Computational Mechanics 31 (2003) 253–261 Ó Springer-Verlag 2003 DOI 10.1007/s00466-003-0428-1

Dynamic and scalar turbulent fluctuation in a diffusion flame of an-axisymmetric methane jet into air A. Hidouri, M. H. Gazzah, H. Ben Tı¨cha, M. Sassi

253 Abstract A study of turbulence/combustion interactions in a relatively large turbulent diffusion flame of an axisymmetric methane jet into air is presented. A first order k–e turbulence closure model is used along with two different models (equal scales and non-equal scales) for the submodel describing the scalar dissipation rate. The flamelet concept is used to model the turbulent combustion along with a joint mixture fraction/strain rate probability density function (PDF) for the prediction of the average parameters of the turbulent diffusion flame. The numerical approach is that of Patankar and Spalding, while the flamelet simulations are obtained from the RUN1DL code of Rogg and co-workers based on a 17 species detailed reaction mechanism. The chosen configuration is that of the experimentally studied turbulent diffusion flame of Streb [1]. A comparison between these experimental results and the obtained numerical ones is thus presented. Relatively good agreements are obtained which show the usefulness of the two-scale model compared to the classical one-scale model for predicting turbulent diffusion flames. Nonetheless some discrepancies are obtained in the outer and downstream regions of the jet, especially in comparison with the experimental data. These are attributed to short coming of the considered turbulence model and soot radiation which is not accounted for. Keywords Turbulent, Jets, Flames, Scalar, Fluctuation List of symbols a laminar strain rate, s
1 D nozzle diameter, m F generalized turbulent parameter G mixture fraction k turbulent kinetic energy, m2 s
2 P probability density Rs time scale ratio r radial distance, m T temperature, K U velocity, m s
1 x axial distance, m z scalar variance Received: 2 May 2002 / Accepted: 31 January 2003

A. Hidouri, M. H. Gazzah, H. Ben Tı¨cha, M. Sassi (&) LESTE-ENI-Monastir, Route de Kairouan, 5019, Monastir, Tunisie e-mail: [email protected]

Greek symbols l dynamic viscosity, kg m
1 s
1 m kinematic viscosity, m2 s
1 r Schmidt number e dissipation rate, m2 s
3 g scalar dissipation rate, s
1 q density, kg m
3 Subscripts 0 reference point b burning part q quenching st stoichiometric

1 Introduction The study of turbulent combustion phenomena presents a great interest in many industrial applications such as burners, internal combustion engines, gas turbines among others. The inherent complexity in many interacting processes existing in this type of reacting turbulent flows renders their complete study very difficult. Turbulence/ chemistry interactions, pollutant formation, radiative transfer effects and flame stability (lift-off and/or extinction) are among the most important phenomena to take in consideration in order to correctly model turbulent nonpremixed flames. Several experimental and numerical studies have been done to harness this complex problem and to develop design tools for turbulent combustion devices. To name a few, Marcus et al. [2] presented a simplified approach to the numerical description of methane air diffusion flames, while Koutmos and Mavridis [3] studied the partial extinction and reignition effects in turbulent non premixed jet flames, and the importance of the subject matter has led to the organization of the annual International Workshop on Measurement and Computation of Turbulent Nonpremixed Flames [4]. However, in this workshop, laboratory pilot type turbulent diffusion flames of several fuel mixtures with co-flows have been chosen to permit proper laser diagnostic experimental conditions in order to validate the numerical models. In this work a study of turbulence/combustion interactions in a relatively large turbulent diffusion flames for an axisymmetric methane jet into air is done. The objective is to extend our numerical code on variable density jets [5, 6] to model turbulent combustion, eventually with pollutant formation and radiative heat transfer, in order to furnish a home made design and optimization tool for local

