Modeling and simulation of the hole pressure problem

Whenever a polymeric or viscoelastic liquid flows over a depression in a channel, the phenomenon of hole pressure occurs. Modeling and simulation for the flow of an Oldroyd-B type fluid passing over a transverse slot is considered here. This type of fluid is a good model for some polymeric liquids. In the model, it is assumed that the extra stress of the solution is the sum of the contribution from the solvent and the contribution from the polymer molecules. The results obtained in the study are computed by using the elastic-viscous split-stress finite element method incorporating the non-consistent streamline-upwind scheme (EVSS/SU finite element method). As a verification of the numerical scheme, the algorithm is first applied to compute the corresponding flow of the upper-convected Maxwell fluid model, a special case of the Oldroyd-B model. Hole-pressure is evaluated for various Deborah numbers (De), and compared with that derived from the Higashitani-Pritchard (HP) theory. The agreement between the two is found to be satisfactory for creeping flow in the De range for which the Higashitani-Pritchard theory is valid. Subsequently, hole-pressure and characteristics of this flow problem are predicted. Furthermore, the effects of fluid elasticity, inertia, and slot geometry on hole-pressure are investigated.