SIMULATION OF COMBUSTION

Transcription

1 SIMULATION OF COMBUSTION

2 OUTLINE SPARK IGNITION MODEL COMBUSTION MODEL KNOCK MODEL ANALYSIS OF CYCLE BY CYCLE VARIABILITY

3 OUTLINE SPARK IGNITION MODEL COMBUSTION MODEL KNOCK MODEL ANALYSIS OF CYCLE BY CYCLE VARIABILITY

4 Motivation FLAME KERNEL FORMATION IS A CRITICAL ISSUE IN ICE SINCE: ITS FEATURES AFFECT THE COMBUSTION DURATION CYCLE-TO-CYCLE VARIABILITY AFFECTS RIGHT EARLY BURNING RATE THE 5%MFB TAKES 35-40% OF TOTAL COMBUSTION DURATION PHYSICAL PROCESS TO BE CONSIDERED PHYSICS OF SPARK DISCHARGE FLOW CONVECTIVE EFFECTS (ARC ELONGATION) TURBULENCE PHYSICAL CHARACTERISTICS OF THE MIXTURE (p, T, φ or pdf of φ)

5 Background CFD IGNITION MODELS ARE COMPLETELY RELIABLE? NO IGNITION TIME AND LENGHT SCALES ARE TOO SMALL TO BE RESOLVED DURING PLASMA FORMATION ELECTRICAL CIRCUIT TOO COMPLEX TO BE MODELLED IN DETAIL COUPLING WITH MAIN COMBUSTION MODEL GRID DEPENDENCY MANY 1D MODELS DECOUPLED FROM CFD SOLVER HAVE BEEN PRESENTED AND REFERENCED IN THE PAPER. THEY WOULD BE CONSIDERED ALL EULERIAN EXCEPT AKTIM AND DPKI.

6 Background LAGRANGIAN TRACKING REVIEW AKTIM MODEL - Duclos and Colin [COMODIA 2001] - The model includes a detailed description of the electrical system - Ignition kernels were modelled by a set of particles uniformly placed DPIK - Fan et al. [SAE paper ] - The flame kernel position is marked by particles CURRENT MODEL EXPECTED CONTRIBUTION PROVIDE AN ALMOST GRID INDIPENDENT MODEL IMPROVE THE PHYSICAL GROUTH OF FLAME KERNEL EXPANSION RATE BASED ON MASS AND ENERGY CONSERVATION PROVIDE A DIRECT COUPLING METHOD WITH A FLAME SURFACE DENSITY MODEL

7 Spark Ignition Model ELECTRICAL SUB-MODEL FOR SPARK PLUG LUMP MODEL BASED ON THE MAIN AVAILABLE SPECIFICATIONS LAGRANGIAN KERNEL SUBMODEL MASS AND ENERGY CONSERVATION SOLVED IN A VARIABLE CONTROL VOLUME DEFINED BY MEAN FLAME SURFACE COUPLING WITH MAIN SOLVER ENFORCED WITH PARTICULAR EMPHASIS ON FLAME SURFACE

8 Spark Ignition Model Lagrangian Ignition Model Electrical submodel LUMP/EASY MODELLING (NO WEAK POINT) PLASMA FORMATION NEGLECTED (time and length scales too short) Energy released during breakdown and glow phases: E bd 2 bd = 2 C bd V d gap gp (Duclos and Colin, 2001) E& glow = f ( E, t) sp Breakdown Voltage evaluated according to (Stone et. Al, Sae 2000): V bd P P = T T unb unb d gap

9 Spark Ignition Model AFTER THE PLASMA PHASE: One flame kernel is deposited and initialized Flame Kernel is discretized by a set of triangular elements which expand radially I-th cell Each of these elements varies its area surface because of expansion and wrinkling by turbulence It contributes to reaction rate in its own reference fluid cells I-th

10 Spark Ignition Model Lagrangian Ignition Model Thermodynamic model Initial kernel conditions after plasma formation (Song and Sunwoo, 2000) : r k, i k 1 = k p 0 d gap E bd T 1 Ti unb π 1/ 2 T i 1 T b = + T k 1 T 1 unb MASS CONSERVATION FOR A LAGRANGIAN SYSTEM unb dm dt k = ρ unb slam, k ( Ak Ξ) Turbulence wrinkling Rearranged -> >An expression for the mean kernel expansion rate dr dt ρ V Ξ A 1 Tk dt dt k unb k k 1 = slam, k ρk k p dp dt

