{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T16:05:03Z","timestamp":1779379503047,"version":"3.53.1"},"reference-count":26,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T00:00:00Z","timestamp":1779321600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>With the development of shipping to harsh marine environment, it is very important to understand the transient behavior of a marine diesel engine in high sea conditions. Wave-induced hull motion will lead to severe load fluctuations and air-fuel ratio imbalance. In this study, an integrated simulation platform coupled with environmental loads, hull dynamics, propeller characteristics and a high-fidelity thermodynamic engine model was constructed to explore the response characteristics of the propulsion system. The model integrates a zero-dimensional multi-zone combustion method, turbocharger dynamic characteristics and an incremental PID governor, and has been verified based on the bench test data of TBD234V12 diesel engine and the 20 m Wigley standard ship. The simulation results under the sea conditions from level 7 to 9 show that the transient load has a nonlinear amplification effect. Specifically, from sea state 7 to sea state 9, the engine load fluctuation range expands by 2.0 times, while the main peak amplitude of speed fluctuation increases by 3.7 times. Furthermore, the peak exhaust pressure rises by 1.8 times, and the exhaust temperature fluctuation amplitude broadens by 35%. Frequency domain analysis further identified the low-frequency energy concentration phenomenon in the exhaust pressure spectrum and the precursor characteristics of compressor surge. The research results quantify the deterioration law of thermodynamic stability and mechanical stress under wave disturbance, and provide an important reference for the formulation of an engine robust control strategy and fatigue life assessment under high sea conditions.<\/jats:p>","DOI":"10.3390\/a19050421","type":"journal-article","created":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T15:02:27Z","timestamp":1779375747000},"page":"421","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Simulation of a Four-Stroke Diesel Engine for Propulsion in Wave"],"prefix":"10.3390","volume":"19","author":[{"given":"Zhe","family":"Chen","sequence":"first","affiliation":[{"name":"Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fan","family":"Shi","sequence":"additional","affiliation":[{"name":"Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5899-1941","authenticated-orcid":false,"given":"Jiawang","family":"Li","sequence":"additional","affiliation":[{"name":"Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guangnian","family":"Li","sequence":"additional","affiliation":[{"name":"Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Mallouppas, G., and Yfantis, E.A. (2021). Decarbonization in Shipping Industry: A Review of Research, Technology Development, and Innovation Proposals. J. Mar. Sci. Eng., 9.","DOI":"10.3390\/jmse9040415"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Xin, R., Zhai, J., Liao, C., Wang, Z., Zhang, J., Bazari, Z., and Ji, Y. (2022). Simulation Study on the Performance and Emission Parameters of a Marine Diesel Engine. J. Mar. Sci. Eng., 10.","DOI":"10.3390\/jmse10070985"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"116927","DOI":"10.1016\/j.oceaneng.2024.116927","article-title":"A mathematical model for ships maneuvering in deep and shallow waters","volume":"295","author":"Yang","year":"2024","journal-title":"Ocean. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Watson, N., Pilley, A.D., and Marzouk, M. (1980). A combustion correlation for diesel engine simulation. SAE Tech. Pap.","DOI":"10.4271\/800029"},{"key":"ref_5","unstructured":"Hendricks, E. Mean value modelling of large turbocharged two-stroke diesel engines. SAE Int. Congr. Expo."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Livanos, G.A., Simotas, G.N., Dimopoulos, G.G., and Kyrtatos, N.P. (2006, January 7\u201310). Simulation of Marine Diesel Engine Propulsion System Dynamics During Extreme Maneuvering. Proceedings of the ASME 2006 Internal Combustion Engine Division Spring Technical Conference (ICES2006), Aachen, Germany.","DOI":"10.1115\/ICES2006-1366"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1504\/IJVD.2007.013675","article-title":"Quasi-linear versus filling and emptying modelling applied to the transient operation of a turbocharged diesel engine","volume":"45","author":"Rakopoulos","year":"2007","journal-title":"Int. J. Veh. Des."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1080\/20464177.2009.11020225","article-title":"Simulation of the dynamics of a marine diesel engine","volume":"8","author":"Maftei","year":"2009","journal-title":"J. Mar. Eng. Technol."