Paper # 070IC-0192 Topic: Internal Combustion Engines 8 th US National Combustion Meeting Organized by the Western States Section of the Combustion Institute and hosted by the University of Utah May 19-22, 2013. PDF-based simulations of in-cylinder combustion in a compression-ignition engine V. Raj Mohan 1, D.C. Haworth 1 and J. Li 2 1 Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA 2 Group Trucks Technology, Volvo Group, Hagerstown, Maryland 21742, USA A transported probability density function (PDF) model is used to simulate the in-cylinder combustion processes in a compression-ignition heavy-duty engine. Heavy-duty vehicles are substantial users of petroleum-based fuels and significant contributors to greenhouse-gas emissions. For these reasons, it is essential to improve the efficiency and reduce the emissions in compression-ignition engines. Several advanced combustion strategies have been explored recently with the goal of decreasing the fuel consumption in compression-ignition engines for heavy-duty vehicles. These strategies include higher pressures, lower temperatures, varying degrees of fuel/air premixing and/or multiple fuels. Therefore, the combustion model should be able to deal with mixed-mode turbulent combustion under widely varying thermochemical conditions and should also be able to accommodate the use of multiple fuels and arbitrary numbers of liquid fuel injection events per engine cycle. The transported PDF model has the distinct advantage of handling all these conditions in a direct manner with minimal approximations. In this paper, recent results from in-cylinder combustion simulations using the transported PDF model for several operating conditions for a heavy-duty engine are presented. The computed pressure traces agree reasonably well with experimental data and respond correctly to variations in engine operating conditions. More importantly, significant differences are found between the results obtained using the transported PDF model that explicitly accounts for the turbulence/chemistry interactions (TCI) and those obtained using a model that do not account for TCI. Marked differences are observed in the computed flame structure and the global quantities between the two models. These differences indicate the extent to which unresolved turbulent fluctuations in composition and temperature influence the mean chemical reaction rates in a compression-ignition heavy-duty engine. 1 Introduction With increasing concern about rising fuel prices, limited petroleum supplies and greenhouse-gas emissions, the call for more advanced, efficient and cleaner compression-ignition engines for heavy-duty vehicles is louder than ever. The number of vehicles on the road is increasing every day and the primary fuels used in their engines gasoline and diesel are derived from petroleum-based crude oil. The natural resources of petroleum are limited and hence there is an increasing demand for more advanced and efficient engines. To meet this demand for advanced, next-generation engines, there has been extensive research all over the world. Reference [1] gives an overview of recent directions in internal combustion engine research. 1
Over the past decade or two, several advanced combustion modes, viz., Homogeneous-Charge Compression-Ignition (HCCI), Low-Temperature Combustion (LTC), Premixed-Charge Compression Ignition (PCCI), High Efficiency Clean Combustion (HECC), Partially Premixed Combustion (PPC), Reactivity-Controlled Compression Ignition (RCCI) and others, have been explored. These advanced modes of combustion include strategies such as higher pressures, lower temperatures, varying degrees of fuel/air premixing, exhaust-gas recirculation (EGR) and/or multiple fuels. Therefore, the CFD models used to explore these advanced combustion modes should incorporate turbulent combustion models which can deal with mixed-mode turbulent combustion from kinetically controlled to turbulent-mixing controlled to premixed flame propagation, and from premixed to non-premixed reactants under largely unexplored thermochemical conditions. They must also be able to accommodate multiple fuels and multiple liquid fuel injection events per cycle. In addition, in chemically reacting turbulent flows such as in-cylinder flows, turbulent fluctuations are coupled with the reaction-rate chemistry in highly non-linear ways. Hence, the combustion models should be able to capture the interactions between the reaction-rate chemistry and the unresolved turbulent fluctuations in composition and temperature. The importance of these turbulence-chemistry interactions (TCI) on ignition, combustion and emissions has been established for engine-relevant conditions in earlier studies [2 6]. Transported probability density function (PDF) methods have the