11 Spark Ignition Model Lagrangian Ignition Model Thermodynamic model If T 3T ad heat conduction equation applies 2 T pl Tpl α 2 = + t 2 r r T pl r + P Q& ρc V p w k Energy Conservation if T<3T ad dh k dt = 1 m k dq dt ch + de dt ele dq dt WV + V k dp dt h m k k dm dt k System is in thermodynamic equilibrium Pressure is uniform in burnt and fresh gases

12 Spark Ignition Model MASS SOURCE TERMS IN I-TH CELL FROM FUEL CONSUMPTION RATE ω& k, i th = ρ unb s lam, k Σ i th (Equivalent to ECFM) ENERGY SOURCE TERMS IN I-TH CELL FROM: 1. Fuel oxidation 2. Spark discharge during breakdown and glow phase FLAME SURFACE DENSITY IN I-TH CELL CONTINUOSLY UPDATED Σ i th = Si th V i th Ξ j-th kernel element surface th S i A = M i= 1 k, j th IGNITION MODEL IS SWITCHED OFF ONCE THE KERNEL RADIUS IS mm -> Reasonable flow lenght resolved in RANS (grid size 0.5 -> 1 mm)

13 Spark Ignition Model Lagrangian Ignition Model Comparison with main Lagrangian models Electrical Model AKTIM has a very sophisticated spark electrical model While in DPIK model is absent Flame Kernel Deposition In present model, only one kernel is considered and its initial radius and temperature are evaluated depending on system characteristics and operating conditions. A reasonble value used in DPIK, while AKTIM adopts a different concept based on presumed multiple kernel ignition probability

14 Spark Ignition Model Lagrangian Ignition Model Comparison with main Lagrangian models Flame expansion velocity Derived from mass conservation according to a lagrangian g approach and accounting for wrinkling. In AKTIM each kernel is convected by gas flow. DPKI simply adds turbulence intensity to laminar flame velocity (questionable) Coupling with Flame surface Models In AKTIM and DPKI is based on the density surface of burning partcile representing the kernel. In the present model Flame surface density is computed according to a spherical kernel expansion which is sensitive to mixture charactetistics and flow conditions. Therefore the ECFM models is inizialized with current Σ value in i-th cells

15 OUTLINE SPARK IGNITION MODEL COMBUSTION MODEL KNOCK MODEL ANALYSIS OF CYCLE BY CYCLE VARIABILITY

16 Combustion model FLAMELET COMBUSTION MODEL (ECFM, Colins et Al. 2003) Σ Σ u% i Σ μ t μ ρ + = + + ( P1 + P2 + P3 ) Σ D t xi xi Sct Sc xi FRESH GAS ENTHALPY TRANSPORT EQUATION ρh ρu% h μ μ h ρ p ε + = ρ t xi x i Sct Sc x i ρo t k u u u h i t h Better accuracy in estimating the evolution of unburned gases thermodynamic conditions during the combustion process

17 KIVA MODELS Ignition model Lagrangian Ignition Model Main Combustion model ECFM Flamelet (Colin 2003) Mono-component Fuel Shell Fuel/Isooctane Laminar flame speed Metchalghi & Keck Turbulence model k-ε+wall function Wall heat transfer Corrected Han and Reitz Flame front chemistry 1-step chemistry Post-flame chemistry Knock model Meintjes and Morgan AnB (Lafossas 2003)

18 Validation 1.2 liters, 4 Cylinders Gasoline Engine Configurations Examined Engine Speed [rpm] IMEP [bar] AFR [ ] Spark Advance Sweep 24.4 to to 34

19 Validation VALIDATION OF CFD MODELS Ignition Combustion velocity Wall heat flux 35 AFR= Comb Vel b SA=24.4 KIVA EXPERIMENTAL 25 re [bar] Pressur WHF 5 a INIT c c.a. [deg ATDC]

20 Reference cycle definition es Engine cycles En ngine cycles Engin ne cycles Engine cycle mbar@2400rpm, AFR=13.2, SA MFB MFB MFB MFB90 cycles Engine mbar@2400rpm, AFR=13.2, SA crank angle ATDC The reference cycle is used for the sake of CFD results validation: it must represent the typical combustion that can be attained for the given operating condition The reference cycle is not necessarily the mean pressure cycle on the crankshaft domain The relationship between the combustion progress (released heat) and the in- cylinder pressure is non-linear, thus a normal distribution in terms of pressure could imply a non-normal distribution in terms of pressure

