Numerical analysis of confined laminar diffusion flame effects of chemical kinetic mechanisms

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  • 1. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976IN INTERNATIONAL JOURNAL OF ADVANCED RESEARCH – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME ENGINEERING AND TECHNOLOGY (IJARET)ISSN 0976 - 6480 (Print)ISSN 0976 - 6499 (Online)Volume 4, Issue 1, January- February (2013), pp. 59-78 IJARET© IAEME: www.iaeme.com/ijaret.aspJournal Impact Factor (2012): 2.7078 (Calculated by GISI) ©IAEMEwww.jifactor.com NUMERICAL ANALYSIS OF CONFINED LAMINAR DIFFUSION FLAME - EFFECTS OF CHEMICAL KINETIC MECHANISMS Ahmed GUESSAB*, Abdelkader ARIS**, Abdelhamid BOUNIF**, Iscander GÖKALP*** * Industrial Products and Systems Innovations Laboratory (IPSILab),Enset, Oran, Algérie - E-mail : (med_guessab@yahoo.fr), Tel. : 00213560706424 ** Laboratoire des Carburants Gazeux et de l’Environnement, Institut de Génie Mécanique,Université des Sciences et de la Technologie, Oran, Algérie. E-mails : (arisaek@yahoo.fr) and (abdelbounif@yahoo.com) *** Laboratoire de Combustions et Système Réactifs, Centre National de la Recherche Scientifique, 1C, Avenue de la Recherche Scientifique, 45071 Orléans, cedex 2, France e-mail : ( gokalp @cnrs-orleans.fr ) ABSTRACT Two chemical kinetic mechanisms of methane combustion were tested and compared using a confined axisymmetric laminar flame: 1-step global reaction mechanism [24], and 4- step mechanism [25], to predict the velocity, temperature and species distributions that describe the finite rate chemistry of methane combustion. The transport equations are solved by FLUENT using a finite-volume method with a SIMPLE procedure. The numerical results are presented and compared with the experimental data [5]. A 4-step methane mechanism was successfully implanted into CFD solver Fluent. The precompiled mechanism was linked to the solver by the means of a User Defined Function (UDF). The numerical solution is in very good agreement with previous numerical of 4-step mechanism and the experimental data. Keywords: Laminar Flame, Axisymmetric Jet, confined, Chemical kinetic, Finite Rate Chemistry. 1. INTRODUCTION Combustion is a complex phenomenon that is controlled by many physical processes including thermodynamics, buoyancy, chemical kinetics, radiation, mass and heat transfers and fluid mechanics. This makes conducting experiments for multi-species reacting flames extremely challenging and financially expensive. For these reasons, computer modeling of 59
  • 2. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEMEthese processes is also playing a progressively important role in producing multi-scaleinformation that is not available by using other research techniques. In many cases, numericalpredictions are typically less expensive and can take less time than similar experimentalprograms and therefore can effectively complement experimental programs. Computational models can help in predicting flame composition, regions of high and lowtemperature inside the burner, and detailed composition of byproducts being produced.Detailed computational results can also help us better predict the chemical structure of flamesand understand flame stabilization processes. These capabilities make Computational FluidDynamics (CFD) an excellent tool to complement experimental methods for understandingcombustion and thus help in designing and choosing better fuel composition according to thespecific needs of a burner. With the advent of more and more powerful computing resources,better algorithms, and the numerous other computational tools in the last couple of decades,CFD has evolved as a powerful tool to study and analyze combustion. However, numerouschallenges are involved in making CFD a reliable and robust tool for design and engineeringpurposes. The numerical simulation is a useful tool because it can easily employ variousconditions by simply changing the parameters. Laminar co-flow diffusion flames are very sensitive to initial conditions andperturbations [1-2]. The gas jet diffusion flame is the basic element of many combustionsystems, such as gas turbines, ram jets, the power-plant and industrial furnaces. In thesesystems, fuel is injected into a duct with a co-flowing or cross-flowing air stream.Furthermore, the fundamental understanding of laminar diffusion flames plays a central rolein the modeling of turbulent diffusion flames through the concept of laminar flamelets and inunderstanding the processes by which pollutants are formed. Consequently, many experimental and numerical studies on confined laminar diffusionflames have been performed: Numerical Simulation of Laminar Co-flow Methane-OxygenDiffusion Flames: Effect of Chemical Kinetic Mechanism [3]. Smooke et al. [4] obtained thenumerical solution of the