{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:22:41Z","timestamp":1760242961597,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2015,1,29]],"date-time":"2015-01-29T00:00:00Z","timestamp":1422489600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this study we summarize and analyze experimental observations of cyclic variability in homogeneous charge compression ignition (HCCI) combustion in a  single-cylinder gasoline engine. The engine was configured with negative valve  overlap (NVO) to trap residual gases from prior cycles and thus enable auto-ignition in successive cycles. Correlations were developed between different fuel injection strategies and cycle average combustion and work output profiles. Hypothesized physical mechanisms based on these correlations were then compared with trends in cycle-by-cycle predictability as revealed by sample entropy. The results of these comparisons help to clarify how fuel injection strategy can interact with prior cycle effects to affect combustion stability and so contribute to design control methods for HCCI engines.<\/jats:p>","DOI":"10.3390\/e17020539","type":"journal-article","created":{"date-parts":[[2015,1,29]],"date-time":"2015-01-29T10:10:02Z","timestamp":1422526202000},"page":"539-559","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Effects of Direct Fuel Injection Strategies on Cycle-by-Cycle Variability in a Gasoline Homogeneous Charge Compression Ignition Engine: Sample Entropy Analysis"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0188-6419","authenticated-orcid":false,"given":"Jacek","family":"Hunicz","sequence":"first","affiliation":[{"name":"Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36,  20-618 Lublin, Poland"}]},{"given":"Alejandro","family":"Medina","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica Aplicada, Universidad de Salamanca, 37008 Salamanca, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9647-8345","authenticated-orcid":false,"given":"Grzegorz","family":"Litak","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36,  20-618 Lublin, Poland"}]},{"given":"Pedro","family":"Curto-Risso","sequence":"additional","affiliation":[{"name":"Instituto de Ingenier\u00eda Mec\u00e1nica y Producci\u00f3n Industrial, Universidad de la Rep\u00fablica,  11300 Montevideo, Uruguay"}]},{"given":"Lev","family":"Guzm\u00e1n-Vargas","sequence":"additional","affiliation":[{"name":"Unidad Profesional Interdisciplinaria en Ingenier\u00eda y Tecnolog\u00edas Avanzadas, Instituto Polit\u00e9cnico Nacional, Av. IPN 2580, L. Ticom\u00e1n, M\u00e9xico DF 07340, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2015,1,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Lavy, J., Dabadie, J.C., Angelberger, C., Duret, P., Willand, J., Juretzka, A., Sch\u00e4flein, J., Ma, T., Lendresse, Y., and Satre, A. (2000). Innovative ultra-low NOX controlled auto-ignition combustion process for gasoline engines: The 4-SPACE project. SAE Tech. Pap.","DOI":"10.4271\/2000-01-1837"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Fuerhapter, A., Piock, W.F., and Fraidl, G.K. (2003). CAI-controlled auto-ignition\u2014the best solution for the fuel consumption\u2014vs. emission trade-off?. SAE Tech. Pap.","DOI":"10.4271\/2003-01-0754"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"46","DOI":"10.4271\/2010-01-0164","article-title":"Thermal and chemical effects of NVO fuel injection on HCCI combustion","volume":"3","author":"Fitzgerald","year":"2010","journal-title":"SAE Int. J. Engines."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Song, H.H., and Edwards, C.F. (2008). Optimization of recompression reaction for low-load operation of residual-effected HCCI. SAE Tech. Pap.","DOI":"10.4271\/2008-01-0016"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Aroonsrisopon, T., Nitz, D., Waldman, J., Foster, D.E., and Lida, M. (2007). A computational analysis of direct fuel injection during the negative valve overlap in an iso-octane fueled HCCI engine. SAE Tech. Pap.","DOI":"10.4271\/2007-01-0227"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/j.fuel.2013.09.079","article-title":"An experimental study of negative valve overlap injection effects and their impact on combustion in a gasoline HCCI engine","volume":"117","author":"Hunicz","year":"2014","journal-title":"Fuel"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1551","DOI":"10.4271\/2012-01-1574","article-title":"The effect of acetylene on iso-octane combustion in an HCCI engine with NVO","volume":"5","author":"Puranam","year":"2012","journal-title":"SAE Int. J. Engines."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Yu, W., Xie, H., Chen, T., Li, L., Song, K., and Zhao, H. (2012). Effects of active species in residual gas on auto-ignition in a HCCI gasoline engine. SAE Tech. Pap.","DOI":"10.4271\/2012-01-1115"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Cao, L., Zhao, H., Jiang, X., and Kalian, N. (2006). Investigation into the effect of injection timing on stoichiometric and lean CAI operations in a 4-stroke GDI engine. SAE Tech. Pap.","DOI":"10.4271\/2006-01-0417"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Koopmans, L., Ogink, R., and Denbratt, I. (2003). Direct gasoline injection in the negative valve overlap of a homogeneous charge compression ignition engine. SAE Tech. Pap.","DOI":"10.4271\/2003-01-1854"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.ijhydene.2010.09.086","article-title":"Biogas upgrade to syn-gas (H2\u2013CO) via dry and oxidative reforming","volume":"36","author":"Lau","year":"2011","journal-title":"Int. J. Hydrog. Energy."