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industrial combustion devices. The complexity of this reactive flow type arises from the strong coupling between the dynamic and scalar fields. The scalar dissipation rate corresponds to the turbulent diffusion of the scalar fluctuations. The study of this dissipation rate and its correlation with the mixture fraction permits better understanding of the interactions between the small and the large scales of the turbulent reacting flow field. For the turbulent transport of the scalar variables, several studies [7, 8] have proposed a model based on different scales of mechanical and scalar turbulence, especially as related to the flamelet concept for turbulent diffusion flames [9, 10]. The turbulent combustion models based on the flamelet concept [11, 12] allow the evaluation of the effects of turbulence on the combustion phenomenon. Assuming that the smallest characteristic length scale of turbulence is larger than the flame front width, these models describe the turbulent diffusion flame by an ensemble of elementary laminar diffusion flames, convected and stretched by the turbulent flow. Flamelets are thus laminar onedimensional flames which are embedded within the turbulent flow field and are subject to the turbulent straining motion, leading to flame stretch. This effect can be quantified by the scalar dissipation rate or strain rate. If the flame stretch is absent, and consequently the chemistry is in equilibrium, the flame structure can be described solely by the mixture fraction. Thus, the principal idea of the flamelet concept consists of introducing a passive scalar (the mixture fraction), which behaves as a nonreacting species diffusing in the gaseous medium and transported by the turbulent flow. The average value of any scalar turbulent parameter (density, temperature, species mass fraction) is then deduced from a probabilistic computation based on a proper chose of a probability density function (PDF). Two methods leading to a convenient form of a PDF describing the turbulent mixture can then be used. The first consists of computing the PDF from a transport equation such as done by Pope [13] for a joint position/velocity/composition PDF. This method allowed to obtain satisfactory results on several real configurations [14–16]. Nevertheless, this approach is limited by the complexity of modeling certain unknown terms which appear in the PDF governing equation. The second method is based on a simple but realistic presumed PDF, which depends on one or more parameters which can vary from one point to another in the turbulent flow field. This last is used in the present work based on a joint mixture fraction/strain rate PDF in the form of a Beta function [17]. Cliflon et al. [18], have shown the efficiency of the assumed Beta PDF subgrid-scale model for large eddy simulation of nonpremixed turbulent combustion with heat release. Since strain rate and scalar dissipation rate are intimately related, special attention has been given to scalar turbulent fluctuation modeling in this work. From measurements on and calculations of turbulent jets and diffusion flames presented in the literature it can be concluded that mechanical and scalar scales are not equal. Cheveray and Tutu [19] have measured a turbulent Prandtl number in a heated round jet and have shown that it was not constant. This observation was confirmed by the measurements of Sarh [20] on a rectangular heated jet.

Furthermore, mechanical to scalar time scale found by Panchapakesan and Lumley [21] in turbulent helium-air jet was not constant. In turbulent diffusion flames, Drake et al. [22] have shown that the turbulent Schmidt number can not be constant, while Dibble et al. [23] have computed the time scale ratio using a second order turbulence model, and have shown that it varies from one point to another in the flow field. Therefore, a transport equation for the scalar dissipation rate must be constructed to circumvent the assumption of equal-scales for scalar and mechanical turbulence. This was mostly done with second order closures, however, Yoshizawa [24] has proposed a consistent first order model within the k–e context using the two-scale-direct-interaction approximation (TSDIA). In the present work, emphasis is made on a comparison between this last two-scales model and the classical algebraic model applied to the turbulent diffusion flame of an axisymmetric vertical jet of methane into air. Methane is injected from a 10 mm nozzle at a temperature of 323 K and at a maximum speed of 69.3 m s
1 , producing a relatively large flame (about 2 m long and a power of 150 KW). The last conditions are chosen to allow a comparison between the obtained numerical results and those found in the literature [1, 25, 26] for the same flame.

2 Problem formulation 2.1 Turbulence model The turbulent reacting axisymmetric jet is modeled using a first order closure method and Favre averaging. The details of the turbulence model are presented in the work of Gazzah et al. [5, 6] where buoyancy effects are neglected. Only details about the transport of the mixture fraction and its variance, which is directly related to the scalar dissipation rate, are presented here. The mixture fraction and its variance are governed by the following two equations (considered in axisymmetric cylindrical coordinates). Conservation equation for the average mixture fraction G~


 r  qU~ G~ ¼ r 



 lt ~ rG rG

00 Conservation equation for   the variance z~ ¼ g~

ð1Þ 2


 lt r  qU~ ~z ¼ r  r~z þ Pz
q~g rz

ð2Þ

where Pz is the production term of scalar fluctuation modeled by:

Pz ¼
cz qu00 g 00

oG~ oxj

ð3Þ

rG and rz are the turbulent Schmidt numbers in the scalar transport model and are both constants equal to 0.9 while cz is a constant equal to 2. Several models have been proposed to determine the scalar dissipation rate ~g which

turbulence values, and it only depends on the jet exit appears explicitly in Eq. (2). In the present study, two models have been used: the classical equal-scale model and velocity. In fact, the computed mixture fraction and scalar fluctuation intensity depends strongly on the value of /0 . the Yoshizawa [24] non-equal scales one. Based on comparison between computational results and experimental ones [7], a value of /0 equal to 5 has been 2.1.1 used in this study. Equal scales model Under the assumption that the dynamic and scalar characteristic times are proportional, the scalar dissipation rate 2.2 Combustion model is given by:

