mechanical engineering lab. 2

Department of Mechanical Engineering

Mechanical Engineering Lab. 2

Velocity Measurements

Professor: Wontae Hwang ([email protected])T.A: Hoonsang Lee (880-7118, [email protected])

Museong Kim (880-7118, [email protected])


Non-dimensional variables used in fluid mechanics

U : freestream velocity

L : characteristic length

ν : kinematic viscosity

ρ : density

A : frontal area

f : vortex shedding frequency

212

212

Re / /

/

/ ( )

/ ( )

D

L

UL UL

St fL U

C Drag U A

C Lift U A


Strouhal number – Karman vortex shedding

Fv

t

Fv

0

T

U

- Van Dyke, “Album of fluid motion”

Force is oscillating by Karman vortex shedding,

which also has a specific frequency.

From measured data,

T : force oscillating period

f : force oscillating frequency

and,

Here,

L : Characteristic length

D : Diameter of cylinder

1f

T

fLSt

U

L D

https://en.wikipedia.org/wiki/Strouhal_number


Resonance due to Karman vortex shedding – Tacoma bridge


Flow Measurement (or Visualization)

Intrusive

Flow Measurement (Visualization)

Non-Intrusive

Quantitative QualitativeQuantitative

Shadowgraph

Schlieren

Dye Particle

LDV PIVPitot Tube Hot Wire

Anemometer


Pitot tube

Hot-wire anemometer

Laser Doppler Velocimetry(LDV)

Particle Image Velocimetry(PIV)

Velocity Measurements


Pitot tube

21

2

PV gz const

Pst : Stagnation pressure

Ps : Static pressure

γ : Specific weight (=ρ×g)

g : Gravitational acceleration

Pitot tube mounted on an airplane

V = 2g(Pst - Ps )

g

Can pitot tubes measure turbulent flow?

Yes, but only mean flow, not turbulence statistics (e.g. fluctuations)


Hot-wire anemometer

Hot-wire Constant Temperature circuit

Wheat stone bridge system

Hot-wire probe

2

w

w

t

Heat generated byelectric resistor = Heat transfer byconvection

( )

I : hot wire current

R : hot wire resistor

T : hot wire temperature

T : temperature of fluid

h : convection coefficient

A : area

V : v

w w tI R hA T T

0 1

elocity

h C C V

The wheat stone bridge measures

the variation of resistance.


Flow Measurement (or Visualization)

Intrusive

Flow Measurement (Visualization)

Non-Intrusive

Quantitative QualitativeQuantitative

Shadowgraph

Schlieren

Dye Particle

LDV PIVPitot Tube Hot Wire

Anemometer


LDV (Laser Doppler Velocimetry)

LDV measures the velocity of gas or liquid by measuring the velocity of small (1

μm diameter) particles introduced into the flow as the particles cross pattern set up

by 2 intersecting laser beams.


PIV (Particle Image Velocimetry)

PIV is the simultaneous measurement of particulate (which follows the

background flow faithfully) velocity vectors at many points, using optical

imaging techniques. The measurements are usually made in planar “slices”

of the flow field.

Particle + Image → Velocity

Re = 7000

4.80

4.39

3.98

3.57

3.16

2.76

2.35

1.94

1.53

1.12

0.71

0.31

-0.51

-0.92

-1.33

-1.73

-2.14

-2.55

-2.96

-3.37

-3.78

-4.18

-4.59

-5.00


Flow characteristics around

a circular cylinder


Karman Vortex (Shedding, Street)


Example of Karman Vortex (Mt. Halla)

NASA, MODIS Rapid Response System


Separation


Bubble length

Re = 3900

Recirculation Bubble

(Formation region)

Length

Separation point

θ

Separation angle

Dividing streamline


Flow characteristics around

a square cylinder


Instantaneous vorticity contour

Re=10000


Mean field

Re=10000

Recirculation Bubble

Length

Fixed separation point


The effect of incidence angle


Introduction to PIV


particle image velocimetry

Successive particle images Velocity vector field


Experimental apparatus

Laser: High power LASER GAM-3000

-3W Green Laser

Camera: Motion Analysis Camera HHC X3

-Resolution : 800X600, Mono

-frame-rate : 1,000fps at full resolution

-exposure time : Min 1ms

High-speed

camera


Seeding particle

Traceability

Small tracer particles must follow

closely the fluid movement

Flow

Water flow : 1 – 100 um solid particle

hollow glass, aluminum, polystyrene

Air flow : 1 – 5 um atomized liquid particle

olive oil, lubricant

2-3 pixel occupancy is optimal in image plane

cylinder

Laser sheet

High-speed

camera


Raw images


Getting velocity vectors



Interrogation Window (IW)

조사구간


Sample image

(800 pixels × 600 pixels)

Interrogation window

One pixel


Sample image


16 pixels

16 pixels





Sample image


32 pixels

32 pixels





• For successful PIV processing,

DI, ∆t, Umax and Vmax should be chosen

to satisfy “the ¼ law”.

