A three dimensional model of a vane rheometer

Vane type geometries are often used in rheometers to avoid slippage between the sample and the fixtures. While yield stress and other rheological properties can be obtained with this geometry, a complete analysis of this complex flow field is lacking in the literature. In this work, a finite element method is used to calculate the isothermal flow parameters in a vane geometry. The method solves the mass and momentum continuity equations to obtain velocity, pressure and then stress fields. Using the total stress numerical data, we calculated the torque applied on solid surfaces. The validity of the computational model was established by comparing the results to experimental results of shaft torque at different angular velocities. The conditions where inertial terms become important and the linear relationship between torque and stress are quantified with dimensionless groups. The accuracy of a two dimensional analysis is compared to the three dimensional results.