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COMBUSTION TECHNOLOGY Lecture 3

Content of Today’s Lecture

• Turbulent Premixed Flames

• Turbulent Nonpremixed Flames

• CANTERA laminar flame analysis

• CANTERA Autoignition Demonstration

• CANTERA Premix Flame Demonstration

Department of ENERGY TECHNOLOGY AAU Thomas Condra 23rd. October 2013✞

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Basic Flame Types

Fuel/Oxidiser Mixing Fluid Motion Examples

laminar flat flame

Bunsen flame

Premixed

turbulent spark-ignited petrol engines

low NOx stationary gas turbine

laminar wood fire

gas heaters

candle

Non premixed

turbulent pulverised coal combustion

aircraft turbine

Diesel engine

rocket motor


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Turbulent Premixed Flames I

• Basic concepts

• Turbulent flow increases the flame propagation, but no evidence that turbulence substantially alters

the chemistry

• No practical universal method to predict turbulent flame behavior

• Three kinds of turbulent-flame regimes:

Wrinkled laminar-flame regime

Distributed-reaction regime

Flamelets-in-eddies regime

• Turbulent flame speed

Sturb =m

Aρu

m reactant flow rate A time averaged flame area ρu unburnt gas density


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Turbulent Premixed Flames II

• Turbulent fluctuation velocity v′rms =

√

(u′)2 + (v′)2 + (w′)2

• Turbulent length scales Integral scale and Kolmogorov scale

l0 integral scale - largest eddy scale

• lk Kolmogorov microscale - the smallest eddy size =

(

v3l0

(v′rms)3

)1/4

• Turbulence Reynolds number Rel0 =v′rmsl0

ν

• Damkohler number: characteristic flow (mixing) time / characteristic chemical time

Da ≡eddy turnover time for largest eddies

chemical reaction time=

τflow

τchem=

l0/v′rms

δL/SL

=

(

l0

δL

)(

SL

v′rms

)

l0 integral scale (eddy size) δL laminar flame thickness

SL laminar flame speed v′rms turbulent fluctuation velocity


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Turbulent Premixed Flame Regimes I


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Wrinkled Laminar-Flame Regime

Wrinkled laminar flame: Flame Thickness δL ≤ Kolmogorov scale lk

• Wrinkled laminar-flame regime

• Chemical reactions occur in thin sheets (thinner than Kolmogorov scale);

• Damkohler number always greater than 1 - Fast chemistry compared to fluid mixing

• Flame becomes wrinkledflame - flame area larger than laminar flame

• Flame speed less dependent on SL → thus less dependent on fuel/air or fuel type

• 3 → 5 times laminar burning speed

Sturb/SL = Aflamelets/A

• Clavin and Williams: St/SL ={

0.5[

1 +(

1 + 8C (≈ 1) v′rms/S

2L

)1/2]}1/2

• Klimov: St/SL = 3.5(

v′rms/SL

)0.7


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Distributed-Reaction Regime

Distributed-reaction flame: Flame Thickness δL > Integral scale - largest eddy sizes l0

• Difficult to achieve in practice

• Requires small integral length scale (l0) and large turbulent intensity simultaneously

• Above requires high velocity in small passages - high pressure loss and less sustainable flame

• Damkohler number always less than unity → Slow chemistry compared to mixing

• Many pollution formation reactions are slow and occur in distributed regions

• Difficult to handle - transport in reaction zone governed by both molecules turbulence


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Flamelets-In-Eddies Regime

Flamelets-in-eddies flame: Integral scale - largest eddy sizes l0 > Flame Thickness δL > Kolmogorov scale lk

• Characterized by moderate Damkohler number and high turbulence (v′rms

SL

>> 1)

• Of special interest: some practical combustion devices operate in this regime

• Close to ideas behind eddy-breakup model

1. Burning zone consists of parcels of unburnt gas and almost fully burnt gas

2. Combustion rate determined by the rate at which parcels of unburnt gas are broken down into

smaller ones (create sufficient interfacial area between unburnt mixture and hot gases to enable

reaction)

3. Thus chemical reaction rates play no role in determining burning rate but combustion completely

controlled by turbulent mixing rates

¯m′′′

F = −ρCFY′

F,rms

(

v′

rms/l0)

volumetric mass burning rate, isotropic turbulence


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Turbulent Nonpremixed Flames I

