Design, Development and Validation of Specialized Fixture for Wind Tunnel to Study Boundary Layer

Design, Development and Validation of Specialized Fixture for Wind Tunnel to Study Boundary Layer

Bhavesh R. Kataria Department of Mechanical Engineering, Vishwakarma Institute of Information

Technology, Pune-48, Maharashtra, India

Vinayak A. Karkhanis Department of Mechanical Engineering, Vishwakarma Institute of Information

Technology, Pune-48, Maharashtra, India

Abstract

Fluid mechanics is considered as one of the core subjects in mechanical engineering. The concepts of this subject are easy to understand when they are shown practically. One of such important concept in fluid mechanics is boundary layer. It has variety of applications in many fields. In practice to study this phenomenon wind tunnel is used as one can have a good control over the test section environment with this instrument. Wind tunnel is not only useful in getting the concept of boundary layer but also to have study of boundary layer over different geometries for different velocities.

In this project, we have developed a specialized fixture for wind tunnel which can take readings over the different points on flat plate and thus will give the nature of boundary layer.

Keywords: Boundary Layer, Wind Tunnel, Specialized Fixture, Testing, Simulation, Validation.

1. Literature Review

   1. Introduction

      Boundary layer is a layer adjacent to a surface where viscous effects are important. When real fluid flows past a solid body or a solid wall, the fluid particles adhere to the boundary and condition of no slip occurs. This means that the velocity of fluid close to the boundary will be same as that of boundary. If the boundary is not moving, the velocity of fluid at the boundary will be zero. Further away from the boundary, the velocity will be increasing gradually and as a result of this variation of velocity, the velocity gradient will exist. The velocity of fluid increases from zero velocity on

      the stationary boundary to the free stream velocity of the fluid in the direction normal to the boundary.

      Figure 1. Velocity Variation over Flat Plate

      Three main parameters that are used to characterize the size and shape of a boundary layer are the boundary layer thickness, the displacement thickness, and the momentum thickness.

      1. The boundary layer thickness ( )

         It is used for a thickness beyond which the velocity is essentially the free-stream velocity (U). The velocity in boundary layer increases towards U in an asymptotic manner.

      2. The displacement thickness (*)

         It is the distance by which the surface would have to be moved parallel to itself towards the reference plane in an ideal fluid stream of velocity (U) to give the same mass flow as occurring between the surface and the reference plane in a real fluid.

         Figure 2. Displacement Thickness over Flat Plate

      3. The momentum thickness ( )

      I t is the distance by which a surface would have to be moved parallel to itself towards the reference plane in the viscid fluid stream of velocity

      (U) to give the same total momentum as existing between the surface and the reference plane in a real fluid.

   2. Regions of Boundary Layer

      Figure 3. Boundary Layer over Flat Plate (Y Scale Enlarged)

      In physics and fluid mechanics, a boundary layer is the layer of fluid in the immediate vicinity of a bounding surface where the effects of viscosity are significant. In other words, it is a thin layer of viscous fluid close to the solid surface of a wall in contact with a moving stream in which (within its thickness ) the flow velocity varies from zero at the wall (where the flow sticks to the wall because of its viscosity) up to Ue at the boundary, which approximately (within 1% error) corresponds to the free stream velocity as shown in the figure.

      The boundary layer can be divided into the following three regions:

      1. Laminar Flow Region

      2. Transition Flow Region

      3. Turbulent Flow Region

      1. Laminar flow region

         A laminar flow is defined as the type of flow in which fluid particles move along a well defined paths or stream line. In this, the fluid layers slide smoothly one over the other adjacent layer. Laminar flow is also referred as stream-line flow or viscous flow.

         Reynolds number for this region over a flat plate is less than 3E+05.

         Some of the typical examples of laminar flow are flow of a fluid over a plate, viscous liquids (e.g. honey) poured out of bottle, etc.

