Simulation of Lifted Diesel Sprays using a newly developed Combined Level-set Flamelet Model 1* 1 S.Vogel , N.Peters 1 Institute for Combustion Technology RWTH Aachen University, Aachen, Germany Under lower temperature or very high Exhaust Gas Recirculation (EGR) the stabilization at the lift-off length (LOL) is caused by premixed flame propagation. A newly developed G-equation model coupled with Multiple Representative Interactive Flamelets (G-MRIF) is used to predict multiple auto-ignitions as well as premixed flame propagation. How- ever at high temperatures the numerical simulations strongly indicate that the lift-off length (LOL) is defined by auto- ignition. Introduction A method using statistical moments is employed This paper deals with the improvement of mod- according to Mauß [8] and Frenklach and Harris els for Diesel sprays. Pickett et al. [1, 2] observed [9]. that for very small Diesel sprays no detectable Laminar flame speeds were calculated using amount of soot is formed inside the flame. The the in-house code Flamemaster [10]. For these reason for this is the spatial separation of the fuel- calculations the previously described IDEA me- rich zones in the spray from the diffusion flame chanism was used. These calculations show that downstream. Because the lift-off length (LOL) is n-decane is consumed during first auto-ignition, in large there is enough time available to premix oxi- contrast to α-methyl-naphthalene, which is quite dizer and fuel. This results in a leaner and more stable. During this investigation, flame speeds then premixed-like combustion, where little soot is were calculated based on the full mechanism for formed. For this beneficial kind of combustion situations before and after first-stage auto-ignition. mode to occur, it is necessary that the resulting A similar investigation for n-heptane has been LOL is much larger than the liquid penetration done by Honnet and Peters [11]. If the upstream length of the fuel. conditions are those after first-stage ignition, calcu- lations fo n-heptane at 1 atm had shown a signifi- Computational Model cant increase in laminar flame speed. The resulting The CFD code used in this work is AC-FluX flame speed at the elevated pressures for the (formerly known as GMTEC), a flow solver based IDEA fuel is not very different for the two cases; on Finite Volume methods [3] which employs un- therefore it is possible to use the speed before structured, mostly hexahedral meshes. AC-FluX is auto-ignition. Hence, only one laminar flame speed documented in detail by Khalighi et al. [4] and in table was used in this paper; an example for 50 particular by Ewald et al. [5]. AC-FluX solves for bar is shown in Fig. 2. This flame speed calcula- the partial differential equations of continuity, the tions are used to fit splines for a flame speed table Navier-Stokes equations, an equation for the total according to Ewald [12]. Therefore gaps as they enthalpy, and two equations modeling the turbu- appear in Fig. 1, which are caused by non- lence (k-epsilon-model). converging calculations, are filled. The applied spray model is a Discrete Droplet Model (DDM) and is the standard technique for current combustion codes. The applied breakup model (Kelvin-Helmholtz-Rayleigh-Taylor) was developed at the Engine Research Center (ERC), and was first introduced by Patterson and Reitz [6]. Collision and evaporation are based on the work by Amsden et al. [7]. A surrogate fuel for Diesel called IDEA consist- ing of 70% n-decane and 30% α-methyl- naphthalene (in volume) was developed within the Integrated Development on Engine Assessment (IDEA) project. IDEA has nearly the same chemical and physical behavior as European Diesel. The complete chemical reaction mechanism comprises 999 elementary reactions and 116 chemical spe- cies. The formation, growth, and oxidation of soot particles is described by a kinetically based model. Fig. 1: Laminar flame speeds at 50 bar * Corresponding author: s.vogel@itv.rwth-aachen.de Towards Clean Diesel Engines, TCDE2009 For non-premixed combustion, oxidator and fuel auto-ignition), and the other state is behind the are mixed during combustion. In