32 nd International Symposium on Combustion, Montr ´ eal, QC, Canada (2008) - Paper Poster Modelling of Autoignition for Methane-Based Fuel Blends using Conditional Moment Closure Ahmad El Sayed, Adrian Milford and C´ ecile Devaud Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, Canada 1 Introduction Research on methane combustion is motivated by some exclusive features of natural gas such as its low cost, abundance, and low emissions. Natural gas is made of different hydrocarbons of varying concentrations, primarily methane. The strategy of using additives is increasingly utilized to enhance methane combustion and reduce emissions. In this study, first-order Conditional Moment Closure (CMC) is implemented to investigate the autoignition of non-premixed CH 4 , CH 4 /C 2 H 6 , CH 4 /H 2 , and CH 4 /N 2 - air mixtures over a wide range of pre-combustion air temperatures. Detailed and optimized chemical kinetics mechanisms are used for each fuel blend. The results are compared to shock tube experiments. 2 Conditional Moment Closure (CMC) ◮ The CMC method was formulated independently by Bilger and Klimenko for turbulent non-premixed combustion [1]. ◮ Fluctuation in scalar quantities such as the species concentrations and enthalpy (or temperature) are associated with the conserved mixture fraction. ◮ These scalar quantities are conditionally averaged on the mixture fraction, and their conditional transport equations are solved. ◮ In CMC, detailed chemical kinetics can be included at a low computational cost. 3 Shock Tube Experiments Shocktubefacility[2] Experiment Fuel is injected at high pressure and low tem- perature along the cen- treline of the shock tube into lower pressure pre- heated air for a specific duration. ExperimentalConditions[2] Injector diameter (d ) 0.275 mm Injection duration (t i ) 1.0 ms Fuel pressure (P i ) 120 bar Fuel temperature (T i ) 294 K Air pressure (P o ) 28.9 bar Air temperature (T o ) 1200-1400 K 4 Numerical Solution ◮ The standard k-ǫ model is used for the turbulent flow fields (CFD) calculations. ◮ CMC is implemented for the reacting flow calculations. ◮ The CFD and CMC calculations are decoupled based on the cold mixing assumption. ◮ The CMC equations are cross-stream averaged as Transient ∂ Q ∂ t = A Spatial Transport −  {〈u x |η 〉} R + −  D t 〈ρ〉 ˜ P ∂ (〈ρ〉 ˜ P ) ∂ x  R + −  ∂ D t ∂ x  R +  ∂ Q ∂ x + {D t } R + ∂ 2 Q ∂ x 2 + 1 2 {〈χ|η 〉} R + ∂ 2 Q ∂η 2 Micro−Mixing + 〈 ˙ ω |η 〉 〈ρ|η 〉 Chemical Source B where {F } R + =  R 0 F (t , x , r ) ˜ P (t , x , r ,η )rdr  R 0 ˜ P (t , x , r ,η )rdr ◮ The β -PDF is used to model the PDF ( ˜ P ) [1], Girimaji’s model [3] and the Amplitude Mapping Closure (AMC) [4] for the conditional scalar dissipation (〈χ|η 〉), the linear model for the conditional velocity (〈u |η 〉) and a first order closure for the source term (〈 ˙ ω |η 〉) [1]. ◮ Under the assumptions of no radiation and negligible pressure work, the equation above is valid for both species concentrations and enthalpy. ◮ CDS is used for diffusion, UDS for convection and the implicit scheme for the transient term. ◮ A 3-step fractional method (operator splitting) is implemented to solve sequentially for A, then B and finally A. ◮ CFD mesh: 0.1 m (length) × 0.029 m (radius) axisymmetric domain with 259×72 unevenly- spaced nodes in the axial and radial directions, respectively. ◮ CMC mesh: 63 unevenly-spaced nodes. ◮ The stiff ODE solver VODE [5] and CHEMKIN II [6] are employed. 