**2. Modeling and simulations**

This section deals with the combustion simulations on the four-stroke singlecylinder direct injection compression ignition engine running at a constant speed of 1500 rpm, injection timing of 25° BTDC with diesel and 20% blend of Jatropha biodiesel. Standard finite volume method of computational fluid dynamics (CFD) is capable of simulating the two-phase engine flow. Three-dimensional Navier–Stokes equations are solved with k-ε turbulence model. The details of combustion simulations carried out for half-cycle by considering the two strokes compression and

*CFD Combustion Simulations and Experiments on the Blended Biodiesel Two-Phase Engine Flows DOI: http://dx.doi.org/10.5772/intechopen.102088*

expansion at zero load condition are presented below. **Figure 1** shows the front view and 3D view of the geometry model. The model is a four-stroke diesel engine with 4 valves and 4 ports for air sucking inlets and hot gas outlets. The green portion in **Figure 1** is the assembly of a cylinder and piston. Specifications are made from the standard engine KIRLOSKAR AV-1 model. The mathematical models in CFD begin with representation of combustion chamber geometry (meshing of engine). The meshing of the geometry model **Figure 2** is generated using the pre-processor of ANSYS Fluent 15.0 version.

The fluid chamber bottom of ICE is modelled with 450,570 elements and 470,654 nodes. The fluid chamber top of ICE is modelled with 9795 elements and 13,544 nodes. Fluid piston of ICE is modelled with 66,443 elements and 73,360 nodes. The model domain consists of 526,808 elements and 557,558 nodes. Mesh

**Figure 1.** *Geometry model. (a) Front view. (b) 3D view.*

**Figure 2.** *Geometry mesh.*

parameters of IC sector are: Reference size = 0.947 mm; Minimum mesh size = 0.19 mm; Maximum mesh size = 0.474 mm; and the chamber body mesh size = 1.487 mm with 3 inflation layers.

The complex physical phenomenon of combustion flows in IC engines (see **Figure 2**) can be understood by solving the following 3-Dimensional Naiver-Stokes (N-S) equations with the Reynold's Average Navier–Stokes (RANS) model [13–15] and the k-ε turbulence model [16, 17].

N-S equations:

$$\frac{\partial v\_j}{\partial \mathbf{x}\_j} = \mathbf{0} \tag{1}$$

$$
\rho \left( \frac{\partial v\_i}{\partial t} + v\_j \frac{\partial v\_i}{\partial \mathbf{x}\_j} \right) = -\frac{\partial P}{\partial \mathbf{x}\_i} + \mu \frac{\partial}{\partial \mathbf{x}\_j} \left( \frac{\partial v\_i}{\partial \mathbf{x}\_j} \right) \tag{2}
$$

RANS model:

$$\frac{\partial \bar{w}\_i}{\partial \mathbf{x}\_j} = \mathbf{0} \tag{3}$$

$$
\rho \left( \frac{\partial \bar{v}\_i}{\partial t} + \bar{v}\_j \frac{\partial \bar{v}\_i}{\partial \mathbf{x}\_j} \right) = \frac{\partial \bar{P}}{\partial \mathbf{x}\_i} + \mu \frac{\partial}{\partial \mathbf{x}\_j} \left( \frac{\partial \bar{v}\_i}{\partial \mathbf{x}\_j} \right) - \rho \frac{\partial \bar{u'\_i} u'\_j}{\partial \mathbf{x}\_j} \tag{4}
$$

$$-\rho u\_i^{\bar{\cdot}} u\_j^{\prime} = \mu\_t \left( \frac{\partial \bar{v}\_i}{\partial \mathbf{x}\_j} + \frac{\partial \bar{v}\_j}{\partial \mathbf{x}\_i} \right) \tag{5}$$

$$\rho \left( \frac{\partial \bar{v}\_i}{\partial t} + \frac{\partial \bar{v}\_i}{\partial \mathbf{x}\_j} \right) = -\frac{\partial \bar{P}}{\partial \mathbf{x}\_i} + \frac{\partial}{\partial \mathbf{x}\_j} \left[ (\mu + \mu\_t) \left( \frac{\partial \bar{v}\_i}{\partial \mathbf{x}\_j} \right) \right] \tag{6}$$

k-ε turbulence model:

$$
\rho \left( \frac{\partial k}{\partial t} + \frac{\partial (kv\_j)}{\partial \mathbf{x}\_j} \right) = \frac{\partial}{\partial \mathbf{x}\_j} \left[ \left( \mu + \frac{\mu\_t}{\sigma\_k} \right) \frac{\partial k}{\partial \mathbf{x}\_j} \right] + \mu\_t \boldsymbol{\chi}^2 - \rho \boldsymbol{\xi} \tag{7}
$$

Here ρ is density; μ is dynamic viscosity; u and v are velocity components in x and y directions; p refers to pressure; μ<sup>t</sup> is the eddy or turbulent viscosity; *ξ* is the rate of heat dissipation; *k* is the turbulent kinetic energy; *σ<sup>k</sup>* ≈1, is model constant. The RANS models are created with variations referred to over bars and apostrophes in Eqs. (3)–(6) for incompressible fluids. Eqs. (5) and (6) are used for evaluating the Reynolds 'stress equivalent to the average gradients of velocity (equivalent to shear stress). The k-ε turbulence model (7) will be used for the gas and liquid phase [18].

