formal report 1- full report
TRANSCRIPT
-
8/3/2019 Formal Report 1- Full Report
1/15
F3: Drag on a Cylinder
Experiment conducted 7/11/11
Report written10/12/11
Principal investigators:
Michael Golden, William Barraclough
Author: Michael Golden
-
8/3/2019 Formal Report 1- Full Report
2/15
Contents
Summary 1
1- Introduction 2-3
2- Procedure 4
3- Results 5-7
4- Discussion 8
5- Conclusions 9
References 10
Appendices 11-14
-
8/3/2019 Formal Report 1- Full Report
3/15
Summary
The main purpose of this experiment was to measure theprofile drag of a cylinder in a real (viscous) fluid by measuring
the distributive pressure around the surface. In this case, the
profile drag refers to the retarding force acting on a body
moving through a fluid parallel and opposite to the direction
of motion. A circular cylinder with a single hole, to which was
attached a manometer, was inserted into a wind tunnel and
progressively turned leeward against the fluid flow, all thewhile pressure was measured at regular 5 increments. The
resulting pressure readings were then plotted on to a graph in
order to determine the positive upstream, negative upstream
and negative downstream flows. The sum of these flows was
found, and from this the Reynolds number of the flow was
calculated. This number was then checked against the British
Standard value and found to be relatively accurate,accounting for expected experimental & statistical
inaccuracies.
-
8/3/2019 Formal Report 1- Full Report
4/15
Introduction
The goal of this experiment was to accurately measure the profile drag of an object subjected to aconstant flow of a real (i.e. viscous to some degree) fluid within a wind tunnel, and from there
compare it to accepted values of the British Standard.
The object used was a circular cylinder of uniform diameter, which was placed in a wind tunnel and
subjected to an air flow of constant speed. The only feature on the otherwise smooth and uniform
cylinder was a small whole through which air could pass. Connected to this hole was a micro
manometer, there to measure the pressure differential between the cylinder surface pressure and a
static pressure tapping in the wall of the tunnel.
The 'drag' of a cylinder is defined as the retarding force acting on a body moving through a fluid
parallel and opposite to the direction of motion[1]
In an inviscid fluid (Inviscid, in this case, being defined as a fluid that can have no supporting
stress, and thus no energy dissipation[2]), the cumulative force of the pressure on the side of the
cylinder facing the flow would be perfectly equal to the pressure on the leeward (downstream) side
of the cylinder. This can be determined from the definition of 'Inviscid': an inviscid fluid is perfectly
frictionless, thus any molecules, upon meeting an obstruction, flow perfectly around it. As both
friction and pressure are manifestations of the same thing (namely, the force exerted on two objects
when they collide), if the fluid is frictionless, there will be no differential in pressure either.
In a real fluid, however, there is (obviously) friction (measured, in this case, by viscosity). As a
result of this, the forces in state around the cylinder do not cancel, there is a net drag force betweenthe upstream and downstream sides, and a 'wake' [3] .of flow disturbed by the object is formed. This
phenomenon can be clearly seen with any real fluid. Of particular real-world note in terms of real
world applications would be all manner of aircraft. The very principals by which the aerodynamics
of aircraft are determined are intrinsically and inextricably linked to the theory behind this
experiment. A plane that was designed without taking into account drag, pressure differentials and
airflow is a plane with an extremely short flight duration.
-
8/3/2019 Formal Report 1- Full Report
5/15
p-p0
R
airflow
Figure 1. Section of a test cylinder
For the section of the cylinder shown in figure 1, p is the surface pressure obtained from the hole in
the cylinder surface and p0 is the static pressure obtained from the tapping in the tunnel wall. p-p0 is
the pressure difference measured by the micro manometer.
As drag acts against the the positive streamwise direction, so the pressure force per unit area on any
minimal patch of the cylinder surface placed at degrees to the inflow is .
The drag force of the previously defined patch is the pressure force per unit area multiplied by the
area of the patch. This would then be , where is the area acted upon
for a unit length of the cylinder.
From this equation, the total pressure drag D can be obtained via integration within the limits of =0
and =, remembering, of course, to account for both halves of the cylinder:
In order to enable easier comparison of similar shaped objects without having to account for relative
sizes, it is frequently more expedient to state dimensionless coefficients as opposed to numerical
values. This coefficient may be obtained by dividing the drag force value by a referential force,
equivalent to the force the flow exerts on a flat plate of surface area R, placed normal to the inflow.
This can be written as , where U is the air velocity in ms-1.