two-dimensional axisymmetric laminar co-flowing jet diffusionflame of methane and air both in the confined and the unconfined environment. PrimitiveVariable Modeling of Multidimensional Laminar Flames by Xu et al. [5] to study thetemperature, velocity and concentration profiles of stable species. An Efficient ReducedMechanism for Methane Oxidation with NO Chemistry [6]. Experimental and NumericalStudy of a Co-flow Laminar CH4/Air Diffusion Flames [7, 31]. A numerical simulation of an axisymmetric confined diffusion flame formed between aH2-N2 jet and co-flowing air, each at a velocity of 30 cm/s, were presented by Ellzey et al. [8]and Li et al. [9] investigated a highly over-ventilated laminar co-flow diffusion flame inaxisymmetric geometry considering unity Lewis number and the effects of buoyancy.Thomas et al. [10] Comparison of experimental and computed species concentration andtemperature profiles in laminar two-dimensional methane/air diffusion flame. Shmidt et al.[11], Simulation of laminar methane-air flames using automatically simplified chemicalkinetics. Northrup et al. [12] solution of laminar diffusion flames using a parallel adaptivemesh refinement algorithm. Mandal B.K. et al. [13] Numerical simulation of confinedlaminar diffusion flame with variable property formulation, a numerical model is used forsimulation flame under normal gravity and pressure conditions to predict the velocity,temperature and species distributions. 60
  • 3. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME Since methane is the simplest hydrocarbon fuel available; several studies have focusedon methane-air flames. The oxidation of methane is quite well understood and variousdetailed reaction mechanisms are reported in literature [14]. They can be divided into fullmechanisms, skeletal mechanisms, and reduced mechanisms. The various mechanisms differwith respect to the considered species and reactions. However, considering the uncertaintiesand simplifications included in a turbulent flame calculation, the various mechanisms agreereasonably well [15]. In literature, several mechanisms of methane combustion exist. We cancite: for detailed mechanisms: Westbrook [16], Glarborg et al. [17], Miller and Bowman [18],and recently, Konnov [19], Huges et al. [20], and the standard Gri-mech [21], for reducedmechanisms: Westbrook and Dryer [22], and Jones and Lindstedt [23] (more than 2 globalreaction). In summary, the major works of present paper include comparison between 1-step and 4-step chemical reaction mechanism. A working model was developed that fully coupled acomprehensive chemical kinetic mechanism with computational fluid dynamics in thecommercial software program Fluent modified such as to deal with Westbrook’s and Drayer,[24], Jones et al. [25].2. PROBLEM DESCRIPTION The vertical cylindrical diffusion flame burner is shown in Fig. 1. The burner consistsof two concentric tubes of 12.7 mm and 50.8 mm. Fuel issues through the inner tube and airissues through the outer. The fuel-jet velocity is 0.0455 m/s, with a temperature of 298K. Auniform velocity 0.0988 m/s is specified for the air coflow with a temperature of 298 K. Themethane-jet is supplied at 3.71×10-6 Kg/s, or the Air is supplied at 2.214×10-4 Kg/s. The exitpressure is specified 105 Pa, whereas a zero-gradient pressure conditions is imposed at theinlet. The wall-function treatment is utilized at the walls. The fuel-jet and air coflowcompositions are specified in terms of the species mass fraction and based on the informationprovided about the experiment [5]. Figure 1. Geometry of confined axisymmetric laminar diffusion flame [5]. 61
  • 4. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEMEIn the present computation, the reaction rate is computed by finite-rate for laminar flow. The1-step and 4-step reactions are used in methane combustion (Tabs. 1-2).For the one-step global reaction. No. Reaction Ak βk Ek [j/molK] Reaction orders WD1 CH4+2O2 → CO2+2H2O 1.0e+12 0 1.0e+08 [CH4]0.5 [O2]1.25 Tab. 1. Westbrook and Dryer Global Multi-Step Chemical Kinetics Mechanism for CH4/air combustion and reaction rate coefficients [24].For the four-step reaction. No. reaction Ak βk Ek [Kj/mol] Reaction orders JL1 CH4+0.5O2 → CO+2H2 7.82e+13 0 30.0e+03 [CH4]0.5 [O2]1.25 JL2 CH4+H2O → CO+3H2 0.30e+12 0 30.0e+03 [CH4][H2O] JL3 H2+0.5O2 → H2O 1.21e+18 -1 40.0e+03 [H2]0.25[O2]1.5 JL4 CO+H2O → CO2+H2 2.75e+12 0 20.0e+03 [CO][H2O] Tab. 2. Jones Lindstedt Global Multi-Step Chemical Kinetics Mechanism for CH4/air combustion and reaction rate coefficients [25].3. GOVERNING EQUATIONS The description of a problem in combustion can be given by the the conservationequation of mass, momentum, species concentrations and energy. In primitive variabl wherex and r denote axial and radial coordinates, respectevely, incompressible conservationequations for an axisymmetric, laminar diffusion flame in cylindrical coordinates can bewritten as follows:For the mass: ∂ ρ(U ) 1 ∂( ρV ) (1) + =0 ∂x r ∂rx-momentum: ( ) ∂ ρU 2 1 ∂ (rρ UV ) ∂ P 1 ∂   ∂ U ∂ V  ∂  ∂U  + =− + rµ +  + 2 µ  ∂x r ∂r ∂ x r ∂ r   ∂ r ∂ x  ∂x ∂x (2) 2 ∂   ∂ V ∂ U V  −  µ + +  + ρg x 3 ∂ x   ∂ r ∂ x r r-momentum ( ∂ ( ρUV ) 1 ∂ rρ V 2) ∂ P 2 ∂  ∂V  rµ  2 V − µ 2 + ∂   ∂ U ∂ V  + =− +  µ +  ∂x r ∂r ∂r r ∂r  ∂r  r r ∂ x   ∂ r ∂ x  (3) 2 ∂   ∂V V ∂U  −  µ + +  3 ∂r  ∂r r ∂x   The density is computed from the ideal gas law. 62
