# Smoke Back-Layering Phenomenon under the Combined External Wind and Stack Effects in a Staircase
## 1 Introduction  
With the accelerating process of urbanization in the world, high-rise buildings and super tall buildings have increased dramatically. Fire safety of high-rise buildings has attracted extensive attention in recent years due to the continuous disastrous high-rise building fires, such as the New CCTV tower fire in 2009 and the Grenfell Tower fire in 2017. Compared to normal compartment fires, the fire behavior in high-rise buildings has some special features, including (1) the specific smoke transport due to complex building structures [1] and (2) a windy environment around the buildings. During fires, many vertical sharts in high-rise buildings, such as emergency stairwells, elevator sharts, and ventilating ducts, will become the potential paths of smoke spread. The smoke will spread from the fire floor to the other floors, causing fatalities far away from the fire origin [2]. The stack effect is the main driven force of smoke movement inside the staircase, which is caused by the pressure difference generated from the density difference of hot gases and cold airs inside and outside of the building [3]. Many characteristic parameters of the smoke movement driven by stack effect were studied, such as the vertical temperature and pressure distribution [4, 5], rising velocity of the smoke propagation [6, 7], and the neutral plane position [8]. Additionally, correlations to predict deflection characteristics of the tilted flame under stack effect were established [9]. Untenable conditions occurred quicker when fires were wind-driven [10], and the wind environment around the building cannot be neglected. Most scholars have researched wind effects on compartment fires, including the height and temperature distribution of the external flame under cross wind [11], external flame projection probability under assisting wind environment [12], and temperature evolution inside a compartment under opposing wind environment [13]. Wind effects on high-rise building fires are more complicatedowing to the interaction of the wind and stack effect, resulting in special smoke movement phenomenon and flame behaviors in a room connected to a shaft. [PERSON] et al. [14] found that, when the wind velocity was lower than a critical value, the flame tilted towards the outdoor at early stage and then tilted towards the shaft eventually due to the stack effect. A non-dimensional number was also proposed to determine the flame tilting direction. Later, [PERSON] et al. [15] proposed a quantitative model to predict the rise time of plume front under the combined effects of external wind and stack effect. However, the fire source was always located on the first floor in their studies. Then, they could observe that the smoke flowed upward inside the staircase when stack effect overcame the external wind and flowed outside the fire room when the stack effect could not overcome the external wind. However, the fire may occur on any floor in real fires. When the fire source was located on the ninth floor, [PERSON] et al. [2] found the smoke moved downward and flowed out from the lower opening with a positive pressure ventilation in the staircase. As they focused on the effect of pressurized air leakage on smoke prevention, the characteristics of the downward moving smoke and its influencing factors were not studied further. The smoke moved downward inside the staircase when the thermal buoyancy was not larger enough to overcome the inertia force of the wind, the so-called \"smoke back-layering phenomenon\". The smoke back-layering distance was defined as the length of the reserving smoke flow downstream when the wind velocity was larger than the critical velocity [16], which was influenced by the heat release rate (HRR) of fires and the open stair door below the fire floor. The stair doors were kept open to improve the natural ventilation in some high-rise residences sometimes. This poses new challenges in determining the smoke management in fire, as the smoke movement pattern could affect smoke exhaust efficiency.