## 4 Method  
In partial admission conditions, the efficiency is lower than the equal admission conditions. The entropy generation of the interspace region, S.s (suction-side) passage, and P.s (pressure-side) passage significantly increase in partial admission rather than equal admission [8]. The highest entropy generation of the interspace area occurs near the tongues region where the high-velocity fluid from the flowing entry mixes with the lower velocity fluid in the non-flowing region [8]. This mixing, which dissipates some useful work, can be eliminated by changing the geometry of two stator vanes in the tongue region, with the aim of isolating two sectors completely. Efficiency was studied in four unequal admission cases when isolating was applied, and without isolating.  
Figure 5 presents the blade numbers and their surface pressure in partial and equal admission.  
As can be seen in Figure 5, even at equal admission, surface pressure on the rotor blades is not equal, which is because of non-uniform inlet pressure from volute. The difference in surface pressure level on the rotor blades in partial admission is more severe due to the unequal mass flow of volute entries. In some passages, the pressure of the pressure side is higher than the pressure of the suction side and reversely in some others; the pressure of the pressure side is lower than the pressure of the suction side. In both the equal and partial cases, there are some passages with equal surface pressure on both sides (passages 10-11 in the equal case, and passages 4-5 in partial admission).  
Figure 4: Effective area versus pressure ratio.  
Figure 5: **(a)** Surface pressure on the all of the turbine blades in equal and partial admission; **(b)** definition of blade passages.  
The pressure difference magnitude of the passage sides can affect the flow behavior inside the rotor passages. To study the effect of this pressure gradient, two passages that have similar surface pressure but on the reverse side were selected in both cases. Passages 5-6 and 6-7 in equal admission, and passages 3-4 and 9-20 in partial admission were selected because of their equivalent inequality.  
For convenience in investigating the effectiveness of this inequality, the surface pressure ratio (SPR) number is defined with Equation (7):  
\[\text{Surface Pressure Ratio (SPR)}=\frac{\text{Pressure side Surface Pressure}}{\text{Suction Side Surface Pressure}} \tag{7}\]  
Passages with similar SPR in partial and equal admission are selected and demonstrated in Table 4 and Figure 6. Such a strategy for passage selection made it possible to study the effect of the pressure gradient and pressure level on the vortices' behavior through the rotor passages.  
The flow vorticity intensity is calculated and showed on contours of vorticity in five sections in streamwise locations. Three vortex cores in the passage were recognized; their intensity and the vortices' center location was investigated. The chosen passages in both the cases and section locations and orientation are depicted in 3D and also a blade-to-blade two-dimensional (2D) view in Figure 6.  
Then, the total pressure loss contours of the understudied rotor passages were depicted in the four sections in the span-wise direction. Also, the velocity components gradient was depicted in meridional sections for equal and partial admission.