## 7 Conclusions  
In this paper, a model for extrapolating the performance maps of twin-entry and dual-volute radial inflow turbines in terms of different flow admission conditions, rotational speed, and blade to jet speeds ratios is presented. For the development of the model, both double entry turbines were tested at different flow admission conditions in a special turbocharger gas stand. The procedure for analyzing the performance maps of this type of turbines is outlined in this paper, and the detailed discussions are presented in [12]. Systematizing the performance maps of double entry turbines gave the awareness to model any double entry turbine as if it is formed of two VGTs and made it possible to extrapolate the maps to off-design conditions. For extrapolating the reduced mass flow parameter of double entry turbines, the method uses seven calibration coefficients for each branch, which are fitted using the available turbine map dataset. Seven coefficients are fitted independently using the turbine map corresponding to Entry 1, and the other seven are adjusted using the turbine map corresponding to Entry 2. The reduced mass flow coefficients must be fitted first since one of them is used for estimating the rotor flow inlet angle of each turbine branch and they are used in the efficiency model equation. Due to the assumption of each turbine inlet being an individual turbine, their apparent efficiencies are computed using the respective branch turbine inlet temperature and mixed temperature available at the outlet of the turbine. Therefore, to take into account these mixing effects in the efficiency model, the based VGT efficiency model has been refined by analyzing the twin-entry turbocharger experimental data. Eventually, a new corrected mixed flow efficiency model has been developed in this paper, and that model uses 11 calibration coefficients to fit the efficiencies of both turbine branches. The model is also validated using the dual-volute turbine data of each volute and the results are in accordance with the experimental information. It is also essential to take into account the geometrical simplifications of different double entry turbines demonstrated in this paper while fitting both reduced mass flow and apparent efficiency models. After fitting the calibration coefficients of a double entry turbine, for extrapolation purposes, a system with the reduced mass flow and apparent efficiency of both individual turbine branches must be solved together, using an iterative procedure, as the mass flow and apparent efficiency variables of each branch are interconnected. The extrapolation results show good agreement with the experimental data for both twin-entry and dual-volute turbines. From the results, it can be concluded that both reduced mass flow and apparent efficiency models can extrapolate beyond normal turbine map measured range in whatever mass flow ratios, reduced turbine speed, and blade to jet speed ratio for each turbine branch. One of the main advantages of the model is that it can be used for both twin-entry and dual-volute turbines just by giving attention to the geometrical simplifications while fitting the type of turbine. It is essential to have a standard turbine map of each turbine branch measured in nearly adiabatic conditions and with at least two extreme flow conditions (one in each turbine branch (_MFR_ 0 and 1)) and also one full admission flow state (where the flow is equally shared in between the entries of the turbine). These three flow admission conditions are needed to fit the coefficients of reduced mass flow and apparent efficiency model and also for extrapolating to other _MFR_s. However, the more information there is on the flow conditions in each turbine branch, the better is the performance of the extrapolation capabilities of the model.