Modeling of Moderately Swirling Turbulent Non

Modeling of Moderately Swirling Turbulent Non-premixed Flames A. Zucca*, D. L. Marchisio, A. A. Barresi Dipartimento di Scienza dei Materiali ed Ingegneria Chimica Politecnico di Torino, Torino – ITALY

1. 1. INTroduction Even if the goal of reducing NOx emissions pushes towards the use of premixed combustion, moderately swirling turbulent non-premixed flames are still widely employed in both industrial furnaces and gas turbines, because of their stable and safe behaviour in a wide range of fuels and operating conditions. Computational Fluid Dynamics (CFD) has become in recent years a key tool for the design of combustion systems, providing valuable information on aero-thermal characteristics of the combustion chamber, emissions, and allowing preliminary screening of different design options. Moreover, CFD results are often used as boundary conditions for subsequent thermo-structural Finite Element Analysis (FEA) of combustion components. It is clear that in an industrial framework it is important to obtain the most accurate results with the simplest and most robust models; several different approaches have been developed in the past decades to optimally integrate chemistry and fluid dynamics in turbulent reacting flows such as turbulent flames. In this work, the description of turbulence-chemistry interaction is based on the fluid probability density function (PDF) approach. The proposed model belongs to the so-called presumed PDF methods, and is usually referred to as the Finite-Mode PDF or MultiEnvironment model, which has been already successfully employed for modelling precipitation and crystallization in turbulent systems. The distribution is represented by a finite sum of Dirac delta functions, centered in some particular values of the independent variable (nodes) and weighted by some weight functions, representing the related probabilities. The Finite-Mode PDF model has been applied to the study of lab-scale turbulent nonpremixed flames, and compared with other standard models for turbulence-chemistry interaction, already available in commercial CFD codes. The proposed model has been implemented as User-Defined Functions within the commercial CFD code FLUENT 6.1. 2. 2. GOVERNING EQUATIONS Finite-mode PDF models assume that the presumed joint-composition PDF has the following functional form:

f Φ (Ψ; x, t ) =

Ne

Ne

n =1

α =1

[

]

∑ pn (x, t ) ∏ δ ψ α − φα n (x, t )

where Ne is the number of modes or environments, Ns is the dimension of the composition vector, pn is the probability associated with environment n, and Φ n is the composition vector in environment n [1]. The number of modes Ne is usually variable between 2 and 4, and each *

Current affiliation: GE Oil&Gas Nuovo Pignone S.p.A - Firenze - Italy

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Combustion Colloquia 2009

32nd Meeting on Combustion

mode can be thought of as an environment with particular features. Depending on the modelling choice, one could model the system by two partially mixed and reacting environments (Ne=2), or two unmixed and non-reacting environments, containing each one of the reactants, and a mixed environment where the reaction occurs (Ne=3), or two unmixed environments and two reacting environments (Ne=4). During the mixing process the unmixed environments disappear (i.e. their probability is decreased) while the mixed one(s) are generated (i.e. their probability is increased). In general, a certain degree of freedom is left to the modeller, that yet can accommodate the first three moments of the PDF, forcing in other words the PDF to integrate to one and to have expected value and variance well described. The resulting transport equations for probabilities and for the weighted compositions in each environment are (repeated indices imply summation):

∂pn % ∂pn ∂ 2 pn +U j − ( Γ + Γt ) = Gn ( p ) + cnp , ∂t ∂x j ∂x j ∂x j ∂ sα ∂t

n

+ U% j

∂ sα ∂x j

n

− ( Γ + Γt )

∂ 2 sα

n

∂x j ∂x j

= M n ,α ( p,s ) + pn S ( φ

n

)+c

s n ,α

,

where U% i is the Favre averaged i-th component of the velocity vector, Γ is the molecular diffusivity, Γt is the turbulent diffusivity, Gn ( p ) is the source term for probability (due to molecular mixing), sα

n

= pn φα

n

is the probability-weighted concentration of component

α in node n, M n ,α ( p, s ) is the rate of change of sα

pn S ( φ

n

n

due to molecular mixing, and

) is the average chemical source term, exactly calculated from the local composition

