Section 14.1: Description of the Equilibrium Mixture Fraction/PDF Model. Section 14.2: Modeling Approaches for Non-Premixed Equilibrium Chemistry

Transcription

1 Chapter 14. Combustion Modeling Non-Premixed In non-premixed combustion, fuel and oxidizer enter the reaction zone in distinct streams. This is in contrast to premixed systems, in which reactants are mixed at the molecular level before burning. Examples of non-premixed combustion include methane combustion, pulverized coal furnaces, and diesel (compression) internal-combustion engines. Under certain assumptions, the thermochemistry can be reduced to a single parameter: the mixture fraction. The mixture fraction, denoted by f, is the mass fraction that originated from the fuel stream. In other words, it is the local mass fraction of burnt and unburnt fuel stream elements (C, H, etc.) in all the species (CO 2, H 2 O, O 2, etc.). The approach is elegant because atomic elements are conserved in chemical reactions. In turn, the mixture fraction is a conserved scalar quantity, and therefore its governing transport equation does not have a source term. Combustion is simplified to a mixing problem, and the difficulties associated with closing non-linear mean reaction rates are avoided. Once mixed, the chemistry can be modeled as in chemical equilibrium, or near chemical equilibrium with the laminar flamelet model. These models are presented in the following sections: Section 14.1: Description of the Equilibrium Mixture Fraction/PDF Model Section 14.2: Modeling Approaches for Non-Premixed Equilibrium Chemistry Section 14.3: User Inputs for the Non-Premixed Equilibrium Model Section 14.4: The Laminar Flamelet Model Section 14.5: Adding New Species to the prepdf Database c Fluent Inc. November 28,

2 Modeling Non-Premixed Combustion 14.1 Description of the Equilibrium Mixture Fraction/ PDF Model The non-premixed modeling approach involves the solution of transport equations for one or two conserved scalars (the mixture fractions). Equations for individual species are not solved. Instead, species concentrations are derived from the predicted mixture fraction fields. The thermochemistry calculations are preprocessed in prepdf and tabulated for look-up in FLUENT. Interaction of turbulence and chemistry is accounted for with a probability density function (PDF). Information about the non-premixed mixture fraction/pdf model is presented in the following subsections: Section : Benefits and Limitations of the Non-Premixed Approach Section : Details of the Non-Premixed Approach Section : Restrictions and Special Cases for Non-Premixed Modeling See Section 14.2 for an overview of modeling and solution procedures, and Section 14.3 for instructions on using the model Benefits and Limitations of the Non-Premixed Approach Advantages of the Non-Premixed Approach The non-premixed modeling approach has been specifically developed for the simulation of turbulent diffusion flames with fast chemistry. For such systems, the method offers many benefits over the finite rate formulation described in Chapter 13. The non-premixed model allows intermediate (radical) species prediction, dissociation effects, and rigorous turbulencechemistry coupling. The method is computationally efficient in that it does not require the solution of a large number of species transport equations. When the underlying assumptions are valid, the non-premixed approach is preferred over the finite rate formulation c Fluent Inc. November 28, 2001

3 14.1 Description of the Equilibrium Mixture Fraction/ PDF Model Limitations of the Non-Premixed Approach! As detailed in Section , the non-premixed approach can be used only when your reacting flow system meets several requirements. First, the FLUENT implementation requires that the flow be turbulent. Second, the reacting system includes a fuel stream, an oxidant stream, and, optionally, a secondary stream (another fuel or oxidant, or a non-reacting stream). Finally, the chemical kinetics must be rapid so that the flow is near chemical equilibrium. These issues are detailed in Sections and Note that the non-premixed model can be used only with the segregated solver; it is not available with the coupled solvers Details of the Non-Premixed Approach Definition of the Mixture Fraction The basis of the non-premixed modeling approach is that under a certain set of simplifying assumptions, the instantaneous thermochemical state of the fluid is related to a conserved scalar quantity known as the mixture fraction f. The mixture fraction can be written in terms of the atomic mass fraction as [213] f = Z i Z i,ox Z i,fuel Z i,ox (14.1-1) where Z i is the elemental mass fraction for some element, i. The subscript ox denotes the value at the oxidizer stream inlet and the subscript fuel denotes the value at the fuel stream inlet. If the diffusion coefficients for all species are equal, then Equation is identical for all elements, and the mixture fraction definition is unique. The mixture fraction is thus the elemental mass fraction that originated from the fuel stream. Note that this mass fraction includes all elements from the fuel stream, including inert species such as N 2, and any oxidizing species mixed with the fuel, such as O 2. If a secondary stream (another fuel or oxidant, or a non-reacting stream) is included, the fuel and secondary mixture fractions are simply the mass c Fluent Inc. November 28,

4 Modeling Non-Premixed Combustion fractions of the fuel and secondary streams. The sum of all three mixture fractions in the system (fuel, secondary stream, and oxidizer) is always equal to 1: f fuel + f sec + f ox = 1 (14.1-2) This indicates that only points on the plane ABC (shown in Figure ) in the mixture fraction space are valid. Consequently, the two mixture fractions, f fuel and f sec, cannot vary independently; their values are valid only if they are both within the triangle OBC shown in Figure f ox 1 A f sec 1 C 0 O B 1 f fuel Figure : Relationship of f fuel, f sec,andf ox FLUENT discretizes the triangle OBC as shown in Figure Essentially, the primary mixture fraction, f fuel, is allowed to vary between zero and one, as for the single mixture fraction case, while the secondary mixture fraction lies on lines with the following equation: f sec = p sec (1 f fuel ) (14.1-3) where p sec is the normalized secondary mixture fraction and is the value at the intersection of a line with the secondary mixture fraction axis c Fluent Inc. November 28, 2001

5 14.1 Description of the Equilibrium Mixture Fraction/ PDF Model 1 C p sec f sec 0 O f fuel B 1 Figure : Relationship of f fuel, f sec,andp sec Note that unlike f sec, p sec is bounded between zero and one, regardless of the f fuel value. An important characteristic of the normalized secondary mixture fraction, p sec, is its assumed statistical independence from the fuel mixture fraction, f fuel. Note that unlike f sec, p sec is not a conserved scalar. The normalized mixture fraction definition for the second scalar variable is used everywhere except when defining the rich limit for a secondary fuel stream, which is defined in terms of f sec. Transport Equations for the Mixture Fraction Under the assumption of equal diffusivities, the species equations can be reduced to a single equation for the mixture fraction, f. The reaction source terms in the species equations cancel, and thus f is a conserved quantity. While the assumption of equal diffusivities is problematic for laminar flows, it is generally acceptable for turbulent flows where turbulent convection overwhelms molecular diffusion. The mean (time-averaged) mixture fraction equation is c Fluent Inc. November 28,

6 Modeling Non-Premixed Combustion = ( ) t (ρf)+ (ρ vf) µt f + S m + S user (14.1-4) σ t The source term S m is due solely to transfer of mass into the gas phase from liquid fuel droplets or reacting particles (e.g., coal). S user is any user-defined source term. In addition to solving for the mean mixture fraction, FLUENT solves a conservation equation for the mean mixture fraction variance, f 2 [105]: ( ) ( ) ( ρf 2 + ρ vf µt ( ) 2 = f 2 )+C g µ t 2 f C d ρ ɛ t σ t k f 2 +S user (14.1-5) where f = f f. The constants σ t, C g,andc d take the values 0.85, 2.86, and 2.0, respectively, and S user is any user-defined source term. The mixture fraction variance is used in the closure model describing turbulence-chemistry interactions (see below). For a two-mixture-fraction problem, f fuel and f 2 fuel are obtained from Equations and by substituting f fuel for f and f 2 fuel for f 2. f sec is obtained from Equation by substituting f sec for f. p sec is then calculated using Equation , and p 2 sec is obtained by solving Equation with p sec substituted for f. Solution for p 2 sec instead of f 2 sec is justified by the fact that the amount of the secondary stream is relatively small compared with the total mass flow rate. To a first-order approximation, the variances in p sec and f sec are relatively insensitive to f fuel, and therefore p 2 sec is essentially the same as f 2 sec. The Non-Premixed Model for LES For large eddy simulations (LES), an equation for the mean mixture fraction is solved, which is identical in form to Equation except that µ t is the subgrid-scale viscosity. A transport equation is not solved for the mixture fraction variance. Instead, it is modeled as 14-6 c Fluent Inc. November 28, 2001

7 14.1 Description of the Equilibrium Mixture Fraction/ PDF Model f 2 = C var L 2 sgs f 2 (14.1-6) where C var = user-adjustable constant L sgs = subgrid length scale Mixture Fraction vs. Equivalence Ratio The mixture fraction definition can be understood in relation to common measures of reacting systems. Consider a simple combustion system involving a fuel stream (F), an oxidant stream (O), and a product stream (P) symbolically represented at stoichiometric conditions as F+r O (1 + r) P (14.1-7) where r is the air-to-fuel ratio on a mass basis. Denoting the equivalence ratio as φ, where φ = (air/fuel) actual (air/fuel) stoichiometric (14.1-8) the reaction in Equation , under more general mixture conditions, can then be written as φ F+r O (φ + r) P (14.1-9) Looking at the left side of this equation, the mixture fraction for the system as a whole can then be deduced to be f = φ φ + r ( ) Equation is an important result, allowing the computation of the mixture fraction at stoichiometric conditions (φ = 1) or at fuel-rich conditions (e.g., φ>2). c Fluent Inc. November 28,

8 Modeling Non-Premixed Combustion Relationship of f to Species Mass Fraction, Density, and Temperature The power of the mixture fraction modeling approach is that the chemistry is reduced to one or two conserved mixture fractions. All thermochemical scalars (species mass fraction, density, and temperature) are uniquely related to the mixture fraction(s). Given a description of the reacting system chemistry, and certain other restrictions on the system (see Section ), the instantaneous mixture fraction value at each point in the flow field can be used to compute the instantaneous values of individual species mole fractions, density, and temperature. If, in addition, the reacting system is adiabatic, the instantaneous values of mass fractions, density, and temperature depend solely on the instantaneous mixture fraction, f: φ i = φ i (f) ( ) for a single fuel-oxidizer system. If a secondary stream is included, the instantaneous values will depend on the instantaneous fuel mixture fraction, f fuel, and the secondary partial fraction, p sec : φ i = φ i (f fuel,p sec ) ( ) In Equations and , φ i represents the instantaneous species mass fraction, density, or temperature. In the case of non-adiabatic systems, this relationship generalizes to φ i = φ i (f,h ) ( ) for a single mixture fraction system, where H is the instantaneous enthalpy (identical to H as defined in Equation ): H = j m j H j = j [ ] T m j c p,j dt + h 0 j (T ref,j ) T ref,j ( ) If a secondary stream is included, 14-8 c Fluent Inc. November 28, 2001

9 14.1 Description of the Equilibrium Mixture Fraction/ PDF Model φ i = φ i (f fuel,p sec,h ) ( ) Examples of non-adiabatic flows include systems with radiation, heat transfer through walls, heat transfer to/from discrete phase particles or droplets, and multiple inlets at different temperatures. Additional detail about the mixture fraction approach in such non-adiabatic systems is provided on page The details of the functional relationship between φ i (species mass fraction, density, and temperature) and mixture fraction (Equations through ) depend on the description of the system chemistry. You can choose to describe this relationship using the flame sheet (mixed-isburned), equilibrium chemistry, or non-equilibrium chemistry (flamelet) model, as described below. Models Describing the System Chemistry FLUENT provides three options for description of the system chemistry when you use the non-premixed modeling approach. These options are: The Flame Sheet Approximation (Mixed-is-Burned): The simplest reaction scheme is the flame sheet or mixed-is-burned approximation. This approach assumes that the chemistry is infinitely fast and irreversible, with fuel and oxidant species never coexisting in space and complete one-step conversion to final products. This description allows species mass fractions to be determined directly from the given reaction stoichiometry, with no reaction rate or chemical equilibrium information required. This simple system description yields straight line relationships between the species mass fractions and the mixture fraction, as shown in Figure Because no reaction rate or equilibrium calculations are required, the flame sheet approximation is easily computed and yields a rapid calculation. However, the flame sheet model is limited to the prediction of single-step reactions and cannot predict intermediate species formation or dissociation effects. This often results in a serious overprediction of peak flame temperature, especially in those c Fluent Inc. November 28,

10 Modeling Non-Premixed Combustion systems that involve very high temperature (e.g., systems using pre-heat or oxygen-enrichment). Equilibrium Assumption: The equilibrium model assumes that the chemistry is rapid enough for chemical equilibrium to always exist at the molecular level. An algorithm based on the minimization of Gibbs free energy [120] is used to compute species mole fractions from f. Figure shows the resulting mole fractions for a reacting system that includes 10 species in the combustion of methane in air. The equilibrium model is powerful since it can predict the formation of intermediate species and it does not require a knowledge of detailed chemical kinetic rate data. Instead of defining a specific multi-step reaction mechanism (see Chapter 13), you simply define the important chemical species that will be present in the system. FLUENT then predicts the mole fraction of each species based on chemical equilibrium. FLUENT allows you to restrict the full equilibrium calculation to those situations in which the instantaneous mixture fraction is below a specified rich limit, f rich. In fuel-rich regions (e.g., equivalence ratio greater than 1.5 ) when the instantaneous mixture fraction exceeds f rich, FLUENT assumes that the combustion reaction is extinguished and that unburned fuel coexists with reacted material. In such fuel-rich regions the composition at a given value of mixture fraction is computed from the composition of the limiting mixture (f=f rich ) and that of the fuel inlet stream (f=1) based on a known stoichiometry. The stoichiometry is either supplied by you or determined automatically from chemical equilibrium at the rich limit (f=f rich ). This approach, known as the partial equilibrium approach, allows you to bypass complex equilibrium calculations in the rich flame region. The latter are time-consuming to compute and may not be representative of the real combustion process. When a full equilibrium approach is required, you can simply define the rich limit as f rich =1.0. Guidelines on the choice of which species to include in the equilibrium calculation are provided in Section The species you include must exist in the chemical database accessed by prepdf c Fluent Inc. November 28, 2001

11 14.1 Description of the Equilibrium Mixture Fraction/ PDF Model Note that the species included in the equilibrium calculation should probably not include NO x species, as the NO x reaction rates are slow and should not be treated using an equilibrium assumption. Instead, NO x concentration is predicted most accurately using the FLUENT NO x postprocessor where finite rate chemical kinetics are incorporated. Non-Equilibrium Chemistry (Flamelet Model): In combustion models where non-equilibrium effects are important, the assumption of local chemical equilibrium can lead to unrealistic results. Typical cases in which the equilibrium assumption breaks down are modeling the rich side of hydrocarbon flames, predicting the intermediate species that govern NO x formation, and modeling lift-off and blow-off phenomena in jet flames. Several approaches are available to overcome these modeling difficulties on a case-by-case basis; in FLUENT the partial-equilibrium/ rich-limit approximation (described above) can be used to model the fuel-rich side of the hydrocarbon flames. Flamelet models have been proposed as a more general solution to the problem of moderate non-equilibrium flame chemistry. See Section 14.4 for details about the laminar flamelet model in FLUENT. PDF Modeling of Turbulence-Chemistry Interaction Equations through describe the instantaneous relationships between mixture fraction and species mass fraction, density, and temperature as given by the equilibrium, flamelet, or mixed-is-burned chemistry model. The FLUENT prediction of the turbulent reacting flow, however, is concerned with prediction of the time-averaged values of these fluctuating scalars. How these time-averaged values are related to the instantaneous values depends on the turbulence-chemistry interaction model. FLUENT applies the assumed shape probability density function (PDF) approach as its closure model when the non-premixed modeling approach is used. The PDF closure model is described in this section. c Fluent Inc. November 28,

12 Modeling Non-Premixed Combustion Mass Fraction, Y and Enthalpy, h h Y F Y O YP 0 f st 1 Mixture Fraction, f Figure : Species Mass Fractions and Enthalpy Derived Using the Flame Sheet Approximation KEY CH4 O2 CO2 H2O N2 CO H2 M o l e F r a c t i o n 1.00E E E E E E E E E E E E+00 Mixture Fraction F CHEMICAL EQUILIBRIUM INSTANTANEOUS SPECIES COMPOSITION prepdf V4.00 Fluent Inc. Figure : Equilibrium Species Mole Fractions Computed Based on Chemical c Fluent Inc. November 28, 2001

13 14.1 Description of the Equilibrium Mixture Fraction/ PDF Model Description of the Probability Density Function The probability density function, written as p(f), can be thought of as the fraction of time that the fluid spends at the state f. Figure illustrates this concept. The fluctuating value of f, plotted on the right side of the figure, spends some fraction of time in the range denoted as f. p(f), plotted on the left side of the figure, takes on values such that the area under its curve in the band denoted, f, is equal to the fraction of time that f spends in this range. Written mathematically, 1 p(f) f = lim T T τ i ( ) i where T is the time scale and τ i istheamountoftimethatf spends in the f band. The shape of the function p(f) depends on the nature of the turbulent fluctuations in f. In practice, p(f) isexpressedasa mathematical function that approximates the PDF shapes that have been observed experimentally. ƒ ƒ ƒ τ i τ i p( ƒ) Figure : Graphical Description of the Probability Density Function, p(f) c Fluent Inc. November 28,

14 Modeling Non-Premixed Combustion Derivation of Mean Scalar Values from the Instantaneous Mixture Fraction The probability density function p(f), describing the temporal fluctuations of f in the turbulent flow, has the very beneficial property that it can be used to compute time-averaged values of variables that depend on f. Time-averaged values of species mole fractions and temperature can be computed (in adiabatic systems) as φ i = 1 0 p(f)φ i (f)df ( ) for a single mixture fraction system. When a secondary stream exists, the average values are calculated as φ i = p 1 (f fuel )p 2 (p sec )φ i (f fuel,p sec )df fuel dp sec ( ) where p 1 is the PDF of f fuel and p 2 is the PDF of p sec. Here, statistical independence of f fuel and p sec is assumed, so that p(f fuel,p sec )= p 1 (f fuel )p 2 (p sec ). Similarly, the true time-averaged fluid density, ρ, can be computed as for a single mixture fraction system, and ρ = ρ = p(f) df ( ) 0 ρ(f) p 1 (f fuel )p 2 (p sec ) df fuel dp sec ( ) ρ(f fuel,p sec ) when a secondary stream exists. ρ(f)orρ(f fuel,p sec ) is the instantaneous density obtained using the instantaneous species mole fractions and temperature in the gas law equation. Equations and provide a more accurate description of the time-averaged density than the alternate approach of applying the gas law using time-averaged species and temperature c Fluent Inc. November 28, 2001

15 14.1 Description of the Equilibrium Mixture Fraction/ PDF Model Using Equations and (or Equations and ), it remains only to specify the shape of the function p(f) (orp 1 (f fuel )and p 2 (p sec )) in order to determine the local time-averaged state of the fluid at all points in the flow field. The PDF Shape The shape of the assumed PDF, p(f), is described in FLUENT by one of two mathematical functions: the double delta function the β-function The double delta function is the most easily computed, while the β- function most closely represents experimentally observed PDFs. The shape produced by these functions depends solely on the mean mixture fraction, f, and its variance, f 2. The choice of these functions (and others, such as the clipped Gaussian) have their basis in experimental measurements of concentration fluctuations [17, 105]. A detailed description of each function follows. The Double Delta Function PDF The double delta function is given by 0.5, f = f f 2 p(f) = 0.5, f = f + f 2 0, elsewhere ( ) with suitable bounding near f =1andf = 0. One example of the double delta function is illustrated in Figure As noted above, the double delta function PDF is very easy to compute but is invariably less accurate than the alternate β-function PDF. For this reason, it should be employed only in special circumstances. c Fluent Inc. November 28,

16 Modeling Non-Premixed Combustion p(f) f f Figure : Example of the Double Delta Function PDF Shape The β-function PDF The β-function PDF shape is given by the following function of f and f 2 : p(f) = f α 1 (1 f) β 1 f α 1 (1 f) β 1 df ( ) where [ ] f(1 f) α = f 1 f 2 ( ) and [ ] f(1 f) β =(1 f) 1 f 2 ( ) Figures and show the form of the β function for two conditions of f and f c Fluent Inc. November 28, 2001

17 P ro D en s it P ro D en s it 14.1 Description of the Equilibrium Mixture Fraction/ PDF Model KEY 5.53E E+00 b a b il 3.32E+00 i t y 2.21E+00 y p 1.11E E E E E E E E+00 Mixture Fraction F BETA PROBABILITY DENSITY FUNCTION F-Bar = 3.00E-01, F-Fluc = 5.00E-03. prepdf V4.00 Fluent Inc. Figure : β-function PDF Shapes for f =0.3andf 2 = KEY 1.63E E+01 b a b il 9.78E+00 i t y 6.52E+00 y p 3.26E E E E E E E E+00 Mixture Fraction F BETA PROBABILITY DENSITY FUNCTION F-Bar = 1.00E-01, F-Fluc = 1.00E-02. prepdf V4.00 Fluent Inc. Figure : β-function PDF Shapes for f =0.1andf 2 =0.01 c Fluent Inc. November 28,

