NUMERICAL SIMULATION OF A GASEOUS FUELED ( METHANE ) COMBUSTOR

ln this study the combustion characteristics of the turbulent combustion of a gaseous fuel (methane) in a cylindrical combustion chamber were predicted numerically. For this reason; the equation of continuity, momentum, energy, chemical reaction rate, turbulent kinetic energy and turbulent kinetic energy dissipation rate equations were solved in polar coordinates using the K-e turbulence model. The change of the axial velocity component, effective pressure, fuel mass fraction, mass fraction of the total combustion products, mass fraction of CO2 , turbulent kinetic energy, turbulent kinetic energy dissipation rate and total enthalpy in the 3-dimensional turbulent polar region were predicted for different angle positions. The results were presented for e = 72° for this study. The effect of fuel/air momentum was investigated on flow, heat and combustion characteristics. The chemical reaction rate was determined using the eddy-break up model. The design of combustors has relied almost exclusively on emprical methods previously. By the advances in computational fluid dynamics techniques, the modelling of combustion phenomena has been the subject of much research in recent years. The principle objective of this paper is the modelling of three dimensional turbulent flow phenomena. A threedimensional , steady and turbulent combustion involving chemical reaction is considered for this purpose. The numerical studies for predicting fluid flow and heat tansfer characteristics mostly use the k-e model fOf the turbulence[1, 2]. The popularity of this model is due to its capability of predicting a wide range of flows with minimum adjustement of the coefficients and its relative simplicity in formulation. Studies on gaseous turbulent diffusion flames mostly used the k-e turbulence model and one-step chemical reaction, such as [3]. They used the eddy-break-up combustion model and flux method radiation model. Khalil et. al [4, 5] investigated the flow and heat transfer characteristics of gas-fired furnaces for reacting flows. By comparing three combustion models, they found that two-delta and eddy-breakup models were more accurate. Nikjooy et. al [6] studied the modelling of jet and swirl stabilized reacting flows in axisymetric combustors. Ma et. al [7] developed a two-dimensional spray combustion code for investigating the spray flame in a gas turbine combustor. They studied heat and mass transfer in a liquidfueled gas turbine combustor numerically. They used the modified k-£ model to describe the turbulent flow field and the generalized Rasin-Rammler equation to evaluate the fuel droplet size distribution in the spray. Liou et. al [8] reported a numerical study of turbulent nonreacting and reacting flows in a ducted rocket combustor with an algebraic stress turbulence model and a finite-rate combustion model. Karasu et. al [9] reported a numerical study of separating and reattaching turbulent flow over backward-facing steps. The practical advantage of modelling studies for combustion units is that once such a model is developed one can predict the performance of the combustor without performing the experiments which is really a difficult task. Also before designing the equipment for combustion, one has to investigate the effect of certain conditions and parameters on the combustion process. The objective of this study is to investigate the effect of fuel-to-air momentum ratio on the performance of a gaseous fueled(methane) combustor for the steady state and reacting flow case in three dimensions. The effect of fuel-to-air momentum ratio was investigated on effective pressure, temperature distribution, axial velocity, composition of the combustion products and the unburnt fuel, the turbulent kinetic energy, turbulent kinetic energy dissipation rate and the total enthalpy along the combustion unit. The variation of these parameters with momentum ratio along the radial direction were also predicted. 2.1. Governing Equations In this study, we consider the problem of three-dimensional combustion unit containing turbulent flowing fluids, including chemical reaction. The schematic diagram of the combustion unit is shown in Figure 1. The equations of conservation of mass and momentum in the gas phase, the equation of energy are given below.

