Numerical simulation of shear-thinning flow problems in mixing vessels

In many applications of chemical and process engineering numerous important flow situations appear, in which the shear-thinning properties of the fluid dominate the normal stress effects and time-dependent elastic effects. A mixed finite element method for steady incompressible flow is presented taking as a basis the model of a generalized Newtonian fluid. An augmented Lagrangian functional is constructed corresponding to the equations of motion and the continuity constraint together with appropriate boundary conditions. The treatment of the resulting nonlinear system of equations by the Newton-Raphson scheme is made for general models of the viscosity function. The linear subproblems are solved by Uzawa's algorithm. The method is applied to the numerical simulation of various mixing problems in cylindrical unbaffled vessels. The computations were performed for a real polymer liquid (CMC in water), where the viscosity data were found experimentally and were fitted to a suitable mathematical model. Several numerical results are discussed and as far as possible compared with experimental data.