  • 5. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME4. SPECIES TRANSPORT EQUATIONSThe conservation of species (i) transport equation takes the following general form [26]:  →  → ˆ∇ . ρ u Y i  = −∇ . J i + R i + S i (4)   Where Ri is the net rate of production of species i by chemical reaction and Yi is themass fraction of species i. An equation of this form will be solved for N-1 species where N isthe total number of fluid phase chemical species present in the system. Si is the rate of →creation by addition from the dispersed phase plus any user-defined sources. J i is thediffusion flux of species i, which arises due to concentration gradients. The diffusion flux inlaminar flows can be written as:→J i = − ρD,m ∇.Yi i (5) Here Di,m is the diffusion coefficient for species i in the mixture. The reactions rates thatappear in Equation (4) as source terms Ri can be computed from Arrhenius rate expressions.Models of this type are suitable for a wide range of applications including laminar orturbulent reaction systems, and combustion systems including premixed or diffusion flames.4.1. Treatment of species transport in the energy equation For many multi-component mixing flows, the transport of enthalpy due to speciesdiffusion n → ∇. ∑ hi J i  (6)  i =1  Can have a significant effect on the enthalpy field and should not be neglected. Inparticular, when the Lewis number: λLei = (7) ρC p Di ,mλ is the thermal conductivity. For any species is far from unity, neglected this term can lead to significant errors. Fluentwill include this term by default. In cylindrical coordinates equation (6) can be written as follows: 63
  • 6. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME ∂ ( ρUh ) 1 ∂ (rρ Vh ) 1 ∂  λ ∂ h  ∂  λ ∂ h  r +   + = ∂x r ∂r r ∂r  Cp ∂r  ∂ x Cp ∂ x      1 ∂  λ n ∂Cj  ∂  λ n ∂Cj  +  C ∑ j r r ∂r  ( ) h Le − 1 − 1 j  ∂xC ∑ j + ∂r   ( ) h Le − 1 − 1 j ∂x   p j =1  p j =1  (8)4.2. The laminar finite rate model The laminar finite-rate model computes the chemical source terms using Arrheniusexpressions, and ignores the effects of turbulent fluctuations. The model is exact for laminarflames, but is generally inaccurate for turbulent flames due to highly non-linear Arrheniuschemical kinetics. The net source of chemical species i due to reaction am computed s thesum of the Arrhenius reaction sources over the NR reactions that the species may participatein: NRRi = Mw,i ∑Ri,kˆ ˆ (9) k=1 ˆ Where Mw,i is the molecular mass of species i and Ri ,k is the molar rate ofcreation/destruction of species i in reaction k. Reaction may occur in the continuous phasebetween continuous phase species only, or at resulting in the surface deposition or evolution ˆof a continuous-phase species. The reaction rate, Ri , k , is controlled either by an Arrheniuskinetic rate expression or by mixing of the turbulent eddies containing fluctuating speciesconcentrations.4.3. The Arrhenius Rate Chemical kinetic governs the behavior of reacting chemical species. As explained earlier,a combustion reaction proceeds over many reaction steps, characterized by the productionand consumption of intermediate reactants. Several conditions determining the rate ofreaction are the concentration of reactants and the temperature. The concentration of thereactants affects the probability of reactant collision, while the temperature determines theprobability of the reaction occurring given a collision. In general, a chemical reaction can bewritten in the form as follows: N N∑υi,k Ai ⇔∑υ"i,k Aii=1 i=1 (10)WhereN = number of chemical species in the systemυi,k = Stoichiometric coefficient for reactant i in reaction kυ"i,k = Stoichiometric coefficient for product i in reaction kAi = chemical symbol denoting species ikf,k = forward rate constant for reaction kkb,k = backward rate constant for reaction k 64