CCD camera

Laser

U

∆t

Field of view


DI

PIV – The ¼ law

∆t : too large

∆t : too small

T+∆t

T+∆t T

T


|Umax ∆t| < DI /4

|Vmax ∆t| < DI /4

• For successful PIV processing,

DI, ∆t, Umax and Vmax should be chosen

to satisfy “the ¼ law”.

CCD camera

Laser

U

∆t

Field of view


DI

PIV – The ¼ law

“The ¼ law”

where

Umax, Vmax : the maximum velocity

∆t : time interval between two images

DI : the size of interrogation window


Case 1 Case 2

PIV – The ¼ law

DI

1

2

1

2

Interrogation window (size: DI)



Case 1

|∆x1| < DI /4,

|∆y1| < DI /4

Case 2

|∆x2| > DI /4,

|∆y2| > DI /4

PIV – The ¼ law

DI

1

2

∆x1

∆y1

1

2∆x2

∆y2



“The ¼ law”

Case 1

|∆x1| < DI /4,

|∆y1| < DI /4

Case 2

|∆x2| > DI /4,

|∆y2| > DI /4

PIV – The ¼ law

DI

1

2

∆x1

∆y1

1

2∆x2

∆y2


Vector Processing

i

j

i

j

T+∆t T



Vector Processing

i

j

i

j

0 1 2 3 4

0

1

2

3

4


Vector Processing

IW i

j

0 1 2 3 4

0

1

2

3

4

1


IW i

j

Vector Processing

0 1 2 3 4

0

1

2

3

4

1 1


IW i

j

Vector Processing

0 1 2 3 4

0

1

2

3

4

1 1

2


IW i

j

Vector Processing

0 1 2 3 4

0

1

2

3

4

1 1

20


IW i

j

Vector Processing

0 1 2 3 4

0

1

2

3

4

1 1

20

1


IW i

j

Vector Processing

0 1 2 3 4

0

1

2

3

4

1 1

20

1 1


Displacement = (1,1)

IW i

j

Vector Processing

R(p,q)

p

q

0 1 2 3 4

0

1

2

3

4

1 1

21

1 1 0

1

1

The goal of vector processing is to find the most

matched points between the two interrogation windows!!

R p q IW i j SW i p j qi

M

j

N

( , ) ( , ) ( , )

0

1

0

1


Purpose

• To understand the principle of Particle Image velocimetry

• To measure and analyze the velocity field around a circular cylinder

• To measure and analyze the velocity field around a square cylinder


Procedures

Experiment A

• Fill water in the water tunnel.

• Turn on the power, laser and computer.

• Mix the particles with surfactant.

• Turn on the pump and increase the power of pump to flow water.

• Execute the camera program and observe the field of view.

• Execute the PIV program and get the velocity data.

• Repeat the above procedures with changing the power of pump.

• Velocity field data will be uploaded on the ‘maelab’ after experiments.

(http://maelab.snu.ac.kr/)

http://maelab.snu.ac.kr/


Exp. A : Introduction to PIV

< Water tunnel, test-section > < Field of view >

800px, 47mm

60

0p

x, 3

4m

m

< Interrogation window>

We can get one velocity

vector from one

interrogation window • ¼ Law (rule) ?

“Particle displacement should not

exceed ¼ of the interrogation

window size”

: A rule of thumb

① Interrogation Window

② ¼ Law

Laser sheet DI = 32px

DI = 32px

• Real size of interrogation window

800px : 47mm = 32px: DI , DI = 47x32/800 =1.88mm

• Applying ¼ law

Dx £ 14 DI =1.88 / 4 = 0.47mm

Dx £ 14 DI

Assume U¥ = 40mm/s

40 ´ Dt £ 0.47, Dt £ 0.01s

Camera speed: 100 fps

Flow-vision: 10000ms


Exp. A : Introduction to PIV

③ Pump calibration

Pump output vs Free-stream velocity (5, 10,15, 20)

Pump output

[Hz]5 10 15 20

④Averaging velocity field

• Picture 300 images

• Obtain 150 instantaneous velocity fields

…

img 1 img 2 img 3 img 4 img 299 img 300

• Calculate 1 averaged velocity field (Matlab)

How can we get free-stream velocity from PIV data?

U¥

[mm/s]


Results and Discussions-Exp. A

<Report> -Recommended plotting software: Tecplot

1. Explain the experimental setup and the procedure of PIV technique.

2. Calculate and plot the time-averaged velocity field from vector

fields. (Use Matlab for the calculation.)

