Application of full flow field reconstruction to a viscoelastic liquid in a 2D cross-slot channel

Abstract

High quality flow kinematics reconstruction from noisy and spatially scattered data requires the use of a regularization technique. Enforcing incompressibility, we employ the recently proposed Tikhonov regularization method combined with a high-order finite element approximation in its stream function formulation. The method is applied to experimental particle tracking velocimetry data, obtained for an incompressible polymer melt in a cross-slot channel. To overcome a potential regularization bias, where the velocity changes rapidly over small distances, regularization is performed on the departure of the velocity field from its Newtonian counterpart. It is compared with a more trivial approach, in which the data are smoothed locally and the velocity gradient fields computed using finite differences. The reconstructions are evaluated in terms of the quality of the streamlines and the velocity gradient histories. Regularization leads to significant noise reduction and to an improved utility of existing data for subsequent applications as we demonstrate by analyzing the principal stress-difference obtained by applying a constitutive equation to the reconstructed flow fields.