# Comparison of Cooling Different Parts in a High Pressure Ratio Centrifugal Compressor
## 1 Introduction  
Centrifugal compressors generate a high pressure ratio in a small size. They can be used in areas where a high pressure ratio in a small space is desirable; for example, in compact gas turbines, helicopters and turbochargers. The trend in centrifugal compressors is towards a high pressure ratio on a smaller scale. This increases the power density, saves energy and also reduces emissions. Future turbochargers, for example, are required to have a compressor with a pressure ratio up to 5.8 for continuous operation [1]. Unfortunately, the development of high pressure ratio centrifugal compressors faces some limitations. In order to have an increment in the pressure ratio, the impeller rotational speed has to increase. Higher rotational speed intensifies the mechanical stress on the impeller disk. Meanwhile, the solid impeller temperature increases because of the higher temperature of the flow. This degrades the impeller integrity. [PERSON] et al. [2] reported that the maximum pressure ratio that an impeller can bear drops from 4.6 down to 4.2 if the effects of the temperature variations on the ultimate tensile stress of the impeller are being considered. Furthermore, higher rotational speed increases the flow speed and Mach number. This produces shock waves and degrades the efficiency of the compressor. Compressor efficiency is substantial, especially in high pressure ratio conditions. In a turbocharger with a pressure ratio of six, compression work in the compressor requires half of the engine power [3]. This shows that a slight improvement in compressor efficiency saves a significant amount of work. Many studies have sought to increase the efficiency in a centrifugal compressor by aerodynamicredesign and modification of the blade shape [4; 5; 6]. However, the aerodynamic improvement of blades reached its limits, and new improvements need a complex 3D manufacturing process. Effective cooling in a compressor improves the efficiency by changing the thermodynamical path of the compression. Furthermore, a suitable cooling method at the right place can cool down the impeller. Different methods of cooling have been used in compressors. Inlet wet cooling is a common method in gas turbines to increase the efficiency [7; 8]. In this method, water is added to the inlet air flow to reduce the inlet air temperature by evaporation. This method has gained popularity because of its effectiveness, simple installation and low cost [9; 10]. However, this method degrades the blades' integrity by ice formation before the leading edge. This method has a negative effect on the compressor's surge margin [11; 12]. Furthermore, a large amount of water is needed for the continuous operation, which is not always available. Another method to avoid these negative effects is to utilize a heat exchanger at the inlet. The cooling source can be an absorption chiller, active magnetic cooler or Vapor Compression Refrigeration (VCR). [PERSON] et al. [13] illustrates that using an absorption chiller for inlet air cooling in a gas turbine increases the output power by 11.3%. This improvement can be further increased if somehow the pressure drop caused by the heat exchanger in the main flow can be prevented. Shell cooling or cooling on the external walls in a centrifugal compressor can be used to cool down the fluid flow, as well as the impeller. The cooling power source can be the same as the sources used for charge air cooling as mentioned in the last paragraph. A secondary flow can flow inside some jackets attached to the walls to cool them down. [PERSON] et al. [14] used shell cooling for all of the external walls in a centrifugal compressor. A huge improvement in the compressor performance, as well as a noticeable reduction in impeller temperature have been obtained by shell cooling. [PERSON] et al. [15] studied the effect of cooling inside the casing near the back plate on the impeller temperature and found that with an appropriate cooling rate, the impeller temperature can be reduced effectively.