# Aerodynamic and Structural Characteristics of a Centrifugal Compressor Impeller
## 2 Methodology  
The commercial software ANSYS 19.2 was used for the present one-way FSI steady static analysis. The three-dimensional model of the centrifugal compressor impeller was generated in the BladeGen feature of Workbench using the design parameters given in Table 1. The impeller meridional profile distribution is shown in Figure 1. The fluid field was numerically simulated by the CFX program to obtain the distribution of pressure using the Finite Volume Method (FVM). Once the mesh was created in TurboGrid, the initial parameter defining the aerodynamic simulation was set in CFX-Pre and then solved in CFX-Solver. The total pressure and the total temperature at the inlet were set to 1.0 bar and 298.16 K, respectively. The operating conditions were within the thermodynamic region where the ideal gas law is valid, and hence, the working fluid, air, was considered as an ideal gas. The designed mass flow rate was set at the outlet for steady-state simulation. No slip boundary conditions were assumed at the solid walls of the impeller domain; the total temperature and pressure conditions at the impeller inlet were set; and appropriate constraints on displacements were applied to the FEA model. The rotational speed was applied with respect to the Z-direction in terms of the number of Revolutions Per Minute (spin speed, RPM). The structured mesh was generated with the TurboGrid tool, and the computational domain with mesh is shown in the Figure 2. Grids were refined near the wall regions such that Y+ was less than 5 to resolve the solution accurately. After the mesh independence study, for the twelve-blade configuration, it was found that for a further increment in the mesh after 1 million, the difference in the efficiency results was less 0.01 %, as shown in Figure 3. Hence, the computational domain with 1 million meshes was used in this study for the 12-blade configuration. Similarly, for 6-, 8-, 10-, 15-, and 20-blade configuration, the domains with 0.74-, 0.78-, 0.82-, 1.2- and 1.3-million meshes, respectively, were used. The K-\(\omega\) shear-stress-transport turbulence model, which blends the k-\(\omega\) model near the boundary layer region and the k-\(\epsilon\) model away from the boundary layer region, was adapted in this study to approximate the turbulence parameters. The numerical iteration was considered to be a converged solution after the residuals of the equations fell below \(10^{-4}\). A numerical three-dimensional solid model of the entire impeller was created in Design Modeler, and for FE analysis, the material was assumed to be isotropic, i.e., the material had the same elastic properties in all directions. For structural analysis, Grade 5 titanium alloy, Ti-6 Al-4V(G5), was considered as the impeller material, and the corresponding material property details are listed in Table 2. The temperature effects were neglected as it was considered that the temperature along the blades was constant. The cylindrical hub surface was locked against radial and tangential movements, i.e., nodes between the impeller and axle shaft were fully constrained. The blades were firmly attached to the impeller hub along with their inner profiles. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Details** \\ \hline Rotational velocity & 73,000 rpm \\ Impeller outer diameter & 123 mm \\ Impeller width & 3.6 mm \\ Impeller suction diameter & 51.4 mm \\ Impeller hub diameter & 15 mm \\ Discharge diameter & 129.16 mm \\ Discharge width & 2.99 mm \\ Length in axial direction & 86.63 mm \\ Axial length of main blades & 36.60 mm \\ Axial length of splitter blades & 17.10 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Design parameters of the centrifugal compressor impeller. Figure 1: Meridional section of blade profile of the impeller. The surface pressure field on the impeller blades obtained from CFD analysis can be directly applied as the loading using an interface to connect fluid flow and structural strength analyses.