Quasi-Three-Dimensional Simulation of Viscoelastic Flow through a Straight Channel with a Square Cross Section

Abstract

When a viscoelastic fluid flows in a straight channel with a noncircular cross section, a secondary flow is developed. We discussed the effect of flow characteristics on the secondary flow of the viscoelastic fluid through a straight channel with a square cross section by the viscoelastic flow simulation using the finite element method. The Phan-Thien Tanner (PTT) model was employed as the constitutive equation. The second normal stress difference N₂ contributes to the secondary flow motion of a viscoelastic fluid through a straight channel with a square cross section. The degree of the secondary flow expressed by the maximum streamline function |ψ_max| depends on the recoverable shear for the second normal stress difference −N₂/2σ , where σ is shear stress. According to the distribution of N₂ on the cross section, the flow direction of the secondary flow depends on the pressure drop generated by N₂. The elongational flow characteristics also contribute to the secondary flow state. On the whole, the degree of the secondary flow increases with the strain-hardening. However, the contribution of elongational flow characteristics to the secondary flow is smaller than that of −N₂/2σ.