A Computer Model of Hole-Pressure Measurement in Poiseuille Flow of Visco-Elastic Liquids.

摘要

Liquid-filled holes used for pressure measurements of visco-elastic liquids give rise to systematic hole pressure 'errors'. Tanner and Pipkin have presented analysis for flows of a second order fluid in which they derive a simple relation between the first normal stress difference and the hole pressure for flow situations where Reynolds numbers are very small. Implicit in the analysis is the assumption that the streamlines are symmetric about the hole center line. In this paper, using a numerical solution, we investigate the relationship between the hole pressure and the first normal stress difference for a range of Reynolds numbers where inertial effects are not negligible. The ratio of hole pressure/first normal stress difference is found to vary from 0.25 to 0.16 as the Reynolds number is varied from 1 to 10. Streamline patterns are presented for Poiseuille flow of a second order fluid over a slot cut into one wall of an otherwise straight channel. Various geometries are considered. The results naturally include those for an incompressible Newtonian liquid at non-zero Reynolds numbers. (Author)