Comparison of Evaporation in Conventional Diesel and Bio-Fuel Droplets in Engine Cylinder

Abstract

Renewable energy resources are need of the hour at the current energy scarcity scenario in the world. Scientist and researchers are finding the ways to replace the conventional energy resources with the renewable ones. It is fact that fossils are going to be obsolete in future. One third of global energy is being consumed by the transportation sector. All the amount of this energy comes from the fossils that contain the hydrocarbons in their composition. Efforts are being made to replace the fossils with the renewable energy resources. In this regard, biofuels are emerged as a replacement of the diesel fuels. There are several processes in the engine cylinder from atomization of fuel until the exhaust of gases. One of them is the evaporation of fuel droplets. In the present work, evaporation characteristics of conventional diesel fuel and biofuels is described by comparing them in different working conditions. Modeling of evaporation phenomenon using computational fluid dynamics (CFD) techniques and the effects of in cylinder conditions is also explained. Results show that biofuel droplets show a better evaporation rate at the high operating conditions in the engine cylinder.

1. Introduction

Renewable energy refers to energy sources that are replenished naturally and continuously in a relatively short period, unlike non-renewable sources such as fossil fuels. Renewable energy sources include solar, wind, hydro, geothermal, and biomass, among others. These sources of energy are considered renewable because they can be replenished over time through natural processes, such as the sun’s energy replenishing solar panels or wind turbines, or the regrowth of crops for use in biomass energy. This makes renewable energy a sustainable alternative to traditional non-renewable energy sources, which will eventually run out and can have negative impacts on the environment [1]. Renewable energy sources are sources of energy that are replenished naturally and continuously in a relatively short period of time [2]. Some of the most common sources of renewable energy include:

1. Solar energy: Energy derived from the sun by solar panels or other devices that convert sunlight into electrical or thermal energy [3].

2. Wind energy: Energy generated by the movement of wind, typically using wind turbines [4].

3. Hydro energy: Energy generated by the movement of water, typically with hydroelectric dams or other water-based power generation systems [5].

4. Geothermal energy: Energy derived from the heat produced by the Earth’s core, typically through the use of geothermal power plants [6].

5. Biomass energy: Energy generated from organic matter, such as crops, wood, and waste products, through the process of combustion, anaerobic digestion, or other means [7].

6. Tidal energy: Energy generated from the movement of tides, typically by tidal turbines or other ocean energy systems [8].

7. Biofuels, which are fuels made from biological materials such as crops and waste [9].

All these sources of renewable energy are sustainable and do not deplete the earth’s resources or produce harmful greenhouse gas emissions.

There are several reasons why we need renewable energy:

1. Sustainable energy supply: Renewable energy sources are replenished naturally and continuously, making them a sustainable alternative to non-renewable sources of energy, such as fossil fuels, which will eventually run out [10].

2. Reduction of greenhouse gas emissions: The use of renewable energy sources, such as solar and wind power, results in fewer greenhouse gas emissions, which contribute to climate change, compared to the use of non-renewable energy sources, such as coal and natural gas.

3. Improved energy security: Renewable energy sources are typically dispersed and decentralized, making them less vulnerable to disruption and more resilient in the face of natural disasters or political conflicts [11].

4. Job creation: The development and deployment of renewable energy technologies can create new jobs in the fields of engineering, manufacturing, construction, and installation, among others.

5. Economic benefits: Renewable energy sources can reduce the cost of energy over time, as the cost of renewable energy technologies continues to decline. They can also stimulate local economies by attracting investment and reducing the need for expensive energy imports [12].

6. Health benefits: The use of renewable energy sources can reduce air and water pollution, leading to improved public health and reduced healthcare costs [13].

Overall, renewable energy can help address many pressing global challenges such as climate change, energy security, job creation, and sustainable development. Fossils are the preserved remains or evidence of ancient plants, animals, or other organisms that lived in the distant past. They can take many forms, including bones, teeth, shells, footprints, and even impressions of leaves or insects. Fossils are typically found in sedimentary rock, such as sandstone or limestone, but can also be found in volcanic ash or ice. Fossilization is the process by which the remains of ancient organisms become fossils. This process can occur through a variety of mechanisms, including preservation in sediment, freezing in ice, or preservation in amber. In most cases, minerals replace the original organic material over time, creating rock-like fossils [14].