• Most common type of flame

• Common domestic oil and gas burners

• Diesel engine combustion

• Pulverised coal flames in power plants

• After-burners in military jet aircraft

• Flaring in refineries or oil fields

• Pool or natural fires

• Supplementary burners in gas-turbine combined cycle plants

• Stabilise flame by:

Strong recirculation zones - by swirling reactants

Behind bluff body (gutter)

• Many burners/flames often a combination of premixed and non-premixed

• Premixing - for practical reasons or to reduce NOx - lower ’peak’ temperature

• Premixed burners - more difficult to control - (turndown) and more susceptible to combustion

pulsations


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Turbulent Nonpremixed Flames II

• Interested in:

- Flame shape and size

- Flame holding and stability

- Heat transfer

- Pollutant emissions

• Jet flames

• Liftoff

• Liftoff distance

• Blowout


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Turbulent Nonpremixed Flames III

• Low flowrate - laminar flame

Length independent of Djet

Only depends on flow

• Increase flow

Transition to turbulence

Flame shortens

• Increase flow - turbulent

Flame still attached

• Increase flow - base holes form

Flame liftoff

• Increase flow

Increase liftoff distance

• Increase flow

Blowout - NOT desirable

• Turbulent flame length

Flow independent (almost)

Port diameter dependent


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Turbulent Nonpremixed Flames Length I

• Visible flame length longer than temperature / concentration measured lengths (65% → 80%)

• Factors affecting flame length:

1. Relative importance of initial jet momentum flux versus buoyant forces - Frf

2. Stoichiometry

3. Ratio of nozzle fluid to ambient gas density - ρe/ρ∞

4. Initial jet diameter - djet

• Flame Froude number characterises buoyancy effect

Small value - flame dominated by buoyancy - simplified flame analysis neglects buoyancy

Large value - initial jet momentum controls mixing

Frf =note error in Turns(2.ed)Vef

3/2s

(

ρeρ∞

)1/4 [∆TfT∞

gdj

]1/2∆Tf : characteristic combustion temperature rise

L∗ =Lffs

dj (ρe/ρ∞)1/2: for Frf < 5 L∗ =

13.5Fr2/5f

(

1 + 0.07Fr2f

)1/5: for Frf ≥ 5 L∗ = 23


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Turbulent Nonpremixed Flames Length II

• Flame in gravity and zero-gravity conditions

• Short jet flame height with buoyancy

• Notice (almost) independence of flow

• Smaller stoichiometric mixture fractions (fs = 1ν+1) -

longer the flame

Because get larger air amount entrained per kg fuel

• Increasing the density of the nozzle fluid produces the same

effect as increasing the nozzle diameter


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Flame Stabilisation

• Methods of turbulent flame stabilization

Low-velocity bypass ports - hand held propane torches

Refractory burner tiles - often combined with swirler

Bluff-body flame-holders

Swirl or jet-induced recirculating flow - rapid increase in flow area creates recirculating zone

• Creation of strong recirculation zone of hot products close to the burner throat

1. Ignites unburned gases

2. Provides a zone where local turbulent flame speed matches local flow velocity


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Premixed Flame - Numerical Solution Method I

What are the aims of this section ?

1. To introduce the basis equations involved

2. To introduce the numerical strategy used

3. To introduce the solution parameters used - to achieve convergence

What is this section based upon ?

The CHEMKIN PREMIX flame manual

Why CHEMKIN when we are using CANTERA ?

Because the techniques used in CANTERA, for all intents and purposes, is the same as CHEMKIN


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Premixed Flame - Numerical Solution Method II• The equations involved are:

Continuity M = ρuA

Energy MdT

dx−

1

cp

d

dx

(

λAdT

dx

)

+A

cp

K∑

k=1

ρYkVkcpkdT

dx+

A

cp

K∑

k=1

ωkhkWk = 0

Species MdYk

dx+

d

dx(ρAYkVk) − AωkWk = 0 (k = 1, . . . ,K)

