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Boundary Layer

TITLE : FLAT PLATE BOUNDARY LAYER

OBJECTIVES

The objective of this experiment are as follows:

To measure the boundary layer velocity profiles and observes the growth of the

boundary layer for flat plate with smooth and rough surfaces.

To measure the boundary layer properties for the measured velocity profiles.

To study the effect of surface roughness on the development of boundary layer.

INTRODUCTION

The concept of boundary layer was first introduced by Ludwig Prandtl, a German

aerodynamicist in 1904. The boundary layer concept provided the link that had been

missing between theory and practice. Furthermore, the boundary layer concept

permitted the solution of viscous flow problems that would have been impossible through

application the Navier-Stokes equation to the complete flow field.

As for flow in a duct, flow in a boundary layer may be laminar or turbulent. There is no

unique value of the Reynolds number at which transition from laminar to turbulent flow

occur in a boundary layer. Among the factors that affect boundary-layer transition are

pressure gradient, surface roughness, heat transfer, body forces and free stream

disturbances.

In many real flow situations, a boundary layer develops over a long, essentially flat

surface. A qualitative picture of the boundary layer growth over a flat plate is shown in

figure 1 below.

Figure 1.1: Boundary layer on a flat plate (Vertical thickness exaggerate greatly)

Boundary Layer

THEORY

Some measures of boundary layers are described in figure 1.2 below.

Figure 1.2 : Boundary Layer thickness definitions

The boundary layer thickness, , is defined as the distance from the surface to the point

where the velocity is within 1 percent of the stream velocity. The displacement thickness,

*, is the distance by which the solid boundary would have to be displaced in a

frictionless flow to give the same mass deficit as exists in the boundary layer.

The momentum thickness, , is define as the thickness of a layer of fluid of velocity, U

(free stream velocity), for which the momentum flux is equal to the deficit of momentum

flux through the boundary layer. The Blasius’s exact solutions to the laminar boundary

yield the following equations for the above properties.

Boundary Layer

Due to the complexity of the flow, there is no exact solution to the turbulent boundary

layer. The velocity profile within the boundary layer commonly approximated using the

1/7 power law.

The properties of boundary layer are approximated using the momentum integral

equation, which result in the following expression.

Another measure of the boundary layer is the shape factor, H, which is the ratio of the

displacement thickness to the momentum thickness, H = */. For laminar flow, H

increases from 2.6 to 3.5 at separation. For turbulent boundary layer, H increases from

1.3 to approximately 2.5 at separation.

EXPERIMENT APPARATUS

Boundary Layer

The experiment set up consists of:

1. Airflow Bench

2. Test Apparatus

3. Total and static tube pressure probes and multi tube manometer.

PROCEDURES

On-off switch

Damper control rod

Plenum outlet

Boundary Layer

1. The apparatus has been set up on the bench as shown on figure 4 uses the flat plate

with the smooth surface for the first part of the experiment.

2. Set the pitot tube about 15mm away from the edge of the central plate.

3. Adjust the position of the central plate to set the measurement plane at the required

distance from the leading edge, say 40mm.

4. Switch on the fan and adjust the air speed to set the free stream air velocity at

medium speed.

5. Reading of the total pressure is measured using the Pitot tube for a range of about

10 points as the tube is traversed towards the plate. Initially the readings should be

almost constant showing that the probe is in the free stream outside the boundary

layer. Should it not be so, go back and start further from the plate.

6. As the pressure begins to fall the increment of advance should be reduced so as to

clearly define the velocity profile. The pressure reading will not fall to zero as the

Pitot tube has a finite thickness. A further indication that the wall has been reached is

that the pressure readings will be constant.

7. Repeat the experiment to set the measurement plane at 150 mm.

8. Repeat the entire experiment for the rough surface.

RESULT AND CALCULATION

Boundary Layer

TABULATION OF DATA AND SAMPLE CALCULATION:

