# Influence of Impeller Speed Patterns on Hemodynamic Characteristics and Hemolysis of the Blood Pump
## 2 Materials and Methods
### Steady-State Simulation of the Hydrodynamic Characteristics of the Blood Pump  
CFD is an effective method to obtain the hydrodynamic characteristics of blood pumps and the cardiovascular system [17; 18]. Blood is considered as a Newtonian fluid in large vessels where the shear strain is high; in the present study, blood was basically simplified to a Newtonian fluid for modeling, simulation, and experimental research [6; 19]. Therefore, the viscosity of the blood was set at 3.5 cp. The blood density was set at 1055 kg/m\({}^{3}\). The inlet boundary condition of the blood pump was the blood flow rate, and the outlet boundary condition was the outflow. When analyzing the flow field of the centrifugal blood pump, it is often considered that the flow characteristic in the pump is a three-dimensional incompressible viscous turbulent flow field. According to the theory of fluid mechanics and the blood flow state in the pump chamber, the flow field is solved using the continuity equation, momentum equation, and \(k-\varepsilon\) turbulence model. With the conditions of constant density, the continuity equation was reduced to:  
\[\frac{\partial v_{1}}{\partial x_{1}}+\frac{\partial v_{2}}{\partial x_{2}}+ \frac{\partial v_{3}}{\partial x_{3}}=0, \tag{1}\]  
where \(v_{i}\) (\(i\) = 1, 2, 3) is the Cartesian component of the velocity vector. The momentum conservation equation in the \(i\) direction was as follows:  
\[\frac{\partial(\rho v_{i})}{\partial t}+\frac{\partial(\rho v_{i}v_{j})}{ \partial x_{j}}=-\frac{\partial p}{\partial x_{i}}+\frac{\partial\tau_{ij}} {\partial x_{j}}+\rho g_{i}, \tag{2}\]  
where \(v_{j}\) (\(j\) = 1, 2, 3) is the directional coordinates, \(v_{i}\) (\(i\) = 1, 2, 3) is the respective components of the velocity vector in the \(x_{i}\) direction, \(p\) is the static fluid pressure, \(t\) is time, \(\tau_{ij}\) is the stress tensor, \(\rho\) is the fluid density, and \(g_{i}\) is the gravitational force in the \(x_{i}\) direction.  
The relative motion of the impeller relative to the volute in the computational domain was simulated by the multiple reference frame model. The coordinates of the dynamic reference frame were set on the impeller, and the impeller wall was set as the rotating wall. In the simulation model, the interface between the dynamic and static regions was set as the interface for data transmission, as shown in Figure 3, and the rest of the wall was set as a wall without sliding. The near-wall area was processed by the standard wall function method, and the solver adopted the semi-implicit method for pressure-linked equations (SIMPLEEs) algorithm. The residual of the calculation results reached \(10^{-4}\), which confirmed the end of the calculation.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Diversion Zone** & **Impeller Channel** & **Inlet Channel and Volute** & **Outlet Channel** & **Total** \\ \hline
108,000 & 420,600 & 930,500 & 182,900 & 1,642,000 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Number of grid units in each part of the blood pump simulation model.  
Figure 3: Mesh section of the simulation model of the flow field of the blood pump; the mesh with smaller characteristic scale was refined and densified.  
The hemodynamic characteristics of the blood pump under different working conditions were analyzed. The impeller speed ranged from 2800 to 3000 rpm, and the flow rate ranged from 2 to 7 L/min. The steady-flow field of the blood pump was solved and analyzed using the ANSYS Fluent software. The pressure difference between the inlet and the outlet of the blood pump at a specific speed and a flow rate was obtained, and the H-Q curve of the blood pump was drawn.