Equation of State ρ =pW

RT

M Mass flow rate (independent of x) T Temperature Yk Mass fraction of species k

p Pressure u Local velocity of fluid mixture ρ Density

Wk Molecular mass of kth species R Universal gas constant λ Thermal conductivity of mixture

W Mean molecular mass of mixture cpk Specific heat of kth species

ωk Molar rate production (unit volume) - from Arrhenius expression hk Enthalpy of kth species

Vk Diffusion velocity of kth species A Cross section area of stream tube


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Premixed Flame - Numerical Solution Method III

• Two general types of premixed flames (actually CANTERA has more):

Burner-stabilised flame - where M is known, mass flux fractions specified at cold boundary

Freely propagating flame - M is not known (may give start ”guess“) - this is treated here

• Transport properties are needed - multicomponent diffusion coefficients, thermal conductivities and

thermal diffusion coefficients

• Transport properties: two possible methods of description

Mixture-Averaged Transport properties

Multicomponent Transport properties - the more ”sophisticated“ method

• Boundary conditions:

Temperature and species gradients ”nearly“ vanish at cold boundary (i.e. inlet)

All gradients vanish at hot boundary (i.e. outlet)

Yk,J − Yk,J−1

xJ − xJ−1

= 0TJ − TJ−1

xJ − xJ−1

= 0

• Remember that gravity does not ”appear“ in the equations

• Physical extent is given - initial-grid = [0.0, 0.001, . . . 0.05, 0.1] (in metres)


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Premixed Flame - Numerical Solution Method IV

• Finite difference approximations used - backward difference and central difference (equation 11 p. 15)

• First and second derivative in energy equation - use central difference

• Finite-difference flow equations - form a system of nonlinear algebraic equations

• Use a hybrid Newton (damped) method to solve

• Taking φ as variable - function as F (φ):

φn+1 = φn−

(

∂F (φn)

∂φ

)−1

F (φn)

• The term∂F (φn)

∂φis the Jacobian - Never calculate the inverse!

• Save time by re-using Jacobian for a number of iterations - ”Jacobian Age“ (setMaxJacAge(2, 2))

• Initial approximations on a very coarse mesh

• New mesh points added in regions where the solution or its gradients change rapidly (refine-grid = 1)


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Premixed Flame - Numerical Solution Method V

• If Newton iteration fails to find the steady-state solution - then attempt to solve a psuedo-transient

problem

• Psuedo-transient problem - much more stable - is much more certain to converge

• Why not use transient method from the start?

• Because it takes MUCH LONGER time to calculate

• So try Newton - no convergence - then take some time steps

• Then try Newton steady-state solution - no convergence - take more time steps

• If time stepping diverges - then restart

• Restarting:

Change the Fixed temperature (tfix = ) - lowest level ≃ 400 K

Decrease Jacobian age (setMaxJacAge)


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Premixed Flame - CANTERA Simulation I

298

0

500

1000

1500

2000

2500

0 0.02 0.04 0.06 0.08 0.10

0.05

0.1

0.15

0.2

Tem

perature

(K)

Mole

fraction

Distance from burner inlet (m)

Premixed Free Flame at 1 atm and 298 Kstoichiometric combustion of (kmol)

CH4(1), O2(2) and N2(7.52)

T (K)O2

CO2

H2OCOCH4


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Premixed Flame - CANTERA Simulation II

298

0

500

1000

1500

2000

2500

0 0.02 0.04 0.06 0.08 0.10

1000

2000

3000

4000

5000

6000

7000

8000

Tem

perature

(K)

Mole

fraction(ppm)



CH4(1), O2(2) and N2(7.52)

T (K) OH O


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Premixed Flame - CANTERA Simulation III

298

0

500

1000

1500

2000

2500

0.03 0.0325 0.035 0.0375 0.040.00

0.05

0.10

0.15

0.20

Tem

perature

(K)

Mole

fraction



CH4(1), O2(2) and N2(7.52)

T (K)O2

CO2

H2OCOCH4


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Premixed Flame - CANTERA Simulation IV

298

0

500

1000

1500

2000

2500

0.03 0.0325 0.035 0.0375 0.040

1000

2000

3000

4000

5000

6000

7000

8000

Tem

perature

(K)

Mole

fraction(ppm)



CH4(1), O2(2) and N2(7.52)

T (K) OH O


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