Bertin J.J., 2002, Aerodynamics for
Engineers , 4th edition, Prentice Hall.
Panton R.L., 2005, Incompressible Flow, Wiley.
von Kármán T., 1963, Aerodynamics, McGraw-Hill, pp.
68-72, 85.
van Dyke M., 1982, An Album of Fluid Motion, Parabolic
Press, pp. 28-31. 1 Eric W. Weisstein. (2007) Cylinder Drag. Online. Available from: http://scienceworld.wolfram.com/physics/CylinderDrag.html

Morgans, A (2011) Measurement
of the pressure distribution on a circular cylinder. Department of
Aeronautics, Imperial College London.
Anderson, J. D, Jr. (2011) Fundamentals of Aerodynamics. 5th edition.
Singapore, McGraw Hill.
Roshko, A. (1961). Experiments on the flow past a circular
cylinder at very high Reynolds number. Journal
of Fluid Mechanics, Online 10, 345-356 doi:10.1017/S0022112061000950.
Cheung, C. K. & Melbourne, W. H.
(1980) Wind tunnel blockage effects on a circular cylinder in turbulent
flows. 7th Australian
Hydraulics and Fluid Mechanics Conference, 18-22 August 1980, Brisbane.
pp. 127-130. Online Available from: http://www.mech.unimelb.edu.au/people/staffresearch/AFMS%20site/7/CheungMelbourne.pdf

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.References:

This experiment showed that the potential
flow theory is invalid in real life due to the viscous nature of the flow.
There tends to be a separation of laminar and turbulent boundary layers
separate at certain angular positions, leading to an increase in pressure drag.
With an increase in the Reynolds number the boundary layer tends to transit
from laminar to turbulent with the separation occurring towards the rear face
leading to a significant drop in the coefficient of friction

Conclusion:

 

·        
Presence of the pitot static
tubes facing the oncoming flow adversely affects the flow.

·        
Error due to blockage effects.
The errors in reading tend to propagate even after ensuring corrective measured
to negate the blockage effects.

b)     
Physical

·        
Error in ensuring that the zero
degree tapping of the cylinder is towards the oncoming flow. It was mandatory
to maintain the stillness of cylinder by hand.

·        
Parallax error during reading
of multitube manometer.

a)     
Human:

There were two classes of error

Error Analysis:

 

 

 

 

 

 

·        
It is applied to aircraft
operating in lower Reynolds numbers such as gliders. They make use of vortex
generators to delay boundary layer separation by encouraging the boundary layer
to transit from laminar to turbulent.

·        
This is the reason behind the
dimples on golf balls, fluff on tennis balls and stitching on cricket balls to
enhance their performance.

In actual
life, due to the adverse pressure gradient acting on the boundary layer the
laminar layer tends to separate before the maximum thickness of the cylinder.
Comparatively, the turbulent boundary layer is less susceptible to an adverse
pressure gradient. This means that the separation is delayed to the rear
surface of the cylinder. By tripping the boundary layer, though the skin
friction is increased at higher Reynolds numbers, the pressure drag reductions
at the lower Reynolds numbers outweighs that concern. Applications of this
result:

 

Figure 13: Coefficient of drag on a circular cylinder
as a function of Reynolds number.

Figure 12: Measured pressure distributions on a
circular cylinder compared with theoretical distribution calculated assuming
ideal flow. (From Bertin and Smith, 1989)

 

 

 

Figure 11: Flow as visualised for a critical Reynolds number.

 

 

Figure 10: Flow as visualised for a sub-critical
Reynolds number.

