Best Practice Advice AC7-03

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Turbulent Blood Flow in a Ventricular Assist Device

Application Challenge AC7-03   © copyright ERCOFTAC 2021

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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 integrate the blood components (size order of erythrocytes ≈ 10-6 m) 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.

• 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. The cannulas should placed sufficiently far away (four and seven times the impeller diameter, respectively) from the guide vanes. Preliminary URANS studies showed in Reference [3] that the used distances are sufficient in order to prevent negative influences of the boundary conditions on the results.

• It is 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 LES:

• In order to guarantee that the greatest amount of turbulence within the VAD is directly resolved, a special treatment of the computational grid is necessary. This is especially the case for the near-wall resolution, since the energy-containing vortices, which need to be resolved by LES, scale linearly inverse with the wall distance. In order to resolve these vortices, a high grid resolution in all spatial directions is necessary. Therefore, we orient the grid characteristics on literature recommendations for wall-resolving LES, with a near-wall grid, which fitted the upper limits of $\Delta _{x}^{+}\leq 50$ and $\Delta _{z}^{+}\leq 20$ for the grid widths in the flow and spanwise direction. Furthermore, the first wall-normal node had a maximal dimensionless distance of $y_{1}^{+}\leq 1$ and the grid growth factor was $r_{g}=1.05$ near the wall. Additionally, further grid quality measures should be kept, to minimize discretization errors and obtain a proper convergence behavior. Grid angles should be larger than 20, aspect ratios smaller than 5 in the core flow region and the mesh expansion factor smaller than 20. Furthermore, the interfaces between the single domain are created as evenly as possible, in order to guarantee a smooth progression of the transported flow variables across the interfaces.

• A adequate grid resolution for LES can be checked by the power-loss-analysis from section CFD Simulations .

For URANS:

• The extended grid convergence study shows that discretization errors are crucial for blood damage prediction based on the equivalent stresses. Even when the similation indicates a small discretization error for the pump characteristics, the error can be significant for the blood damage prediction results

• The coarser grid resolution - espacially in the near-wall region - leads to a lower values for blood damage compared to the results computed with LES

Physical Modelling

The fluid mechanical evaluation of the pump characteristics (head, efficiency) shows that the URANS can satisfactorily reproduce these quantities with the applied setup. However, for the hemodynamic evaluation, the similarity in stress progression depending on the operation point. At the partial load point, the equivalent stresses are similar to LES and the blood damage prediction results deviate less between both methods. At the nominal operation point, the deviations in equivalent stresses are larger, which also leads to larger differences in the blood damage prediction. Despite the quantitative differences between URANS and LES, a modeled turbulent parameter from the URANS turbulence model should always be included in the shear stress definition (Equation (6.2.)). Otherwise the difference to the reference will be even larger, which could massively bias the blood damage prediction (see stresses larger than 9 Pa in Table 5.3 and 5.4 in Evaluation).

Recommendations for Future Work

Two recommendations can be made on the experimental and numerical side:

• On the one hand, it would be worthwhile to have more experimental validation data, e.g. of the turbulent kinetic energy, in order to perform a fluid mechanical investigation and validation of these quantities in the VAD as well.

• On the other hand, hybrid URANS-LES models appear suitable to fill the trade-off between high accuracy (LES) and low computation time (URANS). It would be interesting to see how a hybrid LES model computes the hemodynamical parameters compared to the presented methods.

References

[x] Torner, B.; Konnigk, L.; Wurm, F.H.: Influence of Turbulent Shear Stresses on the Numerical Blood Damage Prediction in a Ventricular Assist Device. International Journal of Artificial Organs 42(12). 2019. https://doi.org/10.1177/0391398819861395. 2021

[x] Konnigk, L.; Torner, B.; Bruschewski, M.; Grundmann, S.; Wurm, F.-H. (2021): Equivalent Scalar Stress Formulation Taking into Account Non-Resolved Turbulent Scales. In: Cardiovascular Engineering and Technology 12(3), pp. 251-272 . https://doi.org/10.1007/s13239-021-00526-x

[2]Torner, B.; Konnigk, L.; Abroug, N.; Wurm, F.-H. (2020): Turbulence and Turbulent Flow Structures in a Ventricular Assist Device. In: International Journal for Numerical Methods in Biomedical Engineering 37(3), e3431. https://doi.org/10.1002/cnm.3431

[x] Wisniewski, A.; Medart, D.; Wurm, F.H., Torner, B.: Evaluation of Clinically Relevant Operating Conditions for Left Ventricular Assist Device Investigations. International Journal of Artificial Organs 2020. https://doi.org/10.1177/0391398820932925 - Winner of the ESAO SAGE Award 2020 for the Best Selected Paper in the International Journal of Artificial Organs in 2020. 2019

[x] Konnigk, L.; Torner, B.; Hallier, S.; Witte, M.; Wurm, F.H.: Grid-Induced Numerical Errors for Shear Stresses and Essential Flow Variables in a Ventricular Assist Device: Crucial for Blood Damage Prediction? Journal of Verification, Validation and Uncertainty Quantification 3(4). 2019. https://doi.org/10.1115/1.4042989.

[x] Torner, B.; Konnigk, L.; Hallier, S.; Kumar, J.; Witte, M.; Wurm, F.-H. LES in a Rotary Blood Pump: Viscous Shear Stress Computation and Comparison with URANS. International Journal of Artificial Organs (2018): https://doi.org/10.1177/0391398818777697.

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Contributed by: B. Torner — University of Rostock, Germany

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© copyright ERCOFTAC 2021