Fossils are important for several reasons:

1. They provide evidence of past life on Earth, including information about the diversity, distribution, and evolution of ancient organisms.

2. They can be used to date the rock layers in which they are found, providing important information about the Earth’s history and geology.

3. They provide insight into ancient environments, including information about past climate and the types of organisms that lived in a particular area.

4. Fossil fuels such as natural gas, coal, and oil, on the other hand, are formed from the remains of animals and plants that were buried under sediment and were then subjected to heat and pressure over millions of years [15].

There are several types of fossils, including:

1. Body fossils: Body fossils are the remains of an organism’s physical structure, such as bones, shells, and teeth. They provide direct evidence of the anatomy and biology of ancient organisms and are often used to study the evolution and diversity of species over time.

2. Trace fossils: These are the indirect evidence of ancient organisms, such as footprints, burrows, or coprolites (fossilized feces).

3. Molds and casts: These are formed when a fossilized organism dissolves away, leaving a negative impression or mold in the rock. A cast is formed when this mold is filled with mineral deposits.

4. Petrified fossils: These are formed when mineral deposits replace the original organic material of a fossil, creating a rock-like fossil.

5. Carbon films: These are extremely thin layers of carbon that have been left behind by the decay of organic material. They can reveal the fine details of an organism’s structure.

6. Amber fossils: These are formed when organisms are trapped and preserved in tree sap, which hardens into amber over time.

7. Per mineralized fossils: These are formed when minerals fill the spaces within bones and shells, preserving them in great detail.

8. Original remains: These fossils still have their original materials such as bone, teeth, shells, etc. [16].

All these types of fossils can provide important information about ancient organisms and environments and have a wide range of scientific applications. The lifetime of fossils can vary widely depending on the type of fossil and the conditions under which it formed. Some fossils, such as those found in amber, could be well preserved for millions of years, while others, such as those found in surface sediments, may only be preserved for a few thousand years. The preservation potential of a fossil also depends on the type of organism, the environment in which it lived, and the conditions under which it died. For example, organisms that lived in environments with high sedimentation rates, such as near river deltas or oceanic currents, are more likely to be buried and preserved as fossils than those that lived in environments with low sedimentation rates. Similarly, organisms that are rapidly buried after death, such as those that are transported to the bottom of the ocean by a volcanic eruption or landslide, are more likely to be preserved as fossils than those that are exposed to the elements for long periods of time before being buried [17].

In general, the most common types of fossils are body fossils, such as bones and shells, and trace fossils, such as footprints, which can be preserved for millions of years under the right conditions. Other types of fossils, such as carbon films and original remains, may only be preserved for a few thousand years [18]. Fossil fuels such as natural gas, coal, and oil, on the other hand, are formed from the remains of animals and plants that were buried under sediment and were then subjected to heat and pressure over millions of years. The process of fossilization can take millions of years, and once formed, these fossil fuels can be stored in the Earth’s crust for millions of years more [19].

The combustion of fossil fuels, such as coal, oil, and natural gas, can have a range of negative environmental effects. Some of the most significant effects include:

1. Greenhouse gas emissions: The burning of fossil fuels releases carbon dioxide (CO₂) and other greenhouse gases into the atmosphere, which contribute to global warming and climate change.

2. Air pollution: The burning of fossil fuels also releases a range of pollutants into the air, such as sulfur dioxide, nitrogen oxides, and particulate matter, which can harm human health and the environment.

3. Water pollution: Fossil fuel extraction and processing can also pollute water resources, including the contamination of surface and ground water with chemicals and heavy metals.

4. Land degradation: Fossil fuel extraction can cause land degradation, including the destruction of natural habitats, deforestation, and soil erosion [20].

