###### Abstract  
The widespread trend of pursuing higher efficiencies in radial turbochargers led to the prompting of this work. A 3D-printed model of the static parts of a radial variable geometry turbine, the vaned nozzle, and the volute, was developed. This model was up-scaled from the actual reference turbine to place sensors and characterize the flow around the nozzle vanes, including the tip gap. In this study, a computational model of the scaled-up turbine was carried out to verify the results in two ways. For this model, firstly compared with an already validated CFD turbine model of the real device (which includes a rotor), its operating range was extended to different nozzle positions, and we checked the issues with rotor-state interactions as well as the influence of elements such as the screws of the turbine stator. After showing results for different nozzle openings, another purpose of the study was to check the effect of varying the clearance over the tip of the stator vanes on the tip leakage flow since the 3D-printed model has variable gap height configurations. turbocharger; radial turbine; CFD analysis; nozzle vane; variable geometry turbine +
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Commonly, the expansion stage in small-size turbochargers is composed of a radial turbine which counts a volute, a stator, and a rotor. The function of the first two elements is to condition the flow at the rotor inlet efficiently so that it transforms kinetic energy into mechanical energy to move the centrifugal compressor at the engine intake. The volute and stator geometry design can compromise the fluid behavior, and this is key for the rotor to achieve better efficiencies, something which authors such as [20] have researched. For this reason, the stator can have, in some turbines, movable vanes that control and adapt the flow depending on the operating conditions. These variable geometry nozzles in the stator help to extend the operating range of the turbine; meanwhile, the matching with the compressor side can be achieved by the use of a ported shroud [21]. Uniform distribution over the 360 degrees of the radial stator is important to then adapt the flow at the rotor inlet, a matter of interest in [22], where they tested flow behavior for twin-entry turbines as two separated single VGT solutes. Therefore, while some authors focus on a volute casing optimization, as in [23], the stator and its vanes must be designed according to an aerodynamic geometry that has the least possible amount of energy losses [24; 25; 26]. Conventional design criteria for each turbine part (volute, stator, and rotor) focus primarily on ideal gas, but new systems under development such as hydrogen or industrial gases, such as S-CO\({}_{2}\), require further research on radial turbines [27]. The use of new propulsion systems, alternative to diesel and gasoline engines, need to have a turbocharging system suitable for their needs; therefore, work on these geometries is still in progress in multiple areas. There are many challenges to overcome with these kind of turbines, especially when they are attached to a compressor and the variable operating conditions could lead to undesirable consequences, as it could be the mistuned bladed disc effect, treated by several authors [28; 29]. Internal flow is a high-interest research area which is producing multiple articles in different fields of study: in the case of [30], the phenomena of compressibility is analyzed, alongside the areas where there is greater incidence of shock waves with different nozzle openings. Authors from [31] have developed high-order models for radial turbines. On the other hand, in [32], an up-scaled experimental turbine model was presented.