Evaluation AC7-03

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Turbulent Blood Flow in a Ventricular Assist Device

Application Challenge AC7-03   © copyright ERCOFTAC 2021

Evaluation

Experimental Validation of URANS and LES

For simulations in turbopumps, hydraulic characteristics such as the head $H$ are among the most important result variables. Also in the field of CFD applications in VADs, it is common to use the head to validate the numerical calculation. In fact, the measurement of the head is the only experimental validation of the numerical calculation in a large number of literature studies. Since the pressure in the pump is coupled via the governing equations to the rest of the flow field, the comparison of the heads can be used as the first stage of flow field validation in VADs.

Fig. 5.3. Validation of the numerically calculated pressure heads $H$ with experimental data. The figure shows the head curve for $n=7'900~1/min$.

The experimental and numerical results are given in Figure 5.3. For the operating point at $Q=4.5~l/min$, a good agreement between numerics and experiment can be observed with a deviation of $\Delta H/H_{exp}=-0.12\%$ for LES and $\Delta H/H_{exp}=-4.82\%$ for URANS. For the smaller flow rate $Q=2.5~l/min$ the deviation are slightly larger with $\Delta H/H_{exp}=-4.84\%$ for LES and $\Delta H/H_{exp}=-5.66\%$ for URANS.

In summary, the discrepancy between numerically and experimentally determined head is still within an acceptable range for both LES and URANS. From this, it can be concluded that the numerical model is valid to reproduce the real pressure buildup of the VAD.

Fluid Mechanical & Hemodynamical Evaluation of URANS

Hydraulic Efficiencies $\eta _{h}$

The hydraulic efficiencies of the impeller (index: $i$) and the whole pump (index: $p$) are plotted in Tab. 5.1. The deviation between the URANS and the reference LES case are minor for both operation points with a maximal deviation of $+3.2~\%$. It can be concluded that the turbulence-modelling URANS method can reflect the efficiencies, and hence the global losses, as accurately as the turbulence-resolving LES method.

Table 5.1 Hydraulic efficiencies of the impeller and the whole pump.

Flow Rate	Parameter	LES	URANS	Relative deviation to LES [%]
$Q=4.5~l/min$	$\eta _{h,i}~[\%]$	$49.1$	$48.8$	$-0.6$
$Q=2.5~l/min$	$\eta _{h,i}~[\%]$	$46.8$	$48.3$	$+3.2$
$Q=4.5~l/min$	$\eta _{h,p}~[\%]$	$34.2$	$33.1$	$-3.3$
$Q=2.5~l/min$	$\eta _{h,p}~[\%]$	$29.7$	$29.5$	$-0.7$

Equivalent Shear Stresses $\tau _{eff}$

The computed equivalent stresses $\tau _{eff}$ are plotted for both operation points in Fig. 5.4. The stresses from the reference LES are compared to the URANS computations with stress formulations (Eq. (6.1) and (6.2) in the Description) with and without the contribution of the modeled parameter $\epsilon _{mod}$. As can be seen from the LES results, relevant stresses above 9 Pa (threshold for vWF degradation) and 50 Pa (platelet activation) are present within the flow channel of the rotor and the outlet guide vane. These stresses are significantly underresolved, when a stress formulation is used, which do not account for the modeled contribution (w/o $\epsilon _{mod}$). With inclusion of $\epsilon _{mod}$, the stresses are closer to the LES results. Especially for partial load ($Q=2.5~l/min$), similar results are observable. Greater deviations in computed stresses are noticable for the nominal load point $Q=4.5~l/min$ between LES and URANS. Despite the URANS can reflect the high stresses in the gap vortex and the trailing edge flow regions (red areas), the relevant regions in the blade channels cannot be adequately reflected. In the blade channel, complex interactions between secondary flows (explained in the Description section) occur, which are directly resolved by the LES. The URANS turbulence model cannot adequately model the impact of these complex turbulent flow interactions on the equivalent stress field.

