## 3 Results and Discussion
### Effects of Radial Gap Ratio on Vaned Diffuser Performance
Figure 19: Absolute Mach number distribution superimposed with isolines at 50% span at the peak efficiency point of M\({}_{\text{u}}\) = 1.16 (design speed) for various radial gap ratios. Figure 20: Absolute Mach number distribution superimposed with isolines at 50% span at the peak efficiency point of M\({}_{\text{u}}\) = 0.69 for various radial gap ratios. Diffuser pressure recovery (\(\mathrm{C_{P}}\)) is one of the most common factors for evaluating the diffuser performance [37], which is the capability of the diffuser to diffuse. As flow decelerates at the diffuser exit, the higher static pressure that can be gained is the higher pressure recovery for the diffuser. Figures 22 and 23 present the pressure recovery for the various radial gap sizes and maximum pressure recovery for five tip-speed Mach numbers and six radial gap ratios. The maximum pressure recovery for \(\mathrm{M_{u}}\) = 0.69 and 0.93 occurs at a radial gap ratio of 1.06. Following this, it has a descending trend by enhancing the gap ratio, but the deviation is small. However, for \(\mathrm{M_{u}}\) = 1.05, 1.11 and 1.16, it has an ascending trend with an increase in the radial gap ratio, which reaches its highest value at a radial gap ratio of 1.08. After this, it is dropped out by enlarging the distance between the impeller trailing edge and diffuser leading edge. Figure 21: Absolute Mach number contour superimposed with isolines at 50% span for the lowest and highest radial gap when: (**a**) \(\mathrm{M_{u}}\) = 1.16 (design speed); (**b**) \(\mathrm{M_{u}}\) = 0.69. By increasing the radial gap ratio, the space in the region of the diffuser leading edge increases, thus, the mixing of non-uniform flow in diffuser leading edge increases. Therefore, a larger radial gap ratio should have a higher loss. However, as Figures 24 and 25 demonstrate, when \(\mathrm{M_{u}}\geq 1\), there is a turning when the diffuser leading edge and the impeller trailing edge are closer than radial gap ratio of 1.08 and a smaller radial gap ratio has a higher loss coefficient. The shock wave can be responsible for this phenomenon. As it is already mentioned, when \(\mathrm{M_{u}}\geq 1\), the shock wave in the smaller radial gap ratio is stronger than that in the higher radial gap ratio. Therefore, a smaller radial gap ratio has a higher loss coefficient. Figure 23: Maximum diffuser pressure recovery coefficients for five tip-speed Mach numbers and six various radial gap ratios. Figure 22: Diffuser pressure recovery coefficient. a higher loss coefficient. Finally, from a radial gap ratio larger than 1.08, the effect of shock the wave decreases and a smaller radial gap ratio has a smaller loss coefficient. With regards to Figures 24 and 25, at a low tip-speed Mach number (0.69 and 0.93), a smaller radial gap ratio compared to a larger radial gap ratio has less loss. The minimum value of the loss coefficient occurs at the radial gap ratio of 1.04, which then increases by raising the gap ratio. In comparison, at the high tip-speed Mach number (1.05, 1.11 and 1.16), the minimum value of the loss coefficient has  
Figure 24: Diffuser loss coefficient for five tip-speed Mach numbers and six radial gap ratios. Figure 15:0 Minimum diffuser pressure loss coefficient for five tip-speed Mach numbers and various radial gap ratios. the peak amount at a radial gap ratio of 1.04 before it drops to a minimum amount at the radial gap ratio of 1.08. Afterward, it increases with an increase in the radial gap ratio. It can also been seen that for all radial gap sizes, a compressor with higher tip-speed Mach number has a higher loss. The total skin friction drag force equation (Equation (2)) can justify this phenomenon. An increase in fluid velocity leads to an increment in the friction drag force, resulting in an increase in pressure drop. Therefore, the friction drag force increases and the pressure drop in diffuser grows. Therefore, a larger tip-speed Mach number have a higher loss coefficient.