Drag on Cylinders from an Integrated Pressure Distribution

Drag on Cylinders from an Integrated Pressure Distribution



by



Hieu Nguyen



School of Engineering
Grand Valley State University



Laboratory Module 8

EGR 365 – Fluid Mechanics
Section 03



Instructor: Dr. David Blekhman

July 5, 2006
• Drag on Cylinders from an Integrated Pressure Distribution
o Introduction
 Observing pressure distribution of a cylinder
 Determining the coefficient of drag via integration
 Comparing the differences in flow behavior between a smooth surface and
a rough surface
o Purpose
 To measure the drag on a cylinder in cross-flow by integrating the surface
pressure distribution.
o Apparatus
 Wind tunnel
 4-in diameter by 12-in cylinder w/strip simulating rough surface on the
side
 Tape measure
 Manometer

Figure 1: Diagram of apparatus used in the experiment.

o Procedure
 Verify the dimensions of the cylinder
 Set the wind tunnel speed where pressure is between 1.7 to 2.1 in. H
2
O
 Measure pressure at infinity (tube position 0) and pressures along the
cylinder at the remaining tube positions
o Theory

 Equations used
• ܨ
ௗ௥௔௚
ൌ
׬
݀ܨ
ௗ௥௔௚
ൌ
׬
ሺ
݌ െ ݌
ஶ
ሻ
஺
݀ܣ כ ܿ݋ݏߠ
• ܥ
஽
ൌ
ଵ
ଶ
׬
ܥ
௣
ܿ݋ݏߠ݀ߠ
ଶగ
଴

o Results and Discussion
 Ideas
• Very odd that pressure all around the cylinder save three positions

were negative; reason for negative pressure readings was that
stagnation pressure was low to begin with
• Coefficient of drag for simulated rough surface was lower
compared to smooth surface due to rough surface promoting
delaying the separation of flow, creating a smaller wake and thus
less drag
• Reynolds number of experiment was 197488, which means
pressure forces are more dominant than viscous forces

Figure 3: Plot of pressure measurements versus radial position

Figure 4: Plot of experimental and theoretical pressure coefficients
o Error Analysis
 Error propagation not calculated for coefficient of drag due to indirect
measurement of property
 Discrepancy between a theoretical drag coefficient value of 1.25 to
experiment drag coefficient was 4 percent
o Conclusion
 Drag on rough side of cylindrical rod was less than drag on smooth
surface due to delay of separation of flow from body
 Discrepancy between theoretical and experimental drag coefficient was
low





Drag on Cylinders from an Integrated Pressure Distribution
Introduction
In a previous laboratory, the determination of drag coefficient for a cylindrical rod was

calculated using a linear momentum balance. In this experiment, the calculation of the drag
coefficient of a cylindrical rod was performed using an integrated pressure distribution. The
comparison between the coefficient of drag for a rough and smooth surface was also discussed.

Purpose
To measure the drag on a cylinder in cross-flow by integrating the surface pressure
distribution.

Apparatus
The experiment was performed using a 4-in diameter by 12-in cylinder placed inside of
the wind tunnel. The cylinder contained 24 pressure taps drilled in at about half of its height.
Pressure was measured using a U-tube manometer and the pressure indicator of the wind tunnel.
Figure 1 shows the diagram of the apparatus; Figure 2 shows an in-depth look of the cylinder
with the pressure taps.


Figure 1: Schematic of the apparatus used in the laboratory.



Figure 2: Close up of the cylindrical rod with drilled pressure taps.
Procedure
• The dimensions of the cylinder were verified using a digital Vernier caliper.
• Wind tunnel speed was set to an air speed where the indicated pressure was 2.0 in. H
2
O.
• Pressure at infinity (tube position 0) and pressures along the cylinder at the remaining
tube positions were measured and recorded.

Theory

Equation (1) was used to determine the drag coefficient of the cylindrical rod,

ܥ
஽
ൌ
ி
೏ೝೌ೒
భ
మ
ఘ௎
ಮ
మ
(1)

where C
D
is the coefficient of drag, F
drag
is the drag force on the object, ρ is the density of the air,
and ܷ
ஶ
is the air velocity at infinity (before flow comes in contact with the object). When air
flows around the cylinder, there is a pressure distribution around its surfaces, which can be
integrated to calculate the drag force F
drag
, as shown in Eq. (2)

ܨ
ௗ௥௔௚
ൌ

׬
݀ܨ
ௗ௥௔௚
ൌ
׬
ሺ
݌ െ ݌
ஶ
ሻ
஺
݀ܣ כ ܿ݋ݏߠ (2)

where p is the measured pressure and the differential surface area dA is the length of the cylinder
multiplied by the radius and the differential angle θ, or

݀ܣ ൌ ܮܴ݀ߠ (3)

Substituting Eqs. (2-3) into Eq. (1) yields the following equation (4).

