Unsteady shear flow of nonlinear viscoelastic fluids with finite elements (Q1821637)

Using a single integral constitutive equation, a method is presented for the numerical calculation of unsteady shear flows of elastic shear- thinning fluids through circular pipes. The equation of motion for this flow problem together with the constitutive equation leads to a partial integro-differential equation, which has to be solved under given initial and boundary conditions. For the numerical treatment of the initial-boundary value problem we use finite elements in position and the Euler-backward-difference method for the time integration. Although we apply this implicit method, there is only a system of linear equations to be solved in every time step. The numerical method is used for the quantitative prediction of the flow enhancement due to longitudinal oscillations of the pipe wall. The theoretical results agree well with experimental findings. Predictions for a hypothetical inelastic fluid lead to mean flow rates up to 35\% below the experimental data. Thus, not only the shear-thinning, but also the elasticity of the fluid contributes significantly to the flow enhancement.