© fluent inc. 4/12/20151 fluent software training trn-99-003 combustion modeling in fluent

© Fluent Inc. 04/18/231

Fluent Software TrainingTRN-99-003

Combustion Modelingin FLUENT

© Fluent Inc. 04/18/232


Outline

Applications Overview of Combustion Modeling Capabilities Chemical Kinetics Gas Phase Combustion Models Discrete Phase Models Pollutant Models Combustion Simulation Guidelines

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Applications Wide range of homogeneous

and heterogeneous reacting flows

Furnaces Boilers Process heaters Gas turbines Rocket engines

Predictions of: Flow field and mixing

characteristics Temperature field Species concentrations Particulates and pollutants

Temperature in a gas furnace

CO2 mass fraction

Stream function

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Aspects of Combustion Modeling

Dispersed Phase Models

Droplet/particle dynamicsHeterogeneous reactionDevolatilizationEvaporation

Governing Transport EquationsMassMomentum (turbulence)EnergyChemical Species

Combustion Models

PremixedPartially premixedNonpremixed

Pollutant Models Radiative Heat Transfer Models

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Gas phase combustion Generalized finite rate formulation (Magnussen model) Conserved scalar PDF model (one and two mixture fractions) Laminar flamelet model (V5) Zimont model (V5)

Discrete phase model Turbulent particle dispersion

Stochastic tracking Particle cloud model (V5)

Pulverized coal and oil spray combustion submodels Radiation models: DTRM, P-1, Rosseland and Discrete Ordinates (V5) Turbulence models: k-, RNG k-, RSM, Realizable k-(V5) and LES (V5) Pollutant models: NOx with reburn chemistry (V5) and soot

Combustion Models Available in FLUENT

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Modeling Chemical Kinetics in Combustion Challenging

Most practical combustion processes are turbulent Rate expressions are highly nonlinear; turbulence-chemistry interactions

are important Realistic chemical mechanisms have tens of species, hundreds of

reactions and stiff kinetics (widely disparate time scales) Practical approaches

Reduced chemical mechanisms Finite rate combustion model

Decouple reaction chemistry from turbulent flow and mixing Mixture fraction approaches

Equilibrium chemistry PDF model Laminar flamelet

Progress variable Zimont model

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Generalized Finite Rate Model Chemical reaction process described using global mechanism. Transport equations for species are solved.

These equations predict local time-averaged mass fraction, mj , of each species.

Source term (production or consumption) for species j is net reaction rate over all k reactions in mechanism:

Rjk (rate of production/consumption of species j in reaction k) is computed to be the smaller of the Arrhenius rate and the mixing or “eddy breakup” rate.

Mixing rate related to eddy lifetime, k /. Physical meaning is that reaction is limited by the rate at which turbulence

can mix species (nonpremixed) and heat (premixed).

R Rj jkk

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Setup of Finite Rate Chemistry Models

Requires: List of species and their properties List of reactions and reaction rates

FLUENT V5 provides this info in a mixture material database. Chemical mechanisms and physical properties for the most common

fuels are provided in database. If you have different chemistry, you can:

Create new mixtures. Modify properties/reactions of existing mixtures.

© Fluent Inc. 04/18/239


Generalized Finite Rate Model: Summary

Advantages: Applicable to nonpremixed, partially premixed, and premixed combustion Simple and intuitive Widely used

Disadvantages: Unreliable when mixing and kinetic time scales are comparable (requires

Da >>1). No rigorous accounting for turbulence-chemistry interactions Difficulty in predicting intermediate species and accounting for

dissociation effects. Uncertainty in model constants, especially when applied to multiple

reactions.

© Fluent Inc. 04/18/2310


Conserved Scalar (Mixture Fraction) Approach: The PDF Model

Applies to nonpremixed (diffusion) flames only Assumes that reaction is mixing-limited

Local chemical equilibrium conditions prevail. Composition and properties in each cell defined by extent of turbulent

mixing of fuel and oxidizer streams. Reaction mechanism is not explicitly defined by you.