~g ¼ Rs~e~z=k~

ð4Þ

where Rs ¼ ðk~=~eÞ=ð~z=~ gÞ is the ratio of dynamic (momentum) to scalar (density, temperature, mass fraction, or mixture fraction) time scales. A ratio of 2 has been used by Beguier et al. [27] giving:

~g ¼ 2~e~z=k~

ð5Þ

Using a first order turbulence closure model, a constant value of Rs implies a constant value of the turbulent Schmidt number.

2.1.2 Non-equal scales model The transport of a scalar parameter in a turbulent jet has been modeled using the non-equal scales approach of Yoshizawa [24] based on the TSDIA method. The used governing equation for the scalar dissipation rate is:   D~g 1 D~z 1 D~e ¼ ~g k1 þ k2 ð6Þ ~z Dt ~e Dt Dt where D=Dt ¼ o=ot þ ~ u  r and the right hand side of this equation is a combination of the variance transport equation and the kinetic energy dissipation rate one. Based on separation of variables, the analytical solution of the last equation is put under the following form according to [7]

~g ¼ /~zk1 ~ek2

ð7Þ

2.2.1 Diffusion flamelet structure The laminar diffusion flamelet structure is controlled by heat and mass transfer. The flamelet is very thin, and with introducing the mixture fraction in a transformation of the coordinate system, one can determine its structure by onedimensional transport equations. The turbulent flow effect on the flamelet is parameterized and imposed through the instantaneous scalar dissipation rate. This parameter is expressed in s–1 and can be interpreted as the inverse of a characteristic mixing time. According to the last coordinate transformation, this parameter contains implicitly the effect of convection and normal diffusion to the stoichiometric flamelet surface (G ¼ Gst with Gst ¼ 0:055 for methane/air). For an opposed flow diffusion flame, the scalar dissipation rate g is proportional to the flamelet strain rate ab [28]. In the present study, the flamelet simulations are obtained from the RUN-1DL code of Rogg and co-workers [29, 30] based on a 17 species detailed reactional mechanism. Figure 1 shows the mass fractions of the major species distributions across the methane/air diffusion flamelet for a strain rate of 300 s
1 . The influence of this parameter is well pronounced on the temperature profile of the flamelet in Fig. 2. This last shows that the maximum temperature occurs at stoichiometry, and that this maximum value decreases with increasing strain rate. Libby and Williams [28] determined a limiting value of the strain rate beyond which the flame is extinguished. This is 505 s
1 for the

with / a dimensional reference value which depends on the flow considered, the coefficients k1 and k2 must take well defined values. From similarity behavior of a round turbulent jet, a relation under the form k1 þ 2k2 ¼ 2 has been used [7]. This last study has shown, by exploratory calculation, a greater influence on the solution for k1 than for k2 and the values of 1 and 0.5 have been proposed for those two constants, respectively. These are different from k1 = 1.2 and k2 = 0.306 which have been chosen by Yoshizawa based on complete turbulence in the inertial zone part of the kinetic energy spectrum. The coefficient /, in the above equation, has dimensions and depends on the initial conditions. Therefore, it must empirically be determined for each different flow. The dimension of / are m
1 s1=2 based on k1 = 1 and k2 = 0.5. According to similarity characteristics considerations, the form of / ¼ /0 ðUDÞ
1=2 has been used, with /0 a non–dimensional coefficient independent from the exit velocity U and the diameter D of the jet [7]. Therefore, any change in the initial conditions while / is kept constant would change the solution, even in the far field. However, Fig. 1. Mass fraction profiles of CH4, O2, CO2, CO and H2O for a it is shown that the solution does not depend on the initial methane/air flamelet at a strain rate of 300 s
1

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Pb ¼

Zaq

P~ðaÞda

and ð1
Pb Þ ¼

Z1

P~ðaÞda

ð11Þ

aq

0

Thus giving


 F~ ¼ ð1
Pb ÞF0 G~ þ

Zaq 0

PðaÞda

Z1

F ðG; aÞP~ðGÞdG

0

ð12Þ

256

And letting

F~ðaÞ ¼

Z1

F ðG; aÞdG

ð13Þ

0

one obtains Fig. 2. Temperature profiles for methane/air flamelets at strain rates of 100 s
1 and 300 s
1