  • 7. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME Equation (10) is valid for both reversible and non-reversible reactions. For non-reversiblereactions, the backward rate constant kb,k is simply omitted. The summations in Equation (10)are for all chemical species in the system, but only species involved as reactants or productswill have non-zero stoichiometric coefficients, species that are not involved will drop of theequation except for third-body reaction species. The molar rate of creation/destruction of ˆ ˆspecies i’ in reaction k, Ri ,k , in Equation (4) Ri ,k is given by:  N N η"   [ ] Ri ,k = Γ(υ"i,k − υ ,k ) k f,k ∏ C j j,k − kb,k ∏ C j j,k  ˆ η  [ ] (11)  j =1 j =1 Where:Cj = Molar concentration of each reactant or product species j [Kmol m-3]η j ,k = Rate exponent for reactant j’ in reaction kη"jk = Rate exponent for product j’ in reaction kΓ = represents the net effect of third bodies on the reaction rate.This term is given by: NΓ = ∑γ j,k Cj (12) jWhere γ jk is the third-body efficiency of the jth species in the kth reaction. The forwardrate constant for reaction k, kf,k, is computed using the Arrhenius expressionk f, k = Ak T βk exp (− E k /RT ) (13)Where:Ak = pre-exponential factor (consistent units)βk = temperature exponent (dimensionlessEk = activation energy for the reaction [J Kgmol-1]R = universal gas constant (8313 [J Kmol-1K-1])The values of υ i , k ,υ" , k ,η , k ,η" i , k , β k , A k , E k and γ j k can be provided the problemdefinition. If the reaction is reversible, the backward rate constant for reaction k, kb,k, iscomputed from the forward rate constant using the following relation: k f,kk b,k = (14) KkWhere k k is the equilibrium constant for the k-th reaction. Computed from: NR  ∆S k0 ∆H k  Patm ∑ (υ i ,k −υ i ,k )  k =1 0K k = exp   R −   RT  (15)  RT  Where Patm denotes atmospheric pressure (101325Pa). The term within the exponentialrepresents the change in Gibbs free energy, and its components are computed as follows: 65
  • 8. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME N 0∆S k ° S R = ∑ (υ" i,k − υ i,k ) i i = 1 R (16)∆H k0 N 0 RT = ∑ (υ " i ,k − υ i ,k ) hR i (17) i = 1Where S i0 and hi0 are, respectively, the standard-state entropy and standard-state enthalpyincluding heat of formation.5. SIMULATION DETAILS The governing equations are solved using the CFD package Fluent [26] modified withUser Defined Functions in order to integrate the reaction rate formula proposed byWestbrook et al. [24] and Jones et al. [25]. We have used finite-rate approach. Fluent wasutilized due to its ability to couple chemical kinetics and fluid dynamics. In computationalfluid dynamics, the differential equations govern the problem are discretized into finitevolume and then solved using algebraic approximations of differential equations. Thesenumerical approximations of the solution are then iterated until adequate flow convergence isreached. Fluent is also capable of importing kinetic mechanisms and solving the equationsgoverning chemical kinetics. The chemical kinetics information is then coupled into fluiddynamics equations to allow both phenomena to be incorporate into a single problem. Thereare many options to specify when setting up a computational fluid dynamics model. Theoptions used in this work are presented in Tabs. 3 and 4. Pressure 0.3 Density 0.5 Body forces 1 Momentum 0.7 Yi 0.9 Energy 0.4 Table 3. Under-relaxation factors. Solver Type Pressure Based Viscous Model Laminar Gravitational Effect On 2D-Space Axisymmetric Pressure-Velocity Coupling SIMPLE Momentum Equations Discretization First Order Upwind Species Equations Discretization First Order Upwind Energy Equations Discretization First Order Upwind Table 4. Computational model step. The SMPLE algorithm [27] of velocity-coupling was used in which the massconservation solution is used to obtain the pressure field at each flow iteration. The numerical 66
  • 9. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEMEapproximations for momentum, energy, and species transport equations were all set to firstorder Upwind. This means that the solution approximation in each finite volume wasassumed to be linear. This saved on computational expense. In order to properly justify usinga first order scheme, it was necessary to show that the grid used in this work had adequateresolution to accurately capture the physics occurring within the domain. In other words, theresults needed to be independent of the grid resolution. This was verified by runningsimulations with higher resolution grids. In a reacting flow such as that studied in this work,there are significant time scale differences between the general flow characteristics and thechemical reactions. In order to handle the numerical difficulties that arise from this, theSTIFF Chemistry Solver was enabled in Fluent. The STIFF Chemistry Solver integrates the individual species reaction rates over a timescale that is on the same order of magnitude as the general fluid flow, alleviating some of thenumerical difficulties but adding computational expense. For more information about thistechnique refer to Fluent [26]. Overall, the computational model solved the following flowequations: mass continuity, r momentum, x momentum, energy, and n-1 species conservationequations where n is the number of species in the reaction. The