Results:

 

   
xi.           
Conduct a series of tests to
determine the shape and form of the circular cylinder wake at a fixed Reynolds
number.

     
x.           
Conduct a series of tests to
determine the pressure distribution and drag coefficient on the circular
cylinder at a fixed Reynolds number, and compare with inviscid theory.

   
ix.           
Also note the reading of the
static Pitot probe.

viii.           
Using the manometer, measure
the pressures of corresponding to each pressure tap.

  vii.           
Note the maximum speed of the
tunnel. After sometime lower it to approximately half the maximum speed.

   
vi.           
Secure all the items in tunnel
and turn on the facility and gradually change the speed.

     
v.           
Record the atmospheric air
conditions and its properties.

   
iv.           
Check for zero errors of
manometers.

   
iii.           
Determine the connections
between the pressure taps on the cylinder surface, the cylinder angle and the
tubes of the multitube manometer.

     
ii.           
Do the same for the reference
Pitot static and also ensure that it is pointing in the right direction.

       
i.           
Record the dimensions and
position (x,y,z) of the cylinder model relative to the test section.

Procedure

Figure 9: Smoke flow visualisation tunnel

The stagnation pressure can also
be measured by the static Pitot probe. The stagnation pressure in inviscid
steady flow always remains constant and equal to its free stream value. The
stagnation pressure coefficient is 1 here. Due to viscous effects that can be
encountered inside the edge of a turbulent wake, like that shed by the
cylinder. the stagnation pressure tends to drop and hence, the stagnation
pressure coefficient will always be less than 1. This property of the
stagnation pressure coefficient makes it a very good indicator of the edge and
extent of a wake.

.

D. Instrumentation for
measuring the cylinder wake
A two axis manual traverse gear is mounted towards the back of the wind tunnel
test section. In this gear, a Pitot-static probe is mounted. Tygon tubes
transmit the pressures sensed by the Pitot-static to the manometer. Scales
attached to the horizontal and vertical axes of the traverse allow us to adjust
the relative position of the
Pitot probe in the cross plane A second Pitot-static probe is used to determine
the velocity distribution in the cylinder wake. If  po 
and p represent the Pitot and static pressure sensed by the probe then
the ratio of the local velocity to the free stream velocity is given by

C. Instrumentation for
measuring the pressure distribution on the cylinder surface
The pressure coefficient is denoted as Cp with p
representing the pressure at the cylinder surface. At its midspan, the circumference
of the cylinder is embedded with 36 one-millimeter diameter pressure taps at 10
degree intervals which sense the surface pressure p and transmit it
through a series of Tygon tubes of 3 mm outside diameter. First is using the multitube
manometer. All the Tygon tubes are initially connected to it. The Tygon tubes
transmit the pressure at each tap to the top of each water column in the
manometer. For pressures lower than atmospheric, the colored water moves up the
tube. If the pressure is higher the level of the colored water subsides. The
change in height of the fluid column is used to infer the pressure p
(relative to atmospheric) using the hydrostatic equation. The principle
advantage of the multi-tube manometer is that it provides an easily understood
way of simultaneously visualizing the pressure distribution on the entire
circumference of the circular surface. The disadvantage of this system is that
it is difficult to read the change in fluid heights with much accuracy,
particularly at lower free stream speeds.

A reference probe monitors the
velocity and pressure of the free stream. The probe has two pressure
connections to it. One on the axis is connected to the Pitot, or stagnation port
and thus registers the stagnation pressure of the free stream po. i.e, the
pressure produced due to choking of flow halt at the mouth of the tube. The
connection on the other side of the probe is connected to the static ports on
the side of the probe which registers the actual pressure of the free
stream p.
The difference in these pressures is related
to the free stream velocity. To sense this pressure difference and the free
stream velocity the probe, through two Tygon tubes, is connected to a digital
manometer, that can measure pressures in kPa or inches of water column. Tube
carrying the static pressure from the reference probe has a T connector in it.
With the tunnel off the manometer should read zero.

A multitube manometer capable of measuring up
to 40 pressures simultaneously is available for use with the open jet wind
tunnel. The manometer is filled with water. All the manometer tubes are
connected at one end to a reservoir of fluid (ref. fig. 7) which is open to
atmosphere. At the other end each tube is connected to the pressure to be
measured. The manometer is thus sensitive to pressures relative to atmospheric.

