This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell(UCM)constitutive equation.A Marker-and-Cell approach is employed to represen...This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell(UCM)constitutive equation.A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed.The complete free surface stress conditions are employed.The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method.The resulting equations are solved by the finite difference method on a 3D-staggered grid.By using an exact solution for fully developed flow inside a pipe,validation and convergence results are provided.Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.展开更多
基金We gratefully acknowledge the support given by the Brazilian funding agencies:FAPESP(grants 04/10988-4,04/16064-9,03/12612-9),CAPES(grants BEX 012070,BEX 1837/06-0)and CNPq(grant 304422/2007-0).
文摘This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell(UCM)constitutive equation.A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed.The complete free surface stress conditions are employed.The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method.The resulting equations are solved by the finite difference method on a 3D-staggered grid.By using an exact solution for fully developed flow inside a pipe,validation and convergence results are provided.Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.
