Type Of Internal Combustion Engine Research Articles

Analysis of the Principle and Applications of Four-stroke Engines in Transportation

Abstract. Four-stroke engines a type of internal combustion engine (IC engine) that can turn the heat provided from the fuel to work, and they are mainly classified as two groups, which are gasoline engines and diesel engines. Four-stroke engines can be applied to high power machines because of its high thermal efficiency. In four-stroke engines, the piston reaches the dead center four times in the cylinder to complete a cycle. This cycle includes the taking in of gas, the compression, the ignition, the expansion and the exhaustion of gas. In gasoline engine, this cycle is called the Otto cycle, and in diesel engine, this cycle is called the Diesel cycle. The greatest difference between these two engines is that they burn different types of fuel. In that way, the procedure of converting the heat to work is different. To help this cycle performs better economically and more efficiently, additional attachments such as hybrid engine and computer assistance are used. This research summarizes and analyses the application of four-stroke engines in land transportation, in aviation and in marine transportation, and this article gives a possible prediction to the future trend of the technology advancements of engines in transportation based on the analyses.

A Comparative Analysis of Friction and Energy Losses in Hydrogen and CNG Fueled Engines: Implications on the Top Compression Ring Design Using Steel, Cast Iron, and Silicon Nitride Materials.

Optimizing the design of the top compression ring holds immense importance in reducing friction across both traditional Internal Combustion (IC) engines and hybrid power systems. This study investigates the impact of alternative fuels, specifically hydrogen and CNG, on the behavior of top piston rings within internal combustion (IC) engines. The goal of this approach is to understand the complex interplay between blow-by, fuel type, material behavior, and their effects on ring friction, energy losses, and resulting ring strength. Two types of IC engines were analyzed, taking into account flow conditions derived from in-cylinder pressures and piston geometry. Following ISO 6622-2:2013 guidelines, thick top compression rings made from varying materials (steel, cast iron, and silicon nitride) were investigated and compared. Through a quasi-static ring model within Computational Fluid Dynamics (CFD), critical tribological parameters such as the minimum film and ring friction were simulated, revealing that lighter hydrogen-powered engines with higher combustion pressures could potentially experience approximately 34.7% greater power losses compared to their heavier CNG counterparts. By delving into the interaction among the fuel delivery system, gas blow-by, and material properties, this study unveils valuable insights into the tribological and structural behavior of the top piston ring conjunction. Notably, the silicon nitride material demonstrates promising strength improvements, while the adoption of Direct Injection (DI) is associated with approximately 10.1% higher energy losses compared to PFI. Such findings carry significant implications for enhancing engine efficiency and promoting sustainable energy utilization.

RETRACTED: Research on the kinetics characteristics and in-cylinder combustion of opposed rotary piston engine for different power output modes

As a new type of internal combustion engine, opposed rotary piston (ORP) engine has the advantages of simple structure and high working frequency, and can achieve high power density. Consequently, it stands as an ideal power source for hybrid power systems and unmanned aerial vehicles. The ORP engine has different power output modes, corresponding to different piston rotation and volume evolutions of combustion chamber. However, the effect of power output modes on kinetics characteristics and in-cylinder combustion of ORP engines are still uncovered. In this paper, the kinematic model of an ORP engine is established for scenarios involving power output by different shafts (Shaft 1 and Shaft 3). Meanwhile, the piston rotation patterns and cylinder volume variations are investigated correspondingly. Further, three-dimensional numerical model of the ORP engine is established, enabling analysis of in-cylinder combustion characteristics, engine performance, as well as nitrogen oxides (NOx) emissions. The results indicate that the volume variations of all cylinders follow a consistent pattern under the power output by Shaft 3. A pair of opposed cylinders features longer durations of intake and expansion strokes, and shorter durations of compression and exhaust strokes, the other pair of combustion chambers is the opposite under the power output by Shaft 1. The engine demonstrates a charging efficiency of 95.36 %, with corresponding indicated thermal efficiency and indicated power output of 38.08 % and 40.9 kW, respectively. The two adjacent cylinders present significantly different operation processes in the case of the power output by Shaft 1, achieving charging efficiencies of 94.29 % and 89.11 %, respectively, with the indicated thermal efficiency of 34.49 % and 31.60 %. The corresponding minimum indicated specific fuel consumption under the two power output modes are 211.7 g/kW∙h and 243.7 g/kW∙h, respectively, accompanied by NOx emission factors of 25.3 g/kW∙h and 17.6 g/kW∙h. With the given range of ignition timing, a trade-off relationship exists between the engine performance and NOx emissions. The power density of the case of power output by Shaft 3 is superior to that of Shaft 1.

