# CFD and Experimental Comparison for Micro-Pump Performance in Space Applications: A Case Study
## 2 Materials and Methods
### CFD Case Setup
#### 2.2.2 Centrifugal Pump  
The full pump simulations were performed using a coarser mesh, suitable for steady-state RANS modeling, due to the high computational cost associated with LES for the entire pump domain. Nevertheless, the RANS simulations were validated against experimental measurements to ensure reliability. The numerical simulations were conducted under steady-state conditions using the ANSYS CFX solver, with mesh generation carried out in ANSYS Meshing (ANSYS 2022 R2), following established best practices for turbomachinery simulations as outlined by [PERSON] et al. [41] The RANS equations were solved using the standard k-\(\varepsilon\) turbulence model, widely used for turbomachinery applications due to its balance between accuracy and computational efficiency. A finite volume method was employed, with a second-order upwind scheme for convective terms and second-order central differencing for diffusive terms.  
A grid independence study was performed for the computational domain of the impeller, including the labyrinth seal regions, to ensure that the numerical results were  
Figure 8: Grid size justification for the LES simulation: (**a**) \(\text{E}_{\text{resolved}}/\text{E}_{\text{total}}\): (**b**) Integral Length Scale (local distribution); (**c**) Cubic root of the cell volume (local distribution).  
not sensitive to mesh resolution. Five different mesh densities were tested, ranging from 4.3 million to 11.98 million elements. The simulations were conducted at the nominal operating point of the centrifugal pump, which was selected as the design point for this analysis. The primary differences between mesh levels were in the volume mesh size within the blade passage and labyrinth cavities, as well as refinements in the inflation layers near walls to capture boundary layer effects more accurately. For the 9.22 million element mesh, the inflation mesh had 10 layers with a growth rate of 1.3.  
Key output parameters--such as pressure distribution, velocity field, and hydraulic efficiency--were monitored and compared across the different mesh resolutions. The results for the 9.22 million and 11.98 million element meshes showed negligible variation (less than 1%), indicating that mesh convergence had been achieved. Therefore, Mesh 4 (9.22 million elements) was selected for subsequent simulations, as it provided an optimal balance between accuracy and computational cost (see Figure 9).  
The mesh representation for the entire domain is shown in Figure 10, which includes the mesh of the impeller, a section through it, and the volute mesh.  
These studies guided the grid resolution used in the full pump simulations. However, due to computational constraints, a formal mesh convergence study for the complete pump assembly was not carried out. As a result, some uncertainty remains in the global CFD predictions.  
Therefore, the overall computational domain consisted of approximately 30 million elements. Figure 11 illustrates the computational domain along with the applied boundary conditions. At the inlet, a constant total pressure and temperature were imposed, while the outlet boundary condition was defined by varying flow rates along the operating line. No-slip, adiabatic wall conditions were applied throughout the domain. Stationary walls within the rotating domain were treated as counter-rotating to compensate for the impeller motion, and a Frozen Rotor interface was used to couple the impeller and volute domains [42]. To ensure consistency with the experimental setup, which was conducted under similitude conditions, deionized water was used as the working fluid [43].  
Figure 9: Total pressure variation versus number of mesh elements.  
A high-order advection scheme was imposed in all cases, with double precision. For convergence of the case, the RSM residuals (target below \(10^{-5}\)), domain imbalance (below 1%) and a monitoring point positioned on the outlet domain (stable variation of the pressure) were checked.