**1. Introduction**

Underground ventilation provides enough airflow to the workings to dilute and remove noxious gases and dust. Furthermore, underground ventilation supplies O2 where it has been depleted and controls temperature. Noxious gases may come from strata rock (e.g., CH4, CO2, H2S, Rn), be generated by underground machinery (e.g., CO, CO2, NOx), or be a consequence of blasting operations (CO, NOx) [1,2]. Two systems are used for mine ventilation purposes, namely, principal and ancillary. The former provides air to the overall mine, establishing general air circulation. The latter is used in developing workings and galleries and provides fresh air to specific areas in the mine. The ancillary ventilation of mine galleries is similar to that used in tunnels under construction. The main difference between them is that, for tunnel ventilation purposes, outside air is directly conducted to the face, whereas in mine ventilation fresh air has to be diverted from the main ventilation system into the working faces.

The favorite ventilation system for ancillary mine ventilation is the forcing system. Forcing is preferred over exhaust ventilation, as the fresh air coming along the roadway usually enters the duct straight away without sweeping the face first [3] (p. 7). The physics of this ventilating system is similar to a that of free jet that progressively opens, reducing its velocity until it reaches zero. The region in which the air is immobile is termed "the dead zone", and it is separated by distance from the face "dz" (Figure 1). In this zone, ventilation takes place by natural diffusion rather than being directly swept by the air current. The distance between the duct end and the dead zone is the air jet range, which is termed "the effective distance" (ez). The sum of both distances is the space between the duct end and the face (ds). The limit case occurs when there is no dead zone so that "ez" is equal to "ds".

**Figure 1.** Section (S), dead (dz) and effective zones (ez) for a drivage forcing ventilation system.

The most simple reference range for ez is less than 15 m (e.g., [3] (p. 7)). Other authors consider "ez" as a function of the gallery section (S) so that ez be less than 4 <sup>√</sup> *<sup>S</sup>* or less than 6 <sup>√</sup> *S* (e.g., [4] (p. 381)). Moreover, others consider the gallery section and a parameter "a", which is usually 0.07, in which case *ez* <sup>&</sup>lt; 0.5 - *S* 1 + <sup>1</sup> 2*a* = 4 √ *S* 12 − 15 m [5] (p. 245). Finally, additional approaches consider the ventilation duct as a reference, in which case "ez" should be 10–15 times as large as its diameter [6]. All legal requirements worldwide follow one of these recommendations, without getting into the physics of the dead zone formation.

Computational fluid dynamics (CFDs) has become an important tool for most fluid dynamics engineering problems, thus playing an emerging role in mine ventilation systems design [7]. Its popularity is mainly due to its low cost and capability of measuring parameters, which are difficult or almost impossible to obtain experimentally, as well as its fast assessment and adaptability to varying design conditions. In this context, CFDs may offer insight into the mechanics of dead zone formation.

The first CFDs in the field of mine ventilation were started by Herdeen and Sullivan (1993) and Srinivasa et al. (1993), who used a Eulerian–Lagrangian formulation. Since the apparition of modern commercial software, CFDs models have been used in several aspects of mine ventilation. Thus, extensive studies have been conducted in the field of dust transport (e.g., [7,8]) and heat transfer. The latter is important the case of heat fires and explosions in longwall working faces (e.g., [9,10]). Moreover, Sasmito et al. [11] studied air conditioning as a complement to ventilation for heat control in dead-end tunnels. Furthermore, Yuan and Smith [12] studied the low-temperature oxidation of coal using unsteady-state simulations. Likewise, Shi et al. [13] developed a CFDs model for coal spontaneous combustion under goaf gas drainage conditions.

As concerns auxiliary ventilation, Diego et al. [14] compared traditional and CFDs models for calculating losses in a dead-end circular tunnel, highlighting the advantages of CFDs over traditional calculations. Toraño et al. [15] studied auxiliary ventilation roadways driven with roadheaders, but their results cannot be directly transferred for dead-end tunnel ventilation. Sasmito et al. [16] performed a computational study on gas control in a room and pillar coal mine. Toraño et al. (2009) [17] modeled methane behavior, but did not consider blasting gases, in coal mines ancillary ventilation. Li, Aminossadati and Wu [18] studied ancillary ventilation in super large developments. Onder, Sarac and Cevik studied the ventilation of a cul-de-sac, but focused on fan–duct interaction rather than on the flow outside the duct. Fang, Yao and Lei conducted a parametrical study but did not consider the cross-sectional area as a variable [19]; thus, the magnitude of the effects associated with the whole set of parameters is yet to be established. Szlazak et al. [20] and Reed and Taylor [21] indicated that ancillary ventilation has been conducted under old-fashioned guidelines. As a consequence, it can be concluded that there is still a lack of knowledge concerning ventilation setup influence on dead zone formation in an empty heading. All things considered, the main aim of this study is to determine the correlations among the main factors influencing the effective distance in cul-de-sac ventilation so that their respective influences can be quantified. The following parameters are taken into account: tunnel section, flow rate and position with regard to the tunnel axis. This distance was first assessed based on the flow field patterns obtained, and later on a mixture model of air and NO2.

The rest of the paper is organized as follows. Section 2 defines the geometries, exposes the discretization, presents the equations solved by the CFDs model, defines the boundary conditions, indicates the software configuration, describes the criteria followed for the delimitation of the dead zone and explains the mixture model. Section 3 discusses the delimitation of the dead zone and presents the correlation for dead-end-to-face distance, based on both flow field patterns and flow field patterns plus the mixture model correction. We conclude the paper in Section 4.
