SPH simulations of a viscoelastic flow around a periodic array of cylinders confined in a channel

In this paper a numerical study on the performance of the Smoothed Particle Hydrodynamics method (SPH) in the case of a flow of a viscoelastic liquid around a linear array of cylinders confined in a channel is presented. Numerical convergence in the case of a low Reynolds number Newtonian flow was demonstrated by Ellero et al. in [Int. J. Numer. Methods Eng. 86 (2011) 1027]. Here viscoelastic effects are incorporated in the SPH scheme according to the Oldroyd-B model presented in [Phys. Rev. E 79 (2009) 056707]. Good agreement of the dimensionless drag force acting on the cylinder with literature data is observed for a wide range of Weissenberg numbers We. The case of closely spaced cylinders is also investigated and the impact of We on the solution discussed. It turns out that in this case the Newtonian solution exhibits a stable secondary flow represented by two counter-rotating vortices. When elasticity is considered, above a critical Weissenberg number Wec these vortices become unstable, breaking the plane symmetry and producing a quasi-periodic flow of mass in and out of the gap region between cylinders. Correspondingly, the flow becomes increasingly unsteady and a dramatic increase in the cylinder’s drag is observed. The results are in qualitative agreement with experimental observations made on Boger liquids under similar flow conditions.

► We study the viscoelastic flow of an Oldroyd-B fluid around a periodic array of cylinders using the SPH method.
► We examine the total drag and flow behaviour for different values of elasticity and cylinder separation distances.
► For close cylinders, at large Weissenberg numbers the flow becomes time-dependent.
► For increasing elasticity, the flow become increasingly unsteady and the cylinder drag raises abruptly.