Wyniki wyszukiwania - BazTech

1

Proper orthogonal decomposition analysis of an atomized fuel spray of marine diesel engine

Grochowalska Joanna, Wrzask Klaudia, Kapusta Łukasz Jan

Combustion Engines

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2026

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R. 65, nr 1

167--175

EN

Most marine vessels are powered by diesel engines. Unfortunately, fuel combustion releases harmful toxic compounds into the atmosphere. The International Maritime Organization (IMO) regulates these emissions, making their reduction essential for engineers and scientists. The fuel combustion process in a marine diesel engine's cylinder precedes the fuel spray injection and atomization. Fuel spray's flow fluctuations and vortex structures significantly impact the combustion. This paper presents research using the Mie Scattering optical technique to analyze snapshot sequences of spray patterns recorded with a high-speed camera. These snapshots are the results of experimental research on atomized fuel sprays with a marine diesel engine injector within a constant volume chamber. The influence of different chamber backpressures on the fuel spray is studied. The Proper Orthogonal Decomposition (POD) method is promising for quantitatively analyzing spray structures and flow characteristics. This research demonstrates how different chamber conditions affect the decay of the POD singular values, which typically indicate flow characteristics like coherence and fluctuations.

2

Multi-Symptom Diagnostic Investigation of the Working Process of a Marine Diesel Engine: Case Study. Part 2 Simulation Diagnostics

Korczewski Zbigniew, Varbanets Roman, Minchev Dmytro, Rudnicki Jacek

Polish Maritime Research

|

2025

|

nr 4

87--96

EN

This second part of our manuscript deals with the diagnostic capabilities of the Blitz-PRO utility computer program. These capabilities form the basis of the Weichai WP4 engine’s digital twin, in terms of multi-symptom identification of selected states of the engine’s fed system and valve train system. These states include the use of non-standard fuel, the wear of precision pairs of the high-pressure fuel pump, and mismatched camshaft positioning during engine assembly after maintenance. The basic assumptions of the mathematical model of the diesel engine used in Blitz-PRO are outlined here, and numerical experiments are conducted on the model to simulate the behaviour of the Weichai WP4 engine after the introduction of the considered states. Based on the results of numerical simulations of the working process, a relational model is proposed, which forms the basis for diagnostic reasoning. A comparative analysis of the changes in the diagnostic parameters of the relational model and the resulting syndromes enables early detection of similar states of fuel-fed systems for similar engine types.

3

Multi-Symptom Diagnostic Investigation of the Working Process of a Marine Diesel Engine: Case Study. Part 1. Measurement Diagnostics

Korczewski Zbigniew, Rudnicki Jacek, Varbanets Roman, Minchev Dmytro

Polish Maritime Research

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2025

|

nr 2

50--61

EN

The manuscript discusses the issue of diagnostic informativeness of measurement signals recorded during electronic indication of marine engine cylinders. It was noted that the “ fault-syndrome” relations of the diagnostic model determined on this basis are usually ambiguous, which forces the need to search for additional symptoms that ultimately confirm the diagnosis. A method of multi-symptom recognition of disturbances in the engine’s working process is presented by means of measurement experiments carried out on a real object and numerical experiments, with the appropriate usage of its “digital twin”. In the first part of the manuscript, the possibilities of carrying out diagnostic conclusions about the technical health of the valve timing system of a single-cylinder, naturally aspirated Farymann Diesel type D10 marine engine were examined based on simultaneous measurements of its standard operating parameters, exhaust gas composition, in-cylinder pressure and acoustic vibrations generated from the cylinder head by the working fuel injector and cylinder valves. Selected metrological issues of conductiong such measurements. As a result of the engine tests, extensive wear of the camshaft cams was identified, which resulted in premature closing of the exhaust valve and delayed opening of the intake valve. The shifts in the valve timing were so significant that there was practically no valves openning overlap in the cylinder flushing phase. To finally verify the primary formulated diagnosis, dynamic measurements of the engine valve timing were conducted using external inductive sensors, and then the camshaft was dismantled from the engine and subjected to direct optical examinations.

4

Multi-criteria analysis of the emission of harmful compounds from a marine diesel engine fueled with a mixture of marine fuel and n-butanol

Bogdanowicz Artur, Socik Paweł, Zadrąg Ryszard, Zacharewicz Marcin, Wirkowski Paweł

Combustion Engines

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2025

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R. 64, nr 4

9--15

EN

The article analyses in detail the impact of adding n-butanol to marine fuel on the emission of harmful compounds in diesel engines used in maritime transport. The applied multi-criteria analysis showed that introducing n-butanol as a fuel additive can significantly reduce the emission of substances such as nitrogen oxides (NOx), carbon monoxide (CO), and carbon dioxide (CO2), which consequently reduces the negative impact on the natural environment. In addition, the studies confirm that the mixture does not affect the operational efficiency of engines, which means that it can be used without the need to introduce major changes to the infrastructure or to the vessels themselves. Nevertheless, the authors emphasise that further research is necessary, especially at higher concentrations of n-butanol, to optimise this method in terms of long-term ecological and economic benefits and to ensure its full effectiveness. The conclusions indicate the potential of this technology, but they emphasise that it will be crucial to carry out additional tests to minimise the risk of possible negative side effects.

5

Comparison of methods for diagnosing marine IC engines based on working medium parameters including exhaust gas specific enthalpy

Puzdrowska Patrycja

Combustion Engines

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2025

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R. 64, nr 2

3--13

EN

The article points out methods currently used to diagnose marine engines in operation. The development of tools and programs for implementing these methods was pointed out. The problem of unsatisfactory measurement susceptibility of marine engines was highlighted. Three methods of parametric diagnosis are presented: measurement of in-cylinder parameters and in exhaust gas duct, numerical simulation due to computer software, and calculations based on the Wibe function. Unfitness states that were analyzed during tests are presented: reduced injection pressure, obstructed intake air duct, and reduced compression ratio. The specific enthalpy of the exhaust gas within one engine cycle was determined as a new diagnostic parameter. As a supplement, thermograms of the engine in various states of inoperability were presented. The results obtained were compared, and a series of conclusions were presented. It was evaluated that numerical simulation is an excellent tool for planning experimental studies. Tests on the engine in operation were found to be the most diagnostically reliable.

6

Fault diagnosis of marine diesel engine based on multi-scale time domain decomposition and convolutional neural network

Li Congyue, Cui Dexin

Polish Maritime Research

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2024

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nr 3

85--93

EN

Marine diesel engines work in an environment with multiple excitation sources. Effective feature extraction and fault diagnosis of diesel engine vibration signals have become a hot research topic. Time-domain synchronous averaging (TSA) can effectively handle vibration signals. However, the key phase signal required for TSA is difficult to obtain. During signal processing, it can result in the loss of information on fault features. In addition, frequency multiplication signal waveforms are mixed. To address this problem, a multi-scale time-domain averaging decomposition (MTAD) method is proposed and combined with signal-to-image conversion and a convolutional neural network (CNN), to perform fault diagnosis on a marine diesel engine. Firstly, the vibration signals are decomposed by MTAD. The MTAD method does not require the acquisition of the key phase signal and can effectively overcome signal aliasing. Secondly, the decomposed signal components are converted into 2-D images by signal-to-image conversion. Finally, the 2-D images are input into the CNN for adaptive feature extraction and fault diagnosis. Through experiments, it is verified that the proposed method has certain noise immunity and superiority in marine diesel engine fault diagnosis.

7

Evaluation of the impact of the thermal state of a diesel engine on its efficiency

Zacharewicz Marcin, Zadrąg Ryszard, Bogdanowicz Artur, Socik Paweł, Wirkowski Paweł, Hołownia Jakub

Combustion Engines

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2024

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R. 63, nr 1

30--36

EN

The paper presents the results of model and empirical research on the influence of the thermal state of a diesel engine (oil temperature) on its indicated (thermal) efficiency. The paper contains a test plan, including a description of the test object, test equipment, and measurement points on a real object. In the following part, the results of tests carried out on a real object (laboratory single-cylinder engine) and the results of model tests obtained on the original engine model are presented. The results are presented both in tabular and graphical form. The obtained test results allowed to determine the relative value of the influence of the engine's thermal state on its efficiency for various operating conditions (load and rotational speed).