n-th species was determinedby the simple fact that the summation of mass fractions in the system must equal one. The combustion system, the vertical, cylindrical diffusion flame burner [5] as can be seenin Figure 2, consists of two concentric tubes through which the fuel and air issue,respectively. The burner nozzle was set as inlet with a uniform velocity normal to theboundary. The exhaust of the burner was set as an atmospheric pressure outlet. The wallswere set as adiabatic with zero flux of both mass and chemical species. Due to the geometryof the model, only half of the domain needed to be modeled since a symmetry conditioncould be assumed along the centerline of the burner. Figure 2. Schematic diagram of the laminar co-flow diffusion flame. 67
  • 10. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME The Computational domain and boundary conditions used are also shown. Thecomputational space seen in Fig. 2 given a finite volume mesh is divided by a staggered non-uniform quadrilateral cell (Fig. 3). The computational domain extends for 0.3 m after theburner nozzle, and 0.00508 m from the centerline. These dimensions correspond to 48djet and0.8djet, respectively. A total number of 1500 (50 × 30 ) quadrilateral cells were generatedusing non- uniform grid spacing to provide an adequate resolution near the jet axis and closeto the burner where gradients were large. The grid spacing increased in the radial and axialdirections since gradients were small in the far-field. Figure 3. Mesh of combustion chamber.6. RESULTS In this study, we investigate the effect of two mechanisms models 1-step globalmechanism [24] and 4-step mechanism [25] on the laminar diffusion flame. The 5 species ( 4-step) reduced mechanism has been implemented and tested in Fluent. Fluent has UDF capabilities to allow for such implementation. The precompiledmechanism was linked to the solver by the means of a User Defined Function (UDF). TheUDF communicates the chemical source terms the solver through the subroutine ‘Define NetReaction Rates’. The subroutine then returns the molar production rates of the species giventhe pressure, temperature, and mass fractions. The predictions from the present simulation arecompared with the experimental results [5] for the same operating conditions. Radialdistributions of temperature, axial velocity and major product species (CO2, H2O, CO, N2 andH2) concentrations at a height of 1.2 cm, 2.4 cm and 5 cm above the burner rim are shown.Clearly the figures show a good agreement between the predict values with 4-step mechanismand experimental values. We begin by comparing the computational cost of the two kinetic models in terms of theaverage CPU (execution) time per time step. The relative elapsed CPU times are compared inTable 5. Kinetic model Species Reaction CPU Nb. Time/iter. (s) iterations 1-step [WD] 05 01 0.00396 635 4-step [JL] 06 04 0.0454 2845 Table 5. Average execution time per time step. 68
  • 11. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME In the 4-step mechanism [25], more reaction equations are computed, them more CPUtime is spent and more difficult it is to convergence. That in general the computational costincreases with the number of reaction-step and species and more difficult it is to convergence. Figure 4 shows the contour plot of the temperature for temperature fields from thesimulation using the ‘WD’ and ‘JL’ mechanism (Fig. 4b and 4c) compared with experiment[5] (Fig. 4a). Is noticed that the smallest flame is predicted by the 1-step model ‘WD’,whereas the largest flame is predicted by the 4-step model ‘JL’ (Fig. 4c) and it is observedthat the predicted maximum temperature calculated for the laminar co-flow diffusion flameusing different chemical kinetic schemes for 1-step model is 2218 K, but in the 4-stepscheme, it is 1955 K. The maximum center-line temperature reported by Xu and al. is 2180K. The 1-step mechanism assumes that the reaction products are CO2 and H2O, the total heatof reaction is over predicted. In the actual situation, some CO and H2 exist in the combustionproducts with CO2 and H2O. This lowers the total heat of reaction and decreases the flametemperature. The 4-step mechanism includes CO and H2, so we can get more detailedchemical species distribution. Figure 4. Shape and size of the flame CH4/Air. The maximum temperature predicted by the detailed-chemistry schemes (4-step) aremuch closer to the experimental results in literature [6-7] than the results predicted by the 1-step mechanism, indicating the importance of finite-rate chemistry for diffusion flames of thistype. An accurate balance between transport and chemical reaction rates is needed to predictaccurately the flame temperature and this cannot be provided by simple one-step mechanismsfor the diffusion flame. Radial composition profiles of CH4 O2, CO2, H2O, CO, H2 and N2 atseveral axial locations (x=1.2, 2.4, 5.0 cm) are shown on fig. 5-9 and the test results for Xu etal. [5] are also shown. For O2, both results are the same and the 1-step global mechanism andthe 4-step mechanism over predict the CO2 concentration. From fig. 5-6 and 7, the H2O 69
