• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12
  13. 13
    13
  14. 14
    14

Experimental Techniques; Analysis of Boundary Layer Data.

Extracts from this document...

Introduction

Joseph Gransden        Case Study 3: Experimental Techniques        10/05/07

CASE STUDY 3: Experimental Techniques; Analysis of Boundary Layer Data

By Joseph Gransden

Department of Mechanical Engineering, Nottingham University

The following report is an experimental study of Boundary layer data obtained using hot-wire anemometry. In particular, the report presents and analyses mean velocity and turbulence intensity profiles as well as turbulence statistics. The aim is to discover the best methods of presenting and analysing data in order to determine and explain some of the turbulence phenomena by discussion of the data and its implications.

RESULTS  

Firstly the hot wire anemometer output voltage is calibrated using King’s Law against the velocities that are initially measured with a pitot tube or vane anemometer.

Hot-wire Calibration Data

Mean

Mean

Hot-wire

Velocity

Voltage

E

E2

U

U1/2

Volts

m/s

1.4227

2.02407529

1.02

1.00995

1.4466

2.09265156

1.222

1.105441

1.4687

2.15707969

1.441

1.200417

1.5002

2.25060004

1.785

1.336039

1.5204

2.31161616

2.029

1.42443

1.534

2.353156

2.198

1.482565

1.5507

2.40467049

2.434

1.560128

1.5684

2.45987856

2.689

1.639817

1.5837

2.50810569

2.928

1.71114

1.5979

2.55328441

3.16

1.777639

1.6115

2.59693225

3.407

1.845806

1.6252

2.64127504

3.656

1.912067

1.6366

2.67845956

3.886

1.971294

1.6488

2.71854144

4.132

2.032732

1.6599

2.75526801

4.378

2.092367

1.6712

2.79290944

4.629

2.151511

1.6814

2.82710596

4.869

2.206581

KINGS LAW

E2 = A + B(U)1/2

Where, B = slope =

0.6718895

from chart overleaf

and A = y - intercept =

1.35315794

Therefore,

E2 = 1.353 + 0.672(U)1/2

image00.png

This calibration then allows for the mean and fluctuating velocities (turbulence intensity) to be determined.

...read more.

Middle

The boundary layer thickness has been approximated here using the definition provided by F.M White. That is:

Boundary Layer thickness,        δ = ywhere u = 0.99U0

U/U0

dy

1-U/U0

Trap Areas

U/U0*(1-U/U0)

