## 2 Problem Formulation
### Computational Aspects
#### 2.3.1 Unsteady RANS (URANS) Simulations for Computational Fluid Dynamics (CFD) Validation  
Air was assumed as an incompressible fluid with constant physical properties (\(\rho=1.2\) kg/m\({}^{3}\), \(\mu=1.8\times 10^{-5}\) kg/m\(\cdot\)s). The boundary conditions at the supply sections were based on the supply flow rate values, measured in the experiments, and the effective cross-sectional area of the supply section. The mean value of volume flow rate entering the room through one supply section (averaged in time and overall 16 supply sections, Table 2) was equal to 190 m\({}^{3}\)/h (mass flow rate of 0.0647 kg/s). The area of the supply section was decreased as compared with the \(l_{\rm in}\) value given in Section 2.1. The cross-section of the supply channel has smaller length then \(l_{\rm in}\) (Figure 1d); the effective opening length \(l_{\rm in,\,effective}=0.177\) m was set in the URANS computations that gave the mean inlet velocity value of \(U_{\rm bulk}=4.26\) m/s (it corresponds to the local velocity values detected in the first set of measurements).  
The uniform distribution of \(U_{\rm bulk}\) was set at each supply section of each fan coil (being an inlet for the computational domain). The Reynolds number calculated using the supply section width was equal to \(Re=\rho w_{\rm in}\)\(U_{\rm bulk}/\mu=2\times 10^{4}\). Two cases with different airflow angle values, \(\theta=25^{\circ}\) and \(\theta=45^{\circ}\), were considered (they correspond to the fixed positions of the lower during the measurements, cases #2 and #3, Table 1). At the outlet boundaries (i.e., at each square suction section of each fan coil), the pressure outlet boundary condition was set assuming uniform pressure distribution. A no-slip boundary condition was set at the solid walls.  
A quasi-structured grid consisted of hexahedral cells was built with the grid generator ANSYS ICEM CFD 18.2. The total cell number was 33 million cells; the cells with the smallest size were located in the corners of the inlet and outlet sections: the dimensions of these cells were \(3\times 3\times 3\) mm. The cells adjacent to the solid walls had the same height of 20 mm (the only exception was the solid wall at the surface of the fan coils). Depending on the local flow features, this height corresponds to the normalized distance from the center of the first near-wall cell to the wall, \(y^{+}\), in the range from the values less than one up to values exceeding 60. The sensitivity analyses of different computational parameters influence on the CFD results were performed previously and are discussed in [37]. In particular, the results of the mesh sensitivity analysis were presented in detail in [37].  
The turbulence modelling of the airflow in the room was performed using the URANS approach coupled with the standard \(k\)-\(\epsilon\) turbulence model in combination with the enhanced wall treatment. To specify the inlet boundary conditions for the turbulence characteristics the ratio of the turbulent to molecular viscosity of \(v_{\text{turb}}/v=10\) and the turbulent intensity of 5% were set at each supply section.  
The numerical simulations were performed using the CFD package ANSYS Fluent (version 18.2) based on the finite volume method with the cell-centered variable arrangement. The iterative SIMPLEC method was used to link the continuity and momentum equations. The second-order schemes for the spatial and time discretization were chosen. The value of the time step was 0.5 s. The time step value, \(\Delta t\), was varied in [37], from \(\Delta t=0.004\) s to \(\Delta t=0.5\) s, and it was found that the lower frequencies and the time-averaged flow patterns were the same in the \(\Delta t\) range considered. The computations were performed using the resources of Peter the Great St.Petersburg Polytechnic University Supercomputer Center (scc.spbstu.ru). In total, up to 504 cores were used for the parallel computations.