# Design of an Axial Turbine for Highly Downsized Internal Combustion Engines
## 4 Results  
### Turbine Design Preliminary Results  
As illustrated in Figure 15, the low difference in efficiency for small-aspect ratio blades for prismatic and 3D blades is validated, as it is in the order of 3%. After verifying this hypothesis with the design of turbines for low engine revs (Table 2), these turbines were mapped in order to investigate the suitability of the designs for the requirement of the compressor and engine at higher pressure ratios and mass flow rates. In Table 2 velocity ratio (u/c0) are provided (tip speed, u, and absolute flow velocity, C0); width and height d_h and H_blade respectively. This process demonstrated that designing the turbine at lower engine revs may result in the turbine going into a sonic choking regime too early at higher engine revs, and therefore not producing enough power for the compressor. The representative condition was achieved at 154,609 revolutions per minute (rpm) with a flow velocity (absolute) of 571 m/s and an efficiency of 49.52%. The design point was then shifted to 4000 engine rpm, as this is the point where the OEM compressor has its higher efficiency. In fact, as illustrated in the Ricardo Wave results table (Table 3), the turbine has its max efficiency at the highest turbocharger shaft rpm. Moreover, the turbine is always slightly bypassed by the Electronic Control Unit (ECU), as demonstrated by the large difference in mass flow rate between the compressor and turbine (Table 3). This happens because the OEM turbine was fitted to the engine without being specifically designed for it, while the compressor works without any bypass at full performance. Further, this operating point was closer to the design point chosen by [13] for a similar Ford EcoBoost engine (design point at 5000 engine rpm for a 1600 cc engine), thus further confirming the suitability of such a decision. Table 4 shows the distinct size ranges for the design of the turbines at the new design point. It was decided to divide the design space into four size ranges with diameters that are multiples of the OEM turbine minimum hub diameter, while the blade height ranges were selected to allow for Hypothesis 1 to be verified, as specified above. Table 4 highlights the aggregated input data for a turbine design range at the design point, and was used to calculate part of the input data in the AxSTREAM preliminary design module from others available from the Ricardo Wave turbocharger solution data. \begin{table}
\begin{tabular}{l|r|r|r|r|r|r|r} \hline Turbocharger data & \multicolumn{2}{|c|}{**Range 1**} & \multicolumn{2}{|c|}{**Range 2**} & \multicolumn{2}{|c|}{**Range 3**} & \multicolumn{2}{|c}{**Baseline**} \\ \hline
**Properties** & **Prismatic** & **3D** & **Prismatic** & **3D** & **Prismatic** & **3D** & **Radial** \\ \hline
**Shaft inertia kg*m*2** & 7.78E-07 & 8.46E-07 & 8.17E-07 & 9.08E-07 & 8.09E-07 & 8.24E-07 & 1.38E-07 \\ \hline
**Compressor inertia kg*m*2** & 3.48E-06 & 3.48E-06 & 3.48E-06 & 3.48E-06 & 3.48E-06 & 3.48E-06 & 3.48E-06 \\ \hline
**Total turbine plus shaft inertia kg*m*2** & 2.38E-06 & 3.40E-06 & 8.13E-06 & 8.46E-06 & 1.66E-05 & 1.30E-05 & 5.30E-06 \\ \hline
**Total turbocharger rotors inertia kg*m*2** & 5.85E-06 & 6.88E-06 & 1.16E-05 & 1.19E-05 & 2.01E-05 & 1.65E-05 & 8.77E-06 \\ \hline
**Total du/dp (kW*s)*1** & 1.13E-04 & 9.13E-05 & 6.39E-05 & 6.21E-05 & 3.77E-05 & 4.64E-05 & 5.74E-05 \\ \hline
**Normalized Total do/dp (kW*s)*1** & 1.96 & 1.59 & 1.11 & 1.08 & 0.66 & 0.81 & 1 \\ \hline \end{tabular}
\end{table} 
Table 3: Overall turbocharger rotor performance. Figure 15: Efficiency vs. size ranges and blade types for low engine revolution turbines. Figure 17: 3D Range 1 turbine map (\(y\)-axis: shaft speed in rpm (1000 s); \(x\)-axis: turbine pressure ratio). The legend at the top right-hand side indicates the range of total-to-static turbine efficiency. Figure 18: Prismatic Range 2 turbine map (\(y\)-axis: shaft speed in rpm (1000 s); \(x\)-axis: turbine pressure ratio). The legend at the top right-hand side indicates the range of total-to-static turbine efficiency.