1D simulations of second-grade fluids with shear-dependent viscosity

Abstract

The full 3D system of equations for the motion of a non-Newtonian incompressible second-grade fluid in an uniform rectilinear pipe is generalized by introducing a shear-dependent viscosity function of power law type. The system is then simplified using a 1D hierarchical model based on the director theory approach to fluid dynamics. An axisymmetric unsteady relationship between mean pressure gradient (wall shear stress, respectively) and volume flow rate over a finite section of the pipe is derived from this theory. Attention is focused on some numerical simulations of unsteady flows in pipes with rigid and impermeable walls and on the analysis od perturbed flows.