      2. Turbulent flow region

         A flow is said to be turbulent flow in which the fluid particles move in a zigzag way. In this case, the fluid particles have the velocity in the transverse direction to the principal direction of flow having variable magnitude of velocity. In turbulent flows, eddies formation takes place which are responsible for high energy loss.

         Reynolds number for this region over a flat plate is greater than 5E+05.

         Some of the typical examples of turbulent flow are smoke of cigarette, flow of water from a fully opened water tap, etc.

      3. Transition flow region

      This region lies in between the laminar flow and the turbulent flow. The flow change from laminar to turbulent is not sudden but it changes gradually.

      Reynolds number for this region over a flat plate lies between 3E+05 and 5E+05.

   3. Applications of Boundary Layer

1. Aerodynamics (airplanes, rockets, projectiles)

2. Hydrodynamics (ships, submarines, torpedoes)

3. Transportation (automobiles, trucks, cycles)

4. Wind engineering (buildings, bridges, water towers)

5. Ocean engineering (breakwaters, cables)

1. Test Apparatus

   1. Wind Tunnel

      Wind tunnel is one of the most important apparatus used in the experimental analysis in the field of aerodynamics and fluid flow. Its purpose is to provide a region of controlled air flow into which models can be inserted.

      Wind tunnel consists of the following sections:

      1. Bell mouth with an air straighter

      2. Setting chamber and contraction cone

      3. Transparent test section

      4. Diffuser section

      5. Drive unit section

      The tunnel is of simplest tube section open type along which air is propelled. A fan downstream of working section usually provides the propulsion.

      Wind tunnel is made in a single mould by using Fiber Reinforced Plastic (FRP) which gives a smooth inner surface and less leakage.

      The room containing the tunnel is in fact part of the tunnel, since it provides a path by which air returns from the downstream end to upstream end

      Figure 4. Wind Tunnel

      1. Bell Mouth and Entry

         The entry is shaped to guide the air smoothly into the tunnel. Proper flow separation here would give less turbulence and uniformity in velocity in the working section. An air space of 2 to 2.5 meter is provided.

      2. Setting Chamber and Contraction Cone

         The bell mouth is followed by a setting chamber that leads to a contraction, which increases the velocity of flow. The function of this section is to make the flow parallel and more uniform. This is connected with working section or test section. The setting chamber usually includes a honey comb and nylon mesh screens to filter and stabilize the incoming air flow.

      3. Transparent Test Section

         Tunnel has a 300 mm x 300 mm x 1000 mm test section with two windows to insert te models or probes. The test section consists of accessories to hold the instruments and models for facilitating the motion of the model in all directions relative to air stream.

      4. Diffuser Section

         The test section is followed by a divergent duct. The divergence results in a corresponding reduction in

         the flow speed. Diffuser reduces dynamic pressure, which leads to reduction in power losses at the exit. Leaving the diffuser, the air escapes into the atmosphere.

      5. Drive Unit Section

      The drive unit consists of an axial fan and a motor. A five blade fan is coupled to the motor which is fitted on a sturdy mild steel frame. Motor is controlled by a variable frequency drive, which gives a smooth variation of air velocity in test section. An anemometer is provided to read the air velocity and accordingly to set the desired value of air velocity by increasing or decreasing the motor speed.

