Numerical Calculation of Hole-Pressure Error for Viscoelastic Fluids

Abstract

Hole pressure error, Pe; , in the creeping flow of viscoelastic fluids between two parallel plates was calculated numerically by means of Marker and Cell (MAC) method which is easy to develop into the calculations of a three-dimensional flow. The constitutive model used is the Rivin-Ericksen second- order fluid model with variable coefficients.First, calculations in a two-dimensional flow were carried out in order to clarify the effects of geometric dimensions and shear-thinning viscosity on Pe; . Pe; was found to depend on the geometry, i.e., the width and the depth of the slot and the channel height, and the shear-thinning viscosity. Next, calculation of a three-dimensional flow across a square hole was attempted in order to estimate the effect of the second normal stress difference. It was found that the value of Pe; increases monotonically with increasing -N2; /N1;, where N1; and N2; are the first and second normal stress differences.