Finally, dividing the former equation for total pressure drag by , and remembering that
can be written as and thus replacing the relevant values
with that, we end up with:
where Cd = Coefficient of Drag
p = Surface pressure
p0 = Static pressureU = Air velocity
= Angle of incidence Equations on this page taken from data book[3]
-
8/3/2019 Formal Report 1- Full Report
6/15
Procedure
As described in the introduction, the experiment was conducted using a small wind tunnel
containing a circular cylinder; this cylinder had a small hole drilled into it, to which was attached a
micro manometer measuring the pressure on the wall of the cylinder against the static pressure at apoint on the wall of the tunnel. The cylinder was allowed to rotate my means of a small wire
extending out of the top of the wind tunnel with a protractor inset to allow for easy referral when
changing the angle of incidence of the hole.
The experiment was begun by bringing the wind tunnel up to a suitable speed (in this case the exact
speed itself was not relevant, so long as it remained constant for the entire duration of testing). The
first point measured was with the area containing the pressure sensor upstream, directly facing
against the direction of the flow; from now on this point shall be known as 0.
At this point the pressure was taken from the readout of the micro manometer three times, in order
to acceptably account for the inevitable variations in pressure due to an inherently unstable flow.This instability was not born of any specific failures in the enactment of the experiment itself, but
rather an expected product of chaos theory- the flow of fluid in a three dimensional space being an
emergent phenomenon, thus being naturally chaotic & impossible to predict on a small level whilst
still demonstrating a relatively consistent pattern on a macro level. The average & standard
deviation was thence taken from the three results in order to provide a relatively trustworthy
indicator of the overall pattern within the data.
Having collected the data from the 0 position, the dial was then adjusted, rotating the focus area of
the cylinder to 5 from the air flow. Once again, three measurements were then taken from this
position and an average determined.
This procedure was then repeated at 5 increments all the way to 180 (focus point directly facing
away from flow, minimum exposure to oncoming fluid). The result of this was a set of results &
averages for pressure ranging from 0 to 180.
Some significant difficulties encountered during the undertaking of the experiment included:
-Problems with the delicacy of the apparatus rotating the cylinder, potentially resulting in
rotational increments of slightly more or slightly less than 5. In order to alleviate this, in
future it would be advisable to utilise more robust apparatus.
-Issues of extreme variability of results due to an unstable flow. There are two principal
issues here that, if addressed, would likely negate much of the resultant difficulty:
-The wind tunnel was not a closed system, and was in fact based within a
large, open room, with potential for significant variability in terms of
pressure & temperature; this would naturally have had a significant
effect on the air flow. A solution to this would involve placing the wind
tunnel within a sealed area, allowing for greater control over ambient
environmental conditions.
-Despite attempts to account for the unstable pressure variance by taking
multiple readings, it still likely had a statistically significant effect on
the results. Thus, in the event this experiment is repeated, it would be
advisable to take a much larger sample base from which to determine
the averages- ten sets of results would likely be sufficient.
-
8/3/2019 Formal Report 1- Full Report
7/15
Results
As described in the Procedure, three results were taken for each position in 5 increments, from
which the average and the standard deviation were calculated. The raw results (including multiple
results per iteration & standard deviation values) are posited in the Appendices
[a]
. The data shownbelow in Figure 2. is the average pressure (Pa) for each increment, the sine of each angle (to 2 d.p),
and the coefficient of pressure for each result.
Figure 2. Flow measurement in Pipes Measured Data with respect to flow rate (kg/s) in column 1
Pressure (Pa) Sin (angle) Cp
0.00 112.00 0.00 1.00
5.00 100.00 0.09 0.89
10.00 88.00 0.17 0.79
15.00 69.30 0.26 0.62
20.00 37.30 0.34 0.33
25.00 20.00 0.42 0.18
30.00 -0.30 0.50 0.00
35.00 -31.00 0.57 -0.28
40.00 -59.00 0.64 -0.53
45.00 -74.67 0.71 -0.67
50.00 -88.30 0.77 -0.79
55.00 -97.00 0.82 -0.87
60.00 -95.00 0.87 -0.85
65.00 -87.67 0.91 -0.78
70.00 -85.00 0.94 -0.76
75.00 -82.00 0.97 -0.73
80.00 -78.00 0.98 -0.70
85.00 -75.00 1.00 -0.67
90.00 -74.00 1.00 -0.66
95.00 -72.00 1.00 -0.64
100.00 -70.00 0.98 -0.62
105.00 -70.00 0.97 -0.62
110.00 -71.33 0.94 -0.64
115.00 -69.00 0.91 -0.62
120.00 -72.00 0.87 -0.64
125.00 -70.67 0.82 -0.63
130.00 -70.67 0.77 -0.63
135.00 -73.33 0.71 -0.65
140.00 -74.33 0.64 -0.66
145.00 -72.67 0.57 -0.65
150.00 -73.33 0.50 -0.65
155.00 -74.00 0.42 -0.66
160.00 -72.00 0.34 -0.64
165.00 -71.67 0.26 -0.64
170.00 -74.00 0.17 -0.66
175.00 -74.00 0.09 -0.66
180.00 -71.67 0.00 -0.64
-
8/3/2019 Formal Report 1- Full Report
8/15
Figure 3. Graph of Pressure difference -v- angle
Having calculated the coefficient Cp for each pressure reading and the sine of the angle, the next
step was to plot this to the graph, Figure 4, shown below.
