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

.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