1. Smooth surface with distance from the leading edge, x = 40

Room temperature: 30 C

air = 1.177 kg/m3

= 1.30 x 10-5 m2/s

oil = 784 kg/m3

Free stream velocity, U = m/s

= m/s

= 16.96 m/s

Reynolds number, Rex =

=

= 52184.6

2. Smooth surface with distance from the leading edge, x = 150


Boundary Layer

air = 1.177 kg/m3

= 1.30 x 10-5 m2/s

oil = 784 kg/m3

Free stream velocity U = m/s

= m/s

= 16.96m/s

Reynolds number, Rex=

=

= 195692.3

3. Rough surface with distance from the leading edge, x = 40


air = 1.177 kg/m3

Boundary Layer

= 1.30 x 10-5 m2/s

oil = 784 kg/m3


= m/s

= 18.43m/s

Reynolds number, Rex =

=

= 56718.2

4. Rough surface with distance from the leading edge, x = 150


air = 1.177 kg/m3

= 1.30 x 10-5 m2/s

oil = 784 kg/m3

Boundary Layer


= m/s

= 16.96 m/s

Reynolds number, Re =

=

= 195692.3

TABLE:

Table 1: Tabulation of data for smooth surface with x = 40mm

Micrometer readingy (mm)

Static pressure

manometer,h (mm)

Total pressure

manometer, h (mm)

Differential manometer

heighth (mm)

Free stream

velocity,(m/s)

Reynolds number

Boundary Layer

0 100 122 22 16.96 52184.62 0.767 0.179

0.5 100 126 26 18.43 56707.69 0.705 0.208

1.0 100 128 28 19.13 58861.54 0.680 0.218

1.5 100 128 28 19.13 58861.54 0.680 0.218

2.0 100 128 28 19.13 58861.54 0.680 0.218

2.5 102 130 28 19.13 58861.54 0.680 0.218

3.0 102 130 28 19.13 58861.54 0.680 0.218

3.5 102 130 28 19.13 58861.54 0.680 0.218

4.0 102 130 28 19.13 58861.54 0.680 0.218

4.5 102 130 28 19.13 58861.54 0.680 0.218

Table 2: Tabulation of data for smooth surface with x = 150mm


Static pressure

manometer,h (mm)

Total pressure

manometer, h (mm)


heighth (mm)

Free stream

velocity,U (m/s)

Reynolds number

0 100 122 22 16.96 195692.3 0.767 0.179

Boundary Layer

0.5 100 126 26 18.43 212693.3 0.705 0.208

1.0 100 128 28 19.13 220730.8 0.680 0.218

1.5 100 130 30 19.80 228469.3 0.657 0.225

2.0 100 130 30 19.80 228469.3 0.657 0.225

2.5 100 132 32 20.45 235962.1 0.636 0.232

3.0 102 132 30 19.80 228469.3 0.657 0.225

3.5 102 132 30 19.80 228469.3 0.657 0.225

4.0 102 132 30 19.80 228469.3 0.657 0.225

4.5 102 132 30 19.80 228469.3 0.657 0.225

Table 3: Tabulation of data for rough surface with x = 40mm


Static pressure

manometer,h (mm)

Total pressure

manometer, h (mm)


heighth (mm)

Free stream

velocity,U (m/s)

Reynolds number

0 100 126 26 18.43 56718.2 0.705 0.208

0.5 100 128 28 19.13 58861.5 0.680 0.218

Boundary Layer

1.0 100 128 28 19.13 58861.5 0.680 0.218

1.5 100 130 30 19.80 60925.1 0.657 0.225

2.0 102 130 30 19.80 60925.1 0.657 0.225

2.5 102 130 30 19.80 60925.1 0.657 0.225

3.0 102 130 30 19.80 60925.1 0.657 0.225

3.5 102 130 30 19.80 60925.1 0.657 0.225

4.0 102 130 30 19.80 60925.1 0.657 0.225

4.5 102 130 30 19.80 60925.1 0.657 0.225

Table 4: Tabulation of data for rough surface with x = 150mm


Static pressure

manometer,h (mm)

Total pressure

manometer, h (mm)


heighth (mm)

Free stream

velocity,U (m/s)

Reynolds number

0 100 122 22 16.96 195692.3 0.767 0.179

0.5 100 124 24 17.71 204349.1 0.734 0.195

Boundary Layer

1.0 100 126 26 18.43 212693.3 0.705 0.208

1.5 100 128 28 19.13 220730.8 0.680 0.218

2.0 102 130 28 19.13 220730.8 0.680 0.218

2.5 102 130 28 19.13 220730.8 0.680 0.218

3.0 102 130 28 19.13 220730.8 0.680 0.218

3.5 102 130 28 19.13 220730.8 0.680 0.218

4.0 102 130 28 19.13 220730.8 0.680 0.218

4.5 102 130 28 19.13 220730.8 0.680 0.218

A. Sample calculation for boundary layer thickness, , displacement thickness, , momentum thickness, and shape factor, H by using experimental.