18 Modeling Non-Premixed Combustion Importantly, the PDF shape p(f) can be computed at all points in the flow in terms of its first two moments, namely mean, f, and variance, f 2.Thus,givenFLUENT s prediction of f and f 2 at each point in the flow field (Equations and ), the known PDF shape can be computed and used as the weighting function to determine the timeaveraged mean values of species mass fraction, density, and temperature using, Equations and (or, for a system with a secondary stream, Equations and ). This logical dependence is depicted visually in Figure for a single mixture fraction. (When a secondary stream is included, the PDF shape will be computed for the fuel mixture fraction, f fuel, and the secondary partial fraction, p sec,and the order of the calculations is different, as shown in Figure ) PDF Shape p(ƒ) = p (ƒ, ƒ 2 ) Chemistry Model φi (ƒ) 1 φ i = o p(ƒ) φ (ƒ) dƒ i Look-up Table φ = φ (ƒ, ƒ 2 i i ) Figure : Logical Dependence of Averaged Scalars φ i on f, f 2,and the Chemistry Model (Adiabatic, Single-Mixture-Fraction Systems) Non-Adiabatic Extensions of the Non-Premixed Model Many reacting systems involve heat transfer to wall boundaries, droplets, and/or particles by convective and radiative heat transfer. In such flows the local thermochemical state is no longer related only to f, but also c Fluent Inc. November 28, 2001

19 14.1 Description of the Equilibrium Mixture Fraction/ PDF Model to the enthalpy H. The system enthalpy impacts the chemical equilibrium calculation and the temperature of the reacted flow. Consequently, changes in enthalpy due to heat loss must be considered when computing scalars from the mixture fraction. Thus, the scalar dependence becomes φ i = φ i (f,h ) ( ) where H is given by Equation In such non-adiabatic systems, turbulent fluctuations should be accounted for by means of a joint PDF p(f,h ). The computation of p(f,h ) is not practical for most engineering applications, however. The problem can be simplified significantly by assuming that the enthalpy fluctuations are independent of the enthalpy level (i.e., heat losses do not significantly impact the turbulent enthalpy fluctuations). When this is assumed, we again have p = p(f) and φ i = 1 0 φ i (f,h )p(f)df ( ) Determination of φ i in the non-adiabatic system thus requires solution of the modeled transport equation for time-averaged enthalpy: ( ) kt t (ρh )+ (ρ vh )= H c + S h ( ) p where S h accounts for source terms due to radiation, heat transfer to wall boundaries, and heat exchange with the second phase. Figure depicts the logical dependence of mean scalar values (species mass fraction, density, and temperature) on FLUENT s prediction of f, f 2,and H in non-adiabatic single-mixture-fraction systems. When a secondary stream is included, the scalar dependence becomes and the mean values are calculated from φ i = φ i (f fuel,p sec,h ) ( ) c Fluent Inc. November 28,

20 Modeling Non-Premixed Combustion PDF Shape p(ƒ) = p (ƒ, ƒ 2 ) Chemistry Model φi (ƒ, H *) 1 φ = p(ƒ) φ (ƒ,h* i )dƒ o i Look-up Table φ = φ (ƒ, ƒ 2 i i,h*) Figure : Logical Dependence of Averaged Scalars φ i on f, f 2, H, and the Chemistry Model (Non-Adiabatic, Single-Mixture-Fraction Systems) φ i = φ i (f fuel,p sec, H )p 1 (f fuel )p 2 (p sec )df fuel dp sec ( ) As noted above, the non-adiabatic extensions to the PDF model are required in systems involving heat transfer to walls and in systems with radiation included. In addition, the non-adiabatic model is required in systems that include multiple fuel or oxidizer inlets with different inlet temperatures or that include flue gas recycle. Finally, the non-adiabatic model is required in particle-laden flows (e.g., liquid fuel systems or coal combustion systems) since such flows include heat transfer to the dispersed phase. Figure illustrates several systems that must include the non-adiabatic form of the PDF model. Note that even if your system is non-adiabatic, you may want to perform the much simpler adiabatic calculation as an initial exercise. This will allow you to bound the non-adiabatic analysis in an efficient manner, as described in Section c Fluent Inc. November 28, 2001

21 14.1 Description of the Equilibrium Mixture Fraction/ PDF Model Q wall or Q radiation Fuel f = 1 Oxidant f = 0 (a) Heat Transfer to Domain Boundaries and/or Radiation Heat Transfer Oxidant T = T 1 Fuel Oxidant T = T 2 (b) Multiple Fuel or Oxidant Inlets at Different Temperatures Oxidant Liquid Fuel or Pulverized Coal (c) Dispersed Phase Heat or Mass Transfer (e.g., Liquid Fuel or Coal Combustion) Figure : Reacting Systems Requiring Non-Adiabatic Non- Premixed Model Approach c Fluent Inc. November 28,

22 Modeling Non-Premixed Combustion Restrictions and Special Cases for the Non-Premixed Model Restrictions on the Mixture Fraction Approach The unique dependence of φ i (species mass fractions, density, or temperature) on f (Equation or ) requires that the reacting system meet the following conditions: The chemical system must be of the diffusion type with discrete fuel and oxidizer inlets (spray combustion and pulverized fuel flames may also fall into this category). The Lewis number must be unity. (This implies that the diffusion coefficients for all species and enthalpy are equal, a good approximation in turbulent flow). When a single mixture fraction is used, the following conditions must be met: Only one type of fuel is involved. The fuel may be made up of a burnt mixture of reacting species (e.g., 90% CH 4 and 10% CO) and you may include multiple fuel inlets. The multiple fuel inlets must have the same composition, however. Two or more fuel inlets with different fuel composition are not allowed (e.g., one inlet of CH 4 and one inlet of CO). Similarly, in spray combustion systems or in systems involving reacting particles, only one off-gas is permitted. Only one type of oxidizer is involved. The oxidizer may consist of a mixture of species (e.g., 21% O 2 and 79% N 2 )andyou may have multiple oxidizer inlets. The multiple oxidizer inlets must, however, have the same composition. Two or more oxidizer inlets with different composition are not allowed (e.g., one inlet of air and a second inlet of pure oxygen). When two mixture fractions are used, three streams can be involved in the system. Valid systems are as follows: c Fluent Inc. November 28, 2001

23 14.1 Description of the Equilibrium Mixture Fraction/ PDF Model Two fuel streams with different compositions and one oxidizer stream. Each fuel stream may be made up of a mixture of reacting species (e.g., 90% CH 4 and 10% CO). You may include multiple inlets of each fuel stream, but each fuel inlet must have one of the two defined compositions (e.g., one inlet of CH 4 and one inlet of CO). Mixed fuel systems including gas-liquid, gas-coal, or liquid-coal fuel mixtures with a single oxidizer. In systems with a gas-coal or liquid-coal fuel mixture, the coal volatiles and char are treated as a single composite fuel stream. Coal combustion in which volatiles and char are tracked separately. Two oxidizer streams with different compositions and one fuel stream. Each oxidizer stream may consist of a mixture of species (e.g. 21% O 2 and 79% N 2 ). You may have multiple inlets of each oxidizer stream, but each oxidizer inlet must have one of the two defined compositions (e.g., one inlet of air and a second inlet of pure oxygen). A fuel stream, an oxidizer stream, and a non-reacting secondary stream. The flow must be turbulent. It is important to emphasize that these restrictions eliminate the use of the non-premixed approach for directly modeling premixed combustion. This is because the unburned premixed stream is far from chemical equilibrium. Note, however, that an extended mixture fraction formulation, described in Chapter 16, can be applied to premixed and partially premixed flames. Figures and illustrate typical reacting system configurations that can be handled by the non-premixed model in FLUENT. Figure shows a premixed configuration that cannot be modeled using the non-premixed model. c Fluent Inc. November 28,

24 Modeling Non-Premixed Combustion 60% CH 4 40% CO 21% O 79% N 2 2 f = 1 f = 0 (a) Simple Fuel/Oxidant Diffusion Flame f = 0 35% O 65% N % CH 4 40% CO 35% O 65% N 2 2 f = 1 f = 0 (b) Diffusion System Using Multiple Oxidant Inlets 60% CH 4 20% CO 10% C 3 H8 10% CO 2 21% O 79% N 2 2 f = 1 f = 0 60% CH 4 20% CO 10% C H % CO 2 f = 1 (c) System Using Multiple Fuel Inlets Figure : Chemical Systems That Can Be Modeled Using a Single Mixture Fraction c Fluent Inc. November 28, 2001

25 14.1 Description of the Equilibrium Mixture Fraction/ PDF Model CH /CO/C H Oxidant CH /C H (a) System Containing Two Dissimilar Fuel Inlets 21% O 2 Fuel 35% O 2 (b) System Containing Two Dissimilar Oxidant Inlets Figure : Chemical System Configurations That Can Be Modeled Using Two Mixture Fractions c Fluent Inc. November 28,

26 Modeling Non-Premixed Combustion CH 4 O 2 N 2 Figure : Premixed Systems CANNOT Be Modeled Using the Non-Premixed Model Using the Non-Premixed Model for Liquid Fuel or Coal Combustion You can use the non-premixed model if your FLUENT simulation includes liquid droplets and/or coal particles. In this case, fuel enters the gas phase within the computational domain at a rate determined by the evaporation, devolatilization, and char combustion laws governing the dispersed phase. In the case of coal, the volatiles and the products of char can be defined as two different types of fuel (using two mixture fractions) or as a single composite off-gas (using one mixture fraction), as described in Section Using the Non-Premixed Model with Flue Gas Recycle While most problems you solve using the non-premixed model will involve inlets that contain either pure oxidant or pure fuel (f = 0 or 1), you can include an inlet that has an intermediate value of mixture fraction (0 <f<1) provided that this inlet represents a completely reacted mixture. Such cases arise when there is flue gas recirculation, as depicted schematically in Figure Since f is a conserved quantity, the mixture fraction at the flue gas recycle inlet can be computed as or ṁ fuel +ṁ recyc f exit =(ṁ fuel +ṁ ox +ṁ recyc )f exit ( ) c Fluent Inc. November 28, 2001

27 14.1 Description of the Equilibrium Mixture Fraction/ PDF Model f exit = ṁ fuel ṁ fuel +ṁ ox ( ) where f exit is the exit mixture fraction (and the mixture fraction at the flue gas recycle inlet), ṁ ox is the mass flow rate of the oxidizer inlet, ṁ fuel is the mass flow rate of the fuel inlet, ṁ recyc is the mass flow rate of the recycle inlet. If a secondary stream is included, and f fuel,exit = ṁ fuel ṁ fuel +ṁ sec +ṁ ox ( ) p sec,exit = ṁ sec ṁ sec +ṁ ox ( ) ṁ R f exit ṁ F f = 1 ṁ O f = 0 f exit Figure : Using the Non-Premixed Model with Flue Gas Recycle c Fluent Inc. November 28,

28 Modeling Non-Premixed Combustion 14.2 Modeling Approaches for Non-Premixed Equilibrium Chemistry The FLUENT software package offers two different ways to model nonpremixed equilibrium chemistry. You can choose either a single- or twomixture-fraction approach depending on how many streams you have. prepdf stores information about the streams in look-up tables, which are then used by FLUENT to solve for the mixture fraction, enthalpy, and scalar quantities. For more information about prepdf, see Section Single-Mixture-Fraction Approach To keep computation time to a minimum, much of the calculation required for the non-premixed model is performed outside of the FLUENT simulation by preprocessing the chemistry calculations and PDF integrations in a separate code, called prepdf. Figure illustrates how the computational effort is divided between the preprocessor (prepdf) and the solver (FLUENT). In prepdf, the chemistry model (mixed-is-burned, equilibrium chemistry, or laminar flamelet) is used in conjunction with the assumed shape of the PDF to perform the integrations given in Equations , , and/or These integrations are performed within prepdf and stored in look-up tables that relate the mean thermochemical variables φ i (temperature, density and species mass fractions) to the values of f, f 2 s,andh. Notethatthescaled mixture fraction variance is used for tabulation, where f 2 s is defined as f 2 s = f f (1 f) (14.2-1) Equations , , and (for non-adiabatic systems) are solved in FLUENT to obtain local values of f, f 2,andH Two-Mixture-Fraction Approach For the two-mixture-fraction (secondary stream) case, the preprocessor prepdf calculates the instantaneous values for the temperature, density, and species mass fractions (Equation or ) and stores them in the look-up tables. For the adiabatic case with two mixture fractions, c Fluent Inc. November 28, 2001

29 14.2 Modeling Approaches for Non-Premixed Equilibrium Chemistry prepdf: Integration: φ i 1 = o p(ƒ ) φ ( ƒ, H*)dƒ i Look-up Table φ = φ (ƒ ƒ,, H*) i i s 2 FLUENT: 1. Solve ƒ, ƒ 2, H* 2. Look up Scalars φ i Figure : Separation of Computational Tasks Between FLUENT and prepdf for a Single-Mixture-Fraction Case c Fluent Inc. November 28,

30 Modeling Non-Premixed Combustion the look-up tables contain ρ, T,andY i as functions of the fuel mixture fraction and the secondary partial fraction. For the non-adiabatic case with two mixture fractions, the 3D look-up table contains the physical properties as functions of the fuel mixture fraction, the secondary partial fraction, and the instantaneous enthalpy.! The PDFs p 1 and p 2 of the fuel mixture fraction and the secondary partial fraction, respectively, are calculated inside FLUENT from the values of the solved mixture fractions and their variances. The PDF integrations for calculating the mean values for the properties are also performed inside FLUENT (using Equation or , together with Equation or its non-adiabatic equivalent). The instantaneous values required in the integrations are obtained from the look-up tables. Note that the computation time in FLUENT for a two-mixture-fraction case will be much greater than for a single-mixture-fraction problem since the PDF integrations are being performed in FLUENT rather than in prepdf. This expense should be carefully considered before choosing the two-mixture-fraction model. Also, it is usually expedient to start a twomixture-fraction simulation from a converged single-mixture-fraction solution. Figure illustrates the division of labor between prepdf and FLU- ENT for the two-mixture-fraction case The Look-Up Table Concept Look-Up Tables for Adiabatic Systems Figure illustrates the concept of the look-up tables generated by prepdf for a single-mixture-fraction system. Given FLUENT s predicted value for f and f 2 at a point in the flow domain, the time-averaged mean value of mass fractions, density, or temperature (φ i )atthatpoint can be obtained from the table. FLUENT first uses Equation to compute the scaled mixture fraction variance f 2 s because the singlemixture-fraction look-up tables contain property data as a function of f and f 2 s, rather than f and f 2. The table, Figure , is the mathematical result of the integration of Equation There is one look-up table of this type for each scalar c Fluent Inc. November 28, 2001

31 14.2 Modeling Approaches for Non-Premixed Equilibrium Chemistry prepdf: Calculation: φ i = φ (ƒ,p,h*) i fuel sec Look-up Table φ i = φ (ƒ,p,h*) i fuel sec FLUENT: Solve ƒ,ƒ,p,p,h* fuel fuel sec sec 2. Look up scalars φ i 3. Compute p (ƒ ) 1 fuel 4. Compute p (p ) 2 sec 5. Compute φ i Figure : Separation of Computational Tasks Between FLUENT and prepdf for a Two-Mixture-Fraction Case c Fluent Inc. November 28,

32 Modeling Non-Premixed Combustion of interest (species mass fractions, density, temperature). In adiabatic systems, where the instantaneous enthalpy is a function only of the instantaneous mixture fraction, a two-dimensional look-up table, like that in Figure , is all that is required. Scalar Value Scaled Variance Mean Mixture Fraction Figure : Visual Representation of a Look-Up Table for the Scalar φ i as a Function of f and f 2 in Adiabatic Single-Mixture-Fraction Systems For a system with two mixture fractions, there will be a look-up table for each instantaneous scalar property φ i as a function of the fuel mixture fraction f fuel and the secondary partial fraction p sec (Equation ), as shown in Figure The look-up table structure is summarized in Table D Look-Up Tables for Non-Adiabatic Systems In non-adiabatic systems, where the enthalpy is not linearly related to the mixture fraction, but depends also on wall heat transfer and/or radiation, a look-up table is required for each possible enthalpy value in the system. The result is a three-dimensional look-up table, as illustrated in Figure , which consists of layers of two-dimensional tables, each one corresponding to the normalized heat loss or gain. The first layer or slice corresponds to the maximum heat loss for the system, where all the c Fluent Inc. November 28, 2001

33 14.2 Modeling Approaches for Non-Premixed Equilibrium Chemistry Instantaneous Scalar Value Secondary Partial Fraction Fuel Mixture Fraction Figure : Visual Representation of a Look-Up Table for the Scalar φ i as a Function of f fuel and p sec in Adiabatic Two-Mixture-Fraction Systems points in the look-up table are at the minimum temperature defined in the problem setup. The maximum slice corresponds to the heat gain that occurs when all points have reached the maximum temperature defined. The zero heat loss/gain slice corresponds to adiabatic operation. Slices interpolated between the adiabatic and maximum slices correspond to heat gain, and those interpolated between the adiabatic and minimum slices correspond to heat loss. The three-dimensional look-up table allows FLUENT to determine the value of each mass fraction, density, and temperature from calculated values of f, f 2, and H. This three-dimensional table is the visual representation of the integral in Equation For two-mixture-fraction problems, the 3D look-up table allows FLUENT to determine the instantaneous values for the scalar properties from instantaneous values of f fuel, p sec,andh. The three-dimensional table is the visual representation of Equation These instantaneous values are used to perform the integration of Equation See Table for a summary of the look-up table structure. c Fluent Inc. November 28,

34 Modeling Non-Premixed Combustion normalized heat loss/gain n+1 normalized heat loss/gain n Scalar Value normalized heat loss/gain n-1 Scaled Variance Mean Mixture Fraction Figure : Visual Representation of a Look-Up Table for the Scalar φ i as a Function of f and f 2 and Normalized Heat Loss/Gain in Non- Adiabatic Single-Mixture-Fraction Systems c Fluent Inc. November 28, 2001

35 14.2 Modeling Approaches for Non-Premixed Equilibrium Chemistry normalized heat loss/gain n+1 Instantaneous Scalar Value normalized heat loss/gain n normalized heat loss/gain n-1 Secondary Partial Fraction Fuel Mixture Fraction Figure : Visual Representation of a Look-Up Table for the Scalar φ i as a Function of f fuel, p sec, and Normalized Heat Loss/Gain in Non- Adiabatic Two-Mixture-Fraction Systems c Fluent Inc. November 28,

36 Modeling Non-Premixed Combustion Summary of Look-Up Table Formats Table summarizes the look-up table format for different types of non-premixed models. Table : Look-Up Table Formats Type of Model Adiabatic Non-Adiabatic single mixture fraction f, f 2 s f, f 2 s, H two mixture fractions f fuel, p sec f fuel, p sec, H 14.3 User Inputs for the Non-Premixed Equilibrium Model A description of the user inputs (in prepdf and FLUENT) for the nonpremixed equilibrium model is provided in the following sections: Section : Problem Definition Procedure in prepdf Section : Informational Messages and Errors Reported by prepdf Section : Non-Premixed Model Input and Solution Procedures in FLUENT Section : Modeling Liquid Fuel Combustion Section : Modeling Coal Combustion Problem Definition Procedure in prepdf As illustrated in Figures and , the solution of chemically reacting flows using the non-premixed equilibrium approach begins with the problem definition in prepdf. For a single-mixture-fraction problem, you will perform the following steps in prepdf: c Fluent Inc. November 28, 2001

37 14.3 User Inputs for the Non-Premixed Equilibrium Model 1. Define the chemical species to be considered in the reacting system model and choose the chemical description of the system. The default equilibrium chemistry option should invariably be used. If you are modeling a mixing problem without reaction, or if a solution cannot be obtained with the equilibrium option and alternate species components are not acceptable, you may want to use the infinitely fast chemistry option. 2. Indicate whether or not the problem is adiabatic. 3. Choose the PDF (probability density function) shape that will be used to describe the turbulent fluctuations in the mixture fraction. The default Beta PDF should be selected unless you have a special reason to use the double-delta PDF. 4. Compute the look-up table, containing mean (time-averaged) values of species mass fractions, density, and temperature as a function of mean mixture fraction, mixture fraction variance, and enthalpy. The contents of this look-up table will reflect your preceding inputs describing the turbulent reacting system. The look-up table is the output of prepdf. It is the stored result of the integration of Equations (or ) and The look-up table will be used in FLUENT to determine mean species mass fractions, density, and temperature from the values of mixture fraction (f), mixture fraction variance (f 2 ), and enthalpy (H ) as they are computed during the FLUENT calculation of the reacting flow. See Section 14.2 and Figures and For a problem that includes a secondary stream (and, therefore, a second mixture fraction), you will perform the first three steps listed above for the single-mixture-fraction approach, and then prepare a look-up table of instantaneous properties using Equation or The following step-by-step procedure explains how to use prepdf, taking you through the problem definition procedure and explaining how your inputs are used. c Fluent Inc. November 28,

38 Modeling Non-Premixed Combustion Step 1: Start prepdf The way you start prepdf will be different for UNIX and Windows systems. The installation process (described in the separate installation instructions for your computer type) is designed to ensure that the prepdf program is launched when you follow the appropriate instructions. If it is not, consult your computer systems manager or your Fluent support engineer. Starting prepdf on a UNIX System On a UNIX machine, type prepdf at the command prompt. Starting prepdf on a Windows System For a Windows system, there are two ways to start prepdf: Click on the Start button, select the Programs menu, select the Fluent.Inc menu, and then select the prepdf program item. (Note that if the default Fluent.Inc program group name was changed when prepdf was installed, you will find the prepdf menu item in the program group with the new name that was assigned, rather than in the Fluent.Inc program group.) Start from an MS-DOS Command Prompt window by typing prepdf at the prompt. Before doing so, however, you must first modify your user environment so that the MS-DOS Command utility will find prepdf. You can do this by selecting the program item Set Environment, which is also found in the Fluent.Inc program group. This program will add the Fluent.Inc directory to your command search path c Fluent Inc. November 28, 2001