Gas turbine aero engine fault detection using Geo-TLSVM and digital twin with multimodal data analysis

DT is the digital representation of physical systems to simulate real situations in a digital version. Here, the DT of the GaT-AE is created for the Fault Detection (FD) process. The GaT is a type of internal combustion engine that uses the air as the working fluid to propel the flight. However, the incorporation of big data analysis in the DT model is challenging in previous works. So, a multimodal GaT-AE fault identification system is proposed. First, the 3D print of the GaT-AE is created. Then, the data is collected from both built-in sensors and DT. Afterward, the multimodal data is pre-processed and balanced by using HT-QNN and QADASYN, respectively. Next, the features are processed by GT-PFS, and finally, the faults are detected by Geo-TLSVM. The analysis proved that the developed model outperformed the other state-of-the-art model with its effective FD rate of 97.24%.

A REVIEW OF EGR APPLICATION FOR AUTOMOTIVE INDUSTRY

Exhaust gas recirculation (EGR) has been widely adopted as an effective strategy to reduce harmful emissions and improve fuel efficiency in internal combustion engines. This review paper aims to provide a comprehensive analysis of the utilization of EGR in various types of internal combustion engines. The review covers the principles of EGR operation, its effects on engine performance, emission reduction capabilities, challenges, and prospects. By evaluating the existing literature and research findings, this paper seeks to offer insights into the potential of EGR as a crucial technology for sustainable and environmentally friendly auto-motive propulsion systems.

Four variants of turbofan, turbojet, turboprop and ramjet engines and their future prospects

A jet engine is a sophisticated machine that has revolutionized the aviation industry. It is a type of internal combustion engine that uses air as its oxidizer and fuel to produce thrust. The third law of motion, which states that there is an equivalent and opposite response to every action, governs how the engine functions. Compressed air is combined with fuel, ignited in the combustion chamber, and then expelled out of the jet engine at a high rate of speed to create propulsion. The development of jet engines has been a long and arduous process, with many different designs and configurations over the years. Early jet engines were inefficient, noisy, and prone to failure. However, technological advances have created more efficient and reliable engines in various applications, from commercial aviation to military aircraft and even spacecraft. The efficiency and reliability of jet engines have transformed air travel, enabling faster and more efficient travel over long distances. This has increased global connectivity, economic growth, and cultural exchange. However, jet engines also have environmental impacts, such as noise pollution and greenhouse gas emissions, which have led to the development of more environmentally friendly engines.

Characterization of particulate matter emissions from internal combustion engines using δ13C values: Impact of engine operation conditions and fuel type on PM10 isotopic composition

Stable carbon isotope ratio of particulate emissions from internal combustion engines (ICEs) is an important characteristic in atmospheric carbonaceous PM source studies. Long-term measurements (2009–2020) of δ13C values of commercial fuels in Lithuania were conducted to evaluate the current isotopic composition of the fuel due to the changing share of renewable energy sources (RES). In this work, we present experimental results on stable carbon isotope ratio (δ13C) in PM10 emitted by different types of ICEs (two-stroke and four-stroke), including on-road transport and non-road mobile machinery. Different driving scenarios were simulated on a test bench (idling, NEDC, different torque, and speed). At idle, the average δ13C(PM10) values of different fuel types were determined: −27.80‰ for gasoline, −28.97‰ for diesel, − 27.89‰ for biofuel-C3, and −16.95‰ for biofuel-C4. Isotopic fractionation during combustion in ICEs depended on fuel type. The magnitude of Δ13C was 3‰ for gasoline, 2‰ for diesel, 1.5‰ for biofuel-C3, and 0.6‰ for biofuel-C4. The δ13C values of ICEs-generated PM10 were found to be dependent on the amount biobased components such as hydrotreated vegetable oil (HVO) to the fuel. However, insubstantial differences were found between the δ13C of PM derived from pure diesel and from an ethanol/diesel blend (E40).

