Evaluation of shear rate formulations through steady uniform non-Newtonian fluid flows in the context of shallow-water equations

ABSTRACT Non-Newtonian rheology effects, such as pseudoplasticity and viscoplasticity, are understood shear stresses, incorporated to the energy slope term in Shallow-Water Equations (SWE). However, non-Newtonian stresses dependent of rate, whose formulation is a function gradient velocity profile bottom. This study investigated two rate formulations that commonly applied SWE literature: 1) non-parameterized function; 2) based on Herschel-Bulkley rheological model. Their influence steady uniform flows fluids was evaluated through numerical-theoretical comparisons. A Lax-Friedrichs scheme implemented solve system allowed employing formulations. Experimental tests were carried out numerical simulations hypothetical scenarios performed. It found presented deviation normal depth up 14% comparison with theoretical solution, while model provided good agreement, corroborated by punctual Computational Fluid Dynamics (deviation less than 2%) experimental data. The ratio both strongly correlated depth, indicating does not provide an acceptable result flow.