39 14.3 User Inputs for the Non-Premixed Equilibrium Model The Thermodynamic Database prepdf uses a thermodynamic database [112] and must be able to access the database file, THERMO.DB. This file must be present in the directory where you run prepdf, or it must be accessed through an environment variable, THERMODB, which points to the location of this file. In most installations, you will be running prepdf using procedures supplied by Fluent Inc. and these procedures will set this environment variable for you. Step 2: Allocate Memory TheamountofmemoryusedbyprePDF cannot be changed once it has been allocated, without restarting the application. You must, therefore, take care to allocate enough memory for the maximum number of points in the PDF table, species, and flamelets that you are planning to use. The parameters for which you can modify memory allocation are as follows: Maximum Number of Species is the maximum number of species in the PDF table. The default value is 20, and this parameter can be increased up to a value of 65. Maximum Number of f-mean Points is the maximum number of mixture fraction points in the PDF table. The default value is 45, and this parameter can be increased up to a value of 100. Maximum Number of f-var Points is the maximum number of mixture fraction variance points in the PDF table. The default value is 22, and this parameter can be increased up to a value of 30. Maximum Number of Enthalpy Points is the maximum number of enthalpy points in the PDF table. The default value is 45, and this parameter can be increased up to a value of 100. Maximum Number of Scalar Dissipation Points in Adiabatic Flamelet PDF Table has a default value of 45, and can be increased up to a value of 100. c Fluent Inc. November 28,

40 Modeling Non-Premixed Combustion Maximum Number of Flamelets is the maximum number of flamelets in the flamelet model. The default value is 20, and this parameter can be increased up to a value of 30. You can set these parameters in the Memory Allocation panel (Figure ). Setup Memory Allocation... Figure : The Memory Allocation Panel in prepdf When you click Apply, memory will be allocated for these parameters. If you need to allocate more memory later in the setup process, you will need to save an input file, exit prepdf, and restart. Then, allocate the appropriate amount of memory, read the input file into prepdf, and continue the problem setup. Note that, if you read an input file or PDF file without first allocating memory, prepdf will allocate memory based on the number of species and points specified in the file. If the number is less than the default allocation, the default memory will be allocated. If it is more, memory adequate for the number of species and points in the file will be allocated c Fluent Inc. November 28, 2001

41 14.3 User Inputs for the Non-Premixed Equilibrium Model Step 3: Initialize the Problem Definition Once you have allocated memory, your first task in prepdf is to define the type of reaction system and reaction model that you intend to use. This includes selection of the following options: Addition of a secondary stream Partially premixed model option (see Chapter 16) Adiabatic or non-adiabatic modeling options (see Section )! Equilibrium chemistry model or stoichiometric reaction (mixed-isburned) model (see Section ) Procedures for setting up flamelet PDF models are described in Section Beta PDF or Double-Delta PDF (see Section ) Empirically defined fuel and/or secondary stream composition Your subsequent inputs and the inputs that prepdf will expect from you depend on these choices. You can make these model selections using the Define Case panel (Figure ). Setup Case... Each of these modeling choices is described in detail below. Be sure to click Apply after completing your inputs. Enabling a Secondary Inlet Stream If you are modeling a system consisting of a single fuel and a single oxidizer stream, you do not need to enable a secondary stream in your PDF calculation. As discussed in Section , a secondary stream should be enabled if your PDF reaction model will include any of the following: c Fluent Inc. November 28,

42 Modeling Non-Premixed Combustion Figure : The Define Case Panel in prepdf c Fluent Inc. November 28, 2001

43 14.3 User Inputs for the Non-Premixed Equilibrium Model two dissimilar gaseous fuel streams: In these simulations, the fuel stream defines one of the fuels and the secondary stream defines the second fuel. mixed fuel systems of dissimilar gaseous and liquid fuel: In these simulations, the fuel stream defines the gaseous fuel and the secondary stream defines the liquid fuel (or vice versa). mixed fuel systems of dissimilar gaseous and coal fuels: In these simulations, the fuel stream must define the coal and the secondary stream must define the gaseous fuel. See Section regarding coal combustion simulations with the non-premixed combustion model. mixed fuel systems of coal and liquid fuel: In these simulations, the fuel stream must define the coal and the secondary stream must define the liquid fuel. See Section regarding coal combustion simulations with the non-premixed combustion model. coal combustion: Coal combustion can be more accurately modeled by using a secondary stream. The fuel stream must define the char and the secondary stream must define the volatile components of the coal. See Section regarding coal combustion simulations with the non-premixed combustion model. a single fuel with two dissimilar oxidizer streams: In these simulations, the fuel stream defines the fuel, the oxidizer stream defines one of the oxidizers, and the secondary stream defines the second oxidizer.! Using a secondary stream substantially increases the calculation time for your simulation since the multi-dimensional PDF integrations are performed in FLUENT at run-time. Choosing Adiabatic or Non-Adiabatic Options You should use the non-adiabatic modeling option if your problem definition in FLUENT will include one or more of the following: c Fluent Inc. November 28,

44 Modeling Non-Premixed Combustion radiation or wall heat transfer multiple fuel inlets at different temperatures multiple oxidant inlets at different temperatures flue gas recycle liquid fuel, coal particles, and/or heat transfer to inert particles Note that the adiabatic model is a simpler model involving a two-dimensional look-up table in which scalars depend only on f and f 2 (or on f fuel and p sec ). If your model is defined as adiabatic, you will not need to solve the enthalpy equation in FLUENT and the system temperature will be determined directly from the mixture fraction and the fuel and oxidant inlet temperatures. The non-adiabatic case will be more complex and more time-consuming to compute, requiring the generation of threedimensional look-up tables in prepdf. However, the non-adiabatic model option allows you to include the types of reacting systems described above. Select Adiabatic or Non-Adiabatic under Heat transfer options in the Define Case panel. Using the Adiabatic Calculation to Determine Inputs to the Non-Adiabatic Model Even if your FLUENT model will ultimately need to include non-adiabatic effects, you may benefit from starting the analysis with an adiabatic calculation in prepdf. This simpler calculation can be used to fine-tune the inputs to the non-adiabatic model, identifying the peak temperature that needs to be considered in the non-adiabatic case and identifying which chemical species are significant and need to be considered. Thus the adiabatic prepdf calculation provides you with an understanding of the system that can help you to develop an efficient non-adiabatic model. Choosing the Chemistry Model In general, the equilibrium chemistry model is recommended over the stoichiometric reaction model. In this approach the concentration of species c Fluent Inc. November 28, 2001

45 14.3 User Inputs for the Non-Premixed Equilibrium Model of interest are determined from the mixture fraction using the assumption of chemical equilibrium (see Section ). With this model, you can include the effects of intermediate species and dissociation reactions, producing more realistic predictions of flame temperatures in combustion models. In contrast, the stoichiometric reaction (mixed-is-burned) modeling option provides a less accurate single-step description of the system chemistry. When you choose the equilibrium chemistry option, you will have the opportunity, in Step 8, to use a partial equilibrium model.! Select Equilibrium Chemistry or Stoichiometric Reaction under Chemistry models in the Define Case panel. If you want to model non-equilibrium chemistry, you should use the flamelet modeling approach described in Section Procedures for using this model is presented in Section Choosing the Chemistry Model for Non-Reacting Systems If you are using the non-premixed combustion model to consider a nonreacting system, choose the Stoichiometric Reaction option in the Define Case panel. When you are prompted to input the stoichiometric coefficients for each species (Step 7, below), simply input zeros for all species. Choosing the PDF Shape The shape of the PDF you select will have some impact on the results you obtain. In general, the default β-function PDF shape matches experimental observations of f fluctuations much better than the doubledelta function, and should be the one used. The double-delta function, on the other hand, is more efficient computationally during the generation of look-up tables in prepdf. Since the look-up table generation is a pre-processing step, the double-delta PDF should be used only in special circumstances. When a secondary stream is included, you will not choose the PDF type in prepdf. This step will occur in FLUENT instead. Select Delta PDF or Beta PDF under PDF models in the Define Case panel. c Fluent Inc. November 28,

46 Modeling Non-Premixed Combustion Empirical Definition of the Fuel Stream(s) The empirical definition option provides an alternative method for defining the composition of the fuel or secondary stream. When you do not select this option, you will define which chemical species are present in each stream and the mass or mole fraction of each species, as described below, in Step 5. When an empirically defined fuel or secondary stream is used, you will follow a different procedure for determining the chemical composition of the stream: 1. Define the list of chemical species present in the stream (following the suggestions below, in Step 4), using the Define Species panel. The choice of species is not altered by your use of the empirical definition option, except that you must also include atomic elements (C, H, N, S, and O) and combustion products (CO 2 and H 2 O) which are used for the calculation of the lower heating value of the fuel. 2. In the Composition panel (Step 5, below), you will not input mass or mole fractions for each species. Instead, you will input the atomic composition of the stream (atom mole fractions of C, H, N, S, and O), its lower heating value, and its mean specific heat. prepdf will compute the mole fraction of each chemical species from these inputs. The heat of formation of an empirical fuel stream is calculated from the heating value and the atomic composition. The fuel inlet temperature and fuel specific heat are used to calculate the sensible enthalpy. prepdf performs an equilibrium calculation, using the atomic composition and enthalpy, and returns the equilibrium molar species composition and temperature of the fuel. Note that the empirical definition option is available only with the full equilibrium chemistry model. It cannot be used with the stoichiometric or partial equilibrium models, since equilibrium calculations are required for the determination of the fuel composition. If your empirically defined fuel is a gaseous fuel, you should be aware of the modeling issues related c Fluent Inc. November 28, 2001

47 14.3 User Inputs for the Non-Premixed Equilibrium Model to gas-phase fuel inlet temperature in full equilibrium systems (see Step 8, below). The option for defining an empirical fuel stream is particularly useful for coal combustion simulations (see Section ) or for simulations involving other complex hydrocarbon mixtures. Because empirical fuels use the full equilibrium model, which impacts your flow boundary conditions at gas-phase fuel inlets, the empirical definition option is not generally recommended for gaseous fuels. Turn on Fuel stream or Secondary stream under Empirically Defined Streams in the Define Case panel to define a fuel or secondary stream empirically. Step 4: Define the Chemical Species to be Considered One of your most important modeling inputs will be the selection of species to be included in the description of the reacting system. All species that you include must exist in the chemical database and you must enter their names in the same format used in the database. You can include a maximum of the number of species you entered in the Memory Allocation panel (see Step 2 above) when you use the non-premixed model. (Note the additional requirements mentioned below for defining species when you have an empirically defined fuel stream.) The number of species and their names are entered using the Define Species panel (Figure ). Setup Species Define... The steps for defining your species are as follows: 1. Specify the number of species you will define in the Maximum # of Species field. (You can change the maximum number of species at any time by incrementing the counter.) 2. Define your first species by selecting it in the Database Species dropdown list. This list contains a complete listing of the species in the database. The species name will appear in the Defined Species list. 3. Increase the Species # field (either use the counter arrow or type in the new value and press <RETURN>) and select the next species c Fluent Inc. November 28,

48 Modeling Non-Premixed Combustion Figure : The Define Species Panel in prepdf from the Database Species list. Continue in this manner until all of the species you want to include are shown in the Defined Species list. 4. When you are satisfied with your selections, click Apply and close the panel. If you need to alter a species selection, click on the species name in the Defined Species list and then select a new species from the Database Species drop-down list. Choosing Species for Empirically Defined Streams For an empirically defined fuel or secondary stream, you must choose the constituent elements in addition to the species that make up the chemical system. The elements allowed are C, H, N, S, and O. Also, the c Fluent Inc. November 28, 2001

49 14.3 User Inputs for the Non-Premixed Equilibrium Model species CO 2 and H 2 O must be selected since they are the combustion products for the calculation of the lower caloric (heating) value of the fuel. If you are considering S (sulfur), you will also need to add SO 2 in the species list. Including Solid and Liquid Species Solid and liquid species can be included in the thermodynamic calculations as well as gases. They are indicated by an L or an S in parentheses after the species name. If you select a solid or liquid species, you must define the species density in the Condensed Species Densities panel (Figure ). Setup Species Density... Figure : The Condensed Species Densities Panel in prepdf In the panel, choose each solid or liquid species in the Defined Species list and enter its Density. Note that this density should be the density of the condensed phase species and not the apparent density of the particles as defined in FLUENT. For example, in coal combustion, you should enter the density of C(s) and not the apparent density of the coal. When you have set the density for all solid and liquid species, click Apply and close c Fluent Inc. November 28,

50 Modeling Non-Premixed Combustion the panel. Guidelines on Choosing the Species to Include In the combustion of simple hydrocarbons, many species and radicals have been identified. Although you could, in principle, define an equilibrium system that includes a large number of species, you should limit your system description to those species that are of the most significance. The following suggestions may be helpful in the definition of the system chemistry: In high-temperature flames (i.e., T > 2000 K) include radicals such as H, O, and OH. These radicals are produced in dissociation reactions at high temperatures and can have a significant impact on peak flame temperatures. For heavy hydrocarbon fuels (e.g., fuel oils), lighter hydrocarbons (CH 4,C 2 H 4, etc.) will be formed in the rich mixture as a result of pyrolysis and gasification reactions. For coal combustion, volatiles may be represented by a mixture of CH 4 (or a heavier hydrocarbon) and CO. Char in the coal should be represented by C(s). Follow the other general guidelines outlined here to determine the other species that should be included in the combustion system. If you want to consider the water content in a coal fuel, include H 2 O(l). Include the liquid water content as part of the fuel composition. Alternately, the water content can be included using vapor phase H 2 O. (See Section for additional information.)! If soot formation is of interest, C(s) can be included in the fuel stream definition. However, you should note that the equilibrium model will not represent the complex finite rate chemistry which is usually associated with soot formation. Care should be taken to distinguish atomic carbon, C, from solid carbon, C(s). Atomic carbon should be selected only if you are using the empirically-defined input method c Fluent Inc. November 28, 2001

51 14.3 User Inputs for the Non-Premixed Equilibrium Model Combustion products should always include CO 2 and H 2 O. In addition, you may want to include CO and H 2.NotethatH 2 should not be included alone as it is produced in the water-gas shift reaction, CO + H 2 O CO 2 +H 2. If your fuel composition is known empirically (e.g., C 0.9 H 3 O 0.2 ), use the option for an empirically-defined stream (see Step 3). For hydrocarbon combustion systems, it is recommended that you include C(s) and H 2 O(l). If you wish to include the sulfur that may be present in a hydrocarbon fuel, note that this may hinder the convergence of the equilibrium solver, especially if the concentration of sulfur is small. It is therefore recommended that you include sulfur in the calculation only if it is present in considerable quantities. The simplest way to model sulfur is to represent it as SO 2 and S(l), where SO 2 will be formed in oxygen-rich mixtures and S(l) will be formed in fuel-rich mixtures. A more elaborate description of a sulfur-containing fuel-oxidizer system could include SO 2,H 2 S, COS, S(l), CS 2,andS 2. It is extremely important that your choice of species provide a sensible description of the system chemistry. If this is not the case, the equilibrium calculation may fail to converge or may produce incorrect results. The species included in the equilibrium calculation should probably not include NO x species, as the NO x reaction rates are slow and should not be treated using an equilibrium assumption. Instead, the NO x concentration is predicted most accurately using the FLUENT NO x postprocessor, where finite-rate kinetics are included. (See Section 17.1.) Note that it is not important to include NO x predictions with the combustion simulation since the NO x species are present at low concentrations and have little impact on the combustion process. Modifying the Database If you want to include a new species in your reacting system that is not available in the chemical database, you can add it to the database files, c Fluent Inc. November 28,

52 Modeling Non-Premixed Combustion THERMO.DB (used by prepdf) andthermodb.scm (used by FLUENT). The format for THERMO.DB is detailed in [112]. You can generate the thermodb.scm file in prepdf using the File/Write/Thermodb... menu item. File Write Thermodb... FLUENT will recognize the new species if the thermodb.scm file is in the directory where FLUENT is started. To permanently store the new species in the standard database, copy the new species data from the generated thermodb.scm file to the default thermodb.scm file, as described in Section If you choose to modify the standard database files, you should create copies of the original files. Step 5: Define the Fuel and Oxidizer (and Secondary-Stream) Compositions After defining the species that will be considered in the reaction system, you must define their mole or mass fractions at the fuel and oxidizer inlets and at the secondary inlet, if one exists. (If you choose to define the fuel or secondary stream composition empirically, you will instead enter the parameters described at the end of this step.) For the example shown in Figure c, for example, the fuel inlet consists of 60% CH 4, 20% CO, 10% CO 2, and 10% C 3 H 8. This information is input using the Composition panel (Figure ). Setup Species Composition... The procedure for defining mole or mass fractions is as follows: 1. Under Stream, select the Fuel, Oxidiser, or Secondary option. 2. Under Specify Composition In..., indicate whether you want to enter Mole Fractions or Mass Fractions. 3. Select a species from the Defined Species list and then enter its mole or mass fraction in the selected stream (fuel, oxidizer, or secondary) by typing in the Species Fraction field. Repeat this process for all species in the Defined Species listuntilyouhavesetallmoleor mass fractions for the selected stream c Fluent Inc. November 28, 2001

53 14.3 User Inputs for the Non-Premixed Equilibrium Model Figure : The Composition Panel in prepdf c Fluent Inc. November 28,

54 Modeling Non-Premixed Combustion 4. Input the mole or mass fractions for each of the other streams by selecting the appropriate option (i.e., one that you did not choose in step 1) and repeating step When you are satisfied with all the settings, click the Apply button and close the panel. You can check the current setting for a species in a particular stream by selecting the stream and choosing the species name in the Defined Species list. Un-Normalized Mole or Mass Fraction Inputs If you input un-normalized mole or mass fractions when you are defining the compositions, prepdf will scale your inputs so that they sum to unity, and inform you (in an Information dialog box) that the mole or mass fractions will be normalized. Defining the Fuel Composition for Liquid Fuels If your FLUENT model considers combustion of fuel that is evaporated from liquid droplets, the composition of the vaporized fuel should be defined in prepdf. Defining the Fuel Composition for Coal Combustion If your FLUENT model involves coal combustion, the fuel and secondary stream compositions can be input in one of several ways. You can use a single mixture fraction (fuel stream) to represent the coal, defining the fuel composition as a mixture of volatiles and char (solid carbon). Alternately, you can use two mixture fractions (fuel and secondary streams), defining the volatiles and char separately. In two-mixture-fraction models for coal combustion, the fuel stream represents the char and the secondary stream represents volatiles. See Section for more detailed descriptions of modeling options and input procedures for coal combustion c Fluent Inc. November 28, 2001

55 14.3 User Inputs for the Non-Premixed Equilibrium Model Composition Inputs for Empirically-Defined Fuel Streams As mentioned in Step 3, you can define the composition of a fuel stream (i.e., the standard fuel or a secondary fuel) empirically instead of by specifying mole or mass fractions. For an empirically-defined stream, you will enter atom fractions, the lower caloric (heating) value of the fuel (with the combustion product assumed to be water vapor and CO 2 ), and the mean specific heat of the fuel. The steps are as follows: 1. Enable the Fuel (or Secondary) option under Stream. 2. Select each element in the Defined Species list and enter its Atom Fraction. 3. Enter the Lower Caloric Value and Specific Heat of the Fuel (or Secondary) stream. 4. When you are satisfied with all the settings, click the Apply button and close the panel. Equilibrium Corrections to Fuel Composition Note that for the full equilibrium option (i.e., when the fuel rich limit set in Step 8 is 1), prepdf will also perform an equilibrium calculation for the fuel stream inputs (e.g., at f = 1). As a result, you may find that prepdf will modify your inputs of fuel composition and temperature if the fuel system, as defined by your inputs, is not at equilibrium. For example, if you define the fuel as 0.5 CO and 0.5 CH 4 at 300 K, prepdf will correct the fuel to 0.35 C(S), 0.14 CH 4, CO, CO 2,and H 2 at 751 K, which is the corresponding equilibrium composition.! Equilibrium calculations will always be used when you define your fuel empirically, since only the full equilibrium method is available for such cases. If you define the fuel using species mole or mass fractions, the correction will occur only when the full equilibrium option is used. If your fuel is a liquid or solid (coal) fuel, the equilibrium correction will have no impact on your model setup. For gas-phase fuels, the effect of the equilibrium calculation on the fuel c Fluent Inc. November 28,

56 Modeling Non-Premixed Combustion composition and temperature is an important modeling issue that impacts your flow boundary conditions at gas-phase fuel inlets in FLUENT. If you are modeling a gaseous fuel, and you are using the full equilibrium model or empirical definition of the fuel, you should review the additional information on this topic that is included under Step 8, below. Step 6: Define Operating Conditions The thermodynamic operating conditions of your reacting system are required for construction of the look-up table and computation of the equilibrium chemistry model. These conditions are input using the Operating Conditions panel (Figure ). Setup Operating Conditions... Each of these inputs is described below. Remember to click the Apply button when you are done. Absolute Pressure is used to extract appropriate property data from the database and in the calculation of chemical equilibrium via the minimization of the Gibbs free energy. Min. Temperature is used to determine the lowest temperature for which the look-up tables are generated (see Figure ). Your input should correspond to the minimum temperature expected in the domain (e.g., an inlet or wall temperature). The minimum temperature should be set K below the minimum system temperature. This option is available only when the Equilibrium Chemistry model is selected in the Define Case panel. Max. Temperature is used to determine the highest temperature for which the look-up tables are generated (see Figure ). It should be set to a value about 100 K above the peak temperature predicted by prepdf for the adiabatic system calculation. Note that if your input of the peak temperature is too low, prepdf s calculation of the look-up tables will fail. This option is available only when the Equilibrium Chemistry model is selected in the Define Case panel. Inlet Temperature contains temperature inputs for the fuel, oxidant, and secondary stream inlets: c Fluent Inc. November 28, 2001

