3.1 Overall pump performance
Figure 3 shows predicted H-Q curves in comparison with experimental results for both pumps. For CH-VAD, the H-Q curves predicted using LES are more consistent with the trend of experimental curves. The average difference with experimental values is approximately − 5.86%, while for URANS and RANS the differences are − 9.14% and − 19.94% respectively. Furthermore, the pressure heads at high flow rates were highly underpredicted for RANS. The underprediction for URANS was pronounced as well. For Heartmate III, the slope of the LES H-Q curves also agrees better with experimental results compared with RANS and URANS.
Table 4
Predicted pump hydraulic performance: pressure head, efficiency and secondary flows
Model | Condition (rpm; L/min) | P (mm Hg) | Hydraulic efficiency(%) | Secondary flow (L/min) | Ratio of the secondary flow (%) |
CH-VAD | 2900;5 | 80 | 34.81 | 0.31 | 6.20 |
3700;8 | 110 | 37.25 | 0.46 | 5.75 |
2800;2 | 85.6 | 21.19 | 0.26 | 13.00 |
2800;5 | 67.7 | 32.98 | 0.25 | 5.00 |
3200;2 | 112.0 | 19.78 | 0.34 | 17.00 |
3200;5 | 97.3 | 34.28 | 0.31 | 6.20 |
3200;7 | 73.5 | 32.13 | 0.34 | 4.86 |
Heartmate III | 5700;5 | 80 | 44.08 | 0.60 | 0.68 | 25.60 |
7600;8 | 110 | 40.82 | 0.66 | 0.69 | 16.88 |
5000;2 | 79.6 | 31.43 | 0.51 | 0.84 | 67.50 |
5000;5 | 46.7 | 36.70 | 0.51 | 0.52 | 20.60 |
6000;2 | 120.3 | 30.07 | 0.62 | 1.08 | 85.00 |
6000;5 | 93.1 | 44.49 | 0.59 | 0.82 | 28.20 |
6000;7 | 43.3 | 29.13 | 0.53 | 0.42 | 13.57 |
*Ratio of the secondary flow (%) is the ratio of secondary path flow to inlet flow. The secondary flow of Heartmate III is calculated as the sum of leakage flows at the upper clearance (left column under header “Secondary flow”) and lower clearance (right column).
Table 4 shows predicted pump hydraulic performance. The hydraulic efficiency of CH-VAD decreases at low flow rate, but remains above 30% at higher flow rate (7L/min). The Heartmate III has higher efficiency at 5 L/min. However, both the pressure head and efficiency of Heartmate III decrease significantly at high flow rate. The efficiency difference between CH-VAD and Heartmate III at 8 L/min and 110 mm Hg is less than 5 L/min and 80 mmHg. The H-Q curve of Heartmate III is much steeper compared with CH-VAD (cf. Figure 3). As shown in Table 4, the ratio of the secondary flow to the main flow depends on the working condition for both pumps. The ratio is higher for conditions of higher pump speed and lower inlet flow rate. Overall, the secondary flow rate for Heartmate III is higher, due to high leakage flows in the larger secondary flow gaps abover and underneath the rotor.
Table 5
Overall hydraulic loss Wf and its distribution in different subdomains
Model & condition | Normal pressure (5L/min, 80 mm hg) | Hypertension (8L/min, 110 mmhg) |
CH-VAD | Heartmate III | CH-VAD | Heartmate III |
Total (W) | 1.64 | 1.14 | 3.31 | 2.89 |
Inlet (W) | 0.01 | 0.02 | 0.03 | 0.07 |
Impeller (W) | 0.81 | 0.70 | 1.68 | 1.87 |
Secondary flow path (W) | 0.7 | 0.35 | 1.19 | 0.71 |
Volute & outlet (W) | 0.13 | 0.07 | 0.41 | 0.23 |
efficiency (%) | 34.81 | 44.08 | 37.25 | 40.82 |
*Wf (W) represents hydraulic loss, defined as the difference of the shaft power and effective power: Wf =T*ω- P*Q, where T is the torque excerted on the fluid, ω is the pump speed.
As shown in Table 5, the overall hydraulic loss of CH-VAD was considerably higher at 5 L/min and 80 mmHg compared with Heartmate III. The U-shaped secondary flow path of CH-VAD is narrow, long and with larger surface area, leading to a loss of almost twice that of Heartmate III. At 8 L/min and 110 mmHg, the difference of the overall hydraulic loss between the two pumps decreases. In the region of impeller, the loss of Heartmate III was even lower than that of CH-VAD. The difference in the overall hydraulic loss mainly lies in the regions of impeller and secondary flow path for both conditions.
