## 1 Introduction  
Centrifugal compressors are widely used in industry [1] and small gas turbine engines. A high-pressure ratio will be the goal orientation for centrifugal compressors, as this leads to saving energy, reducing emission and raising power density [2]. With increasing applications of high-pressure ratio centrifugal compressors, several institutes, such as German Aerospace Center (Deutsches Zentrum fur Luft- und Raumfahrt; DLR) [3] and Mitsubishi Heavy Industries (MHI) [4], have conducted many studies researching them. However, the high-pressure ratio centrifugal compressors suffer from narrow stable flow range [5] and low efficiency [6]. When the pressure ratio is high, a compact engine and low manufacturing costs are the goals for solving these problems [7]. Therefore, to improve the performance of high-pressure ratio centrifugal compressors, a considerable of researchers have conducted several surveys. [PERSON] and [PERSON] [8] discussed the considerations for selecting the appropriate geometries in designing a high pressure ratio centrifugal compressor. [PERSON] et al. [9] experimentally studied the effects of diffuser geometry on stall inception. [PERSON] et al. [10] and [PERSON] et al. [11] investigated on the improvement of stable flow range in high-pressure ratio centrifugal compressors. [PERSON] et al. [12] realized that the volute's asymmetry has a great impact on the performance of a high-pressure ratio turbocharger compressor, affecting stability and efficiency, which is correlated with pressure ratio. The compressor performance strongly depends on the various design parameters. The design of a compressor is restrained by numerous aerodynamic remarks. [PERSON] et al. [PERSON] et al. (2017) presented that aspect ratio, pitch-chord ratio and blade fillet with the slot configuration on the blade have a significant effect on the cascade performance. Another important design parameter, tip clearance, was studied by [PERSON] et al. [PERSON] et al. (2017). They investigated the various value of the axial tip clearance (3.9% to 11.3% of the impeller exit height) of a centrifugal compressor with a pressure ratio of 6.0. They concluded that the pressure ratio and efficiency of the impeller, as well as the compressor stage for all flow rates, are reduced by increasing the tip clearance. Impeller-diffuser interaction can play a major role in enlarging the improvement of the centrifugal compressor, as it is an important part of the compressor. Therefore, it is essential to create an acceptable design for this part. The impeller-diffuser interaction has a direct and considerable influence on the flow field in addition to the performance of the compressor stage and its components. The impeller-diffuser interaction refers to the area between impeller trailing edge and diffuser leading edge. The impeller-diffuser interaction excitation mechanism for a centrifugal compressor was studied by [PERSON] (2000). [PERSON] et al. [PERSON] et al. (2008) and [PERSON] et al. [PERSON] et al. (2008) found that for diffuser parts, using a vaned diffuser is a common way of obtaining high performance. Using different sizes for the radial gap between the impeller trailing edge and vane diffuser leading edge can support the impeller-diffuser interaction [PERSON] et al. (2017). The radial gap ratio and its effects on the performance of low-pressure ratio centrifugal compressors has been investigated thoroughly. By investigating the influence of the blade row on the performance of centrifugal compressor, [PERSON] et al. [PERSON] et al. (2010) came to the conclusion that by increasing the impeller and diffuser interaction, a loss is generated. Radial gap ratio also affects the impeller tip leakage. By increasing the radial gap ratio, slip and blockage diminish and loss increases [PERSON] et al. (2010). [PERSON] et al. also presented that the radial gap ratio has an optimal value and if the radial gap ratio is less than this value, the detriment of the increased loss will surpass the benefit of decreased slip and blockage.