PSI - Issue 71

Rahul Tarodiya et al. / Procedia Structural Integrity 71 (2025) 241–247

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The geometry and mesh for the 90-degree elbows connected in series is generated using the code ANSYS ICEM. Each elbow has a diameter (D) of 50.8 mm and a radius (R) of 75 mm. The setup includes an upstream pipe of 2133.6 mm (42D) leading to the first elbow and a downstream pipe of 558.8 mm (11D) following the second elbow. The length of the connecting pipe between the two elbows is varied to investigate the effects of different lengths, specifically 3D, 8D, 16D, 30D, and 50D. The geometry is meshed using the O-grid method, with a finer mesh near the wall. Mesh independence is assessed to determine the optimal mesh size, resulting in a final mesh of approximately 3.2 million hexahedral elements (for 3D connecting length). The minimum orthogonal quality of this mesh is 0.6. The structured mesh of the geometry with 3D connecting length between two elbows is illustrated in Fig. 1.

Fig.1 A schematic of geometry, boundary conditions, and mesh used for simulation.

Fig. 2 Comparison between predicted erosion thickness loss and experimental results (Solnordal et al. 2015) at bend extrados.

2.2. Boundary conditions and solution procedure Solid particles and gas enter the pipe through the inlet at a specified velocity, with the boundary condition set as 'velocity inlet,' and exit through the outlet with the boundary condition 'pressure outlet.' The pipe surface is assigned wall boundary conditions. A two-way turbulence coupling is selected between the two phases. The particle trajectory is calculated using a discrete random walk (DRW) model. For the simulation, sand particles with a density of 2650 kg/m³ are used. The pipe material is taken as stainless steel 316 (SS316) of density 7990 kg/m 3 and hardness of 183 GPa. The mass flow rate of particles is maintained at 0.00347 kg/s in all cases. The pressure-velocity coupling in solving the flow field is handled by the SIMPLEC algorithm. Standard discretization is applied for pressure, while second-order upwind discretization is used for momentum and turbulent kinetic energy. The solution is assumed to be converged when residuals drop below 10⁻⁵. 2.3. Erosion model The empirical model of Oka is adopted to predict the erosion ratio (ER). To estimate elbow erosion, many investigators (Peng and Cao 2016; Adedeji and Duarte 2020) found close agreement on erosion prediction to the experimental data by adopting Oka model (Oka et al. 2005; Oka and Yoshida 2005). The predictive equation of Oka model for erosion ratio (ER) is of the form: ( ) 90 ER ER f =  (3) where, ER 90 is the erosion ratio at normal incidence given by 2 3 k k (4) where, v p,ref = 104 m/s and d p,ref = 326 µm are the reference particle impact velocity and size, respectively, ρ t is the target material density (kg/m 3 ), and H V is the target material Vickers hardness (GPa). The diameter exponent (k 3 ) for a sand particle is considered 0.19, and the velocity exponent (k 2 ) is correlated to the material hardness as 1 p p bk 9 ER 10 K(aH ) − =  90 t V p,ref p,ref v d v d                