57 14.3 User Inputs for the Non-Premixed Equilibrium Model Figure : The Operating Conditions Panel in prepdf Fuel is the temperature of the fuel inlet in your model. In adiabatic simulations, this input (together with the oxidizer inlet temperature) determines the inlet stream temperatures that will be used by FLUENT. In non-adiabatic systems, this input should match the inlet thermal boundary condition that you will use in FLUENT (although you will enter this boundary condition again in the FLUENT session). If your FLU- ENT model will use liquid fuel or coal combustion, define the inlet fuel temperature as the temperature at which vac Fluent Inc. November 28,

58 Modeling Non-Premixed Combustion! porization/devolatilization begins (i.e., the Vaporization Temperature specified for the discrete-phase material see Section 19.11). For such non-adiabatic systems, the inlet temperature will be used in prepdf only to adjust the look-up table grid (e.g., the discrete enthalpy values for which the look-up table is computed). Note that if you have more than one fuel inlet, and these inlets are not at the same temperature, you must define your system as non-adiabatic. In this case, you should enter the fuel inlet temperature as the value at the dominant fuel inlet. prepdf uses your input of fuel and oxidizer inlet temperatures to determine the fuel and oxidizer enthalpies. When the full equilibrium model is used (rich limit of 1.0), the equilibrium calculation performed at f = 1 may result in a modified fuel composition and temperature. If you are using the full equilibrium model for a gaseous fuel (or if you are using an empirically defined gaseous fuel), you should be aware of how this equilibrium adjustment of the fuel temperature impacts your fuel inlet boundary conditions in FLUENT. See Step 8, below. Oxidiser is the temperature of the oxidizer inlet in your model. The issues raised in the discussion of the input of the fuel inlet temperature (directly above) pertain to this input as well. Secondary is the temperature of the secondary stream inlet in your model. (This item will appear only when you have defined a secondary inlet.) The issues raised in the discussion of the input of the fuel inlet temperature (directly above) pertain to this input as well. Nonadiabatic Flamelet Temperature Limits contains inputs for the temperature limits of a non-adiabatic flamelet system. These inputs are required only if you are using the laminar flamelet model and you have defined your case as non-adiabatic. See Section for more information on flamelet inputs c Fluent Inc. November 28, 2001

59 14.3 User Inputs for the Non-Premixed Equilibrium Model Step 7: Define the Reaction Stoichiometry The input of the reaction stoichiometry is required when you choose to use the stoichiometric reaction (mixed-is-burned) chemistry model. If you are using the partial equilibrium approach (rich limit defined) you may also choose to define the system stoichiometry at the rich limit (see below). In either case, your input of reaction stoichiometry defines a simple one-step reaction between fuel species and oxidant species. Consider, for example, the following very simple system: CH 4 +2O 2 CO 2 +2H 2 O prepdf requires that you input the molar stoichiometric coefficients as follows for this simple system: 1 for CH 4,2forO 2, 1 forco 2,and 2 for H 2 O. Note the convention that the product stoichiometry is entered with a negative number. You can input the coefficients using the Stoichiometric Coefficients panel (Figure ). Setup Species Stoichiometry... Figure : The Stoichiometric Coefficients Panel in prepdf c Fluent Inc. November 28,

60 Modeling Non-Premixed Combustion Select each species in the Defined Species list and enter its stoichiometric coefficient in the Coefficient field. When you have set the coefficients for all species, click Apply and close the panel. Input of Stoichiometry for Fuel Mixtures If your fuel stream consists of more than one species, you will need to input the stoichiometry for the composite reaction. Suppose, for example that your fuel contains 40% CH 4 and 60% CO by volume. Two moles of O 2 are required for each CH 4 and 0.5 moles of O 2 are required for each mole of CO. The molar stoichiometric coefficient for O 2 would thus be input as (0.4 2) + ( ) = 1.1. The molar stoichiometry for each product species would be determined in a similar fashion. The final stoichiometry would then be (0.4CH CO) + 1.1O 2 CO H 2 O (14.3-1) Input of Stoichiometry for Two Fuel or Oxidant Streams Defining stoichiometry for a two-mixture-fraction problem is similar to that for a single-mixture-fraction problem with a single, mixed fuel stream (described above). Consider, for example, the following two-fuel system: one inlet of CO, one inlet of CH 4, and one inlet of O 2. A single reaction will be defined: CH 4 +CO+2.5O 2 2CO 2 +2H 2 O (14.3-2) Input of Stoichiometry for Partial Equilibrium Calculations As described in Section , you can define a rich limit on the mixture fraction when the equilibrium chemistry option is used. Input of the rich limit is accomplished using the Solution Parameters panel, described below. For mixture fraction values above this limit, prepdf will suspend the equilibrium chemistry calculation and will compute the composition based on mixing of the fuel with the composition at the rich limit. When you choose this partial equilibrium approach, you can let prepdf compute the composition at the rich limit using equilibrium or you can input c Fluent Inc. November 28, 2001

61 14.3 User Inputs for the Non-Premixed Equilibrium Model the stoichiometry to be assumed at the rich limit. Generally, you should choose to use the equilibrium calculation of the composition at the rich limit unless you have experimental data (e.g., laminar flame data) that you want to represent through the input of stoichiometric coefficients. Step 8: Define Parameters Used in Creation of the Look-Up Table prepdf requires several inputs that are used in the creation of the lookup tables. Several of these inputs control the number and distribution of discrete values for which the look-up tables will be computed. These parameters are input using the Solution Parameters panel (Figure ). Setup Solution Parameters... Figure : The Solution Parameters Panel in prepdf The solution parameters are as follows: Non-Adiabatic Model contains parameters related to non-adiabatic models c Fluent Inc. November 28,

62 Modeling Non-Premixed Combustion Enthalpy Points is the number of discrete values of enthalpy at which the three-dimensional look-up tables will be computed. This input is required only if you are modeling a non-adiabatic system. In general, you should choose the number of enthalpy points to be one and a half to two times the number of mean mixture fraction points considered. The default value of 31 enthalpy points may be sufficient for your model, or you may want to increase this number (up to a maximum of 45). The number of points required will depend on the chemical system that you are considering, with more points required in high heat release systems (e.g., hydrogen/oxygen flames). Fuel Mixture Fraction contains parameters related to the fuel mixture fraction: Fuel Mixture Fraction Points is the number of discrete values of f at which the look-up tables will be computed. For a twomixture-fraction model, this value will also be the number of points used by FLUENT to compute the PDF if you select beta for the Probability Density Function in the Species Model panel (see Section ). Increasing the number of points will yield a more accurate PDF shape, but the calculation will take longer. Automatic Distribution enables the automatic discretization of the fuel mixture fraction and its variance. This feature optimizes the distribution of the discrete mixture fraction values by clustering them around the peak temperature value. The automatic discretization is recommended in most cases. Distribution Center Point (available only when Automatic Distribution is disabled) determines the distribution of the requested number of discrete values of f. The requested number of points will be distributed on either side of the center point with more points concentrated near the center point and fewer at the endpoints. If the center point is defined as 0.5 (the default), the values will be distributed uniformly over the range between 0 and 1. Generally, you should choose this value to be on the rich side of the stoichiometric value of f. This will c Fluent Inc. November 28, 2001

63 14.3 User Inputs for the Non-Premixed Equilibrium Model create more points (and hence better resolution and accuracy) in the stoichiometric range and below where the calculation is most critical. Determination of the stoichiometric value of f is discussed below. Note that you should not set the center point above 0.8 or below 0.2. Mixture Fraction Variance Points is the number of discrete values of f 2 s at which the look-up tables will be computed. The number of mixture fraction variance points should be roughly one-half the number of mean mixture fraction points requested. Lower resolution is required because the variation along the f 2 s axis is, in general, slower than the variation along the f axis of the look-up tables. Secondary Partial Fraction contains parameters related to the (optional) secondary partial fraction: Secondary Partial Fraction Points is the number of discrete values of p sec at which the look-up tables will be computed. Like Fuel Mixture Fraction Points, FLUENT will use the Secondary Partial Fraction Points to compute the PDF if you choose the beta PDF option (see Section ) for a two-mixture-fraction model. A larger number of points will give a more accurate shape for the PDF, but with a longer calculation time. Automatic Distribution enables the automatic discretization of the secondary partial fraction and its variance. The automatic discretization is recommended in most cases. Distribution Center Point (available only when Automatic Distribution is disabled) determines the distribution of the requested number of discrete values of p sec. The requested number of points will be distributed on either side of the center point with more points concentrated near the center point and fewer at the endpoints. If the center point is defined as 0.5 (the default), the values will be distributed uniformly over the range between 0 and 1. For an oxidant or non-reacting secondary stream, you should keep this default value. For a secondary fuel stream, you should generally choose this value to be on the rich side of the stoichiometric value of p sec. This will crec Fluent Inc. November 28,

64 Modeling Non-Premixed Combustion ate more points (and hence better resolution and accuracy) in the stoichiometric range and below where the calculation is most critical. Determination of the stoichiometric value of f sec is discussed below. You can then use Equation to determine the corresponding value for p sec.notethatyou should not set the center point above 0.8 or below 0.2. Equilibrium Chemistry Model contains parameters related to the equilibrium chemistry model (see Section ). You will not set these if you have chosen the stoichiometry chemistry model or if you have used the empirical definition option for fuel composition. Fuel Rich Flamability Limit controls the equilibrium calculation for the fuel mixture fraction. A value of 1.0 for the rich limit implies that equilibrium calculations will be performed over the full range of mixture fraction. When you use a rich limit that is less than 1.0, equilibrium calculations are suspended whenever f or f fuel exceeds the limit. This partial equilibrium model is a useful approach in hydrocarbon combustion calculations, allowing you to bypass complex equilibrium calculations in the fuel-rich region. The efficiency of partial equilibrium will be especially important when your model is non-adiabatic, speeding up the preparation of the look-up tables. If you use a rich limit below 1.0, prepdf will ask if you want to define the reaction stoichiometry at the rich limit or if you would like the program to compute the rich limit composition using equilibrium chemistry: If you choose the automatic calculation, prepdf will determine the composition at the rich limit using the equilibrium c Fluent Inc. November 28, 2001

65 14.3 User Inputs for the Non-Premixed Equilibrium Model calculation. If you do not choose the automatic calculation, you must input the molar stoichiometry at the rich limit using the Stoichiometric Coefficients panel (see Step 7, above). Secondary Rich Flamability Limit controls the equilibrium calculation for the secondary mixture fraction. If your secondary stream is not a fuel, you should keep the default value of 1. For a secondary fuel stream, you can consider modifying the value to use the partial equilibrium model. A value of 1.0 for the rich limit implies that equilibrium calculations will be performed over the full range of mixture fraction. When you input a rich limit that is less than 1.0, equilibrium calculations are suspended whenever f sec exceeds the limit. (Note that it is the secondary mixture fraction f sec and not the partial fraction p sec that is used here.) See the description of the Fuel Rich Flamability Limit above for details. Equilibrium Calculations in Fuel Rich Mixtures Experimental studies and reviews [23, 213] have shown that although the fuel lean flame region approximates thermodynamic equilibrium, chemical kinetics will prevail under fuel rich conditions. Therefore, when using prepdf for non-empirically defined fuels, the partial equilibrium model is strongly recommended. As described above, this approach suspends the equilibrium calculations in the rich mixture. Guidelines on how to set the rich limit values are given below. If you are using the full equilibrium approach (rich limit of 1 or empirically defined fuel), you should be aware that prepdf will perform an equilibrium calculation for the fuel (e.g., at f = 1). The resulting equilibrium fuel composition and temperature will, in most cases, differ from your original inputs defining the fuel. This indicates that the fuel composition and temperature, as defined by you, were not at equilibrium conditions. When prepdf adjusts the fuel composition and temperature to new equilibrium values, you will receive a warning message: c Fluent Inc. November 28,

66 Modeling Non-Premixed Combustion! The purpose of this warning is to alert you that the fuel inlet temperature and composition have been modified to new equilibrium values. This information is important because it impacts how you will define gaseous fuel inlet boundary conditions in FLUENT, as follows. The new equilibrium fuel temperature and composition define the fuel density at gas-phase fuel inlet boundaries in FLUENT. This equilibrium density should be used to compute the appropriate inlet velocity, preserving the desired mass flow rate of the fuel. You can determine the equilibrium fuel density using the VIEW-ALPHA/DENSITY text command in prepdf at the final discrete F-MEAN point (f = 1). In non-adiabatic systems, the density you should use is that on the enthalpy slice corresponding to your fuel inlet temperature. If your fuel inlet temperature is equal to the temperature you input in the Operating Conditions panel in prepdf, you should examine the density on the adiabatic enthalpy slice. If you have multiple fuel inlets at different inlet temperatures, you can perform an adiabatic calculation at each temperature to determine the equilibrium density. Although prepdf will compute a new equilibrium temperature for the fuel, you should use your original prepdf input of fuel inlet temperature when you define a gas-phase fuel inlet in FLUENT. FLUENT uses this original, non-equilibrium fuel temperature to compute the inlet fuel enthalpy. (This enthalpy is the same as that used in the prepdf equilibrium calculation.) Based on this inlet enthalpy, FLUENT will determine the equilibrium temperature, composition, and density at the fuel inlet. If you are modeling a liquid or coal fuel using the discrete phase model, the modified equilibrium fuel temperature and composition do not impact your inputs in FLUENT c Fluent Inc. November 28, 2001

67 14.3 User Inputs for the Non-Premixed Equilibrium Model Determining the Stoichiometric and Rich Limit Values of Mixture Fraction Determination of the rich limit mixture fraction is an important part of your inputs in the Solution Parameters panel. Generally, you should choose the rich limit to be equal to 1.5 to 2 times the stoichiometric mixture fraction: f rich 2.0f s (14.3-3) The stoichiometric mixture fraction, in turn, can be computed from the air-to-fuel mass ratio, r, as described in Section (Equation ). Alternately, you can estimate the stoichiometric mixture fraction by examining the instantaneous temperature vs. mixture fraction predicted by prepdf for your adiabatic system. The maximum temperature will occur near the stoichiometric mixture fraction. The combustion of methanol in air provides an example of how you can compute the stoichiometric mixture fraction. Written in terms of molar stoichiometry, the reaction is CH 3 OH + 1.5(O N 2 ) CO 2 +2H 2 O+5.64N 2 (14.3-4) To compute the stoichiometric mixture fraction, first write the reaction on a mass basis, in terms of the stoichiometric air-to-fuel ratio, r, and the equivalence ratio, φ. The reaction becomes φ CH 3 OH + r(o N 2 ) (φ + r) Products (14.3-5) where r = Using Equation , the stoichiometric mixture fraction (φ =1.0)isthen f s = φ φ + r = 1 =0.134 (14.3-6) and the fuel rich mixture fraction, taken at φ =2.0,is c Fluent Inc. November 28,

68 Modeling Non-Premixed Combustion f rich = 2 =0.237 (14.3-7) Extension of this exercise to a fuel consisting of a mixture of hydrocarbons is straightforward, with Equation simply taking on a more general form. Consider, for example, a fuel-air system in which the fuel is comprised of 60% CH 4 and 40% CO: (0.6CH CO)+z(O N 2 ) xco 2 +yh 2 O+3.76zN 2 (14.3-8) After balancing this equation and solving for z, you can compute the airto-fuel mass ratio and then compute the stoichiometric mixture fraction as described above. Rich Limit Values for Secondary Streams If the secondary stream is an oxidizer or an inert, the rich limit for the secondary stream should be set to 1. If it is a second fuel, the single fuel system analysis above applies, since the secondary rich limit is defined in terms of secondary mixture fraction, f sec (not secondary partial fraction, p sec ). Step 9: Save Your Inputs When all of the preceding procedures are complete, you should save your inputs to an input file: File Write Input... This file contains all of your inputs defining the reaction system in prepdf. You will have the option to save either a binary (unformatted) file or a formatted (ASCII, or text) file. You can read and edit a formatted file, but it will require more storage space than the same file in binary format. Binary files take up less space and can be read and written by prepdf more quickly, but they cannot be transferred between all machine types c Fluent Inc. November 28, 2001

69 14.3 User Inputs for the Non-Premixed Equilibrium Model Step 10: Compute the Look-Up Tables After saving your inputs, you can initiate the computation of the look-up tables by prepdf: Calculate PDF Table The computations performed in prepdf for a single-mixture-fraction calculation culminate in the discrete integration of Equation (or ) as represented in Figure (or Figure ). For a twomixture-fraction calculation, prepdf will calculate the physical properties using Equation or its adiabatic equivalent. These computations may take only a few moments for simple systems or they may require up to an hour for a complex system (e.g., non-adiabatic systems with 10 or more species). prepdf reports progress as the calculation proceeds. Below, sample output is shown for an adiabatic, single-mixturefraction calculation: c Fluent Inc. November 28,

70 Modeling Non-Premixed Combustion (*)- INITIALIZING AT ADIABATIC ENTHALPY LINE...ADIABATIC CALCULATION... POINTS TO-GO EQUILIBRIUM DELTA-PDF T(K) = F-MEAN = 0.04 F-VAR = T(K) = F-MEAN = 0.04 F-VAR = T(K) = F-MEAN = 0.04 F-VAR = T(K) = F-MEAN = 0.04 F-VAR = T(K) = F-MEAN = 0.04 F-VAR = T(K) = F-MEAN = 0.04 F-VAR = T(K) = 467. F-MEAN = 0.96 F-VAR = T(K) = 467. F-MEAN = 0.96 F-VAR = T(K) = 467. F-MEAN = 0.96 F-VAR = T(K) = 467. F-MEAN = 0.96 F-VAR = T(K) = 467. F-MEAN = 0.96 F-VAR = (*)- CALCULATION SUCCEEDED After completing the equilibrium calculation at the specified number of mixture fraction points, prepdf reports that the calculation succeeded. The resulting look-up tables take the form illustrated in Figure (or Figure , for non-adiabatic systems). These look-up tables can be plotted using the graphics tools available in prepdf, as described below in Step 12. Note that in non-adiabatic calculations, the report includes information on the enthalpy point currently considered: c Fluent Inc. November 28, 2001

71 14.3 User Inputs for the Non-Premixed Equilibrium Model (*)- INITIALIZING ENTHALPY AT TEMPERATURE LIMITS...NON-ADIABATIC CALCULATION... POINTS TO-GO H-POINT EQUILIBRIUM DELTA-PDF T(K) = 298. F-MEAN = 0.00 F-VAR = T(K) = 334. F-MEAN = 0.00 F-VAR = T(K) = 888. F-MEAN = 0.00 F-VAR = T(K) = F-MEAN = 0.00 F-VAR = T(K) = F-MEAN = 0.00 F-VAR = T(K) = F-MEAN = 0.00 F-VAR = T(K) = F-MEAN = 0.00 F-VAR = T(K) = F-MEAN = 0.00 F-VAR =.000 You may notice that non-adiabatic calculations terminate before the tabulated number of points under TO-GO is zero. This is simply because the final calculations, at mixture fraction equal to 1.0, do not include multiple variance points. For a two-mixture-fraction calculation, prepdf will print the following information during the calculation: (*)- INITIALIZING AT ADIABATIC ENTHALPY...ADIABATIC CALCULATION / SECONDARY STREAM... POINTS TO-GO EQUILIBRIUM PROGRESS-VARIABLES T(K) = 600. F-FUEL = P-SECND = T(K) = F-FUEL = P-SECND = T(K) = F-FUEL = P-SECND = T(K) = F-FUEL = P-SECND = T(K) = F-FUEL = P-SECND = T(K) = F-FUEL = P-SECND = T(K) = F-FUEL = P-SECND = T(K) = F-FUEL = P-SECND = T(K) = F-FUEL = P-SECND = The resulting look-up tables take the form illustrated in Figure (or c Fluent Inc. November 28,

72 Modeling Non-Premixed Combustion Figure , for non-adiabatic systems). These look-up tables can be plotted using the graphics tools available in prepdf, as described below. For a non-adiabatic calculation, the current enthalpy point will be shown as in the example output listed above for the non-adiabatic single-mixturefraction calculation. Stability Issues in prepdf Complex chemistry and non-adiabatic effects may make the equilibrium calculation more time-consuming and difficult. In some instances the equilibrium calculation may even fail. You may be able to eliminate any difficulties that you encounter using one of the following techniques: Try the calculation as an adiabatic system. Adiabatic system calculations are generally quite straightforward and can provide valuable insight into the optimal inputs to the non-adiabatic calculation. Using the adiabatic results, you can determine the maximum temperature expected and correct this important input to the nonadiabatic case. You can determine which species are important to the reacting system, and eliminate those that are unimportant. This information can be obtained by a simple review of the lookup tables generated by the adiabatic calculation. Selecting an appropriate temperature range and an appropriate list of chemical species to include will greatly simplify the non-adiabatic calculation. You might also simplify the non-adiabatic calculation by a better choice of the rich cut-off limit, as described in Step 8, and adjust the mixture fraction center point to capture the adiabatic temperature curve more adequately. Try reducing the number of species considered. Simplify your model of the reacting system. If your system includes heavy hydrocarbons, be sure that you are including basic hydrocarbons such as CH 4 in the system. Additional stability issues may arise for solid or heavy liquid fuels that have been defined using the empirical fuel approach. You may find that c Fluent Inc. November 28, 2001

