A coupled boundary/finite-element approach for the three-dimensional simulation of air venting in blow molding and thermoforming

We examine the three-dimensional potential ßow of a ßuid (air) inside a cavity as it is induced by the advancement of an isotropic homogeneous membrane (parison) of general shape. This problem is of direct relevance to the processes of blow molding and thermoforming whereby air is evacuated through a number of vents of various sizes that are optimally positioned on the surface of the mold. The membrane material is assumed to obey the MooneyÐRivlin constitutive model, and the resulting deformation Þeld is obtained using a Galerkin based Þnite-element method. The ßow Þeld in the domain bounded by the inßating membrane and the cavity (mold) is obtained using the boundary-element method. The accuracies of the original Þnite- and boundary-element codes are assessed separately against existing numerical results and analytical solution. The coupled Þnite/boundary element formulation is used to examine the air ßow inside a rectangular mold with an insert and through a number of vents of various sizes at each pressure step of inßation. The accuracy of the coupled method is assessed on the basis of conservation of mass of air ßow