Visualization of potential in a flow

8/18/2019 Visualization of potential in a flow

1/17

AM2540 lab report:

Topic:Visualization of potential flows

Experiment 1: Study of potential flows around a cylinder.

Experiment 2: Study of Vortex Shedding around a cylinder.

Submitted by Group 15

ME14B064: Sourav Debnath

ME14B065: K. S. Sourya Varenya

ME14B066: Srikanth Gummadavalli

ME14B067: Surya Varun


2/17

EXPERIMENT 1: STUDY OF POTENTIAL FLOWS AROUND ACYLINDER.

Aim:

The objective of the experiment is to study potential flows around a cylinder.Qualitative stream line pattern is to be recorded for the cylinder andcompare it with theoretical model.

Theory :

1. Stream function: the difference between the stream function values atany two points gives the volumetric flow rate (or volumetric flux)through a line connecting the two points.

For defining the stream function, the flow velocity components willhave to be:

= and = − For a streamline, the value of this stream function is constantthroughout.

2. The potential flow solution for the stream function for flow past acircular cylinder centred at origin in r - θ coordinates is=r sin()1−

3. Uniform upstream velocity is calculated by:

= 4. For calculating the difference in stream function between twoconsecutive streamlines at the upstream uniform velocity region, thefollowing approximation can be done:

= ≈ΔΔ


3/17

Between any two streamlines, Δ will be constant. We will measure the Δ between two consecutive streamlines and compare with theoretical model

Experimental setup :

The experimental setup consists of two sections of a tank, betweenwhich the flow is regulated. At the outlet of the pump, a flowmeteris installed to regulate the inlet flow. Two glass sheets are placed ontop of the tank surface to create the test section. The separationbetween the two glass-sheets is approximately 2 mm. Water is madeto flow between the two sections of the tank, through the testsection. Liquid dye is contained in a separate reservoir and isinjected between the glass sheets through a needle. The dye is usedto visualize the flow.


4/17

Procedure :

1. Fill the reservoirs with water.

2. Insert the specimen in the gap between the glass sheets afternoting its dimensions.

3. Fill the Dye reservoir at the side with the Dye.

4. Adjust the stop cock for the desired low flow rate to avoidunsteadiness.

5. Illuminate from behind using diffuse light and take aphotograph, including the specimen and the upstream regionwhere the stream lines are parallel in the photograph.

6. Measure the flow rate.

7. Repeat the procedure for other specimens, drain the water &dye solution after the experiment


5/17

Observations and Conclusions:

Photoshop has been used to bring contrast in the actual image sincechanging the threshold in the Matlab wouldn ’t eliminate the shadows.

Greyscale image of streamlines only filtering the yellow and red colour.

Jet map applied to Binary Stream of the picture.


6/17

Then the data has been analysed at θ = 90o 1. Qualitative analysis for circular cylinder:

Q = 1000 L/hour

= 2.78 × 10 -4 m 3 /sec

Width (w) = 600mm

Depth (d) = 2mm

Diameter (cylinder) = 6.24 cm

= =0.2317 /

2. Image analysis:

=19124 = 0.153

Here we have 5 streamlines and hence we can measure 4 values as differencebetween for different streamlines.

d = 59.44mm

∆ mm) ∆ x10 -3) 17.17 3.9614.40 3.3219.77 4.5618.23 4.21


7/17

From the equation =r sin()1− ∆ mm) ∆ x10 -3) 17.17 5.3214.40 3.9819.77 5.1418.23 4.56


8/17

Result:

The plot obtained from the theoretical model

=r sin()1− Is as follows:

The upstream velocity is =0.2317 / Comparing the ∆ from experiment and theoretical model,

. ∆ x10 -3) ∆ x10 -3) 1-2 5.32 3.962-3 3.98 3.323-4 5.14 4.56

4-5 4.56 4.21


9/17

EXPERIMENT 2: STUDY OF VORTEX SHEDDING AROUND ACYLINDER.

Aim:

To study the dependence of non- dimensional vortex shedding frequency onthe Reynolds number for cylindrical bodies of different diameters.

When, 900 < Re < 1.3 × 10 5

Apparatus Used :

1. A tank 2.5m × 1.5m having depth of 150mm.

2.

At one end we have two sets of Aluminum disks which are connectedto a motor.3. Those are rotating in opposite directions with same speed horizontally

and creating a flow.4. The flow is guided to the test section where cylinders of different

diameters can be placed.5. The flow rate is adjusted by controlling the speed of motor.6. With this apparatus we can produce 0.01 m/s to 0.2 m/s flow speed.7. Water (made black in color by dissolving a dye), is used as the fluid

and Aluminum powder (which is in white color) is used as the tracer.

Theory :

1. the flow of fluid may be complicated as its Reynolds number go onincreasing

2. At low Re (< 1) there will be symmetry in the flow of fluid around thebody.

3. Vortex: In fluid dynamics, a vortex is a region, in a fluid medium, in

which the flow is mostly rotating on an axis line, the vortical flow thatoccurs either on a straight-axis or a curved-axis.The vorticity (the curl of the flow velocity) is very high in a core regionsurrounding the axis, and nearly nil in the greater vortex; and thepressure drops with proximity to the axis of the vortex.

4. Karman Vortex Street:It is a repeating pattern of swirling vortices caused by the unsteadyseparation of flow of a fluid around blunt bodies.

5. When Re >80, the successive vortices will be produced around thebody which have opposite sense of circulation.


10/17

6. The circulation around the cylinder changes sign periodically resultingin an oscillating lateral force on the cylinder. ( as shown in fig .)