3.2 Flow field
The instantaneous flow field of the two blood pumps at the two typical conditions (5L/min, 80 mmHg and 5L/min, 110 mmHg) obtained using LES on the fine grid (25.34 million for CH-VAD and 25.06 million for Heartmate III, cf. Table 3) are used for subsequent flow field analysis and comparative evaluation of two pumps. After the pressure head had reached statistical convergence, instantaneous solution was collected at the point when the pressure head matched the average pressure head (see Fig. 4(a)&(c)), which is also the target pressure head (80 mmHg or 110mm Hg). This corresponds to the timing when the blade was just about to sweep across the volute tongue (cf. Figure 4).
CH-VAD
Figure 5 shows the streamlines of CH-VAD colored with eddy viscosity (reflecting loss in turbulent flows) at different cross-sectional planes representing different blade heights. Eddy viscosity At 10% and 50% blade heights, the incidence angles at the blade leading edge were very small (see Fig. 5(a)-(d)). Since the outlet of secondary flowpath locates at the rear of the blade passage, little flow disturbance was observed in the front part of the blade passage at 50% blade height. The flow field at the rear of the blade passage was affected by tip leakage flow and leakage flow from secondary flow path, with increasing flow loss. At 10% blade height, the flow in the front part of the blade passage is more affected by hub clearance leakage flow and secondary flow passage leakage flow. The flow of 90% blade height section is strongly disturbed by tip clearance leakage flow, with large incidence angle. At 5 L/min, 80 mmHg, flow separation at 50% blade height was not observed. At 8 L/min, 110 mmHg, the influence of leakage flows on the flow field at the rear part of the blade passage was pronouced, resulting in high flow loss.
At 5 L/min and 80 mmHg, the disturbance of tip clearance leakage flow spreads to multiple upstream flow channels, as shown in Fig. 6(a). Most of the leakage flows enter the adjacent channel and caused recirculation in the channel, affecting a large part of the channel. A small amount of leakage flow moved further upstream and entered the tip clearance of the next blade, interfering with the flow in the corresponding blade passage. At 5 L/min and 80 mmHg, the tip clearance leakage flow is of a similar pattern, though the cicrculation is smaller and limited to upper half of the blade passage (cf. Figure 6(b)). There are also leakage flows in the hub clearance of the leading edge of the blade, part of which enters the blade passage or even the tip clearance, causing disturbance to the main flow, as shown by the red arrow in Fig. 6(c).
Figure 7 shows the leakage flow from secondary flow path, and its influence on the flow field in the impeller region. The streamlines were colored using the effective scalar stress \({{\tau }_{eff}}_{ }\), following definition in (Wu et al. 2019):
$${\tau }_{eff}=\sqrt{\rho \mu {\epsilon }_{tot}}.$$
3
where \(\rho\) and \(\mu\) are density and molecular viscosity of blood respectively, \({\epsilon }_{tot}\) is total energy dissipation. \({\tau }_{eff}\) has been show is a proper metric which reflects the local stress level and hydraulic loss in the flow field (Wu et al. 2019, 2020, 2021a, 2021b). The leakage flow affects the 2 ~ 3 adjacent upstream blade passages and interferes with the main flow. Part of it became tip clearance leakage flow. Moreover, the effective stress exceeds 50 Pa in places such as the exit of the secondary flow path and tip clearance, causing potential blood damage such as platelet activation (Fraser et al. 2012).
Figure 8 shows the streamlines inside the secondary flow path of CH-VAD. At 5 L/min and 80 mmHg, the flow was Taylor-Couette laminar flow without Taylor vortex, as shown in Fig. 8(a). The Taylor numbers were 1731 and 2484 for the inner and outer channel of the U-shaped secondary flow path respectively, less than the critical value of 3400. The effective stress in the outer channel was about 75 Pa. At 8 L/min and 110 mmHg, flows remained Taylor-Couette laminar flows, though Taylor number for the outer channel was 3748 and slightly higher than the critical value. The stress of the outer channel was approximately 115 Pa.
