Flow and Pressure Drop of Highly Viscous Fluids in Small Aperture Orifices

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Bohra, Lalit Kumar
Garimella, Srinivas
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A study of the pressure drop characteristics of the flow of highly viscous fluids through small diameter orifices was conducted to obtain a better understanding of hydraulic fluid flow loops in vehicles. Pressure drops were measured for each of nine orifices, including orifices of nominal diameter 0.5, 1 and 3 mm, and three thicknesses (nominally 1, 2 and 3 mm), and over a wide range of flow rates (2.86x10sup-7/sup Q 3.33x10sup-4/sup msup3/sup/s). The fluid under consideration exhibits steep dependence of the properties (changes of several orders of magnitude) as a function of temperature and pressure, and is also non-Newtonian at the lower temperatures. The data were non-dimensionalized to obtain Euler numbers and Reynolds numbers using non-Newtonian treatment. It was found that at small values of Reynolds numbers, an increase in aspect ratio (length/diameter ratio of the orifice) causes an increase in Euler number. It was also found that at extremely low Reynolds numbers, the Euler number was very strongly influenced by the Reynolds number, while the dependence becomes weaker as the Reynolds number increases toward the turbulent regime, and the Euler number tends to assume a constant value determined by the aspect ratio and the diameter ratio. A two-region (based on Reynolds number) model was developed to predict Euler number as a function of diameter ratio, aspect ratio, viscosity ratio and generalized Reynolds number. This model also includes data at higher temperatures (20 and le; T and le; 50supo/supC) obtained by Mincks (2002). It was shown that for such highly viscous fluids with non-Newtonian behavior at some conditions, accounting for the shear rate through the generalized Reynolds number resulted in a considerable improvement in the predictive capabilities of the model. Over the laminar, transition and turbulent regions, the model predicts 86% of the data within and plusmn25% for 0.32 l/d (orifice thickness/diameter ratio) 5.72, 0.023 and beta; (orifice/pipe diameter ratio) 0.137, 0.09 Resubge/sub 9677, and 0.0194 and mu;subge/sub 9.589 (kg/m-s)
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