3.2 Construction of computational domain and mesh for experiment-2

The computational domain is a 70 m long tunnel with a rectangular cross section (width 6 m, height 2.7 m). A CAD model of an LHD vehicle was designed and imported into the computational domain. The location of the exhaust is at the rear end of the LHD. The exhaust flow is a mixture of DPM and air. Figure 6(a) shows the CAD model representing the vehicle, and Figure 6(b) shows the experimental gallery with LHD. Figure 7(a) shows the mesh generated for the complex surfaces of the vehicle and (b) shows the details of the computational domain and mesh made up of about half-million computational cells. Finer cells were used to capture details of the flow in regions such as small gaps and adjacent to solid surfaces.

#### 3.3 Setting up the flow conditions

Intake air was supplied through the inlet of the gallery with 1.26 m/s velocity for experiment-1 and 2 m/s for experiment-2 at 300 K temperature. DPM was released from the smoke pipe with a velocity of 29 m/s and temperature of 323 K. For these investigations, DPM is treated as a gas, chemical reactions were not considered. The Boussinesq approximation was used to simulate buoyancy and the effect of turbulence was taken into account.

#### 3.4 Governing equations

To model turbulent flow of mine air, Reynolds-Averaged Navier-Stokes equation was used. In Reynold's averaging, the solution variables in the exact

Figure 6.

CFD model of man riding vehicle and experimental gallery. (a) LHD—CAD model. (b) Experimental gallery with LHD.

Figure 7.

Surface mesh on LHD & mesh in gallery with LHD. (a) Surface mesh of LHD. (b) Surface mesh of LHD & gallery.

Navier-Stokes equations are consisting of time averaged and fluctuated components for velocity components [25].

$$
\underline{u}\_i = \overline{u}\_i + \underline{u}'\_i \tag{4}
$$

Where ū<sup>i</sup> and ui 0 are mean and fluctuating velocity components (i = 1, 2, 3).

Reynolds-averaged Navier-Stokes (RANS) equation was obtained by substituting time and average velocity in momentum equation:

$$\frac{\partial \rho}{\partial t} + \frac{\partial}{\partial \mathbf{x}\_i} (\rho u\_i) = \mathbf{0} \tag{5}$$

$$\frac{\partial}{\partial \mathbf{x}} \left( \rho u\_i \right) + \frac{\partial}{\partial \mathbf{x}\_j} \left( \rho u\_i u\_j \right) = -\frac{\partial p}{\partial \mathbf{x}\_i} + \frac{\partial}{\partial \mathbf{x}\_j} \left[ \mu \left( \frac{\partial u\_i}{\partial \mathbf{x}\_j} + \frac{\partial u\_j}{\partial \mathbf{x}\_i} - \frac{2}{3} \delta\_{\vec{y}} \frac{\partial u\_l}{\partial \mathbf{x}\_l} \right) \right] + \frac{\partial}{\partial \mathbf{x}\_j} \left( -\rho \left. \overline{u\_i \cdot u\_j} \right> \right) \tag{6}$$

Where �ρ ui ,uj , is Reynolds stress can be solved with Boussinesq hypothesis and Reynolds stress models (RSM). In Boussinesq hypothesis, the Reynolds stress are related to the mean velocity gradient [25].

$$-\rho \,\overline{u\_i \cdot u\_j}^\* = \mu\_t \left(\frac{\partial u\_i}{\partial \mathbf{x}\_j} + \frac{\partial u\_j}{\partial \mathbf{x}\_i}\right) - \frac{2}{3} \left(\rho k + \mu\_t \frac{\partial u\_k}{\partial \mathbf{x}\_k}\right) \delta\_{ij} \tag{7}$$

To determine turbulent viscosity μt, k � ε model was used.

$$
\mu\_t = \rho \mathbf{C}\_\mu \frac{k^2}{\varepsilon} \tag{8}
$$

Where C<sup>μ</sup> is a constant, k is the turbulence kinetic energy and ε is the turbulent dissipation rate and turbulent heat transport is modeled using the concept of the Reynolds analogy to turbulent momentum transfer. The modeled energy equations are as follows:

$$\frac{\partial}{\partial t}(\rho E) + \frac{\partial}{\partial \mathbf{x}\_i} [u\_i(\rho E + p)] = \frac{\partial}{\partial \mathbf{x}\_j} \left[ \left( k + \frac{c\_p \mu\_t}{\sigma\_k} \right) \frac{\partial T}{\partial \mathbf{x}\_j} + u\_i(\tau\_{ij})\_{\text{eff}} \right] + \mathbf{S}\_h \tag{9}$$

