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Basics of ComputationalCombustion ModellingDr. Gavin Tabor

Combustion p.1

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Why study Combustion?

Combustion of hydrocarbons important fuel source Power generation Aircraft, rocket propulsion Cars etc Marine applications

Combustion rapid chemical reaction between fueland oxidant (air). Usually involves fluid flow.Understand + model processes improve powergeneration, decrease polutants.

Combustion p.2

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Physical basis

Complex area of investigation : Combustion affects fluid flow. Heat release T change physical properties. Alsobuoyancy drives flow

Fluid flow affects combustion. Brings reactantstogether, removes products. Can determinerate of combustion, and even extinguish flame.

Overall, combustion rapid chemical reactionbetween fuel and oxidiser.However details vary treat different regimesdifferently.

Combustion p.3

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Combusion regimes

Non-premixed combustion Regions of fuel + oxidiser separate, Combustion occurs at interface

Premixed combustion Fuel and oxidiser mixed at molecular level Regions of burned and unburned gas,

separated by (thin) flame Partially premixed combustion

somewhere between

Combustion p.4

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Some examples

Premixed : Spark ignition (IC) petrol engines Lean burn gas turbines Household burners Bunsen burner (blue flame regime)

Partially premixed : Direct injection (DI) petrol engines Aircraft gas turbines

Combustion p.5

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Examples non-premixed

Non-premixed : Diesel engines Aircraft gas turbines Furnaces Candles, fires

Combustion p.6

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Flame structure

Premixed combustion Flame propagating in laminar flow is characterisedby :

Laminar flame speed sL,thickness lF

Combustion rate controlled by molecular diffusionprocesses (DL diffusivity)

Combustion p.7

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Chemistry

Dimensional analysis gives :

lF =DLsL

linking these processes.Chemical reaction time

tL =lFsL

Combustion p.8

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Turbulent flame structure

This is more complex. Turbulence characterised by

turbulence intensity u

Integral, Kolmogorov scales lI ,

Turbulent Reynolds number ReT =ulI

Characteristic turbulent eddy turnover time

tT =lIu

Combustion p.9

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Damkhler number

Compare importance of turbulence and combustion Damkhler number

Da =tTtL

=lIsLulF

ratio of eddy turnover time to burning effect of turbulence on chemical processes

Other measures :lF / Measure of local distortion of the flameu/sL Relative strength of turbulence.

Combustion p.10

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Flame structure

In more detail, 3 regions :Oxidant

Fuel

T

PreheatZone

InnerLayer

OxidationLayer

Flame Propagation

Combustion p.11

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Flame structure

1. a preheat zone,2. an inner layer of fuel consumption,3. the oxidation layer.

Thickness of the inner layer

l = lF

For stoichoimetric methane at 1 atmosphere,

lF = 0.175 mm and = 0.1

Combustion p.12

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Non-premixed combustion

No obvious characteristic velocity scale Define a characteristic diffusion thickness lD Flame still divided into fuel consumption and

oxidation layers Oxidation layer

l = lD

of more importance.

Combustion p.13

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Modelling direct approach

We can approach the problem in a simple way : Combustion chemical reaction process

combining reactants to form products Write balance equations for species Solve together with continuity and momentum

equations

Combustion p.14

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Mass fraction

Define Mass fraction Yi the mass of the species per unit massof the mixture.Transport equation

Yit

+.Yiu = .DiYi + Si

Source term represents addition/removal due tocombustion

Combustion p.15

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Temperature equation

Also need transport equation for some measureof the energy say temperature T .

T

t+.Tu = .DT + ST

Source term represents radiation, pressure work,energy release.

Combustion p.16

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Reactive scalars

Often group everything together asreactive scalars

i = {Y1, Y2, . . . , Yn, T}

with transport equation

it

+.iu = .Dii + Si

Combustion p.17

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Problems

Problems with this approach :1. n often quite large!

Elementary reaction mechanisms detail 100s ofreactions for combustion process. InvokeQSSA to reduce to manageable proportions(1-5).

2. Turbulence still unaccounted for!!Turbulence introduces too many details tocalculate. Use Reynolds averaging to eliminatedetails, replace by a model.

Combustion p.18

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Moment methods

Turbulence modelling replace small scale detailof turbulence with (cheaper) turbulence model.Similar process used in combustion modelling average to remove details, then substitute a model.Density of fluid variable use Favre averaging.

ux(x, t) = ux + u

x

Hereux = 0 and thus ux =

ux

Combustion p.19

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Favre averaging

Useful for modelling when density varies : NSEcontain terms such as

uxuy

Using Favre averaging this becomes

uxuy = uxuy + uxu

y

Use this to derive mean flow equations(Favre-averaged NSE) and equations for k and a turbulence model for compressible flow.

Combustion p.20

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Moment methods cont.

Favre averaged equation for reactive scalars :

it

+.iu = .Dii .ui + Si

High Re, so molecular diffusivity D can be ignored.Two terms cause problems :

.ui representing turbulent transportand

Si the mean chemical source term

Combustion p.21

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Specific models

Different combustion models arrise from differentapproaches to these terms range from cheap andinaccurate to precise and expensive.E.g. Eddy Breakup Model Spalding (1971) assumes turbulent mixing determines chemical

reaction rate gives simple model for chemical source term combine with k model for turbulence cheap to compute. Requires extensive tuning.

Combustion p.22

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PDF Transport

Probability Distribution Function methods turbulence can be described/modelled in

terms of correlation functions turbulent processes combustion can also be

described/modelled in terms of correlations joint PDF of velocity and reactive scalars

P (u, ;x, t)

Potentially more accurate. Also very expensive.

Combustion p.23

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Flamelet methods

Main alternative methodology.High Re,Da flame fronts very thin consideras 2d sheet which : separates burnt and unburnt gas (premixed

combustion) separates fuel and air (non-premixed) is distorted by mean flow and by turbulence propagates by burning.

Location of flame sheet specified by indicator function.

Combustion p.24

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Indicator function

Premixed combustion : progress variable

c =T TuTb Tu

or c =YPYP,b

0 < c < 1 : 1 represents burned gas, 0 unburned.Some intermediate value represents flame centre.

Combustion p.25

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1-d representation

Plotting c across the flame :

c

c = 0.5 = flame centre0

1

BurnedUnburned

Combustion p.26

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Flame wrinking

Flame will be wrinkled by turbulence on scales toosmall to simulate

Combustion p.27

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Averaging

Average equation

c

t+.cu = .uc + Sc

Need to model :

ucturbulent transport termSc reaction term

but now have a manageable set of equations.

Combustion p.28

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Other models

Other versions flame surface density G-equation Non-premixed combustion

use mixture fraction Z.

Combustion p.29

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Counter-gradient transport

Final note : modelling of uc often uses gradienttransport assumption

uc = Dtc

However this is frequently wrong counter-gradienttransport.

Combustion p.30

Why study Combustion?Physical basisCombusion regimesSome examplesExamples -- non-premixedFlame structureChemistryTurbulent flame structureDamk"ohler numberFlame structureFlame structureNon-premixed combustionModelling -- direct approachMass fractionTemperature equationReactive scalarsProblemsMoment methodsFavre averagingMoment methods cont.Specific modelsPDF TransportFlamelet methodsIndicator function1-d representationFlame wrinkingAveragingOther modelsCounter-gradient transport