5. Health impacts: Air pollution from fossil fuel combustion can lead to respiratory and cardiovascular disease, as well as cancer [21].

6. Acid rain: The burning of fossil fuels release sulfur dioxide and nitrogen oxides, which can lead to acid rain, which can harm plants, animals, and buildings.

7. Oil spills: The transportation of oil and oil products by ships and pipelines can lead to oil spills, which can have devastating effects on marine life and coastal environments [20].

Overall, the combustion of fossil fuels can have severe environmental impacts and contributes to climate change, air pollution, water pollution, land degradation and health impacts.

Biofuels are fuels that are derived from biomass, or organic matter such as plants, crops, and waste materials. They are renewable energy sources, as they can be replenished on a regular basis [21]. There are several types of biofuels, including:

1. Bioethanol: This fuel is made from fermented crops, such as corn, sugarcane, wheat. It is often used as a gasoline additive which is being used in order to increase fuel efficiency and reduce greenhouse gas emissions.

2. Biodiesel: A diesel fuel type which is actually extracted from vegetable oils, animal fats, or recycled cooking oils. It is also used in conventional diesel engines.

3. Biogas: This is a type of fuel made from the decomposition of organic matter, such as food waste, manure, or sewage. It can be used to generate heat, electricity, or as a transportation fuel.

4. Biojet fuel: This fuel is extracted from plant-based oils or animal fats, specifically designed for use in aircraft.

Biofuels have several benefits, including minimizing the reliance on the fossil fuels, bring down carbon emissions, creating new jobs in agriculture and biofuels production, and improving energy security by reducing the reliance on imported oil. However, there are also some potential drawbacks to biofuels, including the competition for land and water resources with food production, the environmental impact of growing crops specifically for biofuels, and the fact that some biofuels may not be as energy efficient as conventional fossil fuels [22].

The composition of biofuels depends on the specific type of biofuel in question. However, some of the most common components of biofuels include:

1. Ethanol: Ethanol is extracted from crops such as corn, sugarcane, and wheat. It is often used as a gasoline additive which is being used in order to increase fuel efficiency and reduce greenhouse gas emissions.

2. Methanol: Methanol is another type of alcohol that can be made from biomass, such as wood waste, and is used as a fuel or as a starting material for the production of other chemicals.

3. Vegetable oils: Biodiesel is often made from vegetable oils, including soybean oil, palm oil, or canola oil.

4. Animal fats: Biodiesel can also be made from animal fats, such as tallow or chicken fat.

5. Glycerol: Glycerol is a byproduct of the production of biodiesel and is commonly used as a feedstock to produce other chemicals.

6. Biogas: Biogas is actually mixtures of hydrocarbon gases which mainly includes the mixture of methane and carbon dioxide that is produced through digestion of organic matter in absence of oxygen, such as food waste, manure, or sewage.

7. Algal oils: Algal oils are oils that are produced from microalgae and can be used as feedstocks to produce biofuels [23].

The composition of biofuels can vary depending on the specific feedstock used and the production process, but in general, they are composed of organic compounds such as alcohols, acids, and esters. These organic compounds have a lower carbon content and release less carbon dioxide when burned compared to fossil fuels, making them a more sustainable and environmentally friendly alternative [24].

Following are the resources of biofuels:

1. Agricultural crops: Biofuels such as bioethanol and biodiesel which are mainly present in sugarcane, soybeans, and canola.

2. Forest residues: Biofuels can be made from waste products generated by the forest industry, such as sawdust and bark.

3. Food waste: Organic waste is another main source such as food waste, manure, and sewage.

4. Algae: Algal biofuels are produced from microalgae and can be used to produce biofuels such as biodiesel and bio jet fuel.

5. Cellulosic crops: Biofuels can be produced from crops that are high in cellulose, such as switchgrass, corn stalks, and sugarcane bagasse.

6. Animal fats: Biodiesel can be made from animal fats such as tallow and chicken fat.

Overall, the range of biofuels sources is quite diverse, and the specific sources used will depend on a range of factors, including the availability of feedstocks, the cost of production, and the specific type of biofuel being produced [25].