3. Plot the frequency of pump versus the measured velocity with PIV,

using the results from procedure 1 and obtain linear curve-fitted relation.

(The result will be also used for Experiments B and C.)


Procedures

Experiment B

• Set up a 5mm circular cylinder.







• Drain the water.

• Repeat the above procedures with changing a circular cylinder from 5mm to 8.2mm.

• Copy the velocity data to your USB.


Exp. B : Flow-field past a circular cylinder

① Experimental setup

• 2 circular cylinders

• Diameter (D) : 5mm, 8.2mm

•

• Using ¼ law & the results from Exp. A,

obtain ∆𝑡 and the pump output for given Re #

② Pre-requisites

• Streamline, streakline, pathline

• Vorticity

(3-D)

• Non-dimensionalization

(2-D)

U¥Re ,d

U D fDSt

U

1 1

2 2

i j k

vx y z

u v w

1

2z

v u

x x

, , , , ?x y u v

x y u vD D U U

D



③ Instantaneous flow-field past a circular cylinder

ϴL

: Stagnation point: Separation point

ϴ: Separation angle

L : Recirculation length

③Averaged flow-field past a circular cylinder

Karman vortex sheddingf

f : vortex shedding frequency

U¥

U¥



④ Boundary-layer separation (White, Ch. 7)

x,u

y,v

• By viscosity (no slip condition)

boundary layer occurs

• Du/dx=0, separation point

• Due to adverse pressure

gradient

“u profile”

0dp

dx 0

dp

dx

2

2

1

wall

u dp

y dx


Results and Discussions - Exp. B

<Report> - plotting program: Matlab

1) Calculate and plot the time-averaged velocity field from vector fields.

2) Obtain the recirculation region and calculate the recirculation length using the

result from procedure 1.

3) Plot the time-averaged vorticity contours from the time-averaged velocity, and

compare them with the instantaneous fields.

4) Plot the time-averaged streamlines and compare them with the instantaneous

ones.

5) Calculate the Strouhal (St) number.

6) Calculate the turbulent kinetic energy of each experiments and plot the results.

Measure a transverse distance between the locations of peak points and a stream-

wise distance between the trailing edge of cylinder and peak point. Discuss this

results.

7) Repeat the above procedure 1~6 for the other cylinder. Compare the results of

two experiments, in terms of the dynamic similarity in fluid mechanics.

8) Determine whether the flows are turbulent or laminar. (Can they be

determined?) Provide your supporting arguments with the definition of turbulent

flow and laminar flow


Procedures

Experiment C

• Set up a square cylinder

which incidence angle is 0 degree.







• Drain the water.

• Repeat the above procedures with changing the incident angle of rectangular cylinder.

• Copy the velocity data to your USB.


① Square cylinder

• Characteristic length :

length of one side(square, triangle)

Exp. C: Flow-field past a square cylinder

ϴU¥

45

ϴ: Angle of attack

5 mm

0

U¥


② Flow characteristics

Fixed separation point

Recirculation region


<Instantaneous flow field>

<Time-averaged flow field>


③ Drag coefficient (𝐶𝐷)

Square :

Triangle :


0 45vs

0 60vs

2

2

1

2

C1

2

D

D

DragC

U A

Drag

U l

(3-D)

(2-D)

• Research papers and compare CD according to the angle of attack.

• Explain the difference of CD according to the angle of attack, based on the

PIV result.

Department of Mechanical & Aerospace Engineering

Results and Discussions-Exp. C

<Report> - plotting program: Matlab

1) Calculate and plot the time-averaged velocity field from vector fields

2) Obtain the recirculation region, recirculation length and separation point using

the result from procedure 1.

3) Plot the time-averaged vorticity contours from the time-averaged velocity, and

compare them with the instantaneous fields.

4) Plot the time-averaged streamlines and compare them with the instantaneous

ones.

5) Calculate the Strouhal (St) number.

6) Calculate the turbulent kinetic energy of each experiments and plot the results.

Measure a transverse distance between the locations of peak points and a stream-

wise distance between the trailing edge of cylinder and peak point. Discuss this

results.

7) Discuss the experimental results of two different incidence angles.

8) Which 𝐶𝐷 is bigger? (In order to obtain 𝐶𝐷 of the cylinders, refer to the relevant

papers including similar Re data.) Based on your experimental data and literature

survey, explain the reason why the drag of that cylinder is larger than the other?


Scoring Standards


Evaluation

Velocity experiment

Total score: 25

Report: 10 Quiz: 5 Attitude: 10

Exp. A, B, C Each 3 points

Preliminary report X

Result report (due a week)

At class time or 301-1215

Exp. A - 3 problems

Exp. B - 2 problems

Exp. C - 2 problems

Lateness -1 point

Absence -2 points

Two lateness = One absence

mechanical engineering lab. 2

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