Generalized reynolds number for non-newtonian fluids

An extended version of the generalized Reynolds number was derived to characterize the duct flow of non-Newtonian gelled fluids of the Herschel-Bulkley-Extended (HBE) type. This number allows also estimating the transition from laminar to turbulent flow conditions. An experimental investigation was conducted with a capillary rheometer for several non-Newtonian gelled fluids to evaluate the introduced HBE-generalized Reynolds number R_{egen HBE. A good correlation between the experimental results and the theory could be found for laminar flow conditions. For one of the examined gelled fuels, the necessary high Reynolds numbers could be realized so that the transition from the laminar to the turbulent flow regime could be measured. Because of its general description, the HBE-generalized Reynolds number can also be applied to Newtonian liquids as well as to non-Newtonian fluids of the Herschel-Bulkley (HB), Ostwald-de-Waele (power-law, PL), and Bingham type.}