Abstract
A new Lagrangian–Eulerian method for the simulation of viscoelastic free surface flow is proposed. The approach is developed from a method in which the constitutive equation for viscoelastic stress is solved at Lagrangian nodes, which are convected by the flow, and interpolated to the Eulerian grid with radial basis functions. In the new method, a backwards-tracking methodology is employed, allowing for fixed locations for the Lagrangian nodes to be chosen a priori. The proposed method is also extended to the simulation of viscoelastic free surface flow with the volume of fluid method. No unstructured interpolation or node redistribution is required with the new approach. Furthermore, the total amount of Lagrangian nodes is significantly reduced when compared to the original Lagrangian–Eulerian method. Consequently, the method is more computationally efficient and robust. No additional stabilization technique, such as both-sides diffusion or reformulation of the constitutive equation, is necessary. A validation is performed with the analytic solution for transient and steady planar Poiseuille flow, with excellent results. Furthermore, the proposed method agrees well with numerical data from the literature for the viscoelastic die swell flow of an Oldroyd-B model. The capabilities to simulate viscoelastic free surface flow are also demonstrated through the simulation of a jet buckling case.
Highlights
Viscoelastic free surface flows are of significant importance for many industrial processes
Oldroyd-B model, which has the constitutive equation λ τ + τ = 2ηS, (22)
The method was developed from a previously proposed method, in which the fluid momentum and continuity equations were solved on a stationary Eulerian octree grid, while the viscoelastic constitutive equation was solved along the trajectories of Lagrangian nodes which were convected by the flow
Summary
Viscoelastic free surface flows are of significant importance for many industrial processes. This includes polymer extrusion, additive manufacturing, seam sealing, and adhesive joining. In such processes, the viscoelastic properties of the flow, such as the flow history, can have major influence on the quality of the final product. Production time and raw materials may be subject to a large cost. Extensive manual effort and physical testing may be necessary to optimize the process in terms of product quality, material consumption, and production cycle time. Numerical tools can be helpful in reducing the manual preparation time, as they offer the possibility to replace a significant part of the physical testing with computer simulation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
