Keywords: biodiesel, fuel drop size, FAME, HVO, diesel engine
  1. Introduction
The use of biofuels is growing in the world. The EU directive prescribes that by the year 2020 10% of the energy used in the transport sector must be constituted by biofuels \cite{Kuut}. The Paris Agreement aims to increase further the share of biofuels in the transport sector. Several studies have been performed on the use of biofuels in internal combustion engines. The main focus has been on the effects of biofuels on engine ‘s exhaust gases, work surfaces, fuel preservation, blending with fossil fuels etc. The results show that when, for example, biodiesel (for example, FAME or RME) is used as engine fuel, then the level of soot decreases in exhaust gases. At this point, the decrease of the level of soot in exhaust gases is explained by more efficient combustion as biodiesel contains oxygen \cite{Xue11,Haz09,Ozs09,Utl08,ozg07,Kap06,Rey06,Rah04,Ulu04,Cho06,Lin09,QiD09,Lap08,Kim10,Men08,Hul06,Gum10,Pal10,Ram05,Sha09,Gur10,Zhu10,Ryu10,Luj09,Che09,Des09,Tso07,Rah07,Aga06,Puh05,Can05,Can03,Sen00,Haa01,Sah07,Bai09,WuF09,Ulu09,Lin091,Tzi09,Zhe08,Tat07,Kal03,Lap02,Jun06,Mon01,Gra03,Wan00,Car02,Kad03,Lap00,Arm06,Yam01,Lap081,Lap05,Din08,Fon17}.
At the same time, when HVO is used, the level of soot in engine exhaust gas is also reduced \cite{Boh18,VoC18}. Therefore, the oxygen content in the fuel cannot be used as the actual reason for explaining the reduction of the level of soot.
In order to provide a better overview, a theoretical analysis of the injection of biofuels into engine must be performed. Nowadays there is no summary available on the injection mechanisms of the biofuels, the behavior of fuel drops in fuel sprays and the distinctive features of the behavior of biofuels compared to regular fuels. As the drop size is an important factor in determining fuel evaporation and combustion in engine cylinder, then this analysis may provide some explanations about the formation of fuel sprays of biofuels and about the characteristics of the combustion of biofuels.
Therefore, the aim of the article is to provide an overview of the behavior of fuel drops and their size in fuel sprays when various biodiesels (hereinafter biofuels) are used. The reason for determining of drop size and behavior is the possible assessment of the quality of air-fuel mixture in order to explain the reduction of soot emission when biofuels are used. The theoretical part is based on the fuel drops’ formation models, which are used to perform the calculations to describe the behavior of various biofuels in the fuel spray. The article describes the formation of fuel drops, points out their impact parameters and analyses the behavior of the drops of biofuels in the fuel spray.
The main theoretical assumptions on which this paper is based:
  1. Sprayed fuel drops are being considered as (symmetrical) physical bodies, which have the ability to bounce, coalesce and separate from each other \cite{Bre11,Nik09,Nob95,LiJ16,Liu161}.
  2. The ability to bounce, coalesce and separate from each other is dependent of the intrinsic and the environmental physical properties (pressure, temperature, etc.) \cite{Qia97,Vol15,Ant16}.
  3. The spraying process is considered as a two-phase event: primary breakout of the fluid and the formation of droplets. Several theories describe this event: WAVE-RT, WAVE-TAB, WAVE-KH, etc., each with a respective mathematical interpretation \cite{Rei86,Rei87,ORo87}.
The detailed mathematical background will be discussed in Sections 3 (Parameters describing fuel drop formation and collision), 4 (Fuel drop size after leaving the injector), 5 (Hybrid breakout model) and 6 (Mathematical representation of reflexive and stretching separation).
The topic of the article is related to the scope of the Journal of the Power and Technologies by the theme of renewable energy. The article provides an overview of the behaviour of biofuels’ drops in the spray, what is more, it supplements the database of the journal with explanations of the problems of biofuels’ spray.
  1. Problem description
When biofuels, for example, FAME, is used as fuel in a diesel engine, then generally the soot level decreases in the exhaust gas and the number of soot particles, emission of carbon dioxide and nitrogen compounds increases in the exhaust gas. The increased level of nitrogen compounds and CO2 and the reduction of soot level is caused by the more efficient combustion of biofuels (HVO, FAME) in the engine. The more efficient combustion is justified by the biofuel’s oxygen content, which improves the combustion of the fuel. In addition, sources discuss thoroughly the carbon-hydrogen ratio in the fuel \cite{Ram05,Puh05,Can05,Ulu09,Fon17,Boh18,VoC18}.
Unfortunately, the reasons given in these scientific sources are not in conformity with generally known theories, because, for example, the diesel engine always works with lean mixture, where the value of the air-fuel equivalent ratio is usually greater than 1.25. For turbo engines, this value is greater than ~4 \cite{Die06}. Therefore, the cylinder of a diesel engine contains theoretically sufficient amount of oxygen for the complete combustion of fuel. In addition, the engine tests of HVO fuel are in contradiction with the FAME results. The HVO fuel does not contain oxygen, but the soot level in the emission gas is reduced. It is also questionable how the carbon-hydrogen ratio affects the emission gas. If we presume that for the engine to work on same load, the same amount of energy must be added and this is derived from the fuel carbon-hydrogen ratio, then the fuel added to the engine has always the same magnitude of carbon-hydrogen atoms. Further, the test results show a contradiction in fuel properties and fuel behavior during injection.
Table 1 compares the physical properties of diesel fuel (DF), HVO and FAME obtained by testing according to the standard EN-590. The properties of gasoline are obtained from source \cite{Bud01}. In order to avoid the fuel’s possible different properties listed in sources, the data listed in the table has been obtained by testing. In the table, gasoline has been given as reference fuel for comparing low viscosity fuels with high viscosity fuel. Table 1 shows, for example, that the viscosity of HVO and FAME is greater than that of diesel fuel. According to general knowledge, when the viscosity of the fuel increases, the fuel drop size in the fuel spray should increase, which also increases the combustion time. The longer combustion time prevents large fuel drops from combusting completely, which increases the level of soot in the emission gas. In our case, this is in contradiction with the results given in previous studies. When comparing fuel weight fractions, then HVO fuel contains lighter fractions compared to diesel fuel. It can be said about the FAME fuel that this fuel contains significantly more heavy fractions compared to diesel fuel (when the temperatures of the evaporated parts (10%-90%) of fuel are compared). Likewise, the heavy fractions of fuel need more time for combustion. Therefore, the soot level of emission gas of the FAME fuel must be at least in the same magnitude as diesel fuel. The following chapters provide an overview the behavior of fuel drops in the fuel spray and describe the effect of the properties of biofuels on the fuel drop size.
Table 1. Properties of diesel fuel and biofuels used in diesel engines.