## 1. Introduction

Dry deposition of aerosol particles in duct air flow over a backward-facing step (BFS) is of significant relevance in built environments and energy engineering, such as for particle removal devices, building ventilation systems, and pulverized coal burners [

1,

2,

3,

4]. As a BFS can greatly modify flow structure and turbulent kinetic energy (TKE) distribution, particle dispersion and deposition in BFS flow are quite different from the case of uniform duct flow [

5]. Particle deposition in a uniform duct has been well studied. However, particle deposition characteristics and behaviors in BFS flow have been seldom examined. Therefore, more attention needs to be paid to this important issue to improve the efficiency of many related energy and environmental engineering devices.

Particle deposition characteristics in duct air flow are complicated and determined by many factors, such as the properties of the particles (density, size, and shape), gravitational effect, Brownian diffusion, turbulent flow structures (turbulent eddies and turbulent kinetic energy distributions), geometric structure of the duct, temperature difference in flow fields (thermophoresis), and humidity of the air (three-phase flow) [

4,

5,

6]. For particle deposition in a vertical duct, particle deposition velocity will firstly decrease, then increase greatly, and finally remain constant when particle relaxation time increases, as the mechanisms of particle deposition greatly change from small to large particle sizes [

7,

8]. For low particle relaxation time, Brownian diffusion and turbulent vortex are dominant factors for particle deposition [

9,

10]. However, particle inertia is much more significant than particle relaxation time increases [

11,

12].

In recent years, the research method for particle deposition in duct air flow has dramatically changed. Compared with experimental study and theoretical prediction, numerical simulation has become the main way to study particle deposition [

13,

14,

15]. As it is challenging to experimentally measure or theoretically predict particle deposition behaviors in duct air flow with complicated duct geometries, computational fluid dynamics (CFD) methods are heavily used to predict particle deposition behaviors in complex turbulent flow fields. The Eulerian–Eulerian and Eulerian–Lagrangian methods are the two main methodologies used to predict duct flow particle deposition. The first method treats particles as a pseudo-fluid and models particle motion as fluid flow [

16]. However, the second method tracks particle movement trajectories and solves the Newtonian kinetic equation for each particle [

17]. The Eulerian–Eulerian approach neglects the difference between the velocities of the air flow and particle motion, which results in errors opposite to the physics. The Eulerian–Lagrangian method can accurately simulate particle movements by tracking the trajectories of each particle. Thus, the discrete particle model (DPM) (Lagrangian method) was adopted in the present study.

For the uniform duct case, Zhao and Chen [

18] investigated the deposition characteristics of particles in ventilation ducts by using the Eulerian–Eulerian approach. Zhang and Chen [

19] predicted the deposition velocity of particles in a uniform duct by using the

$\overline{{{v}^{\prime}}^{2}}-f$ turbulence model. The Reynolds stress model (RSM) proved to be the most accurate Reynolds-averaged Navier–Stokes (RANS) model compared with other turbulence models by Tian [

20] and Gao [

21] because the RSM includes turbulent anisotropy while other turbulence models assume turbulent isotropy. For the nonuniform duct case, Haber [

22] and Lee [

23] predicted the deposition behaviors of particles in expanding and contracting alveolus by solving the creeping flow equations, as the flow velocities in their cases were quite slow. This method can capture the basic flow eddies. They found that particle deposition velocity increases due to the capture of flow eddies near the wall. Li et al. [

24] studied particle deposition in air duct flow over an obstacle. They found that interception of obstacles can obviously increase particle deposition velocity. Iacono et al. [

25] compared deposition characteristics of spherical and nonspherical particles in turbulent ribbed pipe flow by using large eddy simulation (LES). The results showed that nonspherical particles would not accumulate before the ribbed surface, which is quite different from spherical particles. Benedetto et al. [

26] and Sarli and co-workers [

27,

28] examined dust deposition in air flow inside an explosion chamber. Dust mainly accumulates at the walls and this tendency is stronger with an increase of dust nominal concentration and diameter.

Particle deposition in BFS duct flow is quite complicated and influenced by many factors. Moreover, it is challenging to measure particle motions in near-wall regions by experiments. Therefore, studies on particle deposition in BFS flow are very limited, and the related deposition behaviors and mechanisms remain unclear. Nevertheless, CFD can be a powerful tool to study particle deposition characteristics in BFS ducts. Thus, this study investigated particle deposition in BFS flow using the Reynolds stress model and the discrete particle model. The influencing factors on particle deposition characteristics, including different air flow velocities, particle sizes, and expansion ratios of the BFS duct, were considered in the study. Turbulent air flow fields, particle movement trajectories, particle deposition velocities, and deposition efficiency considering flow drag were obtained and analyzed carefully. Moreover, the deposition mechanisms of BFS flow were studied and compared with a uniform duct case.