Research Papers

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

[+] Author and Article Information
Lucas Konnigk

Institute of Turbomachinery,
Faculty of Mechanical Engineering and
Marine Technology,
University of Rostock,
Albert-Einstein-Straße 2,
Rostock 18055, Germany
e-mail: lucas.konnigk@uni-rostock.de

Benjamin Torner

Institute of Turbomachinery,
Faculty of Mechanical Engineering and
Marine Technology,
University of Rostock,
Albert-Einstein-Straße 2,
Rostock 18055, Germany
e-mail: benjamin.torner@uni-rostock.de

Sebastian Hallier

Institute of Turbomachinery,
Faculty of Mechanical Engineering and
Marine Technology,
University of Rostock,
Albert-Einstein-Straße 2,
Rostock 18055, Germany
e-mail: sebastian.hallier@uni-rostock.de

Matthias Witte

Institute of Turbomachinery,
Faculty of Mechanical Engineering and
Marine Technology,
University of Rostock,
Albert-Einstein-Straße 2,
Rostock 18055, Germany
e-mail: matthias.witte@uni-rostock.de

Frank-Hendrik Wurm

Institute of Turbomachinery,
Faculty of Mechanical Engineering and
Marine Technology,
University of Rostock,
Albert-Einstein-Straße 2,
Rostock 18055, Germany
e-mail: hendrik.wurm@uni-rostock.de

1Corresponding author.

Manuscript received December 15, 2017; final manuscript received February 19, 2019; published online April 1, 2019. Assoc. Editor: Marc Horner.

J. Verif. Valid. Uncert 3(4), 041002 (Apr 01, 2019) (10 pages) Paper No: VVUQ-17-1037; doi: 10.1115/1.4042989 History: Received December 15, 2017; Revised February 19, 2019

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.

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Grahic Jump Location
Fig. 1

Numerical model of the analyzed VAD with a two-bladed rotor, an inlet guide vane with five blades, and a three-bladed outlet guide vane

Grahic Jump Location
Fig. 2

Left: section of the computational grid in the rotor for finest and coarsest meshes; right: detailed view of the mesh in gap between rotor and casing

Grahic Jump Location
Fig. 3

Section of FDA's benchmark testcase nozzle with sudden expansion (edited from Ref. [41]). Red lines represent locations where the uncertainty estimation was conducted with time-averaged velocity results.

Grahic Jump Location
Fig. 4

(a) Centerline velocity and (b) velocity profile. Black solid line: experimental data with uncertainties. Dashed line: results from CFD literature results. Red circles: Our results obtained on the finest grid with estimated uncertainties. Experimental and CFD data from group which also used k−ω model and contributed to the round robin study are obtained from the website.2

Grahic Jump Location
Fig. 5

(a) Comparison of time-averaged velocity profile from bottom wall to channel center between literature data from Moser et al. [42] (black line) and our DNS (red rots). The calculated uncertainties are barely visible at most of the data points and (b) comparison between exact solution (black line) and solution obtained on the coarsest grid (red dots) with calculated uncertainties.

Grahic Jump Location
Fig. 6

Pressure heads via the rotor (top). The line shows the fitHr¯=109.3−3.66×107hi2. Pressure heads via the pump (bottom). The line shows the fitHp¯=74.5−7.49×107hi2. The error bars mark the numerical uncertainties (deviations in percent).

Grahic Jump Location
Fig. 7

Global volume integral of shear stresses over the pump. The line shows the fit Iτ=1.14×10−4−0.017×hi0.89. The error bars mark the numerical uncertainties (deviations in percent).

Grahic Jump Location
Fig. 8

Upper left: volume in pump which exceeds 9 Pa. The line shows the fitVτ¯>9 Pa=1.98×10−6−7.78hi2. Upper right: volume in pump which exceeds 50 Pa. The line shows the fitVτ¯>50 Pa=2.61×10−7−1.90×10−3hi1.25. Bottom: volume in pump which exceeds 150 Pa. The line shows the fitVτ¯>150 Pa=3.37×10−8−0.48hi2.08. The error bars mark the numerical uncertainties (deviations in percent).

Grahic Jump Location
Fig. 9

Time-averaged wall shear stresses on the surface of the rotor (top) and leading edge (bottom) between coarsest (UR-1) and finest (UR-7) mesh

Grahic Jump Location
Fig. 10

Volumes with shear stresses over 150 Pa in the rotor of the VAD between finest (UR-7) and coarsest (UR-1) mesh



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