Figure 4. Graph of Cp -v- Sine(angle)
-
8/3/2019 Formal Report 1- Full Report
9/15
From here the graph was numerically integrated by calculating the area under each portion of the
graph (positive upstream, negative upstream and negative downstream), and the sum of these areas,
Cd, was determined.
Positive Cp upstream:
Total area = 0.283
Negative Cp upstream
Total area = 0.2859
Negative Cp downstream
Total area = 0.643
Sum of areas, Cd = 1.2119 Complete calculations can be found in Appendices[b]
With the total coefficient Cd calculated, it was possible from here to determine the Reynold's
Number of the flow. The Reynold's number is a dimensionless number that expressed the ratio of
forces of inertia to viscosity.[4] The full method of how this was calculated can be seen in the
appendices[c]
Re = 12702 (5 s.f)
Finally, the coefficient of drag Cd as measured in the experiment was compared with the officially
accepted calculated value as determined from a chart showing accepted differences in coefficients
according to shape[e]
Calculated Cd = 1.2
Measured Cd = 1.2119
This difference is small enough to be accounted for in statistical and practical error analysis and assuch can be accepted as a reasonably successful result.
-
8/3/2019 Formal Report 1- Full Report
10/15
Discussion
At the conclusion of the section of this report detailing the results of the experiment, it was shown
that the measured Cd, 1.2119, matched the expected calculated Cd of 1.2 rather well, with a
divergence of just 0.99%.
[d]
Considering the latent instability in the environment within which theexperiment was conducted, this may be considered a successful result.
As stated previously, the experimental factor that initially caused the most concern whilst
conducting the experiment was that of the environment. The primary piece of apparatus in the
experiment was the wind tunnel, and much of the calculation was based upon an assumption of a
steady air flow. As the wind tunnel did not take its air flow from a closed system, it was understood
that atmospheric conditions would play a significant factor in the flow itself and thus they were of
large concern.
Unfortunately, the area the experiment was conducted in was a large, open lab, with multiple
entrances & exits, and large numbers of people passing through frequently. The effects of suchunaccounted variables would be to introduce instabilities into the fluid flow, and potentially have a
significant effect on the results. Fortunately, it would seem that these unknown factors did not have
as disastrous an effect on the experiment as feared; it would be reasonable to assume, however, that
they are the largest factor in the small difference between the calculated coefficient and the
observed coefficient.
In order to understand why such an experiment is necessary at all however, one must first
understand the difference between a real and an inviscid fluid. Put simply, an 'inviscid' or 'perfect'
fluid is one that has zero viscosity; viscosity in this context being defined as a fluid property that
related the magnitude of fluid shear stresses to the fluid strain rate, or more simply, to the spatial
rate of change in the fluid velocity field[3].. Thus a circular cylinder of the same kind in theexperiment subjected to a flow of an inviscid fluid would experience no drag. All fluids (barring
some exceptional so-called 'super-fluids') are subject to internal resistance and shear force. In a
perfectly steady one-dimensional flow, this would not be an issue; however when a viscous fluid is
forced to move around an object within a three-dimensional flow (in this case the circular cylinder),
its internal friction prevents it from steadily and perfectly moving- the change of direction of some
of the flow causes a change in velocity relative to the rest of the flow. In a fluid not subject to
internal resistance or shear force this would not be a problem, but in a real fluid this relative
dichotomy of velocities causes turbulence and drag.
The study of turbulence and drag around an object, whatever the shape, is a fundamental aspect of
engineering design, particularly in nautical and aeronautical engineering. Although a simpleexample, the application of experiments such as this is fundamental to all successful design
projects involving vehicles moving in a fluid, whether that fluid be air or water.
