*2.4. Turbulence Model*

The equations above were solved using the SIMPLE scheme for the pressure–velocity coupling. In addition, for turbulence modeling, a k-ε model was selected [24]. The k-ε model is a two-equation

model, which aims at resolving the turbulence using two parameters: the turbulence kinetic energy (*k*) and the dissipation rate (ε).

The equations solved by this model are listed as Equations (8) and (9) [23]:

$$\frac{\partial}{\partial t}(\rho k) + \frac{\partial}{\partial \mathbf{x}\_i}(\rho k \mu\_i) = \frac{\partial}{\partial \mathbf{x}\_j} \left[ (\mu + \frac{\mu\_l}{\sigma\_k}) \frac{\partial k}{\partial \mathbf{x}\_j} \right] + \mathbf{G}\_k + \mathbf{G}\_b - \rho \varepsilon - \mathbf{Y}\_M + \mathbf{S}\_{\mathbf{k}} \tag{8}$$

$$\frac{\partial}{\partial t}(\rho \varepsilon) + \frac{\partial}{\partial \mathbf{x}\_i}(\rho \varepsilon u\_i) = \frac{\partial}{\partial \mathbf{x}\_j} \left[ (\mu + \frac{\mu\_l}{\sigma\_\varepsilon}) \frac{\partial \varepsilon}{\partial \mathbf{x}\_j} \right] + \mathbb{C}\_{1\varepsilon} \frac{\varepsilon}{k} (\mathcal{G}\_k + \mathbb{C}\_{3\varepsilon} \mathcal{G}\_b) - \mathbb{C}\_{2\varepsilon} \rho \frac{\varepsilon^2}{k} + \mathbb{S}\_{\varepsilon} \tag{9}$$

Where:

$$
\mu\_t = \rho \mathcal{C}\_{\mu} \frac{k^2}{\varepsilon}
$$

$$
\mathcal{C}\_{3\varepsilon} = \tanh\left|\frac{v}{u}\right|
$$
