Development lengths for non-newtonian flows in pipes and tubes based on the wall shear stress

Summary

The development length needed for tube flows to re-adjust from a uniform to the fully-developed velocity profile is usually defined as the length required for the centerline velocity to reach 99% of its fully-developed value. This definition, however, may be quite inaccurate in non-Newtonian flows with almost flat velocity distributions near the centerline, since the velocity far from the axis of symmetry develops more slowly. Shear-thinning and viscoplasticity may cause the flow close to the centerline to evolve faster than that closer to the walls. Thus, alternative definitions of the development length have been proposed for viscoplastic flows. Given that blood exhibits shear thinning, we numerically solve the flow development of power-law fluids in pipes and calculate the development length as a function of the radius, determining the global development length along with the standard centerline estimate. We also consider an alternative definition, based on the evolution of the wall shear stress. Results have been obtained for values of the power-law exponent ranging from 0.

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