73 14.3 User Inputs for the Non-Premixed Equilibrium Model for rich fuel mixtures the equilibrium calculation produces very low temperatures and eventually fails. This indicates that strong endothermic reactions are taking place and the mixture is not able to sustain them. In this situation, you may need to raise the heating value of the fuel until prepdf produces acceptable results. Provided that your fuel will be treated as a liquid or solid (coal) fuel, you can maintain the desired heating value in your FLUENT simulation. This is accomplished by defining the difference between the desired and the adjusted heating values as latent heat (in the case of combusting solid fuel) or heat of pyrolysis (in the case of liquid fuel). Informational Messages and Errors Reported During the prepdf Calculation prepdf may report a variety of error messages or informational reports as it computes the equilibrium chemistry and generates the look-up tables. These messages are detailed in Section Step 11: Save the Look-Up Tables The look-up tables computed by prepdf are stored in a file that you will read into FLUENT. FLUENT will use the tables to extract the species, density, and temperature fields from the mixture fraction field that it predicts as part of the flow-field calculation. The look-up tables must be saved before you exit from prepdf. File Write PDF...! The file can be saved as formatted (ASCII, or text) or binary (unformatted), for either FLUENT 4 or FLUENT 6. Be sure to save a PDF file for the appropriate solver. In addition to reading the PDF file into FLUENT for the flow analysis, you can read it back into prepdf at a later date if you want to examine the look-up tables using the graphics tools described below, in Step 12. (All types of PDF files can be read back into prepdf.) c Fluent Inc. November 28,

74 Modeling Non-Premixed Combustion Step 12: Graphics and Alphanumeric Reports in prepdf prepdf supplies a number of utilities that allow you to examine the result of the look-up table computations. Reviewing the Beta PDF Shape You can plot the shape of the beta PDF using the Beta-Pdf panel (Figure ). Display Beta PDF... Figure : The Beta-Pdf Panel in prepdf This utility simply plots the function, Equation , for any value of f (Mean Mixture Fraction) andf 2 (Mixture Fraction Variance) thatyou define in the panel. Figure illustrates two of the many forms that the beta PDF shape may take. Note that none of your inputs in prepdf will change the beta PDF shape for a given pair of f and f 2. (Since the β PDF plots are just for general informational purposes, you can plot them even when you are working on a two-mixture-fraction problem, for which the PDFs will be calculated in FLUENT.) c Fluent Inc. November 28, 2001

75 14.3 User Inputs for the Non-Premixed Equilibrium Model Reviewing Instantaneous Values in Adiabatic Single-Mixture-Fraction Systems You can plot the variation of instantaneous species concentration, density, or temperature with the instantaneous mixture fraction using the Property Curves panel (Figure ). Display Property Curves... Figure : The Adiabatic Property Curves Panel in prepdf You can select temperature, density, species, or enthalpy as the variable to be plotted using the Plot Variable drop-down list. The resulting displays show how these quantities vary with mixture fraction and can be used to determine the stoichiometric value of mixture fraction, the peak temperature expected, and the most important species in the system. Figures and show instantaneous values derived for a very simple hydrocarbon system. For adiabatic systems, you can also write property data to a file in the format used by the XY plotter in FLUENT. To write an XY plot file containing property data, use the WRITE-XY-FILE text command in prepdf: VIEW-GRAPHICS PROPERTY-CURVES WRITE-XY-FILE When you select this command, you will be asked to select the property to be written and specify a name for the file: c Fluent Inc. November 28,

76 Modeling Non-Premixed Combustion KEY CH4 O2 CO2 H2O N2 CO H2 M ol e F ra c ti o n 1.00E E E E E E E E E E E E+00 Mixture Fraction F CHEMICAL EQUILIBRIUM INSTANTANEOUS SPECIES COMPOSITION prepdf V4.00 Fluent Inc. Figure : Instantaneous Species Mole Fractions Derived From the Equilibrium Chemistry Calculation KEY 3.28E+03 T e m p e r a t u r e 2.62E E E E E E E E E E E+00 Mixture Fraction F CHEMICAL EQUILIBRIUM INSTANTANEOUS TEMPERATURE (KELVIN) prepdf V4.00 Fluent Inc. Figure : Instantaneous Temperature Derived From the Equilibrium Chemistry Calculation c Fluent Inc. November 28, 2001

77 14.3 User Inputs for the Non-Premixed Equilibrium Model COMMANDS AVAILABLE FROM PROPERTY-CURVES: PLOT WRITE-XY-FILE QUIT (PROPERTY-CURVES)- wxy COMMANDS AVAILABLE FROM WRITE-XY-FILE: TEMPERATURE DENSITY SPECIES ENTHALPY QUIT (WRITE-XY-FILE)- te ENTER NAME OF XY PLOT FILE (S)- DEFAULT- sample.xy Later, during your FLUENT session, you can read and plot this data using the File XY Plot panel. Plot File... Reviewing Instantaneous Values in Adiabatic Two-Mixture-Fraction Systems If your problem includes a secondary stream, in addition to choosing the variable to be plotted, you must also specify a constant value of the fuel mixture fraction or the secondary partial fraction at which the property curve should be drawn. Choose either fraction under Constant Value of and specify its Value. The selected variable will be plotted as a function of the fraction that is not held constant. In Figure , the secondary partial fraction is held constant at 0.05, and the plot shows how temperature varies with fuel mixture fraction. Reviewing Instantaneous Values in Non-Adiabatic Systems If your single-mixture-fraction system is non-adiabatic, you can still review the variation of instantaneous scalar values with the instantaneous mixture fraction. In the non-adiabatic case, because the instantaneous results depend on the mean enthalpy value, you will specify the mean mixture fraction, its variance, and the mean enthalpy value at which the variable will be displayed. The Property Curves panel (Figure ) c Fluent Inc. November 28,

78 Modeling Non-Premixed Combustion KEY 3.28E E+03 T e m p e r a t u r e 1.97E E E E E E E E E E+00 F Fuel CONSTANT SECONDARY PARTIAL FRACTION INSTANTANEOUS TEMPERATURE (KELVIN) prepdf V4.00 Fluent Inc. Figure : Instantaneous Temperature Plotted for a Two-Mixture- Fraction Case contains the fields required to input these parameters in non-adiabatic systems. Display Property Curves...!! Select temperature, density, species mass fraction, or enthalpy as the variable to be plotted using the Plot Variable drop-down list. Then enter the Mean Mixture Fraction, Mixture Fraction Variance, andmean Enthalpy at which to display the selected variable. Click Display to generate the graphical display. Note that you cannot plot instantaneous property curves for a nonadiabatic two-mixture-fraction case. You will instead plot the look-up tables of instantaneous values using the Nonadiabatic-Table panel. Note also the following important difference in the Property Curves display for adiabatic and non-adiabatic cases. For adiabatic cases, the instantaneous property curves correspond to the values of the look-up tables at f 2 s = 0. In non-adiabatic systems, however, the property curves c Fluent Inc. November 28, 2001

79 14.3 User Inputs for the Non-Premixed Equilibrium Model Figure : The Non-Adiabatic Property Curves Panel in prepdf represent only the intermediate values of the properties prior to the PDF integrations, and therefore do not correspond to any of the values in the PDF look-up tables. In order to examine the values stored in the lookup tables for a non-adiabatic case you should use the Nonadiabatic-Table panel. Reviewing the 2D Look-Up Tables Computed by prepdf for a Single Mixture Fraction You can use either graphics or alphanumerics to display the 2D PDF look-up tables generated for single-mixture-fraction adiabatic systems. To plot the tables, use the Pdf-Table panel (Figure ). Display PDF Table... Using the Plot Variable drop-down list, you can display the look-up table for temperature, density, or any individual species fraction (defined in the Species Selection panel that appears when you choose SPECIES). Figure illustrates the look-up table generated for temperature in a simple hydrocarbon combustion model. Similarly, you can use the VIEW-ALPHA command, available in the text interface, to display the c Fluent Inc. November 28,

80 Modeling Non-Premixed Combustion Figure : The Pdf-Table Panel in prepdf look-up table in tabular form at each point in the discrete mean/variance matrix: MAIN VIEW-ALPHA VIEW ALPHA: TEMPERATURE (K) F-VAR F-MEAN= E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+03 Reviewing the 2D Look-Up Tables Computed by prepdf for Two Mixture Fractions! It is important for you to view your temperature and species tables in prepdf to ensure that they are adequately but not excessively resolved. Inadequate resolution will lead to inaccuracies, and excessive resolution will lead to unnecessarily slow calculation times in FLUENT c Fluent Inc. November 28, 2001

81 14.3 User Inputs for the Non-Premixed Equilibrium Model 2.3E+03 T E 1.9E+03 M PE R A T U R E K 1.5E E E E E E-01 SCALED-F-VARIANCE 1.00E E E E E E E E E E+00 F-MEAN PDF TABLE - CHEMICAL EQUILIBRIUM MEAN FLAME TEMPERATURE prepdf V4.00 Fluent Inc. Figure : Two-Dimensional Look-Up Table for Temperature Generated by prepdf for a Simple Hydrocarbon System (Single-Mixture- Fraction, Adiabatic System) c Fluent Inc. November 28,

82 Modeling Non-Premixed Combustion You can use either graphics or alphanumerics to display the 2D lookup tables of instantaneous properties generated for two-mixture-fraction adiabatic systems. To plot the tables, use the Property-Table panel: Display Property Table... Figure : The Property-Table Panel You will use this panel exactly as described above for the Pdf-Table panel, but the resulting plot will show the selected variable as a function of instantaneous fuel mixture fraction and secondary partial fraction (instead of as a function of mean fuel mixture fraction and variance). Alphanumeric reports are generated in the same way as for single-mixturefraction calculations, but the report will list the f fuel, p sec points instead of the mean/variance matrix. VIEW ALPHA: TEMPERATURE (K) P-SEC F-FUEL= E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E c Fluent Inc. November 28, 2001

83 14.3 User Inputs for the Non-Premixed Equilibrium Model Reviewing the 3D Look-Up Tables for Single-Mixture-Fraction Non-Adiabatic Systems The look-up tables generated for single-mixture-fraction non-adiabatic systems contain the mean temperature, density, and species concentrations as a function of three quantities: mean mixture fraction, mixture fraction variance, and mean enthalpy. Consequently, when you ask to display the look-up tables in alphanumerics or graphics, you will be displaying them slice-by-slice. The graphical display begins with the Nonadiabatic-Table panel (Figure ). Display Nonadiabatic-Table... Figure : The Nonadiabatic-Table Panel in prepdf In this panel, you can select the variable to be plotted in the Plot Variable drop-down list. Next, you must define how the three-dimensional array of data points available in the look-up table are to be sliced: which discrete independent variable (either f or H ) is to be held constant and whether the constant value is to be selected as a numerical value (choose Value as the Plot type) or by discretization index (choose Slice as the Plot type). If you choose the latter approach, click the Slice... button to select the discretization index slice that you want. c Fluent Inc. November 28,

84 Modeling Non-Premixed Combustion Figure : The Slice Panel in prepdf In the Slice panel (Figure ), select which discretized variable is to be constant (Enthalpy or F-Mean) and then pick the Slice # (discretization index). For example, in the panel in Figure , a look-up table generated at the tenth discrete value of mean enthalpy has been requested. As discussed in Section 14.2, each slice actually corresponds to a normalized heat loss or gain. The enthalpy slice index corresponding to the adiabatic case is displayed in the Adiabatic Slice # field. To generate the plot, click Apply and close the Slice panel, and then click Display in the Nonadiabatic-Table panel. A sample plot is shown in Figure Alternately, you may want to define a slice of the 3D look-up table based on a specific value of one of the independent quantities. When this is the case, select the Value option under Plot type in the Nonadiabatic-Table panel. To set the slice, click the Value... button to open the Lookup Points panel (Figure ). In this panel, you can select a slice of the 3D table that corresponds to: constant value of mean enthalpy (Enthalpy Values and Constant Enthalpy options) c Fluent Inc. November 28, 2001

85 14.3 User Inputs for the Non-Premixed Equilibrium Model 2.4E+03 T E 2.0E+03 M PE R A T U R E K 1.6E E E E E E-01 SCALED-F-VARIANCE 1.00E E E E E E E E E E+00 F-MEAN MEAN ENTHALPY SLICE NUMBER 23 MEAN FLAME TEMPERATURE FROM 3D-PDF-TABLE prepdf V4.00 Fluent Inc. Figure : Display of a Single Slice of the Three-Dimensional Look- Up Table in a Non-Adiabatic System (Single Mixture Fraction) constant value of mean mixture fraction (Constant F-Mean Value) adiabatic enthalpy (Enthalpy Values and Adiabatic Relationship options) In addition, you supply the physical value of the selected quantity in the Value field. When the adiabatic enthalpy option is selected, you must supply the Fuel and Oxidiser Inlet Temperature instead of the fixed value. prepdf uses this information to construct the adiabatic relationship between enthalpy and mixture fraction that is used to slice the table. The adiabatic enthalpy option is very useful, as it allows you to generate adiabatic (2D) look-up tables for various combinations of fuel and oxidizer inlet temperatures from your 3D look-up table generated for the non-adiabatic system. Finally, you can set the Refinement Factor, which determines the resolution of the plotted curve. A refinement factor of 1.0 (the default) implies that the plot will use the same number of discrete points that c Fluent Inc. November 28,

86 Modeling Non-Premixed Combustion Figure : The Lookup Points Panel in prepdf you requested in the Solution Parameters panel. Increasing this factor will cause prepdf to compute and display additional data points, yielding a smoother plot but requiring some time to compute. To generate the plot, click Apply and close the Lookup Points panel, and then click Display in the Nonadiabatic-Table panel. Reviewing the 3D Look-Up Tables for Two-Mixture-Fraction Non-Adiabatic Systems The look-up tables generated for two-mixture-fraction non-adiabatic systems contain the instantaneous temperature, density, and species concentrations as a function of three instantaneous quantities: fuel mixture c Fluent Inc. November 28, 2001

87 14.3 User Inputs for the Non-Premixed Equilibrium Model fraction, secondary partial fraction, and enthalpy. As for the singlemixture-fraction case described above, you will use the Nonadiabatic- Table panel to display the look-up table. The procedure is exactly the same as that described above, except that you can choose only enthalpy slices or values on which to display the look-up table Informational Messages and Errors Reported by prepdf The following messages may be issued by prepdf during the case setup, the calculation of the look-up tables, or postprocessing. The source of the message and the action required by you, if any, are detailed here. BOTTOM TEMPERATURE TOO HIGH From: Solver Cause: The minimum temperature defined for the non-adiabatic calculation is higher than the inlet temperatures. Action: Correct the minimum temperature value. CALCULATIONS INTERRUPTED CONTINUE? (ELSE RETURN TO MAIN MENU) From: Solver Cause: Ctrl-C has been pressed. Action: Typing N will cause the solver to abort to the main menu and all previous equilibrium iterations will be lost. Typing Y or RETURN will cause the calculations to continue. ENTHALPY CURVE GENERATION FAILED From: Graphics c Fluent Inc. November 28,

88 Modeling Non-Premixed Combustion Cause: For the non-adiabatic single-mixture-fraction case, prepdf was unable to construct the instantaneous enthalpy curve required for the calculation of the instantaneous property curves. Action: Modify your input of mixture fraction, variance, or enthalpy for the property curve plot. ENTHALPY HIGHER THAN ENTHALPY CEILING From: Graphics Cause: For the non-adiabatic single-mixture-fraction case the enthalpy input for the calculation of the instantaneous property curves is too high. Action: Decrease the enthalpy value for the property curve plot. ENTHALPY LOWER THAN ENTHALPY FLOOR From: Graphics Cause: For the non-adiabatic single-mixture-fraction case the enthalpy input for the calculation of the instantaneous property curves is too low. Action: Increase the enthalpy value for the property curve plot. ERROR: NO ATOMS EXIST TO DEFINE THE EMPIRICAL STREAM From: Setup Cause: The empirical fuel stream option has been selected but no elements have been defined from which to construct the fuel. Elements allowed are C, H, O, S, and N. Action: Add the elements C, H, O, S, and N in the species list. ERROR: NO CARBON DIOXIDE SPECIES EXISTS c Fluent Inc. November 28, 2001

89 14.3 User Inputs for the Non-Premixed Equilibrium Model From: Setup Cause: The empirical fuel stream option has been selected but CO 2 species has not been defined. CO 2 is needed to calculate the heat of formation of the empirical fuel from its heating value Action: Add CO 2 in the species list. ERROR: NO WATER VAPOR SPECIES EXISTS From: Setup Cause: The empirical fuel stream option has been selected but H 2 O species has not been defined. H 2 O is needed to calculate the heat of formation of the empirical fuel from its heating value. Action: Add H 2 O in the species list. ERROR OPENING TEMPORARY LINKING FILE From: Files or Setup Cause: prepdf was unable to open the file DBLINK used for temporary storage of thermodynamic data. Action: Make sure you have write permission in the working directory. ERROR WRITING TEMPORARY LINKING FILE From: Files or Setup Cause: prepdf was unable to write the file DBLINK used for temporary storage of thermodynamic data. Action: Make sure there is space on the disk. FAULT AT STOICHIOMETRIC REACTION CALCULATION FOR F-MEAN = xx c Fluent Inc. November 28,

90 Modeling Non-Premixed Combustion From: Solver Cause: This message may appear for one of the following reasons: the temperature limits are not sufficient the stoichiometry defined is incorrect. the rich flammability limit with the automatic stoichiometry calculation has been used and the value of rich flammability limit has been set too low. Action: Check inputs of temperature limits. Check inputs of stoichiometry. Check the setting of rich flammability limit. INCORRECT STOICHIOMETRY DEFINED From: Solver Cause: The stoichiometry defined does not satisfy the element balance. Action: Check inputs of stoichiometry. SETTING UP DATA BASE LINK FILE FAILED From: Files or Setup Cause: prepdf was unable to access the thermodynamic properties database. Action: Make sure the instructions for installation of prepdf have been followed and all the environment variables are set correctly. TOP TEMPERATURE TOO LOW From: Solver Cause: The maximum temperature defined for the non-adiabatic calculation is lower than the adiabatic flame temperature for this mixture c Fluent Inc. November 28, 2001

91 14.3 User Inputs for the Non-Premixed Equilibrium Model Action: Increase the maximum temperature limit. It is recommended that this is set at T adiabatic K. The adiabatic flame temperature T adiabatic can be calculated by performing an adiabatic calculation and reviewing the instantaneous temperature vs. mixture fraction curves predicted by prepdf. UNABLE TO CALCULATE COMPOSITION AT F-MEAN xx AND TEMPERATURE xxxx K From: Solver Cause: The equilibrium calculation has failed. This may happen for the following reasons: The species list defined is not adequate. The mixture is liquid for the conditions the equilibrium solver has entered. Action: Try using better temperature limits. Experiment with the species list, using an adiabatic calculation, adding or removing species based on the amount formed over the mixture fraction range. Try moving the rich flammability limit closer to the stoichiometric mixture fraction. UNABLE TO CALCULATE ENTHALPY CURVE AT I-FMEAN = xx J-FVAR = xx K-ENTH = xx From: Solver Cause: For the non-adiabatic calculation, prepdf was unable to construct the instantaneous enthalpy curve required for the PDF calculation. Action: This message should not appear. support. Contact Fluent customer c Fluent Inc. November 28,

92 Modeling Non-Premixed Combustion Non-Premixed Model Input and Solution Procedures in FLUENT The non-premixed model setup and solution procedure in FLUENT differs slightly for single- and two-mixture-fraction problems. Below, an overview of each approach is provided. Note that your FLUENT case file must always meet the restrictions listed for the non-premixed modeling approach in Section In this section, details are provided regarding the problem definition and calculation procedures you follow in FLUENT. Single-Mixture-Fraction Approach For a single-mixture-fraction system, when you have completed the calculation of the mixture fraction/pdf look-up tables in prepdf, you are ready to begin your reacting flow simulation in FLUENT. InFLUENT, you will solve the flow field and predict the spatial distribution of f and f 2 (and H if the system is non-adiabatic or χ st,d if the system is based on laminar flamelets). FLUENT will obtain the implied values of temperature and individual chemical species mass fractions from the look-up tables. Two-Mixture-Fraction Approach When a secondary stream is included, FLUENT will solve transport equations for the mean secondary partial fraction (p sec ) and its variance in addition to the mean fuel mixture fraction and its variance. FLUENT will then look up the instantaneous values for temperature, density, and individual chemical species in the look-up tables, compute the PDFs for the fuel and secondary streams, and calculate the mean values for temperature, density, and species. Note that in order to avoid both inaccuracies and unnecessarily slow calculation times, it is important for you to view your temperature and species tables in prepdf to ensure that they are adequately but not excessively resolved c Fluent Inc. November 28, 2001