Reacting system treated using chemical equilibrium calculations (prePDF). Solves transport equations for mixture fraction and its variance, rather

than species transport equations. Rigorous accounting of turbulence-chemistry interactions.

© Fluent Inc. 04/18/2311


Mixture Fraction Definition

The mixture fraction, f, can be written in terms of elemental mass fractions as:

where Zk is the elemental mass fraction of some element, k. Subscripts F and O denote fuel and oxidizer inlet stream values, respectively.

For simple fuel/oxidizer systems, the mixture fraction represents the fuel mass fraction in a computational cell.

Mixture fraction is a conserved scalar: Reaction source terms are eliminated from governing transport equations.

OkFk

Okk

ZZ

ZZf

,,

,

© Fluent Inc. 04/18/2312


Systems That Can be Modeled Using a Single Mixture Fraction

Fuel/air diffusion flame:

Diffusion flame with oxygen-enriched inlets:

System using multiple fuel inlets:

60% CH4 40% CO21% O2 79% N2

f = 1

f = 0

35% O2 65% N2

60% CH4 40% CO

35% O2 65% N2

f = 1

f = 0

f = 0

60% CH4 20% CO 10% C3H8 10% CO2

21% O2 79% N2

f = 1

f = 0

f = 1

60% CH4 20% CO 10% C3H8 10% CO2

© Fluent Inc. 04/18/2313


Equilibrium Approximation of System Chemistry

Chemistry is assumed to be fast enough to achieve equilibrium. Intermediate species are included.

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PDF Modeling of Turbulence-Chemistry Interaction

Fluctuating mixture fraction is completely defined by its probability density function (PDF).

p(V), the PDF, represents fraction of sampling time when variable, V, takes a value between V and V + V.

p(f) can be used to compute time-averaged values of variables that depend on the mixture fraction, f:

Species mole fractions Temperature, density

p V VTT

ii

( ) lim

1

© Fluent Inc. 04/18/2315


PDF Model Flexibility

Nonadiabatic systems: In real problems, with heat loss or gain, local thermo-chemical state must

be related to mixture fraction, f, and enthalpy, h. Average quantities now evaluated as a function of mixture fraction,

enthalpy (normalized heat loss/gain), and the PDF, p(f). Second conserved scalar:

With second scalar in FLUENT, you can model: Two fuel streams with different compositions and single oxidizer stream

(visa versa) Nonreacting stream in addition to a fuel and an oxidizer Co-firing a gaseous fuel with another gaseous, liquid, or coal fuel Firing single coal with two off-gases (volatiles and char burnout products)

tracked separately

© Fluent Inc. 04/18/2316


Mixture Fraction/PDF Model: Summary

Advantages: Predicts formation of intermediate species. Accounts for dissociation effects. Accounts for coupling between turbulence and chemistry. Does not require the solution of a large number of species transport

equations Robust and economical

Disadvantages: System must be near chemical equilibrium locally. Cannot be used for compressible or non-turbulent flows. Not applicable to premixed systems.

© Fluent Inc. 04/18/2317


The Laminar Flamelet Model

Temperature, density and species (for adiabatic) specified by two parameters, the mixture fraction and scalar dissipation rate

Recall that for the mixture fraction PDF model (adiabatic), thermo-chemical state is function of f only

can be related to the local rate of strain

Extension of the mixture fraction PDF model to moderate chemical nonequilibrium

Turbulent flame modeled as an ensemble of stretched laminar, opposed flow diffusion flames

2)/( xf ),( fii

© Fluent Inc. 04/18/2318


Laminar Flamelet Model (2) Statistical distribution of flamelet ensemble is specified by the PDF

P(f,), which is modeled as Pf (f) P (), with a Beta function for Pf (f) and a Dirac-delta distribution for P ()

