THERMAL AND INERTIAL CORRECTIONS FOR THE HOLE PRESSURE PROBLEM

Abstract

The hole pressure problem is an area of active research in non-Newtonian fluid mechanics. the objective being to relate hole pressure measurements to a property of polymeric liquids known as the first normal stress difference. The present work focuses on the Higashitani-Pritchard theory (HP theory). which is successfully extended to include nonisothermal and inertial effects. The nonisothermal hole pressure problem is studied computationally for the first time, and the computational results verify the theoretical predictions to within 3% over a wide range of conditions; this indicates that the HP theory is highly successful in predicting the nonisothermal effect. Inertial effects are included rigorously in the HP theory, also for the first time. The extended HP theory proposed in this work provides conclusive evidence as to the reasons for the failure of the Newtonian hole pressure as a correction factor at higher Reynolds numbers. Hence a computational investigation of the inertial effects is a worthwhile problem for future study.