A first investigation on using a 1000+ species reaction mechanism for flame propagation and soot emissions in CFD of SI engines F.A. Tap *, D. Goryntsev, C. Meijer, A. Starikov Dacolt International BV (The Netherlands) 1. Introduction Amongst the various combustion models published in literature [1], the Flamelet Generated Manifold (FGM) [2] is a promising approach, combining detailed chemistry and turbulence-chemistry interaction models with engineering runtimes. In this study, the FGM combustion model is applied to a Port Fuel Injection (PFI) Spark Ignition (SI) engine. Dacolt has developed a portable FGM implementation [3] available for various CFD codes including ANSYS FLUENT, OpenFOAM, CONVERGE TM and FIRE TM ; Converge v2.2 [4] is used in this work. The FGM look-up tables are generated with Tabkin, a dedicated software program for the generation of CFD look-up tables for advanced combustion models [5]. The look-up tables are based on igniting homogeneous reactor chemistry calculations and have 6 dimensions: pressure, fresh gas temperature, Exhaust Gas Recirculation (EGR), mixture fraction, progress variable and progress variable variance. The simulated PFI SI engine case represents a default tutorial of Converge v2.2. Experimental data is not available for this case; as a reference, the case is computed with the default settings using the detailed chemistry combustion model (SAGE [4]). The chemical mechanism is read by the CFD code and solved in every cell (or cluster of cells when using the multi-zone approach) at every time step. The empirical Hiroyasu [4] soot model is used for a first estimate of soot formation and oxidation. With the Tabkin FGM model, the effects of the chemical mechanism and the effect of Turbulence- Chemistry Interaction (TCI) modeling on turbulent flame propagation and soot emissions are investigated. Two reaction mechanisms are investigated: 1. LIU: a 48-species iso-octane mechanism [6] as available from the Converge PFI SI tutorial; this mechanism is used both for detailed chemistry and FGM. 2. LLNL: a 1389-species gasoline surrogate model from Lawrence Livermore National Laboratories [7]; this mechanism is used only with Tabkin FGM. For the turbulence-chemistry interaction, in Tabkin FGM the TCI model is based on a presumed β-pdf model for the progress variable variance. Although this PDF shape may not be the most appropriate one to represent a turbulent premixed flame [1] it is quite a practical distribution from a numerical point of view. The use of the progress variable variance can be switched on or off, enabling or disabling the TCI model. 2. Engine case description The test case is a standard tutorial of Converge v2.2 named si8_sage_pfi. The simulation contains a 360º degree cylinder model including intake and exhaust ports and valve motion. The engines speed is 3000 RPM and iso-octane is used as surrogate fuel model. The computational domain and mesh are shown in Figure 1. The simulation starts during the exhaust stroke and ends at before Exhaust Valve * Corresponding author: ferry.tap@dacolt.com 1
Opening of the next cycle. The calculation includes the effect of residual gases and therefore simulation is initialized with burnt gases in the cylinder. In the intake system, a region near the intake valve contains a mixture of fuel and air. A peripheral part of the intake duct is initialized with air only. The fuel spray injection is initialized at 480.0 Crank Angle (CA) before Top Dead Center (TDC), the duration of injection is 191.2 CA. During the intake stroke, the mixing between fresh and burnt gases is simulated and hence the amount of trapped exhaust gas is determined from the fluid dynamics. Ignition spark timing starts 15º before TDC. The spark model is the default energy deposit model, where the spark is represented by an imposed energy source. Default settings are used in all simulated cases. Figure 1: Computational domain (left) and mesh (right). 3. Turbulence-chemistry interaction investigation Figure 2 presents the simulation results in terms of in-cylinder pressure (left) and apparent heat release rate (right) for detailed chemistry with the LIU mechanism (i), Tabkin FGM with the LIU mechanism without TCI (ii) and Tabkin FGM with the LIU mechanism with TCI (iii), respectively. Figure 2: In-cylinder pressure (left) and apparent heat release rate (right). The first observation is that the Tabkin FGM model without TCI burns much slower than detailed chemistry. For the Tabkin FGM case, the slow flame propagation speed is simply linked to the fact that the progress variable equation is propagated with laminar flame speed. In the detailed chemistry case, a reaction-diffusion system of equations is solved for and the flame speed is mainly driven by turbulent diffusion. The second observation is that the Tabkin FGM model with TCI burns faster than detailed chemistry and much faster than Tabkin FGM without TCI. The difference between the Tabkin FGM cases with and without TCI is explained by the difference between laminar and turbulent flame speed. Accounting for progress variable variance yields a broadened turbulent flame brush as to be expected from a RANS simulation [1], as illustrated in Figure 3 below. 2
