Proveden

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Computer Fluid Dynamics E181107
2181106
CFD8
Combustion, multiphase flows
Remark foils with black background could be
skipped, they are aimed to the more advanced
courses
Rudolf Žitný, Ústav procesní a zpracovatelské
techniky CVUT FS 2010
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COMBUSTION
CFD8
Use EBU (Eddy Breakup models)
Laminar flame
Premixed (only one inlet stream of mixed fuel and
oxidiser)
Homogeneous reaction in gases
Turbulent flame
Use mixture fraction method (PDF)
Laminar flame
Non premixed (separate fuel and oxidiser inlets)
Liquid fuels (spray combustion)
Turbulent flame
Combustion of particles (coal)
Lagrangian method-trajectories of a
representative set of droplets/particles in a
continuous media
Lagrangian method-trajectories of a
representative set of droplets/particles in a
continuous media
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COMBUSTION
CFD8

• Premixed combustion
• Fuel and oxidiser are mixed first and even then
  burn

uL burning velocity (umsin?)
Bunsen laminar flame
?
um
flame front
Flat flame
um
Bunsen burner fully premixed. Colour corresponds
to radicals CH (photo Wikipedia)
porous plate
R.N. Dahms et al. / Combustion and Flame (2011)
Laminar premixed flames are characterised by a
narrow flame front (front width depends upon the
rate of chemical reaction and diffusion
coefficient). Laminar burning velocity (uL) must
be greater than the velocity of flow (um) in case
of a flat flame front, otherwise the flame will
be extinguished (in fact this is the way how to
determine the burning velocity experimentally).
Example flat laminar flame in porous ceramic
burner. Nonuniform transversal velocity profile
is manifested by a conical flame front, and the
flame front cone angle depends upon burning
velocity uLum sin? . Example Bunsen burner. In
case of turbulent flow the flame front is wavy
and fluctuating (flamelets, the turbulent flame
can be viewed as an ensemble of premixed laminar
flames). Example Combustion in a cylinder of
spark ignition engine, gas turbines in power
plants. Advantage of the premixed combustion In
a gas turbine operating at a fuel-lean condition
high temperatures and associated NOx formation
are avoided. Soot formation is also suppressed.
Disadvantage Risk of uncontrolled explosion of
premixed reactants.
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COMBUSTION
CFD8

• Nonpremixed combustion
• Fuel and oxidiser enter combustion chamber as
  separated streams. Mixing and burning take place
  simultaneously (nonpremix is called diffusive
  burning).

Laminar coflow (left) counter flow (right).
Nonpremixed flames unlike premixed flames do not
propagate. Flame simply cannot propagate into the
fuel side because there is no oxygen, neither to
the oxidising region with lack of fuel. Only
burned products diffuse to both sides of the
flame front. Flame front position corresponds to
stoichiometric ratio fuel/air there is also the
highest temperature. In turbulent nonpremixed
flames the flamelet concept can be used again.
Chemistry of nonpremixed combustion is more
complicated because on one side of the flame
front is the fuel-rich burning accompanied by
formation of sooth and on the air side a fuel
lean combustion occurs. Existence of glowing
sooth is manifested by yellow luminiscence. Exampl
es Industrial burners, combustion engines.
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COMBUSTION
CFD8

• Flame size
• The size (length) of a nonpremixed burning jet
  can be estimated from the velocity of jet and
  from the diffusion time necessary for mixing in
  the transversal direction. Burke and Schumann
  (1928), Ind.Eng.Chem 20998

Velocity of circular jets decreases with the
distance from nozzle (u1/x) however this
approximation assumes a constant velocity at axis
and also cylindrical form of jet, having radius r
of fuel nozzle. Mixing length (r) is associated
with the mixing time by theory of penetration
depth
and the height of flame h is estimated as the
product of the mixing time and axial velocity
This is qualitatively correct conclusion stating
that the flame length is proportional to flowrate
and indirectly proportional to diffusion
coefficient (Warnatz 1996 documents the
diffusion coefficient effect by comparing the
height of flame at hydrogen combustion that is
2.5 shorter than the flame height at carbon
monoxide combustion)
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COMBUSTION aims
CFD8