   2. Specifications

      Table 1. Specifications of Wind Tunnel

      PARAMETER			DESCRIPTION
      Type			Open Type Wind Tunnel
      Test Section
      1. Main duct			Mild Steel with Powder Coating
      2. Side glass			Acrylic Sheet- 8mm thick
      3. Size			300 mm x 300 mm x 1000 mm
      Blower Fan			5 Blades- Aluminum Die Cast
      A.C. Motor			3 HP- 2880 rpm
      1. Speed Variation			10% to 100% by Frequency Drive Controller
      2. Make			Delta
      3. Mode			400 V; Class VFS7- 4037p; 2.1 kW- VFD
      Air Velocity Section	in	Test	1 to 50 m/s
      Duct Material			Fiber Reinforced Plastic (FRP)
      Passage for Air Flow			9.5 m
      Contraction Ratio			9:1
      Lift/Drag Force Sensor			0 to 20 kg Beam Type Load Cell
      Load Indicator			0 to 20 kg- 2 Channel/0.01 kg Resolution
      Pitot Tube Diameter			7.951 mm
      PARAMETER			DESCRIPTION
      Inclined Manometer			0 to 50 mm Static Head
      Multi Tube Manometer
      1. Height			300 mm
      2. Number Tubes		of	16 Poly Vinyl Chloride (PVC)
      Manometer Inclination			0 to 90 degrees

      Anemometer
      1. Velocity Range	0 to 30 m/s
      2. Display	Digital
      Strain Gauge Balance	Two Channel
      Capacity
      Lift Force	0 to 20 kg
      Drag Force	0 to 20 kg

2. Fixture Design

   1. Fixture Overview

      Table 2. Fixture Overview

      COMPONENT	MATERIAL	DIMENSIONS (mm)	QTY
      Base
      1. Base plate	Acrylic	235x125x4	1
      2. Base strip	Acrylic	200x15x6	2
      Slider
      1. Slider plate	Acrylic	485x125x5	1
      2. Slider block	Acrylic	71x65x20	1
      3. Slider block disc	Mild steel	Ø40×3	1
      4. Slider rod	Mild steel	Ø9×135	2
      5. Vertical sliding plate	Acrylic	149x49x10	1
      6. Vertical static plate	Acrylic	149x49x10	1
      7. Micrometer holder	Aluminum	Ø45×20	1
      Guideway
      1. Guideway strip	Acrylic	185x25x6	2
      2. Guideway limiting strip	Acrylic	155x15x6	1
      Stud guide
      1. Detachable stud guide	Acrylic	155x65x15	1
      Bush	Acrylic	Ø9×25	2
      Pitot tube	Copper	Ø8	1
      Micrometer	Mild steel	0 to 5	1
      Ball bearing	Mild steel	OD 20 ID 9	2
      Stud with knob	Mild steel	Ø8×275	1
      Scale and pointer	Mild steel	150	2

   2. Fixture Model

      Figure 5. Fixture Model in CATIA V5R20

      Figure 6. Fabricated Fixture

3. Test Procedure

1. The flat smooth surface (flat plate) was kept on a stand firmly, at the test section of the wind tunnel.

2. The wind tunnel was set up with the fixture having a pitot tube. The pitot tube was placed at the leading edge and attached to an inclined manometer to get the manometric height.

3. Then the wind tunnel was turned on.

4. Readings were taken at 10 different points within boundary layer gradually increasing y (distance measured from the surface) from 0 mm to 5 mm.

5. The manometric height was noted carefully.

6. The test was repeated adjusting the pitot tube at 0, 20, 40, 60, 80, 100, 120, 140, 160, 180,

200 mm from the leading edge of the flat plate.

Figure 7. Test Setup

1. Observations and Testing

   1. Experimental Data

1. Length of plate = 200 mm

2. Free stream velocity = 37 m/s

3. Density of air = 1.225 kg/m3

4. Dynamic viscosity of air = 1.79E-05 Ns/m2

5. Velocity at sections can be calculated by using:

   1. The working fluid, air, was an incompressible fluid as the testing was done in the low speed wind tunnel

   2. A standard atmospheric condition of the air is assumed

      5.2.2. Nomenclature

      Table 3. Nomenclature

      SYMBOL	DESCRIPTION
      	Air density
      u	Velocity at sections
      U	Free stream velocity
      	Dynamic viscosity
      L	Length of the plate
      Y	Distance from the surface
      Re	Reynolds number
      X	Distance from the leading edge
      	Boundary thickness

      5.3. Tables and Graphs

      Table 4. