Development of a comprehensive framework for cycle-resolved knock tendency evaluation through combined LES and Look-up table techniques

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1 Development of a comprehensive framework for cycle-resolved knock tendency evaluation through combined LES and Look-up table techniques Stefano Fontanesi, Alessandro d Adamo, Stefano Paltrinieri University of Modena and Reggio Emilia Christopher J. Rutland University of Wisconsin-Madison Cycle-to-Cycle variability (CCV) in a highly turbocharged GDI engine is simulated by means of Large-Eddy Simulation (LES) and the numerical framework is validated against experimental data at the test-bed at Knock Limited Spark Advance (). Moreover, the arising of knock makes mandatory the use of a very limited spark advance (SA), and to account for chemical kinetics of the unburnt gas a simplified look-up table approach has been coupled with the LES simulations. A chemical model for a gasoline surrogate to reproduce a European RON98 gasoline is chosen and simulations of the most extreme cycles are conducted at different SA to confirm the proximity of knock onset and the intake side of the combustion chamber is identified as the most knock-prone location.. INTRODUCTION Large-Eddy Simulation is widely accepted as the right tool to simulate CCV in internal combustion engines (ICE). Its application in multi-cycle simulations allows to study the unsteady phenomena causing CCV as well as their consequences, which strongly limit the engine setup. Several studies have been carried out in the latest years on the topic, as the computational cost of LES is becoming more and more affordable also for industrial research of complex geometries and flows, as the ones related to ICEs. In this work a V8 spark-ignition (SI) engine is modeled, with a pentroof head and 4 valves per cylinder. Following the recent trends of the SI engines, increase in engine efficiency are attained through the combined use of turbocharging and direct injection of gasoline (GDI). The experimental condition analyzed is the full load/peak power operating point, which resulted strongly limited by knock onset at the engine testbed. 2. NUMERICAL FRAMEWORK 2. Physical models The combustion simulations have been carried out by means of Star-CD v.4.7 provided by CD-adapco. The subgrid scale viscosity is modeled by means of the standard Smagorinsky model, and an ad-hoc version of ECFM-3Z is used, capable of accounting for both resolved and subgrid strain and curvature []. The ignition model used for the simulations is based on the imposition of a profile of partially burnt gas, needed to initialize the progress variable of the combustion model. The growth of the progress variable just after the spark time is demanded to a so-called Eulerian AKTIM model, based on the same physics as the RANS Lagrangian counterpart, but using the progress variable c as initial flame kernel tracer. As far as spray is concerned, the Reitz model for droplet breakup and the Bai one for droplet-wall interaction are adopted. No liquid film model is considered. An extended review of the status of LES modeling in ICE can be found in the work by Rutland [2]; in the context outlined the LES framework presented in this paper is addressed to as hybrid approach. Boundary conditions at the intake and exhaust ports are derived from a -D model of the whole engine, which was carefully tuned in terms of port gasdynamics through the comparison with experimental measurements by means of fast-response pressure transducers. Therefore, the adopted boundary conditions are periodic signals, and do not account for the slight cycle-to-cycle fluctuation detected during the post-processing of the raw data from the pressure and temperature probes; as a consequence, no CCV is directly imposed through the boundaries. However, in a previous work by the authors [3] the boundary-related CCV emerged as a negligible cause for CCV of in-cylinder phenomena, if compared to the randomness of both turbulence and mean flow structures originated during the flow through the valve curtains and the subsequent deviation below the exhaust valves, so the choice is considered acceptable. As far as wall temperatures are concerned, they are once again derived from the -D model of the same engine, as provided by the engine manufacturer. The wall heat transfer is modeled by the Angelberger model. The initial condition for the first LES cycles is a RANS cycle, tuned on the ensemble average pressure available trace from the

