good! How is this possible?

Wright et al., “Influence of turbulence–chemistry interaction for n-heptane spray combustion under diesel engine conditions with emphasis on soot formation and oxidation”, Comb. Theory Modelling, 2014

Sandia diesel-like experiment: focus on soot

21

Two-equation model for soot (mass fraction, number density), including model for differential diffusion of soot particles (due to Kronenburg and Bilger), basic model due to Leung and Lindstedt. See paper for details.


22DI: “Direct Integration” (no combustion model, “laminar chemistry”)


23

For conventional diesel combustion, not big difference of overall observable (if system is kinetics controlled). This is why people did it!But for cases with significant mixing and oxidation, CMC much better than DI. Including proper turbulent combustion model gives generality.

Heavy-duty diesel engine

24

“0D-CMC”: Integrate N over whole engine volume; give this N to the CMC code (i.e. CMC reduces to transient flamelet)

“2D-CMC”: Two-dimensional CMC equation in space

Good agreement for overall pressure trace and heat release rate.

In this engine, N is relatively low relative to the N_critical ; hence local differences in N do not result in significant differences in Qa.

Wright et al, IJER, 2009


25

75%

load100%

load


26

NOx : getting absolute value is just luck; but trends imply good overall success of the model.

In this configuration, most of the NOx is due to the thermal (Zel’dovich) mechanism; hence success to capture trend means success to capture temperature OK.

For systems with lower NOx (and those with prompt NOx being the dominant route), turbulent combustion models and chemical schemes have not been fully validated yet.

Gas turbine combustors

27

Primary & secondary

atomization, dispersion

Chemical mechanism,

turbulence-chemistry

interactions

Heat loss,

radiationNOx, CO, soot,

Temperature

profile, velocity,

vorticity

Flame location Aerodynamics

Thermo-acoustics

(coupling with combustor

acoustics)RED: Usual targets

BLUE: Models

Heat transfer


28

General comments:

- Spray initial conditions: very important for success of overall simulation

- Combustion model: important for Lean-Premixed Prevapourisedconcepts and others with quick mixing

- Chemistry: very important for soot, NOx, local and global extinction- Do we have good enough schemes for kerosene chemistry?

- Aerodynamics: due to strong swirl, curved streamlines, dilution jets, cooling flows, simple RANS does not work too well. Migration to LES has taken place in academia and is taking place in industry.

- Radiation: could become important, as accuracy improves


29

Next few slides:

- Some comments on extinction of flames with swirl

- Results from CH4 jet diffusion flames (Sandia F), CH4 swirl flames (Sydney & Cambridge): validation of LES/CMC for local and global extinction

- Results from Cambridge swirl spray flame: validation of combustion model for spray local extinction

- Demonstration of calculation of realistic gas turbine combustor including soot.

30

Capturing extinction is one of the “Holy Grails” of turbulent combustion theory.

Can we predict blow-off curve with CFD? There is evidence we are making good

progress. Used here as an example of finite-rate kinetic effects to demonstrate

how modelling helps.

0

50

100

150

200

250

0 5 10 15 20 25

Air velocity, m/sA

FR

Lean extinction

Rich extinction

Lean ignition

Rich ignition

Ahmed & Mastorakos, CNF, 2007

The practical ignition/blow-off loop: must run lean so that NOx, CO, soot are low

31

Basic considerations

Extinction is due to competition between fluid mechanics & chemistry.

Manifested in critical strain rate in laminar counterflow flames, well-

stirred reactor critical points, S-shaped curve etc. Laminar flame

extinction is reasonably well understood.

Turbulent flames - local:

- Premixed: Karlovitz number

- Non-premixed: scalar dissipation (Sandia D-F; Sydney series)

- Spray: Not studied much

Turbulent flames – global:

- how do localised extinctions lead to global extinction?

- is it “extinction” or “destabilisation”?

32

Blow-off in gas turbine afterburners: perhaps the first flame stabilisation problem studied

Bluff-body stabilized lean premixed

CH4-air flame close to blow-off, Ub

= 31.4 m/s, Φ = 0.66 (Kariuki PhD)

From Glassman, 4th ed.

(1) Knowledge from afterburner-type geometry must be extended to

non-premixed & spray flames and to short flames.

(2) More detailed research needed.

