CFD and Kinetic Analysis of Bluff Body Stabilized Flame

CFD and Kinetic Analysis of Bluff Body Stabilized ame A. Dicorato, E. Covelli, A. Frassoldati, T. Faravelli, E. Ranzi Dipartimento di Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, ITALY INTRODUCTION The analysis of experimental burners and their detailed chemical and fluidynamic studies are useful tools to investigate turbulent non premixed flames and minimize the environmental impact of industrial devices. This paper presents the CFD simulation of the turbulent nonpremixed bluff-body stabilized flame experimentally investigated at the University of Sidney and Sandia Laboratories [1]. Different combustion models have been tested and the results compared with experimental data in order to evaluate the effect of increasingly detailed kinetic schemes. The models were based on the mixture fraction/pdf approach (equilibrium, laminar flamelets), the Finite Rate-Eddy dissipation model and the Eddy dissipation concept model (EDC). EXPERIMENT The Bluff-body burner has been presented as a target case at TNF Workshops [2]. Some new calculations are presented for validation against the experimental velocity and compositional data. The data are freely accessible to researchers on the internet [1]. The compositional measurements (flame HM1) were taken at the Turbulent Diffusion ame Laboratory at Sandia s CRF, while the flow field measurements at Sydney University Heat Laboratory (equivalent flame HM1E). The bluff-body stabilized burner is located in a co-flowing air stream. The flame is unconfined and fed with a mixing of natural gas (50% vol) and hydrogen (50% vol). As shown in figure 1, the burner has a central conduct with a diameter of 3.6mm for the fuel jet, situated within a 50mm diameter ceramic faced bluff-body. The burner is located in a wind tunnel. The central fuel jet mixes with the co-flow air stream, resulting in a turbulent unconfined diffusion flame. The flame is stabilized by the intense mixing of fuel and air in the recirculation zone behind the bluff-body, as well as by the transport of hot products back to the burner zone. Central fuel jet Wind tunnel Bluff body HM1E Central fuel jet bulk velocity: 108 m/s Co-flowing air bulk velocity: 35 m/s HM1 Central fuel jet bulk velocity: 118 m/s Co-flowing air bulk velocity: 40 m/s Fuel delivery Fig. 1. Scheme of the bluff-body stabilized burner and HM1 flame image [1]. 1

SIMULATION Mathematical modeling The flame was simulated with the uent 6.1 code using a 35,000 cells non-uniform unstructured computational grid in a steady 2D-axisymmetric approach. The grid was adapted to give high resolution in the flame region close to the inlets and save computational efforts elsewhere. For the spatial resolution the First-Order Upwind Scheme was adopted. The algorithms PRESTO and SIMPLE are respectively used for the pressure interpolation and for the coupling of pressure and velocity. The radiative heat transfer of the unconfined flames is calculated with the P1 model. The Standard k-ε model has known shortcoming for predicting round jets. In particular, the standard k ε model overpredicts the decay rate and the spreading rate of a round jet. Modifications suggested by McGuirk and Rodi for the parameter C ε1 lead to a value of 1.60 for self-similar round jets [3,4]. The modified k-ε model performs very well and was used in order to avoid the additional computational expense of the Reynolds stress model and concentrate on the study of turbulence-chemistry interactions. Both axial and radial calculated velocity profiles agree very well with the experimental data. Different models are used for the description of the turbulence/chemistry interactions and their advantages and limitations are discussed: - Fast chemistry assumption with mixture fraction\pdf approach: - uilibrium model (Infinitely fast chemistry) - Steady laminar flamelets model (Fast chemistry) - Generalized finite rate approach: - Eddy dissipation model - Finite-rate/eddy-dissipation model (FR/ED) - Eddy dissipation concept model (EDC) Fast chemistry assumption with mixture fraction\pdf approach The fast chemistry assumption approach can be used conveniently in combustion modeling but cannot be extended to conditions where the finite rate chemistry has significant effects, as oxidation of CO, formation of trace species (NO and soot) and extinction conditions. The basic assumption of the fast chemistry approach is that the instantaneous thermochemical state of the fluid is related to a conserved scalar quantity known as the mixture fraction. In this way the species transport equations can be reduced to a transport equation for the mixture fraction. The temperature and thermo-chemical variables are calculated with the chemical equilibrium or the flamelets model, from the local value of the mixture fraction. The equilibrium model assumes that the chemistry is rapid enough for chemical equilibrium to always exist at the molecular level. In order to take into account the fuel rich flammability limit, the equilibrium calculation is restricted to values of mixture fraction lower than a critical value f rich, assuming: f rich 2 f st = 0. 098 [5]. The equilibrium calculation include 17 chemical species which belong to Skeletal25 kinetic model [6]. NOx species are not included, as the NOx reaction rates are slow and should not be treated using an equilibrium assumption. The Laminar amelets model views the turbulent flame as consisting of an ensemble of stretched laminar flamelets [7,8]. In a near-equilibrium diffusion flame 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 non-equilibrium in turbulent flames due to aerodynamic straining by the turbulence. When the chemical time-scale is lower than the fluid convection time-scale, the species can be 2

