MS Thesis Presentation by Lalit K Bohra

Tuesday, July 6, 2004

(Dr. Srinivas Garimella, Chair )

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

__Abstract__

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), over wide ranges of flow rates
(2.86×10^{-7} < Q < 3.33×10^{-4} m^{3}/s) and temperatures (-30 <
T < 10^{o}C). 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 < T < 50^{o}C) 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 ±25% for 0.32 < l/d (orifice thickness/diameter
ratio) < 5.72, 0.023 < ß (orifice/pipe diameter ratio) < 0.137,
0.09 < Re_{ge} < 9677, and 0.0194 < µ_{ge} < 9.589 (kg/m-s).

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