Non-Newtonian Fluid Apparent Viscosity Correlation Between Experimental Data and Computational Fluid Dynamics Results, A Case Study From Automatic Transmission Fluid Filtration Industry

Abstract

Abstract Evidence of a Non-Newtonian behavior of automatic transmission fluid at sub-zero conditions was presented by several authors such as Khalil et. al. Accurate viscosity data of this fluid at cold conditions are critical, especially in the very competitive automotive industry. The proper design of a transmission fluid filter, this is, the calculation of the effective area of filtration media, depends heavily on this information. Technical difficulties of viscosity measurements by different shear rates at subzero conditions are driven by its cost and accuracy. In order to solve this issue, here is presented an alternative indirect viscosity measurement. By assuming Darcy’s law behavior on a fluid flow through a simple single flat sheet media configuration, for a given temperature and shear rate, apparent viscosity was calculated. This paper shows a correlation between Computational Fluid Dynamics (CFD) results and Test data. Effective shear rates in the porous media were obtained from fluid velocities at media face and porous media grade. It was observed a consistent shear thickening behavior. Results of applying this viscosity correlation, at the filter design stage, gave us a much better prediction of pressure drop performance in the actual filter test stage. An average of 40% difference between measured pressure drop and predicted pressure drop CFD was observed before applying this factor. The test data to CFD result difference was reduced to 10% average. In addition to this correlation on porous media flow, a simple analysis of internal flow through a circular tube was analyzed. The Darcy-Weisbach equation gave us a theoretically calculated pressure drop for a given flow rate, tube inner diameter, and length. Associated Computational Fluid Dynamics simulation was conducted at the same boundary flow conditions. Test data from this analysis were compared to theoretical calculations and this CFD results. This last analysis it was clearly observed the apparent viscosity dependence on shear rate. This is, for a given temperature and fluid, different flow rates showed pressure drop values that implied different fluid apparent viscosities. This work set the path to develop correcting factors on viscosity values for pressure drop hand calculations in the automatic transmission filter porous media. Filter designers can dimension the porous media effective area in a more precise fashion, especially for operating conditions in very cold conditions, where this non-Newtonian behavior is frequently observed. Also, transmission fluid makers could use this data to better develop oil blends to avoid this cold freeze characteristic.