  • 12. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEMEprofile first increases with radial distance, peaks at 7.5 mm in predicted result (Fig. 5-6) and6.75mm in experimental result and 5.25mm (Fig. 7) in predict result and 4.5 mm inexperimental result, then decreases to zero. The higher H2O concentration in the experimentaldata is caused by the moisture carried by the re-entrant flow from the exit due to recirculationin the burner. The comparison of H2 and CO is shown in Fig. 8 and 9. The 1-step model neglects the energy-absorbing pyrolysis reaction and over predicts thetemperature by about 200-250K. The 4-step model is lower than the experimental result by50-100K (Fig. 10, 11 and 12). The chemical reaction model mainly affects the species andthe temperature distribution and has a little effect on velocity. This disagreement between thenumerical and experimental data has been observed by Bhadraiah et al. [3], Liu et al. [7]and Mitchell et al. [28]. As well, even though they were employing a detailed chemistry as acombustion model. In fact, this over prediction is physically consistent with the highertemperature predictions and flame length that produces a large buoyancy force andrecirculation zone in the burner [13]. A comparison of species profiles obtained by thepresent study and by Xu et al.[5] showed that the present predictions are in better agreementwith the experimental data at the fuel side; however, the predictions of Xu and Smooke [5] atthe oxidizer side agreed more favorably with the data than those of the present study. Thisdiscrepancy may be due to the deployment solution of the governing equations in nonconservative and conservative forms and the numerical solution techniques utilized in thesetwo studies. The radial profiles of axial velocity for two axial locations are shown in fig. 13.The agreement between the prediction and measurement is very good. The axial velocityaway from the centreline decreases at all heights and becomes very low beyond a radialdistance [3-7]. 0,50 0,45 Exp. [5] CH4 Exp. [5] H2O 0,40 Exp. [5] O2 Exp. [5] CO2 0,35 4-step (JL) 1-step (WD) Mass Fraction 0,30 0,25 0,20 0,15 0,10 0,05 0,00 0,000 0,003 0,006 0,009 0,012 0,015 Radial distance (m) Figure 5. Radial profiles of the species mass fractions at x=1.2cm. 70
  • 13. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME 0,40 Exp. [5] CH4 0,35 Exp. [5] H2O Exp. [5] O2 0,30 Exp. [5] CO2 4-step (JL) 1-step (WD) 0,25 Mass Fraction 0,20 0,15 0,10 0,05 0,00 0,000 0,003 0,006 0,009 0,012 0,015 Radial distance (m) Figure 6. Radial profiles of the species mass fractions at x=2.4cm 0,40 Exp. [5] O2 0,35 Exp. [5] CO2 Exp. [5] H2O 0,30 Cal. 4-step (JL) Cal. 1-step (WD) 0,25 Mass Fraction 0,20 0,15 0,10 0,05 0,00 0,000 0,003 0,006 0,009 0,012 0,015 Radial distance (m) Figure 7. Radial profiles of the species mass fractions at x=5cm. 71
  • 14. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME 0,05 Reduced mechanism (J-L)[25] Cal. x=5 cm 0,04 Cal. x=2.4 cm Cal. x=1.2 cm Exp. [5] x=1.2 cm Exp. [5] x=2.4 cm Mass Fractio of H2 0,03 Exp. [5] x=5 cm 0,02 0,01 0,00 0,000 0,003 0,006 0,009 0,012 0,015 Radial Distance (m) Figure 8. Radial H2 mole fraction profiles. 0,05 Reduced mechanism (JL)[25] Cal. x=2.4cm 0,04 Cal. x=1.2cm Cal. x=5cm Exp. [5] x=2.4cm Mass Fraction of CO Exp. [5] x=1.2cm Exp. [5] x=5cm 0,03 0,02 0,01 0,00 0,000 0,003 0,006 0,009 0,012 0,015 Radial distance (m) Figure 9. Radial CO mole fraction profiles. 72
  • 15. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME 2500 x=1.2cm Exp. [5] Cal. 4-step (JL) 2000 Temperature (K) Cal. 1-step (WD) 1500 1000 500 0 0,000 0,003 0,006 0,009 0,012 0,015 Radial Distance (m) Figure 10. Radial temperature profiles at x=1.2cm 2500 x=2.4 cm Exp. [5] 2000 Cal. 4-step (JL) Cal. 1-step (WD) Temperature (K) 1500 1000 500 0 0,000 0,003 0,006 0,009 0,012 0,015 Radial Distance (m/s) Figure 11. Radial temperature profiles at x=2.4 cm 73
  • 16. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME 2500 x=5 cm Exp. [5] 2000 Cal. 1-step (WD) Cal. 4-step (JL) Temperature (K) 1500 1000 500 0,000 0,003 0,006 0,009 0,012 0,015 Radial Distance (m) Figure 12. Radial temperature profiles at x=5cm. 3,0 Exp. [5] x=1.2 cm Exp. [5] x=5 cm 2,5 Cal. 4-step (JL) Cal. 1-step (WD) Cal. 4-step (JL) Cal. 1-step (WD) Axial Velocity (m/s) 2,0 1,5 1,0 0,5 0,0 0,000 0,003 0,006 0,009 0,012 0,015 Radial Distance (m) Figure 13. Radial profiles of axial velocity. 74