Following are the processes that occur in the cylinder:

1. Cavitation in nozzle

2. Primary break up

3. Secondary break up

4. Evaporation of fuel droplets

5. Combustion of fuel droplets

6. Exhaust effect

Cavitation is a phenomenon that can occur in nozzles, particularly in high-speed fluid flow applications. It occurs when the pressure of the fluid become less than the vapor pressure, which eventually resulted in bubble formation. These bubbles can then collapse, and released energy like in the form of shock waves, turbulence, and high-velocity fluid jets. This can cause damage to the nozzle and reduce the efficiency of the fluid flow. In a nozzle, cavitation can happen when the fluid pressure become lower than its vapor pressure due to the high velocity of the fluid as it flows through the nozzle. This can result in the formation of vapor bubbles, which can then collapse and cause damage to the nozzle and surrounding areas. To prevent cavitation, the design of the nozzle must be optimized to maintain a high fluid pressure, or the fluid must be kept at a temperature above its boiling point. Other methods of preventing cavitation include adding a suction device, such as a venturi, to increase the fluid pressure, or reducing the fluid velocity by reducing the flow rate or increasing the nozzle diameter.

It can cause damage to the nozzle and reduce the efficiency of fluid flow, so it is important to prevent or mitigate cavitation in high-speed fluid flow application [26]. Primary breakup refers to the initial fragmentation of a fluid stream into smaller droplets or particles. This process occurs when a fluid stream is forced through a small opening or nozzle, or when it is subjected to high-velocity flow, turbulence, or other forms of shear stress. Primary breakup is important in various steps during industrial processes, such as spray dying, atomization, and fuel injection, as well as in natural phenomena such as rain formation. The dispersion of fuel droplets produced during primary breakup can create impact on the efficiency and effectiveness of the process. To control and optimize primary breakup, a variety of techniques can be used, including the design of the nozzle or other dispersion device, the addition of surfactants or other agents to reduce surface tension and promote droplet formation, and the control of fluid velocity and turbulence [27]. Secondary breakup refers to the fragmentation of droplets into much smaller droplets that occurs after the initial primary breakup of a fluid stream. This process typically occurs when the primary droplets collide or interact with each other, leading to further fragmentation and the formation of smaller droplets. Secondary breakup is an important factor in many industrial processes, such as spray drying, atomization, and fuel injection, as well as in natural phenomena such as rain formation. To control and optimize secondary breakup, the techniques are same as mentioned in primary break up process, including the modifications in nozzle design, the control of fluid velocity and turbulence, and the use of additives to modify the physical properties of the fluid [28]. Evaporation of fuel droplets refers to the process by which the liquid fuel droplets present in an engine’s combustion chamber are converted into vapor. This process is an essential part of the internal combustion engine, as it allows the fuel to mix with air and burn to produce power. Fuel droplets are formed during the atomization process, which occurs when the liquid fuel is forced through a small opening, such as a fuel injector, to produce a spray of fine droplets. These droplets then enter the engine’s combustion chamber, where they face high temperatures and pressure. The evaporation of fuel droplets is impacted by a few factors, including the size and distribution of the droplets, combustion chamber temperature and pressure, the chemical composition of the fuel, and the presence of other substances, such as air or vapor. To optimize the evaporation of fuel droplets, a few strategies can be employed, including the use of fuel injectors with specific design features, the addition of special additives to the fuel, and the control of engine parameters, such as temperature, pressure, and air-fuel ratio [29]. For combustion of fuel droplets refers to the process by which the vaporized fuel in an engine’s combustion chamber reacts with air to release energy. This reaction is commonly referred to as burning. The combustion of fuel droplets is a critical part of the internal combustion engine, as it provides the energy needed to power the engine. The combustion process is initiated when the vaporized fuel and air are mixed in the proper ratio to support ignition. This mixture is then subjected to a spark or compression, which triggers the reaction [30]. The exhaust effect refers to the phenomenon in which the flow of exhaust gases from an engine or other combustion device affects the behavior of the combustion process. This effect can cause impact on the performance and efficiency of the engine or device. The exhaust effect can result from a few factors, including the velocity, temperature, and pressure of the exhaust gases, as well as their chemical composition. For example, the pressure and velocity of the exhaust gases can create a pressure differential that influences the flow of air and fuel into the combustion chamber, leading to changes in the combustion process [31]. The exhaust effect can also play a role in the formation of emissions and pollutants, as the pressure and temperature conditions in the exhaust stream can influence the conversion of harmful substances into other forms. To mitigate the negative effects of the exhaust effect, a variety of strategies can be employed, including the use of exhaust gas recirculation systems, catalytic converters, and other after-treatment technologies. In summary, the exhaust effect refers to the phenomenon in which the flow of exhaust gases from an engine or other combustion device affects the behavior of the combustion process. Strategies can be employed to mitigate the negative effects of the exhaust effect [32].

