## 2 Methods
### Experimental Study
where \(V\) is the air flow velocity (m/s); \(W\) is the HRR from the heat source (W); and \(L\) is the characteristic size of the channel (m). The indices \"b\" and \"m\" indicate the bench and mine working, respectively. If expression (2) follows directly from the condition of conservation of the Froude number, then expression (3) additionally includes the condition of conservation of temperatures [41]. An important point is that when choosing the main parameters of the bench based on similarity, the Reynolds number was not taken into account. It is impossible to simultaneously satisfy the Froude and Reynolds criteria without changing the type of medium being studied in the test bench. As noted in [42], when the turbulent flow is fully developed, the viscous stress force becomes less significant for the formation of the large-scale flow structure, i.e., the true value of the Reynolds number becomes less significant. The Froude criterion, which is the ratio of buoyancy forces to flow inertia forces, is key when analyzing large-scale flow structures formed under conditions of thermal convection or an ignition source. However, within the framework of this work, we selected the parameters of the bench to maintain the range of Reynolds numbers at which the regime of fully developed turbulence is realized in the channel (\(Re>10,000\)). For the same reason, associated with the low importance of viscous forces, researchers do not use the Rayleigh criterion, which characterizes the ratio of buoyancy forces to viscous forces, when developing smaller benches for analyzing fires in tunnels and mine workings. The [PERSON] criterion, however, is important when considering problems in media moving in laminar or transient flow regimes [43], as well as in problems with larger temperature differences [44]. It is important to note that the HRR from local ignition sources in mine workings significantly depends on time [45]. The short duration of peak HRR values in practice leads to an equivalent HRR often being used, which is the average HRR value over a given time period of the fire [46]. The equivalent value of HRR from fires involving various mining equipment (loading and hauling machines, drilling rigs, and dump trucks) reaches 8 MW. The equivalent value of HRR from the ignition of extended heat sources, such as conveyor belts, is slightly higher [6], but they were not the subject of this study. For this reason, considering (3), it is sufficient to reproduce the HRR of the heating source as 30.8 kW in a laboratory bench, corresponding to the smallest equivalent hydraulic diameter of mine workings in potash and polymetallic mines in Russia (3.6 m). This value is slightly higher than the maximum HRR currently achievable in laboratory conditions (22 kW). This indicates that the developed test bench is primarily applicable for analyzing the patterns of heat and mass transfer processes in underground workings with a characteristic cross-sectional diameter of more than 4 m. However, in our opinion, it can also be useful in analyzing air exchange in mine workings with a smaller cross-section, allowing one to qualitatively capture the basic patterns of heat and mass transfer processes. The following instruments were used to carry out measurements at the bench:  
1. A Testo 405i hot-wire anemometer (Testo SE & Co. KGaA, Titisee-Neustadt, Germany) with absolute measurement errors of \(\pm(0.1+0.05V)\) m/s for velocity (\(V\)) and \(\pm 0.5\)\({}^{\circ}\)C for temperature (\(T\)). 2. A Testo 405V1 hot-wire anemometer with absolute measurement errors of \(\pm(0.1+0.05V)\) m/s and \(\pm 0.5\)\({}^{\circ}\)C.
3. A Testo 445 multi-function climate measuring instrument with absolute measurement errors of \(\pm(0.1+0.01\cdot\
u)\) m/s and \(\pm 0.3\)\({}^{\circ}\)C.
4. A Fluke 922 micromanometer (Fluke Corporation, Everett, WA, USA) with an absolute measurement error of \(\pm 1\%+1\) Pa.
5.