Simulation of Piloted CH4 and Air Flame Aaron Khan Technical University of Madrid Combustion and Reactions Resume Piloted flame D is an experimental flame that will be used as a comparison for this report. ANSYS Fluent and its combustion simulation capabilities will be utilised to model this flow. The generated flame will be analysed utilising combustion theory and the results compared with experimental data. 1 INTRODUCTION Partially premixed combustion theory will be utilised to generate a turbulent piloted flame. The simulation set up was constructed in such a way as to match the experimental data for flame D (Barlow, 2007). The cylindrical flame will be modelled utilising a 2D axis-symmetric model to simply computation. The problem is set up with a partially premixed inlet, a burned inlet and a fresh oxidizer stream as shown in Figure 1. ANSYS Fluent was utilised to simulate the combustion and post process the data. The modelling decisions made and the flame analysis was discussed to justifying the selected regimes. 2 OBJECTIVES The objectives of this paper is to: - - Model Flame D via ANSYS Fluent, by constructing a 2D axis-symmetric model and create an appropriate mesh. Justify modelling sources via theory and results. A comparison between the simulation and experimental results will be made. 3 APPROACH To begin the model, a simple 2D set up was generated with a symmetry line to reduce computation. Figure 1: Model Configuration The turbulent flame has the below operating condition: 𝑈𝑗𝑒𝑡 = 49.6 𝑚 , 𝑅𝑒 = 22400 , 𝐷𝑗𝑒𝑡 = 7.2 𝑚𝑚 𝑠 𝑈𝑝𝑖𝑙 = 11.4 𝑚 , 𝐷 = 18.2𝑚𝑚 𝑠 𝑝𝑖𝑙 𝑈𝐶𝑜𝑓 = 0.9𝑚 𝑠 Figure 2: Geometry set up 4 SPATIAL/TEMPORAL DISCRETIZATION - Pressure: Second Order Upwind. Although being more computationally expensive, this method does provide a more accurate solution. If the difficultly of converging the solution becomes troublesome, using a first order for a handful of iterations will be beneficial. - Momentum: Second order upwind. Like the pressure, this method also increases accuracy but at the cost of computation and convergence. - - Turbulent kinetic energy: First Order Upwind. It is a first order discretization interpolation which is the easiest method to converge. However, it becomes only first-order accurate. Turbulent dissipation rate: First Order Upwind. - Progress Variable: Second Order Upwind. - Mean Mixture Fraction: Second Order Upwind. - Mixture Fraction Variance: Second Order Upwind. - Progress Variable Variance: Second Order Upwind. The system was defined using the below boundary conditions: - Velocity Inlet: Defines the velocity magnitude at the entry normal to the boundary at a specified turbulent intensity, viscosity ratio and temperature. - Pressure Outlet: Pressure is fixed at the outlet domain. Other parameters specified is temperature, turbulent intensity and viscosity ratio. - Symmetric Condition: Defines the condition where the - Wall: Defines a non-permeable boundary. The no slip condition is also applied. A simple face mesh was utilised in conjunction with conformal boundaries. The mesh was designed via edge sizing and to obtain an acceptable mesh. The statistics are shown below. 5 EXECUTION Fluent is run with double precision and in parallel with 8 cores and 1 GGPU. The solution set up utilised to run this simulation is given below: - Turbulence: realisable 𝑘 − 𝜖 model with standard wall function as the near-wall treatment. - The energy equation is turned on. - Solver: To simplify the simulation, the fluid is considered as incompressible. - Time: Steady - Scheme: SIMPLE - Spatial Discretisation Gradient: Green Gauss Cell based. The Green Gauss Theorem computes the gradient of the scalar at the cell centre. The particular method of cell based gradient evolution takes the arithmetic average of the values at the neighbouring cell centres. 1 (∇𝜙)𝑐0 = ∑𝑓 ̅̅ 𝐴𝑓 (Green-Gauss Theorem) 𝜙̅̅𝑓 ⃗⃗⃗⃗ 𝑣 ̅̅̅̅𝑓 = 𝜙𝑐0 −𝜙𝑐1 (Cell based gradient Evolution) 𝜙 2 The simulation was set up as partially premixed combustion. Due to the configuration with non-uniform equivalence ratios. The state relation is key in setting up solution of the combustion process by making assumptions of the chemical state and the flame front. Both the Chemical Equilibrium and the Steady Diffusion Flamelet assume that the premixed flame front is infinitely thin. The Flamelet Generated Manifold (FGM) assumes that the thermochemical states in a turbulent flame are similar to the states in a laminar flame. The solution is defined or tracked by the mixture fraction and progress variable. The FGM model allows the flame to be extinguished and the assumption of thin and intact flamelets is not a part of this model. This type of set up is predominately utilised for partially premixed combustion where majority of the incoming gas is premixed as is the gas of this flame. The model solves for not