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1177\/1468087413512312","article-title":"A modeling framework for second law analysis of low-temperature combustion engines","volume":"15","author":"Mamalis","year":"2014","journal-title":"Int. J. Engine Res"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.apenergy.2013.09.056","article-title":"Understanding optimal engine operating strategies for gasoline-fueled HCCI engines using crank-angle resolved exergy analysis","volume":"114","author":"Saxena","year":"2014","journal-title":"Appl. Energy."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Koopmans, L., Backlund, O., and Denbratt, I. (2002). Cycle to cycle variations: Their influence on cycle resolved gas temperature and unburned hydrocarbons from a camless gasoline compression ignition engine. SAE Tech. Pap.","DOI":"10.4271\/2002-01-0110"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2887","DOI":"10.1016\/j.proci.2006.07.133","article-title":"Understanding the transition between conventional spark-ignited combustion and HCCI in a gasoline engine","volume":"31","author":"Daw","year":"2007","journal-title":"Proc. Combust. Inst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1649","DOI":"10.1016\/j.apenergy.2010.11.040","article-title":"Characteristics of cyclic heat release variability in the transition from spark ignition to HCCI in a gasoline engine","volume":"88","author":"Sen","year":"2011","journal-title":"Appl. Energy."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"995","DOI":"10.4271\/2012-01-1106","article-title":"Understanding the dynamic evolution of cyclic variability at the operating limits of HCCI engines with negative valve overlap","volume":"5","author":"Stefanopoulou","year":"2012","journal-title":"SAE Int. J. Engines."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.apenergy.2011.09.018","article-title":"Controlling cyclic combustion timing variations using a symbol-statistics predictive approach in an HCCI engine","volume":"92","author":"Ghazimirsaied","year":"2012","journal-title":"Appl. Energy."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.apenergy.2011.07.002","article-title":"Statistical analysis of the cyclic variations of heat release parameters in HCCI combustion of methanol and gasoline","volume":"89","author":"Maurya","year":"2012","journal-title":"Appl. Energy."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1243\/146808705X30558","article-title":"Characterizing the thermal sensitivity of a gasoline homogeneous charge compression ignition engine with measurements of instantaneous wall temperature and heat flux","volume":"6","author":"Chang","year":"2005","journal-title":"Int. J. Engine Res."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Song, K., Xie, H., Li, L., Lu, J., Li, C., and Gao, Z. (2013). Disturbance observation and rejection method for gasoline HCCI combustion control. SAE Tech. Pap.","DOI":"10.4271\/2013-01-1660"},{"key":"ref_22","first-page":"1004","article-title":"Combustion timing variability in a light boosted controlled auto-ignition engine with direct fuel injection","volume":"15","author":"Hunicz","year":"2013","journal-title":"J. Vibroeng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/j.conengprac.2011.12.002","article-title":"Model predictive control of HCCI using variable valve actuation and fuel injection","volume":"20","author":"Ravi","year":"2012","journal-title":"Control Eng. Pract."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2885","DOI":"10.1016\/j.proci.2008.06.029","article-title":"Analysis of cyclic variability in spark-assisted HCCI combustion using a double Wiebe function","volume":"32","author":"Glewen","year":"2009","journal-title":"Proc. Combust. Inst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.conengprac.2013.11.008","article-title":"Cycle-to-cycle modeling and sliding mode control of blended-fuel HCCI engine","volume":"24","author":"Bidarvatan","year":"2014","journal-title":"Control Eng. Pract."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2811","DOI":"10.1103\/PhysRevE.57.2811","article-title":"Observing and modelling nonlinear dynamics in an internal combustion engine","volume":"57","author":"Daw","year":"1998","journal-title":"Phys. Rev. E."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/j.chaos.2006.05.053","article-title":"Patterns in the combustion process in a spark ignition engine","volume":"35","author":"Litak","year":"2008","journal-title":"Chaos Soliton Fractal"},{"key":"ref_28","first-page":"H2039","article-title":"Physiological time-series analysis using approximate entropy and sample entropy","volume":"278","author":"Richman","year":"2000","journal-title":"Am. J. Physiol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.expthermflusci.2010.09.007","article-title":"An experimental study of fuel injection strategies in CAI gasoline engine","volume":"35","author":"Hunicz","year":"2011","journal-title":"Exp. Therm. Fluid Sci"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"112801","DOI":"10.1115\/1.4007319","article-title":"Effects of charge preheating methods on the combustion phasing limitations of an HCCI engine with negative valve overlap","volume":"134","author":"Olesky","year":"2012","journal-title":"J. Eng. Gas Turbines Power"},{"key":"ref_31","unstructured":"Kantz, H., and Schreiber, T. (1997). Nonlinear Time Series Analysis, Cambridge University Press."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/2\/539\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:42:09Z","timestamp":1760215329000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/2\/539"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,29]]},"references-count":31,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,2]]}},"alternative-id":["e17020539"],"URL":"https:\/\/doi.org\/10.3390\/e17020539","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2015,1,29]]}}}