Improved smoothed particle hydrodynamics simulation of eXtended Pom-Pom viscoelastic fluid

Viscoelastic fluids are widely present in nature and industrial production, and the study of their complex rheological properties has important academic value and application significance. In this paper, an improved smoothed particle hydrodynamics (SPH) method is proposed to numerically simulate the viscoelastic flow based on the eXtended Pom-Pom (XPP) model. In order to improve the accuracy of the calculation, a kernel gradient correction discrete format without kernel derivative calculation is adopted. In order to prevent fluid particles from penetrating the solid wall, an enhanced boundary processing technology is proposed. To eliminate the tensile instability, an artificial stress is coupled into the momentum equation of conservation. Based on the XPP model, the viscoelastic Poiseuille flow and the viscoelastic droplet impacting solid wall problem are simulated by using the improved SPH method. The effectiveness and advantages of the improved SPH method are verified by comparison the SPH solutions with the analytical or finite difference method solutions. The convergence of the improved SPH method is further evaluated by using several different particle sizes. On this basis, the influence of rheological parameters such as Reyonlds number Re, Weissenberg number Wi, solvent viscosity ratio β, anisotropy parameter α, relaxation time ratio γ and molecular chain arm number Q on the flow process is deeply analyzed. For the viscoelastic Poiseuille flow, the higher Re, Wi, and α are, the larger the steady-state velocity is; the larger γ and Q are, the smaller the steady-state velocity is; the larger β is, the weaker the velocity overshoot is, but it does not affect the steady-state velocity. For the viscoelastic droplet problem, the larger Re and Wi are, the faster the droplet spreads; the larger β is, the weaker the droplet shrinkage behavior is, but it does not affect the final spreading width of droplet; the larger α is, the larger the droplet’s spreading width is; the larger γ is, the stronger the droplet shrinkage behavior is; the larger Q is, the weaker its influence on the droplet’s spread width is. The improved SPH method in this paper could effectively describe the complex rheological properties and the free surface variation characteristics of viscoelastic fluid based on XPP model.