## 1 Introduction  
Particle-laden turbulent flows in curved pipes are essential components of almost all industrial process equipment, including power production, chemical and food industries, heat exchangers, nuclear reactors, and engine exhaust ducts, hence understanding their behavior is of great interest. The numerical study of turbulent flow through curved pipes is complex, so there are relatively few reports dealing with the use of numerical methods focusing on the influence of flow conditions and geometry on the accumulation of particles. In 1997, [PERSON] et al. numerically studied a turbulent flow loaded with solid particles through a 90\({}^{\circ}\) bend pipe using RANS (Reynolds Averaged, Navier Stokes Equations) along with the Reynolds stress model to solve the transport phase flow field while accounting for turbulent fluctuations in the equation of motion of the particles. Additionally, they developed an empirical model that considered the influence of Stokes number, Reynolds number and radius on particle accumulation [1]. [PERSON] et al. (2006) simulated the experimental case treated by [PERSON] et al. (1983) for two Reynolds numbers(Re = 1000 and 10,000) and several particle sizes using Large Eddy Simulation (LES) to solve the transport phase and a Lagrangian tracking model to solve the particle motion, obtaining acceptable results [2; 3].  
[PERSON] et al. (2012) carried out a systematic numerical study to generate the computational guidelines to model and validate the turbulent flow through curved pipes by means of RANS equations and Lagrangian tracking, using the commercial code ANSYS FLUENT [4]. Recently, [PERSON] et al. (2016) investigated the effect of curvature on particle distribution in a multiphase turbulent flow through a curved pipe, for this purpose they used DNS and Lagrangian tracking, for Re = 11,700 and three different radii of curvature [5]. Finally, [PERSON] et al. (2017) conducted a study on the formation of strings (deposition lines) of solid particles in gas flows through sharp turns (bends). Experiments were conducted in which high-speed videos were recorded and analyzed for solid concentration profiles that were compared with CFD simulations using LES and RANS turbulence models; in both simulations and experiments, flows with solid loadings of 35%, 42% and 51% were considered. The results of the study demonstrate that both RANS and LES can accurately predict particle string formation. Additionally, a strong relationship between local solids concentration and gas vorticity was observed [6].  
Overall, different numerical studies have been carried out to explore the effect of geometry and flow characteristics on the accumulation of particles in curved pipes. However, there was no evaluation based on the Stokes number, as no formulation of it adapted to the geometry and the physical characteristics of turbulent flow in bends is available. For this reason, in this study a methodology for predicting the degree of accumulation in concentration of solid particles in a 90\({}^{\circ}\) bend pipe by means of Stokes numbers specifically formulated for that configuration.  
The document is organized as follows. First, in Section 2, we describe the physical model, the validation of the numerical method, and the ad hoc formulated Stokes numbers. In Section 3, we show the distribution and concentration of particles generated in the bend pipe (for the reference case C12d1) and discuss the effect of the indicated parameters (dp, Re, Rc/R) at the point of maximum concentration and possible accumulation mechanism. This is followed by the numerical characterization by means of the Stokes numbers, and the general accumulation conditions are identified. The last section summarizes the main results and conclusions.