2 [ bar ] experiments. As it will be described later, the activity presented in the paper is derived from a previously carried out full-cycle one [3] [4] which was preliminary validated in terms of knock tendency []. For this latter, a complete mesh (with intake and exhaust ports) was used. In order to limit the computational cost of the simulations while accounting for the autoignition chemistry, just the closed-valve portion of the cycle is considered, i.e. the computational grid covers the in-cylinder domain, while both intake and exhaust ports are neglected; a cycle-specific solution mapping procedure is used to provide the initial conditions for the closed-valve LES simulations. The resulting mesh consists of about 23 cells at TDC and 78 at midcompression stroke. 2.2 Knock Model The model used for knocking prediction is based on the hypothesis of a single-stage autoignition behavior. The autoignition delay of the unburnt mixture depends upon the local values of pressure, temperature, equivalence ratio and residuals for each computational fluid cell, which act as input values for a multi-linear interpolating routine internally developed at Gruppo Motori of University of Modena and Reggio Emilia. The routine calculates an interpolated delay and this operation is performed at every iteration. The local delay governs the increase of the mass fraction of an intermediate fictitious species Y IG for autoignition as defined by Lafossas et al. [6]: dy IG dt = Y TF τ 2 +4( τ) Y IG YTF τ () The Y IG species accounts for the intermediate products and the radical pool formation that are responsible of the hightemperature autoignition. The numerical criterion used to trigger knock is the equality in the values of the mass fractions for the intermediate species Y IG and that of the fuel tracer Y TF, i.e. the fuel as a non-reactive species. Once this definition is adopted, it is immediate to define a derived scalar variable, called, as the difference between the two species (2): x, t = Y TF x, t Y IG x, t (2) As a final remark, this model is implemented as a passive tool to predict the arising of abnormal combustion in a postprocessing phase. For this reason, even in case of knock the in-cylinder pressure trace do not show the fluctuations which would be expected due to the impulsive heat release, but knock is identified in a post-processing stage by means of the Knock Tolerance function. 3. RESULTS AND DISCUSSION 3. Combustion Validation The activity presented in the paper is the continuation of a previous one, which is now briefly resumed for the sake of clarity. A set of 2 full-cycles including combustion were calculated, in order to validate the general modeling framework against experimental data at (Knock Limited Spark Advance). A few results are reported in Figure a-b in terms of in-cylinder pressure and mass fraction burnt (MFB). For this preliminary set of analyses neither autoignition modeling nor knock prediction were carried out. 2 In-cylinder Pressure Mass Fraction Burnt Figure (a), left: in-cylinder pressure for 2 cycles at ; (b), right: MFB for the same cycles. 2

3 [ bar ] [ bar ] [ bar ] [bar] [bar] In the present activity, the validation is extended to a larger numerical dataset and a deeper analysis of results is carried out. Given a chemical model for the gasoline surrogate, two increases in SA are evaluated to analyze the knock onset location. Maximum In-cylinder Presssure 9. In Cycle no. Figure 2. Peak pressure for the 2 cycles at. 8 Figure 3. Combustion chamber division in sectors; intake side on the right, exhaust side on the left. 3.2 Influence of CCV on Knock Tendency Given the broad range of in-cylinder conditions highlighted by the previous activity [], it is reasonable to expect a similar variability also for chemical kinetics. This is resumed by the local value of the function, positive if autoignition has not yet occurred. One fuel surrogate is chosen for unburnt chemistry modeling, here named RON98-E, explicitly modeled to match the actual behavior of the gasoline used in the experiments, i.e. a commercial RON98 European gasoline. This is based on the Toluene-nHeptane-Ethanol-Isoctane mechanism by J.C. Andrae et al. [7] and a proprietary blend was provided by the fuel supplier with the specific target of correctly matching the autoignition behavior. Three cycles from the available LES database are here investigated, with the aims to both replicate the level of CCV of the extended database and to analyze it in terms of knock tendency. In particular, the selected cycles are an intermediate cycle (, p max 94 bar) and those with the minimum and maximum in-cylinder pressure peak (respectively, p max 88 bar, and, p max 2 bar) (Figure 2). The cycles are then used to analyze the effects of variation in the Spark Advance (SA). The in-cylinder pressure results for the three investigated SAs are illustrated in Figure 4 a-c: In-cylinder Pressure Mass Fraction Burnt In-cylinder Pressure (Step ) Crank 76 Angle Figure 4. In-cylinder pressure for the 3 selected cycles under the 3 SA investigated: (a) left, case; (b) middle, SA Increase (Step ); (c) right, (Step 2). The reasons for the very different combustion behaviors are to be found in the very early stages of flame development. Measurements in a spherical region centered in the spark plug evidence fluctuations in mixture quality as well as in flow characteristics around spark discharge in the immediate surroundings of its occurrence (Figure ): In-cylinder Mass Pressure Fraction Burnt (Step 2). 7 3

4 [ m/s ] Equivalence Ratio Spark Region (Step 2) (Step ) Figure. (a), left: equivalence ratio around spark plug; (b), right: velocity magnitude in the same region. Figure (a) shows that all the cycles undergo rich mixtures at the spark plug, independently of the specific SA. However, for, the cycle with the mixture quality closest to the stoichiometric () is the one with the highest in-cylinder pressure, while the richest one () is the lowest peak pressure one. At increased SA, the difference in mixture quality between cycle A and reduces, and also the pressure traces are closer (Figure 4 b-c); this is a consequence of the more similar ignition quality of the mixture for increased spark advances. However variations still remain, as the analogous analysis of the velocity magnitude around the spark plug illustrates. The cycle with the slowest combustion () is the one experiencing the most intense flow field at the spark plug. This is thought to combine with the excessively rich mixture through the convection of the flame kernel close to the combustion chamber walls, thus producing a relatively slow flame onset. The difference in flame displacement as well as in the volume of burnt gas is then highlighted in Figure 6 a-b: Velocity Magnitude Spark Region (Step 2) (Step ) Figure 6. (a), left: Flame front section for the highest peak pressure cycle; (b), right: same visualization for the lowest combustion cycle. As stated above, three different SAs are compared in the paper: and two progressive increase of it, namely Step and Step 2. Every cycle is then examined with respect to its relative SA, in order to provide coherent comparisons. The combustion regularity of each of the cycles is assessed starting from the function (Equation 2), and a very late CA is chosen to observe the chemical status of the unburnt mixture, i.e. CA asoc (after Start of Combustion). The probability density functions of for the three adopted SAs are reported in Figures 7 a-c: 4