unique characteristic of allowing the best available gas-phase chemical mechanisms and other submodels (e.g., to capture physical processes such as liquid fuel sprays, soot and radiation heat transfer) to be carried directly into turbulent flames with minimal further approximations required to account for the effects of turbulent fluctuations [7, 8]. The PDF model can also deal with multiple combustion regimes without explicitly specifying any particular regime. Many CFD models for compression-ignition engine studies use combustion models which neglect the effects of TCI. For instance, a locally well-stirred reactor (WSR) model uses the cell-mean values of composition and temperature directly in the chemical mechanism, thereby ignoring the effects of TCI. This paper further explores the importance of TCI in compression-ignition engines by comparing results from in-cylinder combustion simulations in a heavy-duty engine using the PDF model and the WSR model. 2 Physical Models and Numerical Methods The mean momentum, pressure and turbulence model equations are solved using a segregated, pressure-based, time-implicit finite-volume method. The discretizations are second-order in space and first-order in time. A modeled transport equation for the joint PDF of species mass fractions and mixture specific enthalpy is solved using a hybrid Lagrangian particle/eulerian mesh (LPEM) method. The turbulence is modeled using a standard two-equation model. The turbulent transport terms in the PDF equation are modeled using the gradient transport model, and the scalar mixing is modeled using interaction-by-exchange-with-the-mean (IEM). To model gas-phase chemistry of diesel fuel used in experiments, a 40-species skeletal n-heptane chemical mechanism [9] is used. The liquid fuel-spray is modeled using a stochastic Lagrangian parcel method, where the liquid mass is represented by a finite number of statistical parcels. Each parcel represents a group of droplets having the same properties. These models are implemented in a commercial CFD code, STAR-CD [10]. 2
Table 1: Load and initial compositions for the four engine operating conditions Case 1 Case 2 Case 3 Case 4 Load Part-load Part-load Full-load Full-load O 2 18.68 16.51 17.89 18.84 N Initial composition (% mass) 2 75.72 75.26 75.55 75.75 CO 2 4.06 5.96 4.75 3.92 H 2 O 1.54 2.27 1.81 1.49 To simulate compression/expansion processes in the engine, a moving computational grid is generated in which one layer of cells deforms/expands at any instant of time while the size of all the other cells remains constant. Each layer of cells is removed, one at a time, during compression while the same layer of cells is added to simulate the expansion stroke. A 1/6th (60 degrees) wedge sector mesh represents a bowl-in piston compression-ignition engine. Intake and exhaust ports are not modeled. Simulations begin at 60 btdc and continue until 120 atdc. Four different engine operating conditions at 1213 rpm two at full-load and two at part-load are simulated to examine the effect of EGR and the response of the models at different load conditions. The fuel injector is mounted near the top of the chamber on the centerline, with the spray directed along the bisecting plane of the sector mesh and angled down into the bowl. Exhaust gas recirculation (EGR) is modeled by modifying the initial composition to include appropriate mass fractions of CO 2, H 2 O, O 2 and N 2 for a given EGR percentage. Table 1 shows the initial compositions for the four operating conditions. 3 Results and Discussion Figure 1 shows the comparison of the pressure traces predicted by the two models PDF model and WSR model with experimental data for the four different operating conditions. The predictions from the PDF model are in better agreement with experimental data than those from the WSR model. Clear differences can be observed in the pressure traces between the two models after the injection of the fuel, especially at the peak for all four operating conditions. For the PDF model, a notional particle representation is used, where the evolution of these particles yields the same one-point, one-time Eulerian PDF as the real fluid system. Therefore, there is a distribution of particle properties, and hence ignitability, in each cell for the PDF model compared to the local cell-level mean values for WSR model. This explains the lowering of the peak values for the PDF model which is in closer agreement to the measured data. Remaining differences between model and experiment may be from the simplified representation of the geometry and the spray model parameters. They could also be due to the difference in fuels used in experiments (diesel) and simulations (n-heptane). Significant differences are also observed in the computed flame structures between the two models - one that accounts for TCI (PDF model) and one which neglects TCI (WSR model). Figures 2 and 3 show the computed mean temperature and the mean OH mass fraction contours at 5 atdc 3