33

Bluff-body stabilised premixed flames (Dawson et al, Proc Comb Inst 33:1559-1566, 2011)

f same, U increases

OPEN

ENCLOSED<OH*>

Prior to BO

Bluff-body stabilised premixed flames (Dawson et al, Proc CombInst 33:1559-1566, 2011)

34

Flames increasingly closer to blow-off condition(Kariuki et al, Comb Flame, 2012)

Local data from PIV & OH-PLIF:

high u’ gives Ka~12 at location of

extinction. This is much higher than

the limit for igniting a turbulent

premixed flame (Ka~2 ; from

Bradley et al.).

s

Increasing UHigh f Low f

s

35

Blow-off event: OH* and planar Mie (aerosol in reactants)

Reactants penetrate from

downstream end of RZ, not

from the sides. Anchoring point

fails less than downstream.

Blow-off event lasts ~20 ms

(many d/U)

OH*: orange

Mie: grey

36

Approach to extinction: simultaneous CH2O & OH PLIF to image reaction rate (PROCI 35th, 2014)

Reaction inside RZ & fragmentation; flame-flame touching.

Surprising large amounts of CH2O in RZ and thickening of preheat zone.

f=0.75

f=0.68

OH-PLIF CH2O-PLIF CH2O x OH

37

Locally high Ka?

Our knowledge on critical Ka for premixed flames is mostly based on ignition

experiments (e.g. spark a mixture; let kernel grow a little; see if flame

propagates). Some decisions needed what constitutes “good” from “failed” flame

(Bradley, Shy, and many others).

Presence of hot products behind flame affects extinction drastically, allowing very

high Ka locally:

Opposed jet flames (e.g. recent work from Gomez)

Premixed jet in hot co-flow (Dunn et al. experiment from Sydney; modelling)

Related to MILD combustion (lack of clearly-defined ignition/extinction)

Lack of hot products in RZ (fresh reactants, partially-burnt fluid), caused by local

extinction at downstream regions of high Ka, seems to be the main route for

global blow-off of recirculating premixed flames. This is not “destabilisation” in

the sense of flow velocity / turbulent flame speed inbalance.

38

Premixed Non-premixed Spray

All dimensions in mm.

Swirling recirculating flames: 3 types of flame in same burner (Cavaliere et al., FTaC, 2013)

Swirling recirculating flames: 3 types of flame in same burner (Cavaliere et al., FTaC, 2013)

Blow-off of spray flames

Blow-off is not instantaneous, when viewed with kHz diagnostics(Cavaliere, Kariuki, Mastorakos, FTaC, 2013)

39

SPRAY OH*, 5 kHzSPRAY, 30 Hz

40

Ub=19.6 m/s, Φ=0.51 Ub=19.9 m/s, Φ=0.31 Ub=18.3m/s, Φ=0.13,

PREMIXED NON-PREMIXED SPRAY

Blow-off event: OH* & OH-PLIF (5kHz)

OH*

OH-PLIF

Blow-off event: OH* & OH-PLIF (5kHz)

41

Various liquid fuels: Images far from blow-off

Ethanol Decane DodecaneHeptane

OH

PLIF

<OH* >

(Ruoyang Yuan, PhD, 2015;

In. J Spray Comb Dyn 2018)

Various liquid fuels: Images far from blow-off

42

Images close to blow-off

OH

PLIF

<OH* >

Ethanol Decane DodecaneHeptane

Approach to extinction ➔ very fragmented reaction sheet

Images close to blow-off

Large Eddy Simulation: can blow-off be predicted?

43

Combustion sub-grid model critical: balance of strain & reaction must be included

somehow.

LES with CMC (Garmory & Mastorakos, PROCI 33) has been shown to predict

well the Sandia Flame “F”.

So, can we predict global blow-off dynamics and condition in recirculating

flames?

44

LES-CMC: CMC Equation has all the needed ingredients to capture extinction

Conditionally filtered reacting scalar

Chemical source term – 1st order closure, i.e. f(Qa) only

Conditionally filtered velocity – responsible for propagation

Conditionally filtered scalar dissipation rate – responsible

for local extinction

Sub-grid conditional

flux – propagation

45

LES/CMC captures localized extinction (Garmory &

Mastorakos, PROCI, 33rd, 1673-1680, 2011)

Overall very good agreement for Sandia D & F

xst - OH OH <YOH|h>

LES/CMC captures localized extinction (Garmory & Mastorakos, PROCI, 33rd, 1673-1680, 2011)

46

LES/CMC of the CH4 non-premixed TECLFAM flame (Ayache & Mastorakos, FTaC, 2013)

Stoichiometric contour, coloured by OH

Localised extinction and flame liftoff captured.