Finite volume equations are crucial for CFD simulations to handle fluid boundary layers on surfaces [19, 20]. The shear gap is heavily influenced by boundary conditions. Fluid near the wall (i.e., layer close to the wall) is the viscous sub-layer, whereas above this layer is dominated by turbulent shears. The laminar pressurestress relation is

$$\frac{\nu \mathcal{C}\_{\mu}^{0.25} k^{0.25}}{\frac{\tau\_w}{\rho}} = \nu^\* = \mathcal{y}^\* = \frac{\rho \mathcal{C}\_{\mu}^{0.25} k^{0.25} \mathcal{y}}{\mu} \tag{8}$$

Here *y* is the cell's close-to-wall position; *v* is the medium fluid speed; and C<sup>μ</sup> is nearly equal to 0.09. It is more precise to calculate near-wall gradients using constrained equivalences when the laminar stress–strain relationship is important. *CFD Combustion Simulations and Experiments on the Blended Biodiesel Two-Phase Engine Flows DOI: http://dx.doi.org/10.5772/intechopen.102088*

The near-wall grid involves substantially larger number of cells, which increases computational time.

The temperature at the ICE-cylindrical chamber bottom and top surfaces is 567 K. The ICE-cylindrical-piston wall temperature is also specified as 567 K. The wall temperature of ICE-piston is 645 K. The wall temperature is 602 K on ICEsector-top-faces. Relaxation of crank angles are: Engine speed = 1500 rev/min.; Crank radius = 55 mm; Piston pin-offset = 0 mm; Connecting rod length = 165 mm; Cylinder bore length = 110 mm; and Cylinder bore diameter = 90 mm. **Table 1**


#### **Table 1.**

*Injection Properties.*


#### **Table 2.**

*Biodiesel and diesel properties [2].*


#### **Table 3.**

*Thermo-physical properties of diesel and biodiesel.*

provides the injection properties. **Tables 2** and **3** provide thermo-physical properties of diesel, Jatropha oil methyl ester (JOME) and its B-20 blend for combustion simulations. The properties are measured from TPS 500S with Kapton and Teflon sensors.

Fuel starts to penetrate into the combustion chamber at 728°C for the diesel as well as biodiesel. Due to the high viscosity of the B-20 Jatropha leads to poor atomization. As in [21], the temperature rise during the fuel spray is around 2770°C for diesel and 2670°C for biodiesel (see **Figures 3** and **4**). As in [22], B-20 Jatropha exhibits high magnitude of velocity for atomization due to viscosity on fuel spray. Hot air presence prior to the fuel injection evaporates the fuel just beyond fixed length (which is called a break-up the length). Engine cylinder spray is around 50–100 atmosphere. At that time, fuel is injected into the chamber. Since the

#### **Figure 3.**

*Visualization of spray at 728° for diesel.*

#### **Figure 4.**

*Visualization of spray at 728° for B-20 Jatropha.*

*CFD Combustion Simulations and Experiments on the Blended Biodiesel Two-Phase Engine Flows DOI: http://dx.doi.org/10.5772/intechopen.102088*


#### **Figure 5.**

*Velocity contour plot at the time of spray for diesel.*


#### **Figure 6.**

*Velocity contour plot at the time of spray for B-20 Jatropha.*

high-velocity jet has to mix with compressed air in a small interval of time thereby B-20 blend exhibits slightly low velocity magnitude (see **Figures 5** and **6**).

Fuel injection starts at 724°C and ends at 740°C. During fuel injection temperature varies from 500 to 2770°C. But at the end of the compression stroke, diesel temperature varies from 500 to 2360°C, whereas biodiesel temperature varies from 500 to 2180°C. Since B-20 blend is having less heat of vaporization when compared to that of diesel, heat transfer lowers the local air temperature as observed in [23]. Similarly, the magnitude of velocity for B-20 blend is slightly lower than that of diesel (see **Figures 5** and **6**).

**Figures 7** and **8** show the variation of temperature after the combustion for diesel and B-20 Jatropha. Temperature varies from 443 to 705°C for the diesel, whereas it varies from 437 to 685°C for biodiesel. Slightly low temperature variation is noticed for the B-20 blend. This could be due to high diffusion burning phase for