2. Modeling evaporation of fuel droplets

Modeling the evaporation of droplets under different conditions is described in [33] in detail. Numerical modeling of droplet evaporation involves the conservation equations of mass, energy and momentum. Apart from these equations droplet evaporation involve the heat transfer and mass diffusion phenomenon. When heat is transferred to the droplet then the mass of droplet is lost. Turbulence is also a key part of the evaporation modeling at elevated temperature and pressure conditions. Evaporation of fuel droplets for diesel and biodiesel fuels is numerically modeled and verified in [34, 35, 36, 37] and model was applied in Ansys Fluent. The numerical model equations are given in detail as follows.

2.1 Continuity equation

The general continuity equation is given in the following form.

$$\frac{\partial \rho }{\partial t}+\nabla .\left(\rho \overrightarrow{v}\right)=S_m$$E1

Mass of the fuel droplet is conserved by the Eq. (1). The term on the right side of the equation is the source term. This term implies the mass of fuel droplets added into the engine cylinder from the atomization of fuel in form of spray.

2.2 Momentum equation

Conservation of momentum equation is applied to account for the momentum associated with the droplet. When the liquid fuel is injected into the combustion chamber, it has some velocity by which it travels along the piston head. As the liquid fuel is sprayed, there are certain forces, which are associated with the fuel droplets. These forces include the inertial forces, body forces, gravitational forces and drag forces. All these forces are taken into account by applying the momentum equation, which is given as (2).

$$\frac{\partial }{\partial t}\left(\rho \overrightarrow{v}\right)+\nabla \left(\rho \overrightarrow{v}\overrightarrow{v}\right)=-\nabla p+\nabla \left(\overline{\overline{\tau }}\right)+\rho \overrightarrow{g}+\overrightarrow{F}$$E2

$$\overline{\overline{\tau }}=\mu \left[\left(\nabla \overrightarrow{v}+\nabla {\overrightarrow{v}}^T\right)-\frac{2}{3}\nabla .\overrightarrow{v}I\right]$$E3

2.3 Energy equation

For droplet evaporation following energy is solved in the Ansys Fluent. Fuel droplet enters in the hot environment after the compression stroke in the engine cylinder. When the droplet is injected in form of fine spray at high pressure in the hot environment, it absorbs the heat present in the engine cylinder. The amount of energy transfer is governed by the Eq. (4), which involves the latent heat and diffusion heat flux parameters.

$$\frac{\partial }{\partial t}\left(\mathit{\rho E}\right)+\nabla \left(\overrightarrow{v}\left(\mathit{\rho E}+p\right)\right)=\nabla \left(k_{\mathit{eff}}\nabla T-\sum _j{h}_j{\overrightarrow{J}}_j+\left({\overline{\overline{\tau }}}_{\mathit{eff}}.\overrightarrow{v}\right)\right)+S_h\frac{1}{2}$$E4

$$E=h-\frac{p}{\rho }+\frac{v^2}{2}$$E5

$$h=\sum _j{Y}_j{h}_j$$E6

$$h_j=\underset{T_{\mathit{ref}}}{\overset{T}{\int }}{c}_{p,j}\mathit{dT}$$E7

2.4 Species transport equation

This equation associated with the diffusion of mass of liquid fuel into the continuous phase. This is a convection-diffusion equation used to solve for the j species. This equation is solved to predict the local mass fraction of the species in the combustion chamber. It involves the binary diffusion coefficient of the fuel droplets and turbulent Schmidt number, which are used to govern the local mass fraction of liquid fuel specie in the continuous phase, which is compressed air.