ܥ
஽
ൌ
௅ோ
ଶ௅ோ
׬
௣
௣
ಮ
ܿ݋ݏߠ݀ߠ (4)

Cancelling length L and radius R and introducing the limits of integration of a cylinder yields Eq.
(5), the coefficient of drag of the object as an integrated pressure distribution
ܥ
஽
ൌ
ଵ
ଶ
׬
ܥ
௣
ܿ݋ݏߠ݀ߠ
ଶగ
଴
(5)

where the coefficient of pressure C
p
is the ratio of the measured pressure to pressure at infinity,
or:

ܥ
௣
ൌ
௣
௣
ಮ
(6)

Results and Discussion
Appendix A contains the results of the pressure measurements taken during the

experiment. A graph of the measurements is shown in Figure 3. From Figure 3, it can be seen
where the wake is formed (behind the cylinder between radial positions of 60 degrees to 240
degrees). Another feature of Figure 3 is the dramatic drop in pressure at radial positions 250
degrees to 285 degrees. Located at these positions was a strip of tape with what appeared to be
silica beads attached to it, simulating a rough surface. This rough surface caused turbulent air
flow at this section of the cylinder, which increased pressure at this region. Also, all but two
pressure measurements along the cylinder were negative. This may be attributed to starting the
wind tunnel at a low pressure. As the flow moves around the cylinder, it becomes accelerated,
and according to Bernoulli's principle, the pressure at accelerated flow should decrease. Thus,
negative pressure was measured.


Figure 3: Graph of the results of the pressure measured.
The theoretical and experimental pressure coefficients around the cylinder is shown in
graphical form in Figure 4. As was seen in Figure 3, the pressure coefficients decrease
drastically as the flow moves around the rough surface of the rod. Comparing the theoretical
model to the experimental model, it can be seen that the behavior of the flow behind the cylinder
does not resemble the flow of the theoretical model. Under the theoretical model, flow
streamlines and pressure distribution on the front and back end of the cylinder are mirror images
(see Figure 5) and the net drag force is zero [1]; fluid flow does not separate from the surface of
the object due to the absence of friction. For the experimental model, flow is not frictionless and
as the fluid moves across the surface and towards the rear of the cylindrical rod, it begins to
separate and develops a wake behind the rod, creating drag (see Figure 6 for an approximation of
real viscous fluid flow). The wake can be seen in Figure 4 as an almost constant pressure
coefficient from a radial position of 45 degrees to 235 degrees. An adverse pressure gradient
behind the cylinder also contributes to the separation of fluid flow at that region.


Figure 4: Graph of the experimental and theoretical pressure coefficient of the cylindrical rod
versus radial position.

Figure 5: Diagram showing frictionless flow around a cylindrical cross-section [2].

Figure 6: Diagram showing viscous fluid flow around a cylindrical cross-section [3].


Figure 7 shows a graph of the pressure coefficient as a function of the cosine of the radial
position. From Figure 7, it can be seen that the coefficient of pressure is largest behind the
cylindrical rod. Where the flow crosses the rough surface can also been seen in Figure 7, where
the coefficient of pressure is at its lowest at -1.326 at a radial position of 300 degrees. Equation
(5) was used to determine the coefficient of drag. Since one half of the cylinder contained the
smooth surface and the other half contained the rough surface, the integration was broken up,
with the limits of integration of ߠ ൌ 0 to ߠ ൌ ߨ representing the smooth surface and θ = π to θ =
2π representing the rough surface. The coefficient of drag were C
D
= 1.43 and C
D
= 1.17 for the
smooth and rough surfaces, respectively (see Appendix A for calculations). The coefficient of
drag for the entire rod was C
D
= 1.30.



Figure 7: Graph of the pressure coefficient as a function of the cosine of radial position.
Notice that the drag coefficient of rough surface is less than the smooth surface. The rough
surface delays the separation of the flow from the surface, which causes a smaller wake to be

developed behind the cylinder, thus reducing drag and drag coefficient. Figure 8 shows the
different wake areas for both a smooth ball and a dimpled ball (which represents the rough
surface of the experimental model).


Figure 8: Diagram comparing a sphere with a smooth surface and a golf ball with a dimpled
surface representing the rough surface of the experimental model [4].


Error Analysis
Propagated error for the coefficient of drag was not calculated since it was indirectly
measured. The discrepancy between the theoretical and experimental values, if the theoretical
C
D
value is 1.25,was 4 percent (see Appendix A for calculation).

Conclusion
The coefficient of drag between the smooth and rough surfaces of the cylindrical rod
were found using the integrated pressure distribution and it was found that the drag coefficient of
the smooth surface was greater than the rough surface. This is due to the delay of flow
separation caused by the rough surface, which decreases drag at that region of the rod. The error
between the theoretical and experimental drag coefficients was low (at 4 percent), but could have
been lower if the pressure was read accurately using the manometer instead of the pressure
indicator on the wind tunnel, which did not produce and an accurate reading.


REFERENCES
1. Fleischmann, S: "Drag on Cylinders From an Integrated Pressure Distribution." Fluid
Mechanics - EGR 365 Design-Based Fluid Mechanics Laboratory. Padnos College of
Engineering and Computing, 2006.

2. pilotsweb.com/principle/lift.htm
3. www.allstar.fiu.edu/aero/Flow1.htm
4.