93 14.3 User Inputs for the Non-Premixed Equilibrium Model Step 1: Start FLUENT and Read a Grid File Start your FLUENT session in the usual way, as described in Section 1.5, and then read in a grid file. The number and types of inlets in your model must meet the constraints of the non-premixed modeling approach, as discussed in Section and illustrated in Figures , , and Starting a Non-Premixed Calculation From a Previous Case File! You can read a previously defined FLUENT case file as a starting point for your non-premixed combustion modeling. If this case file contains inputs that are incompatible with the current non-premixed combustion model, FLUENT will alert you when the non-premixed model is turned on and it will turn off those incompatible models. For example, if the case file includes species that differ from those included in the PDF file created by prepdf, these species will be disabled. If the case file contains property descriptions that conflict with the property data in the chemical database, these property inputs will be ignored. See Step 2, below, for important information about PDF files created by previous versions of prepdf. Step 2: Activate the Non-Premixed Combustion Model Preliminaries Before turning on the non-premixed combustion model, you must enable turbulence calculations in the Viscous Model panel. Define Models Viscous... If your model is non-adiabatic, you should also enable heat transfer (and radiation, if required). Define Models Energy... Define Models Radiation... Figure illustrates the types of problems that must be treated as non-adiabatic. Note, however, that the decision to include non-adiabatic c Fluent Inc. November 28,

94 Modeling Non-Premixed Combustion effects is made in prepdf. FLUENT will turn off the energy equation if your prepdf inputs are for an adiabatic system. Enabling Non-Premixed Combustion Before any other modeling inputs (e.g., setting of boundary conditions or properties) you should turn on the non-premixed combustion model, because activating this model will impact how other inputs are requested during your subsequent work. The non-premixed combustion model is enabled in the Species Model panel. Define Models Species... Figure : The Species Model Panel in FLUENT Select Non-Premixed Combustion under the Model heading. When you click OK in the Species Model panel, a Select File dialog box will immediately appear, prompting you for the name of the PDF file containing the look-up tables created in prepdf. (The PDF file is the file you saved using the File/Write/PDF... menu item in prepdf after computing the look-up tables.) FLUENT will indicate that it has successfully read the specified PDF file: c Fluent Inc. November 28, 2001

95 14.3 User Inputs for the Non-Premixed Equilibrium Model Reading "/home/mydirectory/adiabatic.pdf"... read 5 species (binary c, adiabatic prepdf) pdf file successfully read. Done. After you read in the PDF file, FLUENT will inform you that some material properties have changed. You can accept this information; you will be updating properties later on.! You can read in an altered PDF file at any time by using the File/Read/Pdf... menu item. Recall that the non-premixed combustion model is available only when you used the segregated solver; it cannot be used with the coupled solvers. Also, the non-premixed combustion model is available only when turbulence modeling is active. If you are modeling a non-adiabatic system and you wish to include the effects of compressibility, re-open the Species Model panel (Figure ) and turn on Compressibility Effects under PDF Options. This option tells FLUENT to update the density, temperature, species mass fraction, and enthalpy from the PDF tables to account for the varying pressure of the system. When the non-premixed combustion model is active, you can enable compressibility effects only in the Species Model panel. For other models, you will specify compressible flow (ideal-gas, boussinesq, etc.) in the Materials panel. Using PDF Files Created by Previous Releases of prepdf PDF files created by prepdf 1 cannot be read into FLUENT or into prepdf 4 (the current version). If you have prepdf 1 files, read the input file into prepdf 4, recalculate the look-up tables, and save a new PDF file to be read into FLUENT. As noted in Section , prepdf 1 input files that were created for coal combustion systems must be modified before computing the PDF look-up tables in prepdf 4. PDF files created by prepdf 2 can be read into FLUENT, but it is recommended that you recalculate the look-up tables in prepdf 4. In these versions of prepdf, the mixture fraction variance was not scaled to its c Fluent Inc. November 28,

96 Modeling Non-Premixed Combustion Figure : The Species Model Panel With Available PDF Options maximum value while building the PDF table. This resulted in a lowerresolution table, especially for lower mixture fraction values, and at mixture fraction values close to 0 and 1. To take advantage of a more advanced PDF table look-up scheme, you can read a PDF or input file created by prepdf 2 into prepdf 4 and recalculate the look-up table. Two-mixture-fraction PDF files created in prepdf 2 should be read into prepdf 4 and written out in FLUENT 6 format. (Two-mixture-fraction PDF files written by prepdf 2 cannot be read directly into FLUENT.) Table summarizes the recommended procedures for using old PDF files in FLUENT. Retrieving the PDF File During Case File Reads The PDF filename is specified to FLUENT only once. Thereafter, the filename is stored in your FLUENT case file and the PDF file will be automatically read into FLUENT whenever the case file is read. FLUENT will remind you that it is reading the PDF file after it finishes reading the rest of the case file by reporting its progress in the text (console) window c Fluent Inc. November 28, 2001

97 14.3 User Inputs for the Non-Premixed Equilibrium Model Table : Using Old PDF Files in FLUENT PDF file type Readable in Readable Recommended prepdf 4? in FLUENT? Procedure prepdf 1 input files only no Read input file into prepdf 4, recalculate PDF table, and write a PDF file in FLUENT 6format. prepdf 2 (single mixture fraction) prepdf 2 (two mixture fractions) yes yes Read input or PDF file into prepdf 4, recalculate PDF table, and write a PDF file in FLU- ENT 6format. yes no Read PDF file into prepdf 4 and write apdffileinflu- ENT 6format. prepdf 3 yes yes prepdf 3 files are compatible with both prepdf 4and FLUENT 6. c Fluent Inc. November 28,

98 Modeling Non-Premixed Combustion Note that the PDF filename stored in your case file may not contain the full name of the directory in which the PDF file exists. The full directory name will be stored in the case file only if you initially read the PDF file through the GUI (or if you typed in the directory name along with the filename when using the text interface). In the event that the full directory name is absent, the automatic reading of the PDF file may fail (since FLUENT does not know which directory to look in for the file), and you will need to manually specify the PDF file. The safest approaches are to use the GUI when you first read the PDF file or to supply the full directory name when using the text interface. Step 3: Define Boundary Conditions Input of Mixture Fraction Boundary Conditions When the non-premixed combustion model is used, flow boundary conditions at inlets and exits (i.e., velocity or pressure, turbulence intensity) are defined in the usual way. Species mass fractions at inlets are not required. Instead, you define values for the mean mixture fraction, f, and the mixture fraction variance, f 2, at inlet boundaries. (For problems that include a secondary stream, you will define boundary conditions for the mean secondary partial fraction and its variance as well as the mean fuel mixture fraction and its variance.) These inputs provide boundary conditions for the conservation equations you will solve for these quantities. The inlet values are supplied in the boundary conditions panel for the selected inlet boundary (e.g., Figure ). Define Boundary Conditions... Input the Mean Mixture Fraction and Mixture Fraction Variance (and the Secondary Mean Mixture Fraction and Secondary Mixture Fraction Variance, if you are using two mixture fractions). In general, the inlet value of the mean fractions will be 1.0 or 0.0 at flow inlets: the mean fuel mixture fraction will be 1.0 at fuel stream inlets and 0.0 at oxidizer or secondary stream inlets; the mean secondary mixture fraction will be 1.0 at secondary stream inlets and 0.0 at fuel or oxidizer inlets. The fuel or secondary mixture fraction will lie between 0.0 and 1.0 only if you are modeling flue gas recycle, as illustrated in Figure and discussed c Fluent Inc. November 28, 2001

99 14.3 User Inputs for the Non-Premixed Equilibrium Model Figure : The Velocity Inlet Panel Showing Mixture Fraction Boundary Conditions c Fluent Inc. November 28,

100 Modeling Non-Premixed Combustion in Section The fuel or secondary mixture fraction variance can usually be taken as zero at inlet boundaries. Input of Thermal Boundary Conditions and Fuel Inlet Velocities If your model is non-adiabatic, you should input the Temperature at the flow inlets. While the inlet temperatures were requested in prepdf (as the Fuel Inlet Temperature, Oxidiser Inlet Temperature, and (if applicable) Secondary Inlet Temperature in the Operating Conditions panel), these inputs were used only in the construction of the look-up tables. The inlet temperatures for each fuel, oxidizer, and secondary inlet in your nonadiabatic model should be defined, in addition, as boundary conditions in FLUENT. It is acceptable for the inlet temperature boundary conditions defined in FLUENT to differ slightly from those you input in prepdf. If the inlet temperatures differ significantly from those in prepdf, however, your look-up tables may provide less accurate interpolation. This is because the discrete points in the look-up tables were selected based on the inlet temperatures as defined in prepdf. When you are using the full equilibrium model (rich limit of 1.0), prepdf will in most cases predict a modified equilibrium fuel temperature and composition. As detailed in Section , your inlet velocity at gasphase fuel inlets should be based on the density corresponding to this adjusted temperature and composition. The temperature at the gasphase fuel inlet, however, should be retained at the value you used to define the fuel inlet in prepdf. Similar equilibrium adjustments may occur, under unusual circumstances, at oxidizer inlets and your inputs should be determined in the same way. Wall thermal boundary conditions should also be defined for non-adiabatic non-premixed combustion calculations. You can use any of the standard conditions available in FLUENT, including specified wall temperature, heat flux, external heat transfer coefficient, or external radiation. If radiation is to be included within the domain, the wall emissivity should be defined as well. See Section for details about thermal boundary conditions at walls c Fluent Inc. November 28, 2001

101 14.3 User Inputs for the Non-Premixed Equilibrium Model Step 4: Define Physical Properties When you use the non-premixed combustion model, the material used for all fluid zones is automatically set to pdf-mixture. This material is a special case of the mixture material concept discussed in Section The constituent species of this mixture are the species that you defined in prepdf; you cannot change them in FLUENT. When the non-premixed model is used, heat capacities, molecular weights, and enthalpies of formation for each species considered are extracted from the chemical database, so you will not modify any properties for the constituent species in the PDF mixture. For the PDF mixture itself, the density is determined from the look-up tables and the specific heat is determined via the mixing law discussed in Section 7.5.4, using specific heat values for the constituent species obtained from the chemical database (thermodb.scm). The physical property inputs for a non-premixed combustion problem are therefore only the transport properties (viscosity, thermal conductivity, etc.) for the PDF mixture. To set these in the Materials panel, choose mixture as the Material Type, pdf-mixture (the default, and only choice) in the Mixture Materials list, and set the desired values for the transport properties. Define Materials... See Chapter 7 for details about setting physical properties. The transport properties in a non-premixed combustion problem can be defined as functions of temperature, if desired, but not as functions of composition. In practice, since turbulence effects will dominate, it will be of little benefit to include even the temperature dependence of these transport properties. If you are modeling radiation heat transfer, you will also input radiation properties, as described in Section 7.6. Composition-dependent absorption coefficients (using the WSGGM) are allowed. Step 5: Solve the Flow Problem The next step in the non-premixed combustion modeling process in FLU- ENT is the solution of the mixture fraction and flow equations. First, c Fluent Inc. November 28,

102 Modeling Non-Premixed Combustion initialize the flow. By default, the mixture fraction and its variance have initial values of zero, which is the recommended value; you should generally not set non-zero initial values for these variables. See Section for details about solution initialization. Solve Initialize Initialize... Next, begin calculations in the usual manner. Solve Iterate... During the calculation process, FLUENT reports residuals for the mixture fraction and its variance in the fmean and fvar columns of the residual report: iter cont x-vel y-vel k epsilon fmean fvar e e e e e e e e e e e e e e e e e e e e e+0 (For two-mixture-fraction calculations, columns for psec and pvar will also appear.) Under-Relaxation Factors for PDF Equations The transport equations for the mean mixture fraction and mixture fraction variance are quite stable and high under-relaxation can be used when solving them. By default, an under-relaxation factor of 1 is used for the mean mixture fraction (and secondary partial fraction) and 0.9 for the mixture fraction variance (and secondary partial fraction variance). If the residuals for these equations are increasing, you should consider decreasing these under-relaxation factors, as discussed in Section Density Under-Relaxation One of the main reasons a combustion calculation can have difficulty converging is that large changes in temperature cause large changes in density, which can, in turn, cause instabilities in the flow solution. FLU- ENT allows you to under-relax the change in density to alleviate this c Fluent Inc. November 28, 2001

103 14.3 User Inputs for the Non-Premixed Equilibrium Model difficulty. The default value for density under-relaxation is 1, but if you encounter convergence trouble you may wish to reduce this to a value between 0.5 and 1 (in the Solution Controls panel). Tuning the PDF Parameters for Two-Mixture-Fraction Calculations For cases that include a secondary stream, the PDF integrations are performed inside FLUENT. The parameters for these integrations are defined in the Species Model panel (Figure ). Define Models Species... Figure : The Species Model Panel for a Two-Mixture-Fraction Calculation The parameters are as follows: Compressibility Effects (non-adiabatic systems only) tells FLUENT to upc Fluent Inc. November 28,

104 Modeling Non-Premixed Combustion date the density, temperature, species mass fraction, and enthalpy from the PDF tables to account for the varying pressure of the system. Probability Density Function specifies which type of PDF should be used. You can pick either double delta (the default) or beta in the dropdown list. These choices are the same as what you saw in prepdf for the single-mixture-fraction case. (See Section ) The double delta PDF has the advantage of being faster than the beta PDF, and it is the default. The beta function, however, may be a more accurate representation of the PDF. Number of Flow Iterations Per Property Update specifies how often the density, temperature, and specific heats are updated from the lookup table. Remember that when you are calculating two mixture fractions, the updating of properties includes computation of the PDFs and can be quite CPU-intensive. You should generally not reduce the Number of Flow Iterations Per Property Update below the default value of 10, unless you are experiencing convergence difficulties. For simulations involving non-adiabatic multiple strained flamelets, looking up the four-dimensional PDF tables can be CPU-intensive if a large number of species exist in the flamelet files. In such cases, the Number of Flow Iterations Per Property Update controls the updating of the mean molecular weight, which involves looking up the PDF tables for the species mass fractions. Step 6: Postprocessing the Non-Premixed Model Results in FLUENT The final step in the non-premixed combustion modeling process is the postprocessing of species concentrations and temperature data from the mixture fraction and flow-field solution data. The following variables are of particular interest: Mean Mixture Fraction (in the Pdf... category) Secondary Mean Mixture Fraction (in the Pdf... category) c Fluent Inc. November 28, 2001

105 14.3 User Inputs for the Non-Premixed Equilibrium Model Mixture Fraction Variance (in the Pdf... category) Secondary Mixture Fraction Variance (in the Pdf... category) Fvar Prod (in the Pdf... category) Fvar2 Prod (in the Pdf... category) Mass fraction of (species-n) (in the Species... category) Mole fraction of (species-n) (in the Species... category) Concentration of (species-n) (in the Species... category) Static Temperature (in the Temperature... category) Enthalpy (in the Temperature... category) These quantities can be selected for display in the indicated category of the variable-selection drop-down list that appears in postprocessing panels. See Chapter 27 for their definitions. In all cases, the species concentrations are derived from the mixture fraction/variance field using the look-up tables. Note that temperature and enthalpy can be postprocessed even when your FLUENT model is an adiabatic non-premixed combustion simulation in which you have not solved the energy equation. In both the adiabatic and non-adiabatic cases, the temperature is derived from the look-up table created in prepdf. Figures and illustrate typical results for a methane diffusion flame modeled using the non-premixed approach Modeling Liquid Fuel Combustion Using the Non-Premixed Model Liquid fuel combustion can be modeled with the non-premixed model. In prepdf, the fuel vapor, which is produced by evaporation of the liquid fuel, is defined as the fuel stream, and the oxidizer (e.g., air) inlet composition is defined as the oxidizer stream. (See Section ) The liquid fuel that evaporates within the domain appears as a source of the fuel mixture fraction, f, when the non-premixed model is used. c Fluent Inc. November 28,

106 Modeling Non-Premixed Combustion 1.00e e e e e e e e e e e+00 Contours of Mean Mixture Fraction Figure : Predicted Contours of Mixture Fraction in a Methane Diffusion Flame 1.35e e e e e e e e e e e+00 Contours of Mass fraction of co2 Figure : Predicted Contours of CO 2 Mass Fraction Using the Non-Premixed Combustion Model c Fluent Inc. November 28, 2001

107 14.3 User Inputs for the Non-Premixed Equilibrium Model Within FLUENT, you define the liquid fuel model in the usual way. The gas phase (oxidizer) flow inlet is modeled using an inlet mixture fraction of zero and the fuel droplets are introduced as discrete-phase injections (see Section 19.9). The property inputs for the liquid fuel droplets are unaltered by the non-premixed model, and should be input as usual (see Section 19.11). Note that when you are requested to input the gas phase species destination for the evaporating liquid, you should input the species that comprises the fuel stream as defined in prepdf. Note that if the fuel stream was defined as a mixture of components in prepdf, you should simply select one of these components as the evaporating species. FLUENT will ensure that the mass evaporated from the liquid droplet enters the gas phase as a source of the fuel mixture that you defined in prepdf. The evaporating species you select here is used only to compute the diffusion controlled driving force in the evaporation rate Modeling Coal Combustion Using the Non-Premixed Model! Coal combustion can be modeled with the non-premixed approach, using either a single mixture fraction (fuel stream) or using two mixture fractions (fuel stream and secondary stream). This section describes the modeling options and special input procedures for coal combustion models using the non-premixed approach. Note that prepdf 4 uses a different formulation for coal combustion than that used in prepdf 1. If you have a coal combustion system defined in a prepdf 1 input file, you can read that input file into prepdf 4 but you will have to modify the definition of the coal composition before computing the new prepdf 4 PDF look-up tables. Using a prepdf 1 input file in prepdf 4, without making the required modifications to the definition of coal composition, will result in an incorrect PDF lookup table. The correct prepdf 4 procedures for definition of the fuel composition are described in this section. PDF files created by prepdf 2 or 3 will have the correct inputs for coal composition, so you need not change them. You may however, want to consider recomputing the look-up tables in prepdf 4, as described in c Fluent Inc. November 28,

108 Modeling Non-Premixed Combustion Section If you have a two-mixture-fraction PDF file from prepdf 2 or 3, you will need to read it into prepdf 4 and write it out in FLUENT 6format. Non-Premixed Modeling Options for Coal Combustion There are three basic non-premixed modeling options for coal combustion:!! When coal is the only fuel in the system, you can model the coal using two mixture fractions. When this approach is used, one stream is used to represent the char and the other stream is used to represent volatiles. Generally, the char stream composition is represented as 100% C(s). The volatile stream composition is defined by selecting appropriate species and setting their mole or mass fractions. Alternately, you can use the empirical method (input of atom fractions) for defining these compositions. Using two mixture fractions to model coal combustion is more accurate than using one mixture fraction as the volatile and char streams are modeled separately. However, the two-mixture-fraction model incurs significant additional computational expense since the multi-dimensional PDF integrations are performed at run-time. When coal is the only fuel in the system, you can choose to model the coal using a single mixture fraction (the fuel stream). When this approach is adopted, the fuel composition you define includes both volatiles species and char. Char is typically represented by including C(s) in the species list. You can define the fuel stream composition by selecting appropriate species and setting their mole fractions, or by using the empirical method (input of atom fractions). Definition of the composition is described in detail below. Using a single mixture fraction for coal combustion is less accurate than using two mixture fractions. However, convergence in FLU- ENT should be substantially faster than the two-mixture-fraction model. When coal is used with another (gaseous or liquid) fuel, you must model the coal with one mixture fraction and use a second mix c Fluent Inc. November 28, 2001

109 14.3 User Inputs for the Non-Premixed Equilibrium Model ture fraction to represent the second (gaseous or liquid) fuel. The stream associated with the coal composition is defined as detailed below for single-mixture-fraction models. Defining the Coal Composition in prepdf: Single-Mixture-Fraction Models When coal is modeled using a single mixture fraction (the fuel stream), the fuel stream composition can be input using one of the following two methods: Conventional approach: Define the mixture of species in the coal and their mole or mass fractions in the fuel stream: 1. Use the Define Species panel to select a list of species present in the coal combustion system (e.g., C 3 H 8,CH 4,CO,CO 2, H 2 O(l), H 2 O, H 2, OH, H, O, C(s), O 2,andN 2 ). 2. Using the Composition panel, select the fuel stream and then define the mole or mass fractions of each of the species that are present in the coal fuel. Note that C(s) is used to represent the char content of the coal. For example, consider a coal that has a molar composition of 40% volatiles and 60% char on a dry ash free (DAF) basis. Assuming the volatiles can be represented by an equimolar mixture of C 3 H 8 and CO, the fuel stream composition defined in the Composition panel would be C 3 H 8 =0.2, CO = 0.2, and C(s)=0.60. Note that the coal composition should always be defined in prepdf on an ash free basis, even if ash will be considered in the FLUENT calculation. The following table illustrates the conversion from a typical mass-based proximate analysis to the species fraction inputs required by prepdf. Note that the conversion requires that you make an assumption regarding the species representing the volatiles. Here, the volatiles are assumed to exist as an equimolar mix of propane and carbon monoxide. c Fluent Inc. November 28,

110 Modeling Non-Premixed Combustion Proximate Analysis Weight % kg Moles Mole (DAF) (DAF) Fraction (DAF) Volatiles 30 C 3 H CO Fixed Carbon (C(s)) Ash (Total) Moisture in the coal can be considered by adding it in the fuel composition as liquid water, H 2 O(l). The moisture can also be defined as water vapor, H 2 O, provided that the corresponding latent heat is included in the discrete phase material inputs in FLUENT. Empirical fuel approach: Use the Empirically Defined Streams option for the fuel stream. This method is ideal if you have an elemental analysis of the coal. 1. Use the Define Species panel to select a list of species present in the coal combustion system (e.g., C 3 H 8,CH 4,CO,CO 2, H 2 O(l), H 2 O, H 2,OH,C(s),O 2,andN 2 ). In addition, you must select atomic C, H, N, S, and O. 2. In the Composition panel, select the fuel stream and then define the molar atom fractions of C, H, N, S, and O in the fuel stream. In addition, you will input the lower heating value and mean specific heat of the coal. prepdf will use these inputs to determine the mole fractions of the chemical species you have included in the system. Note that for both of these composition input methods, you should take care to distinguish atomic carbon, C, from solid carbon, C(s). Atomic carbon should only be selected if you are using the empirical fuel input method c Fluent Inc. November 28, 2001