$$\frac{\partial }{\partial t}\left(\rho Y_j\right)+\nabla .\left(\rho \overrightarrow{v}{Y}_j\right)=-\nabla .{\overrightarrow{J}}_j+R_j+S_j$$E8

$${\overrightarrow{J}}_j=-\left(\rho D_{\mathrm{j},m}+\frac{{\mu }_t}{{\mathit{Sc}}_t}\right)\nabla Y_j-D_{T,j}\frac{\nabla T}{T}$$E9

$${\mathit{Sc}}_t=\frac{{\mu }_t}{\rho D_t}$$E10

2.5 Particle force balance equation

Inertial force on the fuel droplet is balanced by the particle drag force, gravitational force and external body force and is given by the following equation. Calculation of drag force involves the coefficient of drag and relative Reynolds number of the droplet. Apart from these, droplet diameter and density of liquid fuel are required to calculate the drag force on the droplet.

$$\frac{{\mathit{dv}}_p}{\mathit{dt}}=F_d\left(v-v_p\right)+\left({\rho }_p-p\right)\frac{g_x}{{\rho }_p}+F_x$$E11

$$F_d=\frac{18\mu }{{\rho }_p{d_p}^2}.\frac{C_{d}Re}{24}$$E12

$$Re=\frac{\rho d_p}{\mu }\left|u_p-u\right|$$E13

2.6 Heat transfer equation

Heat is transferred to the droplet by following equation. When droplet is injected into the combustion chamber, the droplet absorbs the heat present in the cylinder due to high compression. The heat transfer equation involves the mass of droplet particle, temperature of droplet, ambient temperature of engine cylinder, surface area of droplet and latent heat of vaporization of droplet.

$$m_p{c}_p\frac{{\mathit{dT}}_p}{\mathit{dt}}={\mathit{hA}}_p\left(T_{\infty }-T_p\right)+\frac{{\mathit{dm}}_p}{\mathit{dt}}{h}_{\mathit{fg}}$$E14

2.7 Mass transfer equation

When heat is transferred to the droplet, the mass transfer takes place. Mass of droplet is lost through the diffusion. Mass of droplet is decreased according to the following equation

$$m_p\left(t+\mathit{\Delta t}\right)=m_p\left(t\right)-N_j{A}_p{M}_{\omega ,\mathrm{j}}\mathit{\Delta t}$$E15

$$N_j=k_c\left(C_{\mathrm{j},s}-C_{\mathrm{j},\infty }\right)$$E16

$${\mathit{Nu}}_{\mathit{AB}}=\frac{k_c{d}_p}{D_{j,m}}$$E17

2.8 Turbulence model equations

Turbulence is associated with the fuel droplet during its evaporation and break up regimes in the engine cylinder. The relative Reynolds number given by Eq. (13) predicts turbulence around the fuel droplets. To take into account the turbulence effects around the fuel droplet a turbulence model is mandatory with the evaporation modeling. There are three turbulence models than be applied for the droplet evaporation. These include the Direct Numerical Simulation (DNS), Large Eddy Simulation (LES) and Reynolds Average Navier-Stokes (RANS) model. Transport equations for the Realizable k-e model are given below. Each model has own advantages and limitations. DNS and LES are computationally much expensive than the RANS turbulence model. There are further three classifications in RANS turbulence. Realizable K-epsilon model can be used for the droplet evaporation modeling as it is computationally inexpensive and gives the acceptable results.

