Turbulent Blood Flow in a Ventricular Assist Device

Application Challenge AC7-03 © copyright ERCOFTAC 2021

Test Data

Overview of Tests

An experimental validation was performed for two operation points, the partial load ( $Q=2.5~l/min$ ) and the nominal load ( $Q=4.5~l/min$ ) at a rotational speed of $n=7,900~r/min$ . The investigates VAD model was explained in section Flow Domain Geometry. This was originally created exclusively for numerical investigations. In order to enable an adequate validation of the simulated VAD flow, the following requirements were placed on the experimental model during conceptual design:

Due to the small dimensions and narrow gaps, the model to be manufactured must have tolerances in the range of $10-20~\mu m$ .
In the numerical model, the VAD has no axial gaps between rotating and stationary components. The experimental model must have axial gaps as small as possible between these components.
In the numerical model, a hydraulically smooth flow is assumed in the immediate vicinity of the wall. Also in the experimental model, a hydraulically smooth flow should be present at the walls.
No mechanical drive for the impeller is considered in the numerical model. Since the experimental model requires a drive, it must be placed as free as possible from interference for the flow.
It should be possible to measure various flow variables with the model to be produced. Thus, in the first measurement campaign, the goal is to determine the performance data, as pressure head and hydraulic efficiency. However, the model is also to be used in the future to optically measure velocities or turbulent quantities.

VAD model

To meet the above points, it was decided to make the experimental model from polymethylmetacrylate (PMMA or acrylic glass). Since acrylic glass is a transparent plastic, accessibility for optical measurement techniques is ensured. Furthermore, acrylic glass can be machined well, so that all wetted components could be manufactured from solid material by milling. The fabricated components can be seen in the assembled acrylic model in Figure 2.1. The acrylic model consists of two acrylic blocks that are bolted together and sealed by an O-ring at the interface. Inside the two acrylic blocks, the VAD outside diameters and the diameters of the inlet and outlet pipes are milled. The hydraulic components of the VAD (inlet guide vane, impeller, outlet guide vane) were also made of acrylic glass. Dimensional tolerances of $10~\mu m$ were achieved for all these components. Furthermore, all components were hand-polished to achieve hydraulically smooth flow behaviour.

Fig.2.1 Fabricated acrylic model for the experimental investigations.

For manufacturing reasons, changes were made to the acrylic model compared to the numerical model. For example, chamfers had to be added at the transitions between the hubs and blades of the impeller and guide vanes with radii of $r=0.5~mm$ . Furthermore, axial gaps between the rotating and stationary flow regions are present. However, the gap size could be reduced to a minimum of $0.1~mm$ . The impeller is driven by an electric motor. Power is transmitted from the motor to the impeller via a shaft that passes through the rear acrylic block and the guide vane into the impeller hub. The shaft induces an additional swirl in the flow of the discharge pipe. URANS calculations showed that an additional deviation in head between numerics and experiment of $1~mmHg$ is expected due to the altered discharge flow. Due to the shaft drive, a bend with 30° bend angle had to be integrated into the outlet of the rear acrylic block. Care was taken in the design of this component, which is made of polyoxymethylene, to ensure that the flow deflection would not affect the pressure measurements. The guide vanes are fixed in the acrylic blocks by screws. The guide vanes were arranged to correspond exactly to the numerical model. The impeller is axially beared by a polytetrafluoroethylene thrust bearing at the inlet guide vane and on the opposite side by a spacer in the hub of the outlet guide vane. The radial bearing of the impeller is provided by the shaft, which itself is supported by three ball bearings. Pressure measuring holes were integrated in the acrylic model to determine the head of the VAD. The position and geometry were selected according to literature data. Thus, the measuring holes are each 1.5 (inlet) or 2 pipe diameters (outlet) away from the VAD to allow a sufficient distance of the measuring area from the hydraulic components.Furthermore, four holes offset by 90 were arranged in the measuring area according to the DIN EN ISO 9906. These guarantee the determination of a circumferentially averaged wall pressure, which is used to calculate the pressure head. Diameters of $D=1~mm$ and hole lengths of $L=3~mm$ were selected for the measuring holes.

Test rig

The fabricated acrylic model was integrated into a pump test rig, shown in Figure 2.2. The test rig allows the measurement of the head characteristic curve and the hydraulic efficiency. The test rig consists of a tank (1) with a baffle. The baffle "calms" the fluid and prevents air bubbles from being entrained into the circulation line. A temperature sensor (2) is integrated in the tank. An inlet pipe (3) made of polyvinyl chloride leads from the tank to the acrylic model (4). The velocity profile at the end of the inlet pipe slightly differs from the inlet boundary condition of the CFD. By means of URANS calculations, it was verified that the head differences is approximately 2 mmHg are due to the different inflow conditions.

Fig.2.2 Test rig as CAD model. The numerised components are explained in the text.