8

Influence of Butanol-Diesel Oil Fuel Blends on Marine Engine Vibration Characteristics

Kluczyk Marcin

Advances in Science and Technology. Research Journal

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2024

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Vol. 18, no. 5

372--384

EN

One of the primary sources contributing to vibrations in operational marine diesel engines is the combustion process of fuel injected into the cylinders. Hence, alterations in the injection process and the quality and type of fuel supplied to the engine can modulate the combustion parameters, consequently impacting noise and vibration levels. A literature review on this subject suggests that while some research has been conducted, mainly focusing on small engines in the automotive sector, there's been limited exploration in the marine domain. Despite the recent surge in manufacturers' interest in electrifying road transport vehicles, a similar trend has not been observed in sea transport besides short-range ferries, mainly due to the substantial range requirements of vessels. It is conceivable that the utilisation of liquid fuels in shipbuilding will persist. Presently, the predominant marine fuels are fossil-based, the reserves of which are progressively declining. However, the widespread adoption of alternative fuel additives like butanol holds promise in curbing fossil fuel consumption. One of the conditions to be met by a new commonly used fuel for marine engines is its good properties in limiting the parameters of accompanying processes like vibrations. The article delineates a comparative analysis of parameter values related to the vibrations of a marine engine fueled by different blends of butanol and diesel oil. Laboratory tests were conducted on a six-cylinder marine engine under load using a water brake, encompassing various engine loads to replicate real-world operating conditions accurately.

9

Fault diagnosis of me marine diesel engine fuel injector with novel IRCMDE method

Shi Qingguo, Hu Yihuai, Yan Guohua

Polish Maritime Research

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2023

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nr 3

96--110

EN

As an important component of the fuel injection system, the fuel injector is crucial for ensuring the power, economy, and emissions for a whole ME (machine electronically-controlled) marine diesel engine. However, injectors are most prone to failures such as reduced pressure at the opening valve, clogged spray holes and worn needle valves, because of the harsh working conditions. The failure characteristics are non-stationary and non-linear. Therefore, to efficiently extract fault features, an improved refined composite multi-scale dispersion entropy (IRCMDE) is proposed, which uses the energy distribution of sampling points as weights for coarse-grained calculation, then fast correlation-based filter (FCBF) and support vector machine (SVM) are used for feature selection and fault classification, respectively. The experimental results from a MAN B&W 6S35ME-B9 marine diesel engine show that the proposed algorithm can achieve 92.12% fault accuracy for injector faults, which is higher than multiscale dispersion entropy (MDE), refined composite multiscale dispersion entropy (RCMDE) and multiscale permutation entropy (MPE). Moreover, the experiment has also proved that, due to the double-walled structure of the high-pressure fuel pipe, the fuel injection pressure signal is more accurate than the vibration signal in reflecting the injector operating conditions.

10

Experimental study of fuel combustion and emission characteristics of marine diesel engines using advanced fuels

Changxiong Li, Hu Yihuai, Yang Zy, Guo Hao

Polish Maritime Research

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2023

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nr 3

48--58

EN

In order to explore the potential application of oxygenated fuels, polyoxymethylene dimethyl ethers (PODE), as an alternative fuel for marine diesel engines, the fuel combustion performance and gas emission characteristics of pure diesel oil, diesel-blended PODE, and pure PODE were tested on a marine diesel engine under different running conditions. The experimental results indicate that oxygen consumption can be reduced by diesel-blended PODE and pure PODE. The in-cylinder pressure and exothermic curve were consistent with the trend of diesel oil. Also, the ignition delay of diesel-blended PODE and pure PODE decreased, and the diffusion rate was accelerated, which helped to improve the combustion performance of diesel engines. Diesel blended PODE and pure PODE reduced the particulate matter (PM) emissions by up to 56.9% and 86.8%, respectively, and CO emissions by up to 51.1% and 56.3%, respectively. NOx emissions were gradually decreased with engine load. CO2 emissions were slightly increased, and the effective fuel consumption was increased up to 48% and 132%, respectively. It was shown that PODE could provide comparable power in a marine diesel engine and improve the fuel combustion and gas emission of the engine as a clean alternative fuel for marine diesel engines.

