Figure 1 illustrates a three-dimensional representation of the centrifugal blood pump and its essential structural elements: the inlet, outlet, impeller, and volute. The baseline model was inspired by the general design characteristics of clinically approved centrifugal blood pumps, which are used for short- to medium-term mechanical circulatory support in patients with advanced HF. The inlet and outlet are oriented orthogonally at a 90° angle. The impeller is characterized by a radial, open configuration comprising eight blades, of which four are classified as splitter blades. Prior studies have shown that the incorporation of splitter blades can help regulate the flow field and improve blood compatibility by mitigating flow-induced shear stress and pressure gradients (Wu et al., 2021; Li et al., 2022). A central column within the impeller enhances structural integrity and promotes uniform flow distribution. The impeller is completely supported by an advanced magnetic suspension system, eliminating mechanical contact and reducing wear. This system ensures axial stabilization of the rotor through passive suspension, while radial stability is maintained via a biased magnetic field, facilitating precise control over rotor dynamics. The main design parameters of the blood pump are shown in Table 1.

The selection of the secondary flow path clearance range (600–1,000 μm) was based on two primary considerations. First, geometric constraints inherent to the overall pump head design necessitate compatibility with the magnetic levitation system. In fully maglev pumps, the impeller, housing, and magnetic suspension components must be tightly integrated, which places specific limits on feasible clearance dimensions. Second, the clearance range must support adequate hydraulic performance, including pressure head, efficiency, and flow stability. To identify an optimal configuration with favorable hydraulic and hemolytic performance, an orthogonal experimental design was employed to optimize geometric parameters. Two factors were selected for the secondary clearance design: the inner clearance (L₁) and the outer clearance (L₂), each defined at five levels. Using the orthogonal design principle, a total of 25 test combinations were generated, as summarized in Table 2.

Experimental tests were carried out to evaluate the hydraulic performance of the baseline pump. The experimental setup is depicted in Figure 2. The pump head was fabricated from transparent polycarbonate (PC) material, with both internal and external surfaces polished to minimize flow resistance. A water–glycerol mixture (viscosity of 0.0035 Pa·s at 24°C) was used to match blood viscosity. Although this Newtonian fluid does not capture the shear-thinning behavior of real blood, prior studies suggest that in high-shear regions (>100 s⁻¹), the approximation remains valid for hydraulic performance validation. The inlet and outlet pressures were measured using digital pressure sensors (model GP-M001, Keyence), while an ultrasonic flow meter (model FD-XS20, Keyence) was used to capture the volumetric flow rates. To assess the pump’s performance under different operating conditions, various experimental scenarios were established by adjusting the pump’s rotational speed and the proportional valve on the outflow tubing. These adjustments allowed for a comprehensive evaluation of the pump’s hydraulic characteristics. It was assumed that maintaining the rotational stability of the motor shaft would not significantly affect the fluid dynamics. The pump was tested across a range of rotational speeds, from 2,500 to 3,500 rpm, with 24 operational tests conducted to record pressure head and flow rate data.

As illustrated in Figure 3, a range of particle trace numbers was selected to assess their predictive accuracy for hemolysis. It was observed that when the particle trace number reached 1,600, the hemolysis value remained relatively stable, even with further increases in the number of traces. In order to minimize the calculation error as much as possible, the subsequent HI prediction experiments utilized 2,000 particle traces for calculations.

A mesh independence analysis was conducted to validate the adequacy of mesh quality for precise computational results (see Table 3). Four different mesh resolutions, ranging from coarse to fine, were created, and corresponding fluid dynamic simulations were performed to assess the impact of mesh density on the pump head. The predicted pressure head stabilized beyond 2.5 million elements, with Case 3 (3.95 million elements) yielding an error of less than 0.4% compared to the finest mesh. Considering both computational efficiency and accuracy, the third mesh configuration was selected for all subsequent analyses. The grid elements for different pump models were kept at around four million.

The relationship between the inlet-outlet pressure difference and flow rate (H-Q curves) at a given rotational speed is a key parameter for assessing the hydraulic performance of a blood pump. The simulated results at various rotational speeds were validated against experimental data as shown in Figure 4A. The overall trend of the H-Q curve exhibits a relatively smooth profile, consistent with the characteristics of a centrifugal pump. The maximum error of approximately 9% observed at 3,500 rpm and 0.1 L/min represents the difference between CFD simulation results and experimental measurements.

To further validate the flow characteristics within the pump, the pressure and velocity vector fields of the baseline model were extracted at a flow rate of 5 L/min and a rotation speed of 3,000 rpm. These measurements were taken from the cross-section, as illustrated in Figures 4B, C. Localized low-pressure regions are observed near the leading edge of the blades and the center column. Pressure increases radially from the center toward the periphery, corresponding to the acceleration of fluid outward, which results in a pressure rise. The volute exhibits a uniform distribution, with a pronounced pressure increase observed near the outlet.

