Cycle-to-cycle variations (CCV) pose significant challenges to the performance and reliability of internal combustion engines (ICE). This study investigates the applicability of information entropy as a diagnostic tool to quantify and characterize CCV in ICE subject to exhaust gas recirculation (EGR). Particle image velocimetry (PIV) and flame imaging were used to measure the flow field and flame behavior. The concept of information entropy is related to flow and flame evolution by calculating the Shannon entropy of the turbulent kinetic energy and flow velocity components to assess their sensitivity to CCV. Shannon entropy was applied to the flow velocity components and the turbulent kinetic energy on the tumble plane, where the horizontal component was identified to correlate with high-speed (HC) and low-speed (LC) combustion cycles both, with and without EGR. The turbulent kinetic energy was found to be major driver of HC cycles without EGR, however, it plays a subordinate role with EGR. The conditional Shannon entropy was then applied to assess local fluctuation of the turbulent kinetic energy during ignition from cycle-to-cycle under the influence of the direction of the horizontal velocity component and the presence or absence of the flame, revealing the areas where turbulent kinetic energy fluctuates strongly between different cycles. The results have potential for both computational and experimental studies of ICE, since the use of information entropy as a diagnostic tool allows for early prediction of HC and LC cycles.
ReitzRDOgawaHPayriR, et al. The future of the internal combustion engine. Int J Engine Res2020; 21(1): 3–10.
2.
OnoratiAPayriRVagliecoBM, et al. The role of hydrogen for future internal combustion engines. Int J Engine Res2022; 23(4): 529–540.
3.
AlgerTGingrichJRobertsCMangoldB.Cooled exhaust-gas recirculation for fuel economy and emissions improvement in gasoline engines. Int J Engine Res2011; 12(3): 252–264.
4.
KalghatgiGT.The outlook for fuels for internal combustion engines. Int J Engine Res2014; 15(4): 383–398.
5.
OzdorNDulgerMSherE.Cyclic variability in spark ignition engines a literature survey. SAE Transactions1994: 1514–1552.
6.
PetersonBSickV.High-speed flow and fuel imaging study of available spark energy in a spray-guided direct-injection engine and implications on misfires. Int J Engine Res2010; 11(5): 313–329.
7.
MüllerSHRBöhmBGleißnerMGrzeszikRArndtSDreizlerA. Flow field measurements in an optically accessible, direct-injection spray-guided internal combustion engine using high-speed PIV. Exp Fluids2010; 48(2): 281–290.
8.
BuschbeckMBittnerNHalfmannTArndtS.Dependence of combustion dynamics in a gasoline engine upon the in-cylinder flow field, determined by high-speed PIV. Exp Fluids2012; 53(6): 1701–1712.
9.
BodeJSchorrJKrügerCDreizlerABöhmB.Influence of the in-cylinder flow on cycle-to-cycle variations in lean combustion DISI engines measured by high-speed scanning-PIV. Proc Combust Inst2019; 37(4): 4929–4936.
10.
ZengWSjöbergMReussDL.Combined effects of flow/spray interactions and EGR on combustion variability for a stratified DISI engine. Proc Combust Inst2015; 35(3): 2907–2914.
11.
PetersonBReussDLSickV.On the ignition and flame development in a spray-guided direct-injection spark-ignition engine. Combust Flame2014; 161(1): 240–255.
12.
StiehlRBodeJSchorrJKrügerCDreizlerABöhmB.Influence of intake geometry variations on in-cylinder flow and flow–spray interactions in a stratified direct-injection spark-ignition engine captured by time-resolved particle image velocimetry. Int J Engine Res2016; 17(9): 983–997.
13.
ZhaoLMoizAASomS, et al. Examining the role of flame topologies and in-cylinder flow fields on cyclic variability in spark-ignited engines using large-eddy simulation. Int J Engine Res2018; 19(8): 886–904.
14.
MaldonadoBPKaulBC.Evaluation of residual gas fraction estimation methods for cycle-to-cycle combustion variability analysis and modeling. Int J Engine Res2022; 23(2): 198–213.
15.
KrügerCSchorrJNicolletFBodeJDreizlerABöhmB.Cause-and-effect chain from flow and spray to heat release during lean gasoline combustion operation using conditional statistics. Int J Engine Res2017; 18(1–2): 143–154.
16.
TruffinKAngelbergerCRichardSPeraC.Using large-eddy simulation and multivariate analysis to understand the sources of combustion cyclic variability in a spark-ignition engine. Combust Flame2015; 162(12): 4371–4390.
17.
BodeJSchorrJKrügerCDreizlerABöhmB.Influence of three-dimensional in-cylinder flows on cycle-to-cycle variations in a fired stratified DISI engine measured by time-resolved dual-plane PIV. Proc Combust Inst2017; 36(3): 3477–3485.
18.
HanuschkinAZündorfSSchmidtM, et al. Investigation of cycle-to-cycle variations in a spark-ignition engine based on a machine learning analysis of the early flame kernel. Proc Combust Inst2021; 38(4): 5751–5759.
19.
DreherDSchmidtMWelchC, et al. Deep feature learning of in-cylinder flow fields to analyze cycle-to-cycle variations in an SI engine. Int J Engine Res2021; 22(11): 3263–3285.
20.
SadeghiMTruffinKPetersonBBöhmBJayS.Development and application of bivariate 2D-EMD for the analysis of instantaneous flow structures and cycle-to-cycle variations of in-cylinder flow. Flow Turbul Combust2021; 106(1): 231–259.
21.