in the n-th environment/mode. The terms cnp and cns ,α are diffusive terms that arise due to the finite-mode representation, and are necessary, in non-homogeneous cases, to correctly predict moments of the distribution of order equal to or larger than two. 3. 3. results and discussion The finite-mode PDF method with three environments (Ne=3) has been applied to the simulation of moderately swirling turbulent non-premixed flames. The model has been validated with experimental data provided by the International Workshop on Turbulent NonPremixed Flames on a bluff-body stabilized flame (http://www.ca.sandia.gov/TNF/) fuelled with mixtures of hydrogen and natural gas (1:1 vol., swirling flame with S=0.23). Finite rate chemistry was implemented, with a simple four-step mechanism for methane combustion [2]. The method was compared to other widely used modelling tools such as the beta PDF model, with the assumption of chemical equilibrium, and the laminar flamelet model (which allows the implementation of detailed chemistry to be used in the regions where chemical equilibrium is not reached, due to aerodynamic strain). Turbulence was described by the Reynolds-Averaged Navier-Stokes (RANS) equations approach. The structure of this flame, which is characterized by a low swirl number (S= 0.32), is quite similar to that observed for the non-swirling case [3,4], the global flow patterns being affected more by the presence of the bluff-body than by the tangential component of velocity. A recirculation zone is formed and the high temperature zone converges at first toward the centreline, due to the velocity profile imposed by the recirculation zone and, after the socalled “neck”, it slowly spreads.

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Fig. 1


Radial profiles of temperature at various distances: a) x = 10 mm; b) x = 40 mm; c) x = 80 mm; d) x = 175 mm; RSM. Symbols: experimental data; dashed line: β-PDF; dotted line: laminar flamelets; solid line: 3E-Finite Mode PDF.

Several simulations were carried out coupling three turbulence models (standard k-ε, RNG k-ε and Reynolds Stress Model or RSM) with the three combustion models on a two-dimensional grid (40000 cells). As far as the velocity fields are concerned, as expected, the standard k-ε model gives the worst overall results. If axial velocity profiles are considered, the RNG k-ε model seems to be the best option, while all the other models fail in the prediction of the velocity in the centreline. The swirl velocity is instead better predicted by the RSM, but it is important to note that all the models fail to predict the swirl velocity in the neck region. The correct prediction of the recirculation zone and of the position and velocity of the neck is crucial for the correct prediction of the flow field (and of the temperature field too, as it will be clear later). All the models over-predict the swirl velocity in this section The study of both non-reacting and reacting flow field did not allow to select the best turbulence model for the simulation of this flame, as the performance of each model seems to be different at different heights above the burner; therefore, no reliable conclusions can be drawn. Moreover, the predictions of the turbulence models appear to be strongly affected by the turbulence-chemistry interaction model. For the sake of brevity, the study of temperature and composition fields will be discussed only for the RSM, and the performance of β-PDF, multiple flamelets and three-environments Finite Mode PDF will be compared. As it is possible to see in Fig. 1, the experimental temperature profile is quite flat near the bluff-body, and the temperature is around 1600 K; whereas moving downstream, a local maximum is observed in the radial profiles. The value of this maximum increases up to around 1900 K in the neck region (40 mm above the burner), then it decreases while the flame II-9, 3



converges toward the centreline. The figure clearly shows that the main modelling problem is encountered in the neck region, where all the models fail in the prediction of the temperature profile, underestimating both the temperature and the width of the reacting zone. In the first section (10 mm) the β-PDF model with equilibrium chemistry results in an underestimation of the temperature profile, showing the same behaviour observed for the Bluff-body burner [4]. It is interesting to notice, however, that in this case the β-PDF model predicts a maximum in the radial temperature profile close to the central jet, while with the flamelet model and the Finite Mode PDF model the highest temperature is found near the outer edge of the bluff body. In all the downstream sections the models give quite poor results, even if the Finite Mode PDF model seems to be quite a better option. In the neck section in particular, the qualitative agreement (shape of the profile and position of the maximum) is better for Finite Mode PDF than for other models, even if the temperature is still largely underestimated. The use of a very heavily refined two-dimensional grid (113400 cells) did not improve the results of the simulation, proving the grid independence of the solution. a)

1.2

b)

0.9 0.8 0.7 0.6 0.5 ξ 0.4 0.3 0.2 0.1 0

1 0.8

ξ 0.6 0.4 0.2 0 0

20 r (mm) 30

10

c)

0.6

0

20 r (mm) 30

10

d)

