Lecture 2: Non Premixed Combustion Model 15.0 Release
Advanced Combustion Modeling
Diffusion Flames •
Fuel and Oxidizer enters separately in the combustion zone –
They mix and burn during continuous inter-diffusion
Time required for convection and diffusion is much larger that for chemical reactions •
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Problem can be simplified since it eliminates parameters associated with chemical kinetics
Non-premixed Vs Premixed Combustion •
Non-Premixed Combustion
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Separate streams for Fuel and oxidizer
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Convection or diffusion of reactants from either side into a flame sheet Turbulent eddies distort the laminar flame shape and enhance mixing
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May be simplified to a mixing problem
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Premixed combustion
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Fuel and oxidizer are already mixed at the molecular level prior to ignition Flame propagation from hot products to cold reactants Rate of propagation (flame speed) depends on the internal flame structure Turbulence distorts the laminar flame shape and thus accelerates flame propagation
Fuel Oxidizer
Combustion chamber Non-Premixed
Fuel +
Oxidizer
Combustion chamber
Premixed
Modeling turbulent reacting flows •
Simplify the chemistry –
Use finite rate/eddy dissipation approach •
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Decouple chemistry from flow –
Use mixture fraction approach •
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Considers global chemical reaction mechanisms
Equilibrium chemistry PDF model Laminar flamelet model
Progress variable (premixed model) Mixture fraction and progress variable (partially premixed model)
Model detailed chemistry (stiff chemistry) – –
CPU intensive Typically requires use of very small time steps to achieve numerical stability and convergence •
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Can be impractical
Use of the stiff chemistry solver will allow larger time steps to be used
Combustion Models •
Mixture Fraction Model (Non-Premixed ( Non-Premixed model) – Equilibrium Single and 2 mixture fraction model – Flamelet Steady Unsteady flamelet model •
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Species Transport Model – Fast chemistry Eddy dissipation/finite rate Relax to equilibrium – Detailed chemistry Laminar stiff chemistry solver Eddy Dissipation Concept PDF transport – Surface chemistry •
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Non Premixed Combustion Model 15.0 Release
Advanced Combustion Modeling
Non-premixed model •
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Burke & Schumann (1928), Bilger (1976) suggested a closure based on mixture fraction ( Z ) for turbulent diffusion flames Assumptions involved –
Separate streams for fuel and oxidizer (diffusion flames)
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Equal species diffusion coefficients •
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Suitable for turbulent flows as turbulent diffusion overwhelms
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Unity Lewis number
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Low Mach number flow
With these assumptions –
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Species transport equations can be reduced to a single equation for conserved scalar, mixture fraction ( Z or f ) For mixture fraction equation, the reaction source terms cancel out since elements are conserved in chemical reactions S. P. Burke and T. E. W. Schumann, Indust. Eng. Chem. 20 (1928) p. 998 R. W. Bilger, Combust. Sci. Technol. 13 (1976) p. 155
Non-premixed model (cont…) •
The Favre mean mixture fraction equation
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For chemical equilibrium, scalars like Y i , and T are are uniquely related to the mixture fraction ( f )
. . = .
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–
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∅ = ∅ For non-adiabatic systems: ∅ = ∅ , , For adiabatic systems:
In turbulent flows –
Mean values of scalars are of interest
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The probability density function, P ( f f ) can be employed •
Describes the temporal fluctuations of f in in the turbulent flow
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Mathematical functions like
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Transport equation for variance of mean mixture fraction would be required
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t =
or double
functions can be used
′ . . ′ = . ′ ′
0.85; C g = 2.86 and C d = 2.0
Non-premixed model (cont…) –
Density weighted mean species mass fraction or temperature •
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∅ = ∅
Overall calculation procedure
PDF Shape
Chemical Equilibrium
∅ = ∅
P
= , ′ P
Mean scalar value
∅ = ∅ –
∅ values can be pre-tabulated for given chemistry model (like chemical equilibrium) and assumed PDF shape and looked up whenever required
Mixture fraction •
Mixture fraction ( Z or f )
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= +
1 kg CH4 1 kg O2
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Z = = 1 at fuel inlet
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Z = = 0 at oxidizer inlet
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f = 1/2
atomic elements conservation
In other region •
represents fraction of fuel stream Z represents
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(1 - Z ) represents fraction of oxidizer stream
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Fuel-air ratio =
(−)
× (−) (−)
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Equivalence ratio =
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For methane-air reaction: CH4+2(O2+3.76N2) –
reaction
Z St =
=
=.
