Effect of stress diffusion on the Oldroyd-B fluid flow past a confined cylinder

Abstract

For the Oldroyd-B fluid flow past a cylinder, it has been well known that converged solutions for the stress in the wake downstream of the cylinder cannot be obtained when the Weissenberg number exceeds 0.7. This has been an unresolved problem [M.A. Alves, P.J. Oliveira and F.T. Pinho, Annu. Rev. Fluid Mech., 53:509-41, 2021]. This problem has various origins, such as the validity of numerical methods and the constitutive equation. This study examines the relationship between the convergence with respect to mesh refinement and the thermodynamically modified Oldroyd-B fluid, which has a diffusion term. We show that stress diffusion is thermodynamically natural and contributes to the convergence of the numerical solution for the Oldroyd-B fluid flow past a cylinder. Stress diffusion has typically been neglected because of its small value, although it is inherent to real polymers. The diffusion term does not change the flow behavior significantly but facilitates the determination of a mesh converged stress solution for the Weissenberg number up to 0.8. This result cannot be obtained from the original Oldroyd-B model. It is thus revealed that the diffusion term can effectively stabilize the stress in the region of steep stress gradients.