For smooth surface with x = 40mm

i. Boundary layer thickness, = 15mm

ii. Displacement thickness, = A1 x

= 0.11 x 15

Boundary Layer

= 1.65 mm

iii. Momentum thickness, = A2 x

= 0.061 x 15

= 0.915 mm

iv. Shape factor, H =

=

= 1.803




= 0.0963 x 15

= 1.445 mm


= 0.07 x 15

= 1.05 mm


=

= 1.376

For rough surface with x = 40mm



= 0.0835 x 15

= 1.25 mm


= 0.065 x 15

= 0.975 mm

Boundary Layer


=

= 1.282




= 0.0979 x 15

= 1.469 mm


= 0.0726 x 15

= 1.089 mm


=

= 1.349

B. Sample calculation for boundary layer thickness, , displacement thickness, , momentum thickness, and shape factor, H by using theoretical.

LAMINAR BOUNDARY LAYER


i.

Boundary Layer

ii.

iii.

iv.


i.

ii.

Boundary Layer

iii.

iv.


i.

ii.

Boundary Layer

iii.

iv.


i.

ii.

Boundary Layer

iii.

iv.

TURBULENT BOUNDARY LAYER


i.

Boundary Layer

ii.

iii.

iv.


i.

ii.

Boundary Layer

iii.

iv.


i.

ii.

Boundary Layer

iii.

iv.

For rough surface with x = 150mm (refer to data D)

i.

ii.

Boundary Layer

iii.

iv.

TABLE 5: Table of comparison for smooth and rough surface under experimental value and theoretical.

For smooth surface: 40mm ( Rex =52184.6)

EXPERIMENT( m )

THEORYLAMINAR ( m ) TURBULENT ( m )

15 x 10-3 8.03 x 10-4 1.628 x 10-3

* 1.65 x 10-3 3.333 x 10-4 2.038 x 10-4

0.915 x 10-3 1.287 x 10-4 1.584 x 10-4

H 1.808 2.591 1.287

For smooth surface: 150mm (Rex =195692.3)

EXPERIMENT( m )


Boundary Layer

15 x 10-3 1.528 x 10-3 4.655 x 10-3

* 1.445 x10-3 5.257 x 10-4 5.825 x 10-4

1.05 x 10-3 2.029 x 10-4 4.529 x 10-4

H 1.376 2.591 1.286

For rough surface: 40mm (Rex =56718.2)

EXPERIMENT( m )


15 x 10-3 8.127 x 10-4 1.636 x 10-3

* 1.25 x 10-3 2.796 x 10-4 2.047 x 10-4

0.975 x 10-3 1.079 x 10-4 1.592 x 10-4

H 1.282 2.591 1.286

For rough surface: 150mm (Rex =195692.3)

EXPERIMENT( m )


15 x 10-3 1.584 x 10-3 4.722 x 10-3

* 1.469 x 10-3 5.449 x 10-4 5.909 x 10-4

1.089 x 10-3 2.103 x 10-4 4.595 x 10-4

H 1.349 2.591 1.268

DISCUSSION

The micrometer reading (y) has to be started from 1.0mm as shown in the table 1,

table 2, table 3 and table 4.

The value of displacement thickness (*) is obtained by the graph of .

The value of momentum thickness () is obtained by the graph of .

CONCLUSION

Boundary Layer

This experiment, we can say that the various boundary layer velocity profiles such as

boundary layer thickness (), displacement thickness (*), momentum thickness () and

shape factor (H) are depend on the distance from the leading edge and the surface

condition. All the result is as state in table 5. From the table, the boundary layer property

is increasing between smooth and rough surface. Another facts that we can conclude

are the micrometer reading (y) for the smooth surface is lower than the rough surface. It

is because the free stream at rough surface occurs faster than the smooth surface. Also

as expected is increasing with increasing distance from leading edge for both smooth

and rough surface. From experiment note that shape factor decreasing as distance from

leading edge increasing showing boundary layer is changing from laminar to turbulent.

REFERENCES:

1. FLUID MECHANICS, J. F. Douglas, J. M. Gasiorek, J. A. Swaffield, Third

Edition, Longman Scientific & Technical

2. INTRODUCTION TO FLUID MECHANICS, Robert W. Fox, Alan McDonald,

Second Edition, John Wiley & Sons.