UMERICAL IVESTIGATIO OF THE TURBULECE- COMBUSTIO ITERACTIO I O-PREMIXED CH 4 /AIR FLAMES K. M. Saqr, M. M. Sies, and M. A. Wahid High-Speed Reacting Flow Laboratory, Faculty of Mechanical Engineering, Universiti Tenologi Malaysia, 81310 Sudai - Johor, Malaysia Email: haledsaqr@gmail.com Received 9 April 009; accepted 9 July 009 ABSTRACT The interaction between turbulence and combustion in non-premixed flames is numerically analyzed. The reaction rate is expressed as a function of the large-eddy time scale through applying the Spalding eddy dissipation model. The turbulence energy production and dissipation rates are simulated by the turbulence model. The reacting S equations were spatially discretized and solved through a finite volume scheme and a decoupled pressure-velocity approach, respectively. The flame was assumed to be steady-state, two dimensional and axisymmetric. The reported results include the velocity, temperature and turbulent reaction rate along the flame propagation field. It is found that the elevated augmentation of free stream turbulence intensity reduces the reaction zone significantly, hence, induces the flame extinction process. Keywords: CFD, Combustion, non-premixed flames, turbulence modeling, eddy dissipation model 1 ITRODUCTIO The numerical simulation of turbulent non-premixed flames encounters a major difficulty when it comes to calculating the reaction rate. This difficulty comes, in principle, from the interaction between turbulence and reaction regions (Magnussen, 1981). In non-premixed flames, combustion occurs on the interface between fuel and oxidizer. For this reason, the mixing rate, which radically depends on turbulence, controls the chemical reaction (Warnatz, 006). In the wor of Spalding (Spalding, 1970). the reaction rate is controlled by the largeeddy mixing time. This time equals to the ratio between the local TKE and its dissipation rate. Although turbulence is thought of as a promoting factor to several applied combustion processes, free stream turbulence can be an extinction driving factor for non-premixed flames. When the oxidant is introduced to the combustion chamber with certain turbulence intensity, it achieves good mixing with the fuel. evertheless, if such turbulence intensity is exceedingly high, the flame becomes unstable, feeble, and it is susceptible to extinct. This negative effect, theoretically, comes from the competition between mass and heat diffusion.
70 K. M. Saqr et al. When the turbulence intensity is very high, the interface between the fuel and oxidizer become very chaotic. This in return, prevents the flame from propagating in a homogenous and stable region. At one point, the reaction is both possible and impossible at very close instants of time. The theoretical study of such interrelationship must involve a robust method to express the reciprocating effects of turbulence and heat/mass diffusion of the reaction. Magnussen et al. proposed several mechanisms to couple the effect of molecular mixing due to turbulence and chemical reaction (Magnussen 1976; Magnussen 1981) and (Magnussen et al. 1979). Their most nown and established model is the Eddy Dissipation Model (EDM). The EDM is, in its essence, a modification of the Spalding eddy-brea-up model. The foundation of such wor is to pass over the influence of chemical inetics by replacing the chemical time scale of a certain one-step reaction by the turbulent time scale ( / ). This is based on the idea that the mixing of reactants and products is the factor that determines the chemical reaction rate, in a turbulent flow (Peters 000) Although EDM was firstly devised for premixed combustion, when it comes to integrating such model in a CFD code, it can be used to model non-premixed flames with a reasonable degree of accuracy. A finite volume solver would trac the mass fraction of fuel and oxidizer in each and every cell. The existence of a nonzero value for the turbulent time scale is strictly related with the mixing process. This close relationship comes from the coupling between the convection-diffusion equation for each specie, the conservation equations, and turbulence model equations. There are several variants of the turbulence model (Cebeci 004). The most well nown and established variants are the Launder and Spalding (Launder and Spalding 197), renormalization group (RG) model (Yahot and Orszag 1986), and realizable model (Shih et al. 1995). The ey differences between the three variants exist in the method of calculating turbulence viscosity, the turbulence diffusion of and, and the generation and destruction terms in the ε equation (Jiyuan et al. 008) and (Salas et al. 1999). In this paper, we use the turbulence model, coupled with the EDM, is used in order to investigate the effect of turbulence intensity in the air stream on the combustion characteristics and flow dynamics of methane-air non-premixed flames. The mathematical treatment of the problem is firstly highlighted, followed by an explanation of the implemented numerical method. The results are discussed in the final section of this paper. MATHEMATICAL MODEL The governing equations of the flow field are the reacting conservation equations in the XY Cartesian coordinates. The following assumptions are made to simplify the mathematical treatment of the problem: 1. The reacting flow is assumed to be steady-state. The effect of gravity (i.e. buoyancy) is neglected 3. Radiation heat transfer is neglected
umerical Investigation of the Turbulence-Combustion Interaction 71 4. Combustion is assumed to be stoichiometric and adiabatic (no heat transfer to surroundings) 5. Thermal energy created by viscous shear is neglected ( Br <<1) The governing equations, after simplification, are given below in their differential forms:.1 Conservation of Mass and Species Total mass conservation: V 0 Mass conservation for species V (1) Y () Where and are the mass diffusion velocity and reaction rate for species, respectively. The diffusive term in the equation is subjected to Y 1 0 (3) And the reaction rate is governed by 1 0 (4). Conservation of Momentum for a Reacting Flow p Y f x (5) x x y xx yx X direction: uv 1 p (6) y x y xy yy Y direction: vv Y f y.3 Conservation of Energy The following version of the energy equation was derived based on (Kuo 1986; Poinsot and Veynante 001; Peters 000): 1 h (7) 1 1 M V E p et h V where p V E h h Y 1 T T1 Cp dt (8)
7 K. M. Saqr et al. S V 3 1 T and S V V (9).4 Turbulence Modeling The turbulence model presented by (Spalding 1970) is used to model the turbulent inetic energy and its dissipation rate. Since the flow is treated according to the ideal gas low, only the effect of thermal compressibility is considered to influence the dissipation of turbulent inetic energy (Sarar and Balarishnan 1990). The turbulent inetic energy is obtained from the following equation: (10) t V P Dt t V C1 P C (11) where t C and Dt (1) RT Turbulence intensity is expressed as I 3 (13) u v.5 Combustion Modeling The current model adopts the EDM in order to calculate the effect of turbulent chemical reaction rate. This model taes the minimum of the following rates as the local average reaction rate in equation (Peters 000): Fuel Oxygen AY Fuel Y A Oxygen (14) (15) Products A B Y 1 Product (16) 3 UMERICAL METHOD
umerical Investigation of the Turbulence-Combustion Interaction 73 The computational domain represent a horizontal, axisymmetric reactive flow field, with 00 mm length and 0 mm height. Methane is injected from the left side, from a nozzle of 4 mm diameter. Air is injected in the same flow direction of methane, from a port which surrounds the methane inlet port with an net diameter of 16 mm. The flow field geometry is illustrated in figure 1. 00 mm 0 mm Air Methane Air Figure 1: The flow field geometry for the non-premixed flame The computational domain was spatially discretized to 8385 variable density quadrilateral grid cells as in figure. The flow field variables in each cell was assumed to have an average value at the cell center. This first order upwind scheme was used in order to calculate the pressure, velocity, and temperature through the discretization of equations (1) to (), (5) to (7) (Kari and Patanar 1989). A momentum-weighted averaging method was implemented in order to interpolate the cell-center velocity values to the face values (Rhie and Chow 1983). This technique aims to prevent the instability in the pressure calculations. b Figure : A schematic showing a section of the variable density grid. (a) high density (i.e. fine) grid (b) low density (i.e. coarse) grid The Semi-Implicit Method for Pressure-Lined Equations (SIMPLE) was used to couple the pressure and velocity iterative calculations (Patanar and Spalding 197). An implicit relaxation approach was also employed in order to stabilize nonlinear iterative solution convergence of the pressure field. a 4 RESULTS AD DISCUSSIO Six cases were solved in order to show the effects of inlet air turbulence intensity on the flame characteristics. The air to fuel ratio were fixed at 6.00 in all cases. The turbulence intensity varied from 5% to 100%. Table 1 lists the boundary conditions of the studies cases. Table 1. Boundary conditions of the six cases Case Inlet air turbulence intensity Total inlet mass flow a 5% 0.0035 g/s b 0% 0.0035 g/s c 40% 0.0035 g/s d 60% 0.0035 g/s e 80% 0.0035 g/s f 100% 0.0035 g/s