11

Digital Twin test-bench Performance for marine diesel engine applications

Minchev Dmytro, Varbanets Roman, Shumylo Oleksandr, Zalozh Vitalii, Aleksandrovska Nadiia, Bratchenko Pavlo, Truong Thanh Hai

Polish Maritime Research

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2023

|

nr 4

81--91

EN

The application of Digital Twins is a promising solution for enhancing the efficiency of marine power plant operation, particularly their important components – marine internal combustion engines (ICE). This work presents the concept of applying a Performance Digital Twin for monitoring the technical condition and diagnosing malfunctions of marine ICE, along with its implementation on an experimental test-bench, based on a marine diesel-generator. The main principles of implementing this concept involve data transmission technologies, from the sensors installed on the engine to a server. The Digital Twin, also operating on the server, is used to automatically process the acquired experimental data, accumulate statistics, determine the current technical state of the engine, identify possible malfunctions, and make decisions regarding changes in operating programs. The core element of the Digital Twin is a mathematical model of the marine diesel engine’s operating cycle. In its development, significant attention was devoted to refining the fuel combustion model, as the combustion processes significantly impact both the engine’s fuel efficiency and the level of toxic emissions of exhaust gases. The enhanced model differs from the base model, by considering the variable value of the average droplets’ diameter during fuel injection. This influence on fuel vapourisation, combustion, and the formation of toxic components is substantial, as shown. Using the example of calibrating the model to the test results of a diesel engine under 27 operating modes, it is demonstrated that the application of the improved combustion model allows better adjustment of the Digital Twin to experimental data, thus achieving a more accurate correspondence to a real engine.

12

Diagnostic analysis of exhaust gas with a quickchanging temperature from a marine diesel engine part II / two factor analysis

Puzdrowska Patrycja

Polish Maritime Research

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2023

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nr 3

89--95

EN

The article presents a continuation of research carried out to determine the effect of input parameters (changes in engine structure parameters) on selected output parameters (diagnostic measures), based on quickly changing exhaust gas temperature. A method of determining the simultaneous influence of two input factors (the structure parameter and the engine load) on one output factor was presented, as well as an evaluation of which of the analysed input factors has a stronger influence on the output parameter. The article presents the stages of the experimental research conducted and statistical inference based on the results. Three changing parameters for the structure were reviewed: the active cross-sectional area of the inlet air channel, the injector opening pressure and the compression ratio. Based on the quickly changing temperatures of the exhaust gases, three diagnostic measures were defined and subjected to statistical tests. The following data were averaged over one cycle for a 4-stroke engine operation: the intensity of changes, the specific enthalpy and the peak-to-peak value of the exhaust gas temperature. The results of the two-factor analysis are presented. Conclusions on the analysis are given and a criterion for the selection of a diagnostic measure, depending on the analysed parameter of the structural design of the diesel engine, is proposed. The previous part of the article presented the results of the first stage of the elimination study: the one-factor statistical analysis (randomised complete plan). This paper presents the results of the second stage of the studies: two-factor analysis (block randomised plan), where the significance of the effect of changing the values of the structural parameters on the diagnostic measures were analysed in the background of a variable engine load. The next (third) part will present the results of the calculations and analysis of the interaction coefficient of significance.

13

Evaluation of the influence of the opening pressure of a marine diesel engine injector on the results of numerical simulation of the working cycle and their comparison with the results of the laboratory experiment

Puzdrowska Patrycja

Combustion Engines

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2023

|

R. 62, nr 2

9--14

EN

The article presents the results of a numerical simulation of the working process carried out in a diesel engine. In the applied utility program DIESEL-RK, the laboratory engine Farymann Diesel type D10 was implemented. A selected inoperability of its functional fuel supply system - reduced opening pressure of the injector pinj - was introduced. The values of adequate diagnostic parameters were determined: working gas temperature in the cylinder Tcyl, exhaust gas temperature Texh, combustion (flame) temperature Tcomb and concentration of nitrogen oxides in the exhaust gas NOx. Experimental tests were carried out on the experimental engine with the inoperative condition actually introduced, analogous to the numerical simulation, and the diagnostic parameters Texh and NOx were recorded. The results obtained by numerical simulation of the processes and during the active experiment on the experimental engine were compared.

14

Analysis of the structure of the atomized fuel spray with marine diesel engine injector in the early stage of injection

Grochowalska Joanna, Jaworski Piotr, Kapusta Łukasz Jan

Combustion Engines

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2023

|

R. 62, nr 4

97--103

EN

This paper presents the results of the experimental research of the atomized fuel spray with the marine diesel engine injector in the constant volume chamber. The specificity of the phenomena occurring in the marine engine cylinder was the reason to use the optical visualisation method in the studies - the Mie scattering technique. This work presents an analysis of the influence of different geometry of outlet orifice and opening pressures of marine diesel injector on the macrostructure of the fuel spray. In the results, it was observed that the increased L/D ratio of the outlet orifice of the injector caused: an increase in the spray cone angle and a decrease in the spray tip penetration in the early stage of injection. Furthermore, it was defined that the characteristic of spray tip penetration over time was power, whereas the spray cone angle over time was a logarithmic function.

