## 3 Results
### Gap Height Variation  
Having shown that ST resembles flow behavior appropriately through the gap (when the tip-to-blade height ratio is similar), and taking into account that the modular printed model had two different gap heights, we can study how it affects the variation of the gap on the tip leakage and flow behavior. This comparison is performed with the Reynolds similarity case, since it is the one that showed better agreement with the RT case when compared in previous analysis.  
The leakage vortex varies with both VGT position and gap height, as shown in Figure 14. For the closest position, VGT30, it can be seen how different the vortex is for the 0.5 mm gap in the upper image from the 1.5 mm gap. On SS, there are two generated vortexes, one at mid-chord and the second at the TE; especially for the 1.5 mm gap case, this second vortex is of greater magnitude, affecting the flow that is delivered to the impeller and creating more significant losses. At VGT60, the situation described by [PERSON] et al. (2018) happened, where a first vortex is created on the PS and then the flow is sucked back through the gap to the SS, creating a vortex of greater magnitude in the greater clearance case. However, for the widest opening nozzle position, VGT80, it was found that a greater  
Figure 12: Local Reynolds number distribution in the clearance. ST and RT; VGT60; 0.5 mm tip height. In the figure, legend colors stand for each case, while shapes in gray determine each of the chord positions where data are taken.  
Figure 13: Local Reynolds number distribution in the clearance. ST and RT; VGT30; 0.5 mm tip height. In the figure, legend colors stand for each case, while shapes in gray determine each of the chord positions where data are taken.  
gap diminished the suction effect generated by the PS detachment bubble, observed in [32], thus having lower tip leakage and losses in the vane faces. If volumetric mass flow is calculated through the clearance and normalized with the volume between vane and stator wall, the mass flow ratio through the 0.5 mm gap is higher than the one passing over the 1.5 mm gap. For VGT30, the ratio between these values for different gaps is just 1.05 times greater with the smaller gap, but for greater openings, this ratio rises up to 1.45 for VGT80, meaning that proportionally there are higher tip leakages through smaller gaps, especially for highly opened nozzle positions. This way, it can be said that for extreme closed positions, the importance of reducing the clearance height is more important, since it would reduce the TE vortex and subsequent losses.  
Another way of looking at this tip leakage interaction is by studying different planes through the vane, as in Figure 15. This study was performed on the vanes of the ST for the two different gap heights designed. In this case, velocity convoluted vectors are displayed to make it possible to check vortexes formation and tip leakages all along the vane. However, a detailed view shows that the most significant area of the vane is the TE. For that reason, studied planes are those placed at the 60% and 80% of the chord.  
For the narrowest vane nozzle position, in Figure 15a, it can be seen how the higher clearance mainly affects the TE vortex, with higher tip leakages from PS to SS enlarging the vortex and blocking part of the vane, thus increasing losses.  
Other phenomena can be observed with a broader position, such as VGT60, represented in Figure 15b. As the blade loading for this opening is lower than in the VGT30 case, there is a more negligible suction effect through the gap. For the 1.5 mm gap, the TE vortex tends to be of lower magnitude and more stuck to the vane wall than what happens in the 0.5 mm gap. This result reinforces the crucial importance of reducing the clearance height if the turbine is expected to work at narrow openings, as depicted in Figure 14.  
Figure 14: Tip gap vortex streamlines for two gap configurations and three vane openings. ST; VGT30, VGT60, and VGT80; 0.5 and 1.5 mm tip height.