Spectral Calculations of Viscoelastic Flows: Evaluation of the Giesekus Constitutive Equation in Model Flow Problems

Spectral solutions of viscoelastic flow equations offer significant advantages emanating from their high, exponentially fast converging with mesh refinement, accuracy of the solutions. The analysis of the behavior of the Giesekus model is presented in a) the undulating channel steady-state flow and b) the evolution of Taylor-Couette flow instabilities. By comparison to the results corresponding to an inelastic shear thinning analog, it is shown that the presence of elasticity, while it introduces a minor change in the flow resistance for the flow within an undulating channel, significantly affects the stability of the Couette flow. In aedition, no purely elastic (inertialess) instability is obtained in the Couette flow, in contrast to the Oldroyd-B fluid calculations. Thus, the stabilizing effect of the negative second normal stress, present in the Giesekus model, is verified.

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