Development of SPH for simulation of non-isothermal viscoelastic free surface flows with application to injection molding

Abstract

In the present work, we focus on developing the smoothed particle hydrodynamics (SPH) method for simulation of non-isothermal viscoelastic free surface flows with application to the injection molding process. Specifically, the viscoelastic fluid is governed by the eXtended Pom-Pom (XPP) constitutive equation. The temperature-dependent viscosity and relaxation time are modeled using the Arrhenius relation. The governing equations are discretized by an improved SPH scheme, as presented by Xu and Yu, Appl. Math. Model. 73 (2019) pp. 715–731. We first verify the validity of the SPH method by solving the isothermal/non-isothermal Poiseuille flow of an XPP fluid and comparing the SPH solutions with the analytical solutions or finite volume method solutions. Then, we extend the method to 2D non-isothermal viscoelastic injection molding process of a C-shaped cavity. Some relevant physical information such as temperature, pressure, velocity, flow-induced stresses during the molding process are displayed. The convergence of the method is examined with several different particle sizes. The effects of the Péclet number, Reynolds number, Weissenberg number, viscous ratio, and XPP parameters, on the evolutions of the temperature and flow-induced stresses are analyzed in details. Results for 3D non-isothermal viscoelastic injection molding process of a door handle are lastly presented.