x=3 mm x=30 mm x=3 mm x=30 mm Fig. 2. Velocity, temperature and composition profiles at different distances from the burner surface: comparison between uilibrium assumption () and Steady Laminar amelets model (). considered to be in chemical non-equilibrium. In such cases as NO x formation the laminar flamelet model is not suitable and slow chemistry can be modeled in a post-processing step [9]. Figure 2 shows the comparison between experimental and computed profiles of velocities, temperature, mixture fraction and mass fractions of major chemical species. The prediction of the flow field is satisfactory with all combustion models and thus not discussed for the other models. In the equilibrium calculations the temperature profiles are underestimated in particular in the recirculation zone behind the bluff-body and in the central jet zone. Moreover, at 13 mm from the inlet a temperature hot spot can be observed in the mixing zone between air and the recirculation zone. These discrepancies cannot be attributed to a poor prevision of the mixing between fuel and oxidizer, which turns out to be in good agreement with measurements, in terms of mixture fraction profiles. The shape of CO 2 and H 2 O profiles is similar to the one of the temperature profile; water is generally underestimated while CO 2 is predicted more precisely except for the recirculation zone close to the bluff body where it is less accurate. The predicted CO mass fraction is highly overestimated, confirming that its kinetic behavior in this particular flame is poorly predicted by equilibrium assumption. In general the simulation with the equilibrium assumption clearly does not allow accurate prediction of the HM1 flame characteristics. The steady flamelets library, was obtained by means of the Oppdif code [10] by adopting the reaction mechanism in [11] and stored in look-up tables describing the dependence of flamelets on the scalar dissipation rate and the mixture fraction. The mechanism contains 48 3

chemical species including NOx. In this work, a library of 8 different Strained Laminar amelets with strain rate up to 3000s -1 (extinction) was used in CFD calculations. The comparison with experiments and the previous equilibrium calculations shows that the flamelet approach allowed to significantly improve the prediction of CO and H 2 O, while CO 2 is still underestimated. The model is also able to predict NO but with an expected large overprediction, due to the typical slow chemistry of NOx formation which is not correctly accounted for by the amelets model. Generalized finite rate approach The generalized finite rate approach is based on the resolution of the transport equations for the species involved in the calculation and accounts for the effect of finite rate chemistry. The interaction between turbulence and chemistry is often handled through the Finite Rate- Eddy-Dissipation Model (). The controlling rate is assumed the slower between the kinetic values and turbulent mixing rate. It means that both the Arrhenius and the Eddy- Dissipation rates are calculated for the forward and the reverse reaction separately. In particular conditions, this approach can lead to strong deviations. Let s assume a chemical reaction A+BC+D, kinetically favorite in the forward direction. In the example of table 1, turbulent mixing rate favors the reverse reaction. The application of the concept separately to the direct and reverse reaction can produce a net rate opposite to the kinetic indications. On the contrary, it seems better to first evaluate the net kinetic rate and only then to apply the concept comparing this net rate with the corresponding forward or reverse turbulent mixing rate. In this way the example of table 1 will bring to conclusion in line with kinetics. A UDF (User-Defined-Function) was then implemented in the code to modify the turbulence-chemistry interaction following this approach. A reduced chemical mechanism, proposed by Jones and Lindstedt [12], was used with the Finite rate/eddy dissipation model. The mechanism takes into account the formation of H 2 through pyrolysis reactions in fuel rich regions of the flame and also hydrogen consumption. Figure 3 shows that the agreement is satisfactory for temperature and H 2 O profiles, while CO is overestimated and consequently CO 2 is underestimated. The modified version of the approach, which verifies the consistency with chemical equilibrium for reversible reactions, allows to slightly improve the general agreement between experiments and model predictions especially for CO and CO 2 profiles. Forward rate A+B Reverse rate C+D Net rate Kinetics R K,f R K,r R KIN =R K,f R K,r Turbulent M ixing R T,f R T,r R T,f R K,r R ED =R T,f R K,r M odified R ED-M =min (R KIN, R T,f ) Tab. 1. Example of Finite Rate-Eddy Dissipation Model () and modified According to the EDC model by Magnussen [13] the chemical reactions are assumed to occur in the fine structures, i.e. the small turbulence scales. The model treats the small-scale structures as perfectly stirred reactors (PSRs). The residence time within the fine structures ( * ) is proportional to the Kolmogorov time scale. The basic assumption of the EDC is that chemical reactions are quenched if the characteristic chemical times for limiting species are 4

