A method for implementing time-integral constitutive equations in commercial CFD packages

A method is described for obtaining viscoelastic flow solutions, based upon time-integral constitutive equations, using a general purpose CFD package. The method is general enough to be applied to any available software that has rudimentary input and output facilities and can solve a Stoke's flow pr oblem. From this basis, flexibility of choice of constitutive equation and computational techniques is available. The method is presented in a form ap propriate for solving both planar and axisymmetric flows. Delaunay triangul ation is used to reconstruct a mesh for external code, and stress computati on procedures are performed on this mesh. The method has only two particula r requirements for the CFD package used - it must be able to output nodal v alues (of position and velocity) to file and it must be able to read body-f orces from a file. Two methods of velocity adjustment were compared: an inc remental method and a method whereby the viscoelastic stresses were incorpo rated directly as body-forces. Results and convergence from the two methods were found to be essentially identical, hence the direct body-force method (which is considerably easier to implement) is described in detail. The me thod is applied to a well-known flow problem of LDPE melt through a 4 : 1 a brupt contraction axisymmetric die. Convergence was obtained up to nearly t he highest value of apparent shear rate for which published simulation resu lts are available. Quantitative results for vortex strength, vortex opening angle and Couette correction are presented which are compared with earlier work on the problem using other methods. Agreement is generally good, givi ng confidence in the method. Simulations of planar flows of the same melt a re performed: a decreasing corner vortex was observed. This phenomenon has been observed experimentally for flows of other substances, but is not expe cted for flows of LDPE melt. A parametric study of a critical strain harden ing parameter is conducted to help explain the cause of the results. (C) 19 99 Elsevier Science B.V. All rights reserved.