 F~ ¼ ð1
Pb ÞF0 G~ þ

Zaq

F~ðaÞPðaÞda

ð14Þ

methane/air case. Furthermore, the temperature difference 0 observed on Fig. 2 have a strong influence on chemical In this last expression, the first term is due to non-reactive kinetics of combustion. mixing, while the second is due to reactive mixing. Assuming the flame strain rate to obey a quasi-Gaussian 2.2.2 distribution [31] Flamelet concept for turbulent combustion The turbulent combustion model based on laminar diffu2
 PðaÞ ¼ pffiffiffiffiffiffiffiffiffiffi ð15Þ sion flamelets concept was developed by Peters [11, 12]. 2pra exp
a2 =2r2a The numerical simulation of turbulent combustion is obtained through the resolution of conservation equations for where ra is the variance related to the mean strain rate a~ energy and chemical species, and by using a joint mixture by: fraction/strain rate PDF describing turbulent mixing. rffiffiffi 2 For any turbulent parameter F, the Favre averaged value ra ð16Þ a~ ¼ F~ is then given by: p

F~ ¼

Z 1 Z1 0

0

This leads to a probability of burning given by:

F ðG; aÞP~ðGÞP~ðaÞdG da

ð9Þ



aq Pb ¼ erf a~p1=2



ð17Þ

where P~ðGÞ is the Favre averaged mixture fraction PDF where erf denotes the error-function and a is the strain and P~ðaÞ is the Favre averaged strain rate PDF. The chosen rate at flame extinction. It must be recalledqthat the flame ~ form for PðGÞ is the Beta function giving: strain rate is noted a~, and in order for equation (17) to be 2 a q useful, the dynamical strain rate must be estimated. This is 1 Z Z 6 difficult by the fact that this rate depends on the eddy size. F~ ¼ dG4 F ðG; aÞP~ðGÞP~ðaÞda For large energy containing eddies, it is proportional to 0 0 e=k, while for the psmall ffiffiffiffiffiffiffiffiffi energy dissipating eddies it is 3 proportional to e=2m. The proportionality constants are 1 Z adopted from the study of Sanders and Lamers [32] for a 7 þ F0 ðGÞP~ðGÞP~ðaÞda5 natural gas turbulent diffusion flame. These are 6 and 0.3 respectively. aq The simulation of the reactive part in Eq. (14) with a Z 1 Zaq Z1 number M of flamelets of reactive strain rates ai (i =1 to
 ¼ F ðG; aÞP~ðGÞP~ðaÞda þ F0 G~ P~ðaÞda M) is obtained by neglecting fluctuations. Therefore, the PDF of a is a delta function centered at a ¼ a~, and asaq 0 0 suming that the reactive part of Eq. (14) is described by ð10Þ the structure of a laminar diffusion flamelet F ðG; a Þ, the b b where F0 ðGÞ ¼ FðG~; a ¼ aq Þ is equal the value of F in the following form for F~ is obtained: isothermal mixture of the jet. In this zone, Z1 R 1 the profiles of
 F0 ðGÞ are linear, permitting the integral 0 P~ðGÞF0 ðGÞdG to ~ ð18Þ F ¼ ð1
Pb ÞF0 G~ þ Pb F~b ðG; ab ÞPðGÞdG be replaced by F0 ðG~Þ. The last equation can be simplified 0 using the probability of burning:

In particular, the mean density and temperature of the turbulent reacting mixture are then:


 1 q ¼ ð1
Pb Þq0 G~ þ R 1 p~ðGÞ

ð19Þ

0 qb ðGÞ dG


 T ¼ ð1
Pb ÞT0 G~ þ qPb

Z1

Tb ðGÞ

P~ðGÞ dG qðGÞ

ð20Þ

0

The computation of the mean species mass fractions Yi is analogous to that of the mean temperature.

