# Design, Plant Test and CFD Calculation of a Turbocharger for a Low-Speed Engine
## 3 Results
### CFD Calculations  
The cumulative experience of the authors [32; 33; 34] showed that CFD calculations of centrifugal compressor stages and industrial centrifugal compressors, single-stage and multi-stage, showed approximately similar results: the efficiency characteristic was shifted towards higher flow  
Figure 9: Comparison of design and actual characteristics of the TKR 140E compressor at blade velocity \(u_{2}\) = 150, 200, 250 and 300 m/s. and the loading factor was overestimated at the same time. The authors investigated the influence of different calculation methods:  
- Stationary or unsteady flow. - Interface type, (\"stage\", \"frozen rotor\"). - Turbulence model. - Computational grid, etc. Typical examples of comparing calculated and experimental data are shown in Figure 10.  
The 16 Mw two-stage compressor (Figure 10b) was modeled with gaps \"impeller shroud disk--wall\" and \"impeller hub disk--wall\" (\"CFD (gaps)\" in Figure 10) and by a simplified way (\"CFD (no gaps)\"). The test was a plant test in air. As a result, recommendations were developed as to which formulation of the calculation gives the best result; however, even then it did not meet the requirements of practical engineering applicability. The authors of the paper applied all their previous experience in CFD calculations in order to determine whether the calculation of a centrifugal compressor of an internal combustion engine turbocharger would show better results compared to those obtained earlier. Since the TKR-175E tests were of a preliminary nature, its gas-dynamic characteristics were not modeled. The object of the research was the TKR 140E compressor, calculated together with the inlet nozzle and a part of the pipeline behind the scroll. The geometric model is shown in Figure 11.  
Figure 11: Geometric model of the TKR 140E compressor. Figure 10: (**a**) The 3D impeller and its polytropic work coefficient characteristic [32]; (**b**) a two-stage pipeline compressor 16 MW and its pressure ratio characteristic [33]; (**c**) characteristics of the 1:2 model of a single-stage pipeline compressor of a 32 MW [34]. \(\psi^{*}_{p}\)—polytropic head coefficient by total pressures. The ANSYS/CFX numerical simulation system was used to calculate the gas dynamic characteristics of the compressor. The computational model was built in the form of a finite number of computational cells that describe the flow path geometrically with a set degree of discretization. The grid model of the flow path of the model stage is shown in Figure 12.  
The mesh model used a structured hexagonal grid for the inlet, impeller and diffuser, and an unstructured hybrid mesh for the scroll. To take into account the boundary layer, the thickening necessary to meet the requirements of turbulence models and near-wall functions was set to the boundaries defining the walls of the flow path. The size of the first parietal cell varied in the range of 10-50 microns. The enlargement factor was 1.2-1.5. The total number of cells was \(\sim\)14,886,000. To provide numerical simulation, the computational domain was divided into three domains: an inlet nozzle, an impeller, and a diffuser with a scroll. In this case, for the inlet nozzle and diffuser with a scroll, the equations were solved in a static coordinate system, while for the impeller, the equations were written in a rotating coordinate system. To match the gas-dynamic parameters at the boundary between the impeller and the diffuser, special interface conditions of the \"stage\" type were used, which assumed averaging the flow parameters along the circumferential direction at the boundary with the region located upstream. The total pressure and temperature were set at the inlet nozzle as boundary conditions for all design cases. The mass flow rate was set at the outlet boundary. The walls were considered adiabatic. The calculation was performed assuming a steady flow regime. CFD calculations were done for three rpm: \(n\) = 20,760, 27,900 and 41,400.