conventional Di- flame front (burning). The two flamelet solutions esel modes, the heat release is mainly controlled are identical untill a significant fuel mass of a cer- by diffusion and evaporation. Evaporation is con- tain injection reaches a flame front. If a certain trolled by the injection rate (mass-flow rate, injec- amount gets burnt by the turbulent flame front, one tion velocity) and by the resulting breakup effect. of the flamelet pairs is artificially auto-ignited. The The Representative Interactive Flamelet concept remaining fuel mass is still able to auto-ignite. If a (RIF) [13] allows taking elementary chemistry into natural auto-ignition happens, the G-field is reinitia- account by solving the flamelet equations for the lized. temperature and many chemical species. There- fore, a much more complex chemistry can be Experimental setup of the Aachen vessels solved. The turbulent flow provides the scalar dis- The Aachen measurements presented in this sipation rate which is a parameter in the flamelet work were conducted in two different constant- equations χ and the average pressure p. The ex- flow, high-pressure, high-temperature vessels. The tended RIF concept G-equation model coupled pressure was set up to 50 bar and the temperature with Multiple Representative Interactive Flamelets to 800 K. The energizing duration was 3.5 ms for (G-MRIF) to be used here subdivides the injected all investigated cases. The air stream consisted of fuel mass during the time of injection and thereby pure air and Diesel was used as fuel. The data defines different flamelets. Additionally it also de- was acquired from two different vessels. One was scribes the flame propagation through the G- operated by the Lehr- und Forschungsgebiet La- equation which tracks the turbulent flame front The ser-Messverfahren in der Thermofluiddynamik injected fuel is portioned by injection timing into (LTFD) and the other by the Lehrstuhl für Wärme- different fuel classes, which can be seen in Fig. 2. und Stoffübertragung (WSA). Data on the investi- gated nozzles may be found in table (1). Tab. 1: Investigated nozzles Fig. 2: Definition of the flamelets according to the in- OH was measured using chemiluminescence jection time, based on mass criteria as described in Pauls et al. [14]. The soot mea- surement was made using Laser Induced Incan- The G-equation model is based on the assump- descence (LII) as described in Vogel et al. [15] tion that the instantaneous, turbulent flame, being an ensemble of laminar flamelets, is a thin reac- Simulation setup tive-diffusion layer, embedded in an inert turbulent The computational domain is 18 cm long and flow field. The structure of the laminar flame is has a diameter of 12 cm. The grid has a resolution resolved by the laminar flame speed calculations of about 2.4 mm at the investigated area. Through employing finite-rate chemistry, which provide the local refinement using a maximum level of 3, the laminar bruning velocity sL and the laminar flame resulting grid dimension is about 0.3 mm within the thickness lF. The G-equation model is not only main combustion region. Fig. 3 shows the compu- applicable in the corrugated flamelet regime, but tational domain and the applied local refinement, also in the thin reaction zone regime, since the which allows a very good grid resolution in the effect of turbulence on the structure of the flame- area of interest. The 131 μm nozzle at 1350 bar lets can be taken into account [13]. After a certain injection pressure was used to calibrate the injec- temperature is reached through auto-ignition, a tion parameter. The initial injection parameters flame front is initialized using the G-equation ap- were applied according to Weber et al. [16]. proach. In the G-MRIF model two chemical states A slight recalibration was necessary to adopt are present for every injected flamelet. One is the the spray parameters to the used grid. The values solution in front of the flame front (in the stage of are sufficient for the used application. An improved calibration is made impossible by computational combustion mode is called Auto-Ignition-Induced restrictions (runtime is over two