Turbulent Blood Flow in a Ventricular Assist Device

Application Challenge AC7-03 © copyright ERCOFTAC 2021

Best Practice Advice

Key Fluid Physics

When calculating blood flow through complex medical devices, it should always be kept in mind that blood is a non-Newtonian, multiphase fluid. However, in simulations in ventricular assist devices, blood is approximated as a Newtonian, single-phase fluid. The former is justified because blood has asymptotic viscosity under high shear rates. In the latter, a blood-analogous fluid is assumed, which has comparable density and viscosity to blood. This assumption is necessary because it is impossible with current computational technology to account for the multiphase character of blood in a VAD simulation. This is partly due to the fact that the dimensions of the blood components are much smaller than the vortex structures calculated by the simulation. Therefore, much larger computational grids than in the current literature are needed to accommodate the blood components (size order of erythrocytes ≈ 10-6 m) to be integrated in the simulation.

Application Uncertainties

There are several uncertainties that can explain the differences between experiments and numerics:

It is important that the experimental validation uses a blood analog fluid that adequately represents the simulated fluid properties. As in this study, a mixture of glycerol-water is often used, which has a density 5% greater than the numerical fluid. Despite the same dynamic viscosity, this has an impact on the VAD flow field, since the density in the conservation equations is coupled to the pressure and velocity of the fluid. is coupled. The deviation is estimated to be ≈ 3 mmHg for the present case.

An additional deviation in the head is determined by the influence of the rotating shaft on the flow in the model. The shaft induces an additional swirl in the discharge flow and also "blocks" part of the discharge pipe. From URANS calculations of the VAD with rotating shaft, deviations in in the head of ≤ 1 mmHg were determined.

The inflow conditions between experiment and numerical simulation should be identical. Using additional CFD calculations, the influence on the head between a uniform and developed inflow profile can be estimated to be ≈ 1.5 mmHg.

Furthermore, geometric changes are inevitably present in the experimental model, such as axial gaps between the rotating and stationary regions, which do not exist in the numerical model. These geometric changes will alter the flow field in the experimental pump to some extent compared to the numerical flow, but are generally difficult to estimate.

Computational Domain and Boundary Conditions

Certain conditions have to be considered for domain size and boundary condition assignment:

For the analysis, straight inflow and outflow cannulas are often included included. The cannulas should placed sufficiently far away (four and seven times the impeller diameter, respectively) from the guide vanes. Preliminary URANS studies showed that these distances are sufficient in order to prevent negative influences of the boundary conditions on the results.

It's reasonable that no turbulent perturbations are given at the inlet of the domain. This point is valid, since the Reynolds number was $Re_{pipe}=c_{b}\cdot D/\nu \approx 2300$ in the inflow cannula and no disturbances can be assumed upstream of the inflow cannula. Thus, no transitional flow structures in form of turbulent puffs should be present in the inflow region.

A constant flow rate $Q$ should be defined at the outlet - and not at the inlet - of the domain, to guarantee that vortices with non-uniform pressure distribution can pass the outlet.

Discretisation and Grid Resolution

For URANS:

The extended grid convergence study shows

The coarser grid resolution - espacially in the near-wall region - leads to a lower results for blood trauma compared to the LES results in all blood damage models