Numerical simulations of Phan-Thien-Tanner viscoelastic fluid flows based on the SPH method

Numerical simulations of viscoelastic fluid flows are always a hot issue in the field of computational fluid dynamics and the study of their complex rheological properties has important academic and engineering application value. In the present work, we develop a smoothed particle hydrodynamics (SPH) method for simulating transient viscoelastic fluid flows governed by the Phan-Thien-Tanner (PTT) constitutive equation. To improve the computational accuracy of the SPH method, the mixed symmetric correction algorithm of kernel gradient is implemented. To remove the particle clustering and unphysical fracture in fluid stretching which is named as the tensile instability, the artificial stress model is added into the momentum equation. We firstly apply the proposed SPH method to solve the plane Poiseuille flow of a PTT viscoelastic fluid, in which the effectiveness and advantage of the method are verified by comparing the SPH solution with those obtained by the finite volume method (FVM) and analyzing the l2 norm error of different SPH solutions to the FVM solution. Then, the method is employed to simulate the impact behavior of a PTT viscoelastic droplet with a rigid plate. In particular, we not only investigate the spreading behavior of PTT viscoelastic droplet after impacting the rigid plate, but also for the first time capture and analyze the bouncing behavior of droplet by decreasing the Reynolds number. The influences of the Reynolds number, the Weissenberg number, the solvent viscosity ratio, and the PTT elongational parameter on the droplet dynamics behavior are further deeply studied. Numerical results demonstrate that the SPH method proposed in this paper is a powerful computation tool for simulating PTT viscoelastic fluid flows and is capable of effectively describing their complex rheological properties and free surface variation characteristics.