15

Comparison of selected models useful in ranking the root causes of explosions in marine engine crankcases

Wiaterek Daniel, Chybowski Leszek

Zeszyty Naukowe Akademii Morskiej w Szczecinie

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2022

|

nr 72 (144)

77--85

EN

This article aims to compile, describe and compare three different models taken from the literature describing the causes of explosions in the crankcases of marine engines. Each of the models has a different level of detail and was prepared with a different purpose. However, the same process, explosions in crankcases, was analyzed in all cases. A statistical evaluation of the frequency of events leading to explosions, a model built using failure mode and effects analysis (FMEA) and a model based on fault tree analysis (FTA) are described in turn. The FTA model drawn from the literature formed the basis for further analysis. Values of important measures of all elementary events of the fault tree were calculated using the Birnbaum reliability measure, Vesely-Fussell measure, Birnbaum structural measure, criticality measure and improvement potential. The percentage importance values of all events determined using these importance measures were compared. The results obtained from the application of each model were evaluated. The results of the models were compared with each other, and an approach using all three models supplemented with diversion analysis was proposed.

16

Assessing the topicality of the problem related to the explosion of crankcases in marine main propulsion engines (1972–2018)

Wiaterek Daniel, Chybowski Leszek

Zeszyty Naukowe Akademii Morskiej w Szczecinie

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2022

|

nr 71 (143)

33--40

EN

The purpose of this paper is to present the results of a query aimed at assessing the validity of the topic of crankcase explosions prevention in the main marine engines. The study takes into account the engine type, engine manufacturer, ship’s age, accident severity, ship’s location at the time of the incident, and the share of fatal accidents in the analyzed population of crankcase explosions. One of the primary hazards associated with offshore and deep-sea ship operations – and primarily ship power plants – are fires and explosions that result in accidents and incidents with an average frequency of 60 days. This paper discusses the actuality of crankcase explosion hazards in the main propulsion engines of various types of sea vessels. The assessment was made based on the results of a statistical analysis of historical data from 1972 to 2018. The methodology consisted of three stages: (1) a selection query to obtain the source data, (2) analysis of the obtained results (data separation, extraction of additional information, and statistical analysis), (3) synthesis of the obtained information, and drawing conclusions about the numerical indicators describing the statistical distribution of individual events for the given evaluation criteria. The analysis showed that the risk of crankcase explosions affects ships of all ages – both in crosshead (31%) and trunk piston engines (61%) – and that the number of serious incidents (67%) remained constant over the investigated period. Half of all incidents occurred on vessels younger than 15 years old. 58% of explosions took place in engines of the most popular prime movers manufacturers. The probability that a main engine crankcase explosion will result in injury or death is 17.34%.

17

Multiparameter approximation model of temperature conditions of marine diiesel generator sets, based on Markov chain Monte Carlo

Myrhorod V., Hvozdeva I., Budashko V.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

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2022

|

Vol. 16 No. 4

779--784

EN

In the article we propose a multi-parameter approximation model, based on Markov chain Monte Carlo, which describes the relationship between the temperature regime, operating conditions and electromechanical parameters of marine diesel generator sets. The approximation model is constructed on the basis of the analysis of experimental data of the exhaust gases temperature of marine diesel generator sets in their long-term operation. As a statistical model of random processes of temperature deviations from the approximation model, a Markov process model is proposed that takes into account the possible correlation of the initial data. Since the measuring channels of modern diagnostic systems are digital, due to discretization in time and level, the studied processes form a Markov chain, which makes it possible to establish the important features of such processes. The use of approximation models ensures the stationarity conditions and the correctness of the proposed Markov model in the conditions of multi-mode operation of marine diesel generator sets. The proposed multi-parameter approximation model, based on Markov chain Monte Carlo, allows you to take into account random perturbations that lead to a random change in the output coordinates of the diagnostic object. The proposed improvement of the model makes it possible to ensure its adequacy to real processes of changing the parameters of the temperature regimes of marine diesel generator sets. The proposed multi-parameter approximation model, based on Markov chain Monte Carlo, can be used in the systems of technical diagnostics of marine diesel generator sets in order to increase the reliability of diagnostic conclusions.