Heartmate III
Figure 9 shows the instantaneous streamlines at planes of different blade heights in Heartmate III. It is obvious that the flow angles were much larger than the blade inlet angle. At 50% blade height, flow separations occured at the pressure side of the blades for both work conditions. At 5 L/min, 80 mmHg, the boundary layer reattached at approximately 30% chord length (cf. Figure 9(a)), while at 8 L/min, 110 mmHg, the separation was much stronger, a large area of stall dominated the front part of the blade passage and blocked the mean flows. At 10% blade height, a larger area of low-speed flow separation can be observed on the pressure side of the blade for both conditions. The flow field at 90% blade height is chaotic at both conditions, probably due to the secondary flow from the upper clearance (cf. Figure 1(c)). Overall, eddy viscosity at the hytension condition was remarkably higher than the normal condition, indicating a higher hydraulic loss at 8 L/min, 110 mmHg.
Figure 10 shows streamlines in Heartmate III and indicates the flow directions of main flow as well as leakage flows at 5 L/min, 80 mmHg. Blood flows from the inlet through the impeller, and flows out into the volute. Due to the pressure difference, some blood was push into the upper clearance and joined the main flow channel again (blue arrows), bringing significant disturbing the flows in the blade passages. Figure 11(a)&(c) shows the instantaneous wall shear stress(WSS) distribution on rotor surface. In the upper clearance, the WSS reached up to 200 Pa at 5 L/min, 80 mmHg and 250 Pa at 8 L/min, 110 mmHg. The Taylor numbers were 42600 and 70200 respectively, far exceeded the critical number of 3400. Thus, Taylor vortexes can be observed in the secondary flow path (cf. Figure 10, Fig. 11(a)&(c)).
As shown in Fig. 11(b)&(d), the upper clearance leakage flow the joined the main flow at the center hole and flowed close to the wall. Its influence in the blade passages was mainly limited to upper half blade height at 5 L/min, 80 mmHg, while at 8 L/min, 110 mmHg it’s eddy viscosity was higher.
Figure 12 shows streamlines at the lower clearance of Heartmate III at 5 L/min, 80 mmHg. A part of the main flow did not enter the blade passage, but directly entered the lower clearance instead. It touched the lower casing of the pump, and abruptly changed flow direction (cf. Figure 12(a)). This led to flow dead zone, increasing the risk of blood stasis. Figure 12(b)&(c) shows lower clearance leakage flow, and its influence almost covered the full height of the blade. The combination of leakage flows from the upper clearance and the lower clearance accounted for 25.6% and 16.88% of the inlet flow rates for the two conditions of normal pressure and hypertension respectively. Actual flow rate in the impeller was significantly increased and higher than the inlet flow rate, resulting in large incidence angles as shown in Fig. 9.
Comparison of hydraulic loss in CHVAD and Heartmate III
Figure 13 shows effective stress contours at different blade heights in the impeller region at 5 L/min, 80 mm Hg for the two pumps. At 10% blade height, the flow loss in Heartmate III was higher than CH-VAD. For CH-VAD, the flow at this position was afftected by the hub clearance flow, while for Heartmate III, the main disturbance came from leakage flow from lower hub clearance, which was much stronger than the hub clearance flow in CH-VAD, leading to higher flow losses. The flow losses at the 50% and 90% blade heights for the two pumps were comparable. Even though the disturbance of the upper clearance leakage flow was strong at upper half blade for Heartmate III, since the impeller of CH-VAD is semi-open, its flow field near the blade tip was strongly afftect by the tip clearance flow, causing high flow loss as well. This may explain why overall hydraulic loss was higher in the impeller region for CH-VAD compared with Heartmate III, as reported earlier in Table 5.
Effective stress contours at 8 L/min, 110 mm Hg were shown in Fig. 14. Hydraulic losses increased for both pumps. Nonetheless, the increase of flow losses for Heartmate III was more pronounced. At 10% and 50% blade heights, the flow losses of Heartmate III were higher than CH-VAD, while at the 90% blade height, the flow losses were comparable. This is consistent with Fig. 9, in which large indicence at blade leading edge and stronger separations were observed at 8 L/min, 110 mmHg compared with 5 L/min, 80 mmHg. Table 4 showed the efficiency of Heartmate III decreased significantly at the condition of hypertension, the difference in efficiency between the two pumps decreased by nearly 5.5%. Table 5 shows the overall losses in the impeller of Heartmate III was higher than CH-VAD at 8 L/min, 110 mmHg. Thie observations here are also in line with the findings of Table 4&5.