7. Strouhal number:The frequency of the vortex shedding known as the Strouhal number(non-dimensional number).

S = f / (U∞/D),f = frequency of vortex shedding.D = diameter of the cylinder.

U∞= free stream velocity of the fl The Strouhal number for a cylinder is typically 0.2 over a wide rangeof flow velocities. It depends on the body shape and on the Reynoldsnumber.The objective of the experiment is to explore the dependence of thisnon- dimensional vortex shedding frequency on the Reynolds numberfor 900 < Re < 1.3 × 105.

8. Resonance:In practical life, if the frequency of this vortex shedding is close to thenatural frequency of the object, resonance could occur, resulting instructural damage to object.The Strouhal number relates the frequency of shedding to the velocityof the flow and a characteristic dimension of the body (diameter in thecase of a cylinder). The phenomenon of lock-in happens when thevortex shedding frequency, n, becomes close to a natural frequency of

vibration of the structure. When this happens large and damagingvibrations can result


11/17

Procedure:

1. Switch on the motor and using the knob increase the speed of rotationof disks till a particular speed is reached.

2.

Mark a certain distance on the wooden planks, to calculate the speedof flow (U∞).3. For a particle which is in the center of flow observe the timing to crossthat distance.

4. Repeat this observation three times to calculate the speed of flow.5. Now place the cylinder one in the center of the flow.6. Count the number of proper vortices generated in 10seconds of time

at the back of cylinder (or) Count the number of vortices crossing thescale. Repeat this three times. ( As shown in fig .)

7. Now put cylinder two at the center, count the vortices just like the

above one.8. Repeat the same for cylinder three.9. Analyze the same with two another speeds of disks. Tabulate the data


12/17

Observations:

I.

First time Second time Third time

Average(U∞

Distance(m) 0.86 0.86 0.86 0.076Time (s) 10.68 11.81 11.81Speed(m/s)

0.081 0.073 0.073

Re = 73416

Firsttime Secondtime Thirdtime Average Frequency(f) St=f/(U∞/D No ofvorticesfor D=2cm

8 7 6 7 0.7 0.1842

No ofvorticesfor D=

3.5cm

5 5 5 5 0.5 0.2303

No ofvorticesfor D=5cm

3 3 3 3 0.3 0.1974

II.

First time Second time Third time

Average(U∞

Distance(m) 0.86 0.86 0.86 0.086Time (s) 10.34 9.26 10.39Speed(m/s)

0.083 0.093 0.083

Re = 83076


13/17

Firsttime

Secondtime

Thirdtime

Average Frequency(f) St=f/(U∞/D)

No ofvortices

for D=2cm

8 8 7 7.67 0.767 0.1784

No ofvorticesfor D=3.5cm

6 5 5 5.33 0.533 0.2170

No ofvorticesfor D=

5cm

5 4 4 4.33 0.433 0.2517

III.

First time Second time Third time Average(U∞ Distance(m) 0.86 0.86 0.86 0.163Time (s) 5.42 5.35 5.13

Speed(m/s) 0.159 0.161 0.168

Re = 157458

Firsttime

Secondtime

Thirdtime

Average(f) Frequency(f)

St=f/(U∞/D No ofvortices

for D=2cm

12 11 11 11.33 1.133 0.1390

No ofvorticesfor D=3.5cm

9 8 9 8.67 0.867 0.1862

No ofvorticesfor D=

5cm

7 6 6 6.33 0.633 0.1942


14/17

Precautions:

1. Make sure that the two disks rotate with same speed, sometimes thecable gets loose.

2. With non-wet hands, slowly increase the speed of disks.3. Don’t count the eddy vortices. 4. To calculate the free stream velocity of the fluiwill observe the centered particle of the fluid flow.

5. Place the cylinders exactly in the center of fluid flow.6. Make sure two at least three persons will be sharing the work. (One to

count the vortices, one on the clock and another to note down thevalues.)

Sources of error:

1. Error in observing time2. Error in distance taken to measure the speed of flow.3. Error in counting number of vortices


15/17

Applications:

1. In designing the back shape of car.

2. In designing structures: In low turbulence, tall buildings can producea Kármán street so long as the structure is uniform along its height. Inurban areas where there are many other tall structures nearby, theturbulence produced by these prevents the formation of coherentvortices.Periodic crosswind forces set up by vortices along object's sides canbe highly undesirable, and hence it is important for engineers toaccount for the possible effects of vortex shedding when designing a

wide range of structures, from submarine periscopes to industrialchimneys and skyscrapers.

3. In designing the structure of chimney.


16/17

Result:

2. Finding St. No. using Empirical relation:

St= f ( Re) = 0.198 – (3.9/ Re) ; valid over 250 < Re < 2x10 5

Re St 2 cm) St 3.5 cm) St 5 cm) St average) Theoretical

73416 0.1842 0.2303 0.1974 0.2040 0.19794

83076 0.1784 0.217 0.2517 0.2157 0.19795

157458 0.139 0.1862 0.1942 0.1731 0.19797


17/17

Plot of Re vs trouhal’s no. ( t)

0

0.05

0.1

0.15

0.2

0.25

0.3

7 3 , 4 1 6 8 1 , 0 8 6 8 8 , 7 5 6 9 6 , 4 2 6 1 0 4 , 0 9 7 1 1 1 , 7 6 6 1 1 9 , 4 3 6 1 2 7 , 1 0 6 1 3 4 , 7 7 7 1 4 2 , 4 4 7 1 5 0 , 1 1 6

St(2 cm)

St(3.5 cm)

St(5 cm)

Theoretical

Date post:	07-Jul-2018
Category:	Documents
Upload:	sourya-varenya
View:	219 times
Download:	0 times

Visualization of potential in a flow

Documents