The inside and outside temperatures of the
tunnel is monitored by a digital thermometer fixed to the side of the tunnel
downstream of the test section. The accuracy being 0.1 degrees. Ambient
(atmospheric) pressure is measured by a barometer attached to the right hand
side of the wind-tunnel control panel. The probes can be moved horizontally and
vertically across the test section using a traversing gear. A lead screw,
covered with a shroud of airfoil cross-section moves the probe horizontally. The
probe can be moved vertically by a rack, pinion and ratchet system mounted
outside the flow in steps of 5.7mm.

 

Figure 8: Errors due to misalignment in velocity
measurement made with a Pitot-static probe.

 

Figure 7: Diagram showing connection of a single tube
of the multi-tube manometer.

A 3 mm diameter Pitot-static probe monitors the
flow speed in the test section. An inclined manometer is connected to the Pitot-static
probe. It measures the speed of flow at the upstream end of the test section
where it is assumed to be not affected by the presence of a model. But, placing
a large model in the test section might artificially increase the velocity
sensed by the probe. The manometer has an accuracy of about ±0.02 inches of
water.

 

Figure 6: Mean velocity distribution across an empty
test section of the wind tunnel.

 

B. Open jet
wind-tunnel model and circular cylinder model
The experiment is performed in a 3-foot subsonic wind tunnel. The cylinder
model is mounted in the wind tunnel. The model is preferably made of Plexiglas.
The radius of the cylinder is 70 mm and it has a span of 462 mm. Circular end
plates of radius 152.5 mm minimize the flow around the ends of the cylinder.
These plates tend to make the flow more two dimensional. The cylinder model is
mounted spanwise across the test section. The mount is such that it allows the
cylinder to be rotated about its axis by a measured angle which is indicated by
an attached protractor. This setup, hence, also allows the cylinder to be
placed at different streamwise positions.

T is in Kelvin.

 

m =1.4578 × 10-6  × T 1.5

The temperature is used to infer
the dynamic viscosity of the air using Sutherland’s relation. For SI units,

Figure 5: Setup to test air properties.

A. Instrumentation
for measuring the properties of the air.
The open jet wind tunnel used laboratory atmosphere as the working fluid. The
properties of the air in the lab are dependent on the weather, the most
important properties being its density and viscosity. Instead of measuring density
directly, for accuracy reasons, it is obtained by measuring pressure and
temperature and then using the equation of state for a perfect gas. An aneroid
barometer for measuring atmospheric pressure is provided on the side of the
open-jet wind tunnel control panel. A digital thermometer for measuring
atmospheric temperature is located on the side of the open-jet tunnel adjacent
to the test section. Pressure output is in milibar and the thermometer output
i.e, Celsius or Fahrenheit is setting dependent. The gas constant R in
the equation of state for a perfect gas (p =rRT) is 287 J/kg/K.

Experimentation apparatus, instrumentation
and methods

 

 

 

 

 

 

 

 

 

It is not included in the formula given
for the calculation of drag above.

 

CD should be
determined for smooth cylinders for different values of U. The measurement of static pressure distribution is
done relative to the tunnel static pressure ptunnel prevailing at that location. As

The coefficient of drag can be given as

Using the knowledge of p(R,q), form drag per unit length acting on the
cylinder can be calculated as

 

Figure 4: Measurement of pressure over cylinder
surface.

 

Time-averaged values of forces are
discussed. Hence, the measurements of pressure and velocity are also
time-averages. A single pitot tube is embedded within a circular cylinder
measures pressure distribution p(R, q) (static pressure as a function of q at r= R, at the cylinder surface) where R is the radius of the
cylinder and ? is the angular location on the surface of the cylinder.
Angle q is varied by
turning the position of the cylinder relative to the main flow. In the figure 4 shown below, OA is the Pitot tube, which senses the local surface
static pressure.

 

Figure 3: Inviscid and real pressure distribution
around a circular cylinder.

 

 

For potential flow, coefficient of
pressure is given as:

The total drag in separated flow consists
of both the drags i.e, form drag and viscous drag but the former is greater in
proportion. An asymmetric distribution of the surface pressure on the forward
and rear halves of the cylinder leads to form drag which hence can be measured.
It constitutes a representative value for the total drag.