Modelling the Electric Bus Charging Network Requirements for HVAC Purposes

Wider use of electric buses is hindered by necessity to provide cabin heating for the passengers during winter months, which in cold climates uses up as much energy as driving, thus significantly reducing bus driving range and requiring larger traction batteries, which are expensive. When the lifetime operational costs are included, unless they are heavily subsidized, the battery electric buses have troubles competing with internal combustion engine (ICE) buses in cold weather conditions. For typical ICE buses, the power capacity for heaters is in the range of 50 kW. It would be possible to increase the driving range by using heat accumulators to provide energy for vehicle thermal requirements. These heat accumulators could be recharged in bus stops using wireless charging to minimize battery size. This article describes the results of a mathematical model developed to determine optimum wireless charging power requirements for heat accumulators. The model is created for public transportation system in Riga city based on weather data in years 2017–2022 to provide passenger thermal comfort. The model simulates energy flows for bus movement and heating purposes using worst-case scenario approach. The model analysed 198 916 bus stop data, which were pertinent for weekday travels in Riga city. The analysis covered 1716 individual bus stops and 448 routes. The results showed that the charging availability during the day varied from 3 % to 55 % and on average the total energy needed for heating would be 75.6 kWh. However, in the worst-case scenario, the number rises to 237 kWh making the system too expensive for practical applications. During the research there is a very limited availability of research regarding bus heating requirements. Most of the research on thermal comfort in busses are done in hot climate and consequently mostly concerns air conditioning. The thermal comfort research about cold weather is predominantly about buildings and indoor comfort and could not directly apply, as clothing should be considered. Also, the research shows that the temperatures for comfort are lower for short haul vehicles than for the long-haul ones. All these factors strongly indicate that current conventions on temperature requirements for buses are outdated and coming from ICE buses where the heat came from the engine and was free. Therefore, the next studies should include field research analysing passenger thermal comfort levels in buses in winter to explore if there are additional opportunities for energy savings in bus HVAC systems.

Artificial neural networks for speeding-up the experimental calibration of propulsion systems

Artificial neural networks have proven to be very useful, in different areas of investigation, for the realization of black box models able to represent the relationship between input and output data with high precision. In the automotive sector too, they have found widespread use, particularly for sub-models involving non-linear aspects. Most of these applications are not predictive, but mainly exploit the ability to obtain useful input–output relationships trough learning on scattered data. In contrast, the novelty of this paper is the use of a neural network, trained with experimental data in a portion of the operation area of the system to be calibrated, within a method used for forecasting purposes. The proposed framework consists of an iterative cycle of experimental tests, with control parameters identified by the neural network model, to reduce the time required for calibrating the entire working plan. This type of approach requires knowing the areas where the predictions of the model are sufficiently accurate. Therefore, a study was conducted for three different types of internal combustion engines, to evaluate a general trend of the prediction accuracy of the model, as a function of the distance from the training zone. In particular, the area where the learning was performed (10% of the engine operating plan) was expanded by 200%, with an error of approximately 5 times that of the training phase. Finally, the proposed method was compared with the best fitting surface approach and was found to be significantly reliable and accurate.

Current status and prospect of homogeneous charge compression ignition (HCCI) technology application of transportation

HCCI engine is a new concept in recent decades. HCCI is defined as a type of engine with little application and market proportion. HCCI engines have great potential and prospects in practical engineering applications. However, there is a lack of cognition of HCCI engine development. Therefore, this paper introduces the current status of HCCI technology application and the possible development in the future. Throughout collecting information of some parameters of engines and comparison and analysis, this paper researches the current status and prospect of HCCI engine application. Research shows that, HCCI engine has considerable merits, which are more eco-friendly, higher thermal efficiency and fuel economy, also HCCI engine is not be used in production. In the future, HCCI engine will expand the advantages and occupy market, eventually be the mainstream type of internal combustion engine. In addition, the analysis and research results of this paper will provide reference and reference for the future development of HCCI engine.