The design of combustors has relied almost exclusively on emprical methods previously.By the advances in computational fluid dynamics techniques, the modelling of combustion phenomena has been the subject of much research in recent years.The principle objective of this paper is the modelling of three dimensional turbulent flow phenomena.A threedimensional , steady and turbulent combustion involving chemical reaction is considered for this purpose.The numerical studies for predicting fluid flow and heat tansfer characteristics mostly use the k-e model fOf the turbulence [1,2].The popularity of this model is due to its capability of predicting a wide range of flows with minimum adjustement of the coefficients and its relative simplicity in formulation.Studies on gaseous turbulent diffusion flames mostly used the k-e turbulence model and one-step chemical reaction, such as [3].They used the eddy-break-up combustion model and flux method radiation model.Khalil et. al [4,5] investigated the flow and heat transfer characteristics of gas-fired furnaces for reacting flows.By comparing three combustion models, they found that two-delta and eddy-breakup models were more accurate.Nikjooy et. al [6] studied the modelling of jet and swirl stabilized reacting flows in axisymetric combustors.Ma et. al [7] developed a two-dimensional spray combustion code for investigating the spray flame in a gas turbine combustor.They studied heat and mass transfer in a liquidfueled gas turbine combustor numerically.They used the modified k-£ model to describe the turbulent flow field and the generalized Rasin-Rammler equation to evaluate the fuel droplet size distribution in the spray.Liou et. al [8] reported a numerical study of turbulent nonreacting and reacting flows in a ducted rocket combustor with an algebraic stress turbulence model and a finite-rate combustion model.Karasu et. al [9] reported a numerical study of separating and reattaching turbulent flow over backward-facing steps.The practical advantage of modelling studies for combustion units is that once such a model is developed one can predict the performance of the combustor without performing the experiments which is really a difficult task.Also before designing the equipment for combustion, one has to investigate the effect of certain conditions and parameters on the combustion process.The objective of this study is to investigate the effect of fuel-to-air momentum ratio on the performance of a gaseous fueled(methane) combustor for the steady state and reacting flow case in three dimensions.The effect of fuel-to-air momentum ratio was investigated on effective pressure, temperature distribution, axial velocity, composition of the combustion products and the unburnt fuel, the turbulent kinetic energy, turbulent kinetic energy dissipation rate and the total enthalpy along the combustion unit.The variation of these parameters with momentum ratio along the radial direction were also predicted.

Governing Equations
In this study, we consider the problem of three-dimensional combustion unit containing turbulent flowing fluids, including chemical reaction.The schematic diagram of the combustion unit is shown in Figure 1.The equations of conservation of mass and momentum in the gas phase, the equation of energy are given below.where Vr, Ve, Vz are the radial, polar and axial velocity components, respectively.

Momentum Equations
In cylindrical polar coordinates, the steady-state equations of motion may be conveniently presented in the following three-dimensional form with radial, polar and axial coordinates r, 8 and z, respectively.az az az .r Or az r 00 ae

Energy Equation
The equation of energy can be given as follows:

Turbulence Model
The effects of turbulence can be included in a number of ways of which either by decomposing the velocities into separate terms for the mean and fluctuating components (Reynolds decomposition) and adopting a suitable model for the resulting Reynolds stresses; or by substituting an "effective viscosity" in the existing equations consisting of the molecular viscosity augmented by its turbulent counterpart, !le (the effective viscosity).The latter, which is well known k-c model is normally used [1,2,9,10].This model involves two transport equations for the turbulence characteristics.One governs the distribution through the field of k, the local kinetic energy of the fluctuating motion; the other governs a turbulence characteritics of different dimensions, namely c, the energy dissipation rate [1,2,9,10].
For the turbulent flow the laminar viscosity, !l is replaced by an effective viscosity, !le given by: For the turbulence viscosity, !It described by the turbulence energy k and its dissipation rate c, is given by : where CD is a constant.This turbulence model includes five emprical constants with their recommended values given in Table 1 [10].

3. Combustion Model
In order to complete the formulation the mean reaction rate must be determined.In this work, methane is used to simulate the fuel-rich exhausted gases, a single-step finite-rate rxn is employed, and the stoichiometric combustion equation on a molar basis is