• Primary purpose of CFD analysis is to evaluate
• Temperature field (therefore thermal power, heat
  fluxes through wall)
• Composition of flue gas (environmental
  requirements, efficiency of burning)
• To do this it is necessary to calculate
• Velocities and turbulent characteristics (mixing
  intensity) NS equations
• Transport of individual components (mass balances
  of species)
• Chemical reactions (reaction rates)
• Energy balances (with special emphasis to
  radiation energy transfer)

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COMBUSTION balances
CFD8
mi mass fraction of specie i in mixture kg
of i/kg of mixture ?mi mass concentration of
specie kg of i/m3 Mass balance of species
(for each specie one transport equation)
Because only micromixed reactants can react
Rate of production of specie i kg/m3s

• Production of species is controlled by
• Diffusion of reactants (micromixing) tdiffusion
  (diffusion time constant)
• Chemistry (rate equation for perfectly mixed
  reactants) treaction (reaction constant)

Damkohler number
Daltlt1
Reaction controlled by kinetics (Arrhenius)
Dagtgt1
Turbulent diffusion controlled combustion
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COMBUSTION problems
CFD8
Specific problems related to combustion (two
examples A and B) A) It is not correct to use
mean concentrations in reaction rate equation
Bimolecular reaction AB?C Production rate
locally
globally
Rotating turbulent eddy
B
A
mA mB
t
Actual reaction rate is zero even if the mean
concentrations are positive
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COMBUSTION problems
CFD8
Specific problems related to combustion (example
B) B) It is not correct to use mean temperatures
in reaction rate equation
Bimolecular reaction AB?C Production rate
locally

globally
SNOx
Example NOx production
Underestimated reaction rate follows from
nonlinear temperature dependence of reaction
constant
Tmean
Tmax
Tmin
Actual production rate of NOx
1500 2000
TK
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COMBUSTION enthalpy
CFD8
Enthalpy balance is written for mixture of all
species (result-temperature field)
Sum of all reaction enthalpies of all reactions
It holds only for reaction without phase changes
h cpT
Energy transport must be solved together with the
fluid flow equations (usually using turbulent
models, k-?, RSM,). Special attention must be
paid to radiative energy transport (not discussed
here, see e.g. P1-model, DTRM-discrete transfer
radiation,). For modeling of chemistry and
transport of species there exist many different
methods and only one - mixture fraction method
will be discussed in more details.
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MIXTURE Fraction method
CFD8
Bacon
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MIXTURE Fraction method
CFD8
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)
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MIXTURE Fraction method
CFD8
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
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MIXTURE Fraction method
CFD8
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
mox is the mass fraction of oxidiser at an
arbitrary point x,y,z, while mox,0 at inlet (at
the stream 0)
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.
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MIXTURE Fraction method
CFD8
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 moxmfuel0)
For example the mass fraction of fuel is
calculated as
The concept can be generalized assuming that
chemical reactions are at equlibrium f ? mi
mass fraction of species is calculated from
equilibrium constants (evaluated from Gibbs
energies)
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MIXTURE Fraction method
CFD8
Equilibrium depends upon concentration of the key
component (upon f) and temperature. Mixture
fraction f undergoes turbulent fluctuations and
these fluctuations are characterized by
probability density function p(f). Mean value of
mass fraction, for example the mass fraction of
fuel is to be calculated from this distribution
Mass fraction corresponding to an arbitrary value
of mixture fraction is calculated from equlibrium
constant
Probability density function, defined in terms of
mean and variance of f
Frequently used ? distribution
0 fmean 1
Variance of f is calculated from another
transport equation
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MIXTURE Fraction method
CFD8
Final remark In the case, that mfuel is a linear
function of f, the mean value of mass fraction
mfuel can be evaluated directly from the mean
value of f (and it is not necessary to identify
probability density function p(f), that is to
solve the transport equation for variation of f).
Unfortunately the relationship mfuel(f) is
usually highly nonlinear.
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COMBUSTION of liquid fuel
CFD8
Lagrangian method trajectories, heating and
evaporation of droplets injected from a nozzle
are calculated.
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 Reynolds number
Effect of cloud (?c volume fraction of dispersed
phase-gas)
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COMBUSTION of liquid fuel
CFD8
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MULTIPHASE flows examples
CFD8
and others Hydrotransport, cyclones, free
surfaces, breakup of liquid jets, expanding
foams, aerated reactors, cavitation, mold
filling Phases Gas-liquid Gas-solid Liquid-liqui
d visualisation THERMOPEDIA
Mixer (draft tube)
Fluidised bed reactor or combustor
Spray dryer
Flow boiling
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MULTIPHASE flows methods
CFD8