longer than *. The kinetic model used in the EDC model simulations comes from Kee [6] for methane and hydrogen combustion and has been coupled with the NOx sub-mechanism of San Diego [11]. The number of chemical species considered is 30, involved in 110 reactions. x=45 mm x=45 mm x=45 mm x=45 mm Fig. 3. Temperature profiles and mass fractions at different distances from the burner surface: comparison between original and modified Finite Rate/Eddy Dissipation models. Kinetic mechanism from Jones and Lindstedt [10]. Fig. 4 presents the comparison with measurements and confirms that the inclusion of detailed chemistry in turbulent combustion modeling through the EDC model allowed to significantly improve the predictions of temperature and chemical species. The scheme used in the EDC simulations allows to predict NO x formation and consumption in flames. The results show that the prediction of NO is far less accurate with respect to the other chemical species, which x=45 mm x=45 mm x=45 mm Fig. 4: Temperature profiles and mass fractions at different distances from the burner surface: EDC model including mechanism from Kee [6] coupled with San Diego NO x sub-mechanism [11]. 5

are very well predicted. The shape of the NO profile in flame is correctly reproduced at the different distances from the burner surface, but the absolute value is significantly underestimated. This can be explained because of the high chemical time scale of nitrogen chemistry, much greater than residence time in the fine structures, as already observed also by Magnussen [14]. CONCLUSIONS The modified k-ε model (C ε1 =1.60) performs very well and the prediction of the flow field is satisfactory with all turbulent combustion models and thus not discussed in detail. The effect of increasingly detailed kinetic schemes was studied using different models for the turbulence/chemistry interactions. The modified version of the approach, which verifies the consistency with chemical equilibrium for reversible reactions, allows to improve especially the predictions for species involved in reversible reactions. Simulations with the EDC model revealed the best agreement with experiments in terms of temperature profile and composition. When considering the different approaches based on fast chemistry assumptions, the laminar flamelets model satisfactorily predicted the flame characteristics. It is worth noting that the strength of both EDC and laminar flamelets model relies on the possibility of incorporating detailed chemistry into CFD calculations. In fact, model results obtained with reduced mechanism are, in general, less accurate. However, for both EDC and laminar flamelets model, NO predictions are not sufficiently adequate because of slow NOx chemistry. NOx can be more conveniently predicted in a post-processing step which allows to use detailed kinetics [9]. The advantage of the amelets over the EDC model is the reduced computational time. On the other hand the EDC model predicts more accurately the flame structure. Acknowledgments The work was financially supported by MIUR (COFIN project 2003). REFERENCES 1. http://www.aeromech.usyd.edu.au/thermofluids/ 2. http://www.ca.sandia.gov/tdf/workshop.htlm 3. Hossain M., Jones J.C., Malalasekera W., ow, Turb. and Combustion, 67:217 (2001). 4. Dally, B.B., etcher, D.F. and Masri, A.R., Combust. Theory Modeling, 2:193 (1998). 5. Peters N., Fifteen lectures on laminar and turbulent combustion, ERCOFTAC Summer School, chap. 9, (1992). 6. Peeters T., Numerical Modeling of Turbulence Natural-Gas Diffusion ames., PhD thesis, Delft Technical University, Delft, The Netherlands, (1995). 7. P.A. Libby, F.A. Williams, Turbulent Reacting ows, Academic Press, London, (1994). 8. Williams, F. A., Recent advances in theoretical descriptions of turbulent diffusion flames, in S. N. B. Murthy, editor, Turbulent mixing in Nonreactive and Reactive ows, p 189-208, Plenum Press, New York. 9. S. Frigerio, A. Frassoldati, T. Faravelli, E. Ranzi, "Joint Meeting of Scandinavian-Nordic and Italian Sections of The Combustion Institute", paper 2.11, Ischia 18-21, Sept. 2003. 10. A. E. Lutz, R. J. Kee, J. F. Grcar, and F. M. Rupley. OPPDIF: A FORTRAN Program for Computing Opposed-ow Diffusion ames. Sandia National Laboratories Report SAND96-8243, (1997). 11. San Diego Chemical-Kinetic Mechanisms for Combustion Applications, http://maemail.ucsd.edu/combustion/cermech/sandiego20030830.mec 12. Jones W. P., R. P. Lindstedt, Combustion and ame, 73: 233 (1988). 13. Magnussen B. F., 19 th AIAA Aerospace Science Meeting, St. Louis, Missouri, (1981). 14. Magnussen B. F., CIMAC Conference, Tianjin, China, 4-9 June (1989). 6