18

Wyniki symulacji numerycznej cyklu roboczego silnika o ZS w programie DIESEL-RK oraz ocena ich użyteczności w procesie planowania badań diagnostycznych okrętowego silnika tłokowego

Puzdrowska Patrycja

Journal of Polish CIMEEAC

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2022

|

Vol. 17, no 1

74--82

PL

W artykule przedstawiono wyniki symulacji numerycznej procesu roboczego realizowanego w silniku tłokowym o zapłonie samoczynnym. W zastosowanym programie użytkowym DIESEL-RK zaimplementowano silnik laboratoryjny Farymann Diesel typ D10. Wprowadzono wybraną niesprawność jego układu funkcjonalnego zasilania paliwem - obniżone ciśnienie otwarcia wtryskiwacza pwtr. Wyznaczono wartości adekwatnych parametrów diagnostycznych: temperaturę i ciśnienie gazu roboczego w cylindrze Tcyl i pcyl, temperaturę i ciśnienie spalin wylotowych Tsp i psp, temperaturę spalania (płomienia) Tspal, prędkość spalin wylotowych vsp oraz stężenie cząsteczek NOx. Oceniono użyteczność wyników przeprowadzonej symulacji do wyboru analizowanych parametrów struktury konstrukcyjnej silnika oraz do selekcji parametrów, które mogą być wykorzystane w badaniach diagnostycznych silnika laboratoryjnego.

19

Possibilities for Improving the Cooling Systems of IC Engines of Marine Power Plants

Moshentsev Yuryi, Gogorenko Oleksiy, Dvirna Olha

Advances in Science and Technology. Research Journal

|

2022

|

Vol. 16, no. 3

183--192

EN

Modern cooling systems for large ships are quite complex. As a rule, such systems are common (combined) for the main and auxiliaries engines. With the auxiliary engines running constantly, even when parked, this system design allows to keep it warm and ready for a quick start of the main engines at any time. Currently, various schemes of such systems are used, including those that are irrational from our point of view. At the same time, there are systems whose schemes are quite consistent with our idea of the rational forms of such structures. It is important to note, and it is saying about it in an article, that such schemes may have a number of significant differences, but at the same time they will comply with the rationality principle if certain rules for the formation of such systems are followed. These schemes will have close compactness. It is also important that there is the possibility of further improvement of such schemes based on certain rules. This improvement is possible due to the introduction of additional heat dissipaters and the organization of appropriate chains of heat sources and heat dissipaters. The article discusses various options for rational schemes of the cooling system for the same ship power plant, as well as the possibility of further improvement of this scheme. It is shown that an increase in the number of coolants of the internal circuit coolant from one to three can reduce the total mass of the heat exchanger cores by 18 %.

20

Performance and emission modelling and simulation of marine diesel engines using publicly available engine data

Ghaemi Mohammad Hossein

Polish Maritime Research

|

2021

|

nr 4

63--87

EN

To analyse the behaviour of marine diesel engines in unsteady states for different purposes, for example to determine the fuel consumption or emissions level, to adjust the control strategy, to manage the maintenance, etc., a goal-based mathematical model that can be easily implemented for simulation is necessary. Such a model usually requires a wide range of operating data, measured on a test stand. This is a time-consuming process with high costs and the relevant data are not available publicly for a selected engine. The present paper delivers a rapid and relatively simple method for preparing a simulation model of a given marine diesel engine, based only on the widely available data in the project guides indicated for steady state conditions. After establishing the framework of the mathematical model, it describes how the parameters of the model can be adjusted for the simulation model and how the results can be verified as well. Conceptually, this is a trial and error method, but the presented case example makes clear how the parameters can be selected to reduce the number of trials and quickly determine the model parameters. The necessary descriptions are given through a case study, which is the MAN-B&W 8S65ME-C8 marine diesel engine. The engine is assumed to be connected to a constant pitch propeller. The presented mathematical model is a mean-value zero-dimensional type with seven state variables. The other variables of the engine are determined based on the state independent variables and the input value, which is the fuel rate. The paper can be used as a guideline to prepare a convenient mathematical model for simulation, with the minimum publicly available data.