257

3 Numerical method The numerical resolution of the modeled systems of equations is based on the parabolic type approach of Patankar and Spalding [33]. The details of this approach as applied to variable density turbulent flows are given in the Fig. 3. A comparison between computed and experimental jet work of Chassaing [34] and Gazzah et al. [5, 6]. halfwidths based on velocity and mixture fraction, respectively Scalar profiles of the flamelets as functions of mixture fraction with the strain rate as a parameter are obtained by the RUN-1DL code of Rogg and co-workers [29, 30]. The counterflowing diffusion flames simulating the flamelets are resolved by numerical integration of the boundary similarity equations for conservation of mass, momentum, energy and chemical species. The numerical code is essentially based on a dumped modified Newton method. 4 Results and discussion This section presents the predicted numerical results in comparison with the experimental results of Streb [1], for an axisymmetric methane into air turbulent diffusion flame jet of exit diameter and velocity of 10 mm and 69.3 m s
1 , respectively. In addition, some of the experimental results of Birch et al. [25] for an isothermal jet, and those of Brookes and Moss [26] for a turbulent jet diffusion flame are used for further comparison and validation of the adopted method. Figure 3 shows a comparison between the numerical and experimental turbulent reacting jet halfwidth based on the velocity and mixture fraction profiles, respectively. The halfwidth is defined as radial position at which the jet parameter is equal to half its value on the axis. The observed differences between the numerical and experimental results, especially in the range of x/D from 10 to 70, are due to the k–e first order turbulence closure model whose constants must be adjusted to have the best fit on the hole range of the jet. Further downstream a better agreement is observed. Figure 4 represents the computed axial kinetic energy distribution compared to the experimental values of Streb [1]. A good agreement is obtained for this important turbulent parameter. It is noticed that kinetic energy is not influenced by the choice of the scalar dissipation rate. The mean scalar dissipation rate is computed by both the equal and non-equal scales models. Figure 5 shows the axial distribution of this parameter, according to both models, for the isothermal jet and the diffusion flame jet. For the earlier, the maximum scalar dissipation rate is

Fig. 4. A comparison between the predicted and experimental centerline turbulent kinetic energy

obtained for x=D  5 corresponding to the energy production zone, while its value becomes zero for x/D greater than 30. Both models give approximately the same behavior for this parameter. For the diffusion flame jet, the maximum scalar dissipation rate is observed at x=D  10. This results from thermal expansion due to the flame and from the strong temperature and concentration gradients which increase the diffusion of the scalar turbulent fluctuations. Figure 6 presents the axial distribution of the variance for the isothermal and reactive jets. For the isothermal case, the computed results based on the non equal–scales model seem to better approach the experimental results of Birch et al. [25]. While in the case of the reactive jet, a broadening of the variance distribution is observed for the same reasons discussed above. Figure 7 features the computed axial distribution of the mixture fraction, using the non-equal scales model, for the

258

Fig. 5. Predicted centerline scalar dissipation rate of isothermal and flame jet, using the equal and the non-equal scales model, respectively

Fig. 6. Predicted centerline variance of isothermal and flame jet in comparison with experimental data for the isothermal case

isothermal and diffusion flame jets compared to the experimental results of Birch [25] and Brookes [26], respectively. A good agreement, between the numerical and experimental results, is obtained for this most important turbulent jet parameter. It should be noticed that both models give similar predictions for the mixture fraction field. Further emphasis on the non-uniformity for the time scale ratio, and thus on spatial variation of the turbulent Schmidt number, is obtained from Figs. 8 and 9. Figure 8 shows the axial distribution of the time scale ratio (Rs from Eq. (4)) for the isothermal and flame jets, respectively. It is noted that this ratio is variable up to a certain axial distance (x=D  20 for the isothermal and x=D  30 for flame jet, respectively) before attaining a constant value which depends on the ejected fluid and on the value of /0 discussed above. Furthermore, the radial variations of the time scale ratio, for different

Fig. 7. A comparison between the predicted and experimental centerline mixture fraction for the isothermal and flame jet, respectively

Fig. 8. Axial profile of the time scale ratio in the isothermal and flame jet, respectively

sections of the jet flow field, are shown in Fig. 9. It is noticed that this ratio remains radially variable even for the downstream regions (x=D ¼ 120), especially for the turbulent flame jet. Several earlier studies were concerned with the modification of the turbulence structure induced by the presence of the flame through differents characteristic scales. Dumont et al. [35] and Furukawa et al. [36] discussed turbulence generation within turbulent premixed flames. They suggested that velocity fluctuations increase through the flame front and this is not due to Reynolds stresses, rather it is due to the strong density and viscosity variation between reactants and products of combustion. The strong temperature increase through the flame increases the kinematic viscosity which is directly related to the small turbulent scales resulting in a variation of the turbulent Schmidt number. Pitsch [37] showed, in his study of turbulent