5 Fuel Blends and Chemical Kinetics Mechanisms Mixture (% vol.) Mechanism Species Reactions 100%CH 4 UBC Mech 1.0 [7] 38 192 90%CH 4 + 10%C 2 H 6 UBC Mech 2.0 [8] 54 277 80%CH 4 + 20%H 2 UBC Mech 2.1 [9] 40 194 80%CH 4 + 20%N 2 UBC Mech 1.0 [7] 38 192 6 Ignition Results: ignition delay (t d ) & kernel location (Z ∗ k ) 100%CH 4 (Base Case) Z ∗ k = Z k d ∗ d ∗ = d  P i P o  1/2 0.7 0.75 0.8 0.85 0 0.5 1 1.5 2 2.5 1000/T (1/K) t d (ms) 100%CH 4 - Experimental 100%CH 4 - AMC model 100%CH 4 - Girimaji′s model 0.7 0.75 0.8 0.85 10 20 30 40 50 60 70 80 90 1000/T (1/K) Z * k 100%CH 4 - Experimental 100%CH 4 - AMC model 100%CH 4 - Girimaji′s model 90%CH 4 + 10%C 2 H 6 t d → -24% Z * k → -15% 0.7 0.75 0.8 0.85 0 0.5 1 1.5 2 2.5 1000/T (1/K) t d (ms) 90%CH 4 +10%C 2 H 6 - Experimental 90%CH 4 +10%C 2 H 6 - AMC model 90%CH 4 +10%C 2 H 6 - Girimaji′s model 100%CH 4 - AMC model 0.7 0.75 0.8 0.85 10 20 30 40 50 60 70 80 90 1000/T (1/K) Z * k 90%CH 4 +10%C 2 H 6 - Experimental 90%CH 4 +10%C 2 H 6 - AMC model 90%CH 4 +10%C 2 H 6 - Girimaji′s model 100%CH 4 - AMC model 80%CH 4 + 20%H 2 t d → -13% Z * k → ∼0 0.7 0.75 0.8 0.85 0 0.5 1 1.5 2 2.5 1000/T (1/K) t d (ms) 80%CH 4 +20%H 2 - Experimental 80%CH 4 +20%H 2 - AMC model 80%CH 4 +20%H 2 - Girimaji′s model 100%CH 4 - AMC model 0.7 0.75 0.8 0.85 10 20 30 40 50 60 70 80 90 1000/T (1/K) Z * k 80%CH 4 +20%H 2 - Experimental 80%CH 4 +20%H 2 - AMC model 80%CH 4 +20%H 2 - Girimaji′s model 100%CH 4 - AMC model 80%CH 4 + 20%N 2 t d → +7% Z * k → +8% 0.7 0.75 0.8 0.85 0 0.5 1 1.5 2 2.5 1000/T (1/K) t d (ms) 80%CH 4 +20%N 2 - Experimental 80%CH 4 +20%N 2 - AMC model 80%CH 4 +20%N 2 - Girimaji′s model 100%CH 4 - AMC model 0.7 0.75 0.8 0.85 10 20 30 40 50 60 70 80 90 1000/T (1/K) Z * k 80%CH 4 +20%N 2 - Experimental 80%CH 4 +20%N 2 - AMC model 80%CH 4 +20%N 2 - Girimaji′s model 100%CH 4 - AMC model 7 Chemical Kinetic Analysis Main reaction pathways. Rate of progress (mol/cm 3 .s). 0 0.1 0.2 0.3 0.4 0 10 20 30 40 50 60 η ∆Q T = ∆Q(t,x,η) - ∆Q(0,x,η) (K) 100%CH 4 (T o = 1294 K) 90%CH 4 +10%C 2 H 6 (T o = 1295 K) 80%CH 4 +20%H 2 (T o = 1292 K) 80%CH 4 +20%N 2 (T o = 1304 K) t = 0.55 ms x = 2.25 cm Conditional temperature distribution. 8 Ignition Scalar Dissipation 0.7 0.75 0.8 0.85 0 2 4 6 8 10 1000/T (1/K) {〈χ|η ign 〉} R + (s -1 ) 100% CH 4 90% CH 4 + 10% C 2 H 6 80% CH 4 + 20% H 2 80% CH 4 + 20% N 2 Results using AMC model Ignition conditional scalar dissipation rate of the dif- ferent mixtures using the AMC model [4]. Similar trends are obtained when Girimaji’s model [3] is employed. 9 Conclusions ◮ Reasonable agreement is obtained with the experimental data of Wu [2], with slight underpredictions and overpredictions at high and low air temperatures, respectively. ◮ Ignition delay (t d ) and kernel location (Z ∗ k ) decrease with increasing pre-combustion air temperatures. ◮ The scalar dissipation rate shows an opposite trend and ignition always occurs at low values. ◮ Ignition occurs on the lean side of stoichiometry (≈ 0.022). ◮ The effects of additives are well reproduced: ◮ C 2 H 6 additives decrease t d and Z ∗ k . ◮ H 2 additives decrease t d and do not affect Z ∗ k . ◮ N 2 additives increase t d and Z ∗ k . References [1] A.Yu. Klimenko and R.W. Bilger, Prog. Energy Combust. Sci. 25 (1999) 595–687. [2] N. Wu, Autoignition and emission characteristics of gaseous fuel direct-injection compression-ignition combustion, PhD thesis, University of British Columbia, BC, Canada. [3] S.S. 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