0.35 0.3

0.5

0.25

0.4

ξ

ξ 0.3

0.2

0.15

0.2

0.1

0.1

0.05

0

0 0

10

20 r (mm) 30

0

10

20 r (mm) 30

Fig. 2 Radial profiles of mean mixture fraction: a) x = 10 mm; b) x = 40 mm; c) x = 80 mm; d) x = 175 mm; RSM. Symbols: experimental data; dashed line: β-PDF; dotted line: laminar flamelets; solid line: 3E-Finite Mode PDF. As far as the prediction of major species is concerned, simulated profiles of mixture fraction and main reaction products are shown in Figs. 2, 3, and 4. It is interesting to notice that the mean mixture fraction is underestimated in the outer part of the flame near the neck region, thus explaining the low temperature calculated in those zones. Looking at species concentrations, we can observe that in the same region of the flame (20-50 mm above the burner) both H2O and CO2 mass fractions are largely underestimated, especially in the outer part of the flame (radial coordinate larger than 7 mm), where the temperature is underestimated accordingly. In particular, water mass fraction is underestimated in all the II-9, 4



considered sections. It is worth to notice, however, that the employment of finite rate a)

b)

16.00

16.00

14.00 Y (%)

14.00 Y (%)

12.00

12.00

10.00

10.00

8.00

8.00

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d)

c)

14.00

0

20 r (mm) 30

0

10

20 r (mm) 30

Fig. 3 Radial profiles of water mass fraction: a) x = 10 mm; b) x = 40 mm; c) x = 80 mm; d) x = 175 mm; RSM. Symbols: experimental data; dashed line: β-PDF; dotted line: laminar flamelets; solid line: 3E-Finite Mode PDF. chemistry (with the Finite Mode PDF model) helps to improve significantly the predictions of species composition (and especially of water mass fraction), even if the agreement is not satisfactory. Improvements in the predictions of the composition profiles can be obtained of course by using detailed chemistry, and this will likely benefit also the predictions of temperature and velocity fields. In this case, however, a more detailed treatment of turbulence may be necessary, as all the employed turbulence models failed in the prediction of the features of this flame, and so far a discrimination among the available RANS based model was not possible, none of them giving satisfactory results. The use of more complex models such as the Large Eddy Simulation would be probably helpful for a more accurate modelling of this kind of flame. 4. 4. CONCLUSIONS A moderately swirling bluff-body stabilized flame was modelled using RANS/ PDF based approaches; no discrimination was possible among the different turbulence models, but the results obtained with RANS simulations suggest the employment of more detailed treatments Chemical reaction modelling is very important and is essential to obtain reasonable results especially in terms of temperature profiles. The Finite Mode PDF model proposed in this work for combustion applications, allowing to implement finite rate chemistry, has been shown to give usually better results than β-PDF or laminar flamelets, also with a rather simple

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reaction scheme, but further improvements are foreseeable as both the mixing model and the kinetic scheme will be refined. a)

8.00

b)

8.00

Y (%)

Y (%)

6.00

6.00

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4.00

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0.00

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20 r (mm) 30

10

0

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c)

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Y (%) 6.00

6.00 4.00

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0.00 0

Fig. 4

10

20 r (mm) 30

0.00 0

10

20 r (mm) 30

Radial profiles of carbon dioxide mass fraction: a) x = 10 mm; b) x = 40 mm; c) x = 80 mm; d) x = 175 mm; RSM. Symbols: experimental data; dashed line: β-PDF; dotted line: laminar flamelets; solid line: 3E-Finite Mode PDF.

The next step will be therefore the use of a model with two reacting environments, which will allow to better predict intermediate compounds, thanks to the presence of two reacting environments with different overall composition, and more detailed kinetics, to improve the performance in predicting the flame composition. 5. ACKNOWLEDGEMENTS Partial financial support to this research by the Italian Ministry of University and Research (M.I.U.R.) is gratefully acknowledged (PRIN Project 2003: Combustion formed particulate: mechanisms of formation, low-emission technologies, health and climate effects.). 6. References 1. Fox R.O.: Computational Models for Turbulent Reacting Flows. Cambridge University Press, Cambridge (2003). 2. Jones W.P., Lindsted R.P.: Combust. Flame, 73: 233 (1988). 3. Zucca A., Marchisio D.L., Barresi A.A., Proc. 28th Meeting of the Italian section of the Combustion Institute (P. Salatino and R. Ragucci eds.), Naples, Italy, 4-6 July 2005. CDEdition, pp. IV-10-1/6 (2005). 4. Marchisio D. L., Zucca A., Raman V., Barresi A.A., Fox R.O.:Chemical Engineering Greetings to Prof. Eliseo Ranzi on occasion of his 65th birthday (M. Dente, ed.). AIDIC II-9, 6



& Reed Business Information, Milano, p. 305-325 (2008).

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