## 6 Extrapolating Turbine Performance Parameters
### Twin-Entry Turbine Extrapolation  
For the extrapolation of reduced mass flow parameters, the coefficients in Table 2, which are graphically shown in Figure 12, are used. In the case of apparent efficiency, the fitting coefficients shown in Table 6 are used.  
Figure 26 shows the model extrapolation results against experimental data for both reduced mass flow and apparent efficiency of T#1 TE in Shroud and Hub branches. In Figure 26, the results of some _MFR_s are disclosed, including the unequal, full, and partial admission flows in the turbine. In Figure 26, it is clear that the extrapolation produced by the model (solid lines) at both lower and higher turbine reduced speeds in all the shown _MFR_s are not only in considerable accordance with the experimental data (different symbol points) for both branches but producing expected and consistent results. Figure 26a,b, shows the extrapolation results of reduced mass flow parameters in shroud and hub branch. In the shroud branch, it is notable that there is a small difference between the mass flow parameters at different reduced speeds for a given pressure ratio. This is due to the lower rotor inlet to outlet radius ratio in this branch (see Figure 9); therefore, it acts more like a low trimmed radial inflow turbine. However, this is not the case in hub branch (Figure 26b) due to the higher rotor inlet to outlet radius ratio.  
The Figure 26c shows the extrapolation results of _MFR_ 0.2 where the flow conditions are lower in shroud entry and model able to produce good accordance with the experimental data. However, it is notable that there are some errors found between the extrapolated and measured data at higher reduced speeds. It is worth highlighting that when the shroud branch is working at _MFR_ 0.2, most of the flow expansion is produced by the hub branch and not by shroud one. Therefore, the actual efficiency of this branch should be much lower than the shown apparent efficiency, since it is getting the benefit of the lower mixed outlet temperature generated by the higher expansion in the vicinity branch. Similar results can be found in Figure 26d when the turbine is working at _MFR_ 0.8. In this case, there is more flow in the shroud branch than hub branch.  
Figure 26e,f shows the extrapolation result of unequal admission conditions, where the hub branch is having more flow than the shroud one. In this case, the model is also able to produce with good precision in both limbs at all speeds. Figure 26g,h shows extrapolation result when the turbine is working at almost full admission conditions. The model is able to predict well the peak efficiencies points for both branches. From the experimental data analysis, it was concluded that the maximum apparent efficiencies are always found when there is more flow in the hub side [12]. The extrapolation results from the model also show the same effect, i.e., the peak efficiencies of different reduced speeds can be seen with the higher flows in the Hub branch. Moreover, the extrapolation of having the flows only in Shroud or Hub are well captured by the model, as can be seen in Figure 26i,j. The overall quality of the prediction is high and both the reduced mass flow and apparent efficiency models can bring reasonable extrapolation in all the turbine reduced speeds in both branches.