-
8/3/2019 Formal Report 1- Full Report
11/15
Conclusion
This experiment, although initially subject to some potential unreliability due to environmental
conditions, has been shown to be in line with results calculated from the approved standard to
within a statistically acceptable margin (0.9916..%).
Whilst not breaking new ground in and of itself, the experiment comfortably demonstrates, all
inaccuracies accounted for, the reliability of using the standard coefficients of drag (table shown in
appendices[e]). On this basis, it would be reasonable to call the experiment a success, as the results
observed were in line with the predicted results, and an important demonstration of the difference
between the theoretical action of an inviscid flow and the actual action of a fluid flow subject to
normal viscosity.
Whilst some fluids of negligible viscosity may well exist within laboratory conditions, one cannotexpect to encounter them within the every day applications of fluid mechanics; as such turbulence
and drag are an unfortunate but unavoidable part of most vehicle design, whatever the type. Thus
the results obtained in this experiment, and all others like it, are of paramount importance in all
successful engineering design involving objects moving within a fluid. Whilst simple, the idea
behind this experiment demonstrates the fundamental mechanics necessary to all good design.
-
8/3/2019 Formal Report 1- Full Report
12/15
References
[1] Merriam Webster definition- Drag
http://www.merriam-webster.com/dictionary/drag
Accessed 10/11/11
[2] Clancy, L.J. (1975), Aerodynamics, Pitman Publishing Limited, London.
[3] Efunda, Engineering Reference- Viscosity
http://www.efunda.com/formulae/fluids/glossary.cfm
[4] Department of Engineering Lab Handbook, F3-2,3
[5] Glen Research Centre, Nasa- Reynolds Number
http://www.grc.nasa.gov/WWW/BGH/reynolds.html
-
8/3/2019 Formal Report 1- Full Report
13/15
Appendices
[a] Table of raw results taken from micro manometer; table shows three measurements of
pressure and the mean derived from them for every 5 increment.
Degrees
0 112 120 104 112
5 100 104 96 100
10 88 94 80 88
15 68 76 60 69.33
20 32 37 43 37.33
25 15 20 25 20
30 -9 0 8 -0.33
35 -26 -30 -37 -31
40 -65 -59 -53 -5945 -79 -75 -70 -74.67
50 -94 -88 -83 -88.3
55 -104 -97 -90 -97
60 -105 -95 -90 -95
65 -95 -88 -90 -87.67
70 -70 -86 -90 -85
75 -77 -84 -88 -82
80 -75 -77 -86 -78
85 -72 -75 -81 -75
90 -70 -75 -80 -74
95 -65 -71 -78 -72
100 -64 -70 -77 -70
105 -74 -70 -66 -70
110 -76 -71 -67 -71.33
115 -73 -69 -65 -69
120 -78 -72 -66 -72
125 -75 -70 -67 -70.67
130 -75 -71 -66 -73.33
135 -80 -72 -68 -73.33
140 -80 -74 -69 -74.33
145 -77 -70 -68 -72.67
150 -78 -73 -68 -73
155 -81 -74 -68 -74
160 -74 -72 -68 -72
165 -78 -73 -64 -71.67
170 -78 -74 -70 -74
175 -81 -73 -68 -74
180 -77 -72 -66 -71.67
P1 P2 P3 Pm
-
8/3/2019 Formal Report 1- Full Report
14/15
[b] Full calculations for numerical integration of drag coefficients
Positive Cp upstream:
(0.9 x 0.085) + (0.8 x 0.085) + (0.6 x 0.085) + (0.35 x 0.085) + (0.2 x 0.08) = 0.24125
(8 + 18 + 23 + 10 + 17) x 0.0005 = 0.04175
Total area= 0.283
Negative Cp upstream
(0.3 x 0.07) =+ (0.55 x 0.06) + (0.45 + 0.05) + (0.74 x 0.18) + (0.7 x 0.04) = 0.2494
(19.5 + 12 + 6 + 7 +23.5 + 3 + 2) x 0.0005 = 0.0345
Total area= 0.2859
Negative Cp downstream
0.65 x 0.76 = 0.494
0.24 x 0.6 = 0.144
10 x 0.0005= 0.643
Total area= 0.643
Total area= 1.2119, thus Cd =1.2119
-
8/3/2019 Formal Report 1- Full Report
15/15
[c] Full calculations for determining Reynolds Number
Where Vo = Velocity = 13.59
d = Diameter = 1.43 x 10-4
V = Viscosity = 1.53 x 10-5
(5 sf)
Calculated Cd = 1.2
Measured Cd = 1.2119
[d] Calculation of percentage difference between Calculated coefficient and Measured
Coefficients
=