Where
The mean source term for fuel is calculated from standard kinetic rate expression using local temperature and species concentrations.Since the combustion processes in the combustor are mixing controlled under most conditions, the turbulent fluctiations can significantly alter the reaction rates; therefore an eddy break up model is incorporated into the combustion model to account for the turbulence-chemistry interaction.The mean source term for fuel is thus given by where the chemical kinetic parameters are A = 6.7 Xl0 12 , E = 48.4kcal/mol, a = 0.5,b = 0.2, c = 1.3 according to Westbrook and Dryer [11].When the values of unburnt fuel mass fraction Yfu and the mixture fraction f are known, the mass fraction of other species can be determined by the following relations [12] (15) ( 16) The governing partial differential equations for the conservation of mass, momentum, energy and chemical species for the gaseous phase are rearranged into a general form which can be written as: where the terms are convection (LHS), diffusion, and source terms.A finite domain technique is used for the solution of the equations, which comines features of the methods ofPatankar and Spalding [13].In the PHOENICS code used for the solution of the model equations, the space dimensions are discretized into finite intervals, and the variables are computed at only the finite number of locations at the so-called "grid points".These variables are connected with each other by algebraic equations (finite-domain equations) derived from their differential counterparts by integration over the control volumes or cells defined by the above intervals.Diffusive and source terms have already been discretised in relation to the grid points.The convective term, however, does not contain any information regarding the level of contribution by the neighbouring cells.There are several different discretisation schemes for the convective terms such as central difference, upwind, hybrid and power-law [14].The default in PHOENICS is the hybrid scheme which combines the benefits of central difference and upwind scheme [ 14].
In this study combustion and flow characteristics of methane in a cylindrical combustion unit using the k-E turbulence model and the eddy break up model for chemical reaction were investigated.The effect of fuel-to-air momentum ratio was investigated for this combustion problem.In these analysis, the inlet pressure 0.8 Mpa and the temperature were taken as 773 K.The inlet values of the simulation parameters are given in Table 2. Fuel air mixture and the secondary and the thirtiary air inlets were fed to the combustor in radial directions.The computations were done for a region of grids of lOx 13x6 in radial, axial and polar directions respectively.The turbulent kinetic energy and the turbulence kinetic energy dissipation rate for the air introduced with different velocities are given in Table 3.The vanation of effective pressure, axial velocity, temperature, mass fraction of the unbumt fuel and the mass fraction of CO2 in axial direction were shown for 8=72 and RIRo =0.4 for three fuel-to air momentum ratios (1) in Figures 2-6.As seen in Figure 2, the effective pressure along the length of the combustor increases with an increase in air velocity.Figure 3 shows a decrease in axial velocity with an increase in air velocity As seen in Figure 4, increasing 1 has no significant effect in temperature change along the length of the unit.In Figure 5, it is observed that there is a rapid decrease in mass fraction of unbumt fuel to Z/Zm = 0.4 and after that point not much decrease can be seen and as 1 increases fuel mass fraction values decrease.From Figure 6, mass fraction of CO2 decreases along the length of the combustor and with decreasing 1.In Figures 7-12, the variation of the mass fraction of total combustion products and the unbumt fuel, effective pressure and the temperature change along the radial direction are presented for 1=1.28.In Figure 7, a decrease in unbumt fuel mass fraction and an increase in product fraction are observed in radial direction.In Figure 8, at Z/Zm = 0.4 an increase in unbumt fuel fraction and a decrease in combustion products can be observed in radial direction.At Z/Zm = 0.7, both values show a decrease as seen in Figure 9.At Z/Zm = 0.118 rapid increase in effective pressure and temperature along the radial direction are observed and the pressure and the temperature reach to values of 1360 Pa and 2240 K, respectively (Figure 10).In Figures 10,11 and 12, the variation of effective pressure and temperature along the radial direction were shown for three different combustor lengths, Z/Zm =0.118, 0.40 and 0.70, respectively.As shown in Figure 10, at lower Z/Zm , pressure variation along the radius is more significant.The pressure at RIRo =1 reaches to lower temperatures for increasing Z/Zm.For example for Z/Zm = 0.40 (Fig. 11), the effective pressure is 880 Pa, and for Z/Zm =0.7, it has a value of about 320 Pa. at RIRo =1.The temperature change is more significant at Z/Zm =0.118.It reaches higher temperature at RIRo =1.At Z/Zm =0.118, T=2240 K, at Z/Zm =0.4 T= 1840 K; at Z/Zm =0.7, T= 1720 K. Lower Z/Zm values, temperature and pressure changes are more significant.

Pressure
In Figures 13-15, variation of turbulent kinetic energy, turbulent kinetic energy dissipation rate, and total entalpy along the combustor length for different fuel-to-air momentum ratios were presented for RIRo =0.4 and e = 72°.As seen from these plots, as 1 decreased variation of k, E and total entalpy shift to higher values.Variation of total entalpy along the radial direction for different fuel-to-air momentum ratios at three different positions along the combustor length were given in Figures 16-18.
As seen in these plots, total entalpy values increase as fuel-to-air momentum ratio decrease.It is observed that at the start of the combustion, entalpy variation does not change in radial direction (Figure 16).As it is observed from Figure 17 and 18, total entalpy change decrease with an increase in 1.
For turbulent reacting combustion in a cylindrical combustion unit, increasing the air flow rate from the surfaces of the cylinder, increases the effective pressure in the combustion unit, decreasec the axial velocity and for 1=0.85 lower than these values, no change in velocity can be observed.It is observed that there is not any significant effect of 1 on temperature.As J decreased, unbumt fuel mass fraction is decreased.Decreasing unbumt fuel fraction is a significant result in terms of air pollution as well as combustion efficiency and fuel economy.

Figure 2 .Figure 3 .
Figure 2. The variation of effective pressure (Pe) along the combustor length at different fuel-to-air momentum ratios