5 PDF of PDF of PDF of PDF of PDF of PDF of PDF of PDF of PDF of PDF of PDF of PDF of.. Exhaust Valve - +CA asoc.. Intake Valve - +CA asoc Exhaust Valve 2 - +CA asoc Intake Valve 2 - +CA asoc Figure 7. (a) PDF of for the three cycles at +CA asoc ()... Exhaust Valve - (Step ) +CA asoc.. Intake Valve - (Step ) +CA asoc Exhaust Valve 2 - (Step ) +CA asoc Intake Valve 2 - (Step ) +CA asoc Figure 7. (b) PDF of for the three cycles at +CA asoc (-Step )... Exhaust Valve - (Step 2) +CA asoc.. Intake Valve - (Step 2) +CA asoc Exhaust Valve 2 - (Step 2) +CA asoc Intake Valve - (Step 2) +CA asoc Figure 7. (c) PDF of for the three cycles at +CA asoc (-Step 2).

6 [ mg ] [ mg ] [ mg ] As visible from Figure 7 (a), none of the three cycles shows knocking condition throughout the end-gas region at +CA asoc. Therefore the combustion is assumed to complete regularly for all of them, even for the one with the highest pressure peak (i.e. ); the level of CCV is not sufficient to cause irregular combustion phenomena. This is in agreement with the experimental tuning for. Figure 7 (b), relative to the first increase in SA, shows that for the same relative CA just the cycle with the lowest pressure peak (i.e. ) is completely characterized by autoignitionfree unburnt mixture. The intermediate cycle () shows a moderately-knocking behavior, while is in fullknocking conditions in all the four sectors of the combustion chamber. Finally Figure 7 (c) illustrates that for a further increase in the SA, even (the intermediate one) exhibits hot spots for autoignition in some areas (i.e. Intake Valve sector). 3.3 Analysis of Combustion Development The analysis of the physical status cannot be separated from the amount of residual fuel that participates in an eventual autoignition phenomenon. Moreover, this might be proficiently used as a straightforward input for knock metrics [8]. 2 Mass of Unburnt Fuel Intake Side Exhaust Side 2 Mass of Unburnt Fuel + 3CA Intake Side Exhaust Side 2 Mass of Unburnt Fuel + 6CA Intake Side Exhaust Side Figure 8. Mass of residual fuel for (left), Step (middle) and SA Step 2 (right). As visible, a recurrent trend is identified in a much faster fuel consumption on the exhaust side of the combustion chamber. This is due to the residual tumble motion generated during the intake stroke and accelerated during the compression phase; a residual albeit incoherent flow structure is still able to effectively accelerate the combustion propagation on the exhaust side. 4. CONCLUSIONS A coupled framework of LES and look-up table based chemistry modeling is validated against knock tendency from experiments, and confirms the proximity to develop irregular combustion phenomena as a consequence of CCV. This database will constitute a baseline to evaluate the effect of future engine modifications on combustion regularity and knock tendency.. ACKNOWLEDGMENTS This research is developed as a joint project between Gruppo Motori (University of Modena and Reggio Emilia, Italy) and Engine Research Center (University of Wisconsin-Madison, USA). Ferrari S.p.A. is acknowledged for experimental data and CD-adapco and DIGANARS for software support. 6. REFERENCES S.Richard, O.Colin, O.Vermorel, A.Benkenida, C.Angelberger, D.Veynante Towards large eddy simulation of combustion in spark ignition engines Proceedings of the Combustion Institute 3 (27) Rutland, C. J., Large-eddy simulations for internal combustion engines A review, doi:.77/ Fontanesi, S., Paltrinieri, S., d Adamo, A., Duranti, S., Investigation of boundary condition effects on the analysis of cycle-tocycle variability of a turbocharged GDI engine, International Conference on LES for Internal Combustion Engine Flows, Fontanesi, S., Paltrinieri S., Tiberi A., D'Adamo, A., LES Multi-cycle Analysis of a High Performance GDI Engine, SAE Technical Paper 23--8, 23. Fontanesi, S., Paltrinieri, S., D Adamo, A., Cantore, G., Rutland, C. J., Knock Tendency Prediction in a High Performance Engine Using LES and Tabulated Chemistry, SAE Technical Paper ,23 6. Lafossas, F A., Castagne, M., Dumas, J. P., Henriot, S, Development and Validation of a Knock Model in Spark Ignition Engines using a CFD code, SAE Technical Paper , Andrae, J. C. G., Head, R. A., HCCI Experiments with gasoline surrogate fuels modeled by a semidetailed chemical kinetic model, Combustion and Flame 6 (29) Klimstra, J., The Knock Severity Index A Proposal for a Knock Classification Method, SAE Technical Paper 8433, 984 6