## 2 Computational Fluid Dynamics
### Governing Equations and Turbulence Models  
According to [PERSON] et al. [33], the fundamental equations of fluid dynamics are the basis of CFD modeling. These equations govern the phenomena of continuity, momentum, and heat transfer and are the mathematical formulations of the physical laws that govern all fluid flow, heat transfer, and related phenomena. Through these equations, it is possible to describe the change rate of the interest fluid properties as a function of external forces [23; 24]. The governing equations are as follows:  
* Conservation of Mass (Continuity Equation) establishes that the rate of mass accumulation must balance with the mass flows into and out (Equation (1)). \[\frac{\partial\rho}{\partial t}+\
abla\cdot(\rho\mathrm{U})=0\] (1)
* Conservation of Momentum (Newton's Second Law or Navier-Stokes Equations) establishes that the sum of external forces acting on a fluid particle is equal to its rate of linear momentum change (Equation (2)). \[\frac{\partial(\rho\mathrm{U})}{\partial t}+\
abla\cdot(\rho\mathrm{UU})= \
abla\mathrm{p}+\left[\mu_{\mathrm{r}}\left(\
abla\mathrm{U}+\
abla\mathrm{U} ^{\mathrm{T}}\right)\right]\] (2)
* Conservation of Energy (First Law of Thermodynamics) establishes that the change in internal energy of a fluid particle is equal to the sum of the heat exchanged and the work carried out on the particle (Equation (3)). \[\frac{\partial\big{(}\mathrm{C_{p}T}\big{)}}{\partial t}+\
abla\cdot(-k\
abla \mathrm{T}+\rho\mathrm{C_{p}TU})=0\] (3) where \(\mathrm{C_{p}}\) is the specific heat, in \(\mathrm{J\cdot kg^{-1}\cdot K^{-1}}\); \(k\) is the thermal conductivity, in \(\mathrm{W\cdot m^{-1}\cdot K^{-1}}\); \(\mathrm{p}\) is the pressure, in \(\mathrm{N\cdot m^{-2}}\); \(\mathrm{U}\) is the velocity vector; \(\mathrm{T}\) is the temperature, in \(\mathrm{K}\); \(\mathrm{t}\) is the time, in \(\mathrm{s}\); \(\mathrm{T}\) is the transposition operator; \(\rho\) is the density, in \(\mathrm{kg\cdot m^{-3}}\); and \(\mu_{\mathrm{r}}\) is the dynamic viscosity of the fluid, in \(\mathrm{kg\cdot m^{-1}\cdot s^{-1}}\). In addition to the Navier-Stokes and Energy Conservation Equations, additional phenomena and models should be considered, such as the phenomenon of the transfer of chemical species (humidity, gas concentration, etc.) and the physical models of turbulence, porous media, the production of heat by animals, etc. The inclusion of additional equations and models makes it possible to represent the real situation more faithfully [23; 36]. The Chemical Species Conservation Equation is like the energy conservation equation and represents the spatial and temporal evolution of the transport of chemical species present in the physical system in question, such as water vapors, and gases such as ammonia (NH\({}_{3}\)) and carbon dioxide (CO\({}_{2}\)). The conservation equation of a generic chemical species A can be written according to Equation (4):  
\[\frac{\partial\mathrm{C_{A}}}{\partial t}+\mathrm{U}\cdot\
abla\mathrm{C_{A} }=\
abla\cdot(\mathrm{D}\
abla\mathrm{C_{A}}) \tag{4}\]where \(\rm C_{A}\) is the concentration of chemical species A, in g\(\cdot\)m\({}^{-3}\); and D is the diffusion coefficient, in m\({}^{2}\cdot\)s\({}^{-1}\). Due to its nature, several studies have considered the fluid flow in animal facilities as turbulent, seeking to obtain better results via CFD modeling [37]. In these cases, the flows must be modeled using appropriate turbulence models to ensure that the achieved results agree with the real systems. Four different approaches have been developed to describe turbulent flows: Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), Reynolds-Averaged Navier-Stokes (RANS), and Scale Resolution Simulation (SRS) [33; 38]. In the DNS approach, the Navier-Stokes equations are solved directly on the smallest length and time scales without the need to implement assumptions and/or sub-models. The application of the DNS approach is limited to relatively low Reynolds numbers, and it can be extremely time consuming, greatly limiting its use.