# Comparison of Cooling Different Parts in a High Pressure Ratio Centrifugal Compressor
## 3 Results and Discussion  
### Effects on the Pressure Ratio  
Figure 6 illustrates the compressor total pressure ratio by cooling on different parts with varied cooling powers. The dashed line represents the pressure ratio for the adiabatic compressor, which is a constant value of 6.77. The operating point for all of the result is the design point.  
Figure 5: Numerical model validation.  
Figure 6: Effect of cooling on different walls with varied cooling power on the total pressure ratio.  
Based on Figure 6, shroud cooling increases the compressor pressure ratio the most in all cooling powers. By increasing the cooling power on the shroud, the pressure ratio increases with the largest slope. Cooling power of 500 W on the shroud increases the compressor pressure ratio from 6.77 to 6.84, which is about 1%. By intensifying the cooling power to 2400 W, the pressure ratio increases to 7.08, which is about 4.6%. Cooling power of 2400 W can be achieved by passing cool water flow over fins attached to the outside walls on the casing.  
This result shows that in order to increase the performance of the compressor by cooling, the first part that should be considered is the shroud. On the other side, any heat flow from external or internal source to the shroud reduces the compressor performance effectively. Therefore, the heat transfer to this part should be prevented. Especially for a turbocharger installed in a car, the compressor shroud has to be insulated to prevent the heat flow from the engine and other heat sources.  
Back plate cooling increases the pressure ratio much less than the shroud cooling, but still more than the diffuser cooling. With the cooling power of 500 W, the compressor pressure ratio increases to 6.78, which is about 0.15%. Increasing the cooling power to 2400 W gives a pressure ratio up to 6.84, which is about 1.03%.  
Cooling the shroud and back plate reduces the air flow temperature inside the impeller. This is where the compression process happens. The shroud cooling reduces the main flow temperature directly with the high speed flow crossing over the shroud. The back plate cooling reduces the air temperature inside the gap. This reduces the impeller temperature, and this slightly reduces the main flow temperature. The temperature contour in a mid-plane, along the stream-wise direction, is illustrated in Figure 7.  
Figure 7: Enthalpy-entropy diagram for the compression process with different thermal conditions.  
Cooling the shroud and back plate improves the compression process by changing the thermo-dynamical path. As is shown in Figure 8, in a cooled compression, the final process has a higher pressure compared with the adiabatic compression.  
Diffuser cooling has a small improvement on the pressure ratio. Velocity change, inside a stream line in the diffuser, where there is no work input, can be computed using:  
\[du=-dp/\rho u \tag{5}\]  
It has been proven by [PERSON] [23] that heating increases the velocity. Cooling, on the other hand, should decelerate the flow. This means, for cooling, \(du<0\), and \(dp\) has to be positive in Equation (5). This is why cooling in the diffuser increases the pressure ratio.  
The work input to the compressor varies with cooling on different parts. This is because of the change in the velocity triangle at the impeller's trailing edge. It can be seen that shroud cooling has the highest increase in working input. However, even with the same work input as the adiabatic compressor, shroud cooling will result in a higher pressure ratio because of improved flow and higher efficiency (Table 2).