111 14.3 User Inputs for the Non-Premixed Equilibrium Model Defining the Coal Composition in prepdf: Two-Mixture-Fraction Models If your FLUENT model will represent the coal using both the fuel stream and the secondary stream, one stream is used to represent char and the other stream is used to represent volatiles. (Typically the fuel stream is used to represent the char and the secondary stream is used to represent volatiles, but the reverse is also possible. In the procedures below, it is assumed that the fuel stream represents the char and the secondary stream represents the volatiles.) The fuel stream and secondary stream compositions can be input using one of the following two methods: Conventional approach: Define the mixture of species in the coal and their mole or mass fractions in the fuel and secondary streams: 1. Use the Define Species panel to select a list of species present in the coal combustion system (e.g., C 3 H 8,CH 4,CO,CO 2, H 2 O(l), H 2 O, H 2, OH, H, O, C(s), O 2,andN 2 ). 2. Using the Composition panel, select the fuel stream and define the mole or mass fractions of species used to represent the char. Generally, you will input 100% C(s) for the fuel stream. 3. Using the Composition panel, select the secondary stream and define the mole or mass fractions of species used to represent the volatiles. Empirical fuel approach: Use the Empirically Defined Streams option for the volatile (in this case, secondary) stream. This method is ideal if you have an elemental analysis of the coal. 1. Use the Define Species panel to select a list of species present in the coal combustion system (e.g., C 3 H 8,CH 4,CO,CO 2, H 2 O(l), H 2 O, H 2,OH,C(s),O 2,andN 2 ). In addition, you must select atomic C, H, N, S, and O. 2. Using the Composition panel, select the fuel stream and define the mole or mass fractions of species used to represent the char. Generally, you will input 100% C(s) for the fuel stream. c Fluent Inc. November 28,

112 Modeling Non-Premixed Combustion This procedure assumes that you are not using an empirical input for the fuel stream (char). 3. Using the Composition panel, select the secondary stream and define the atom fractions of C, H, N, S, and O in the volatiles. In addition, you will input the lower heating value and mean specific heat of the coal. prepdf will use these inputs to determine the mole fractions of the chemical species you have included in the system. For example, consider coal with the following DAF (dry ash free) data and elemental analysis: Proximate Analysis Wt % Wt % (dry) (DAF) Volatiles Char (C(s)) Ash 8 - Element Wt % (DAF) Wt % (DAF) C H O N S (Note that in the final column, for modeling simplicity, the sulfur content of the coal has been combined into the nitrogen mass fraction.) You can combine the proximate and ultimate analysis data to yield the following elemental composition of the volatile stream: Element Mass Wt % Moles Mole Fraction C ( ) H O N Total This adjusted composition is used to define the secondary stream (volatile) composition c Fluent Inc. November 28, 2001

113 14.3 User Inputs for the Non-Premixed Equilibrium Model The lower heating value of the volatiles can be computed from the known heating value of the coal and the char (DAF): LCV coal,daf = 35.3 MJ/kg LCV char,daf = 32.9 MJ/kg You can compute the heating value of the volatiles as or LCV vol = 35.3 MJ/kg MJ/kg LCV vol = MJ/kg Note that for both of these composition input methods, you should take care to distinguish atomic carbon, C, from solid carbon, C(s). Atomic carbon should only be selected if you are using the empirical fuel input method. Coal Modeling Inputs in FLUENT Within FLUENT, the coal combustion simulation is defined as usual when the non-premixed combustion model is selected. The air (oxidizer) inlets are defined as having a mixture fraction value of zero. No gas phase fuel inlets will be included and the sole source of fuel will come from the coal devolatilization and char burnout. The coal particles are defined as injections using the Set Injection Properties panel in the usual way, and physical properties for the coal material are specified as described in Section You should keep in mind the following issues when defining injections and discrete-phase material properties for coal materials: In the Set Injection Properties panel, you will specify for the Oxidizing Species one of the components of the oxidizer stream, as defined in prepdf. This species concentration field will be used to calculate the diffusion-controlled driving force in the char burnout law (if applicable). The specification of the char and volatile streams differs depending on the type of model you are defining: c Fluent Inc. November 28,

114 Modeling Non-Premixed Combustion If the coal is modeled using a single mixture fraction, the gas phase species representing the volatiles and the char combustion are represented by the mixture fraction used by the non-premixed combustion model. If the coal is modeled using two mixture fractions, rather than specifying a destination species for the volatiles and char, you will instead specify the Devolatilizing Stream and Char Stream. If the coal is modeled using one mixture fraction, and another fuel is modeled using a second mixture fraction, you should specify the stream representing the coal as both the Devolatilizing Stream and the Char Stream. In the Materials panel, Vaporization Temperature should be set equal to the fuel inlet temperature used in prepdf. This temperature controls the onset of the devolatilization process. Stated inversely, the fuel inlet temperature that you define in prepdf should be set to the temperature at which you want to initiate devolatilization. This way, the look-up tables produced by prepdf will include the appropriate temperature range for your process. In the Materials panel, Volatile Component Fraction and Combustible Fraction should be set to values that are consistent with the coal composition used to define the fuel stream (and secondary stream) composition in prepdf. Also in the Materials panel, you will be prompted for the Burnout Stoichiometric Ratio and for the Latent Heat. TheBurnout Stoichiometric Ratio is used in the calculation of the diffusion controlled burnout rate but has no other impact on the system chemistry when the non-premixed combustion model is used. The Burnout Stoichiometric Ratio is the mass of oxidant required per mass of char. The default value of 1.33 assumes that C(s) is oxidized by O 2 to yield CO. The Latent Heat input determines the heat required to generate the vapor phase volatiles defined in the non-premixed system chemistry. You can usually set this value to zero when the non-premixed model is used, since your definition of volatile species will have been based on the overall heating value of the c Fluent Inc. November 28, 2001

115 14.3 User Inputs for the Non-Premixed Equilibrium Model coal. However, if the coal composition defined in prepdf includes water content, the latent heat should be set as follows: Set latent heat to zero if the water content of the coal has been defined as H2O(L). In this case, the prepdf system chemistry will include the latent heat required to vaporize the liquid water. Set latent heat to the value for water ( J/kg), adjusted by the mass loading of water in the volatiles, if the water content of the coal has been defined using water vapor, H2O. In this case, the water content you defined will be evolved along with the other species in the coal but the prepdf system chemistry does not include the latent heat effect. The Density you define for the coal in the Materials panel should be the apparent density, including ash content. This is to be distinguished from the input of C(s) density in prepdf, wherethe density of dry ash free char should be used. You will not be asked to define the Heat of Reaction for Burnout for the char combustion. This quantity is computed based on your inputs to prepdf. Postprocessing Non-Premixed Models of Coal Combustion FLUENT reports the rate of volatile release from the coal using the DPM Evaporation/Devolatilization postprocessing variable. The rate of char burnout is reported in the DPM Burnout variable. c Fluent Inc. November 28,

116 Modeling Non-Premixed Combustion 14.4 The Laminar Flamelet Model The laminar flamelet approach models a turbulent flame brush as an ensemble of discrete, steady laminar flames, called flamelets. The individual flamelets are assumed to have the same structure as laminar flames in simple configurations, and are obtained by experiments or calculations. Using detailed chemical mechanisms, prepdf can calculate laminar opposed-flow diffusion flamelets for non-premixed combustion. The laminar flamelets are then embedded in a turbulent flame using statistical PDF methods. The advantage of the laminar flamelet approach is that realistic chemical kinetic effects can be incorporated into turbulent flames. As in the equilibrium approach of Section 14.3, the chemistry can be preprocessed and tabulated, offering tremendous computational savings. However, the laminar flamelet model is limited to flames with relatively fast chemistry. The flame is assumed to respond instantaneously to the aerodynamic strain, and thus the model cannot capture deep non-equilibrium effects such as ignition, extinction, and slow chemistry (like NO x ). Information about the flamelet model is presented in the following sections: Section : Introduction Section : Restrictions and Assumptions Section : The Flamelet Concept Section : Flamelet Generation Section : Flamelet Import Section : User Inputs for the Laminar Flamelet Model For general information about the mixture fraction model, see Section c Fluent Inc. November 28, 2001

117 14.4 The Laminar Flamelet Model Introduction In a diffusion flame, at the molecular level, fuel and oxidizer diffuse into the reaction zone where they encounter high temperatures and radical species and ignite. More heat and radicals are generated in the reaction zone, and some diffuse out. In near-equilibrium flames, the reaction rate is much faster than the diffusion rate. However, as the flame is stretched and strained by the turbulence, species and temperature gradients increase, and radicals and heat more quickly diffuse out of the flame. The species have less time to reach chemical equilibrium, and the local non-equilibrium increases. The laminar flamelet model is suited to predict moderate chemical nonequilibrium in turbulent flames due to aerodynamic straining by the turbulence. The chemistry, however, is assumed to respond rapidly to this strain, so as the strain relaxes, the chemistry relaxes to equilibrium. When the chemical time-scale is comparable to the fluid convection time-scale, the species can be considered to be in global chemical nonequilibrium. Such cases include NO x formation and low-temperature CO oxidation. The laminar flamelet model is not suitable for such slowchemistry flames. Instead, you can model slow chemistry using the trace species assumption (as in the NO x model), or using the EDC model (see Section ) Restrictions and Assumptions The following restrictions apply to all flamelet models in FLUENT: Only a single mixture fraction can be modeled; two-mixture-fraction flamelet models are not allowed. The mixture fraction is assumed to follow the β-function PDF, and the scalar dissipation is assumed to follow the double-deltafunction PDF. Empirically-based streams cannot be used with the flamelet model. c Fluent Inc. November 28,

118 Modeling Non-Premixed Combustion The Flamelet Concept Overview The flamelet concept views the turbulent flame as an ensemble of thin, laminar, locally one-dimensional flamelet structures embedded within the turbulent flow field [27, 176, 177] (see Figure ). A common laminar flame used to represent a flamelet in a turbulent flow is the counterflow diffusion flame. This geometry consists of opposed, axisymmetric fuel and oxidizer jets. As the distance between the jets is decreased and/or the velocity of the jets increased, the flame is strained and increasingly departs from chemical equilibrium until it is eventually extinguished. The species mass fraction and temperature fields can be measured in laminar counterflow diffusion flame experiments, or, most commonly, calculated. For the latter, a self-similar solution exists, and the governing equations can be simplified to one dimension, where complex chemistry calculations can be affordably performed. In the laminar counterflow flame, the mixture fraction, f, (see Section for definition) decreases monotonically from unity at the fuel jet to zero at the oxidizer jet. If the species mass fraction and temperature along the axis are mapped from physical space to mixture fraction space, they can be uniquely described by two parameters: the mixture fraction and the strain rate (or, equivalently, the scalar dissipation, χ, defined in Equation ). Hence, the chemistry is reduced and completely described by the two quantities, f and χ. This reduction of the complex chemistry to two variables allows the flamelet calculations to be preprocessed, and stored in look-up tables. By preprocessing the chemistry, computational costs are reduced considerably. The balance equations, solution methods, and sample calculations of the counterflow laminar diffusion flame can be found in several references. Comprehensive reviews and analyses are presented in [27, 51] c Fluent Inc. November 28, 2001

119 14.4 The Laminar Flamelet Model turbulent flame laminar flamelet structure (see detail below) flame fuel x velocity (u ) fuel velocity gradient (a ) fuel temperature (T ) fuel fuel composition velocity (u ) ox velocity gradient (a ) ox oxidizer temperature (T ) ox oxidizer composition fuel-oxidizer distance Figure : Laminar Opposed-Flow Diffusion Flamelet c Fluent Inc. November 28,

120 Modeling Non-Premixed Combustion Strain Rate and Scalar Dissipation A characteristic strain rate for an opposed-flow diffusion flamelet can be defined as a s = v/2d, wherev is the speed of the fuel and oxidizer jets, and d is the distance between the jet nozzles. Instead of using the strain rate to quantify the departure from equilibrium, it is expedient to use the scalar dissipation, denoted by χ. The scalar dissipation is defined as where D is a representative diffusion coefficient. χ =2D f 2 (14.4-1) Note that the scalar dissipation, χ, varies along the axis of the flamelet. For the counterflow geometry, the flamelet strain rate a s can be related to the scalar dissipation at the position where f is stoichiometric by [176]: χ st = a s exp ( 2[erfc 1 (2f st )] 2) π (14.4-2) where χ st a s f st erfc 1 = scalar dissipation at f = f st = characteristic strain rate = stoichiometric mixture fraction = inverse complementary error function Physically, as the flame is strained, the width of the reaction zone diminishes, and the gradient of f at the stoichiometric position f = f st increases. The instantaneous stoichiometric scalar dissipation, χ st, is used as the essential non-equilibrium parameter. It has the dimensions s 1 and may be interpreted as the inverse of a characteristic diffusion time. In the limit χ st 0 the chemistry tends to equilibrium, and as χ st increases due to aerodynamic straining, the non-equilibrium increases. Local quenching of the flamelet occurs when χ st exceeds a critical value c Fluent Inc. November 28, 2001

121 14.4 The Laminar Flamelet Model Embedding Laminar Flamelets in Turbulent Flames A turbulent flame brush is modeled as an ensemble of discrete laminar flamelets. Since, for adiabatic systems, the species mass fraction and temperature in the laminar flamelets are completely parameterized by f and χ st, mean species mass fraction and temperature in the turbulent flame can be determined from the PDF of f and χ st as φ = φ(f,χ st )p(f,χ st ) df dχ st (14.4-3) where φ is a representative scalar, such as a species mass fraction, temperature, or density. In prepdf, f and χ st are assumed to be statistically independent, so the joint PDF p(f,χ st ) can be simplified as p f (f)p χ (χ st ). A β PDF shape is assumed for p f, and transport equations for f and f 2 are solved in FLUENT to specify p f. A double-delta PDF is assumed for p χ,which, like the β PDF, is specified by its first two moments. The first moment, namely the mean scalar dissipation, χ st, is modeled in FLUENT as χ st = C χɛf 2 k (14.4-4) where C χ is a constant with a default value of 2. The scalar dissipation variance is assumed constant and specified by you in prepdf. According to [27], it has become common practice to ignore the scalar dissipation fluctuations. Note, however, that a non-zero scalar dissipation variance will result in a smoother variation of the physical properties along the scalar dissipation coordinate. To avoid the PDF convolutions at FLUENT run-time, the integrations in Equation are preprocessed in prepdf and stored in look-up tables. For adiabatic flows, single-flamelet tables have two dimensions: f and f 2. The multiple-flamelet tables have the additional dimension χ st. For non-adiabatic laminar flamelets, the additional parameter of enthalpy is required. However, the computational cost of modeling flamelets over a range of enthalpies is prohibitive, so some approximations are c Fluent Inc. November 28,

122 Modeling Non-Premixed Combustion made. Heat gain/loss to the system is assumed to have a negligible effect on the species mass fractions, and the flamelet mass fractions at predefined enthalpy levels are used [20, 164]. The temperature is then calculated from Equation for a range of mean enthalpy gain/loss, H. Accordingly, mean temperature and density PDF tables have an extra dimension of mean enthalpy. In prepdf, you can either generate your own flamelets, or import them as flamelet files calculated with other stand-alone packages. Such standalone codes include OPPDIF [147], RIF [8, 9, 181] and RUN-1DL [179]. prepdf can import flamelet files in OPPDIF format or standard flamelet file format. Instructions for generating and importing flamelets are provided in Section and Section Flamelet Generation The laminar counterflow diffusion flame equations can be transformed from physical space (with x as the independent variable) to mixture fraction space (with f as the independent variable) [182]. In prepdf, a simplified set of the mixture fraction space equations are solved [181]. Here, N equations are solved for the species mass fractions, Y i, ρ Y i t = 1 2 ρχ 1 2 Y i Le i f 2 + S i [ ] 1 Y i 2 f 1 [ ( Y i )( ρχ 2 f 2 Le i f + ρχc p k ρχ 1 Le 2 i Le i f )] (k/c p ) f (14.4-5) and one equation for temperature: ρ T t = 1 T 2 ρχ 2 f 2 1 Hi c S i p i c Fluent Inc. November 28, 2001

123 14.4 The Laminar Flamelet Model + 1 [ cp ρχ 2c p f + i 1 [ 4σp c p i ] 1 Y i T c p,i Le i f f ] X i a i (T 4 T 4 b ) (14.4-6) The notation in Equations and is as follows: Y i, T, ρ, and f are the ith species mass fraction, temperature, density, and mixture fraction, respectively. Le i is the ith species Lewis number, as defined in Equation k, c p,i, and c p are the thermal conductivity, ith species specific heat, and mixture-averaged specific heat, respectively. S i is the ith species reaction rate, and Hi is the specific enthalpy of the ith species. The scalar dissipation, χ, must be modeled across the flamelet. extension of Equation to variable density is used [114]: χ(f) = a s 3( ρ /ρ +1) 2 ( 4π 2 ρ /ρ +1 exp 2[erfc 1 (2f)] 2) (14.4-7) An! The last term in Equation is an optically thin model for radiative energy loss from the flamelet. Here, σ is the Stefan-Boltzmann constant, p is the pressure, X i is the ith species mole fraction, a i are polynomial coefficients for the Planck mean absorption coefficients (taken from [83]), and T b is the far-field (background) temperature. Including the radiation term offers the capability of slightly increased accuracy, but may cause flamelets to be extinguished at low strain rates. Hence, the radiation term should be enabled with caution. The default setting in FLUENT is Le i = 1, although prepdf offers the capability to include differential diffusion effects. When activated, the Lewis numbers are automatically calculated from Equation However, the mixture fraction space equations contain considerable simplification, and most often, better results are obtained with the default Le i = 1 setting. This default is recommended, especially for highly diffusive species such as H 2. The differential diffusion option should be used only to tweak a Le i =1solution. c Fluent Inc. November 28,

124 Modeling Non-Premixed Combustion You can adjust the number of grid points used to discretize the mixture fraction space. Since the species mass fractions and temperature are solved coupled and implicit in f space, the memory and time requirements can increase drastically with the number of f grid points, and moderate values are recommended. prepdf also provides parameters to control the stability of the solution of Equations and You can adjust two multiplication factors for the solution s time steps if the solution diverges. Non-Adiabatic Laminar Flamelets For non-adiabatic flamelets, prepdf follows the approach of [20, 164] and assumes that flamelet species profiles are unaffected by heat loss/gain from the flamelet. This implementation treats the heat losses accurately and consistently. Furthermore, no special non-adiabatic flamelet profiles need to be generated, avoiding a very cumbersome preprocessing step. In addition, the compatibility of prepdf and FLUENT with external flamelet generation packages (e.g., OPPDIF, RIF, RUN-1DL) is retained. The disadvantage to this model is that the effect of the heat losses on the species mass fraction is not taken into account. Also, the effect of the heat loss on the extinction limits is not taken into account. In the equilibrium non-premixed model, the temperature limits are constant values T min and T max. For the non-adiabatic flamelet model, these temperature limits are surfaces or functions of mixture fraction and scalar dissipation to more closely bound the enthalpy domain. The bottom temperature surface, T min (f,χ), is calculated as the minimum of the temperature from the flamelet calculation at point (f,χ) and T ad (f) T, but cannot be lower than the globally lowest temperature in the flamelet calculation, T MIN : T min (f,χ)=max(t MIN, min[(t ad (f) T ),T fl (f,χ)]) (14.4-8) The top temperature curve, T max (f,χ), is calculated as the maximum of the maximum environment temperature defined by you, T MAX,the temperature from the flamelet calculation at point f, andt ad (f)+ T + : c Fluent Inc. November 28, 2001

125 14.4 The Laminar Flamelet Model where T max (f,χ)=max(t MAX,T ad (f)+ T +,T fl (f,χ)) (14.4-9) f = mixture fraction χ = scalar dissipation T MIN = globally lowest temperature T MAX = maximum boundary (e.g., hot wall or inlet) temperature in domain T = maximum temperature drop expected because of heat losses T + = maximum temperature rise over the adiabatic temperature curve T fl = temperature in flamelet profile T ad (f) = adiabatic (equilibrium) flame temperature After flamelet generation, the flamelet profiles are convoluted with the assumed-shape PDFs as in Equation , and then tabulated for lookup in FLUENT. You can set the resolution of the look-up table. The assumption is made that both the enthalpy loss/gain and the scalar dissipation do not fluctuate. The PDF tables have the following dimensions: T mean (f mean,f var,h,χ) Y i,mean (f mean,f var,h )forχ = 0 (i.e., equilibrium solution) Y i,mean (f mean,f var,χ)forχ 0 ρ mean (f mean,f var,h,χ) During the FLUENT solution, the equations for the mean mixture fraction, mixture fraction variance, and mean enthalpy are solved. The scalar dissipation field is calculated from the turbulence field and the mixture fraction variance. The mean values of cell temperature, density, and species mass fraction are obtained from the PDF look-up table c Fluent Inc. November 28,