weeks for a single Flame Front (AIIF) by the authors. Recent results case). The ambient condition was chosen as T = show separated second auto-ignition spots be- 800 K and p = 50 bar according to the experiment. tween the flame front and the nozzle, which is a The injection quantities and the injection rates strong indicator that in the experiments the LOL is were taken from Bosch-Tube data at p = 600 bar, also stabilized by auto-ignition, rather than by tur- 900 bar, and 1350 bar injection pressure using bulent flame propagation. standard Diesel fuel. The spray parameters were adopted to match the simulated liquid and gaseous Reference penetration with the experiment and were applied for the whole pressure range. The temperature at [1] L. Pickett and D. Siebers. Non-Sooting, Low Flame which the turbulent flame front is initialized is cho- Temperature Mixing-Controlled DI Diesel Combus- sen to predict the LOL. This temperature is kept tion. Paper No. SAE 2004-01-1399, 2004. [2] L. Pickett, D. Siebers, and C. Idicheria. Relationship constant for all Aachen simulations. The LOL is between ignition process and the lift-off length of di- defined as the shortest distance between the noz- esel fuel jets. Paper No. SAE 2005-01-3843, 2005. zle and the mean turbulent flame front. [3] J. H. Ferziger and M. Peric. Computational Methods for Fluid Dynamics. Springer, 2002. [4] B. Khalighi, S. H. El Thary, D. C. Haworth, and M. S. Huebler. Computation and Measurement of Flow and Combustion in a Four-Valve Engine with Intake Vari- ations. Paper No. SAE 950287, 1995. [5] J. Ewald, F. Freikamp, G. Paczko, J. Weber, D. C. Haworth, and N. Peters. GMTEC: GMTEC Develop- ers Manual. Technical report, Advanced Combustion GmbH, 2003. [6] M. Patterson and R. Reitz. Modeling the Effects of Fuel Spray Characteristics on Diesel Engine Com- bustion and Emission. Paper No. SAE 980131, 1998. [7] A. A. Amsden, P. J. O’Rourke, and T. D. Butler. KIVA II: A Computer Program for Chemically Reactive Flows with Sprays. Technical Report LA-11560-MS, Los Alamos National Laboratories, 1989. [8] F. Mauß. Entwicklung eines kinetischen Modells der Fig. 3: Cutout of the computational grid Rußbildung mit schneller Polymerisation. PhD thesis, RWTH Aachen, 1997. [9] M. Frenklach and S. J. Harris. Aerosol dynamics Results and Discussions modeling using the method of moments. J. Coll. In- terf. Sci., 118:252–261, 1987. [10] H. Pitsch. Flamemaster, a c++ computer program for 0d combustion and 1d laminar flame calculations. Technical report, 2004. [11] S. Honnet and N. Peters. Burning velocity of n- heptane before and after the first stage ignition. Eu- ropean Combustion Meeting, 2003. [12] J. Ewald. A Level Set Based Flamelet Model for the Prediction of Combustion in Homogeneous Charge and Direct Injection Spark Ignition Engines. PhD the- sis, RWTH Aachen, 2006. [13] N. Peters. Turbulent Combustion. Cambridge Uni- versity Press, 2000. [14] C. Pauls, S. Vogel, G. Grünefeld, and N. Peters. Tab. 2: Experimental and simulated LOL Combined Simulations and OHChemiluminescence Measurements of the Combustion Process Using Dif- All results are shown in Tab. 2. The results ferent Fuelsunder Diesel-Engine like Conditions. Pa- show the right general trend. There are two things per No. SAE 2007-01-0020, 2007. noticeable. First, the LOL is increasing with de- [15] S. Vogel, C. Hasse, J. Gronki, S. Anderson, N. Peters, J. Wolfrum, and C. Schulz. Numerical simula- creasing nozzle diameter. Second, the decrease of tion and laser-based imaging of mixture formation, the LOL for the 118 μm nozzle in the simulation is ignition and soot formation in a diesel spray. In Proc. obvious. In the experiments, a decrease of the Combust. Inst., volume 30, pages 2029–2036. The LOL for 270 the 118 μm nozzle was found at 750 Combustion Institute, Pittsburgh, 2004. bar for Diesel and at 1100 bar for the IDEA mix- [16] J. Weber. Optimization Methods for the Mixture ture. For all investigated conditions of the Aachen Formation and Combustion Process in Diesel En- combustion vessel, the turbulent premixed flame is gines. PhD thesis, RWTH Aachen, 2008. stabilized by auto-ignition and therefore this kind of