## 3 Results and Discussions  
Figure 9 illustrates the distribution of density gradients for the complete cascade geometry. Inherently, each passage passes a slightly different mass flow fraction; therefore, it becomes possible to test multiple working points simultaneously, enabling the assessment of how different shockwave patterns influence fluid flow. It is worth mentioning that since the flow angle is identical for all passages, the differences can be regarded as surrogates for slightly different speedlines. Notably, in the first two passages, the shockwave intensity is more pronounced. This diminishes as the mass flow passing through the channel decreases, specifically toward passage 5. Passages 1 and 2 exhibit robust normal shock waves on the splitter and near the leading edge of the main blade. The shock patterns in these two channels indicate that the working conditions are approaching the physical choke point of the passage. However, this is not necessarily equivalent to the speedline choke, in which a negative incidence could also be observed. Therefore, it is more correct to think of these passages as part of the nominal point of a higher speedline. At supersonic speeds, as is the case of the first two blade passages, due to the sudden change in the profile geometry a local disturbance of the flow is created, generating a shock wave. In this case, the shock wave is influenced also by the blade angle of attack and the flow velocity. The intensity of the shock waves formed near the leading edge is relatively mild when contrasted with those generated on the splitter. Consequently, the flow separation induced by this shock wave results in a thin separation layer. The flow structure of the cascade is examined at midspan, and Figures 10 and 11 present the variation in the pressure coefficient for the main blade and splitter, respectively. In Figure 10, the first three channels of the cascade display three zones with significantly reduced pressure coefficients, corresponding to the presence of shock waves attached to the airfoil. In these cases, the intensity of these attached shock waves is notably stronger compared to the lower part of the cascade (i.e., toward passage 5), where the shock waves are only formed in proximity to the leading edge of the blade. Figure 11 depicts the variation of the pressure coefficient for the splitter blade. For this airfoil, shock waves are formed on both the suction and pressure side. Specifically, the first two passages exhibit strong shock intensity, whereas the magnitude of the shock waves reduces for the subsequent passages in the cascade. Figure 9: Density gradient distribution on the linear cascade. The distribution of the Mach number on the near-blade flow field, as shown in Figure 12, indeed confirms the variation in the pressure coefficient mentioned earlier. Notably, areas of local acceleration are observed on the leading edge of the main blade and the mid-cord of the splitter. These regions of acceleration lead to different intensities  
Figure 11: Pressure coefficient (Cp) distribution on the splitter surface—midspan. Figure 10: Pressure coefficient (Cp) distribution on the main blade surface—midspan. of shock structures, ranging from strong structures (near the first passage) to progressively weaker ones as the passage index increases. Since each passage works at a different mass flow, it is worth noting that the difference between the higher and lower mass flow is approximately 9%. This variability in working conditions is the main contributor to the differences in shock intensities and pressure coefficients observed across the cascade geometry. Figures 13 and 14 provide a comparison between the idealized (single-passage flow) and non-idealized periodic passage (full cascade). Each blade row in the full cascade represents a distinct working condition of the vaned diffuser. In all cases, it is evident that the flow structure in the single passage exhibits the same overall pattern as the full cascade.