This work aims to study, by computational simulations, the Non-Newtonian flows in bioreactors. This analysis is of great interest because of the complex rheology of these fluids. In our case the power law for kinematic viscosity is considered. The shear rate tensor components are computed by an iterative relaxation technique, which shows good computational efficiency. A spectral analysis is carried out, in order to study the energy dissipation of the system. In particular a comparison between Newtonian and Non-Newtonian flows is performed for different Reynolds numbers and power law exponents.