• Methods
• Lagrange (see liquid fuel burners, suitable for
  low concentration of particles)
• Mixture (not significant difference between
  phases, e.g. sedimentation)
• Euler (the most frequently used technique for any
  combination of phases)
• VOF (Volume Of Fluid) (evolution of continuous
  interface, e.g. shape of free surface modeling,
  moving front of melted solid)

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MULTIPHASE EULER
CFD8

• For each phase q are separately solved
• Continuity equation (mass balance of phase)
• Momentum balance (each phase is moving with its
  own velocity, only pressure is common for all
  phases)

Mass transfer from phase p to phase q
Velocity of phase q
Volumetric fraction of phase q
Interphase forces
Stresses are calculated in the same way like in
one phase flows
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MULTIPHASE EULER
CFD8
Specific semiemprical correlations describe
interaction terms Mass transfer for example
Ranz Marschall correlation for Sh2 Momentum
exchange
Special models for kpq are available for
liquid-liquid, liquid-solid, and also for
solid-solid combinations
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MULTIPHASE MIXTURE method
CFD8
Mixture model solves in principle one-phase flow
with mean density ?m , mean velocity
vm Continutity equation for mixture Momentum
balance for mixture (with corrections to drift
velocities) Volumetric fraction of
secondary phase (p)
Drift velocities are evaluated from algebraic
models (mixture acceleration determines for
example centrifugal forces applied to phases with
different density)
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MULTIPHASE VOF
CFD8
Evolution of clearly discernible interface
between immiscible fluids (examples jet breakup,
motion of large bubbles, free surface flow)
There exist many different methods in this
category, Level set method, Marker and cell,
Lagrangian method tracking motion of particles at
interface.

• Fluent
• Donor acceptor
• Geometric reconstruction

?0
?0
?
?0
?0
?1
?
?
?
Dissadvantage initially sharp interface is
blurred due to numerical diffusion
?1
?1
?1
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Level Set method
CFD8
The level set method represents a closed curve
(in 2D) or a closed surface (in 3D) ? by using an
auxiliary function ?, called the level set
function. Dimension of level set function is the
dimension of ? 1.
at boundary ?
Properties of level set function ?(x,y,z)
inside ?
Example breakup of bubble
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Level Set method
CFD8
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RADIATION
CFD8
Pollock
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RADIATION
CFD8
Heat flow (W) between gas and wall
Absorptivity of gas corresponding to wall
temperature Tw
Emissivity of gas corresponding to temperature of
gas Ts
Hottels diagram for emissivity of CO2 and H2O as
a function of temperature and pL (pressure x
length)
Kirchhoffs law (?a) EmissivityAbsorptivity at
the same wavelength
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RADIATION Intensity
CFD8
Spherical coordinate system and definition of
solid angle d?
Total power emitted from the small surface dS
The radiation emitted by blackbody surface is
isotropic (intensity Ib is independent of the
direction). Integrating the radiation power for
solid angles covering the whole upper hemisphere
results to relationship between the emissive
power Eb and the intensity Ib
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RADIATION participating media
CFD8
Variation of intensity I is described by the
integro-differential RTE equation that follows
from the photon balance in the control volume
oriented in the selected direction of beam.
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RADIATION Fluent models
CFD8
Radiation models are selected according to
optical thickness of media (flue gas) a.L
aLlt1 DTRM (discrete transf.radiation modelling)
DO (discrete ordinates) 1ltaLlt3 P-1 model
(transport equation for radiation
temperature) 3ltaL Roseland model (simplified P-1
model)
Absorption and scatter