$$\frac{\partial }{\partial t}\left(\mathit{\rho k}\right)+\frac{\partial }{\partial X_j}\left(\rho {\mathit{ku}}_j\right)=\frac{\partial }{\partial X_j}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_k}\right)\frac{\partial k}{\partial X_j}\right]+G_k+G_b-\mathit{\rho \epsilon }-Y_M+S_k$$E18

$$\begin{array}{c}\frac{\partial }{\partial t}\left(\mathit{\rho \epsilon }\right)+\frac{\partial }{\partial X_j}\left(\mathit{\rho \epsilon }{u}_j\right)=\frac{\partial }{\partial X_j}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_{\epsilon }}\right)\frac{\partial \epsilon }{\partial X_j}\right]+\\ \rho C_1\mathit{S\epsilon }-\rho C_2\frac{{\epsilon }^2}{k+\sqrt{\mathit{v\epsilon }}}+C_{1\epsilon }\frac{\epsilon }{k}{C}_3{G}_b+S_{\epsilon }\\ \end{array}$$E19

$$C_1=max\left[0.43,\frac{\eta }{\eta +5}\right],\left(\eta =S\frac{k}{\epsilon }\right),\left(\mathrm{S}=\sqrt{2S_{\mathit{ij}}{S}_{\mathit{ij}}}\right)$$E20

$${\mu }_t=\rho C_{\mu }\frac{k^2}{\epsilon }$$E21

$$C_{\mu }=\frac{1}{A_o+A_s\frac{{\mathit{kU}}^{\ast }}{\epsilon }}$$E22

3. Properties of fuels

Various properties play important roles in the evaporation of fuel droplets in the engine cylinder. These include the density, viscosity, latent heat of vaporization, boiling point, vaporization temperature and volatile component fraction. These properties are given in Table 1 from [34].

Droplet properties	Diesel	Thumba biodiesel
Droplet surface tension (N/m)	0.02521	0.02715
Vaporization temperature (K)	341	341
Specific heat capacity (J/kg K)	2090	1774
Volatile component fraction (%)	100	100
Thermal conductivity (W/m K)	0.149	0.158
Density (kg/m^3)	835	880
Boiling point (K)	447	691.69
Saturation vapor pressure (Pascal)	1329	1329
Latent heat (J/kg)	277,000	229,327
Binary diffusivity (m^2 /s)	3.79 × 10^−6	7.42 × 10^−6
Viscosity (kg/m s)	0.004	0.004664

Table 1.

Properties of fuels.

4. Results and discussion

Evaporation of diesel fuel and biofuel droplets is modeled in [34] using the computational fluid dynamics techniques. In this study, three different ambient temperatures of 623, 823 and 973 K are taken. The diameter of droplet is taken as 20 and 25 μm. There are two different fuels. First one is n-decane diesel fuel and second is Thumba bio-diesel. Numerical model is validated with the most accurate vaporization experiments of Chauveau [38] and the model of Abramzon and Sirignano (AS-1989) [39]. Turbulence effects present in the engine cylinder are also taken into account by applying the K-epsilon realizable turbulence models. Results include the droplet lifetime, increase in temperature of droplet and reduction in velocity of droplet. Results indicate that droplets having larger diameter take more time to evaporate while the small droplet need short time for complete evaporation. It is also observed that at higher temperatures biofuels evaporates faster than the conventional diesel. Complete evaporation of droplets results in the higher thermal efficiency of internal combustion engine. Figure 1 shows the one-sixth sector of piston geometry, which is under consideration. The geometry of piston is divided into 6 equal parts for the simplicity of analysis and inexpensive computations.

Figure 1.

Mesh of one-sixth sector of piston geometry.

In Figure 2, droplet decay profiles of 20-μm fuel droplets of diesel and biodiesel are shown at various ambient temperatures. Three different temperatures of 973, 823 and 623 K are taken for analysis purpose. It is observed that biodiesel droplets have shorter life span in the engine cylinder as compared to the conventional diesel fuel droplets. As the temperature of cylinder increased after the compression stroke, the droplet lifetime is decreased significantly as evident from Figure 2.

