# Design, Plant Test and CFD Calculation of a Turbocharger for a Low-Speed Engine
## 3 Results  
### Design of a Centrifugal Compressor TKR 140E  
Compressor design parameters: \(\overline{m}_{des}\) = 0.62 kg/s, \(\pi_{des}^{*}=p_{ex}^{*}/p_{intl}^{*}\) = 1.61. The turbocharger TKR 140E is for a transport diesel engine converted to gas. It is important to achieve a wide range of flow rates. At a set turbine rpm, the first question of the variant calculation is the choice of the impeller diameter. The variant calculation and preliminary design program calculated the efficiency of each variant using a simplified mathematical model that summarizes the results of the optimal design of 2000 stages [27; 28]. The system of algebraic equations for calculating efficiency is \(\eta^{*}=f\Big{(}\Phi_{des}\), \(\psi_{T\,des}\), \(\overline{D}_{h}\), \(M_{u}\), \(k\), \(\mathrm{Re}_{u}\Big{)}\). Here \(\Phi_{des}=\overline{V}_{intl\,des}/0.785D_{2}^{2}u_{2}\)--flow coefficient, \(\psi_{T\,des}=c_{u2}/u_{2}\)--loading factor, \(\overline{D}_{h}=D_{h}/D_{2}\)--hub ratio, \(M_{u}\), \(k\), \(\mathrm{Re}_{u}\)-similarity criteria's. The program PDCC-G8E serves for a preliminary analysis and uses ideal gas equations. Figure 1 shows the dependence of the efficiency and flow rate for the TKR 140E compressor variants at different loading factors. The highest efficiency was achieved for the variant with \(\psi_{T\,des}\approx\)0.47. For a medium-speed engine with a very long service life, an impeller with its peripheral speed as low as possible is preferred. In order to limit the peripheral speed, we chose the variant with a loading factor higher than the optimal one, namely \(\psi_{T\,des}\) = 0.572. This variant has a peripheral speed of 300 m/s, but according to a variant calculation, the efficiency is 0.43% lower than that of the optimal one. The main parameters of the calculated and selected variants are presented in Figure 2.  
For the selected variant, the PDCC-G8E program performed a preliminary design of the flow path according to an algorithm developed on the basis of special researches [27; 28]. Figure 3 shows the characteristics of a TKR 140E compressor with a flow path before it was optimized. The graphs show how the total pressure ratio \(\pi^{*}=p_{out}^{*}/p_{int}^{*}\), polytrophic efficiency \(\eta^{*}\) and power consumption N (kW) varied with mass flow (kg/s). According to the preliminary design, the compressor efficiency at a design mass flow of 0.62 kg/s is 0.80. The maximum efficiency was 0.842 at a flow rate of 0.44 kg/s. Obviously, when optimizing the flow path, this drawback should be eliminated. Qualitative optimization of the impeller was based on the analysis of the velocity diagrams of the quasi-three-dimensional compressible inviscid flow. The 3 DM.023 program calculated the meridional flow by the quasi-orthogonal method. On axisymmetric stream lines, the calculation was performed by the method of integral equations. The advantage of the method was the calculation of the flow around the leading and trailing edges of the blades, which is impossible when calculating by the mesh method. Velocity diagrams on the shroud streamline in the impeller according to the preliminary design and after optimization are shown in Figure 4.  
According to the preliminary design, the dimensions of the inlet to the impeller were insufficient. The stream entered with a negative incidence angle, which reduced efficiency. After optimization, this and other shortcomings were eliminated. In accordance with the recommendations [29; 30], the outlet angle of the blades \(\beta_{bM2}=f(b_{2})\) increased from the hub to the shroud. According to the recommendations [31], the trailing edge was inclined in the direction of rotation. Negative bulk angle is \(\chi_{2}=-15^{\circ}\). The shape of the blades centerline \(\beta_{bls}=f\big{(}\vec{l}\big{)}\) was adopted with a double curvature, this was necessary to eliminate the \"saddle\" in the velocity diagram on the shroud streamline.