# PUB - A Numerical Approach for the Evaluation of a Capillary Viscometer Experiment

A paper on “A Numerical Approach for the Evaluation of a Capillary Viscometer Experiment” was published at the ASME Symposium on Fluid Power and Motion Control in Bath.

The dynamic viscosity of a fluid is an important input parameter for the investigation of elastohydrodynamic contacts within tribological simulation tools. In this paper, a capillary viscometer is used to analyse the viscosity of a calibration fluid for diesel injection pumps. Capillary viscometers are often used for the determination of viscosities that show a significant dependence on shear rate, pressure and temperature such as polymer melts or blood. Therefore most of the research on corrections of measured viscosities have been made using polymer melts. A new method is presented to shorten the effort in evaluating the capillary experiment.

The viscosity itself can be calculated from experimental data. Essential parameters are the radius of the capillary, its length, the capillary flow and the pressure difference over the capillary. These quantities are used in the Hagen-Poiseuille equation to calculate the viscosity, assuming laminar and monodirectional flow.

According to said equation, the viscosity depends on the geometry and the pressure gradient. A typical capillary viscometer contains three main flow irregularities. First the contraction of the flow at the capillary inlet, second the expansion of the flow at the capillary outlet and third the inlet section length of the flow after which the velocity profile is fully developed.

These flow phenomena cause pressure losses, which have to be taken into account, as well as the altered length of the laminar flow in the capillary. Furthermore, the temperature difference over the capillary also affects the outlet flow.

Therefore, in this paper, a newly developed method is proposed, which shortens the effort in pressure and length correction. The method is valid for viscometers, which provide a single phase flow of the sampling fluid. Furthermore, the proposed correction is suited for arbitrary geometries.

A numerical approach is chosen for the analysis of the experiment. In order to facilitate the experimental procedure of a capillary viscometer, a special algorithm was developed. The numerical approach uses a static CFD simulation, which is recursively passed through. If a termination condition, regarding the pressure difference between two cycles, is fulfilled, the real viscosity can be calculated in the usual way from the Hagen-Poiseuille equation. A special advantage of the proposed experimental evaluation is the general applicability for arbitrary geometries. In this paper, the procedure is validated with a well-known reference fluid and compared to data, which was gathered from a quartz viscometer experiment with the same fluid. Therefore, experiments are conducted with the capillary viscometer and compared at various pressure and temperature levels.