only the transport equations for the mixture fraction and reaction-progress, but also their variance. The mean reaction rate for the reaction-progress variable is calculated using a joint PDF of c and f: 1 1 𝑆̅𝑐 = 𝜌̅ ∫ ∫ 𝑆𝑓𝑙𝑎𝑚𝑒𝑙𝑒𝑡 (𝑓, 𝑐)𝑃(𝑓, 𝑐) 𝑑𝑐 𝑑𝑓 0 0 It is important to note that 𝑓 and 𝑐 are considered statistically independent and hence the joint PDF is the product of the marginal ones. The premixed c equation model was implemented in this combustion model. The instantons transport C equation is: 𝜕(𝜌𝑐) + ∇. (𝜌𝑣𝑐) − ∇. (𝜌𝐷∇𝑐) = 𝑆𝑐 𝜕𝑡 For the turbulent flow, averaging and closing the turbulent flux of 𝑐 results in: 𝜕(𝜌̅ 𝑐̃ ) 𝜇 + ∇. (𝜌̅ 𝑣̃𝑐̃) − ∇. ( ∇𝑐̃) = 𝑆̅𝑐 𝜕𝑡 𝑆𝑐𝑡𝑐 𝑆̅𝑐 = 𝜌𝑢 𝑠𝑇 |∇𝑐̅| This closure term dependence is shifted to the turbulent flame speed which is discussed below. Flame surface density models propose the modelling of the average reaction rate 𝑆𝑐̅ for the reaction progress variable as two distinct components. The first is a flame density and an average flame consumption speed along the flame area. One such model that is available is that of the Extended Coherent Flamelet Model (ECFM). Its formulation is a more refined premixed combustion model than the C-equation model and has a theoretical greater accuracy. However, this advantage is at the expense of robustness and therefore is significantly more challenging to converge. It is for this simplicity, that the C-equation model is utilised. The Peters flame speed model predicts a higher value than Zimont. 6 RESULTS The simulation results indicate a successful simulation. Figure 3 illustrates how the temperature changes closer to the flame centre. It is evident from Figure 10, Figure 11 and Figure 12 that the temperature should reach a maximum near the edge of the flame. This is due to the configuration of the flame and is justified by the temperature contour. The most interesting result is that of the turbulent flame speed, shown in Figure 8. It seems to be at a maximum at the boundary of where the fuel source is and the heat source. This results is indicative of the wrinkled flame front, where there is extreme chemical and turbulent fluctuations. The laminar flame speed seems to uniform further away from the reaction zone. However, closer to the fluctuations, the turbulence Figure 6, show the effects of this wrinkling and stretch the propagating laminar flame sheet increasing the sheet area. The results of this can be seen through the increase in laminar flame speed Figure 7. Turbulent flame speed is an important concept in turbulent combustion and its closure is important in obtaining accurate results. Unlike the laminar flame speed, which is dependent on mixture properties, the turbulent flame speed has a dependency on flow conditions. This additional dependency requires the turbulent flame speed to be modelled. The most commonly used empirical model relates the unstrained laminar flame speed and the turbulent velocity formulation in the larger scale: 𝑛 𝑢′ 𝑠𝑡 = 1 + 𝐶 ( 0) 𝑠𝐿 𝑠𝐿 Rather more complex formulations have been proposed, Zimont and Peters Flame Speed models. The Zimont Turbulent Flame Speed Model is based upon the assumption of small scale turbulence inside the laminar flame is in equilibrium. This results in a turbulent flame speed model that that is purely a function of the large-scale turbulent parameters. This model is only applicable when the Kolmogorov scales are smaller than the flame thickness. 3 1 1 1 𝑈𝑡 = 𝐴(𝑢′ )4 𝑈𝑙2 𝛼 −4𝑙𝑡4 Figure 3: Contours of Temperature Figure 4: Contours of Velocity Magnitude Figure 7: Contours of Laminar Flame Speed Figure 5: Contours of Static Pressure Figure 8: Contours of Turbulent Flame Speed Figure 6: Contours of Turbulent Kinetic Energy Figure 9: Contours of Turbulent Flame Speed Source Figure 10: Contours of Mass Fraction of CH4 Figure 13: Contours of Damkohler Number 7 CONCLUSION AND FUTURE WORK A mesh study conducted with various models should be conducted and a comparison of results should be displayed. Further work should be perform comparing the various turbulent flame speed models as well as the effect of adiabatic model comparison. Figure 11: Contours of Mass Fraction of N2 In conclusion, the simulation was successful, with justification of modelling choices made and combustion results analysed. 8 REFERENCES Barlow, R. S.-Y. (2007). Piloted Methane/Air Jet Flames: Realease 2.1 . Madrid, T. U. (2016). Chapter 1: Reaction and Transport. Master´s Degree in Numerical Simulation in Engineering with ANSYS,. Technical University of Madrid. Madrid, T. U. (2016). Chapter 2: Laminar Premixed Flames. Madrid: Technical University of Madrid. Figure 12: Contours of Mass Fraction of O2 Madrid, T. U. (2016). Master´s Degree in Numerical Simulation in Engineering with ANSYS,. Chapter 6: Turbulent Premixed Combustion. Techical University of Madrid. 9 APPENDICES