21 Reference cycle definition es Engine cycles En ngine cycles Engin ne cycles Engine cycle mbar@2400rpm, AFR=13.2, SA MFB MFB MFB MFB90 The selection of the representative cycles is accomplished by filtering the combustion with MFBxx near the mean values. Pres ssure [bar] mbar@2400rpm, AFR=13.2,SA=24.4 Representative cycles Mean cycle Average cycle c.a. [deg ATDC] The mean cycle in terms of pressure is then evaluated on the basis of the representative cycles.

22 Validation Well tuned combustion models should be able to reproduce experimental behavior when modifying input engine parameter 5 The ignition model plays a key role in the reconstruction of combustion 0 evolution with different spark advance Two different conditions have been simulated: different loads and different air to fuel ratio. Pres ssure [bar] Press sure [bar] mbar@2400rpm, AFR=13.2 SA=24.4 KIVA SA=26.4 KIVA SA=27.4 KIVA SA=28.4 KIVA SA=29.4 KIVA SA=30.4 KIVA SA=32.4 KIVA EXPERIMENTAL c.a. [deg ATDC] 900mbar@3000rpm, AFR=14.6 The simulation is able to describe the 20 variation in combustion velocity as a 10 function of spark advance without tuning parameters c.a. [deg ATDC] SA=21.1 KIVA SA= KIVA SA=25.1 KIVA SA=27.3 KIVA SA=29.2 KIVA SA=33.1 KIVA SA=34.0 KIVA EXPERIMENTAL

23 Validation The first Law oh Thermodynamics is used to extract combustion information from experimental data and from simulation dv 1 dp ROHR γ 0-5 = P γ dϑ γ d ϑ c c stion angles Combu mbar@2400, AFR=13.2 MFB05 EXP MFB25 EXP MFB50 EXP MFB90 EXP MFB05 KIVA MFB25 KIVA MFB50 KIVA MFB90 KIVA Spark Advance The model is able to well represent all the main combustion angles with different operating conditions ion angles Combust mbar@3000rpm, AFR= Spark Advance

24 Validation 30 AFR= AFR=14.6 ions Combustion durati % MFB EXP 5-90% MFB EXP 0-5% MFB KIVA 5-90% MFB KIVA Combustion duratio ons % MFB EXP 5-90% MFB EXP 0-5% MFB KIVA 5-90% MFB KIVA Spark Advance Spark Advance Combustion durations The start of combustion is well represented (MFB5 SI): the high SA cause an increase in the early stages of combustion because of the different thermodynamics at ignition.

25 Ignition model - Conclusion A Lagrangian ignition model has been proposed and validated in real engine configurations The model accounts for: Spark main electrical characteristics (Lump model) Mixture t thermophysical h properties (thermodynamic lagrangian model) The model is based on few, easy to provide, information on spark setup characteristics. The ignition, combustion and wall heat exchange models are validated against experimental data. New statistical observation of experimental results has taken to a new definition of representative cycles. The model proved to be accurate in different operating condition, with a good representation of combustion evolution with respect to different SA

26 OUTLINE SPARK IGNITION MODEL COMBUSTION MODEL KNOCK MODEL ANALYSIS OF CYCLE BY CYCLE VARIABILITY

27 Knock Model CHEMKIN Solution of several chemical equilibrium reactions REDUCED KINETICS Shell Model Time consuming No tuning parameters EMPIRICAL MODEL AnB (autoignition) Imposition autoignition delay Based on experimental evidence

28 AnB KNOCK MODEL (Lafossas et Al, 2002, IFP) The model uses a two step chemistry for the simulation of auto-ignition In the first step a precursor of the auto-ignition is calculated and then, when it reaches a critical concentration, the knock combustion is forced. AUTO-IGNITION DELAY B n T IO θ = A P e 100 A, n, B tuning parameters FUEL CONSUMPTION RATE dy dt Fu Tg Fu k with k 10 = Y A A = e

29 AnB KNOCK MODEL (Lafossas et Al, 2002, IFP) dt The chemical kinetics during auto-ignition delay are not linear 1 ϑ = dy dt p Y P = Precursor = YT F( θ ) where Fu 2 2 δθ KNOCKING CRITERIA Y = Y p T Fu F ( θ ) = Y + 4(1 δθ) Y θ T p Fu

