## 2 Experimental Study  
To develop the flow oriented model as well as extrapolate and interpolate the maps, the twin-entry and dual-volutes turbine measurements are needed. A turbocharger test rig has been designed to investigate this type of turbochargers under a variety of operational conditions, based on the flow simulation of a turbocharger using compressed air [12]. Figure 2 shows the schematic representation of the test rig and its main components. The test rig is fed by a two-stage, oil-free centrifugal compressor, which is the oil-free type and powered by a 450 kW electric motor. The flow capacity ranges 4000-7200 Nm\({}^{3}\)/h and a maximum relative pressure of 5.30 bar can be reached. The combustion chamber shown in Figure 2 is not operated as the tests were performed in quasi-adiabatic conditions with a turbine inlet temperature around 363 K. Downstream of the combustion chamber, the airflow is branched into two pipes, which are called Turbine Entry 1 (for Sh/LV) and Turbine Entry 2 (for H/SV), referring to their positions shown in Figure 3. Each of these branches is instrumented with a V-cone type sensor for measuring the air mass flow rate and a control valve for varying the flow going into the branch, allowing to test the turbocharger with different flow admission conditions. At the downstream of the turbine, a third V-cone sensor is placed for measuring the total mass flow exiting from the turbine. There is also a possibility of changing the outlet conditions of the turbocharger compressor using back-pressure valves. The objective was to obtain the adiabatic efficiency maps of the turbine at different flow admission conditions. The ducts and turbochargers are thermally insulated, as shown in Figure 4b, to reduce the extern al heat transfer. Sensors to measure the parameters such as pressure, temperature, turbocharger speed, and mass flow rate at the essential sections of the various fluids are also available and their measurement precisions are shown in Table 1.  
Figure 3: Gas stand for testing the double entry turbines at different flow admission conditions in steady flow situations. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Sensor Type** & **Range** & **Typical Uncertainty** \\ \hline Gas mass flow & V-cone and & & \textless{1}\% of the \\  & Thermal vortex & & measured values \\ Gas pressure & Piezoelectric & 0 to 5 bar & 12.5 mbar \\ Gas/metal temperature & K-type thermocouple & 273 K to 1500 K & 1.5 K \\ \hline Oil pressure & Piezoelectric & 0 to 5 bar & 12.5 mbar \\ Oil temperature & RTD & 173 K to 723 K & \textless{0.5 K} \\ Oil mass flow & Coriolis & Few tens gr/s & 2 \% of the measured value \\ Turbocharger speed & Inductive sensor & \textless{300 k rpm} & \textless{500 rpm} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of main sensors used in the experimental work, showing their typical uncertainty. Figure 2: Schematic layout of a turbocharger gas stand for testing the double entry turbine. The locations of the main sensors are also shown. Finally, the turbochargers were tested in partial, full, and unequal admission conditions for modeling purpose. It is worth highlighting that the unequal admission was tested by feeding each entry with an unequal amount of steady flow in steady state conditions. The different admission tests are defined according to the mass flow ratio definition [12] as shown in Equation (1), where the actual mass flow rate in shroud/long volume entry has been divided by the overall mass flow rate through the turbine. \[MFR\ =\ \frac{\dot{m}_{Sh/LV}}{\dot{m}_{Sh/LV}+\dot{m}_{H/SV}} \tag{1}\]  
The main points of the turbocharger test facility and the methodology for testing the twin-entry or dual-volute turbine in a quasi-adiabatic state were demonstrated with the measurement uncertainty in earlier work [12]. The experimental data presented in [12] have been used here for the correlation of the model. Similar testing conditions were used for examining the dual-volute turbocharger, and the data were used for the model validation.