Only available for adiabatic systems in V5 Import strained flame calculations

prePDF or Sandia’s OPPDIF code Single or multiple flamelets

Single: user specified strain, a Multiple: strained flamelet library, 0 < a < aextinction

a=0 equilibrium a= aextinction is the maximum strain rate before flame extinguishes

Possible to model local extinction pockets (e.g. lifted flames)

1

0 0

)()(),( dfdPfPf fii

© Fluent Inc. 04/18/2319


The Zimont Model for Premixed Combustion Thermo-chemistry described by a single progress variable,

Mean reaction rate, Turbulent flame speed, Ut, derived for lean premixed combustion and

accounts for Equivalence ratio of the premixed fuel Flame front wrinkling and thickening by turbulence Flame front quenching by turbulent stretching Differential molecular diffusion

For adiabatic combustion,

The enthalpy equation must be solved for nonadiabatic combustion

t

cx

u cx Sc

c

xR c

ii

i

t

t ic

0 1

R U cc unburnt t

p

adp

pp YYc /

adunburnt TcTcT )1(

© Fluent Inc. 04/18/2320


Discrete Phase Model Trajectories of particles/droplets/bubbles are

computed in a Lagrangian frame. Exchange (couple) heat, mass, and

momentum with Eulerian frame gas phase Discrete phase volume fraction must < 10%

Although the mass loading can be large No particle-particle interaction or break up

Turbulent dispersion modeled by Stochastic tracking Particle cloud (V5)

Rosin-Rammler or linear size distribution Particle tracking in unsteady flows (V5) Model particle separation, spray drying,

liquid fuel or coal combustion, etc.

Continuous phase flow field calculation

Particle trajectory calculation

Update continuous phase source terms

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Turbulent dispersion is modeled by an ensemble of Monte-Carlo realizations (discrete random walks)

Particles convected by the mean velocity plus a random direction turbulent velocity fluctuation

Each trajectory represents a group of particles with the same properties (initial diameter, density etc.)

Turbulent dispersion is important because Physically realistic (but computationally more expensive) Enhances stability by smoothing source terms and

eliminating local spikes in coupling to the gas phase

Particle Dispersion: The Stochastic Tracking Model

Coal particle tracks in an industrial boiler

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Particle Dispersion: The Particle Cloud Model

Track mean particle trajectory along mean velocity Assuming a 3D multi-variate Gaussian distribution about this mean

track, calculate particle loading within three standard deviations Rigorously accounts for inertial and drift velocities A particle cloud is required for each particle type (e.g. initial d, etc.) Particles can escape, reflect or trap (release volatiles) at walls Eliminates (single cloud) or reduces (few clouds) stochastic tracking

Decreased computational expense Increased stability since distributed source terms in gas phase

BUT decreased accuracy since Gas phase properties (e.g. temperature) are averaged within cloud Poor prediction of large recirculation zones

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Particle Tracking in Unsteady Flows

Each particle advanced in time along with the flow For coupled flows using implicit time stepping, sub-iterations for the particle

tracking are performed within each time step For non-coupled flows or coupled flows with explicit time stepping, particles

are advanced at the end of each time step

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Coal/Oil Combustion Models

Coal or oil combustion modeled by changing the modeled particle to Droplet - for oil combustion Combusting particle - for coal combustion

Several devolatilization and char burnout models provided. Note: These models control the rate of evolution of the fuel off-gas from

coal/oil particles. Reactions in the gas (continuous) phase are modeled with the PDF or finite rate combustion model.

© Fluent Inc. 04/18/2325


NOx Models NOx consists of mostly nitric oxide (NO).

Precursor for smog Contributes to acid rain Causes ozone depletion

Three mechanisms included in FLUENT for NOx production: Thermal NOx - Zeldovich mechanism (oxidation of atmospheric N)

Most significant at high temperatures Prompt NOx - empirical mechanisms by De Soete, Williams, etc.

