• 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)

    Prediction I predict that the longer the wire is, the more resistance there is. I predict this as the longer the wire is, the longer the crystal lattice is, and therefore the more atoms there are. This is shown in the diagram below.

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

    Extra care should be taken when dealing with the measuring cylinder such preventing it from breaking. Table of results Set 1, Experiment Temperature Difference in density (sphere & syrup) (kg m-3) Time it took (s) Distance travelled (cm) Velocity (ms-1)

  1. Investigation into the effect of temperature on viscosity

    27.2 30.6 27.5 28.4 46.2 290 (17�C) 14.6 14.9 14.7 14.7 24.0 293 (20�C) 9.1 9.5 9.5 9.4 15.3 296 (23�C) 5.7 5.6 9.7 7.0 11.4 299 (26�C) 4.3 4.2 4.3 4.3 7.0 303 (30�C) 3.3 3.5 3.9 3.6 5.8 While carrying out the experiment an unexpected recording was made at 284K (11�C).

  2. Practical Investigation Into Viscosity

    He was not just a scientist, but also the prototype of the modern engineer. In his work can be seen the rigorous error checking that set the standards for later workers. Although Reynolds is best known for his number, few fields of science and engineering are not touched with his life's work.

  1. Measuring the Viscosity of Honey

    the honey put inside the cylinder can be measure easily using (mL) units, which are equal to cm3 . Then the mass of the Cylinder with the honey inside it should be measured also as exact as possible. So that the honey's mass could be found without losing any drop of it .

  2. Investigation into Friction.

    Apparatus * 10 N masses * Smooth hardboard * Rough hardboard * Wooden block of known mass * Force meter calibrated in Newtons * String Method 1. The apparatus was set up as shown in Fig 2. 2. The smooth hardboard was used first as the bottom surface.

  1. Investigating the viscosity of liquids.

    will push the object upwards until it is only partially immersed and displaces exactly its own weight of fluid. On the other hand, if the upthrust on the fully immersed object is less than the object's weight, then there is a net downward force and consequently the object sinks.

  2. Liquid Friction.

    Both these percentage changes show how much smaller the coefficient of viscosity was. radius viscosity viscosity viscosity viscosity (m) ?? ? ? ? No Corrections Ladenburg correction for walls Ladenburg correction for finite cylinder Goldstein correction for inertia 7.90E-04 1.2586 1.2016 1.2553 1.2559 1.59E-03 1.2955 1.1827 1.2887 1.2748 1.96E-03 1.3858

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