Numerical Study of Carreau Fluid Flow in Symmetrically Branched Tubes

Abstract

The non-Newtonian Carreau fluid model is a suitable model for pseudoplastic fluids and can be used to characterize fluids not so different from biological fluids, such as the blood, and fluids involved in geological processes, such as lava and magma. These fluids are frequently conveyed by complex flow structures, which consist of a network of channels that allow the fluid to flow from one place (source or sink) to a variety of locations or vice versa. These flow networks are not randomly arranged but show self-similarity at different spatial scales. Our work focuses on the design of self-similar branched flow networks that look the same on any scale. The flow is incompressible and stationary with a viscosity following the Carreau model, which is important for the study of complex flow systems. The flow division ratios, the flow resistances at different scales, and the geometric size ratios for maximum flow access are studied, based on Computational Fluid Dynamics (CFD). A special emphasis is placed on investigating the possible incidence of flow asymmetry in these symmetric networks. Our results show that asymmetries may occur for both Newtonian and non-Newtonian fluids and shear-thinning fluids most affect performance results. The lowest flow resistance occurs when the diameters of the parent and daughter ducts are equal, and the more uniform distribution of flow resistance occurs for a ratio between the diameters of the parent and daughter ducts equal to 0.75. Resistances for non-Newtonian fluids are 4.8 to 5.6 times greater than for Newtonian fluids at Reynolds numbers of 100 and 250, respectively. For the design of engineering systems and the assessment of biological systems, it is recommended that the findings presented are taken into account.