Adjoint-based sensitivity analysis of viscoelastic fluids at a low deborah number

Abstract

This work performs an adjoint-based sensitivity analysis of a viscoelastic fluid flow around a cylinder in a confined channel. The viscoelastic behavior of the fluid is modeled by the Oldroyd-B constitutive equation and the quantity of interest of the flow is set to the resistance of the cylinder. A set of continuous adjoint governing equations is formulated to quantify the local sensitivities of rheological model parameters on the drag of the cylinder. The adjoint equations are solved together with the original resistance prediction problem, at the Deborah number 0.5. Final outcomes are the field resistance-sensitivity maps for the Oldroyd-B model parameters that imply the local relative importance of different underlying physical mechanisms reflected in the model parameters. In particular, the sensitivity map of relaxation parameter distinguishes two opposing effects of fluid elasticity to resistance of the cylinder depending on the location. While the fluid elasticity near the top and bottom surfaces reduces the resistance, it works adversely near the front and back surfaces. The example illustrates how adjoint-based sensitivity analysis can be utilized for developing effective flow control strategies in many applications working with viscoelastic fluids.