Where k is the thermal conductivity, E is the total energy and τij eff is the deviatoric stress tensor, defined as

$$\left(\left(\mathbf{r}\_{ij}\right)\_{\rm eff} = \mu\_{\rm eff} \left(\frac{\partial u\_j}{\partial \mathbf{x}\_i} + \frac{\partial u\_i}{\partial \mathbf{x}\_j}\right) - \frac{2}{3} \mu\_{\rm eff} \frac{\partial u\_k}{\partial \mathbf{x}\_k} \delta\_{ij} \tag{10}$$

The standard k-ε model is based on the model transport equations for the turbulence kinetic energy (k) and its dispersion rate (ε). The model transport equation for k is derived from the exact equation, while the model transport equation for ε was obtained using physical reasoning and bears little resemblance to its mathematically exact counterpart.

In the derivation of the k-ε model, the assumption is that the flow is fully turbulent, and the effect of molecular viscosity is negligible. As the mine air considered as fully turbulent flow, k-ε model is valid for mine air.

The turbulent kinetic energy, k, and its rate of dissipation, ε, are obtained from the following governing equations [25]:

Analysis of Diesel Particulate Matter Flow Patterns in Different Ventilation and Operational… DOI: http://dx.doi.org/10.5772/intechopen.84651

$$\frac{\partial}{\partial t}(\rho k) + \frac{\partial}{\partial \mathbf{x}\_i}(\rho k u\_i) = \frac{\partial}{\partial \mathbf{x}\_j} \left[ \left( \mu + \frac{\mu\_t}{\sigma\_k} \right) \frac{\partial k}{\partial \mathbf{x}\_j} \right] + \mathbf{G}\_k + \mathbf{G}\_b - \rho \varepsilon - \mathbf{Y}\_M + \mathbf{S}\_k \tag{11}$$

$$\frac{\partial}{\partial t}(\rho \varepsilon) + \frac{\partial}{\partial \mathbf{x}\_i}(\rho \varepsilon \mathbf{u}\_i) = \frac{\partial}{\partial \mathbf{x}\_j} \left[ \left( \mu + \frac{\mu\_t}{\sigma\_\varepsilon} \right) \frac{\partial \varepsilon}{\partial \mathbf{x}\_j} \right] + \mathbf{C}\_{1\varepsilon} \frac{\varepsilon}{K} (\mathbf{G}\_k + \mathbf{C}\_{3\varepsilon} \mathbf{G}\_b) - \mathbf{C}\_{2\varepsilon} \rho \frac{\varepsilon^2}{K} + \mathbf{S}\_\varepsilon \tag{12}$$

Where Gb is the generation of turbulence kinetic energy due to buoyancy, Gk is the production of turbulence kinetic energy due to the mean velocity gradient, YM is the contribution of the fluctuating dilation in compressible turbulence to the overall dissipation rate, C1ε, C2<sup>ε</sup> and C3<sup>ε</sup> are constants. Sk and S<sup>ε</sup> are user defined source terms.

#### 4. Results and discussions

#### 4.1 Experiment 1

Figure 8 shows the DPM cloud in top view. From the figure, high DPM concentration is seen between the smoke pipe side of the vehicle and wall. No DPM concentration is observed near the operator and passenger seat. Downstream of the vehicle, DPM particles spread throughout the whole gallery.

Figure 9 shows the DPM concentration at 1 and 5 m downstream to the vehicle. At 1 m downstream to the vehicle, Figure 9(a) shows that the maximum DPM concentration is near the left half of the roof and the side. Traces of DPM are observed in the blue-green band across the airway, and negligible concentration on the right side. Figure 9(b) shows the DPM concentration at 5 m downstream to the vehicle. The DPM is seen to flow towards the smoke pipe side of the roadway. The maximum DPM concentration is near the middle of the roadway. Figure 9(c) shows the DPM concentration at 10 m downstream to the vehicle. DPM concentration at the middle of the road way is 110 μg/m3 and the right side of the road way 57 μg/m3 .

#### 4.2 Experiment-1 model validation

Table 3 compares the field measurements with results of the CFD simulations. The CFD results are seen to be in fair in agreement the field data, with the difference varying from �14.2 to +14%. In some cases, the simulated values are different

Figure 8. DPM flow pattern—top view, 2D concentration contours in a plane near the ceiling.

#### Figure 9.

DPM concentration at 1, 5 and 10 m downstream of the vehicle. (a) DPM concentration 1 m downstream of the vehicle. (b) DPM concentration at 5 m downstream of the vehicle. (c) DPM concentration 10 m downstream of the vehicle.


#### Table 3.

Comparison of simulated results with experimental results.

from the measured data. This may be because the uneven texture of the gallery surface was not considered in the CFD model.