Contribution is in general small Significant at fuel rich zones

Fuel NOx - Empirical mechanisms by De Soete, Williams, etc. Predominant in coal flames where fuel-bound nitrogen is high and

temperature is generally low.

NOx reburn chemistry (V5) NO can be reduced in fuel rich zones by reaction with hydrocarbons

© Fluent Inc. 04/18/2326


Soot modeling in FLUENT Two soot formation models are available:

One-step model (Khan and Greeves) Single transport equation for soot mass fraction

Two-Step model (Tesner) Transport equations for radical nuclei and soot mass fraction

concentrations Soot formation modeled by empirical rate constants

where, C, pf, and are a model constant, fuel partial pressure and equivalence ratio, respectively

Soot combustion (destruction) modeled by Magnussen model Soot affects the radiation absorption

Enable Soot-Radiation option in the Soot panel

RTEnfformation epCR /

© Fluent Inc. 04/18/2327


Combustion Guidelines and Solution Strategies Start in 2D

Determine applicability of model physics Mesh resolution requirements (resolve shear layers) Solution parameters and convergence settings

Boundary conditions Combustion is often very sensitive to inlet boundary conditions

Correct velocity and scalar profiles can be critical Wall heat transfer is challenging to predict; if known, specify wall

temperature instead of external convection/radiation BC Initial conditions

While steady-state solution is independent of the IC, poor IC may cause divergence due to the number and nonlinearity of the transport equations

Cold flow solution, then gas combustion, then particles, then radiation For strongly swirling flows, increase the swirl gradually

© Fluent Inc. 04/18/2328


Combustion Guidelines and Solution Strategies (2)

Underrelaxation Factors The effect of under-relaxation is highly nonlinear

Decrease the diverging residual URF in increments of 0.1 Underrelax density when using the mixture fraction PDF model (0.5) Underrelax velocity for high bouyancy flows Underrelax pressure for high speed flows

Once solution is stable, attempt to increase all URFs to as close to defaults as possible (and at least 0.9 for T, P-1, swirl and species (or mixture fraction statistics))

Discretization Start with first order accuracy, then converge with second order to improve accuracy Second order discretization especially important for tri/tet meshes

Discrete Phase Model - to increase stability, Increase number of stochastic tracks (or use particle cloud model) Decrease DPM URF and increase number of gas phase iterations per DPM

© Fluent Inc. 04/18/2329



Magnussen model Defaults to finite rate/eddy-dissipation (Arrhenius/Magnussen)

For nonpremixed (diffusion) flames turn off finite rate Premixed flames require Arrhenius term so that reactants don’t burn

prematurely May require a high temperature initialization/patch Use temperature dependent Cp’s to reduce unrealistically high

temperatures Mixture fraction PDF model

Model of choice if underlying assumptions are valid Use adequate numbers of discrete points in look up tables to ensure

accurate interpolation (no affect on run-time expense) Use beta PDF shape

© Fluent Inc. 04/18/2330



Turbulence Start with standard k- model Switch to RNG k- , Realizable k- or RSM to obtain better agreement

with data and/or to analyze sensitivity to the turbulence model Judging Convergence

Residuals should be less than 10-3 except for T, P-1 and species, which should be less than 10-6

The mass and energy flux reports must balance Monitor variables of interest (e.g. mean temperature at the outlet) Ensure contour plots of field variables are smooth, realistic and steady

© Fluent Inc. 04/18/2331


Concluding Remarks

FLUENT V5 is the code of choice for combustion modeling. Outstanding set of physical models Maximum convenience and ease of use

Built-in database of mechanisms and physical properties Grid flexibility and solution adaption

A wide range of reacting flow applications can be addressed by the combustion models in FLUENT.

Make sure the physical models you are using are appropriate for your application.

© fluent inc. 4/12/20151 fluent software training trn-99-003 combustion modeling in fluent

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