30 REFERENCE KNOCK INTENSITY DEFINITION Similar considerations for the reference mean combustion cycle can be applied to define the typical knocking cycle, for the given operating condition. The same procedure described before leads to the definition of a representative cycle, but the high-frequency components are filtered out by averaging different engine cycles. MAPO (Maximum Amplitude of Pressure Oscillations) and KO (Knock Onset) parameters can be used to validate the high-frequency content of the pressure signal MAPO = c max ( TDC+ 70 P ) hp TDC ( hp ) KO = ϑ P > thresholds

31 REFERENCE KNOCK INTENSITY DEFINITION Due to the non-normal distribution, the average MAPO is not the most likely value: the validation is carried out by means of the median MAPO MAPO distribution, rpm, AFR=13.2, SA=37.5 Measured Distribution (MFB5 and MFB50 selection) Median Value (MFB5 and MFB50 selection) Mean Value (MFB5 and MFB50 selection) 25 Engine Cycles MAPO [bar]

32 Validation of knock model The local evolution of pressure at sensor location has been compared to experimental signals 80 Experimental 70 Simulated 60 [bar] In-Cylinder Pressure [ Crankshaft Angle [ ] 950 mbar@4500 rpm, AFR=13.2, SA= Simulated 0.09 Experimental tude [bar] FFT Amplit Frequency [Hz] x 10 4

33 Knock model Knock causes high in-homogeneities in the chamber Exhaust side Spark plug Intakeside

34 Knock model Knock causes high in-homogeneities in the chamber Exhaust side MAPO 7.9 bar Spark plug MAPO 9.4 bar Intake side MAPO 5.8 bar In the reference case knock induces high velocities (charge motion) in the chamber, raising the convective fluxes

35 Knock model EVALUATION OF KNOCK SEVERITY PARAMETERS Autoignition delay has been artificially perturbed in order to cause different severity of knocking condition with a fix Spark Advance The amount of fuel mass involved in autoignition varies form 9% to 15% The aim of the analysis is to find knock severity indexes based on damage risk The indexes must base on information The indexes must base on information available by analyzing local pressure trace

36 Knock model COMBUSTION VELOCITY EVALUATION Fuel consumption rate [g/s] Local fuel consumption rate [g/(s*cm^3)] Knocking combustion involves small volumes with high specific combustion g g p rates

37 Knock model DAMAGE RELATED PARAMETERS: WALL HEAT FLUX In case of severe knocking condition the maximum heat flux at the wall is five times higher than that referring to normal combustions Increase in combustion rate Increase in convective fluxes

38 Knock model DAMAGE RELATED PARAMETERS: WALL HEAT FLUX The difference between the integral value at EVO in case of non-knocking combustion and that of the knocking one can be used as a damage related parameter for knock detection purpose Reference case (blue line) has an integral wall heat flux out of trend with respect to the amount of fuel involved in knockk

39 Knock model During knock the heat losses increase, the net heat release should decrease, being evaluated neglecting the heat exchanges CHRnet [J J] γ dv 1 dplp CHRNET = Plp + V γ 1 d ϑc γ 1 d ϑc KIVA simulation@4500rpm, AFR13.2, SA Sensor spark location - knock Sensor exhaust side - knock 400 Sensor intake side - knock Sensor spark location No Knock 300 The CHRnet is not sensitive to sensor position: a heat flux sensitive knock index can then be based on the evaluation of CHR Crankshaft Angle [ ]

40 Knock model The CHRNET, however, depends on other factors (e.g., combustion phasing, synthesized by MFB50): only cycles with a given value of MFB50 must be taken into account. MAPO values are randomly distributed in non-knocking conditions; as knock happens the correlation between MAPO-CHRNET becomes high. For a given SA only the cycles with average MFB50 are considered (cycles filtering) i The correlation between MAPO and CHRNET is then introduced: KNOCK SEVERITY INDEX

41 Knock model KNOCK SEVERITY INDEX The Cumulative Heat Release based index is sensitive to knock severity (increases with SA, after knock takes place) and is almost linearly related to the simulated heat losses