A ring line (5) made of silicone is arranged around each of the pressure measuring holes in the acrylic model. The ring line leads to a manifold which is connected to the pressure sensors. This allows the static pressure to be measured symmetrically to the circumference. The pressure sensors (6) are arranged at the height of the axis of rotation of the VAD. Behind the acrylic model, a silicone hose (7) leads to the upper circulation line. Downstream of the hose is the volume flow sensor (8) and an angle seat valve (9), which is used as a throttling element. All hoses, lines and internals in the test rig cause pressure losses. It was estimated during the design phase that the operating points investigated on the test rig can be can be set without an auxiliary pump. Furthermore, care was taken to ensure that the flowed-through components are compatible with water-glycerine, which was used as a substitute fluid for blood. Since the test rig components are not connected to each other in a self-supporting manner, it was necessary to construct a supporting structure from aluminum profiles (10). Additionally, torque measurements for the determination of the hydraulic efficiencies were done using an direct torque measurement sensor between the shaft's coupling and the drive motor.

NAME	GNDPs	PDPs (problem definition parameters)		MPs (measured parameters)
	$Re_{p}$	Rotation speed (rpm)	flow rate (l/min)	DOAPs
EXP 1 (nominal load)	$3\cdot 10^{4}$	7,900	4.5	Pressure head, $\eta _{i}$
EXP 2 (partial load)	$3\cdot 10^{4}$	7,900	2.5	PPressure head, $\eta _{i}$

Table 2.1 Summary of the measured pump characteristics.

	Pressure head $H$	Hydraulic efficiency $\eta _{i}$
EXP 1 & EXP 2	pressure_heads.dat	hydraulic_efficiencies.dat

Table 2.2 Data files or the characteristic curves for the pressure head and the hydraulic efficiency.

Description of Experiment

After the drive was gradually ramped up to the nominal speed $n=7900~r/min$ the volume flow for the respective operating point is set using the angle seat valve. After a statistically steady state was reached, the recording of the measurement signals began over a period of 60 s. The measurement was carried out 10 times for all operating points repeated in order to reduce random measurement errors as much as possible.

Fluid, Measured Quantities and Measurement Errors

Fluid in the Experiment

The fluid in the test bench is a mixture of water and glycerine. The mixture is the same dynamic viscosity like the fluid defined in the CFD. In contrast to the fluid in the CFD, however, the water-glycerine mixture has a higher density of $\rho =1100kg/m^{3}$ at a dynamic viscosity of $\mu =3.5mPas$ . URANS investigations with both densities showed that the pressure head between numerics and experiment differ by 3 mmHg due to the different fluid data.

Measured Quantity	Measured range	Measuring device	Systematic error
viscosity	$\nu =1-5~mm^{2}/s$	Ubbelohde viscosimeter	$\Delta \nu _{s}/{\overline {\nu }}=0.17\%$
density	$\rho =1000-1200~kg/m^{3}$	density areaometer	$\Delta \rho _{s}=1kg/m^{3}$
temperature	$\Theta =-10-50^{\circ }C$	thermometer	$\Delta \Theta _{s}=0.5^{\circ }C$

Table 2.3 Measurement equipment for the fluid measurements.

The density and viscosity of the fluid were measured prior to filling the test rig and during the mixing. Table 2.3 summarizes the measurement technology used for this. After filling the test rig and after the measurements, the material data were repeatedly measured and checked for immutability.

Measurement of the Pump Characteristics

To determine the pressure head and the hydraulic efficiency at the operating points, the volume flow, the speed of the drive shaft, the shat's torque the temperature and the static pressure upstream (SS) and downstream (PS) of the VAD must be measured. From the measured pressures, the head H in mmHg is calculated by dividing the pressure difference by 133.332 Pa, which corresponds to a pressure which corresponds to a mercury column of 1mm height. According to (DIN EN ISO 9906, 2012), the measuring technique was selected in such a way that measurements according to class 1 (highest accuracy) are possible. The measuring technique is listed in Table 2.4 listed. It provides either an analog signal in the form of a current/voltage or a digital signal in the form of a pulse signal. To enable conversion and recording of the measured value, a CompactRIO-9063 was equipped with a current input (NI-9203) and a Counter module (NI-9361).

Measured Quantity	Measured range	Measuring signal	Systematic error
flow rate	$Q=0-20~l/min$	pulse (digital)	$\Delta Q_{s}/{\overline {Q}}=1.0\%$
rotational speed	$n=0-11000~r/min$	pulse (digital)	$\Delta n_{s}=10^{-3}~r/min$
termperature	$\Theta =0-100^{\circ }C$	current	$\Delta \Theta _{s}=0.5^{\circ }C+0.0002\Theta$
relative pressure SS	$p=-1.0-0.6~bar$	current	$\Delta p_{s}=0.05\%$ of the span
relative pressure PS	$p=0-0.3~bar$	current	$\Delta p_{s}=0.20\%$ of the end value
torque	$M=0-1000~Nmm$	voltage	$\Delta M_{s}=0.05\%$ of the span

Table 2.4 Measurement equipment for the determination of the pump characteristics.

References

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.

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