## 1 Introduction  
The transmission of respiratory infectious diseases [1; 2; 3; 4] is mainly due to the inhalation of aerosol particles containing bacteria and/or viruses [5]. The typical size range of viral particles is between 0.02 and 0.3 \(\upmu\)m [6]. When a patient coughs or sneezes, a large number of aerosol particles are generated [7], and over 60% of viruses attach to aerosol particles with diameters smaller than 4 \(\upmu\)m [8]. The viruses may remain infectious in droplet nuclei for a long time [9; 10; 11]. The maximum range of virus transmission through aerosols can even exceed 6 km [12]. Several epidemiological studies [13; 14; 15; 16] revealed that the COVID-19 patients in some buildings were distributed on different floors, and the patients had no direct contact with each other. A possible transmission route was through vertical airborne transmission. However, previous investigations [13; 14; 15] mainly analyzed the cross-floor transmission of virus aerosols through drainage and air conditioning systems. Few investigations have explored the potential transmission due to the elevator system. However, in our previous research [17], we found that a sufficient viral load is still present in the cabin when dwellers take the elevator at different times due to limited ACH. Modern high-rise buildings are typically equipped with elevators. The elevator shaft and the protecting doors' clearances connect floors with each other [18]. Even without considering the elevator car motion, a modeling study showed that significant transmission of pollutants across different floors occurred through the elevator shaft and the protecting doors' clearances [19]. The pollutant transmission was merely due to the airflow exchange across floors via the elevator shaft. The airflow exchange through elevators is ascribed to the connection of each floor through the shaft and the generated pressure variation and strong airflow in the shaft due to the elevator car movement. The passengers accessing each floor can also cause air exchange between the lobby and the internal compartment of the elevator car, though such airflow exchange does not fall within the scope of this investigation. On the one hand, the shaft in buildings can enhance the chimney effect due to the buoyancy flow resulting from temperature differences [20]. The shaft can promote ventilation inside the building [21] and thus may carry bioaerosols for transport across floors [16]. Numerical modeling [21; 22] and reduced-scale model tests [23; 24] have been adopted for studying the spread of smoke in the shaft during fire accidents. The smoke can rise quickly along the shaft due to the chimney effect [25]. Pressurizing the shaft [26; 27] can suppress the upward spread of smoke. To minimize the chimney effect, the shaft can be ventilated and cooled [28]. However, these studies mainly focused on the chimney effect itself without consideration of the movement of elevator cars. The movement of the elevator car can generate piston flow [29]. Commonly, elevator cars move at a constant speed [29; 30; 31] except in the very short acceleration or deacceleration stage [32]. The motion of the elevator car has an obvious impact on the distribution of pressure and air velocity in the shaft and lobby [33]. The faster the elevator moves, the greater pressure difference is generated between the lobby and the shaft [34]. Empirical formulas were developed to predict the maximum pressure difference [29], and the accuracy of the models was verified by experimental tests. Both numerical simulation and reduced-scale model tests [35] were adopted to investigate variations in the pressures due to the high-speed elevator car movement. The elevator car movement can impact the smoke dispersion during fires. The up-movement of the elevator car can accelerate smoke dispersion in the shaft [31], while the downward movement of the elevator car can reduce the spread of smoke to other floors to some extent [36]. These studies investigated only an isolated single movement direction of the elevator car.