Viscoelastic fluid flow past a submerged spheroidal body

Abstract

A numerical study has been carried out of the problem of homogeneous, axisymmetric flow of second and third order fluids past a spheroidal body. The numerical solution was shown to agree well with existing analytical solutions for several limiting cases (such as flow past a sphere), and was used to investigate the effects of (a) body shape, (b) free stream conditions, and (c) fluid elasticity on the local velocity and stress fields. The results indicate that while a submerged spheroid gives rise to strong and highly localized stress fields, flow past a sphere creates a stress field of moderate strength extending over larger distances. It was also found that the different free stream velocity fields studied, which included uniform flow, simple extensional flow, and converging flow, resulted in different stress fields the strongest of which was produced by the extensional flow. Finally, it was found that the elasticity of the fluid has a profound effect on the local stresses. The computed flow kinematics were used to calculate the expected molecular orientation through the flow birefringence of the macromolecules. In addition, the free energy change due to flow was computed and the relationship between the free energy and stress fields and their possible bearing on flow-induced phase separation of polymers was considered.