From the work of Edwards and Maurice [45] surrogate formulation can be divided into two main categories. In the first, the goal is focused on matching physical, chemical and combustion properties of the real fuel, such as cetane number, volatility and density. The second approach is focused on the direct emulation of the active functional groups like propyl, methyl and ester groups. The first apprach was followed in this work, and the aim is to improve the CFD simulations, reducing the difference between target and surrogate fuels, also a high computational power is required. The combustion process in DI Diesel engine consists of the following phases, described in detail in the section.2.3:
• Ignition delay
• Premixed Combustion phase
• Mixing-Controlled Combustion phase
• Late Combustion phase
The liquid fuel injected into the combustion chamber is subjected to a physical and chemical phenomena, which characterize the ignition delay period. The liquid jet fuel is sujected to a breakup process generating small droplets. In this first phase, the suface tension is one of the key-properties for the spray breakup model and collision/coalescence model, the liquid viscosity is considered in modeling drop internal flow, wall film motion and drops breakup. After the breakup, the fuel droplets are subjected to an evaporation process, due to the heat flow from the high temperature environment to the single drop of fuel. In this phase, the liquid thermal conductivity is used to evaluate the heat transfer between the drop interior and the outer surface, also the vapor heat capacity is important to determine the temperature distribution and internal energy of the gas mixture which involves the fuel droplets. [46]
Finally, the air-vapor fuel mixture is highly influenced by the geometry of the combustion chamber and turbulent motion in the chamber. Analyzing the chemical process, the fuel is divided into small
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hydrocarbons, and the active radicals favor the spontaneous ignition, up to the premixed phase.
In this phase, some fuel properties are the most important: cetane number, the oxygen content, and the C/H ratio
The cetane number represents the measure for the the selfignitability of the fuels and in this work the cetane numbers for each components are taken from the literature. The oxygen content has an impact on stoichiometry and the soot formation, and the C/H ratio reflects the adiabatic flame temperature and the heat of combustion [47]
The schematic of ignition delay is shown in the Fig. 5-1
Figure 5-1 A conceptual model of ignition delay [48]
In this work, the following target properties are considered to create the surrogate fuel:
• Cetane number CN
• Density ρ
• Lower Heat of Combustion LHC
• C/H mass ratio ……. C/H
• Distillation curve
In Fig. 5-2, the flow chart describes the validation process of the surrogate formulation approach used in this work
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Figure 5-2 Flow Chart validation process
5.2.1 Surrogate Formulation algorithm
The algorithm is proposed by the work of Li et al. [49], which is based in a N-Dimensional space, where N represents the number of the target properties, so the target and surrogate fuel can be identified as two vectors in the space. Finally, through the Euclidean distance between the two vectors, the algorithm can minimize this distance, obtaining the optimal composition for the surrogate. In Fig. 5-3, a representation of this method, considering a ternary mixture is shown:
Figure 5-3 Li et al. Method
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In addition the properties of the mixture have been calculated by estimation methods based on the volume, mass, molar fractions:
Property Estimation
Cetane Number 𝐶𝑁𝑚𝑖𝑥= ∑ 𝑣𝑖𝐶𝑁𝑖
Density 𝜌𝑚𝑖𝑥 = ∑ 𝑣𝑖𝜌𝑖
Lower heat of Combustion 𝐿𝐻𝐶𝑚𝑖𝑥 = ∑ 𝛾𝑖𝐿𝐻𝐶𝑖
C/H mass ratio 𝐶𝐻𝑚𝑖𝑥 = ∑ 𝑋𝑖𝐶𝐻𝑖
Table 5-1 Property estimation
From the Table 5-1 𝑣𝑖, 𝛾𝑖, 𝑋𝑖 respectively represent the volume, mass and molar fraction of the i-component, and the algorithm is created by a MATLAB script, so the Euclidean distance is calculated through the following formula:
𝐸𝐷 = √(𝐶𝑁𝑡𝑎𝑟𝑔𝑒𝑡− 𝐶𝑁𝑚𝑖𝑥)2+ (𝜌𝑡𝑎𝑟𝑔𝑒𝑡− 𝜌𝑚𝑖𝑥)2+ (𝐿𝐻𝐶𝑡𝑎𝑟𝑔𝑒𝑡 − 𝐿𝐻𝐶𝑚𝑖𝑥)2+ (𝐶𝐻𝑡𝑎𝑟𝑔𝑒𝑡− 𝐶𝐻𝑚𝑖𝑥)2 (Eq. 5.1)
5.2.2 Diesel Surrogate
The Diesel fuel is usually composed of 𝐶10~𝐶24 hydrocarbons including [50]:
• 50~65 % alkanes, mostly n-alkanes
• 20~30 % cycloalkanes
• 10~30 % aromatics
The primary hydrocarbons types are:
• n-alkanes, satured straight-chain hydrocarbons
• Iso-alkanes, satured branched-chain hydrocarbons
• Cyclo-alkanes, satured hydrocarbons with one or more satured ring structure
• Aromatics, hydrocarbons with one or more benzene ring structure
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Figure 5-4 Diesel Composition
The fuel Diesel composition is highly variable, which is shown in the Fig. 5-4. In the work of Mueller et al [50], was presented a selection of nine types of candidate components to create two types of 8-component surrogates. This approach leads to a greater precision in numerical results, but it is costly from a computational point of view in CFD simulations. In this way, the surrogate fuel simulates the physical and chemical characteristics of the target fuel to validate its engine performance. For this reason, a brief description is made of the effects of the physical and chemical properties of the diesel surrogate on the fuel spray, through a collection of results available from other work
5.2.3 Effects of physical and chemical properties of Diesel surrogate on fuel spray
The spray characteristics of n-octane, n-dodecane, n-hexadecane and their 3-component mixtures are analyzed by Myong et al. who verified how the components with a higher boiling point influenced the liquid phase length during the vaporization process.
The effects on the spray penetration behaviour for a mixture in different proportions of n-decane/1- methylnaphthalene are analyzed by Aye et al. The results showed that the decrease in the penetration distance and the increase in the spray cone angle are due to the addition of n-decane, which has a lower saturated vapor pressure. The spray and combustion processes of multi components surrogate are studied by Zhang et al and the results showed that the components with larger molecules are mostly distributed around the spray beam. The n-heptane is considered as one of the basic reference components for diesel, in particular Curran et al. constructed a detailed chemical reaction mechanism of n-heptane. The ignition delay behaviour of a selection of n-alkanes, including the n-heptane investigated in the work of Shen et al, is the same over a wide range of pressure and temperature [50].
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