  • 17. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME7. CONCLUSION Numerical computations of axisymmetric laminar diffusion flame for methane in airhave been carried out to examine the nature of flame, distributions of velocity, temperature,and different species concentrations in a confined geometry. Different conservation equationsfor mass, momentum, energy and species concentration for reacting flows are solved in anaxisymmetric cylindrical co-ordinate system. The 1-steps and 4-step chemical reaction ofmethane and air has been considered to capture some of the features of chemical reactionmechanisms. The CFD model based on SIMPLE algorithm predicts velocity, temperature andspecies distributions throughout the computational zone of the cylindrical burner. The predictions from the model match well with the experimental results available inthe literature [5, 28]. That in the general, in the 4-step mechanism, the presence of CO and H2lowers the total heat release and the adiabatic flame temperature is below the values predictedby the 1-step global mechanism and the smallest flame is predicted by the global reaction,whereas the largest flame is predicted by the 4-step mechanism. The results are much closerto the real situation. With engineering consideration for calculation time (or cost) andaccuracy, it recommended to adopt the 4-step mechanism. This study constitutes the initial steps in the development of an efficient numericalscheme for the simulation of unsteady, multidimensional combustion with stiff detailedchemistry.NomenclatureAi Chemical symbol denoting species iAk Pre-exponential factorCp Specific heat [J kg-1K-1]Cj Molar concentration of each reactant or product species j’ (Kmol m-3)Di,m Diffusion coefficient for species i in the mixturedjet Diameter of gas jet [mm]da Diameter of air jet [mm]E Energy totalEk Activation energy [Kj mol-1]gx Acceleration of gravity [m s-2]hi0 Standard-state enthalpyhi Enthalpy of species i [J kg-1]Ji Diffusive flux of species i[mol m-2 s-1]Jq Heat flow caused by the diffusive flux [J m-2 s-1]k k Equilibrium constant for the k-th reactionkb,k Backward rate constant for reaction kkf,k Forward rate constant for reaction kLe Lewis numberMw Molecular weight [Kg mol-1]Mw,I Molecular mass of species iN Number of species in the reactionP Absolute pressure [Pa] 75
  • 18. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEMEqr Heat radiation [J]r Axial coordinates [mm]R Universal gas constant [J Kmol-1K-1]Ri Rate chemical reaction of species iSi Rate of creation by addition from the dispersed phase [mol m3s-1]S i0 Standard- state entropyT Temperature [°K]U Axial velocity [m s-1]V Radial velocity [m s-1]x Radial coordinates [mm]Yi Mass fraction of species iGreek symbolsµ Dynamic viscosity [kg m-1 s-1]υi’ ,k Stoichiometric coefficient for reactant i in reaction kυj’’,k Stoichiometric coefficient for product i in reaction kρ Density [Kg m-3]λ Thermal conductivity [Wm-1K-1]βk Temperature exponentΓ Net effect of third bodies on the reaction rateη j,k Rate exponent for reactant j’ in reaction kη"j,k Rate exponent for product j’ in reaction kAbbreviationsUDF User Defined FunctionsSIMPLE Semi-Implicit Method for Pressure-Linked EquationsWD Westbrook and DryerJL Jones LindstedtACKNOWLEDGMENTS We thank the research laboratory CNRS combustion and reactive systems (CNRSOrléans, France) for the interest, support and assistance they have brought to this work.REFERENCES[1] Chahine M., Gillon P., Sarh B., Blanchard J.N. and Gillard V., Stability of a laminar jetdiffusion flame of methane in oxygen enriched air Co-jet. Chia Laguna, Cagliari, Sardinia,Italy, (2011).[2] Tarhan T. and Selçuk N., Numerical Simulation of a Confined Methane/Air LaminarDiffusion Flame. Turkish J. Eng. Env. Sci. 27 (2003), 275 -290.[3] Bhadraiah, K., and Raghavan V., Numerical Simulation of Laminar Co-flow Methane-Oxygen Diffusion Flames: Effect of Chemical Kinetic Mechanism. Combustion Theory andModeling (2011), vol. 15, Issue 1.[4] Smooke, M. D., Mitchell, R. E. and Keys, D. E., Numerical Solution of Two-DimensionalAxisymmetric Laminar Diffusion Flames. Combustion Science and Technology (1989), 67:85 - 122. 76
  • 19. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME[5] Xu, Y., Smooke, M.D., Lin, P. and Long, M.B., Primitive Variable Modeling ofMultidimensional Laminar Flames. Combustion Science and Technology, 90, 289-313,(1993).[6] Law, K., and, Tianfeng L., An Efficient Reduced Mechanism for Methane Oxidation withNO Chemistry. 5th US Combustion Meeting, Paper # C17, Sandiego, Ca, March 25-28,(2007)[7] Liu F., Ju Y., Qin X., and Smallwood G. J., Experimental and Numerical Study of a Co-flow Laminar CH4/Air Diffusion Flames. Combustion Institute/Canadian Section (CI/CS)Spring Technical Meeting, Halifax, Canada, May 15-18, (2005).[8] Ellzey, J. L., Laskey, K. J. and Oran, E. S., A Study of Confined Diffusion Flames.Combustion and Flame (1991), 84: 249-264.