Figure 3: Temperature contours for 8 CA snapshots. 4. Chemical mechanism investigation Figure 4 presents the comparison between Tabkin FGM simulations with the LIU mechanism and the LLNL mechanism, with the detailed chemistry results included as reference. The only observation to be made is that the pressure and apparent heat release rates are nearly identical for the two Tabkin FGM cases. This result is not intuitively expected given the large difference in mechanism size. However, the combustion happens at nearly homogeneous and nearly stoichiometric conditions. It seems the turbulent flame speed for these conditions is represented in a very similar way by both mechanisms. Figure 4: In-cylinder pressure (left) and apparent heat release rate (right). Figure 5 provides an impression of the (laminar) progress variable source term from the Tabkin table, as a function of progress variable. This progress variable source term is the driving mechanism behind the turbulent flame speed in the CFD simulation. The profiles are quite similar, with a difference in peak value. 3
Figure 5: Progress variable source term as function of progress variable, for Z=0.052, EGR=0.05, P=30 bar, T=900K. 5. Effect on soot emissions As a first step to investigate soot emissions modeling, the Tabkin FGM model is coupled to the Hiroyasu soot model in Converge 2.2 [4]. This model has an empirical formulation for soot formation and oxidation, relying on the acetylene soot precursor (C2H2). In the Tabkin FGM case, the C2H2 concentration is retrieved from the Tabkin FGM look-up table. Figure 6 shows the average mass fraction of C2H2 during the combustion cycle for the two mechanisms with the Tabkin FGM model including TCI. Interestingly, while the pressure curve is nearly identical, the C2H2 profiles are quite different with more than a factor 2 in peak value. This leads to soot mass at EVO as reported in Table 1, with a ~15% difference between the mechanisms. Figure 6: C2H2 mass fraction as function of CA. Table 1: Soot mass [kg] at EVO Mechanism CONVERGE-IC8 LLNL-GASOLINE Soot mass 5.76e-13 4.92e-13 6. CPU time The Tabkin FGM model allows investigating 1000+ species mechanisms in SI engine simulations. The computational cost for all cases is summarized in Table 2. 4
Table 2: Wall time on 32 CPU cores Detailed chemistry FGM without TCI FGM with TCI LIU 25 h 22 h 23 h LLNL 86 h Applying TCI only leads to a small overhead of look-up table generation with Tabkin. Going from 48 to 1389 species induces a significant increase in the time required for table generation with Tabkin, but the overall wall time for the Tabkin + CFD simulation process increases with a factor of 4 in wall time, as the CFD simulation is equally fast in both cases. When using 128 CPU-cores for Tabkin and 32 for Converge, the wall time for the entire simulation with LLNL can be reduced to 48 hours approximately. For the LLNL mechanism, running the detailed chemistry model is still out of scope from a practical point of view, as the estimated runtime is of the order of several months. 7. Conclusion The Tabkin FGM combustion model is used to simulate a PFI SI tutorial case in Converge 2.2. The use of chemistry look-up tables allows investigating both reduced and detailed reaction mechanisms at very modest computational cost. Also, turbulence-chemistry interactions can be easily switched on or off. Enabling or disabling TCI for this PFI SI engine leads to larger differences in flame propagation speed; without TCI, the flame propagates with laminar flame speed and is much slower than with TCI. With TCI, a broadened turbulent flame brush is observed, as would be expected from RANS simulation. For both the reduced and detailed chemistry mechanisms, the global flame behavior is very similar; the pressure curves coincide. Differences appear when looking at soot precursor C2H2, although eventually the observed factor 2 on the peak C2H2 values leads to a modest difference in cylinder-out soot mass. The results illustrate the relative importance of each key ingredient of the turbulent combustion model, e.g. chemistry and turbulence-chemistry interaction for the SI engine application. Comparison to actual engine data will provide further insights and is a next step for this work. With the Tabkin FGM model, it has been demonstrated that it is possible to run SI engine simulations with 1000+ species mechanisms within 48 hours. 8. References 1. T. Poinsot and D. Veynante, Theoretical and numerical combustion. R.T. Edwards (2001) 2. J.A. van Oijen and L.P.H. de Goey, Combust. Sci. Technol. 161 (2000), pp. 113 137 3. Tap, F. and Schapotschnikow, P., SAE Technical Paper 2012-01-0152 4. CONVERGE 2.2.0, Theory Manual. https://convergecfd.com/ 5. http://www.dacolt.com/tabkin 6. Y.-D. Liu et al., Energy Fuels, 26 (2012), pp. 7069 7083 7. M. Mehl et al., Proc. Comb. Inst. 33 (2011), pp. 193-200 5