# Bladeless Heart Pump Design: Modeling and Numerical Analysis
## 3 Numerical Analysis of Bladeless Heart Pump
The tangential connection to the disk segment is changed to a connection, as shown in Figure 3c. This improvement resulted in the elimination of recirculation zones for the nominal flow. Further CFD analysis showed that with a reduced flow the recirculation zone appears at the connection point. Hence, the connection point of the outlet and inlet pipe is repositioned as shown in Figure 3d. Additionally, the distance between the connection pipes is further reduced. The geometric configuration, shown in Figure 3d, achieved a smooth flow in a wide flow range. At extremely reduced flows, a recirculation zone appears in the outlet pipe. Further improvement is obtained by reducing the connection cross section in a way that a smooth transition is achieved. The inlet and outlet pipes are longer and with reduced cross sections, accordingly. This results in a construction of a bladeless centrifugal heart pump that has no stagnation and recirculation zones. In Figure 3a, cross section A-A depicts the fluid separator, shown in Figure 4.  
Figure 3: Cont. Figure 3: The geometric design iterations with streamlines: (**a**) basic design; (**b**) first improvement of the basic design, (**c**) second improvement of the basic design, and (**d**) third improvement of the basic design. The cross section of the flow separator is shown in Figure 4. The flow separator directs the blood flow from the rotational motion between the two disks in the outlet channel. Its main function is to prevent flow recirculation between the disks. In this paper, an ideal separator with no fluid leakage between the separator and the disks is mathematically modeled. The authors of [26] numerically studied the connection between increased hemolysis and shear stresses. Experimental results confirmed that hemolysis increases linearly with exposure time and exponentially with respect to shear stress [26; 27]. CFD simulation investigations indicate exposure times are increased because of stagnation and recirculation zones [28]. The wall shear stress is a parameter that can be used to predict thrombus formation. Thromus formation occurs when wall shear stress is less than 1 Pa [29; 30]. Hemolysis and thrombosis are both linked to shear stress induced trauma to erythrocytes, platelets, and the von Willebrand factor. Hence, when applying CFD simulations, shear stress is the main parameter that is used to predict pump hemocompatibility [34]. Stagnation and recirculation zones are monitored accordingly. Wall shear stress and the shear stresses the cells experienced in the bulk flow are not the same things. While fluid shear stresses near the wall will be the largest, the volume of blood not in contact with the wall should not be neglected. The fluid shear stress for computational domain is expressed as scalar shear stress (SSS), that is calculated from the shear stress components \(\sigma_{ij}\) using the following Equation (23) [35]:  
\[\sigma=\left[\frac{1}{6}\sum(\sigma_{ii}-\sigma_{jj})\left(\sigma_{ii}-\sigma _{jj}\right)+\sum(\sigma_{ij}\sigma_{ij})\right]^{1/2} \tag{23}\]  
The Equation (23) is implemented in ANSYS Fluent with a custom field function. The SSS for the entire volume of the pump was calculated. The residence time is defined with Equation (24) [35]:  
\[t=\frac{V}{Q} \tag{24}\]  
where \(Q\) is the flow rate through the pump and \(V\) is volume of the pump or the rotor, etc.