Instability investigation of creeping viscoelastic flow in a curved duct with rectangular cross-section

In this paper, instability in the creeping viscoelastic flow inside a curved rectangular duct is investigated numerically for the first time. Using the Criminale–Eriksen–Filbey (CEF) model as the constitutive equation, the governing equations are solved by a second order of finite difference method based on the artificial compressibility algorithm in a staggered mesh. The effects of normal stress differences on the flow stability are investigated. The numerical results obtained indicate that the increase of the negative second normal stress difference of viscoelastic fluid causes stability in the creeping flow in curved ducts, however, the increase of the first normal stress difference intensifies the instability. Furthermore, at the special value of Ψ₂/Ψ₁=?0.5, the interaction of the two normal stress differences results in a stable flow field.