Grid-Induced Numerical Errors for Shear Stresses and Essential Flow Variables in a Ventricular Assist Device: Crucial for Blood Damage Prediction?

Abstract

Adverse events due to flow-induced blood damage remain a serious problem for blood pumps as cardiac support systems. The numerical prediction of blood damage via computational fluid dynamics (CFD) is a helpful tool for the design and optimization of reliable pumps. Blood damage prediction models primarily are based on the acting shear stresses, which are calculated by solving the Navier–Stokes equations on computational grids. The purpose of this paper is to analyze the influence of the spatial discretization and the associated discretization error on the shear stress calculation in a blood pump in comparison to other important flow quantities like the pressure head of the pump. Therefore, CFD analysis using seven unsteady Reynolds-averaged Navier–Stokes (URANS) simulations was performed. Two simple stress calculation indicators were applied to estimate the influence of the discretization on the results using an approach to calculate numerical uncertainties, which indicates discretization errors. For the finest grid with 19 × 106 elements, numerical uncertainties up to 20% for shear stresses were determined, while the pressure heads show smaller uncertainties with a maximum of 4.8%. No grid-independent solution for velocity gradient-dependent variables could be obtained on a grid size that is comparable to mesh sizes in state-of-the-art blood pump studies. It can be concluded that the grid size has a major influence on the shear stress calculation, and therefore, the potential blood damage prediction, and that the quantification of this error should always be taken into account.

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

“…In means of grid elements, this led to a 20-times coarser mesh for SST and ORS computations with 400 thousand hexahedral elements. Mesh independence for the RANS setup is ensured and already demonstrated by means of an uncertainty quantification in previous studies 34 using the Richardson extrapolation and approach proposed by Eça and Hoekstra. 7 Both RANS computations were carried out until all residuals dropped below .…”

“…The flow through the nozzle was computed with RANS and SST model using a setup previously described in Reference 34 . Since we use results for the nozzle that we have already generated for other publications, there are no results for the nozzle with Reynolds stress models.…”

“…VADs are mechanical assist devices for patients who suffer from terminal heart failure and are not eligible to wait for a donor heart. Our previous work has focused on the influence of turbulence in VADs, 55 on the verification of VAD flow simulations with RANS and LES, 34 , 35 and on the comparison of results between simulation methods with different influence of turbulence modeling. 54 Turbulence models based on the RANS equations are the most used models in VAD research.…”

“…Our previous as well as other comprehensive sensitivity analyses showed that an increasing resolution of turbulence in the flow leads to an increasing prediction of blood damage. 21 , 34 Since it is still not practicable to include the complete turbulent field in the CFD analysis (by DNS) to calculate the blood damage, methods have to be established to include the unresolved part of the turbulence statistically in the prediction.

Figure 1 Schematic representation of two mean velocity profiles in laminar and turbulent flow with equal mean wall shear stress but different average stresses in the core flow to explain the statements in the study by Quinlan.

…”

Influence of turbulent shear stresses on the numerical blood damage prediction in a ventricular assist device

“…Other aspects are improper turbulence models (in a sense of adding modeled dissipation to the flow) and too dissipative numerical schemes. In this context, blood damage will be greatly underpredicted in a simulation with too small meshes, 42 too large time steps, or improper turbulence models, 40 even when an appropriate blood damage model is applied.…”