PENGARUH MODIFIKASI LUBANG BUANG TERHADAP DAYA DAN TORSI PADA SEPEDA MOTOR 2 TAK

Gasoline engine is one type of internal combustion engine that is widely used as a source of power for vehicles. Gasoline engines produce power from the combustion of fuel in the cylinders. In line with the development of science and technology, there are many improvements and developments of components to add power and torque. The purpose of this study was to determine the effect of modified exhaust cylinder block on power and torque on a 2 stroke Yamaha f1zr motorcycle with a modified exhaust hole height of 26 mm and a standard exhaust hole of 34 mm with a dynotest test to determine power and torque from 2500 RPM to RPM. 8000. The test results show that the maximum power at the modified exhaust hole is 12.5 HP at 7750 RPM while the standard exhaust port gets a maximum power of 11.5 HP at 7750 RPM. For the modified exhaust hole maximum torque is 11.36 Nm at 7750 RPM rotation while the standard exhaust hole obtains a maximum torque of 10.06 Nm at 7750 RPM rotation.Keywords: Power, torque, exhaust hole

Analysis of Exhaust Gas Emissions on Dual Fuel Diesel Engine Single Cylinder Four-stroke with LPG-Diesel Oil

Diesel engine is one of type of internal combustion engine that is applied in industry, including the maritime industry. The increasing use of diesel engines, has a effect on increasing emissions. Diesel engines emissions consist of SOx, NOx, HC, and others. To reduce the emissions, there are many method, one of them is using dual-fuel system. The alternative fuel can be used is Gas, which is easily available, namely LPG or liquefied petroleum gas. To supply LPG to combustion chamber, a converter-kit are needed to be install on diesel engine. There are several previous research that prove that LPG can be used as an alternative in a dual-fuel system and can reduce the emissions. One of them by Ma’amuri (2016) who designed a mechanical LPG-diesel oil as dual-fuel, using a membrane converter. Result of this research provide that good diesel engine performance. In this research, LPG-diesel oil as dual-fuel using converter kit based on ECU or electronic control unit, and then, analyze the diesel engine emissions with experimental method. The purpose of this research is to determine the emissions produced by LPG-diesel oil as dual-fuel with converter kit based ECU. After taking and analytical data, known that the NOx emission from dual fuel diesel engine using ECU-based converter kit is lower than NOx emission from conventional diesel engine with B30 diesel fuel with percentage is 25,61 % for 3ms opening duration of gas injector, 39,99 % for 4 ms opening duration of gas injector and 26,5 % for 5 ms opening duration of gas injector. The NOx emission of conventional diesel engine is 2,46 g/kWh.

Poboljšanje efikasnosti motora sa unutrašnjim sagorevanjem - perspektive primene motora sa slobodnim klipom (fpice) u poljoprivrednom inženjerstvu

The article discusses various schematic diagrams of a reciprocating internal combustion engine (ICE) and shows their main disadvantages, in particular, low efficiency, which, depending on the type of modern ICE, ranges from 0.25 to 0.5. To increase this indicator, the search for more advanced ICE schemes continues. For this purpose, a new schematic diagram of a free-piston internal combustion engine (FPICE) is proposed, in which power is transferred by a hydraulic drive, as a result, the efficiency increases from 30 to 40%.

Динамика судовых дизелей при использовании моторных масел с различными структурными характеристиками

Annotation – The influence of the structural characteristics of engine lube oil on the dynamics of a marine diesel engine is considered. It is indicated that micron layers of marine engine lube oils separating the contact surfaces of marine diesel engines acquire the properties of liquid crystals and are characterized by an ordered molecular structure. The qualitative indicator of this structure is the degree of ordering of the molecules, and the quantitative indicator is the thickness of the ordered (boundary) lubricating layer. It is proposed to determine the structural characteristics of marine engine lube oils (the degree of ordering of the molecules of the boundary layer and its thickness) using the optical method of absorption dichroism. A diagram of an experimental setup is presented that allows such studies to be carried out. It has been experimentally established that for Shell Rimula X15 and Castrol TPL 123 engine lube oils (used in the oil system of the Caterpillar CatC18 marine diesel engine), the thickness of the ordered (boundary) lubricating layer is 14.3 ... 14.7 microns and 16.4 ... 16.6 microns, respectively. The degree of ordering of molecules in the boundary layer for Shell Rimula X15 engine lube oil is in the range of 0.56 ... 0.58, for Castrol TPL 123 engine lube oil – in the range of 0.63 ... 0.64. The results of studies of the dynamics of the CatC18 marine diesel engine by Caterpillar, carried out in the starting mode, as well as at various increases and decreases in load, are presented. As indicators, which were used to assess the dynamics of the diesel engine, the overshoot of the rotational speed and the time to reach a new steady state mode were taken. Experiments have confirmed that Castrol TPL 123 engine lube oil, which has a higher molecular structure in the boundary layer compared to Shell Rimula X15 lube oil, ensures the transient processes of the Caterpillar CatC18 marine diesel engine with less overspeed and less time to reach a new state work. The proposed technology for determining the structural characteristics of engine lube oils can be used for any type and grade of oil (mineral or synthetic, high and low viscosity, used both in circulating and cylinder lubrication systems). The proposed method for assessing the dynamic characteristics of marine diesel engines (by overshoot of the speed and the time to reach a steady state of operation in the event of a change in load) can be used for any types of internal combustion engines (low-, medium- and high-speed; as well as performing the functions of both main and auxiliary engines).