[9] Li, S. C., Gordon, A. S. and Williams, F. A., A Simplified Method for the Computation ofBurke-Schumann Flames in Infinite Atmospheres. Combustion Science and Technology(1995), 104:75 –91.[10] Thomas S.N. and Smyth K.C., Comparison of experimental and computed speciesconcentration and temperature profiles in laminar, two-dimensional Methane/Air diffusionflame. Combustion Science and Technology (1993), Vol. 90, pp1-34.[11] Shmidt .D. J., Segatz, R. U. and Warnatz J., Simulation of laminar methane-air flamesusing automatically simplified chemical kinetics. Combustion Science and Technology,(2000) Vol. 113, pp. 3-16.[12] Northrup S. A., Groth C.P.T., Solution of Laminar Diffusion Flames Using a ParallelAdaptive Mesh Refinement Algorithm. AIAA Aerospace Sciences Meeting and Exhibit,(2005). Reno, Nevada.[13] Mandal B.K., Chowdhuri A.K. and Bhowal A.J., Numerical simulation of confinedlaminar diffusion flame with variable property formulation. International Conference onMechanical Engineering (ICME) 26- 28 December (2009), Dhaka, Bangladesh.[14] Smooke, M. D., Giovangigli, V., Reduced Kinetic Mechanisms and AsymptoticApproximations for Methane-Air Flames, Lecture Notes in Physics, 384 (1991), 2, pp. 29-47[15] Magel, H. C., Schnell, H., Hein, K. R. C., Simulation of Detailed Chemistry in aTurbulent Combustion Flow, Proceedings, 26th Symposium (International) on Combustion,Neapel, Italy, (1996), The Combustion Institute, Pitts burgh, Penn., USA, (1997), pp. 67-74[16] Westbrook, C. K., Applying Chemical Kinetics to Natural Gas Combustion Problems,Report No. PB-86-168770/XAB, Lawrence Livermore National Laboratory, Livermore, Cal.,USA, (1985).[17] Glarborg, P., Miller, J. A., Kee, R. J., Kinetic Modeling and Sensitivity Anal y sis ofNitrogen Oxide Formation in Well Stirred Reactors, Combustion and Flame, 65 (1986), 2,pp. 177-202[18] Miller, J. A., Bow man, C. T., Mechanism and Modeling of Nitrogen Chemistry inCombustion, Progress in Energy and Combustion Sciences, 15 (1989), 4, pp. 287-338.[19] Konnov, A. A., De tailed Reaction Mechanism for Small Hydrocarbons Combustion,(2000) Release 0.5, http://homepages.vub.ac.be/~akonnov/[20] Hughes, K. J., et. al., Development and Testing of a Comprehensive ChemicalMechanism for the Oxidation of Methane, International Journal of Chemical Kinetics, 33(2001), 9, pp. 515-538.[21] Smith G. P., et al., GRIMESH 3.0, http://www.me.berke ley.edu/gri_mech.[22] Westbrook, C. K., Dryer, F. L., Simplified Reaction Mechanisms for the Oxidation ofHydrocarbon Fuels in Flames, Combustion Sciences and Technologies, 27(1981), 1-2, pp.31-43.[23] Jones, W. P., Lindstedt, R. P., Global Reaction Schemes for Hydrocarbon Combustion,Combustion and Flame, 73 (1988), 3, pp. 233-249. 77
  • 20. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 1, January - February (2013), © IAEME[24] Westbrook C.K. and Drayer F.L., “simplified Reaction Mechanisms for the Oxidation ofHydrocarbon Fuel in Flames”, J. of Combustion Science and Technology, Vol.27, pp.31-43,1981.[25] Jones W. P., and Lindstedt R. P., Combustion and Flame 73, 233 – 249 (1988).[26] FLUENT. 2010. “Theory Guide: Release 12.0.” Last modified January 23, (2009).[27] Patankar, S. V., 1980, Convection and Diffusion”, Numerical Heat Transfer and FluidFlow. Hemispherical Publishing Corporation.[28] Mitchell, R. E., Sarofim, A. F. and Clomburg, L. A., Experimental and NumericalInvestigation of Confined Laminar Diffusion Flames, Combustion and Flame (1981),37: 227 -244.[29] Bounif. A., Aris. A., Gökalp. I., Structure of the instantaneous temperature field inlow Damköhler reaction zones in a jet stirred reactor". Combustion Science and Technology,(2000) C.S.T Manuscript No 98-09.[30] Claramunt K., Consul R., Pérez-Segarra C. D. and Oliva A., Multidimensionalmathematical modeling and numerical investigation of co-flow partially premixedmethane/air laminar flames. Combustion and Flame, (2004) 137:444–457.[31] Guessab A., Aris A., and Bounif A., Simulation of Laminar Diffusion Flame typeMethane/Air. Journal of Communication Science and Technology (2008), N. 6, pp. 25-30.[32] Tarun Singh Tanwar , Dharmendra Hariyani and Manish Dadhich, “Flow Simulation(CFD) & Fatigue Analysis (FEA) Of A Centrifugal Pump” International Journal ofMechanical Engineering & Technology (IJMET), Volume 3, Issue 3, 2012, pp. 252 - 269,Published by IAEME.[33] Manish Dadhich, Dharmendra Hariyani and Tarun Singh, “Flow Simulation (CFD) &Static Structural Analysis (FEA) Of A Radial Turbine” International Journal of MechanicalEngineering & Technology (IJMET), Volume 3, Issue 3, 2012, pp. 67 - 83, Published byIAEME.[34] Ajay Kumar Kapardar and Dr. R. P. Sharma, “Numerical And Cfd Based Analysis OfPorous Media Solar Air Heater” International Journal of Mechanical Engineering &Technology (IJMET), Volume 3, Issue 2, 2012, pp. 374 - 386, Published by IAEME. 78