OH*, experiment

47

LES/CMC of the CH4 non-premixed Sydney flame (Zhang & Mastorakos, PROCI 36, 2017)

Localised extinction captured correctly. Validation against

unconditionally- and conditionally-averaged quantities

48

Capturing global blow-off (Tylizczak et al, FTaC, 2014; Zhang et al, PROCI 35, FTaC 2016)

Conventional LES with mixture fraction (passive scalar), low-Ma,

Smagorinski; estimate sub-grid variance of mixture fraction & sub-grid

scalar dissipation; Lagrangian spray, Abramzon-Sirignano single droplet

evaporation. All models used as “validated” for simple flames.

1-step chemistry for C7H16, 19-species reduced for CH4

LES gives mixing and velocity field to CMC code

CMC code gives density to LES code

LES code: PRECISE-UNS from Rolls-Royce plc

CMC code: new unstructured version (UCAM)

Approach: simulate flame at low U; increase to the determined blow-off

U; what does the LES predict?

49

10

12

14

16

18

20

22

24

26

28

30

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Air

velo

cit

y [

m/s

]

Fuel Flow rate [g/s]

Decane

heptane

Blow-off of swirling heptane spray flame: the target experiment (Cavaliere et al., FTaC, 2014)

OH-PLIF of SWH1

Blow-off condition

SWH1: stable

SWH3: blow-off

CFD path

50

Flame structure

OH-PLIF (exp)

Localized extinction

& re-ignition

Reaction rate LES

51

T=0.0550s

T=0.0600s T=0.0650s T=0.0700s

T=0.0750s T=0.0800s T=0.0850s T=0.0900s

Results: Increasing velocity from SWH1 to SWH3

(stoichiometric isosurface, coloured by T) => global

extinction

Simulation at blow-off U predicts fully extinguished flame & no re-ignition!

Results: Increasing velocity from SWH1 to SWH3 (stoichiometric

isosurface, coloured by T) => global extinction

52

Duration of blow-off event

Blow-off lasts ~20ms, not far from experiment

53

Images close to blow-off: heptane spray flame (Yuan

et al, PROCI 35, 2014; Giusti et al, in preparation)

Flame close to blow-off is fragmented, similar to experiment. LES/CMC captures this violent extinction event. Extinction and re-ignition captured (not possible with flamelet models, unless specifically developed for extinction)

LES/CMC of ethanol spray flame close to blow-off (Giusti et al,

PROCI 36, 2017)

54

Images close to blow-off: heptane spray flame (Yuan

et al, PROCI 35, 2014; Giusti et al, in preparation)

Statistics of local extinction at bluff-body edge captured OK.

LES/CMC of ethanol spray flame close to blow-off (Giusti et al,

PROCI 36, 2017)

55

Complete blow-off curve: Non-premixed CH4 flame (Zhang &

Mastorakos, FTaC 2016)

Full blow-off curve predicted to within 25%

Kerosene swirl flame with LES-CMC

56

Domain

Bluff-body (Φ25)

Swirled air inlet annulus (60°) (Φ37)

Hollow 60°spray

Cambridge bluff body non-premixed swirl-stabilized burnerHollow cone kerosene spray was injected from centre of bluff body at 60° with SMD of ~60 μm based on experiments

Kerosene Fuels:❖ A2: conventional Jet A, C11H22

❖ C1: alcohol-to-jet-fuel, C13H28

❖ C5: synthetic fuel, C10H19

Foale, Giusti & Mastorakos, 2020, AIAA SciTech

Stable swirl kerosene flame with LES-CMC

57

LBO condition – kerosene spray flame with CFD

58

CFD blowoff velocity within 15% of experimental value

Sensitive to numerical set-up (choice of chemistry, spray etc)

Doubly-Conditioned Moment Closure for sprays (Sitte & Mastorakos, CNF 2019)

59

EXP by Rouen

Lift-off OK

c=0.1c=0.6

60

A recap and a conclusion on CMC – as an example of the approach of validating a turb combustion model

CMC model was first derived and some closures validated against DNS

(late 90s-early 00s)

RANS/CMC across a range of flames with simple geometries and some

finite-rate kinetics: further validation

LES/CMC of jet flames, swirl flames: degree of local extinction OK

LES/CMC of full blow-off curve: for gaseous flames OK

LES/CMC of local extinction in ethanol swirl spray flame: OK.

