NUMERICAL Analysis of Processes

NAP11

Combustion and multiphase flows. Mass and enthalpy balances, chemical reactions. Combustion chamber with nonpremixed streams of fuel and oxidant (method of mixture fraction). Heterogeneous combustion. Multiphase flows (VOF, Euler method and the method of mixture).

Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010 Baldung

NAP11 Combustion

Homegeneous combustion

Premix (only one inlet stream of premixed fuel and oxygen)

Non premixed (separated fuel and oxidising streams)

Laminar flame

Turbulent flame

Laminar flame

Turbulent flame

mixture fraction method (PDF)

EBU (Eddy Break Up models)

Liquid fuels (sprays)

Solid fuels (powder, coal)

Lagrangian method-trajectories of a representative set of droplets/particles in

a continuous media

Lagrange method-trajectories of particles

NAP11 Combustion single-phase flow

Premix (kinetic combustion)

flameletsflamelets

Turbulent premixuL flame velocity (=umsin)

Fronta hořeníFronta hoření

um

Bunsen laminar flame

um

Porous plate

Planar flame

R.N. Dahms et al. / Combustion and Flame (2011)

Nonpremix (diffusive combustion)

Turbulent nonpremix

palivo+spaliny

vzduch+spaliny

vzduch

Čára stechiometrie

Laminar nonpremix

Flame front

palivo vzduch

Spaliny

NAP11 Combustion

Goals of CFD at combustion modelling

Temperature field, thermal Power, thermal loads of walls

Composition of flue gas (emision NOx)

Basic physical laws

NS equations, k-

Transport of species (mass balances of components)

Chemical reactions (equilibrioum, rate equations)

Energy balance (and radiation)

NAP11 Mass balances

i mass fraction of component i in mixture [kg i]/[kg mixture]i mass concentration [kg i]/[m3]

Mass balance (transport equation for each component)

( ) ( ) ( )i i i i iSut

Production rate of component i [kg/m3s]

Mass balances of all components (hydrocarbons, N2, O2, H2O, CO, CO2, S, SO2, NOx ) in fuel stream, oxidiser stream and flue gas

NAP11 Mass balances

Rate of the components Si production is controlled by the following mechanisms

Diffusion of components (micromixing) – tdiffusion (time constant of diffusion)

Chemical kinetics (rate equation for micromixed reactants) – treaction (halftime of reaction)

Damkohler numberdiffusion

reaction

tDa

t

exp( ) ai i

i i

ES A

RT

S Ck

Da<<1

Da>>1

Kinetic control (Arrhenius)

Diffusion control (turbulent)

According to prevailing mechanism we distinguish diffusion or kinetic burning

NAP11 Mass balancesThe rate of production of a specific component i involves more than one reaction and Si should therefore be calculated as the sum of all ongoing reactions. E.g. combustion of methane, collectively described by a single equation CH4+2O2CO2+2H2O takes place in fact by the reaction mechanism, which is described by a system of 277 differential equations of kinetics in which figures 49 components, such as radicals O, OH, H, ... Actual reaction mechanism is usually substituted by simplified mechanism by only few kinetic equations of the most important intermediate steps. For example the methane combustion can be approximated by two reactions (Peters 2000)

22

224

2

1

22

3

COOCO

OHCOOCH

Rate of CO production can be calculated from the 2 reactions (MCH4=16,MCO=28)

4 4

28 28( )

16 16CO CO CH R CO CHS R R Ck

Assuming that the rate is

controlled by turbulent diffusionRate of the first reaction

NAP11 Reaction rateProblem with the prediction of reaction rate is its nonlinear dependence upon temperature

Bimolecular reaction A+B→C

Reaction rate actual

mean

exp( )

exp( )

A B

A B

ER A

RTE

R ART

exp( ) exp( )E E

RT RT

Reaction rate is underestimated when using the mean temperature instead of the mean value of the Arrhenius term

T[K]

Tmean TmaxTmin

SNOx

Actual production rate of NOx

1500 2000

Example NOx production

By an order of magnitude less production of NOx derived from mean

temperature

NAP11 Enthalpy balanceOnly one equation of enthalpy balance summarising contributions of all reactions is necessary

( ) ( ) ( ) hh hu h S Qt

Sum of reaction enthalpies

h i rii

S S h

Assuming no phase changes h ~ cpT

Radiation emiited by flue gas and absorbed by wall of combustion chamber

NAP11 Enthalpy balance radiation

Volumetric enthalpy source is represented by emission and absorption of radiation.

4 4g S g wQ T A T

Emissivity corresponding to temperature of flue gas Ts

Absorptivity of gas corresponding to wall

temperature Tw

The following relationship is a drastic simplification (P1 model) applicable at high optical densities of flue gas

NAP11 Mixture fraction method f

fuel

oxidiser

Mańy different CFD models are used for description of combustion. The simplest method of mixture fraction can be applied for nonpremixed streams of fuel and oxidiser

Hans Baldung

NAP11 Mixture fraction methodNon-premixed combusion, and assumed fast chemical reactions (paraphrased as “What is mixed is burned or is at equilibrium”)

mfuel

moxidiser

Flue gases

Mass balance of fuel

Mass balance of oxidant

Calculation of fuel and oxidiser consumption is the most

difficult part. Mixture fraction method is the way, how to

avoid it

3

of produced fuel[ ]kg

s m

Mass fraction of oxidiser (e.g.air)

Mass fraction of fuel (e.g.methane)

( ) ( ) ( )fuel fuel fuel fuelu St

( ) ( ) ( )ox ox ox oxu St

NAP11

Stoichiometry

1 kg of fuel + s kg of oxidiser (1+s) kg of product

and subtracting previous equations

( ) ( ) ( ) fuel oxsu S St

Introducing new variable

This term is ZERO due to stoichimetry

Mixture fraction method

fuel oxs ( ) ( ) ( )

( ) ( ) ( )

fuel fuel fuel fuel

ox ox ox ox

s s s su St

u St

NAP11 Mixture fraction methodMixture fraction f is defined as linear function of normalized in such a way that f=0 at oxidising stream and f=1 in the fuel stream

Resulting transport equation for the mixture fraction f is without any source term

( ) ( ) ( )f fu ft

Mixture fraction is property that is CONSERVED, only dispersed and transported by convection. f can be interpreted as a concentration of a key element (for example carbon). And because it was assumed that „what is mixed is burned“ the information about the carbon concentration at a place x,y,z bears information about all other participating species.