Testing a device for starting an internal combustion engine at low temperature and prospects for its application

The starting of the internal combustion engine in conditions of low and critically low ambient temperatures is considered. It is shown that a successful start of an internal combustion engine can be ensured by creating a fuel-air mixture with a high temperature outside the engine compartment. The design of a device for creating such mixture and research experimental data are presented. A new scheme of the starting device is proposed, which can be integrated into various types of internal combustion engines. Keywords: internal combustion engine, starting, low temperature, operation. lysenkojo@mail.ru

Research on the Control Mode of Homogeneous Charge Compression Ignition Combustion Working Process and Its Technical Prospect

The homogeneous charge compression ignition (HCCI) engine is considered an advanced technique, a form of internal combustion in which well-mixed fuel and oxidizer (typically air) are compressed to the point of auto-ignition. HCCI engines have higher thermal efficiency and lower emissions than Spark Ignition (SI) and Compression Ignition (CI) engines. The emissions of NOx can be neglected compared to the CI engine. In addition, a wide variety of fuels, combinations of fuels and alternative fuels can be used in this type of internal combustion engine. Moreover, when investigating the heat release rate of a HCCI engine for both single- and two-stage ignition fuels, the results show that for both fuel types, the cycle changes in the ignition and combustion phases increase with the delay of the combustion phase. Also, the cycle change of iso-octane (the single-stage ignition fuel) is higher than that of PRF80 (the two-stage ignition fuel). This paper will first introduce the control mode of the HCCI engine and then review its current status from the perspective of combustion, emissions, and consumption. After presenting the current status, the authors present suggestions about the prospect of further development with respect to the timing of ignition, the expansion of the engine operating range, and the choice of fuel mixture in this new mode of technology.

A TOOL FOR THE ASSESSMENT OF THERMAL EFFICIENCY OF IDEAL DIESEL CYCLES, PROVIDED TO FUTURE MARINE ENGINEERS

Diesel engines are a type of internal combustion engine widely spread in the maritime sector. In a world depending on fossil fuels, the challenge faced by scientists and professionals consists in the efficient use of this kind of fuels. The future of these engines strongly depends on the efficiency enhancement. Future mechanical engineers have to be trained in order to gain engineering judgement and enterprising attitude. In this respect, this paper deals with a theoretical study focused on the improvement of the efficiency of the ideal Diesel cycle. This type of study was recently introduced in Constanta Maritime University, within Thermodynamics seminar activities, delivered to future marine engineers, enrolled in their third semester. This study will reveal the fact that the efficiency of Diesel cycles is affected by the variation of compression ratio, cut off ratio and specific heats ratio. The results obtained will show that, for the ranges taken into discussion, thermal efficiency might be enhanced by the rise of compression ratio and specific heat ratio values and by lowering cut off ratio values. The study is a predecessor of expensive and time costing experiences and it is also a guidance in the hand of future professionals – able to train them for real solutions.