(a) (b) (c) (d) Figure 1: Computed and measured pressure traces versus crankangle degrees for the four operating conditions. Two computed profiles are shown: one for PDF model and one for WSR model. (a) case 1 (b) case 2 (c) case 3 (d) case 4. Figure 2: Computed mean temperature contours at 5 atdc for case 1 for the two models. Left half: WSR model. Right half: PDF model. 4
Figure 3: Computed mean OH mass fraction contours at 5 atdc for case 1 for the two models. Left half: WSR model. Right half: PDF model. (a) (b) (c) (d) Figure 4: Computed apparent heat-release traces versus crankangle degrees for the four operating conditions. Two profiles are shown: one for the PDF model and one for WSR model. (a) case 1 (b) case 2 (c) case 3 (d) case 4. 5
for case 1 respectively. It can be observed that the peak temperature is lower for the PDF model compared to the WSR model. Similarly, the peak OH level is lower and the profile is more diffuse with consideration of the unresolved turbulent fluctuations in composition and temperature, i.e. for the PDF model. This is consistent with the observations made in an earlier work for diesel-enginelike conditions [2]. The importance of TCI in predicting the combustion processes is further evident from the comparison of the computed apparent heat-release rates between the two models, as shown in Fig. 4. The PDF model spreads out the heat-release in time compared to the WSR model for all the operating conditions. This can also be understood in terms of the distribution of particle compositions and temperatures for the PDF model as opposed to the finite-volume cell-mean values for the WSR model. These differences are more pronounced in the part-load cases (Figs. 4(a) and 4(b)), for which the PDF model has been found to be more effective in predicting the in-cylinder combustion processes. 4 Conclusions Simulations have been performed for four engine operating conditions using the transported PDF model and the WSR model. A 40-species n-heptane chemical mechanism is used to model the gasphase chemistry. Marked differences are observed in the computed flame structure and in global quantities between the two models: one that accounts for TCI (PDF model) and one which neglects TCI (WSR model). The pressure traces are calculated and compared between the two models and with experimental data. The PDF model performs better in predicting the pressure traces for all the operating conditions compared to the WSR model, which clearly highlights the importance of turbulence-chemistry interactions in predicting the in-cylinder combustion processes. These differences are further evident in the computed flame structures and the heat-release traces, and can be attributed to the distribution of particle properties across all the cells for the PDF model compared to the finite-volume cell-mean values for the WSR model. The differences are more pronounced for the part-load operating conditions. Acknowledgments This research has been supported by the U.S. Department of Energy under award no. DE-EE0004232, and by the Volvo Group. The authors are grateful to CD-adapco for providing their STAR-CD CFD code to carry out this research. References [1] Reitz R.D., Directions in internal combustion engine research. Combust. Flame, 160 (2013) 1 8. [2] Bhattacharjee S., PDF modeling of high-pressure turbulent spray combustion for diesel-engine-like conditions. Ph.D. thesis, The Pennsylvania State University, University Park, PA, 2012. [3] Haworth D.C., A review of turbulent combustion modeling for multidimensional in-cylinder CFD. SAE Technical Paper No. 2005-01-0993 (2005). [4] Kung E.H., PDF-based modeling of autoignition and emissions for advanced direct-injection engines. Ph.D. thesis, The Pennsylvania State University, University Park, PA, 2008. 6
[5] Kung E.H. and Haworth D.C., Transported probability density function (tpdf) modeling for direct-injection internal combustion engines. SAE Technical Paper No. 2008-01-0969 (2008). [6] Pei Y., Hawkes E.R., and Kook S., Transported probability density function modeling of the vapor phase of an n-heptane jet at diesel engine conditions. Proc. Combust. Inst., 34 (2013) 3039 3047. [7] Haworth D.C., Progress in probability density function methods for turbulent reacting flows. Prog. Energy Combust. Sci., 36 (2010) 168 259. [8] Pope S.B., PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci., 11 (1985) 3039 3047. [9] Golovitchev V.I. (2000). Chalmers University of Technology, Gothenburg, Sweden; http://www.tfd.chalmers.se/valeri/mech.html. [10] CD-adapco (2012). See http://www.cd-adapco.com. 7