## 3 Comparison with Experimental Data  
Validation of the turbine model can be investigated by four performance parameters defined by Equations (1) to (4). Equation (1) gives the mass flow parameter:  
\[MP_{0}=\left(\frac{\dot{m}\sqrt{T_{01}}}{P_{01}}\right)_{0} \tag{1}\]  
where \(\dot{m}\) is the mass flow rate (\(\approx\)/s), \(T\) is temperature (K), and \(P\) is pressure (Pa). \(PR_{Ts}\) is the dimensionless pressure ratio evaluated using Equation (2):  
\[PR_{Ts}=\frac{\left(\frac{P_{\text{total}}}{P_{\text{static 4}}}\right)}{P_{ \text{total}}} \tag{2}\]  
\(\left(P_{\text{total}}\right)_{01}\) is the total inlet pressure and \(P_{\text{static 4}}\) is the exit static pressure. The velocity ratio is defined by Equation (3):  
\[\frac{U_{3}}{C_{is}}=\left[\frac{N}{\sqrt{T_{0}}}\right]\cdot\frac{\pi\cdot d_{ 2}}{\sqrt{2.C_{p}.(1-\left(\frac{P_{\text{4}}}{P_{01}}\right)^{\frac{2-1}{7}}}} \tag{3}\]  
where \(C_{is}\) is the isentropic flow velocity, \(U\) is the blade speed (m/s), \(N\) is the turbine speed (rev/s), \(d_{2}\) is the rotor mean inlet diameter (m), and \(C_{p}\) is the specific heat capacity for constant pressure (J/kg/K). The efficiency definition is the total-to-static isentropic efficiency calculated by Equation (4):  
\[N_{t-s}=\frac{\tau\omega}{\dot{m}C_{p}T_{01}(1-\left(\frac{P_{\text{4}}}{P_{0 1}}\right)^{\left(\gamma-1\right)/\gamma}} \tag{4}\]  
In this equation, \(\omega\) is the rotational speed (rad/s), \(\tau\) is the torque (Nm), and \(\gamma\) is the ratio of specific heats. The mass flow ratio is evaluated as Equation (5), which is a useful parameter that is used to define the degree of inequality and varies from 1 in full admission to 0 in partial admission [23]. \[MFR=\frac{\ddot{m}_{\text{LP}}}{\ddot{m}_{\text{HP}}} \tag{5}\]  
In this study we use from (1-MFR) which is more instinctive number, because it changes from 0 in equal admission where the inequality is equal to zero, to one in partial admission with \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & **Case 1** & **Case 2** & **Case 3** & **Case 4** & **Case 5** & **Case 6** & **Case 7** & **Case 8** & **Case 9** \\ \hline Total Pressure[pa] At lower inlet & 259,358 & 210,792 & 159,073 & 146,303 & 134,649 & 199,407 & 211,063 & 197,334 & 204,222 \\ Total Pressure[pa] At Upper inlet & 258,085 & 209,949 & 158,700 & 146,002 & 134,605 & WALL & 130,799 & 149,485 & 264,643 \\ \hline \end{tabular}
\end{table} 
Table 3: Boundary condition. maximum inequality. \(\dot{\mathrm{m}}_{\mathrm{LP}}\) is the mass flow of the low-pressure limb, and \(\dot{\mathrm{m}}_{\mathrm{HP}}\) is the mass flow of the high-pressure limb. The results were validated by the experimental measurements of [PERSON] et al. (2010) [PERSON] et al. (2010) for both mass flow parameter and efficiency in a full admission case. Figure 2 presents the relative mass flow parameter versus the total-to-static pressure ratio in equal admission. The mass flow that is characteristic of the model coincides with the experimental data well. Less than an eight percent discrepancy can be seen at the lowest pressure ratio, while at a higher pressure ratio, this is one percent. Figure 3 depicts the relative total-to-static efficiency against the velocity ratio in a full admission case. In the lower efficiencies, the enormous uncertainty in the experimental result, which can be as high as \(\pm 5\%\), leads to more discrepancy [PERSON] et al. (2010), although applying the k-\(\epsilon\) turbulence modeling can be the other reason for this difference. For unequal admission validation, a parameter related to mass flow is required. In this study, the effective area that is a standard parameter in this field is used. The effective area stands from the idea of assuming each entry as a swapping area nozzle, and is defined with Equation (6) [4]. This parameter expresses the swallowing capacity of a turbine. \[A_{eff}=\frac{\dot{m}}{\rho_{\mathrm{s}}\times C_{\mathrm{is}}} \tag{6}\]  
Figure 3: Comparison of computed and measured efficiency against velocity ratio.