Figure 2.

20-μm droplet profiles at different ambient temperatures, reprinted from [34] CC BY 4.0.

In Figure 3, droplet decay profiles for 25-μm fuel droplets are shown. The trend in the profiles is same as in the Figure 2. Biodiesel is evaporated earlier than the diesel fuel. As the ambient temperature increased, evaporation rate is also increased.

Figure 3.

25-μm droplet profiles at different ambient temperatures, reprinted from [34] CC BY 4.0.

In Figure 4, temperature profiles of 20-μm droplets of diesel and biodiesel are shown.

Figure 4.

Temperature profiles of 20-μm fuel droplet at different ambient temperatures, reprinted from [34] CC BY 4.0.

It is observed that the trend in the temperature profiles matches with that of decay in diameter profiles. However, the temperature achieved by the biodiesel droplets is more than the diesel fuel droplets. It is due the fact that the boiling point of the biodiesel is greater than the diesel fuel droplets. The heat up period of the biodiesel gives maximum temperature to the fuel droplets before complete evaporation.

Figure 5 shows the velocity profiles of 20-μm fuel droplets. Residence time of biodiesel droplets is less than the diesel droplets as evident in Figure 5. The lowest velocity is achieved by the biodiesel droplet at 873 K. Diesel fuel droplet has the largest residence time at lower temperature of 623 K.

Figure 5.

Velocity profiles of 20-μm fuel droplet at different ambient temperatures, reprinted from [34] CC BY 4.0.

5. Conclusion

In this chapter, an overview of renewable energy resources in terms of biofuels has been described. A comparison of evaporation of two different fuels is drawn. Several in cylinder processes are described in detail. There are different ways to model the evaporation of liquid fuel droplets. Evaporation results can be obtained by experiments using the high-speed cameras while numerical modeling of evaporation is also a known phenomenon by using the conservation equations of mass, momentum and energy and other droplet equations. These numerical equations can be solved using the commercial soft wares e.g. Ansys, open foam, KIVA and Star CD. Evaporation of diesel and biodiesel fuels is observed at different diameters and different ambient temperatures. It is concluded that at higher temperature biofuel droplets show the fast evaporation rate than the conventional diesel fuel. Droplets with large size take more time to evaporate while the droplets with smaller diameters take lower time to evaporation completely. Thus, biodiesel is a potential alternative fuel for the transportation sector as a replacement of conventional diesel with low emission rate.

Conflict of interest

The authors declare no conflict of interest.

Nomenclature

Ap	surface area of particle (m2)
Cd	drag coefficient
Cp	droplet heat capacity (J/kg K)
Ci, ∞	vapor concentration in bulk gas (kg mol/)
Ci, s	vapor concentration at droplet surface (kg mol/m3)
Dj, m	mass diffusion coefficient of species j (m2/s)
dp	droplet diameter (m)
DT, m	thermal diffusion coefficient of species j (m2/s)
F	external body force (N/m2)
h	convective heat transfer (W/m2 K)
hfg	latent heat of vaporization (J/kg)
I	unit tensor
jj	diffusion flux of species j (kg/s m2)
keff	effective thermal conductivity (W/m K)
kc	mass transfer coefficient (m/s)
mp	mass of particle (kg)
Mw, j	molecular weight of species j (kg/kg mol)
Nj	molar flux of vapor (kgmol/m2 s)
p	static pressure (N/m2)
Re	relative Reynolds number
Rj	net rate of production of species j
Sj	rate of creation by addition from disperse phase
Sct	turbulent Schmidt number
Sm	source term
Sh	heat of chemical reaction
T∞	temperature of continuous phase (K)
vp	velocity of droplet (m/s)
v	velocity of air (m/s)
Yj	mass fraction of species j
ρ	density of air (m3/kg)
ρp	density of particle (m3/kg)
τ	stress tensor (N/m2)
μ	molecular viscosity (kg/ms)
μt	turbulent viscosity (m2/s)