OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 maintains its integrity even when adjusting its tuning coefficients. However, its full documentation remains inaccessible. Put simply, the user can modify the model’s behavior across a broad range of solutions without concern for physical implications. The fundamental equations are provided below. GEKO model equations from [29–32]: ( ) ( ) ; j t k j j k j u k k k P C k t x x x ρ ∂ ρ µ ∂ ρ ∂ ∂ + = µ + + - ρ ω ∂ ∂ ∂ σ ∂ (1) 2 1 1 2 2 3 ( ) ( ) . j t k j j k j u P C F F C CDF t x x x k ω ω ∂ ρ ω µ ∂ ρω ∂ ∂ω ω + = µ + + - ρω + ρ ∂ ∂ ∂ σ ∂ (2) The functions F1, F2 and F3 [29–31] implement the Cnw, Csep and Cnw coefficients, respectively.According to the authors, the Cnw coefficient is designed to modify the model’s behavior within the boundary layer and near the wall, although its influence is expected to be minimal given the use of the near-wall function. The Cjet coefficient, although mentioned in the documentation, is not the primary parameter for enhancing model performance. However, it can be beneficial for circular concentric flows. Given the cylindrical nozzle of the accelerator, this coefficient may have an impact under certain conditions. Ultimately, Csep is deemed the most dominant coefficient, with the aim to enhance performance for significant adverse pressure gradients and to resolve regions with laminar-turbulent transition. Previously, in the case of reacting flow [32], it was found that Csep was the most crucial coefficient for pressure and heat flux criteria, and reducing Csep brought GEKO performance closer to the k-epsilon model. Additionally, in earlier tests for heterogeneous flow with relatively low velocities within the pipe, the GEKO model and its parameters’ variations had only a minor impact on the velocity and wear pattern in the pipe elbow [33]. The Euler-Lagrangian approach, which is well established for such problems [2, 3, 8, 15–19], was used to model the particulate matter. During the accelerator inlet BC calculations, the pressure and temperature were set to match the experimental values for the point being investigated. Solid particles were also introduced, flowing at a rate of 7.65e-6 kg/s, based on the experimental number distribution and a zero velocity assumption (due to a lack of information regarding particle velocity in the precritical section of the accelerator). The particle velocity was made equal to the flow velocity, and a drag law based on particle sphericity was established. For modelling particle wear in CFD, an erosion model must be applied to the erodible surface. Empirical-analytical models are often employed to relate the material removal rate to the flowing particle parameters, including size, velocities, and angle of incidence. When performing these calculations, several empirical coefficients are utilized, generally chosen based on the specific materials being used. Among the most widely employed commercial software is Ansys FLUENT, with the Oka [34] model being one of its most frequently applied components, serving as a cornerstone for investigating grid convergence and turbulence model impact. Grid convergence was investigated by performing calculations on five grids of different dimensionality using the Oka model, the k-epsilon Standard Shear-Stress Transport Turbulence Model, and a turbulent Prandtl number of 0.85. A design point of 5.75 bar at 140 °C was utilized. After evaluating the total specific erosion criterion, a mesh with 1.65 million hexahedral cells in the region between the accelerator and the sample was chosen. The velocity profile criterion was selected to assess the accelerator mesh in the expulsion region. The accelerator area’s final computed grid consisted of 190,000 cells. Results and discussion It is evident that the rate of surface erosion is reliant on the distribution of particle velocities and incidence angles, which is linked to the velocity profile at the outflow from the accelerator. Fig. 4 displays a representative image of the flow at the accelerator outflow and surface flow using the k-epsilon turbulence model. In the normal direction of high-speed flow near the wall, velocity sharply decreases. Nonetheless,
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