# CFD and Experimental Comparison for Micro-Pump Performance in Space Applications: A Case Study
## 3 Results  
### Labyrinth Simulations Using Different Turbulence Models  
Several turbulence models (\(k\)-\(\varepsilon\), SST, and Spalart-Allmaras) were used in the simulations to compare their performance and evaluate their suitability for capturing the specific flow phenomena in the pump. Figure 13 illustrates the wall shear distribution in the labyrinth from steady-state simulations. Among the three models, only the Spalart-Allmaras model predicted Taylor-Couette-like structures, prompting further investigation  
Figure 12: In-house test bench [31]. using unsteady RANS (uRANS) and Large Eddy Simulation (LES). The uRANS study with the SST model did not reveal this flow pattern, and the flow parameters showed no differences between steady-state and unsteady SST simulations. Additionally, a LES was performed (Figure 14), with fine geometrical discretization, which revealed flow patterns similar to those of the SST model and no significant Taylor-Couette-like structures. This suggests that the initial finding with the Spalart-Allmaras model may have been an anomaly or specific to its characteristics. In estimating the seal mass flow (Figure 15), the k-epsilon model exceeds the LES and all other RANS models by approximately 20%. However, for the torque-to-mass flow ratio, the \(k\)-epsilon model is closest to the LES values. All models tend to overestimate these values when compared to the LES results. This suggests that while LES provides a more accurate representation of the physical processes, the RANS models tend to predict higher values for torque and shear stress on the rotating wall. Although the torque (Figure 16) and shear stress on the rotating wall (Figure 17) were significantly lower in the LES simulation compared to all RANS simulations, the LES results were in better agreement with all models except the \(k\)-epsilon model for the other integrated parameters. All values are presented relative to the reference LES value, which is set as 1 and considered the most accurate in the absence of experimental data. The colors are used only to differentiate the LES case from the RANS cases. The wall shear stress was integrated over both the stationary and rotating surfaces of the domain. For the stationary casing, the wall shear stress predictions from most turbulence models were fairly close to the LES results. This suggests that the shear stress on the stationary casing is less sensitive to the choice of turbulence model, with the notable exception of the \(k\)-epsilon model, which deviated significantly from the LES results, indicating a less accurate prediction of wall shear stress on the stationary casing. Figure 13: Wall shear distribution on the front labyrinth—steady case: (a) SA; (b) \(k\)-epsilon; (c) SST. Figure 16: Torque area integrated: (**a**) over the rotating labyrinth and (**b**) over the stationary casing. Figure 14: Wall shear distribution on the front labyrinth—unsteady case. (**a**) LES; (**b**) uRANS. Figure 15: Seal mass flow obtained for the steady and unsteady cases. This suggests a common tendency among RANS models to predict higher frictional forces on the rotating surfaces. Despite this general trend, the k-epsilon model was the closest to the LES results, with only a 10% higher shear stress. Among the RANS models, it displayed the lowest wall shear stress on the rotating labyrinth wall. In terms of integrated parameters, the relationship between mass flow and shear stress reveals some interesting discrepancies. Although the k-epsilon model displayed the lowest shear stress among the RANS models, it overestimated the mass flow by approximately 20%. Overall, while k-\(\epsilon\) predicted the lowest shear stress of the RANS models, this does not explain the overestimation of mass flow, since LES results show even lower shear stress values yet also predict low mass flows rates--consistent with the other RANS models tested. The comparative analysis of wall shear stress between the LES and various RANS models reveals critical insights.