A detailed Computational Fluid Dynamics (CFD) study of transient, turbulent blood flow through a positive displacement left ventricular assist device (LVAD) is performed. Two common models for Non-Newtonian blood flow are compared to the Newtonian model to investigate their impact on predicted levels of shear rate and wall shear stress. Given that both parameters are directly relevant to the evaluation of risk from thrombus and haemolysis, there is a need to assess the sensitivity to modelling non-Newtonian flow effects within a pulsatile turbulent flow, in order to identify levels of uncertainly in CFD. To capture the effects of turbulence, the Elliptic Blending Reynolds Stress Model (EB-RSM) is used in the present study, on account of superior performance of second moment closure schemes previously identified by the present authors. The CFD configuration includes two cyclically rotating valves and a moving pusher plate to periodically vary the chamber volume. An overset mesh algorithm is used for each instance of mesh motion, and a zero gap technique was employed to ensure full valve closure. The LVAD was operated at a pumping rate of 86 BPM (beats per minute) and a systolic duration of 40 percent of the pumping cycle, in line with existing experimental data to which comparisons are made. The sensitivity of the variable viscosity models is investigated in terms of mean flow field, levels of turbulence and global shear rate, and a non-dimensional index is used to directly evaluate the impact of non-Newtonian effects. The clinical relevance of the results are reported along with a discussion of modelling uncertainties, observing that the turbulent kinetic energy is generally predicted to be higher in non-Newtonian flow than that observed in Newtonian flow.