Reddit mentions of Mechanical Circulatory Support: Principles and Applications

First of all, regarding the "bladeless" fan, the vanes of the impeller are practically the same thing. Inside the base of each unit is an impeller. The trick is that it takes advantage of the Bernoulli principle to entrain a greater volume of air, and reduces the amount of loss due to turbulent flow by allowing the expelled gas to build a slight compression within the ring shape prior to exiting. This leads to stagnant pockets, which would be disastrous for a patient.

Secondly, you really don't have to fear the blades. The field of mechanical circulatory support is lead by products that use impellers. The trend over this past decade is to magnetically levitate the impeller in order to allow blood to flow around it on all sides. That said, some designs you may find interesting would be those of diaphragm pumps, peristaltic pumps (as mentioned by /u/chillywillylove), multiple disk centrifugal pumps, and the wild and crazy [read:developing] world of 'capillary action' pumps.

Lastly, I wish you the best of luck.

Some things to brush up on:

• Reynold's number for blood
  
• Relation to flow behavior
  
• The latest, fairly comprehensive publication on the topic
  
• The bible of centrifugal pump design