Fig. 5.4. Equivalent stresses $\tau _{eff}$ of LES and URANS. The equivalent stresses with and without the contribution from the turbulence model $\epsilon _{mod}$ is included. The figure displays a cylindical cut through the rotor and outlet guide vane at a radius of 80% of the outer radius $R_{2}$. Top row: partial load at $Q=2.5~l/min$. Bottom row: nominal load at $Q=4.5~l/min$.

Hemodynamical Evaluation: Hemolysis Value ${MIH}$ and Volumetric Threshold Analysis

The computed MIH-values are shown in Table 5.2. The LES computes highest hemolysis values in both operation points, which is due to the finer spatial and temporal resolution of the stresses. As already could be seen in the stress fields above, the deviation is smallest when the modeled turbulent stresses form the dissipation rate is included with URANS.

Table 5.2 Modified index of Hemolysis ${MIH}$.

case	nominal load $Q=4.5~l/min$	partial load $Q=2.5~l/min$
LES - reference	$59.1$	$83.4$
URANS $w/~\epsilon _{mod}$	$51.9~(-12.2\%)$	$79.8~(-4.3\%)$
URANS $w/o~\epsilon _{mod}$	$50.3~(-14.9\%)$	$67.7~(-19.2\%)$

Table 5.2. and 5.3. show the computed volumes, which exceeds certain stress thresholds for van Willebrand degradation (vWF; >9 Pa), platelet activation (>50 Pa) and hemolysis (>150 Pa). Again, the computed stresses of URANS are lower as with LES. Deviations of maximal $-15.0\%$ ($Q=4.5l/min$) are reached for the stress threshold of 9 Pa and 50 Pa by URANS $w/~\epsilon _{mod}$. Just, at the stress threshold above 150 Pa, larger deviations are observable for all URANS cases, which is due to the coarser near-wall grid density, were highest stresses are present. These near-wall streses affect greatly the numerical hemolysis prediction (Reference [1]).

Table 5.3 Analysis of volumes $I_{\tau _{eff}}$, which exceed the thresholds for vWF degradation (>9 Pa), platelet activation (>50 Pa) and hemolysis (>150 Pa), at partial load.

$Q=2.5~l/min$	$I_{\tau _{eff}>9~Pa}~[\%]$	$I_{\tau _{eff}>50~Pa}~[\%]$	$I_{\tau _{eff}>150~Pa}~[\%]$
LES - reference	$8.41$	$0.87$	$0.12$
URANS $w/~\epsilon _{mod}$	$7.68~(-8.7\%)$	$0.81~(-6.9\%)$	$0.10~(-16.7\%)$
URANS $w/o~\epsilon _{mod}$	$4.22~(-49.8\%)$	$0.65~(-25.3\%)$	$0.09~(-25.0\%)$

Table 5.4 Analysis of volumes $I_{\tau _{eff}}$, which exceed the thresholds for vWF degradation (>9 Pa), platelet activation (>50 Pa) and hemolysis (>150 Pa), at nominal load.

$Q=4.5~l/min$	$I_{\tau _{eff}>9~Pa}~[\%]$	$I_{\tau _{eff}>50~Pa}~[\%]$	$I_{\tau _{eff}>150~Pa}~[\%]$
LES - reference	$11.34$	$0.97$	$0.13$
URANS $w/~\epsilon _{mod}$	$9.64~(-15.0\%)$	$0.84~(-13.4\%)$	$0.10~(-23.1\%)$
URANS $w/o~\epsilon _{mod}$	$6.40~(-43.5\%)$	$0.80~(-17.0\%)$	$0.10~(-23.1\%)$

Larger deviations of maximal $-49.8\%$ ($Q=2.5l/min,>9Pa$) are present for the URANS $w/o~\epsilon _{mod}$. Espacially for the threshold above 9 Pa, approximately half of the volume cannot be computed by stress formulation Eq. (16.2). This is due to the insufficient resolution of turbulent stresses, when the modelled contribution is not included. As can be seen in Fig. 5.4., a great of the stresses above 9 Pa are present in the core flow region of the impeller and outlet guide vane, which can only be reflected by the turbulence model with URANS.

References

[1] 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

[2] 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

[3]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

[4] 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.

[5] 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.

[6] 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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Description

Test Data

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Evaluation

Best Practice Advice

© copyright ERCOFTAC 2021