# Bladeless Heart Pump Design: Modeling and Numerical Analysis
## 3 Numerical Analysis of Bladeless Heart Pump  
Hemodynamic analysis of the heart pump flow is performed using computational fluid dynamics (CFD) available in the ANSYS Fluent 15.0 software (Ansys, Canonsburg, PA, USA). The geometry of the computational domain of the basic design is shown in Figure 1 where the inside radius is \(R_{1}=12\) mm and the outside radius is \(R_{2}=15\) mm. Due to the geometrical symmetry of the heart pump design, the computational domain is defined as one slice of flow in between two rotating disks, with a height of \(h=1\) mm. The final geometry of a computational domain with boundary conditions and mesh is depicted in Figure 2. The outer vertical circular boundary between the two disks and the housing is modeled with the boundary condition of no-slip stationary wall. Vertical surfaces of the inflow and outflow pipes are also modeled as no-slip stationary wall. The boundary between the separator and the fluid is modeled as an impermeable boundary (stationary wall) due to the assumption of an ideal sealing of the flow separator. The boundary condition on the inlet is constant velocity inlet calculated from the pump flow, while the outlet is defined as the outflow. Flat disks are defined as a no-slip moving wall with defined revolutions per minute. The position of the coordinate system in numerical analysis is the same as in the theoretical analysis. Before numerical simulations, a grid independence study was conducted over four grid resolutions to ensure that the simulation results were grid independent. The grid of \(1.1\times 10^{5}\) cell elements and the grid of \(4\times 10^{5}\) cell elements did not have a significant difference in the numerical results (2.21%). Therefore, the accepted mesh consists of \(1.1\times 10^{5}\) cell elements. To ensure quality spatial discretization, the height of the domain is discretized with 20 control volumes. A finer mesh is applied on boundary layers, in regions of geometric detail and connections between the flow separator and inflow and outflow pipes. The orthogonal quality ranges from 0-1, where values close to 0 correspond to a low-quality mesh. The minimum orthogonal quality in all cases is 0.62, depicting the good quality of mesh. Turbulence was modeled using the well-established k-epsilon model [19]. Furthermore, the k-omega SST model was used in several cases for crosscheck [26]. The incompressible Newtonian approximation for blood was employed with a fluid density of \(1050\,\mathrm{kg/m^{3}}\) and a viscosity of \(0.0035\,\mathrm{kg/(m\cdot s)}\)[19]. Figure 2: Final geometry of computational domain with boundary conditions and mesh. The improvements on the pump construction are made through several iterative solutions, as shown in Figure 3. The geometry iterations included different outflow and in-flow positions and geometries of the flow separator, while radii and distance between disk are kept the same. The CFD analysis of the basic design is depicted in Figure 3a. Two recirculation zones appear in the basic design. The smaller one is in the inflow pipe and the larger one in the outflow pipe. Recirculation zones are extremely unfavorable because the blood stays in the pump for a long time and the probability of thrombus formation increases significantly. The main goal is to avoid all recirculation and stagnation zones with geometric improvements of the pump geometry regarding the inlet and outlet position. The first improvement of basic design (Figure 3b) is to eliminate the recirculation zones. Based on the streamlines shown in Figure 3a, the connection of the inlet/outlet pipe to disk is modeled by circular arcs in a way that the flow is gradually directed in a circular direction. Additionally, the distance between the inlet and outlet pipes is reduced. When the outlet pipe connection is curved, as shown in Figure 3b, the flow separates in the outlet pipe and a recirculation zone appears [33]. Therefore, attention was paid to the connection of the outlet and inlet pipe to the disk to avoid recirculation zones.