259

Fig. 11. Predicted radial temperature profiles at x=D ¼ 120, using Fig. 9. Radial profiles of the time scale ratio in the isothermal and the two scalar dissipation rate models, compared with experiflame jet for different axial positions mental data

Fig. 10. Predicted radial temperature profiles at x=D ¼ 10, using the two dissipation rate models

piloted methane/air diffusion flame, that the dynamic to scalar time scale ratio was not constant. Some of the results of the numerical prediction, of the turbulent flame jet structure, using the equal and non-equal scales models are presented in Figs. 10–12 in comparison with some experimental results. Figure 10 presents the computed radial temperature profiles for the reactive jet at x=D ¼ 10, using both equal and nonequal scales models. On the axis, the temperature is that of methane injection, a maximum is obtained at the flame front (r/D ¼ 1.9), and further out its value decreases toward the ambient air temperature. Both models give similar predictions in this region where the velocity gradients are as important as the scalar ones, and thus the fluctuation scales are equivalent (see also Fig. 9). While Fig. 11 shows a disagreement between the two models in the prediction of the temperature radial profile at x=D ¼ 120. This is due to the strong

temperature gradients compared to the small velocity ones in this far downstream region. It is also noticed that the non-equal scales model gives closer predictions to the experimental results of Streb [1]. The observed disagreement especially on the outer part of the jet is essentially due to soot radiation which is not accounted for in the flamelet model. The most important sources of thermal radiation losses in a methane flame jet are H2 O, CO2 and soot particles. However, the latter, where present, are by far the most important. Lockwood and Stolakis [38] showed that maximum mean temperature differences between predictions with and without soot radiation effect can be of the order of 400 K. Lately, Zhang and Ezekoye [39] computed the soot production rate at elevated pressure in methane/air jet diffusion flame, while Brooks and Moss [26] predicted soot and thermal radiation properties in confined turbulent jet diffusion flames. The effect of thermal radiation will thus be incorporated in the numerical model in the early future. Figure 12 features the computed major species axial distributions, using both models, compared to the experimental results of Streb [1]. The observed disagreement between computation and experiment for 10 x=D 70 is due to the overestimation of mixing in this region (see also Fig. 3 and associated discussion). Globally, however better agreement are obtained between the computed flame jet structure (temperature and species) and the experimental data when the non-equal scales model is used. A uniform Schmidt number is thus not realistic for the prediction of a turbulent reactive jet. The variation of the time scale ratio and the choice of the non-equal scales model was discussed in Figs. 8 and 9, however, other aspects of this model are questionable. The reference value / is a dimensionless variable, given by the values k1 and k2 , which renders the physical interpretation of / difficult. Close to the injection nozzle, the value of / is given by the boundary conditions, while the dissipation rate and its variance are close to zero, and no approach has been proposed yet to evaluate / in this region. In the

260

Fig. 12. Predicted centerline mass fractions of CH4 , O2 and H2 O, using the two scalar dissipation rate models, compared with experimental data

present study, the equal scale model has been used in this region.

5 Conclusion A numerical study of the dynamic to scalar turbulent time ratio in the diffusion flame of an axisymmetric methane jet into air has been presented. A first order k–e turbulence closure model is used along with two different models (equal scales and non-equal scales) for the submodel describing the scalar dissipation rate. The flamelet concept is used to model the turbulent combustion a long with a joint mixture fraction/strain rate probability density function (PDF) for the prediction of the average parameters of the turbulent diffusion flames. The numerical approach is that of Patankar and Spalding, while the flamelet simulations are obtained from the RUN-1DL code of Rogg and co-workers based on a 17 species detailed reactional mechanism. The obtained numerical results and in comparison with published experimental ones show the relative efficiency of the non-equal scales approach in predicting the global structure (temperature, and species profiles) of turbulent diffusion flames. However, some sources of discrepancy between the computational predictions and the available experimental data (such as the first order turbulence model, the flamelet combustion model, the choice of /, and soot radiation effects) have been identified and discussed. References 1. Streb H (1993) Untersuchungen zum Einfluß des Auftriebs auf die Mischung und Reaktion in turbulenten Freistrahldiffusionsflammen, Ph. D. thesis. Universita¨ t Karlsruhe, Germany 2. Bollig M, Amable L, Antonio L, Williams FA (1998) A simplified approach to the numerical description of methane air diffusion flames. Twenty-Seventh Symposium on Combustion, pp. 595–603 3. Koutmos P, Mavridis C (1999) A study of partial extinction and reignition effects in turbulent non-premixed jet flames of

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