Numerical simulation in steady flow of Newtonian and shear thickening fluids in pipes with circular cross-section

Process engineering deals with the processing of large quantities of materials and they must be transported from one unit operation to another within the processing environment. This is commonly made through pipelines, where occurs a dissipation of energy due essentially to frictional losses against the inside wall of the pipe and changes in the internal energy. Then it is needed an energy source to keep the fluid moving, commonly a pump. Due to differences in the internal structure, dissipations of energy must be different from Newtonian fluids to shear thickening fluids. Moreover, because of the inherent structure that is exhibited by shear thickening fluids, laminar motion of these fluids is encountered far more commonly than with Newtonian fluids. Rheological experiments confirm that suspensions of Aerosil (R) R816 in Polypropylene glycol (PPG) of low molecular weights (400 and 2000g/mol) exhibit reversible shear thickening behaviour. Cross model fits properly their viscosity curve in the region of shear thickening behaviour. Thus the constitutive equations obtained experimentally have been incorporated into the momentum conservation equation in order to study the reference case of the steady laminar flow in a pipe of circular cross-section, providing us with relevant information including the fully-developed velocity profiles, the friction factor and the entrance length, depending on the rheological properties of each suspension. Our results could be applied to the optimal design and layout of flow networks, which may represent a significant fraction of the total plant cost.