,0 ,0 ,00

1 0 ,1 ,1 ,0 ,0 ,1 ,0

( )

( )fuel ox fuel ox fuel ox ox

fuel ox fuel ox fuel ox

s sf

s s

s

s

NAP11

,0

,1 ,0

oxst

fuel oxoichiof

s

At fuel rich locations (high values of f) holds

ox ,1( =0) 1 1fuel

stoichiostoichio

stoichiofuel

ff

f

ff

0 0stoichio fuelf f

At the point x,y,z where f=fstoichio are all reactants consumed (therefore

ox=fuel=0)

At fuel lean region

Mixture fraction methodKnowing f we can calculate mass fraction of fuel and oxidiser at any place x,y,z

NAP11

Combustion of coal powder, or burning of fuel droplets ejected from a nozzle or a rotating disc (atomizer) are examples of heterogeneous combustion soleved usually by Lagrange method (tracing trajectories of particles moving inside a continuous phase – flue gas).

Baldung

Heterogeneous combustion

mfuel

NAP11

1| | ( )

2D D

dum F

dt

F c A u v u v

Sum of all forces acting to liquid droplet moving in continuous fluid (fluid velocity v is calculated by solution of NS equations)

Relative velocity (fluid-particle)

Drag force

Drag coefficient cD depends upon Re

0.687

5

24 3(1 Re) Re 5 Oseen

Re 1624

(1 0.15Re ) Re 800 Schiller NaumanRe

0.4 1000< Re 3.10 Newton

D

D

D

c

c

c

1 104 105 Re

cD

Newton’s region cD=0.44

Cloud of particles (c volumetric fraction of dispersed phase)

3.70 /D D cc c

Heterogeneous combustion

NAP11

Example: Evaporation of fuel droplet

Diffusion from surface and mass chenges of droplet

22

05 0.33

( ) ( )6

2 0.6Re

p g dif fg s

dm d DD Sh D

dt dt

Sh Sc

Mass fraction of fuel at surface

Sherwood number

Schmidt =/Ddif

Correlation Ranz Marshall for convective mass transfer

Along the particle trajectory it is necessary to calculate: heating, evaporation of volatile fraction, surface reaction. For the modelling of these processes engineering correlations for heat and mass transfer are used.

Heterogeneous combustion

NAP11 Multiphase flows

Baldung

Methods

Lagrange (spray)

Mixture (sedimentation)

Euler (most frequently used)

VOF (free surface)

NAP11 Multiphase flowsFluidised bed Mixer with

central draft tube

Sprey dryer

Anul.tok

slug

Bublin.var

Convective boiling

Visualisation see for example at THERMOPEDIA

NAP11 Euler – multiphase flow

For every phase q is solved

Continuity equation (mass balance of phase q)

Momentum balance

( ) ( )q q q q q pqp

v mt

Volumetric fraction of phase q

Velocity of phase q

Mass transport from phase p to phase q

( ) ( ) ( )q q q q q q q q q q pqp

v v v p Rt

Interphase forces

Stresses calculated in the same way as in onephase flows

NAP11 Model of mixture ASM(Miko Manninen

VIT report)

The method solves in fact a one-phase flow for the mean density m and mean velocity vm

Continuity equation for mixture

Continuity equation for secondary phase p

Momentum balance for mixture (for single velocity)

( ) 0mm mvt

, ,

,

( ) ( ) ( ( ( ) ) ( )

Tm m m m m m m m p p dr p dr p

p

dr p p m

v v v p v v v vt

v v v

,( ) ( ) ( )p p p p m p p dr pv vt

Driftové rychlosti jsou počítány z algebraického modelu na základě zrychlení (gravitace, odstředivé síly), které působí

na složky směsi o různé hustotě

NAP11 Aplikace: Airlift reaktory

Avercamp

NAP11 Aplikace: Airlift reaktory

NAP11 Aplikace: Airlift reaktoryPoužití metody Euler/Euler pro popis probublávaného reaktoru, kde v kapalině jsou malé a velké (Taylorovské) bubliny. Nestejné bubliny jsou považovány za různé fáze.

Řeší se trojice rovnic bilance hmoty pro objemové zlomky fází 1 (podíl kapaliny), 2 (malé bubliny), 3 (Taylorovské bubliny).

Mezifázové síly Mkl se uvažují jen mezi kapalinou a bublinami (ne mezi malými a velkými bublinami navzájem)

Pro každou fázi se řeší rovnice hybnosti:

Krishna, Baten: Eulerian simulations…

NAP11 Aplikace: ASM tok kalu

J. Ling, P.V. Skudarnov, C.X. Lin, M.A. Ebadian: Numerical investigations of liquid–solid slurry flowsin a fully developed turbulent flow region. International Journal of Heat and Fluid Flow 24 (2003) 389–398

Liquid–solid slurry flows. Algebraic Slip Model.