Viscoelastic Numerical Simulation Of Polymer Fluid Based On Hookean Bead-Spring Chain Model

Traditional numerical simulation starting from the continuum mechanics are derived from differential or integral type constitutive equation to describe the relationship between stress and strain, and then solve the problem with the control equation. The theory of molecular dynamics attempts to reveal the interrelationship between the macro-rheological properties of materials and their molecular structures, analyzes the properties of materials in essence, thus increase people's more and more attention, get a rapid development. Many scholars in domestic and foreign use the molecular dynamics model to study the configuration changes of polymer molecules in the flowing process under certain conditions, put forward a series of computational models, and obtained some useful constitutive models. The general process is:first get the kinematical equations from the molecular dynamics, then solve the kinematical equation, and coupled with the macro governing equation to get the polymer configuration informations, finally average ensemble to acquire the mechanical quantities.According to the theory of rheology of polymer not only can get constitutive equation obtained by many continuum mechaincs, but also analyze the shapes of polymer chains in the flowing process. This paper use the micro-macro coupling numerical method to solve the steady-state Couette flow. At the micro scale, use Hookean bead spring model to describe the movements of molecular and its configuration evolutions, at the macro scale, adopt finite difference method to solve the velocity field and stress field.The simulation results show that the velocity field obtained directly by using the bead spring chain molecule is agreement with the document, before the velocity field transition to the steady state, there is a clear overshoot phenomenon; after reaching the steady state, velocity field remains linear distibution, and the stess values of each point on the cross section are close to a constant numerics, these reflct the Newtonian characterstics of fluid.