42 Conclusion - knock model A Lagrangian ignition model has been proposed and validated in real engine configurations The model accounts for: Spark main electrical characteristics (Lump model) Mixture t thermophysical h properties (thermodynamic lagrangian model) The model is based on few, easy to provide, information on spark setup characteristics. The ignition, combustion and wall heat exchange models are validated against experimental data. New statistical observation of experimental results has taken to a new definition of representative cycles. The model proved to be accurate in different operating condition, with a good representation of combustion evolution with respect to different SA

43 Conclusion - knock model The choice of knock model has been driven by the needs of the research: a deeper insight in knocking combustion for better understanding experimental pressure signal The AnB empirical model has been developed and tuned against experimental data. The reconstruction of pressure evolution at spark location is good. The analysis of results has allowed to create a knock severity index based on the Cumulative Net Heat Release in the chamber. The index is based on both on the high and low frequency content of pressure signals and proved to be position in-sensitive.

44 OUTLINE SPARK IGNITION MODEL COMBUSTION MODEL KNOCK MODEL ANALYSIS OF CYCLE BY CYCLE VARIABILITY

45 Cycle by Cycle Variation Reduction of consumption Leaner Combustion Cyclic Variability Cycle by Cycle Variation defined as the non-repeatability of the combustion process on a cycle resolved basis CAUSES AND INFLUENCING FACTORS MIXTURE COMPOSITION CYLINDER CHARGING IGNITION FACTORS IN CYLINDER FLOW FACTORS MIXTURE COMPOSITION Air to fuel ratio Mixture non-homogeneity Fuel type Residual gas fraction

46 Evaluation Of Cyclic Variation Configurations Examined Regime FIXED > 15000rpm Spark Advance Fixed The pressure traces of 200 consecutive cycles have been recorded end filtered with a lowpass analog filter Load WOT The methodology for the measurement of cyclic variability of an internal combustion engine strongly influences its evaluation Mean Lambda > Lambda of g Maximum Laminar Flame Speed Encoder Indicating System Pressure Sensor Charge amplifier Analog Filter Chain Measurement AVL 365, 360 pulses per revolution AVL Indimodul 621 (14 bit, max 800kHz) Kistler Kistler Bessel, 6 poles Pressure Related Parameters P max and ϑp max P ϑ max IMEP and ϑ P ϑ max

47 Coefficient Of Variation of IMEP Std( IMEP) COV = IMEP 100 mean( IMEP) IMEP COV(IMEP) λ REF Work output variations strongly influence engine driveability and performance and it has been demonstrated that they are well related to combustion instability

48 Frequency distribution of IMEP pdf pdf IMEP IMEP Asymmetric pd df pd df IMEP IMEP Care must be taken when using the COV of IMEP for the identification of the variability of an engine, because samples for leaner combustions are not compatible with a gaussian distribution

49 Analysis of exp. pressure traces The higher differences in pressure variability occur during the expansion phase, where the positive work output is generated. This well correlates with the differences in the variability of IMEP Inlet Valve Closing Noise Combustion Start

50 Analysis of heat release Minimum in COV(P) on a crank angle basis can be used as the starting ti point of combustion Heat Release extracted from pressure by using the First Law of Thermodynamics HYPOTHESES: No heat transfer to wall (adiabatic chamber) Fixed Specific Heat Capacity Ratio k=1.3 Theoretical (Rigid) Piston Displacement

51 Combustion angles of MFB Moving towards leaner mixture, the combustion durations increase affecting all the combustion angles Differences are mainly formed in the early stages of combustion (0-5%) and are not sensitively incremented for later angles The laminar flame speed s dependence on air to fuel ratio cannot justify this tendency because it should have been amplified the different trends Increase in the variability of combustion duration as the mixture air index is increased This variability maintains nearly constant during the evolution of the first half of combustion The A/F ratio influences the combustion duration and cyclic variability of the early stages of combustion

52 Experimental analysis: conclusion The statistical investigation of the experimental in-cylinder pressure data recorded d for the different mean lambda shows that: t The cycle-by-cycle variation increases when leaner mixture are considered with respect to the optimum value for the highest flame speed The reduction of IMEP well correlates with the increase of COV of IMEP The variability of work output is closely related to the instability of the early stages of combustion The IMEP distribution can not be described in terms of a gaussian function when the COV increases with leaner conbustion The statistical analysis of combustion angles shows that the cyclic variation affects mainly the initial flame development i.e, 0-5% MFB duration thus suggesting that the cyclic variation is closely related to mixture quality around spark