DingZTruffinKJaySSchmidtMFoucherFBoréeJ.On the use of les and 3d empirical mode decomposition for analyzing cycle-to-cycle variations of in-cylinder tumbling flow. Flow Turbul Combust2023; 111(1): 235–284.
22.
BakerSFangXShenL, et al. Dynamic mode decomposition for the comparison of engine in-cylinder flow fields from particle image velocimetry (PIV) and reynolds-averaged navier–stokes (RANS) simulations. Flow Turbul Combust2023; 111(1): 115–140.
23.
LiuMZhaoFHungDLS. A coupled phase-invariant POD and DMD analysis for the characterization of in-cylinder cycle-to-cycle flow variations under different swirl conditions. Flow Turbul Combust2023; 110(1): 31–57.
24.
BakerSJFangXHBarbatoA, et al. Extracting vector magnitudes of dominant structures in a cyclic engine flow with dimensionality reduction. Phys Fluids2024; 36(2).
25.
ChenHReussDLHungDLSickV.A practical guide for using proper orthogonal decomposition in engine research. Int J Engine Res2013; 14(4): 307–319.
26.
RulliFFontanesiSd’AdamoABerniF.A critical review of flow field analysis methods involving proper orthogonal decomposition and quadruple proper orthogonal decomposition for internal combustion engines. Int J Engine Res2021; 22(1): 222–242.
27.
BarbatoAIacovanoCFontanesiS.Cold-flow investigation of the darmstadt engine with focus on statistical convergence: Experimental and large eddy simulation analysis. Flow Turbul Combust2023; 110(1): 59–89.
28.
DailyJW.Cycle-to-cycle variations: a chaotic process?Combust Sci Technol 1988; 57(4–6): 149–162.
29.
FinneyCEKaulBCDawCSWagnerRMEdwardsKDGreenJB.A review of deterministic effects in cyclic variability of internal combustion engines. Int J Engine Res2015; 16(3): 366–378.
30.
WagnerRMDrallmeierJADawCS.Characterization of lean combustion instability in premixed charge spark ignition engines. Int J Engine Res2000; 1(4): 301–320.
31.
ShannonCE.A mathematical theory of communication. Bell Syst Tech J1948; 27(3): 379–423.
32.
WelchCSchmidtMKeskinenK, et al. The effects of intake pressure on in-cylinder gas velocities in an optically accessible single-cylinder research engine. SAE technical paper 2020-01-0792, 2020.
33.
SchmidtMDingCPPetersonBDreizlerABöhmB.Near-wall flame and flow measurements in an optically accessible SI engine. Flow Turbul Combust2021; 106(2): 597–611.
34.
WelchCSchmidtMIllmannLDreizlerABöhmB.The influence of flow on cycle-to-cycle variations in a spark-ignition engine: a parametric investigation of increasing exhaust gas recirculation levels. Flow Turbul Combust2023; 110(1): 185–208.
35.
WelchCIllmannLSchmidtMDreizlerABöhmB.Experimental evaluation of spark behavior under diluted conditions in an optically accessible engine. Int J Engine Res2024; 25(3): 527–544.
36.
CamesascaMKaufmanMManas-ZloczowerI.Quantifying fluid mixing with the Shannon entropy. Macromol Theory Simul2006; 15(8): 595–607.
37.
PeruginiDDe CamposCPPetrelliMMorgaviDVetereFPDingwellDB.Quantifying magma mixing with the Shannon entropy: application to simulations and experiments. Lithos2015; 236: 299–310.
38.
EngelmannLIhmeMWlokasIKempfA.Towards the suitability of information entropy as an LES quality indicator. Flow Turbul Combust2021; 108(2): 353–433.
39.
PanLYangXYangYB, et al. Experimental study on the influence of barrier structures on water renewal capacity in slow-flow water bodies. Water2022; 14(22): 3757.
40.
MatekunasFA. Modes and measures of cyclic combustion variability. SAE Transactions1983: 1139–1156.
41.
WadekarSJanasPOevermannM.Large-eddy simulation study of combustion cyclic variation in a lean-burn spark ignition engine. Appl Energy2019; 255: 113812.
42.
EngelmannLLaichterJWollnyPKleinMKaiserSAKempfAM.Cyclic variations in the flame propagation in an spark-ignited engine: multi cycle large eddy simulation supported by imaging diagnostics. Flow Turbul Combust2023; 110(1): 91–104.
43.
ShahbakhtiMKochCR.Characterizing the cyclic variability of ignition timing in a homogeneous charge compression ignition engine fuelled with n-heptane/iso-octane blend fuels. Int J Engine Res2008; 9(5): 361–397.
44.
StansfieldPWigleyGJusthamTCattoJPitcherG.PIV analysis of in-cylinder flow structures over a range of realistic engine speeds. Exp Fluids2007; 43(1): 135–146.
45.
Murali KrishnaBMallikarjunaJM. Comparative study of in-cylinder tumble flows in an internal combustion engine using different piston shapes—an insight using particle image velocimetry. Exp Fluids2010; 48(5): 863–874.
46.
DingZTruffinKJayS.Cause-and-effect chain analysis of combustion cyclic variability in a spark-ignition engine using large-eddy simulation, part I: from tumble compression to flame initiation. Combust Flame2024; 267: 113566.
47.
DingZTruffinKJayS. Cause-and-effect chain analysis of combustion cyclic variability in a spark-ignition engine using large-eddy simulation, part II: Origins of flow variations from intake. Combust Flame2024; 267: 113565
48.
BoréeJMaurelSBazileR.Disruption of a compressed vortex. Phys Fluids2002; 14(7): 2543–2556.