},{"key":"ref_9","unstructured":"Wang, H. (2007). Modeling and System Simulation of Large Low-Speed Marine Diesel Engine. [Ph.D. Thesis, Dalian Maritime University]."},{"key":"ref_10","first-page":"193","article-title":"On the cycle mean value modelling of a large two-stroke marine diesel engine","volume":"224","author":"Theotokatos","year":"2010","journal-title":"Proc. Inst. Mech. Eng. Part M J. Eng. Marit. Environ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.oceaneng.2015.04.004","article-title":"Thermodynamic simulation for the investigation of marine Diesel engines","volume":"102","author":"Murphy","year":"2015","journal-title":"Ocean Eng."},{"key":"ref_12","first-page":"158","article-title":"Modeling and simulation of large marine diesel engine propulsion system","volume":"55","author":"Tu","year":"2014","journal-title":"Shipbuild. China"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.ijnaoe.2016.08.004","article-title":"Simulation of a two-stroke diesel engine for propulsion in waves","volume":"9","author":"Yum","year":"2017","journal-title":"Int. J. Nav. Archit. Ocean Eng."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Stoumpos, S., Theotokatos, G., Mavrelos, C., and Boulougouris, E. (2020). Towards Marine Dual Fuel Engines Digital Twins\u2014Integrated Modelling of Thermodynamic Processes and Control System Functions. J. Mar. Sci. Eng., 8.","DOI":"10.3390\/jmse8030200"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"117126","DOI":"10.1016\/j.energy.2020.117126","article-title":"Development of a diesel engine\u2019s digital twin for predicting propulsion system dynamics","volume":"196","author":"Bondarenko","year":"2020","journal-title":"Energy"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Moon, J. (2026). Comparative Analysis of Performance and Emissions of a Two-Stroke Marine Diesel Engine According to CPP Modes. J. Mar. Sci. Eng., 14.","DOI":"10.3390\/jmse14040331"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"129197","DOI":"10.1016\/j.applthermaleng.2025.129197","article-title":"Diesel\u2013Methanol Dual-Fuel engine modeling including combustion characteristics and transient system dynamics","volume":"284","author":"Karystinos","year":"2025","journal-title":"Appl. Therm. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Vollbrandt, J., Coraddu, A., Geertsma, R., and Stapersma, D. (2026). High-fidelity mean value first principle modelling of dynamic response in spark-ignited marine engines: A comparative analysis of gas path and turbocharger representations. J. Mar. Eng. Technol., 1\u201330.","DOI":"10.1080\/20464177.2026.2618326"},{"key":"ref_19","first-page":"103","article-title":"Simulation of the overall ship propulsion plant for performance prediction and control","volume":"111","author":"Kyrtatos","year":"1999","journal-title":"Trans. Inst. Mar. Eng. Ser. C"},{"key":"ref_20","first-page":"617","article-title":"Interaction between ship propulsion plant automation and simulation","volume":"Volume 1","author":"Benvenuto","year":"2005","journal-title":"Maritime Transportation and Exploitation of Ocean and Coastal Resources"},{"key":"ref_21","first-page":"V002T08A069","article-title":"Numerical prediction of the added resistance of ships in waves","volume":"Volume 45400","author":"Ley","year":"2014","journal-title":"Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering"},{"key":"ref_22","unstructured":"Saravanamuttoo, H.I.H., Rogers, G.F.C., and Cohen, H. (2009). Gas Turbine Theory, Pearson Education."},{"key":"ref_23","unstructured":"Liu, C. (2017). Research on Modeling and Simulation of Diesel Engine Based on Modelica Language. [Master\u2019s Thesis, Harbin Engineering University]."},{"key":"ref_24","unstructured":"Qu, X. (2020). Research on Energy Efficiency Optimization of Fuel Cell\/Lithium Battery Hybrid Power Ship Considering Multiple Factors. [Ph.D. Thesis, Wuhan University of Technology]."},{"key":"ref_25","unstructured":"Ding, C. (2022). Research on backstepping fuzzy control and visual simulation technology for dynamic positioning ships in high sea states. [Ph.D. Thesis, Harbin Engineering University]."},{"key":"ref_26","unstructured":"Heywood, J.B. (2018). Internal Combustion Engine Fundamentals, McGraw-Hill."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/5\/421\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T15:09:55Z","timestamp":1779376195000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/5\/421"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,21]]},"references-count":26,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["a19050421"],"URL":"https:\/\/doi.org\/10.3390\/a19050421","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,21]]}}}