 

6.     
In the final regime, the
boundary layer on the forward face transits to turbulent and the point of
separation starts to creep back across the rear face and back onto the front
face. This coupled with the increase in skin friction and wake size again
increases the coefficient of drag.

5.     
A sharp drop in drag is noted
as the Reynolds number approximately reaches 400,000. This is observed due to a
smaller pressure drop which occurs due to the transition of the boundary layer from
laminar to turbulent and reattaching with the cylinder on the rear face.

4.     
As Reynolds number reaches the
order of 103 the laminar boundary layer separated from the front
face of the cylinder and the shear layer starts its transition towards
turbulent form leading to the formation of wake. At this point the drag
coefficient is stable and is approximately equal to one.

3.     
A loss of stability is observed
with further increase of Reynolds number which gives rise to the phenomenon of
von Karman street i.e, alternative shedding of vortices.

2.     
This viscosity tends to affect
the flow at the surface forcing the flow to separate into two separate
vortices.

1.     
At very low Reynolds numbers
balance between the inertial and viscous forces exists in the expression of
Reynolds number. This is called as the Stokes flow whose characteristics are
almost perfect symmetrical streamlines but due to domination of viscous forces,
a lot of drag is experienced.

From figure 2 we can observe that many different
regimes exist. These can be explained as:

 

Figure 2: Coefficient of drag against Reynolds number
for a circular cylinder.

 

From vector
calculus, it is shown that the curl of a gradient is equal to zero, therefore. This also means that the vorticity, or the curl of the
velocity field is zero, i.e. . Hence, potential flow is given by the fact that the
velocity field is equal to the gradient of the velocity potential,. The inviscid assumption gives rise to the d’Alambert
paradox which, hence, results in a cylinder with zero drag. Real flow is viscid
which was a correct observation of Sir Prandtl has a boundary layer which
separates causing drag due to adverse pressure gradient. Therefore, the
Reynolds number affects the drag and the coefficient of drag, CD, as
it is the factor which determines the boundary layer transition.

 

3.     
Incompressible flow.

2.     
Irrotational flow, and,

1.     
Inviscid flow,

Potential
flow is dictated by three assumptions:

 

Theory

 

Additionally, the solution to d’Alambert
paradox via Prandtl’s viscous effects idea will also be determined by
calculating the lift and drag coefficients of the body while accounting for the
effects of blockages.

 

Figure 1: Smoke tunnel visualisation of flow past a
circular cylinder at high order Reynolds number.

 

d)     
Correlate the
pressure distribution with flow visualization images recorded.

c)     
To identify the
point of boundary-layer separation and,

b)     
To calculate form
drag and form drag coefficient by integration.

a)     
To determine the variation of
pressure over the cylinder in a dimensionless form for a chosen range if
Reynolds number.  

The objectives
of the experiment are:

    

 

 

    

Introduction

 

This experiment
depicts that the potential flow theory is invalid for flow around a circular
cylinder and it help to determine the effects on drag due to a change in the
Reynold’s number. The mean and fluctuating pressure distributions were measured
for long smooth and rough surfaced cylinders. The presence of free stream
turbulence at Reynolds number of order 105 suppressed the coherent
vertex on the smooth cylinder and led to the formation of a complex field of
pressure in which the mean pressure distribution was almost found to be
independent of the Reynolds number whereas in the case of rough surfaced
cylinders the pressure distribution was different in the laminar and turbulent
streams. But when the Reynolds number was increased to the order of 107 the
pressure distributions for both the cylinders i.e, smooth and rough surfaced,
was found to be the same.

    

 

    

Abstract

 

 

 

 

 

 

 

 

 

 

 

 

Sr.
No.

Content

Page
Number

1.     
 

Abstract

2

2.     
 

Introduction

2

3.     
 

Theory

3

4.     
 

Experimentation apparatus, instrumentation
and methods

6

5.     
 

Procedure

11

6.     
 

Results

11

7.     
 

Error Analysis

14

8.     
 

Conclusion

14

9.     
 

References

14

 

Table
of Contents