1. Introduction

Low speed, two-stroke, turbocharged diesel engines, are the most common marine propulsion engines used today. These engines are the most efficient exhibiting 50% efficiency. The remaining 50% of the energy released from combustion of fuel is lost to the atmosphere as waste heat.

At the beginning of the development of the internal combustion engine, it was recognized that improvement would be a lengthy and expensive process. Even by the late 1930’s, there had been established methods to calculate a large number of physical processes in the engine. That is, there has been calculations methods developed that analyze the influential parameters of the working processes in the engine and also provides data for the development of new and improved construction methods.

The basis of theoretical engine process calculations are the works of List [1]. Alongside this is the development of methods for the design of the high part of the process, taking into account the increasing number of parameters, Neuman [2], Zinner [3] and Vibe [4].

Due to the large impact of changes to the working fluid in the power and efficiency of the engine, developing calculation methods for the low-pressure part of the process are based on the laws of gas dynamics. The simplest is called the stationary method, which takes into account the processes in the cylinder and distribution devices, ignoring changes of the gas in front of and behind the valve (channel), from the work of List [5] and [6], Orlin and Kruglov [7], also Hassélgruber [8].

Models that are described in the papers of McAuly [9] and Woschni [10] approach the real processes in the engine. The processes in the cylinders are described by differential equations derived from the law of conservation of energy and mass, and from the equation of state of gas. Changes in the properties of the gas due to the compressibility and dissociation were taken into account.

Boy et al in the paper [11] describes in detail the process in a propulsion Diesel engine. The model describes the real process in the engine cylinder, the process in the turbocharger, passage channels, and intake distributor by the method of “full – empty”.

Some background material on two-stroke engines can be found in Heywood [12] and Richard Stone [13]. The gas exchange processes are treated very comprehensively by Sher [14]. The composition of the flows in and out of a two-stroke engine and the cylinder are shown by Sher [14] and Van Basshuysen et al [15]. An experimental study of the flow pattern inside a model cylinder of a uniflow scavenged two-stroke engine is presented by Sher et al [16]. The velocity field as well as the turbulent parameters were mapped under steady-flow conditions with the aid of a hot-wire anemometry technique. Dang and Wallace [17] proposed a simplified version of the various multi-zone models which have been proposed for diesel engines to represent the pure air, mixing and residual zones of the real process, with or without short circuiting. Carlucci at al [18] presented an analytical model for the estimation of the trapping efficiency according to the Oswald diagram to the molar concentration of carbon dioxide and oxygen at  the tailpipe and then according to the mass flow of air and fuel.

Larsen et al. [19] investigated two-stroke diesel machinery for ships, with five varying configurations to explore the trade-off of increased NOx emissions for a reduction in fuel consumption. By implementing a waste heat recovery system through use of an organic Rankine cycle and also a hybrid turbocharger, fuel consumption was lowered by up to 9% and NOx up to 6.5%. While Andreadis et al. [20] uses a large two-stroke marine diesel engine, operating at its full load to explore the pilot injection strategies using simulations of computational fluid dynamics along with an Evolutionary Algorithm. Guan et al. [21] used a modular zero-dimensional engine model that was built in MatLab and Simulink environment to investigate a large two-stoke marine diesel engine’s operation. Engine shop trial values were compared with the derived performance parameters of the engine, which was simulated at steady state conditions. Varbanets et al. [22] purpose of study was to record the methods upon which the ship’s diesel process efficiency can be improved. Under the conditions of the fuel equipment and the normal state of the main diesel system, even load distribution between the cylinders was controlled. In their previous researches, authors investigated the possibility of increasing efficiencies of a low speed two-stroke turbocharged main diesel engine operating with waste heat recovery through combined heat and power production [23, 24].  Spahni et al in the article [25] in particular deals with the new electronically control, two stroke, low speed marine engines.

The aim of this research is to investigate the substances and energy flow through two-stroke low speed Diesel engines. For this reason, a zero-dimensional model of the combustion in the engine shall be developed and calculated the amount and the composition of the exhaust gases. Our results will be compared with measured results of MAN Diesel & Turbo. At the end of this research will be strictly defined parameters of changes in a two-stroke engines with fuel injection.

2. Engine Model Description

The propulsion engine model depicting the main input and output variables, is shown in Figure 1. It is assumed that fluid flow through a propulsion engine is steady. The observer position is stationary with respect to the control volume surrounding the drive motor, in this case, the ship's propulsion engine. In the simplest assessment, in the control volume the fuel and the air are entering, while combustion products, work and heat  and  are taken away at different temperatures T₁ and T₂. For greater accuracy it is assumed that the cylinder oil enters to control volume, and, with combustion products exits emissions as low quantities of environmentally influential substance [26].

Fig. 1. The propulsion engine model depicting main input and output substances and energy flows.