## 2 Problem Formulation
### Computational Aspects
#### 2.3.2 RANS Simulations  
The steady-state RANS simulation was set for the modified geometry model, as compared with the geometry shown in Figure 1a. Namely, the ventilation ducts were removed, and the form of columns and ceiling beams was simplified. The fan coil geometry model was also modified: the fan coils were placed directly at the ceiling, and the height of each fan coil was increased to 0.3 m. The supply opening dimensions were also changed, \(l_{\text{in,RANS}}\times w_{\text{in,RANS}}=0.4\times 0.1\) m, so that the opening area was 3.2 times larger than in URANS problem formulation. Opposite to the URANS problem formulation (and the experimental conditions) with empty room interior, the room for the RANS simulation contained 8 desks, 24 chairs, and 24 persons of simplified shape in seating positions, and one person standing upright. The detailed geometry model for this case was presented in [41]. The RANS simulation was performed for non-isothermal conditions with heat transfer problem solving. At each surface the constant values of heat flux, \(q\), were set (Table 3). The mass flow inlet boundary condition was set at each supply opening, with the mass flow rate of 0.227 kg/s. This increased mass flow rate value allowed to keep almost the same value of the bulk velocity as in URANS computations, \(U_{\text{bulk}}=5\) m/s. Two cases with different air flow angle values were considered again, with the flow angle corresponded to \(\theta=25^{\circ}\) and \(\theta=45^{\circ}\). It was assumed that cooled air is supplied to the room, and the constant temperature value of 17.7 \({}^{\circ}\)C was set at the inlets. A uniform velocity distribution, \(U_{\text{bulk\_out}}=-0.69\) m/s, was set at suction (outlet) fan coil sections. The model included also four addition outlets located at the sidewall \(y=5.4\) m (Figure 1b,c). They were assumed to be open, and the pressure outlet conditions were set there. The grid used in the calculations was built in Gambit 2.4.6 grid generator. The grid consisted of cubic elements and the edge length of each cell was equal to 0.1 m. Thus, a grid suitable for engineering usage was generated, with a small number of cells (approximately 200,000). The chosen coarse grid allowed obtaining a steady-state solution due to high numerical dissipation. The problem was solved in ANSYS Fluent 6.3 using RANS approach connected with \(k\)-\(\omega\) SST turbulence model. The Boussinesq approximation for buoyancy forces was used (according to the thermal balance evaluation the bulk temperature in the room was set to 24.5 \({}^{\circ}\)C). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Section**} & \multicolumn{8}{c}{_Wall_} & \multirow{2}{*}{\
\begin{tabular}{c} **Seated** \\ **Persons** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Standing** \\ **Persons** \\ \end{tabular} } \\ \cline{2-2} \cline{5-8}  & \(x=0\) & & \(x=5.4\) m & & \(y=0\) & \(y=11.8\) m & \(z=0\) & \(z=3.2\) m \\ \hline \(q\), W/m\({}^{2}\) & 2.32 & 11.67 & 10.15 & 8.04 & 17.52 & 18.23 & 51.41 & 43.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Temperature boundary conditions for room interior elements. Velocity time variation records presented in Figure 2 and the data in Table 4 clearly show that the near fan coil velocity characteristics vary much from one supply opening to another. The range of variation of air velocity at the east supply section is the smallest one (0.26 m/s) while the largest one is observed at the north supply section (1.82 m/s). Velocity variation range over the supply sections of fan coil #4 is 1.87 m/s, which is comparable with its range of variation at the north supply section. The range of variation of mean air velocity at the supply sections of fan coil #4 is 0.69 m/s. The smallest mean air velocity appears at the north supply section (3.42 m/s) and the largest one appears at the west supply section (4.11 m/s).