Trap Areas

y

u'/U0

(y/δ)1/7

mm

0.088077447

0.3

0.91192

0.13678838

0.080319811

0.01204797

0.005

0.018977

0.46933

0.103154735

0.1

0.89685

0.09043839

0.092513835

0.00864168

0.0067

0.045354

0.48902

0.124079962

0.1

0.87592

0.08863827

0.108684125

0.0100599

0.0084

0.063321

0.50486

0.15541488

0.1

0.84459

0.08602526

0.131261095

0.01199726

0.01

0.079471

0.51818

0.182124266

0.1

0.81788

0.08312304

0.148955018

0.01401081

0.0117

0.098874

0.52972

0.211948564

0.1

0.78805

0.08029636

0.16702637

0.01579907

0.0134

0.104896

0.53992

0.273886695

0.2

0.72611

0.15141647

0.198872773

0.03658991

0.0167

0.12431

0.55741

0.332334653

0.2

0.66767

0.13937787

0.221888332

0.04207611

0.0201

0.14249

0.57211

0.380250394

0.3

0.61975

0.19311224

0.235660032

0.06863225

0.0251

0.152747

0.59065

0.462601881

0.5

0.5374

0.28928693

0.248601381

0.12106535

0.0334

0.151193

0.61543

0.517238474

0.5

0.48276

0.25503991

0.249702835

0.12457605

0.0418

0.145951

0.63536

0.567915838

0.5

0.43208

0.22871142

0.245387439

0.12377257

0.0502

0.139529

0.65213

0.599502832

0.5

0.4005

0.20814533

0.240099186

0.12137166

0.0585

0.129714

0.66665

0.615678193

0.5

0.38432

0.19620474

0.236618556

0.11917944

0.0669

0.125845

0.67948

0.61744223

0.5

0.38256

0.19171989

0.236207323

0.11820647

0.0752

0.117982

0.69101

0.63524808

0.5

0.36475

0.18682742

0.231707957

0.11697882

0.0836

0.117829

0.70149

0.658847958

1

0.34115

0.35295198

0.224767326

0.22823764

0.1003

0.105211

0.72001

0.672233025

1

0.32777

0.33445951

0.220335785

0.22255156

0.117

0.102512

0.73604

0.680154293

1

0.31985

0.32380634

0.217544431

0.21894011

0.1337

0.102262

0.75021

0.684370372

1

0.31563

0.31773767

0.216007566

0.216776

0.1505

0.096433

0.76294

0.699011857

1

0.30099

0.30830889

0.210394281

0.21320092

0.1672

0.099254

0.77451

0.715766

2

0.28423

0.58522214

0.203445033

0.41383931

0.2006

0.091777

0.79495

0.739622481

3

0.26038

0.81691728

0.192581067

0.59403915

0.2508

0.095419

0.8207

0.780600965

5

0.2194

1.19944139

0.171263099

0.90961041

0.3344

0.088862

0.85513

0.816117886

5

0.18388

1.00820287

0.150069482

0.80333145

0.418

0.084794

0.88283

0.850451416

5

0.14955

0.83357674

0.127183805

0.69313322

0.5016

0.07836

0.90613

0.880719308

5

0.11928

0.67207319

0.105052808

0.58059153

0.5851

0.074942

0.9263

0.912188242

5

0.08781

0.51773112

0.080100853

0.46288415

0.6687

0.067026

0.94414

0.938074298

5

0.06193

0.37434365

0.058090909

0.34547941

0.7523

0.060058

0.96016

0.956916358

5

0.04308

0.26252336

0.041227442

0.24829588

0.8359

0.052861

0.97472

0.974824407

5

0.02518

0.17064809

0.024541782

0.16442306

0.9195

0.044776

0.98809

0.990586663

5

0.00941

0.08647232

0.009324726

0.08466627

1.0031

0.030344

1.00044

0.997052505

5

0.00295

0.03090208

0.002938807

0.03065883

1.0867

0.019951

1.01195

0.99764158

5

0.00236

0.01326479

0.002352858

0.01322916

1.1703

0.014744

1.02272

1.001180482

5

-0.0012

0.00294484

-0.00118188

0.00292745

1.2539

0.009536

1.03285

1.001180482

5

-0.0012

-0.0059024

-0.00118188

-0.0059094

1.3375

0.007602

1.04242

1

10

0

-0.0059024

0

-0.0059094

1.5047

0.00565

1.0601

1

10

0

0

0

0

1.6719

0.005635

1.07618

Bulk Velocity, U0 =

2.44780599

0.99U0 =

2.42332793

Boundary Layer Thickness =

59.81390261

Displacement Thickness

δ* =

10.80487536

mm

Momentum Thickness

θ =

7.500002088

mm

Shape Factor

H =

1.440649647

image15.png

image16.png

To find the correct logarithmic velocity profile the Clauser plot technique was employed varying the friction velocity, u* to ‘match’ the logarithmic region of the profile to the known log law. This provided a graphical means of determining u*. Also on the following is the linear viscous sublayer plot of u+ = y+.

...read more.

Conclusion

  From the PDF a skewness of 1.102 and kurtosis of –0.137. These are analogous to the asymmetry and flatness of the plot respectively. It is already known that in free shear flows the PDF is not Gaussian. The skewness is to the left, hence there is higher frequency of negative streamwise velocities at the position y+ = 2 therefore suggesting maybe a high influence of spanwise, vortical structures in the linear viscous sublayer.  As we are concerned with the region close to the wall the spanwise vortices are in fact induced by the zero velocity retardation at the wall and the shear layer formation.

It is also worth noting that the negative sign on the kurtosis has no significance.

References

  • KLINE et al (1967) “ The structure of turbulent boundary layers”. J of Fluid Mech. Vol 30 pp 741- 773
  • CHOI K-S (2001) “ Boundary layers” Fluid Mechanics 2 notes.
  • WHITE F.M (2000) “Fluid Mechanics”
  • POPE S.B (2000) “Turbulent flows”

...read more.

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Forces and Motion essays

  1. Peer reviewed

    Factors Influencing Resistance of a Wire

    3 star(s)

    This is why wire type very much effects resistance. Temperature of the Wire All atoms vibrate, even in a unit cell when they are tied down with bonds. If the temperature increases so does the rate of vibration. If the atoms are vibrating vigorously then the chances of a collision

  2. Investigation into Friction.

    Graph 2 shows the readings on the force meter (F) in the rough hardboard experiment plotted against the weight being pulled (R). As we can see from Graph 2, there is good correlation of the points. The graph that we have produced is quite similar to the predicted one in

  1. Pressure distribution over a symmetrical airfoil.

    Reynolds number is defined by: RE = Uc/V Where U is the free stream velocity, V is the kinematics velocity and c is the length of the chord.

  2. The effect of the temperature on the viscosity of the syrup.

    Release the sphere inside the syrup as well as starting the stop watch 12) Stop the stop watch as soon as the sphere crosses the line that is marked at the bottom of the measuring cylinder and record the time 13)

  1. Practical Investigation Into Viscosity

    When Re is low, laminar flow dominates and drag is approximately equal to speed X size X dynamic viscosity giving a linear rise in drag with speed (and a squaring of power with speed). On the other hand, when Re is large drag is approximately equal to Speed2 X Size2 X density!

  2. Investigating the viscosity of liquids.

    Moreover, during constant speed, the net forces acting on the ball bearing is zero, and the following equation is valid and can be applied: Upthrust (U) + Viscous Drag (F) = Weight (W) 4?r3?fluidg / 3 6?r?v = 4?r3psteel g / 3 r is the radius of the sphere, ?fluid

  1. Investigation into the effect of temperature on viscosity

    could be measured and the weight/force calculated it makes more sense to keep both the forces (upthrust and ball weight) in the same format to allow them to be easily combined. Ball weight: Mass= 4/3 Pi r3 ?steel Weight of the ball= (4/3 Pi r3 ?steel)

  2. How does height influence velocity.

    The Formula which we will use in the experiment is V = 2GH This shows the speed or velocity will equal the square root of two times gravity times height. The gravity is measured in N/Kg and gravity on earth is 10 N/Kg.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work