NUMERICAL%20Analysis%20of%20Processes

1
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 CVUT FS 2010
Baldung
2
Combustion
NAP11
EBU (Eddy Break Up models)
Laminar flame
Premix (only one inlet stream of premixed fuel
and oxygen)
Homegeneous combustion
Turbulent flame
mixture fraction method (PDF)
Laminar flame
Non premixed (separated fuel and oxidising
streams)
Liquid fuels (sprays)
Turbulent flame
Solid fuels (powder, coal)
Lagrangian method-trajectories of a
representative set of droplets/particles in a
continuous media
Lagrange method-trajectories of particles
3
Combustion single-phase flow
NAP11

• Premix (kinetic combustion)

uL flame velocity (umsin?)
Bunsen laminar flame
?
um
Fronta horení
Planar flame
um
Porous plate
R.N. Dahms et al. / Combustion and Flame (2011)

• Nonpremix (diffusive combustion)

Laminar nonpremix
Turbulent nonpremix
Cára stechiometrie
palivospaliny
Flame front
vzduchspaliny
Spaliny
vzduch
palivo
vzduch
4
Combustion
NAP11

• 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)

5
Mass balances
NAP11
Mass balances of all components (hydrocarbons,
N2, O2, H2O, CO, CO2, S, SO2, NOx ) in fuel
stream, oxidiser stream and flue gas
?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)
Production rate of component i kg/m3s
6
Mass balances
NAP11

• 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)

According to prevailing mechanism we distinguish
diffusion or kinetic burning
Damkohler number
Daltlt1
Kinetic control (Arrhenius)
Diffusion control (turbulent)
Dagtgt1
7
Mass balances
NAP11
The 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
CH42O2?CO22H2O 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)
Rate of CO production can be calculated from the
2 reactions (MCH416,MCO28)
Assuming that the rate is controlled by turbulent
diffusion
Rate of the first reaction
8
Reaction rate
NAP11
Problem with the prediction of reaction rate is
its nonlinear dependence upon temperature
Bimolecular reaction AB?C Reaction rate
actual

mean
SNOx
Example NOx production
Tmean
Tmax
Tmin
Reaction rate is underestimated when using the
mean temperature instead of the mean value of the
Arrhenius term
Actual production rate of NOx
1500 2000
TK
By an order of magnitude less production of NOx
derived from mean temperature
9
Enthalpy balance
NAP11
Only one equation of enthalpy balance
summarising contributions of all reactions is
necessary
Radiation emiited by flue gas and absorbed by
wall of combustion chamber
Assuming no phase changes h cpT
Sum of reaction enthalpies
10
Enthalpy balance radiation
NAP11
Volumetric enthalpy source is represented by
emission and absorption of radiation.
The following relationship is a drastic
simplification (P1 model) applicable at high
optical densities of flue gas
Absorptivity of gas corresponding to wall
temperature Tw
Emissivity corresponding to temperature of flue
gas Ts
11
Mixture fraction method f
NAP11
Many 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
12
Mixture fraction method
NAP11
Non-premixed combusion, and assumed fast chemical
reactions (paraphrased as What is mixed is
burned or is at equilibrium)
Calculation of fuel and oxidiser consumption is
the most difficult part. Mixture fraction method
is the way, how to avoid it
Flue gases
Mass fraction of fuel (e.g.methane)
Mass balance of fuel Mass balance of oxidant
Mass fraction of oxidiser (e.g.air)
13
Mixture fraction method
NAP11
Stoichiometry 1 kg of fuel s kg of oxidiser
? (1s) kg of product
Introducing new variable
and subtracting previous equations
This term is ZERO due to stoichimetry
14
Mixture fraction method
NAP11
Mixture fraction f is defined as linear function
of ? normalized in such a way that f0 at
oxidising stream and f1 in the fuel stream
Resulting transport equation for the mixture
fraction f is without any source term
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.
15
Mixture fraction method
NAP11
Knowing f we can calculate mass fraction of fuel
and oxidiser at any place x,y,z
At the point x,y,z where ffstoichio are all
reactants consumed (therefore ?ox?fuel0)
At fuel rich locations (high values of f) holds
At fuel lean region
16
Heterogeneous combustion
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
17
Heterogeneous combustion
NAP11
Sum of all forces acting to liquid droplet moving
in continuous fluid (fluid velocity v is
calculated by solution of NS equations)
Drag force
Relative velocity (fluid-particle)
Drag coefficient cD depends upon Re
Cloud of particles (?c volumetric fraction of
dispersed phase)
18
Heterogeneous combustion
NAP11
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.
19
Multiphase flows
NAP11

• Methods
• Lagrange (spray)
• Mixture (sedimentation)
• Euler (most frequently used)
• VOF (free surface)

Baldung
20
Multiphase flows
NAP11
Mixer with central draft tube
Fluidised bed
Sprey dryer
Convective boiling
Visualisation see for example at THERMOPEDIA
21
Euler multiphase flow
NAP11

• For every phase q is solved
• Continuity equation (mass balance of phase q)
• Momentum balance

Mass transport from phase p to phase q
Velocity of phase q
Volumetric fraction of phase q
Interphase forces
Stresses calculated in the same way as in
onephase flows
22
Model of mixture ASM(Miko Manninen VIT report)
NAP11

• 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)

Driftové rychlosti jsou pocítány z algebraického
modelu na základe zrychlení (gravitace,
odstredivé síly), které pusobí na složky smesi o
ruzné hustote
23
Aplikace Airlift reaktory
NAP11
Avercamp
24
Aplikace Airlift reaktory
NAP11
25
Aplikace Airlift reaktory
NAP11
Krishna, Baten Eulerian simulations
Použití metody Euler/Euler pro popis
probublávaného reaktoru, kde v kapaline jsou malé
a velké (Taylorovské) bubliny. Nestejné bubliny
jsou považovány za ruzné fáze. Reší se trojice
rovnic bilance hmoty pro objemové zlomky fází ?1
(podíl kapaliny), ?2 (malé bubliny), ?3
(Taylorovské bubliny).
Pro každou fázi se reší rovnice hybnosti
Mezifázové síly Mkl se uvažují jen mezi kapalinou
a bublinami (ne mezi malými a velkými bublinami
navzájem)
26
Aplikace ASM tok kalu
NAP11
Liquidsolid slurry flows. Algebraic Slip Model.
J. Ling, P.V. Skudarnov, C.X. Lin, M.A. Ebadian
Numerical investigations of liquidsolid slurry
flows in a fully developed turbulent flow region.
International Journal of Heat and Fluid Flow 24
(2003) 389398