74 K. M. Saqr et al. Figure 3 shows the temperature pattern for the six cases. The temperature distribution indicates the reaction zone, which in turns, refers to the structure. It is clear that the first three cases are approximately identical in terms of the flame structure, holder, and temperature gradient. The reason behind such similarity is the dominance of the flame induced TKE over the free stream TKE. Thus, the reaction zone is formed and solely controlled by the turbulence generated from the interception between the fuel and air flow streams in the reaction zone. On the contrary, in the three cases corresponding to 60%, 80% and 100% free stream turbulence, the TKE generated in the flame flow field is less than such of the inlet air. Figure 4 draws a quantitative comparison of the flow field TKE and free stream TKE for the six cases. When the free stream TKE prevails over the flow field TKE, two major changes occur in the reaction zone. Firstly, the location of maximum temperature is withdrawn near to higher turbulence intensity (i.e. TKE), which is near to the air inlet port. Secondly, the interception between the inlet air stream, which contains higher TKE than the average of the flame flow field, creates a region of low turbulence intensity, as in figure 5. (a) (b) (c) (d) (e) (f) Figure 3. Flame temperature patterns of the six cases
umerical Investigation of the Turbulence-Combustion Interaction 75 In figure 4, it is clear that the TKE of the inlet air stream increases over the average TKE of the flame flow field starting from case (d). Referring to equation (14), region (I) in figure 4 has high turbulence intensity generated in the combustion zone than that provided in by the free stream turbulence. On the other hand, region (II) has higher turbulence intensity provided by the inlet air than that generated in the combustion zone. The effect of such disagreement is evident in the temperature pattern. Turbulence Kinetic Energy (m.s - ) 10 100 80 60 40 0 Air Free Stream TKE Average Flame Induced TKE I II 0 a b c d e f Figure 4. Comparison of air free stream TKE and average TKE of the flame flow field In order to verify the effect of the free stream turbulence on the reaction zone, a third evaluation is introduced for the axial velocity and turbulent reaction rate in the six cases, as in figures 5 and 6. The turbulent reaction rate is numerically observed to be consistent in the first three cases, as well as the axial velocity profile. This steadiness comes from the dependence of the turbulent reaction rate on the flow induced eddies. In the first three cases, the axial velocity, in fact, increases due to combustion. The heat released by combustion is converted to inetic energy increasing both axial velocity and TKE. The reaction zone length, in the first three cases, has a total axial length and maximum rate of 0.15 m and 0.009 g.mol/m 3.s, respectively. The flame propagation velocity reaches the maximum value of 97 m/s at the outlet. In contrast, in the last three cases, where the inlet air turbulence intensity is higher than the turbulence intensity produced by the strain rate of the flame flow field, the reaction zone is intensified near to the inlet port. Figure 5 compares the turbulent reaction rate and axial velocity profiles along the flame axis. The axial velocity, on the contrary from the previous cases, deteriorates after the reaction zone. The highest turbulent reaction rate exist in a region near to the air inlet port, where the turbulence intensity (i.e. TKE) is much higher than that developed downstream the flame propagation field. Turbulent reaction rate reaches a maximum value of one order of magnitude higher than that in the first three cases. However, the axial reaction zone length decreases drastically to 0.07 m. On the other side, the axial velocity profile taes a route that is strongly lied to the relationship between inlet TKE and the produced TKE. In this sense, the substantially high turbulence dissipation rate, ε, associated with the inlet air stream dissipates the produced TKE after the reaction zone. Case
76 K. M. Saqr et al. (a) (b) (c) Figure 5: Flame propagation velocity and turbulent reaction rate along the flame centerline for cases (a-c) (d) (e) (f) Figure 6: Flame propagation velocity and turbulent reaction rate along the flame centerline for cases (d-f)