Analysis of mechanical energy losses in marine diesels

The object of research is marine diesel engine oils, which provide lubrication, cooling and separation of friction surfaces. The subject of the research is the process of ensuring minimum mechanical losses in marine diesel engines. A problematic point in ensuring the lubrication of the cylinder-piston group and motion bearings is the lack of analytical and experimental studies that establish the relationship between the structural characteristics of engine oils and mechanical losses arising in marine internal combustion engines. The degree of orientational ordering of molecules and the thickness of the boundary lubricating layer are considered as the structural characteristics of engine oils. The determination of these values was carried out using the optical method based on the anisotropy of the light absorption coefficient by the boundary lubricant layer and the isotropic volume of the liquid (engine oil). The assessment of the level of mechanical losses arising in marine diesel engines was carried out according to an indirect indicator – the overshoot of the rotational speed and the time to reach the steady state of operation in the event of a change in load. It has been experimentally established that for engine oils used in marine internal combustion engines, the thickness of the boundary layer can be 15–17.5 µm. Motor oils, which are characterized by a higher ordering of molecules and a thickness of the boundary lubricant layer, ensure the flow of transient dynamic processes with less overshoot and a shorter transient time. This ensures the level of minimal mechanical losses occurring in marine diesel engines. The technology for determining the structural characteristics of engine oils can be used for any type and grade of oil (mineral or synthetic; high or low viscosity; used in both circulating and cylinder lubrication systems). The method of indirect assessment of mechanical losses of marine diesel engines can be used for any types of internal combustion engines of ships of sea and river transport (low-, medium- and high-speed; as well as performing the functions of both main and auxiliary engines).

Comparative analysis of combustion dynamics using three reaction source models

ABSTRACT The OpenFOAM computational fluid dynamics code was used to investigate the performance of three combustion models, namely, Muppala, Zimont and Algebraic. The performance characteristics of these models were tested in a fully premixed (stoichiometric ) modern, high-performance 4-valve, iso-octane, dual overhead cam (DOHC) engine with quasi-symmetric pent roof combustion chamber running at 1500 revolutions per minute. The performance characteristics of the three combustion models were found to be reasonably representative of measurement data that are usually observed in internal combustion engine test bed experiments. The combined or overall duration of the flame development and propagation period for the three models were 5.53 ms, 5.69 ms and 6.04 ms for the Muppala, Zimont and Algebraic models, respectively, and these values correspond to 49.75◦CA, 51.175 CA and 54.425 CAwhich are well within the acceptable degree crank angle range during typical internal combustion engine operations. The maximum pressure with the corresponding degree crank angle positions at which they occur for the Muppala, Zimont and Algebraic models were found to be: and respectively. Furthermore, the results from the present study show that the flame-development period , was almost identical for the three combustion models, whereas the rapid-burning interval , was almost indistinguishable for the three combustion models up to about the 80% mark of the regress variable. In specific terms, the complete salient findings from this study are summarised in the conclusion section of this study.

MODELING THE HEAT CONDITION OF A CYLINDER HOUSING OF A VEHICLE DIESEL

A characteristic feature of the cylinder liners of modern automotive and other types of internal combustion engines, which is confirmed by numerous engine tests, is a significant temperature difference along the height of the working surface - mirrors. Depending on the level of engine boost, temperatures can vary from 250-300℃ in the upper part of the liner, near the combustion chamber, to 80-90 ℃ in the lower part, cooled by a liquid cooler (water or antifreeze). From the point of view of ensuring optimal friction conditions, which are largely determined and depend on the viscosity of the engine oil at a given working temperature of the liner mirror, such temperatures for both the upper and lower parts of the liner are not optimal. The deterioration of friction conditions leads to an increase in mechanical losses, a decrease in the effective performance of the engine as a whole. As shown by the analysis of literature, the improvement of effective indicators, the reduction of mechanical losses in the cylinder-piston group is facilitated by measures to equalize the temperature of the liner in the working area of the compression rings and to bring temperatures to the level of 160–170 ℃. In the presented calculation study, which can be considered as an intermediate stage of refining the design of the cylinder liner in order to optimize the temperature profile of the working surface, the influence of the area of the cooled outer liner surface is considered. An analysis is made of a variant of a serial diesel engine liner 4CHN12 / 14 made of cast iron SCH21-40, and an experimental version, provided that it is made of aluminum alloy AL19 with a corundum working surface. As shown by previous computational studies, the constructive options for a cylindrical sleeve with minor changes to the basic version, which preserve the basic geometric dimensions of the part, in particular the distance between the upper and lower seat faces, do not solve the task of optimizing the temperature profile of the sleeve as for cast-iron sleeves, and liners made of aluminum alloy. The study analyzes the options that provide for more significant changes both in the design of the liner itself and in the design of the cylinder block, namely in the placement of the liner seal belts. For computational research, we use a finite element mathematical model of the thermally stressed state of the liner, refined during engine experiments.