Abstract
A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential upper-convected Maxwell (UCM) fluid through a contraction channel has been chosen as a prototype example. The conservation and constitutive equations are solved using the finite volume method (FVM) in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number (We), further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweep efficiency.
Highlights
This is because under the flowing conditions of reservoir (That is, Reynolds number is smaller), the viscoelastic of fluid plays a important role in fluid flow, the stronger the viscoelastic (That is, Weissenberg number (We) is larger), the stronger the viscoelastic vortex is
The present simulations reinforce the point that the finite volume method (FVM) can be used as a viable alternative for the solution of viscoelastic problems
The present study has been applied to a upper-convected Maxwell (UCM) fluid in a relatively simple geometry, it can be further extended to other more realistic constitutive equations, such as the Phan-Thien-Tanner or Giesekus-Leonov models, etc. and to other geometries encountered in polymer processing
Summary
Numerical simulation of viscoelastic flows has been a powerful tool for understanding the fluid behavior in a variety of processes of both industrial. Polymeric fluids, owing to their viscoelastic characters, are of particular interest in the numerical simulation because of their wide applications in material processing and their different behavior from that of Newtonian fluids in ways which are often complex and striking. Experimental results [2,5,6] indicated the viscoelasticity of polymer solutions can enhance the displacement efficiency, but there have been few theoretical studies on this subject. The presented method succeeds in providing accurate numerical solutions, and elasticity levels up to We = 3.0. The simulation results are presented and conclusions are drawn regarding the use of the FVM for viscoelastic flow simulations
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