Investigation of pollutants formation in a diesel engine using numerical simulation

The current study aims to explore the combustion process in a diesel engine and investigate the behavior of pollutant formation at diﬀerent time events and diﬀerent locations in the combustion chamber. The time event for maximum rate of production of pollutant soot is also investigated. Further, time events are investigate at which almost all the amounts of pollutants soot and nitric oxide have been produced. The combustion simulation is performed on a 3D sector. Finite volume method is used for numerically solving the partial diﬀerential equations that govern the ﬂow along with Transition SST turbulence model. Eddy dissipation model is used for turbulence chemistry interaction. For soot calculation, Moss-Brookes model is used which has less empiricism and theoretically provides superior accuracy.


INTRODUCTION
Demand for diesel engines is increasing due to its recognized thermal efficiency. So we see them feeding the light and heavy duty vehicles. Contrary to gasoline engines, where gasoline is injected into the air on the way to combustion chamber and therefore there is ample time for mixing of air and fuel uniformly before ignition, there is lack of time for making a uniform mixture of air and diesel because diesel is directly sprayed into the compressed hot air in the combustion chamber'. This lack of time is not suitable for the burning process. That is why, diesel engines produces more pollution, such as nitric oxide and soot, than the gasoline engines. This pollution is extremely harmful to lives and the environment and so, is a very serious matter. Improving engine design can reduce pollution, but it is a challenging task. It requires the utmost attention and strenuous efforts of researchers and engineers to manufacture efficient and cheaper eco-friendly engines. The task of reducing pollution can only be accomplished by improving the engine design to achieve a complete and perfect combustion which is highly dependent on the uniformity of the air-fuel mixture. Improving engine design involves investigating the design of air inlet and outlet passages, injector nozzle, combustion chamber and fuel blends [1][2][3][4][5][6][7][8].
Sakata et al. [9] improved the engine design by introducing controlled fuel injection. M. Komno [10] noticed significant reduction in pollutants formation by generating delayed turbulence. The late turbulence increased the air interaction with unburned fuel resulting in increased engine's efficiency. Lin et al. [11] performed numerical simulations for various combustion chamber designs and investigated one which produce less pollutants. Kim et al. [2] studied the impact of fuel spray direction on the combustion and emission characteristics. Wei et al. [12] examined the impact of nozzle angle on the uniformity of air-fuel mixture and its combustion by numerical simulations. Xu et al. [13] examined the effects of bio-diesel blends on soot formation. EL-Seesy et al. [14] studied the process of formation of nitric oxides and soot from the combustion of diesel/jojoba oil blends. In the current study, we investigate formation of pollutants NO and soot during combustion in a diesel engine under operational conditions.

PROBLEM STATEMENT
In this study, we perform a single cylinder combustion simulation to investigate the formation of pollutants soot and nitric oxide (NO) in the combustion chamber. The objective is to analyze the behavior and concentrations of the soot and nitric oxide. Engine specifications are given in Table 1.

Geometric Model
The three dimensional geometric model of the engine is one-sixth of the engine cylinder which is a three dimensional sector as shown in Figure 1. The top boundary of the model is termed as head. The cylinder head is lying in the plane which contains the point P (0, 0, 0) and its normal is the y − axis. The cylinder head is the disk defined by z 2 + x 2 ≤ r 2 , where r = 75 mm. If we consider the cylinder head lying in rθ-plane, then cylinder head for the sector is defined by r = 75 mm and −π/6 ≤ θ ≤ π/6. The head face is extruded along the cylinder axis (negative direction of y-axis) for the length of 176.4097 mm followed by the piston bowl space, see Figure 1. Due to consideration of sector, there appear two additional faces, the periodic faces. The period of simulation expands from 570 • crank angle (CA) to 833 • CA.

Mathematical Model
Mathematical model contains the following sub models.

Flow Model
Mathematical model, that governs the flow, comprise , there is no extra source contributing to govern the flow. In Equation (2.3), k 1 stands for thermal conductivity. These equations are respectively known as continuity, momentum or momentum transport and energy equations.
The general transport equation for any specie φ is given by

Turbulence Model
For turbulence, Transition SST model is used. The model equations are For details of Transition SST model and model constants, see ANSYS Theory Guide 15.0.

