Turbulent Blood Flow in a Ventricular Assist Device

Application Challenge AC7-03 © copyright ERCOFTAC 2021

CFD Simulations

Overview of CFD Simulations

Various large-eddy simulations (LES) and unsteady Reynolds-averaged Navier-Stokes (URANS) computations were carried out using the commercial flow solver ANSYS CFX. All simulations were performed at the nominal operation (design) point of the VAD. In total, five LES computations on different grid sizes were conducted for the verification of the LES results. The simulation at the finest grid was used as the reference case for the comparison with URANS. For the URANS cases, an extended grid convergence study was performed using seven URANS grids to analyze the influence of the spatial discretization on the main assessment parameters. Additionally, URANS computations with different turbulence models were performed on the finest grid for the comparison with the LES results. The used URANS turbulence models were: a $k$ - $\omega$ model, a $k$ - $\omega$ -SST model, and a $\omega$ -based Reynolds stress model.

Computational Domain

The whole VAD was considered in the numerical analysis. A sketch of the computational domain can be seen in Fig. X. Inflow and outflow cannulas were included in the computational domain. The inlet and outlet of the cannulas were placed sufficiently far away (four and seven impeller diameters respectively) from the pump in order to minimze the influences of the boundary conditions on the results.

Block-structured grids with hexahedral-elements were created using ANSYS ICEM CFD. Since URANS and LES have different requirements for grid resolution and quality, two different, final meshes were created: a.) The final mesh for the LES computation has a size of $102M$ elements. The grid was built according to literature recommendations by Fröhlich and Menter for wall-resolving LES methods. Attention was paid that the near-wall grid fitted the upper limits of $\Delta _{x}^{+}\leq 40$ for the grid with in flow direction and $\Delta _{z}^{+}\leq 15$ for the grid width in spanwise direction. Furthermore, the first wall-normal node had a maximal dimensionless wall distance of $y_{1}^{+}\leq 1$ and the grid growth factor was $r_{g}=1.05$ . This meshing strategy has been implemented throughout the whole domain. Grid angles were larger than 23 $^{\circ }$ and the volume change smaller than 5 with apect ratios smaller than 40 at the pumps wall. The aspect ratios were further reduced with increasing wall distance, so that the values range from 1 to 6 in the core flow region.

Fig.3.1 Total Artificial Hearts (TAHs) and Ventricular Assist Devices (VADs), which are currently in clinical use. One TAH, one pulsatile VAD and three turbo pumps are shown.

The final URANS grid is coarser with a total size of $20M$ elements. Mesh quality criteria were kept within the ranges of the ANSYS CFX guidelines with maximum aspect ratios around 100, volume changes smaller than 6, and a minimum angle of $20^{\circ }$ . The mesh near the rotor wall has an area-averaged and maximal wall distance of $y_{1}^{+}=0.7$ and $2.1$ . All other pump parts have $y_{1}^{+}$ -values of one or smaller. Care was taken that the nearest wall layer contains more than 10 cells with a growth rate of $r_{g}=1.2$ . An advanced mesh convergence study of Eça and Hoekstra was performed to check whether the mesh size is appropriate to reflect the fluid mechanical and hemodynamical parameter. Therefore, the final URANS mesh was coarsened to 6 coarser grids with a mesh coarsening factor between 1.06 and 1.15.