126 Modeling Non-Premixed Combustion Flamelet Import prepdf can import one or more flamelet files, convolute these flamelets with the assumed-shape PDFs (see Equation ), and construct lookup tables for use in FLUENT. The flamelet files can be generated in prepdf, or with separate, stand-alone computer codes. Two types of flamelet files can be imported into prepdf: binary files generated by the OPPDIF code [147], and standard format files described in Section and in Peters and Rogg [179]. When flamelets are generated in physical space (such as with OPPDIF), the species and temperature vary in one spatial dimension. The species and temperature must then be mapped from physical space to mixture fraction space. If the diffusion coefficients of all species are equal, a unique definition of the mixture fraction exists. However, with differential diffusion, the mixture fraction can be defined in a number of ways. prepdf provides four methods of computing the mixture fraction profile along the laminar flamelet: Average of C and H: Following Drake and Blint [54], the mixture fraction is calculated as the mean value of f C and f H,wheref C and f H are the mixture fraction values based on the carbon and hydrogen elements. Hydrocarbon formula: Following Bilger et al. [19], the mixture fraction is calculated as where f = b b ox b fuel b ox ( ) b =2 Y C +0.5 Y H Y O ( ) M w,c M w,h M w,o Y C, Y H,andY O are the mass fractions of carbon, hydrogen, and oxygen atoms, and M w,c, M w,h, and M w,o are the molecular c Fluent Inc. November 28, 2001

127 14.4 The Laminar Flamelet Model weights. b ox and b fuel are the values of b at the oxidizer and fuel inlets. Nitrogen method: The mixture fraction is computed in terms of the mass fraction of the nitrogen species: f = Y N Y N,ox Y N,fuel Y N,ox ( ) where Y N is the elemental mass fraction of nitrogen along the flamelet, Y N,ox is the mass fraction of nitrogen at the oxidizer inlet, and Y N,fuel is the mass fraction of nitrogen at the fuel inlet. Read from a file (standard format files only): This option is for flamelets solved in mixture fraction space. If you choose this method, prepdf will search for the mixture fraction keyword Z, as specified in [179], and retrieve the data. If prepdf does not find mixture fraction data in the flamelet file, it will instead use the hydrocarbon formula method described above. The flamelet profiles in the multiple-flamelet data set should vary only in the strain rate imposed; the species and the boundary conditions should be the same. The formats for multiple flamelets are as follows: OPPDIF format: The multiple-flamelet OPPDIF files should be produced using the CNTN keyword in the OPPDIF script. Alternatively, you can use prepdf to merge a number of single-flamelet OPPDIF files into a multiple-flamelet file. Standard format: If you have a set of standard format flamelet files, you should manually merge the files into a multiple-flamelet file. (You can use a text editor or the UNIX cat command to merge the files.) When you import the merged file into prepdf, prepdf will search for and count the occurrences of the HEADER keyword to determine the number of flamelets in the file. For either type of file, prepdf will determine the number of flamelet profiles and sort them in ascending strain-rate order. For flamelets generated c Fluent Inc. November 28,

128 Modeling Non-Premixed Combustion in physical space, you can select one of the four methods available for the calculation of mixture fraction. The scalar dissipation will be calculated from the strain rate using Equation User Inputs for the Laminar Flamelet Model Instructions for using prepdf to create PDF tables from generated and imported flamelets are provided here, along with information about related files and formats. Creating a PDF Table from Generated Laminar Flamelets The procedures for the flamelet calculation approach described in Section are presented in this section. See Section for instructions about starting prepdf. Step 1: Activate Laminar Flamelet Generation To specify the generation of a laminar flamelet library, you will use the Define Case panel (Figure ). Setup Case... In the Define Case panel, select the Laminar Flamelets option under Chemistry models. Then choose Adiabatic or Non-Adiabatic under Heat transfer options. Finally, select Generate under Flamelet options. Step 2: Define the Flamelet Once you have enabled the flamelet generation option, you can use the Flamelet Generation panel (Figure ) to define the flamelet. Setup Flamelet Generation... Step 2a: Import the Chemical System Data The first step in defining the flamelet is to read the species and reaction definitions for the chemical system. The species thermodynamic, transport and reaction data must be in CHEMKIN format [112]. Information about the format of these files is detailed later in this section c Fluent Inc. November 28, 2001

129 14.4 The Laminar Flamelet Model Figure : The Define Case Panel c Fluent Inc. November 28,

130 Modeling Non-Premixed Combustion Figure : The Flamelet Generation Panel c Fluent Inc. November 28, 2001

131 14.4 The Laminar Flamelet Model To read the chemistry file into prepdf, click on the Chemistry Files... buttonintheflamelet Generation panel. When you click this button, a Select File dialog box will open, in which you can specify the chemistry file to be read. Up to 100 species can be included in the flamelet calculation. If the number of species used in the flamelet calculation is greater than n, wheren is the maximum number of species specified in the Memory Allocation panel (see Section ), prepdf will automatically select the n species with the largest concentrations for inclusion in the PDF file. After the chemistry file has been read, the species it contains will appear in the Defined Species list in the Flamelet Generation panel (as shown in Figure ). Step 2b: Define the Fuel and Oxidizer Compositions To define the fuel and oxidizer compositions, you will specify the following parameters under Composition in the Flamelet Generation panel: 1. Select Fuel under Stream. 2. Select a species in the Defined Species list. Select either Mole Fractions or Mass Fractions under Species Composition In... and enter the desired value in the Species Fraction field. 3. When you are satisfied with your entry, select the next species and repeat the process until you have set all mole or mass fractions for the fuel stream. 4. Input the mole or mass fractions for the oxidizer stream by selecting Oxidiser under Stream and repeating steps 1 3. You can check the current setting for a species in a particular stream by selecting the stream and choosing the species name in the Defined Species list. c Fluent Inc. November 28,

132 Modeling Non-Premixed Combustion Step 2c: Set the Flamelet Parameters In the Flamelet Generation panel, enter values for the following parameters under Laminar Flamelet Options. Under Mixture Fraction, set the following parameter: # Grid Points specifies the number of mixture fraction grid points distributed between the oxidizer (f = 0) and the fuel (f = 1). Increased resolution will provide greater accuracy, but since the flamelet species and temperature are solved coupled and implicit in f space, the solution time and memory requirements increase linearly with the number of f grid points. The default value of 32 is enough to resolve the temperature distribution in most cases. Under Scalar Dissipation, set the following parameters: Start (χ st in Equation ) is the scalar dissipation for the first flamelet in the library. When only one flamelet is generated, this will be its selected scalar dissipation. Note that prepdf will generate an equilibrium flamelet corresponding to χ st =0,sotheStart scalar dissipation should be set at a value near 0; the default value of 1 s 1 is usually sufficient. End is the scalar dissipation of the last flamelet if more than one laminar flamelet is being generated (i.e., # Grid Points for the Scalar Dissipation is greater than 1). See below for details. # Grid Points specifies the number of laminar flamelets to be calculated. Grid Center Point is a non-dimensional parameter between 0.1 and 0.9 that clusters the flamelets closer to the Start or End scalar dissipation values. A value of 0.5 will generate a flamelet library with equi-spaced scalar dissipation. In general, when using a large End scalar dissipation, you may want to cluster near the Start scalar dissipation and use a value between 0.1 and 0.5. The maximum scalar dissipation in the flamelet file (End χ st ) should be the scalar dissipation at the extinction limit; i.e., the maximum scalar c Fluent Inc. November 28, 2001

133 14.4 The Laminar Flamelet Model dissipation at which reaction can be sustained. The value of the scalar dissipation at the extinction limit depends on the fuel and oxidizer composition, operating pressure, and chemistry model, and thus determining the value may be sensitive to numerical parameters such as mixture fraction grid resolution in the flamelet computations.! The scalar dissipation at the extinction limit can be estimated by performing a series of flamelet computations at increasing scalar dissipation values and examining the resulting flamelet profiles Do not include an extinguished (i.e., non-combusting) flamelet in the multiple flamelet file. The last flamelet in the file should be the flamelet at the extinction limit, and not an extinguished flamelet. Note that the maximum scalar dissipation value in the reacting flow field may be higher or lower than the scalar dissipation at the extinction limit. If the maximum scalar dissipation in the reacting flow field is significantly lower than the extinction limit value, then the maximum scalar dissipation in the flamelet file may be reduced to a value slightly higher than the maximum flow-field scalar dissipation. You may estimate the reacting flow-field scalar dissipation by following this approach: 1. Solve the combustion problem in FLUENT using the equilibrium model. Later, you can use this solution as the starting point for your laminar flamelet model by simply reading in the new laminar flamelet PDF file. 2. Create a custom field function called mean-scalar-dissipation as defined by the RHS of Equation , and determine the maximum value of the function. You can also choose whether or not to use the Differential Diffusion and Include radiation options. See Section for details. After the flamelet parameters have been defined, click Apply in the Flamelet Generation panel to register the changes. prepdf automatically calculates an approximate value of the stoichiometric mixture fraction, c Fluent Inc. November 28,

134 Modeling Non-Premixed Combustion Stoichiometric f. Note that Stoichiometric f is calculated at the mixture fraction location with the maximum equilibrium temperature, and is thus an approximation of the actual stoichiometric mixture fraction. After calculating the laminar flamelet (see Step 5, below), prepdf will automatically write out the flamelet to a standard flamelet file, then import the flamelet and generate a PDF table. If the solution diverges, you can adjust the values of Initial CFL and Multiply factor under Solution Controls to control the solution algorithm. The first time step is calculated as the explicit diffusion stability-limited time step multiplied by the Initial CFL value. If the solution diverges before the first time step is complete, the Initial CFL value should be lowered. Subsequent time steps are continually multiplied by the Multiply Factor. Ifthesolution diverges after the first time step, this factor should be reduced. Step 2d: Define the Operating Conditions for the Flamelet You can specify the flamelet operating pressure and the temperatures of the inlet streams using the Operating Conditions panel. Setup Operating Conditions... If you are creating a non-adiabatic flamelet, you will need to input the Nonadiabatic Flamelet Temperature Limits, as described below: Min. Temperature is the globally lowest temperature expected, T MIN in Equation Max. Temperature is the maximum boundary (hot wall or inlet stream) temperature in the domain, T MAX in Equation Temperature Drop is the maximum expected temperature drop due to heat loss from the domain ( T in Equation ). Temperature Increase is the maximum expected temperature increase due to heat gain into the domain ( T + in Equation ). The default value of 1500 K for Temperature Drop can be used for most cases involving hydrocarbon combustion. This value can be decreased c Fluent Inc. November 28, 2001

135 14.4 The Laminar Flamelet Model if the boundary conditions suggest moderate heat losses. In problems involving extreme temperature conditions, it might be necessary to increase both the Temperature Drop and Temperature Increase values. You can check whether the FLUENT solution is within the PDF table temperature bounds using the non-premixed-combustion-parameters text command and setting the Enable checking of PDF table temperature limits? option to yes. define models species non-premixed-combustion-parameters See Section for more information about setting operating conditions. Step 3: Set the PDF Table Parameters Once you have defined the flamelet, you will next define the PDF table parameters using the Solution Parameters panel. Setup Solution Parameters... Under Fuel Mixture Fraction, set the number of Fuel Mixture Fraction Points and Fuel Mixture Fraction Variance Points. The default Automatic Distribution clustering in the mixture fraction coordinate is recommended. See Section for details about these parameters. For adiabatic multiple-flamelet problems, you will next set the scalar dissipation parameters in the Flamelet Parameters panel (Figure ). Setup Flamelet Parameters... Under Scalar Dissipation, set the number of Scalar Dissipation Points to approximately the same number of mixture fraction points in your PDF table (Fuel Mixture Fraction Points in the Solution Parameters panel). You can cluster the mean scalar dissipation distribution in the PDF table by modifying the Distribution Center Point. Finally, if you wish to use the double delta assumed shape PDF for the scalar dissipation, set the Scalar Dissipation Variance to a value greater than zero. Please note that the assumed PDF option for scalar dissipation is available only for adiabatic multiple-flamelet cases. c Fluent Inc. November 28,

136 Modeling Non-Premixed Combustion Figure : The Flamelet Model Parameters Panel! If you set the Scalar Dissipation Variance to 0, you will be effectively ignoring turbulent fluctuations in the scalar dissipation, i.e., the mean and instantaneous scalar dissipation will be equal. Step 4: Save an Input File Next you can save an input file containing the flamelet definition and other specifications, using the File/Write/Input... menu item. File Write Input... This can be important if you want to revisit your laminar flamelet setup because this setup is not stored in the PDF file. Step 5: Calculate the Flamelet To calculate the flamelet data, you will use the Calculate/Flamelet menu item c Fluent Inc. November 28, 2001

137 14.4 The Laminar Flamelet Model Calculate Flamelet prepdf will immediately prompt you for the name of the flamelet file. The flamelet profiles will be written to this file automatically when the calculation is complete. The flamelet file will be in the standard file format, and can be imported or merged with other flamelet files, as described in later in this section. After you specify the file name, prepdf will begin the flamelet calculation, reporting its progress in the text window. Just before the flamelet calculation, prepdf will write a monitor file called FLAMELET.MON in your working directory. This file contains the thermodynamic and chemistry information, and can be useful for monitoring and troubleshooting flamelet generation calculations. After the flamelet calculation is complete, prepdf will write the flamelet to disk, and then construct the PDF file. If the flamelet calculation does not converge, decrease the Initial CFL (towards zero) and the Multiply factor (towards 1) in the Flamelet Generation panel, and then recalculate the flamelet data. Step 6: Save the PDF File When prepdf has completed the PDF calculation, you can save the PDF file as usual, with the File/Write/PDF... menu item. See Section ! File Write PDF... You can read the PDF file back into prepdf at a later time for postprocessing. You cannot, however, modify the solution parameters and recalculate the PDF table unless you also import the original flamelet file. Since the PDF table for multiple flamelets is three-dimensional, there are viewing options for both the instantaneous physical properties and the PDF integrated physical properties. These options are described below. When you are satisfied with the PDF file and you have saved it, you can continue the non-premixed combustion modeling procedure in FLUENT. The procedures for setting up and solving a flamelet-based model in c Fluent Inc. November 28,

138 Modeling Non-Premixed Combustion FLUENT are the same as for other non-premixed combustion models. See Section for details. Step 7a: Postprocessing of Adiabatic Multiple-Flamelet Files Reviewing Instantaneous Values When you are plotting instantaneous values using the Property Curves panel (Figure ), you can plot the specified variable for a constant value of Dimensionless Scalar Dissipation. (You can also plot the variable for a constant value of mixture fraction.) Display Property Curves... Figure : The Property Curves Panel Plotting the Scalar Dissipation Distribution You can also plot the distribution of scalar dissipation, using the Display/Scalar Dissipation menu item. Display Scalar Dissipation A scalar dissipation distribution plot is shown in Figure c Fluent Inc. November 28, 2001

139 14.4 The Laminar Flamelet Model KEY 1.00E E+00 S c a l a r D i s s i p a t i o n 6.00E E+00 ( 1 / s ) 2.00E E E E E E E E+00 Flamelet Number SCALAR DISSIPATION DISTRIBUTION prepdf V4.00 Fluent Inc. Figure : Scalar Dissipation Distribution Reviewing 3D Flamelet-PDF Tables For multiple-flamelet models, you can view slices of the 3D flamelet-pdf table using the Flamelet-PDF-Table panel (Figure ). Display Flamelet PDF Table... The look-up tables generated for multiple-flamelet systems contain the mean temperature, density, and species mass fractions as a function of three quantities: mean mixture fraction, mixture fraction variance, and mean dimensionless scalar dissipation. Consequently, when you ask prepdf to display the look-up tables, you will be displaying them sliceby-slice. In the Flamelet-PDF-Table panel, you can select the variable to be plotted in the Plot Variable drop-down list. Next, you must define how the threedimensional array of data points available in the look-up table is to be sliced; i.e., which discrete independent variable (either f or χ st,d )isto be held constant and whether the constant value is to be selected as a numerical Value or by discretization index (Slice number). c Fluent Inc. November 28,

140 Modeling Non-Premixed Combustion Figure : The Flamelet-PDF-Table Panel If you specify Slice as the Plot type, you will select which discretized variable is to be constant (Scalar Dissipation or F-Mean) and then specify the Slice # (discretization index). For example, the panel shown in Figure requests a look-up table generated at the tenth discrete value of scalar dissipation. To generate the plot (see Figure ), click Display. Alternately, you may want to define a slice of the 3D look-up table based on a specific value of one of the independent quantities. When this is the case, select Value as the Plot type. You can then select a slice of the 3D table that corresponds to a constant Scalar Dissipation Value or F-Mean Value, and supply the physical value of the selected quantity in the Value field. Next, you can set the Refinement Factor, which determines the resolution of the plotted curve. A refinement factor of 1.0 (the default) implies that c Fluent Inc. November 28, 2001

141 14.4 The Laminar Flamelet Model 1.8E E+03 T E M PE R A T U R E K 1.2E E E E E E-01 SCALED-F-VARIANCE 1.00E E E E E E E E E E+00 F-MEAN SCALAR DISSIPATION SLICE NUMBER 10 MEAN FLAME TEMPERATURE FROM FLAMELET-PDF-TABLE prepdf V4.00 Fluent Inc. Figure : Display of a Single Slice of a 3D Flamelet-PDF Table the plot will use the same number of discrete points that you requested in the Solution Parameters panel. Increasing this factor will cause prepdf to compute and display additional data points, yielding a smoother plot but requiring some time to compute. Finally, click the Lookup button to access the data to be plotted and then click Display to display the plot. Step 7b: Postprocessing of Non-Adiabatic Multiple Flamelet Files Reviewing Non-Adiabatic Flamelet PDF Tables For non-adiabatic flamelets, you can view slices of the four-dimensional non-adiabatic flamelet tables using the Nonadiabatic-Table panel (Figure ). Display Nonadiabatic Table... The Nonadiabatic-Table panel is also used for viewing the non-adiabatic PDF tables for equilibrium chemistry models. See Section for c Fluent Inc. November 28,

142 Modeling Non-Premixed Combustion Figure : The Nonadiabatic-Table Panel for Flamelets more information about using this panel. In the case of non-adiabatic flamelets, there is the additional parameter of scalar dissipation. In addition to varying the mean enthalpy and mean mixture fraction, you can vary the display of the PDF table by changing the value of Slice # under Scalar dissipation, which gives the table a fourth dimension. For the non-adiabatic multiple-flamelet PDF tables, you can plot the scalar dissipation distribution using the Display/Scalar Dissipation menu item in the same way as for the adiabatic multiple-flamelet PDF tables. Display Scalar Dissipation Creating a PDF Table from Imported Laminar Flamelets The procedure for importing flamelets is very similar to the flamelet generation procedure described above, except that the flamelet generation step is skipped c Fluent Inc. November 28, 2001

143 14.4 The Laminar Flamelet Model Step 1: Activate Flamelet Import In the Define Case panel (Figure ), select the Laminar Flamelets option under Chemistry models. Then choose Adiabatic or Non-Adiabatic under Heat transfer options. Finally, select Import under Flamelet Options. Setup Case...! Once you have enabled flamelet import, you will next define the flamelet model parameters and solution parameters. The parameters for the flamelet model and the solution process must be defined before you import the flamelet file, because prepdf performs the mixture-fraction calculations and generates the PDF look-up table automatically after it reads the data from the flamelet file. Step 2: Set the PDF Table Parameters Step 2a: Non-Adiabatic Table Parameters If you are modeling a non-adiabatic combustor, you will need to set the Nonadiabatic Flamelet Temperature Limits in the Operating Conditions panel, as described in Step 2d on page Setup Operating Conditions... Step 2b: Mixture Fraction Table Parameters You will next set the resolution of the mixture fraction mean and variance in the Solution Parameters panel, as described in Step 3 on page Setup Solution Parameters... Step 2c: Scalar Dissipation and Flamelet Conversion Parameters If you are importing flamelets generated in physical space, such as with OPPDIF [147], prepdf will need to construct a mixture fraction profile from the species field (see Section ). You can access the parameters for this conversion in the Flamelet Model Parameters panel (Figure ). c Fluent Inc. November 28,

144 Modeling Non-Premixed Combustion Setup Flamelet Parameters... Figure : The Flamelet Model Parameters Panel The parameters for the flamelet import are as follows: Pressure Conversion Factor specifies a factor for converting pressure data to SI units. If you are reading OPPDIF data, this parameter should be set to 1, since OPPDIF files report the pressure in Pa. If you are importing standard flamelet files, which are formatted files, you should check for the units of pressure reported in the file and input the appropriate conversion factor for the pressure to be in Pa. Mixture Fraction Calculation specifies which of the methods described in Section should be used to compute the mixture fraction. Read From File is the default and recommended option. If the flamelet file does not contain mixture fraction data, prepdf will report this and use the Hydrocarbon Formula option instead c Fluent Inc. November 28, 2001

145 14.4 The Laminar Flamelet Model Finally, set the scalar dissipation parameters as described in Step 3 on page Step 3: Import the Flamelet File After setting the parameters, you can import the flamelet file. For OPPDIF flamelet files, use the File/Import/Oppdif Flamelets... menu item: File Import Oppdif Flamelets... For standard format flamelet files, use the File/Import/Standard Flamelets... menu item: File Import Standard Flamelets... After you specify the name of a standard format file to be imported, prepdf will ask you if the file was written for mixture fraction values in ascending (starting from the oxidizer inlet), or descending (starting from the fuel inlet) order. By default, it will assume descending order. After reading the flamelet file, prepdf will report the species data and then integrate with the β PDF to generate the PDF look-up table. If the number of species in the flamelet file is larger than the species limit in prepdf, the species with the lowest mass fractions are filtered out. The temperature curves are then constructed and the enthalpy domain is discretized. After this, the PDF integrations are performed. Note that this process may take some time, as four-dimensional tables are being generated. c Fluent Inc. November 28,