Chemical Species Transport
The Transport equation for species produced due to chemical reaction is

Spray Breakup Model
For spray breakup, we used Kelvin-Helmholtz and Rayleigh-Taylor (KHRT) model is used which were designed by [15,16]. The model equations are . (2.13)

Turbulence-Chemistry Interaction
For turbulence-chemistry interaction, Eddy Dissipation model is used which was designed by Magnussen and Hjertager [17]. In this model, the source term R i,r for i-th specie from the reaction r is R i,r = min(R 1 , R 2 ), (2.14) where and (2.16) In above equations, N denotes number of species, Y R and Y P denote respectively the mass fractions of reactant R and product P , A is a constant whose value is equal to 4 and B is a constant whose values is equal to 5.

Soot Model
For soot modeling, the Moss-Brookes model is used. The model equations are (2.18) In above equations Y soot represents the mass fraction of soot, σ soot denotes the turbulent Prandtl number for soot, M denotes the mass concentration of soot, σ nuc denotes the turbulent Prandtl number for nuclei transport, b * nuc denotes the normalized radical nuclei concentration. For further details of this model, see ANSYS Theory Guide 15.0.

NO Model
The species transport equation for thermal NO is given by In above equation, Y N O denotes the gas phase NO mass fraction , D denotes the effective diffusion coefficient. Moreover, the thermal NO formation from the reaction of molecular nitrogen and oxygen is governed by

SOLUTION PROCEDURE
The underlying combustion simulation is performed using IC Engine tool which in included in ANSYS Workbench 15.0. All the tasks of simulation are completed using this tool. Solution procedure contains the steps described in the following subsections.

Discretization of Governing Equations
Finite Volume Method is used for numerically solving the governing equations. The model equations are discretized on each finite volume turning them into system of algebraic equations, which are then solved by multigrid method..

Meshing
As the piston curve is highly non-linear, so to accommodate the piston boundary for appropriate meshing, the computational domain is divided into very few zones. Mesh on the vertical plane passing through middle of the sector, at three different time events, are given in Figure

Initial and Boundary Conditions
In the current study, air is considered as the working fluid. The ideal gas law is used for calculating its density. All cells of the domain are initialized uniformly with; swirl number equal to 1.3, pressure equal to zero Pascal, x and y velocities equal to 0 m/s, Turbulent kinetic energy equal to 1 m 2 /s 2 , turbulent dissipation rate equal to 1 m 2 /s 3 and temperature equal to 300 K.
There are five boundaries of the computational domain. The cylinder top face is assigned a temperature of 602 K, wall of the cylinder is assigned a temperatures of 567 K, face of the piston is assigned a temperatures of 645 K. The remaining two vertical faces are periodic faces.

RESULTS AND DISCUSSION
As the fuel injection starts, and shortly thereafter, the temperature of the compressed air results in burning the fuel. At this stage, the pressure and temperature in the cylinder suddenly increase due to heat of fuel combustion. The pressure in the cylinder achieves the value of 16.745 MPa at 719.75 • CA, see Figure 3(a). This high pressure pushes the piston back. After TDC, the pressure gradually comes down due to expansion. In Figure 3(b), maximum temperature is plotted against the crank angle. Initially, the heat is conducted to the cells near boundaries. Then temperature in the cylinder rises due to compression. Injection of fuel is started at 691 • CA followed by the start of combustion at 694.05 • . The maximum temperature is 894.82 Kat 694.05 • . As the fuel starts to burn, the temperature of the burning zone starts rising and achieves a peak of 2993.141 K at 709.75 • CA. After completion of fuel injection and the compression stroke, temperature curve comes down due to expansion. In Figure 3(c), apparent heat release rate (AHRR) is graphed against the crank angle. Its maximum value is 119.064 at 706.5 • . In Figure 3(d), particle traces colored by temperature are plotted. This plot shows developed fuel spray as well as high temperature burning zone/particles.
In Figure 4(a), soot mass fraction is plotted against the crank angle. The soot curve starts rising slowly near 695 • CA after the ignition of fuel. Slope of the soot curve rises sharply after 704 • CA. There is point of inflection at 704 • CA where the value of soot mass fraction is 0.001640596 and rate of its production is 0.000278294 per crank angle. After this, rate of soot production decreases which flattens the soot curve. The soot curve looks flatten at 750 • CA with soot mass fraction value of 0.005214796. Further, there is minor production of soot. The value of soot mass fraction at the end of simulation is 0.005261718. In Figure  4(b), pollutant NO mass fraction is plotted against the crank angle. The pollutant NO curve starts rising near 700 • CA. The major amount of pollutant NO is produced till 720 • CA, the top dead center, which is 0.000430189. The value of pollutant NO mass fraction at the end of simulation is 0.000432471.