The influence of secondary flow path clearances on hydraulic performance was systematically assessed across 25 orthogonal design combinations (Table 4). The changes in clearance affected the pump volume minimally (<3%), and the variations in pressure head and efficiency remained within ±3% and ±5%, respectively, suggesting a limited influence of secondary flow path clearance adjustments on pump hydraulic performance. Compared with the baseline pump, several configurations significantly improved the hydraulic head and efficiency. Model 16 achieved the highest efficiency (+5.16%), while Model 21 attained the maximum pressure head (+3.10%). However, certain designs, such as Model 13, led to performance deterioration (efficiency −4.53%), indicating sensitivity to structural changes. An increase in clearance results in a higher leakage flow within the secondary flow path.

High SSS areas increase the risk of thrombosis, and identifying high SSS areas in the blood pump is important for predicting the probability of thrombosis. It was classified into three levels: (1) above 9 Pa: induced von Willebrand factor cleavage; (2) above 50 Pa can induce platelet activation; (3) above 150 Pa, associated with hemolysis risk (Fraser et al., 2012). Figure 5 illustrates the volume ratios of SSS exceeding 50 and 150 Pa across the 25 models. The volume fraction corresponding to high shear stress (>50 Pa) ranges from approximately 0.46%–0.51%, indicating that although high shear regions occupy a relatively small portion of the total volume, they still pose a potential risk of hemolysis. For regions with extremely high shear stress (>150 Pa), the volume fraction is even smaller, consistently below 0.0073%. Among all models, Model 2 exhibits the highest proportion of regions with SSS greater than 50 Pa, reaching 0.51%, whereas Model 25 shows the lowest proportion at 0.46%. Regarding the extremely high shear stress (>150 Pa), the baseline pump displays the highest volume ratio of 0.0073%, while Model 25 has the lowest at 0.0057%.

To further illustrate the spatial characteristics of shear stress distribution, the baseline pump model (Model 6) was selected for detailed visualization of SSS, as shown in Figure 6. This configuration exhibits extensive regions exceeding the hemolysis threshold of 150 Pa, with localized high-shear zones observed near the leading edges of the impeller blades, the volute tongue, and the secondary flow path area.

In Figure 7, the impact of the radial clearance size in the secondary path on the average SSS, average RT, and HI value of particle paths is compared. The RT heat map indicates that the overall RT values range from 0.32 to 0.42 s. With the increase of L₂, especially when L₁ is small (such as 600 μm), RT tends to increase initially and then decrease. In contrast, when L₁ and L₂ is larger (such as 900–1,000 μm), the distribution of RT becomes more uniform. The maximum RT occurred at L₁ = 800 μm and L₂ = 1,000 μm (0.419 s), while the minimum value occurred at L₁ = 900 μm and L₂ = 600 μm (0.321 s). The SSS heat map shows relatively small variation across the parameter space, with most values falling between 4.5 and 5.0 Pa. The SSS value reaches the maximum (5.018 Pa) at L₁ = 800 μm and L₂ = 800 μm, whereas the minimum (4.518 Pa) at L₁ = 600 μm and L₂ = 800 μm. When L₁ or L₂ is fixed, SSS does not exhibit a clear monotonic trend but instead shows nonlinear fluctuations, indicating that L₁ and L₂ have a complex coupling effect on shear stress. When L₁ = 600 μm and L₂ = 800 μm, the HI is the lowest at 0.00012%. While the highest HI (0.00016%) appears at L₁ = 800 μm and L₂ = 700 μm. Compared with the baseline pump, the HI shows a minimum reduction of 8.76% and a maximum increase of 23.86%. Overall, HI tends to increase slightly with higher SSS; however, the correlation is not strictly consistent. To quantitatively assess the relative contributions of RT and SSS to hemolysis, a linear regression analysis was performed between the predicted HI and each of the two parameters across 25 simulation cases (Figure 8). The results show that HI exhibited a stronger correlation with SSS (R ² = 0.758) than with RT (R ² = 0.667), indicating that shear-induced damage is more predictive of hemolysis than particle RT.

Turbulent viscosity serves as a key indicator for characterizing the intensity of turbulence within the pump. Figure 9 present the streamlines of three representative pump models, with color maps indicating turbulent viscosity and velocity, respectively. Model 23 exhibits substantially higher turbulent viscosity throughout the pump compared to Models 3 and 5, with Model 5 showing moderately higher values than Model 3. These results indicate that compared with the optimal model, increasing either the inner (L₁) or outer (L₂) secondary clearance leads to a notable increase in turbulence intensity, particularly within the secondary flow path regions.

Calculate the RT, SSS, and HI of the blood pump by 25 groups of orthogonal designs. Table 5 presents the mean values of the three indicators calculated using Equation 5 at each level of each factor. k i = 1 N i K i = 1 N i ∑ j = 1 N i y i , j (5)

The range R in Equation 6 is the difference between the maximum and minimum values of a single prediction result. R = max k 1 , k 2 , … , k i − min k 1 , k , … , k i (6)

The R value reflects the impact of each factor on the optimization; a larger R value indicates a greater influence. As shown in Table 5, the influence of L₁ on average SSS, average RT, and average HI is consistently greater than that of L₂. The minimum average SSS values for factors L₁ and L₂ occur at 700 and 800 μm, respectively. For average RT, the minimum values correspond to 700 μm for L₁ and 700 μm or 900 μm for L₂. When HI is taken as the final optimization objective, the optimal design parameter combination is L₁ = 700 μm and L₂ = 800 μm.