# Bladeless Heart Pump Design: Modeling and Numerical Analysis
## 5 Conclusions  
In this paper, a bladeless heart pump design is proposed. Both theoretical and numerical analysis is used to determine the bladeless heart pump design parameters. The pump design parameters are calculated using the Navier-Stokes equations. For the pump operating point of \(\Delta p=65\) mmHg, \(Q=5.43\) L/min, and \(\omega=6000\) rpm, the design parameters are inner radius \(R_{1}=12\) mm, outer radius \(R_{2}=15\) mm, a distance between disk of \(h=1\) mm, and the number of disks is \(n=6\). The power required to rotate the disks is \(P=1.324\) W.  
The application of computational fluid dynamics is used to define the final geometric design. The evolution of the bladeless heart pump has been continued via improvement of the geometrical aspects to eliminate the recirculation of the blood flow in the inflow and outflow pipes. The turbulence flow regime is modeled with the k-epsilon and k-omega SST turbulence model. The finite volume method has been utilized. The incompressible Newtonian approximation for blood was employed with a fluid density of \(1050\) kg/m\({}^{3}\) and a viscosity of \(0.0035\) kg/(m\(\cdot\)s). It has been shown that the pump does not have recirculation and stagnation zones, which is important from the viewpoint of hemocompatibility.  
Wall shear stress, scalar shear stress, and residence (exposure) time are calculated and used to predict pump hemocompatibility. Stagnation and recirculation zones are monitored accordingly. The shear stress in the rotor is in the range 46-108 Pa and the pump residence time is 0.0194 s. The acceptable amount of wall shear stress is achieved in more than 95% of the pump volume. The exposure residence time in the area with higher values of the wall shear stress is \(5\times 10^{-4}\) s. According to Hellums shear stress-exposure time, the acceptable value of shear stress is 700 Pa for exposure residence time of \(5\times 10^{-4}\) s. The calculated maximum shear stress is 308 Pa, and it is smaller than Hellums. The scalar shear stress SSS in the rotor is within the range between 4.8 \(\times\) 10\({}^{-5}\) and 667.85 Pa. The high SSS (>100 Pa) is in the 10% of the volume, mid SSS (10-100 Pa) is in the 10% of the volume, and the low SSS (0-10 Pa) is in the remaining 80% of the volume between disks.  
Moreover, the \(\Delta p\)-\(Q\) characteristic curve of the bladeless heart pump design is presented. The operating pump conditions can be changed by varying the rotation speed or by adding one or more disks. Due to the positive properties enumerated, the idea of a bladeless pump deserves further development, both numerically and experimentally.  
Conceptualization, V.M. and M.S.; methodology, S.K. and M.S.; software, V.M. and S.K.; validation, V.M., M.S. and B.B.; formal analysis, V.M. and M.S.; investigation, V.M. and M.S.; resources, S.K. and B.B.; data curation, V.M.; writing--original draft preparation, V.M. and M.S.; writing--review and editing, S.K. and B.B.; visualization, V.M.; supervision, M.S. and B.B. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The research is supported by Competitive Funds of Faculty of Mechanical Engineering and Naval Architecture. This study was financially supported by the University of Zagreb.  
The authors declare no conflict of interest.