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Background |
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In many automotive and hydraulic
applications, oil flows through small openings that can be simulated by
small-diameter, square-edged orifices. These fluids (oils) are highly
viscous, and in many instances, their properties show steep dependence on
temperature and pressure. Some of these also exhibit non-Newtonian
behavior, at least at the very low temperatures. Rheological (so called
non-Newtonian) fluids are very frequently encountered in food processing and
chemical industries. While an orifice can successfully be used to simulate
these flows, the most commonly available orifice correlations are those used
for metering applications and developed for large diameter and small aspect
ratios, encountered often in turbulent flow regime. The proposed research
therefore addresses the problem of relating flow rate to pressure drop
across square-edged orifices over a wide range of orifice geometries and
operating conditions while accounting for varying properties and
non-Newtonian behavior. |
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A Typical Orifice
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Motivation/Need for Research |
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Most of the prior research
conducted establishes orifices as constriction type flow meter. The
standard convention for relating orifice flow rate to differential pressure
is through the use of the orifice discharge coefficient (Cd) as:
This treatment of orifice flow is
adequate for flow metering applications especially in turbulent flow
regime. For highly viscous and varying property fluids, this simple orifice
analysis can not predict the flow characteristics correctly. Therefore
there is a need to understand the orifice flow better in the context of
these fluids which can potentially exhibit non-Newtonian behavior. |
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Specific Objectives |
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Establish orifice flow and pressure drop characteristics for
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1 (14.5) < DP < 100
bar(1450 psi)
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– 30 < T < 50oC
¨
0.151 < mge
< 9.589 kg/m-s
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Study wide range of orifice geometries
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Nine orifices (Diameter = 0.5, 1 and 3 mm, Thickness = 1, 2
and 3 mm each)
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b (Diameter ratio, DOr/DPipe)= 0.023,
0.044 and 0.137
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l/d (Aspect ratio) = 0.33, 0.66, 1, 2, 3, 4 and 6
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Analyze and document effects of temperature, orifice geometry
and shear rate
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Develop an experimentally validated model to predict pressure
drop as a function of orifice geometry and operating conditions while
accounting for non-Newtonian behavior |
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Approach |
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A detailed and versatile test facility is
required for conducting experiments over the range of parameters of interest
of this study. Test facility consisting of the test section, a triplex
plunger positive displacement pump, and several heat exchangers to condition
the fluid, numerous pressure transducers and flow meters was fabricated.
The main test section consists of an orifice plate mounted between two
flanges. The flanges are supplied with 1” pipe nipple that provide for
large contraction ratio and sufficient lengths for flow development upstream
and downstream. To maintain system pressure, an accumulator is provided.
Heat exchange fluid in the heat exchanger is supplied by a Mydax Chiller
(Model #1VL72W) that can provide 7 kW (2 tons) of cooling at -50oC.
Controlling pump discharge, back-pressure and bypass valves desired pressure
drop across orifice is obtained. Desired temperature is obtained using
either or both of the heat exchangers. The test facility, schematic and
test section are shown here.
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Experimental Facility
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Schematic of Test Facility
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Test Section
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Sample Findings |
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Tests were conducted to collect
experimental data in terms of pressure drop and flow rate across the
orifice. Absolute pressures were measured at the inlet and outlet of test
section along with differential pressure across it. Therefore, extraneous
major and minor pressure losses were estimated and subtracted from the
measured pressure drops. Typical orifice flow characteristics are shown
below for an orifice with a diameter ratio of 0.044 and an aspect ratio of
3. Similar characteristics were obtained for other 8 orifices. Data were
then non-dimensionalized using Euler number (Eu) and generalized Reynolds
number (Rege). |
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As evident for the figure
on the right, for a given flow rate as the temperature decreases pressure
drop increases. Also, as the flow rate becomes large enough, effect of
temperature diminishes. This is due to approach to the turbulent flow
regime.
It was also found that as
orifice thickness increases (therefore aspect ratio), pressure drop
increases for a given flow rate, temperature and diameter.
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Flow rate for 1 mm Dia.,
3 mm Thick
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Important Implications |
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Analysis of the data using
dimensionless parameters, Eu and Rege, shows that:
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For highly viscous fluids, flow may remain laminar even at
larger flow rates.
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While increase in aspect ratio at a given Rege
increases Eu at smaller Rege; influence of aspect ratio decreases
as higher Rege is approached.
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It was also found that for higher Rege, aspect
ratio exhibits minima at around 2.
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Increase in temperature in the laminar region (smaller Rege)
at a given Rege increases the Eu. This also means that extent of
laminar region increases as temperature increases.
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Shear rate plays significant role in determining the fluid
viscosity couple with temperature.
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Effect of
Aspect Ratio at 10oC
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With insight gained from data analysis, a two region based model is
developed to predict orifice pressure drop given its geometry and operating
conditions. Two regions are defined by Reynolds number. Figure shows
predicted and experimental data. The model predicts 86% of obtained data
within 25% accuracy while average error is 14%. Comparison of predicted and
experimental value of non-dimensional pressure drop (Eu) is presented the
figure below. Resulting orifice model: |
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Range of Applicability:
- 0.32 < l/d < 5.72
- 0.023 < b < 0.137
- 0.09 < Rege < 9677
- 0.019 < mge < 9.589
(kg/m-s)
- 0.19 < mr < 95.89
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Experimental vs. Predicted Eu
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Applications |
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The developed model can
successfully be used to design fluid flow loops in automotive and hydraulic
applications. |
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Ongoing Work/Future Directions |
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Additional experimental
data at extremely low and higher Reynolds number are needed to fully
understand the fluid flow characteristics. It would also be helpful to
investigate viscous heating and its effect on fluid properties therefore
flow characteristics. |
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Sponsors |
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John Deere Project Engineering Center |
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Papers |
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Conference Presentation
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Bohra, L. K., Mincks, L. M. and Garimella, S., "Pressure Drop
Characteristics of Viscous Fluid Flow Through Orifices," 2004ASME
Heat Transfer/Fluids Engineering Summer Conference, Charlotte,
North Carolina, USA, Technical Presentation, July 2004
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