53 Simulation of combustion: λ uniform Initial Flow condition mapped from results of the simulation of intake process (AVL- FIRE v8.4) Good reconstruction of the mean pressure curve tendencies No information on Cyclic Variation lam ( λ,, ) S = f PT Laminar Velocità Flame Laminare Speed KIVA EXP LambdaX 1.2

54 Mixture quality at ignition The analysis of the experimental pressure traces clearly indicated the early stages of combustion as the key processes in the onset of cycle by cycle variation. It is necessary to characterize the local mixture quality at the ignition with respect to: 1. The local cycle by cycle variability of the mixture composition 2. The fuel distribution at the spark plug location and its homogeneity in the combustion chamber A tt t t t t th b ti i t bilit t d ith l Any attempt to reconstruct the combustion instability trends with leaner mixture composition must concern with the imposition of these two information: a RANS methodology is presented for a preliminary parametric assessment of cycle by cycle variation in SI engine

55 Local A/F variability and mixture homogeneity Local Lambda variability, (Baritaud et Al., Combustion And Diagnostics 2006) Mixture homogeneity Length Scale L u Sphere( L u ) 2 4π L u λ() sds = λ mean

56 Description of RANS methodlogy λ = mean REF Laminar Flame Speed Velocità Laminare LambdaX 1.2 Lu The variability of the local value of lambda at ignition is forced in the simulations of combustion The combustion process is initialized by forcing a local lambda different from the mean one. As the flame kernel grows up, the chemical and physical proprieties tend to those of the mean mixture with a linear interpolation based on the ratio between the flame radius and Lu.

57 Description of RANS methodlogy λ = mean REF Laminar Velocità Flame LaminareSpeed LambdaX 1.2 Lu

58 Description of RANS methodlogy λ = REF mean Laminar Velocità Flame LaminareSpeed LambdaX 1.2 Lu

59 Description of RANS methodlogy λ = REF mean Laminar Velocità Laminare Flame Speed LambdaX 1.2 Lu

60 Description of RANS methodlogy λ = REF mean Laminar Velocità Laminare Flame Speed LambdaX 1.2 Lu

61 Statistical analysis of results Velocità Laminare The stochastic variability of the local lambda at the ignition is represented by four different perturbations from the mean value LambdaX 1.2 A statistical analysis of the results of the RANS simulations is possible by imposing the cumulative probability of each sample as a weighting factor

62 Pressure variation analysis EXP The numerical methodology performance in predicting the influence of the AFR on cyclic variability are aligned to experimental evidence The mixture non homogeneity together with the variation on the local value of lambda cause higher variation of pressure traces with leaner combustion KIVA This variation is located in the expansion phase, where the IMEP is mainly created

63 Variation of MFB angles EXP KIVA

64 Variation of IMEP IM MEP COV of IMEP IMEP STD Local Lambda STD Local Lambda 0.08 STD Local Lambda 0.12 Mean Lambda COV of IMEP STD Local Lambda 0.02 STD Local Lambda 0.08 STD Local Lambda 0.12 Mean Lambda The combustion simulations clearly reveal a decrease in IMEP when increasing Air to Fuel ratio The imposition of the variability of local lambda at the ignition has resulted in the identification of an increaseinthevariationofimepfor leaner mixture An increase in the variability of the initial local lambda causes not only an increase of COV of IMEP, but also a decrease of IMEP, because of the non-symmetrically distribution of IMEP over the mean value STD PMI

65 Variation of IMEP lambda REF+0.1 The numerical methodology has well reconstructed the predominant non-symmetric behaviour of the system, though excite with a symmetric one

66 CCV - Conclusion A combined experimental and numerical methodology for the evaluation of the dependence of Cycle by Cycle Variation on mixture composition has been presented The estimation of the cyclic variation was based on the evaluation of the COV of IMEP, but for leanest combustion it has been demonstrated that the distribution of the IMEP is far from being well represented by a gauss-distribution The analysis of pressure data for different air to fuel ratios has revealed the close relation between the early stages of combustion and the cyclic variability A numerical methodology has been developed to analyze the influence of the air to fuel composition on the combustion process. The non-homogeneity of the mixture proved to influence much more the leaner combustions. The cyclic variability has been described by means of RANS simulation, by imposing a given local lambda variability on the combustion models. The results well reconstruct the increase in the cyclic variability of the leaner combustion in terms of IMEP statistic distributions and allow a better understanding of the root causes of cyclic variability of internal combustion engines

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