Next steps: more complex fuels; full blow-off curve, soot, Nox.... Then,

move on to real combustors…

We have made progress. Hierarchical approach absolutely necessary.

• …from the experiment

Unsteady behaviour - thermoacoustics

61 Experiment by A.-M. Kypraiou, PhD 2016, CST 2018, ETFS 2018

The amplitude of the HRR fluctuations increases with the amplitude of the velocity fluctuations.

• Some observations:

a) The flame seems to pulsate in the axial direction

b) Regions with high OH* chemiluminescence signal appear at mid-height and close to the walls

c) The opening of the flame brushes on the two sides of the bluff-body changes in time

Phase-locked OH* chemiluminescencesignal

➢ F = 160 Hz➢ A = 0.3➢ Ub = 15 m/s➢ Global eq. ratio = 0.55

• Can we predict the heat release rate fluctuations?

˗ Good prediction of the phase lag

˗ Good prediction of the HRR fluctuations

Unsteady behavior of the flame

62

EXP

CFD

85 deg

90 deg

Line: EXPStar: CFD

Experiment by A.-M. Kypraiou

• What is the mechanism leading to heat release rate fluctuations?

Unsteady behavior of the flame

63

Stoichiometric mixture fraction isosurface coloured with temperature

a) Axial fluctuation of the flame location

b) Fluctuation of the area of the stoichiometric iso-surface

c) This leads to fluctuations of the heat release rate

The key mechanism leading to the fluctuations of the heat release rate seems related to the fluctuation of the flame surface.

• During the forced cycle the stoichiometricmixture fraction isoline moves in the axialdirection.

Forced non-premixed flame

64

white line = the stoichiometric mixture fractionblack line = zero axial velocity

HRRAxial

velocity

Experiments by A.-M. Kypraiou (CST, 2018, ETFS 2018)

• Instantaneous screenshot of the flame

Instantaneous flame structure

65

▪ The outer surface of the flame is not burning (red arrow)

▪ Rich pockets of mixture impinge the wall (green arrow)

˗ There the flame is close to a fully burning state

˗ Wall effects might need to be included in the computation

white line = the stoichiometric mixture fraction

mixture fraction OH mass fraction CH2O mass fraction HRR Temperature (K)

66

LES/CMC of realistic Rolls-Royce combustor (Giusti et al., ASME J Engng Gas Turb Power 2018)

Working with industry…

67


68


First validation of real combustor CFD against in-situ soot measurements.

Soot location captured OK.

69

LES/CMC soot with sectional model (Gkantonas et al, Fuel, 2020)

Coupling of a soot sectional model from Uni of Napoli (A. D’Anna’sgroup) with LES/CMC. Validation in laminar flame first:

70


Cambridge RQL burner

Mean axial velocity for two flow split ratios

71


Flame location captured OK

72


Sooty locations captured OK.

Trends with flow split captured OK.

Careful: direct comparison not easy!

LBO CFD for premixed

73

CFD code: CCM+ v. 2021.1, thickened flame model, det CH4 chem

LES

Chase LBO condition & flame structure close to LBO

Simulations of Cambridge experimentby Sandeep Jella (Siemens Energy)


74

16 m/s

30 m/s

Sandeep Jella (Siemens Energy)


75

Very broad distributions of CH2O – CFD consistent with experiment

Sandeep Jella (Siemens Energy)

CH2OOH*

OH

CH2O

T

Conclusions – Day 4

Autoignition: kinetically-driven phenomenon. Is strain rate in engines high enough to delay

autoignition?

Structure of flame: mixture fraction-based (flamelet, CMC) and PDF methods work very

well. LEM, EDC demonstrate good results too (check literature).

Extinction: for jet & swirl flames, advanced flamelet, CMC, PDF methods work OK. Full

blow-off curve prediction validated with LES/CMC so far. TFM works well for many gt

combustion problems.

Soot: very sensitive to chemical model; need more experiments; validation for swirl flames

very little.

NOx: very little validation so far (“Delft piloted jet flame”); need similar focused efforts for

swirl flames.

Hierarchical approach: validate across many simpler flames first; across range of

conditions; then you can begin to trust your model and code.

Do not over-claim and over-generalise: turbulent flames can burn you…

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Turbulent Combustion: Modelling and Applications