CO2+2H2O+7.52N2
CO2 H2O CO O2 CH4 f = 1/2
Model set up • • •
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Switch on turbulence model Switch on non premixed combustion model Select chemical equilibrium for state relation definition Specify operating pressure Specify rich flammability limit –
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Little less than 2 times Z st
Thermodynamic data base file mentioned in the file path location would be used for equilibrium calculation Specify composition and temperature for fuel and oxidizer streams
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Calculate PDF table
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Boundary conditions –
Fuel inlet/s
= 1.0 Z =
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Oxidizer inlet/s
= 0.0 Z =
Systems That Can be Modelled With One Mixture Fraction 40% O2 60% N2 60% H2 40% N2 21% O2 79% N2
f = 1
100% C3H8
f = 1
f = 0
40% O2 60% N2
f = 0
m R 60% CH4 15% H2O f = 1 25% CO 21% O2 f exit m F f = 0 f = 1 79% N2 60% CH4 mO f = 1 f = 0 15% H2O 25% CO systems CANNOT CANNOT be modeled using the mixture fraction PDF approach approach Premixed systems
f = 0
f exit
m F m F m
O
The Two Mixture Fractions Model Solve for a second, independent, conserved scalar (mean and variance)
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Computationally expensive since PDF integrations performed at run-time
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Text User Interface option for full tabulation 1 1
p f p 1
fuel
2
psec
f fuel , psec df fuel dpsec
0 0
With a second mixture fraction variable you can model:
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Three gas stream compositions (different species and/or temperature)
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Two fuels and one oxidizer streams
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One fuel and two oxidizer streams
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One fuel, one oxidizer and one inert stream
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Co-firing a gaseous fuel with a liquid or solid particle (coal) fuel
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Two composition discrete phase
Co-firing a liquid fuel with a coal fuel A single fuel with two off gases - significant for coal combustion as volatiles and char burnout can be tracked separately
Systems That Can be Modelled With Two Mixture Fractions
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System with two distinct fuel inlets:
CH4/CO/C3H8 Oxidant CH4/C3H8
21% O2 •
System with two distinct oxidizer inlets:
s=1 f = 0, s = 0 f=1
f=s=0
Fuel
f=1
35% O2
s=1
Mixture Fraction/PDF Approach for Non-Adiabatic systems •
Local thermo-chemical state is related to the mixture fraction and enthalpy i i f , h T h m j h j C p , j dT j 1 T
where •
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N
ref
Turbulent fluctuations are described by a joint PDF, p(f, h*). It is reasonable to assume that enthalpy fluctuations are independent of the enthalpy level itself h F h
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Then the enthalpy can be related to the mixture fraction alone h h f
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The joint PDF now becomes a single variable PDF with p( f ) evaluated as before. p[ f, h*( f )] = p( f )h*-h
Mixture Fraction/PDF Approach for Non-Adiabatic systems Averaged quantities are now evaluated as:
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1
i
d f f , h p f df
i
0
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Enthalpy is determined from the transport equation:
h u h t x
i
i
h t S h h xi xi
where Sh represents enthalpy source terms from radiation or dispersed phase heat exchange
Non-Adiabatic Systems Q wall or Q radiation •
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Heat transfer to domain boundaries and/or radiation heat transfer Multiple fuel or oxidant inlets at different temperatures
Dispersed phase heat transfer
Fuel
f = 1
Oxidant
f = 0
Fuel T = T1 Oxidant Fuel T = T2
Oxidant
f = = 1 f = 0 f =1
Liquid fuel or pulverized coal
PDF table generation generation Non Premixed combustion model is the model of choice for non-premixed gas phase reacting flow problem where the models assumptions are fulfilled (non-premixed inlets, turbulent flow, equilibrium) •
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Easy set up, there is no need to provide a mechanism
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Robust and fast to converge
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No need to select the species for the equilibrium calculation, the user defines the "boundary" species, and the "excluded" species. The equilibrium solver automatically automatically adds any other species in equilibrium
Solution strategies for Non premixed model •
Non-premixed model: –
In general there is no need to solve first the cold flow, or to patch high temperature
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Start with the reacting flow simulation without radiation
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Enable radiation once the main flow feature and temperature temperature field have been established
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Default URF could be too aggressive agg ressive for complex reacting flow system
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The effect of under-relaxation is highly non-linear –
Decrease the diverging residual URF in increments of 0.1
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Under-relax density when using the mixture-fraction PDF model ( 0.7)
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Once solution is stable, attempt attempt to increase energy, energy, mixture and radiation URF’s as close as possible to 1
Compressible Non-premixed Combustion Model •
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Enthalpy –
Enthalpy from PDF tables : h = chemical + thermal (sensible) (sensible)
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Total enthalpy solved in Fluent: H = chemical + thermal + kinetic
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In Fluent, PDF lookup table: h = H – kinetic energy
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Hence, non-adiabatic PDF tables required, even if simulation is adiabatic.
