# CFD and Experimental Comparison for Micro-Pump Performance in Space Applications: A Case Study
## 2 Materials and Methods
### CFD Case Setup  
#### 2.2.1. Labyrinth  
To better understand the fluid flow behavior within the pump, the labyrinth section was studied separately due to its distinct resolution requirements. Both steady and unsteady CFD simulations were performed on the labyrinth section to identify the most suitable modeling strategy for the full pump analysis. For steady-state simulations, three turbulence models were evaluated: \(k\)-\(\epsilon\), SST, and Spalart-Allmaras (SA). For unsteady simulations, two approaches were considered: unsteady RANS (uRANS) and Large Eddy Simulation (LES).  
Different meshes were used for the RANS and LES cases, reflecting their distinct modeling requirements. For the RANS simulations (both steady and unsteady), a coarser mesh was employed, with fewer elements and a more relaxed near-wall resolution. Inflation layers were still applied to capture boundary layer behavior, but the mesh was designed to operate with wall functions, targeting \(y^{+}\) values in the range of 1-300, depending on the turbulence model used. This allowed for computational efficiency while maintaining acceptable accuracy for the RANS-based models.  
In contrast, the LES simulation required a significantly finer mesh to resolve large-scale turbulent structures and capture near-wall dynamics without relying on wall functions.  
Figure 5: Volute geometry: (**a**) top and (**b**) section view.  
A 60\({}^{\circ}\) periodic sector was modeled and 17 inflation layers were applied near the walls, with a first layer height of 10\({}^{-5}\) mm and a growth rate of 1.27. This ensured a \(y^{+}\) value close to 1 throughout wall-bounded regions (Figure 6), in accordance with best practices for wall-resolved LES in complex internal flows [38; 39]. The final LES mesh consisted of approximately 6.1 million elements.  
Figure 7 illustrates the detailed mesh topology near the walls in the LES case. The LES simulation used the WALE (Wall-Adapting Local Eddy-Viscosity) subgrid-scale model in ANSYS CFX, along with second-order spatial discretization and a second-order backward Euler scheme for time integration. The time step was selected to keep the Courant number below 1, ensuring both stability and accurate resolution of turbulent fluctuations.  
All simulations applied smooth, adiabatic wall conditions, with boundary pressures set at 4.5 bara at the inlet and 1.5 bara at the outlet. The working fluid in the labyrinth analysis was HFE 7200, consistent with the properties listed in Table 1.  
\begin{table}
\begin{tabular}{c c} \hline
**Domain** & **Value** \\ \hline \multirow{2}{*}{Pump temperature domain} & Operational: \(-20\)\({}^{\circ}\)C \(\pm\) 50 \({}^{\circ}\)C \\  & Non-operational: \(-30\)\({}^{\circ}\)C \(\pm\) 60 \({}^{\circ}\)C \\  & 500–1000 kg/h at 22 \(\pm\) 2 \({}^{\circ}\)C \\  & \multicolumn{1}{c}{} \\ \end{tabular}
\end{table}
Table 1: Pump operating specifications.  
Figure 6: The \(y+\) distribution on the front labyrinth.  
Figure 7: Mesh representation for labyrinths.  
For the LES discretization, the approach presented in [40] was applied. A user-defined flow field function was implemented to estimate the proportion of calculated to modeled turbulent kinetic energy (TKE).  
\[\frac{E_{resolved}}{E_{model}}=1-\left(\frac{\Delta}{ILS}\right)^{2/3} \tag{2}\]  
\[\Delta=\sqrt[3]{V_{cell}} \tag{3}\]  
\[ILS=\frac{k^{3/2}}{\varepsilon} \tag{4}\]  
The integral length scale (\(ILS\)), see Figure 8, is approximately one order of magnitude larger than the representative cell size in the far field. Within the boundary layer, the flow is primarily modeled by the sub-grid scale, classifying this as a wall-modeled LES case. Figure 8a presents an iso-volume representing the region where 70% of the turbulent kinetic energy is resolved, with a color map illustrating the spatial distribution of the resolution percentage.