Numerical simulation of the viscoelastic flow in a three-dimensional lid-driven cavity using the log-conformation reformulation in OpenFOAM®

Abstract

In this work we implement the log-conformation reformulation for viscoelastic constitutive equations as proposed by Fattal and Kupferman (2004) in the open-source CFD-software OpenFOAM®, which is based on the collocated finite-volume method (FVM). The implementation includes an efficient eigenvalue and eigenvector routine and the algorithm finally is second-order accurate both in time and space, when using it in conjunction with an adequate convection scheme such as the CUBISTA scheme (Alves et al., 2003). The newly developed solver is first validated with the analytical solution for a startup Poiseuille flow of a viscoelastic fluid and subsequently applied to the three-dimensional and transient simulation of a lid-driven cavity flow, in which the viscoelastic fluid is modeled by the Oldroyd-B constitutive equation. The results are presented for both the first-order upwind scheme and the CUBISTA scheme on four hexahedral meshes of different size in order to check for mesh convergence of the results and a tetrahedral mesh to show the applicability to unstructured meshes. The results obtained for various values of the Weissenberg number are presented and discussed with respect to the location of the primary vortex center, streamline patterns and velocity and stress profiles besides others. We are able to obtain sufficiently mesh converged results for Weissenberg numbers, which would have been impossible to obtain without use of the log-conformation reformulation. An upper limit for the Weissenberg number in terms of stability could not be found.