Pressure –
Pressure used in PDF is constant: density calculated as PDF
p PDF ~
RT –
Density in compressible cases calculated as Solver
p Solver ~
RT
pSolver p PDF
PDF
Species and temperature are assumed unaffected by pressure
Compressible Non-premixed Combustion Model •
Use the compressible model with caution… –
The assumption of chemical equilibrium (or near chemical equilibrium with the laminar flamelet model) is increasingly inaccurate at higher flow speeds:
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Flow residence time decreases
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Temperature Temperature decreases and reaction rates drop
The effect of pressure variations, both mean and fluctuating, are neglected in the model: •
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Equilibrium species and temperatures are very sensitive to pressure
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pressure – a 4D table would be required for equilibrium
Non-premixed Combustion Model Advantages Chemistry decoupled from underlying turbulent flow; providing increased stability and efficiency. Accurate tracking of intermediate intermediate species concentrations concentrations and dissociation effects Turbulence-chemistry interactions accounted for rigorously via PDFs Model of choice if underlying assumptions are valid •
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Disadvantages Flow must be turbulent Applicable to non-premixed flames only Chemistry must be close to equilibrium everywhere (Da > 1000) • • •
Laminar Flamelet Model •
Steady and unsteady laminar flamelet model
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Applicability – –
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Application examples – – –
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Flow Regime: Turbulent flow (high Re) Chemistry: Moderately non-equilibrium non-equilibrium due to aerodynamic strain Prediction of lift off and blow off phenomena in jet flames Internal combustion engine (Diesel unsteady flamelet submodel only) Liquid/liquid reacting systems (unsteady flamelet submodel)
Limitations –
Steady approach cannot realistically model phenomena which depend on detailed kinetics (such as ignition, extinction and low-Da flow).
Steady Laminar Flamelet • • •
Turbulent flame modeled as ensemble of stretched laminar flames The laminar flame model is the opposed flow diffusion Extension of mixture fraction/PDF model to moderate chemical non-equilibrium non-equilibrium
turbulent flame
laminar flamelet structure (see detail below) velocity (ufuel)
velocity (uox)
velocity gradient (afuel)
velocity gradient (aox)
temperature (Tfuel)
temperature (Tox)
fuel composition
oxidizer composition fuel-oxidizer distance
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(Kai) is the scalar dissipation rate (1/s) 0; The chemistry chemistry tends to equilibrium equilibrium Chemistry departs from equilibrium with increase in due to aerodynamic straining •
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5
N. Peters (1984) Laminar Diffusion Flamelet Models i n Non-Premixed Turbulent Combustion.Prog.. Energy. Combust. Sci., 10, p. 10, p. 319.
Flamelet Modeling Approach •
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Turbulent flame brush is modeled as an ensemble of discrete diffusion flamelets Density weighted mean species mass fraction or temperature
∅ = , ∅ , , f and are assumed to be independent , = Delta function is assumed for Mean scalar dissipation rate is calculated as = –
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C = 2.0
Instantaneous flamelets
Turbulent flame brush
Model Set Up •
Overall setup and solution procedure is similar to equilibrium closure model –
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Except the state relation calculations
Need to generate/import flamelets –
Flamelet generation from specified reaction mechanism •
CHEMKIN mechanism file –
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Species limit 500
Options to import pre p re generated flamelets –
Standard format
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CFX-RIF
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Oppdif
Single or multiple flamelets –
Single: user specified strain a Multiple: strained flamelet library (up to extinction)
Unsteady Flamelet Models Generalized Unsteady Flamelet Model
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Post-process one or several unsteady marker I n that represents the probability of fuel from nth flamelet, after achieving a converged reacting flow using the steady state flamelet The steady flow solution must be computed with the steady laminar flamelet model The effect of the unsteady flamelets on the flow is neglected The slow-forming species as NOx must be identified before solving The marker probability transport equations are solved simultaneously with the slow species transport equations Y i until the marker diffused out of the domain. The unsteady species mass fraction are computed from
Unsteady Flamelet Models •
Diesel Unsteady Flamelet Model – The chemistry is modeled as a single (or multiple) one-dimensional laminar flamelet
– The flamelet species and energy equations are solved simultaneously with the flow.
– The flamelet equations are advanced for a fractional step using properties from the flow, and then the flow is advanced for the same fractional time-step using properties from the flamelet.
Lifted flame
– Multiple diesel unsteady flamelets allow to consider •
Several combustion events (split injections)
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Lifted spray flames
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Exhaust Gas Recirculation with mixture fraction
– Applications: predicting combustion in compressionignition engines
Same mixture fraction but different reaction progress states
Diesel Unsteady Flamelet Model •
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The initial flamelet condition at the start of the diesel simulation is a mixed-butunburnt distribution For the flamelet fractional time-step, the volume-averaged volume-averaged scalar dissipation, pressure and fuel and oxidizer temperatures, are passed from the flow solver to the flamelet solver Temperature rise during compression accounted using additional term in flamelet energy equation This rise in flamelet temperature due to compression eventually leads to ignition of the flamelet
Summary •
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Mixture fraction approach •
Equilibrium chemistry PDF model
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Laminar flamelet model
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Unsteady flamelet model
Tutorials & additional resources –
Several tutorial available for these models
