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 simulated flow field in a large number of literature studies (e.g., in [4], [5], [28], [29]). Since the pressure in the pump is coupled via the governing equations to the flow field, the comparison of the heads can be used as the first stage of flow field validation in VADs.

Fig. 5.1. 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 5.1. For the operating point at $Q=4.5~l/min$, good agreement between numerical and experimental results 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 deviations 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 both numerical models are valid for reproducing the real pressure buildup of the VAD.

Fluid Mechanical & Hemodynamical Evaluation of LES and URANS

Inner Efficiencies $\eta _{i}$

The inner efficiencies according to Eq. (2) of the impeller (index: $i$) and the whole pump (index: $p$) are given in Tab. 5.1. The deviation between the URANS and the reference LES case are minor for both operation points with a maximum 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 Inner efficiencies of the impeller and the whole pump.

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

Equivalent Shear Stresses $\tau _{eff}$ in the time-averaged flow field

The computed effective stresses $\tau _{eff}$ (Eq. (9) in section Description) are plotted for both operation points in Fig. 5.2. The stresses from the reference LES are compared to the URANS computations (The stresses in the instanteous flow field can also be seen in Fig. 1.3 in Description). 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. In general, the stresses are underpredicted with URANS. Nevertheless, similar hot-spots for significant stresses $\geq 9~Pa$ are observable for the partial operation point ($Q=2.5~l/min$). This is in contrast to the nominal operation point ($Q=4.5~l/min$), where greater deviations in computed stresses are noticable between LES and URANS. Despite the fact that the URANS can reflect the high stresses in the gap vortex and the trailing edge flow regions (red areas marked with (A) and (B)), other relevant regions in the blade channels of the impeller (C) or in the area between the impeller and the outlet guide vane (D) cannot be adequately reflected for the nominal operation point. In these areas of the pump, complex interactions occur between secondary flows are present (explained in Refs. [2] and [27]), which are directly resolved by the LES. In contrast, the URANS turbulence model cannot adequately model the impact of these complex turbulent flow interactions on the effective stress field.

Fig. 5.2. Effective stresses $\tau _{eff}$ of LES and URANS. The figure displays a cylindical cut (explained in Fig. 1.3. in Description) through the rotor and outlet guide vane at a radius of 80% of the outer radius $R_{2}$. Top row: partial operation point at $Q=2.5~l/min$. Bottom row: nominal operation point at $Q=4.5~l/min$. Note 1: The "hard" cut in stresses directly between impeller and outlet guide vane is present due to averaging procedures in different frames of references. Note 2: The blades (I,II and 1-3) and the blade channels are mirrowed to get an overview of the entire blade channels.

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

The computed MIH indices (defined by Eq. (11) in section Description) are shown in Table 5.2. As already could be seen in the stress fields in Fig. 5.2., the LES computes highest hemolysis values in both operation points. This is partly due to the coarser spatial and temporal resolution of the stresses in URANS (also recognizable from the grid convergence study in Fig. 3.3. in the section CFD Simulations). But also the already mentioned insufficient resolution of the secondary structures in the blade channels (and the subsequent stresses) at $Q=4.5~l/m$ leads to the larger deviations at this operation point.

Table 5.2 Modified index of Hemolysis ${MIH}~[-]$ . The constants $(C,\alpha ,\beta )$ of Zhang et al. [30] were used in Eq. (11). The percentage value in brackets indicate the relative deviation between URANS and LES.

case	nominal load $Q=4.5~l/min$	partial load $Q=2.5~l/min$
LES - reference	$59.1$	$83.4$
URANS	$51.9~(-12.2\%)$	$79.8~(-4.3\%)$

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.

Influence of Modelled Turbulent Stresses on the Hemodynamical Evaluation with URANS

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.

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

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© copyright ERCOFTAC 2022