## 4 Conclusions  
The paper presents the development and numerical analysis of a high transonic linear cascade designed to study shockwave structures under different working conditions. A notable advantage of this cascade design lies in its ability to concurrently accommodate different operating conditions, leading to reduced experimental expenses. Additionally, since the flow angle is largely identical for each passage in the cascade, the experiment covers a CFD uncertainty in mass flow as high as 9%--the difference between the lowest and highest mass flows registered in the linear cascade assembly. This is quite conservative, given that modern RANS models are employed. Conversely, if the estimation of the nominal mass flow is regarded as perfect, the differences between the passages could be seen as nominal points on slightly different speedlines. Therefore, the first row would correspond to a higher speedline and row 5 would be associated with an inferior speedline. The computational aspect of this study involved employing the Ansys CFX solver, which facilitated steady simulations for both the linear cascade and single-passage geometry. The results primarily center around the asymmetrical nature of the flow field and can be summarized as follows:  
1. In terms of the position, strength, and number of regions with a high Mach number, the cascade replicated the five different variations in the nominal operation point of the diffuser well. 2. The pressure coefficient distribution matches both the main and splitter vanes. The observed discrepancies are not passage-related in the sense that if a difference in Cp is observed on the splitter, this is not necessarily also observed in the Main vane. Therefore, this indicates that these are some global, cascade-related, 3D effects that warrant further study. 3. The differences between the flow of the upper and lower sections of the complete cascade are approximately 9%. However, the equivalent passage flows--simulated as idealized periodic passages--show differences of only +/ - 5% in mass flow. This feeds into the hypothesis that some 3D effects influenced by the cascade walls and the interaction between the passages exists. 4. All things considered, when designing a similar test rig, users must expect and account for differences between individual flow passages (early in the design stage) and the final rig. Depending on the investigated parameters, such a fixed linear cascade can be useful in the assessment of flow field characteristics under various operating conditions using both numerical and experimental tests, even for higher Mach numbers. Moving forward, this research will be extended to further investigations involving the same linear cascade. Such studies will eventually aim to analyze the effective  
Figure 15: Numerical comparison between enhanced transonic cascade model and single-channel periodic representation: (**a**) full cascade—blade row 2; (**b**) single channel—channel 2.  
ness of passive control methods in mitigating the effects of shock waves in high-speed turbomachinery applications. Conceptualization, O.D., V.D., and M.G. ; methodology, O.D., V.D., and M.G. ; software, O.D., M.G., and V.D. ; validation, O.D., M.G., and V.D. ; investigation, O.D., V.D., and M.G. ; resources, O.D., M.G., and V.D. ; data curation, O.D. ; writing--original draft preparation, O.D. ; writing--review and editing, V.D. and M.G. ; visualization, O.D. and M.G. ; supervision, V.D. and O.D. ; project administration, O.D. ; funding acquisition, O.D. All authors have read and agreed to the published version of the manuscript. This research was supported by a grant of the Ministry of Research, Innovation and Digitization, CCCDI--UEFISCDI, project number PN-III-P2-2.1-PED-2021-4204, within PNCDI III. Not applicable. This work was carried out within the PNCDI III, Project \"Operating range augmentation system through porous walls for centrifugal compressors\", acronym SPACELESS, Grant no.