On the Discretization of the Power-Law Hemolysis Model

Practical implications of the erroneous treatment of exposure time in the Eulerian hemolysis power law model

BACKGROUND

Eulerian and Lagrangian power-law formulations are both widely used for computational fluid dynamics (CFD) to predict flow-induced hemolysis in blood-contacting medical devices. Both are based on the same empirical power-law correlation between hemolysis and the shear stress and exposure time. In the Lagrangian approach, blood damage is predicted by tracking both the stress and exposure time along a finite number of pathlines in the domain. In the Eulerian approach, a scalar transport equation is solved for a time-linearized damage index within the entire domain. Previous analytical work has demonstrated that there is a fundamental problem with the treatment of exposure time in the Eulerian model formulation such that the only condition under which the model correctly represents the true exposure time is in a flow field with no streamwise velocity variation. However, the practical implications of this limitation have yet to be thoroughly investigated.

METHODS

In this study, we demonstrate the inaccuracy of Eulerian hemolysis power-law model predictions due to the erroneous treatment of exposure time by systematically considering four benchmark test cases with increasing degrees of flow acceleration: Poiseuille flow through a straight tube, inclined Couette flow, and flow through a converging tube with two different convergence ratios.

RESULTS

Compared with Lagrangian predictions, we show that, as flow acceleration becomes more pronounced, the resultant inaccuracy in the Eulerian predictions increases. For the inclined Couette flow case, there is a small degree of flow acceleration that yields a discrepancy in the range of 10% between Lagrangian and Eulerian predictions. For flows with a larger degree of acceleration, as occurs in the converging tube flow cases, the discrepancy is considerably larger (up to 257%).

CONCLUSION

The inaccuracy of hemolysis predictions due to the erroneous treatment of exposure time in the Eulerian power-law model can be significant when there is streamwise velocity variation in the flow field. These results may partially explain the extremely large variability in CFD hemolysis predictions reported in the literature between Lagrangian and Eulerian models.

Equivalent Scalar Stress Formulation Taking into Account Non-Resolved Turbulent Scales

PURPOSE

Cardiovascular engineering includes flows with fluid-dynamical stresses as a parameter of interest. Mechanical stresses are high-risk factors for blood damage and can be assessed by computational fluid dynamics. By now, it is not described how to calculate an adequate scalar stress out of turbulent flow regimes when the whole share of turbulence is not resolved by the simulation method and how this impacts the stress calculation.

METHODS

We conducted direct numerical simulations (DNS) of test cases (a turbulent channel flow and the FDA nozzle) in order to access all scales of flow movement. After validation of both DNS with literature und experimental data using magnetic resonance imaging, the mechanical stress is calculated as a baseline. Afterwards, same flows are calculated using state-of-the-art turbulence models. The stresses are computed for every result using our definition of an equivalent scalar stress, which includes the influence from respective turbulence model, by using the parameter dissipation. Afterwards, the results are compared with the baseline data.

RESULTS

The results show a good agreement regarding the computed stress. Even when no turbulence is resolved by the simulation method, the results agree well with DNS data. When the influence of non-resolved motion is neglected in the stress calculation, it is underpredicted in all cases.

CONCLUSION

With the used scalar stress formulation, it is possible to include information about the turbulence of the flow into the mechanical stress calculation even when the used simulation method does not resolve any turbulence.