5 COSLUSIO umerical Investigation of the Turbulence-Combustion Interaction 77 The effects of free stream turbulence on the non-premixed methane-air flame were investigated numerically. The implementation of the EDM with the -ε turbulence model revealed important information about the turbulence-combustion interaction. The elevated values of free stream turbulence were found to have negative effects on the combustion process and flame propagation. Such negative effects decrease the reaction zone size, and axial flame propagation velocity. The competition between the free stream turbulence and flow induced turbulent inetic energy, via the EDM perspective, were the theoretical foundation to justify such negative effects. Future research should verify these results by using different numerical techniques such as the probability density function and different turbulence models. Experimental investigation using laser diagnostics would reveal much more information about the turbulence-combustion interaction at these severe conditions. omenclature Br Cp E f h j Brinman number (dimensionless) Specific heat at constant pressure for species (j.g-1.-1) Stored energy per unit mass (j.g-1) Volume force acting on species in direction () Sensible enthalpy of species (j.g-1) Turbulence inetic energy (TKE) (m.s ) M Molecular weight of species (mol) P T Y Turbulence production (g.m-1.s-3) Temperature () Isentropic expansion factor (dimensionless) Mass fraction of species (dimensionless) Turbulent Prandtl number for, 1.3 (dimensionless) Reaction rate of species (s-1) Dynamic viscosity (g.m-1.s 1) Stress tensor as defined in [16] Dt Turbulent dilatation dissipation term C Constant, 1.44 1 C Constant, 0.09 C Constant, 1.9 h e p R V 1 Enthalpy of formation for species (j.g-1) Effective conductivity (W.m-1.-1) Pressure (Pa) Universal gas constant (dimensionless) Velocity components in X and Y directions (m.s-1)
78 K. M. Saqr et al. t Turbulent Prandtl number for, 1.0 (dimensionless) Macroscopic density (g.m-3) Diffusion velocity of species (m.s-1) Turbulent (eddy) viscosity Differential operator, Kronecer tensorial symbol REFERECES Cebeci T (004). Turbulence models and their application, Springer, pp. 5-9. Jiyuan T, Guan HY, and Chaoqun L (008). Computational fluid dynamics: a practical approach, Butterworth-Heinemann. pp. 50-7. Kari KC and Patanar SV (1989). Pressure-Based Calculation Procedure for Viscous Flows at All Speeds in Arbitrary Configurations. AIAA Journal, 7, pp.1167-1174 Kuo KK (1986). Principles of Combustion, John Wily and Sons. ew Yor, USA. pp. 61-7. Launder BE and Spalding DB (197). Lectures in Mathematical Models of Turbulence. Academic Press, London, England. Magnussen BF (1981). On the Structure of Turbulence and a Generalized Eddy Dissipation Concept for Chemical Reaction in Turbulent Flow. 19th AIAA Aerospace Science Meeting, Jan. pp. 1-15. Magnussen BF and Hjertager BH (1976). On mathematical models of turbulent combustion with special emphasis on soot formation and combustion. Magnussen BF, Hjertager BH, Olsen JG, and Bhaduri D (1979). Effect of Turbulent Structure and Local Concentration on Soot Formation and Combustion in CH Diffusion Flames. 17th International Symposium on Combustion (1978). Combustion Institute, Pittsburg, Pennsylvania, pp.1383-1393, Patanar SV and Spalding DB (197). A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. International Journal of Heat and Mass Transfer, 15, pp. 1787. Peters (000). Turbulent Combustion, Cambridge University Press. pp. 10-36. Poinsot T and Veynante D (001). Theoretical and umerical Combustion. R.T. Edwards Publishing. PA, USA. pp 16-1. Rhie CM and Chow WL (1983). umerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation. AIAA Journal, 1, pp.155-153.
umerical Investigation of the Turbulence-Combustion Interaction 79 Salas MD, Hefner J, and Saell L (1999). Modeling Complex Turbulent Flows, Springer. pp. 59-77. Sarar S and Balarishnan L (1990). Application of a Reynolds-Stress Turbulence Model to the Compressible Shear Layer. ICASE Report 90-18, ASA CR 1800. Shih TH, Liou WW, Shabbir A, Yang Z, and Zhu J (1995). A ew Eddy-Viscosity Model for High Reynolds umber Turbulent Flows - Model Development and Validation. Computers and Fluids, 4(3), pp. 7-38. Spalding DB (1970). Mixing and chemical reaction in steady confined turbulent flames. International 13th Symposium on Combustion. The Combustion Institute. Warnatz J, Maas M, and Dibble RW (006). Combustion: physical and chemical fundamentals, modeling and simulation, experiments, pollutant formation. Springer, pp. 13-6. Yahot V and Orszag SA (1986). Renormalization Group Analysis of Turbulence: I. Basic Theory. Journal of Scientific Computing, 1(1), pp. 1-51.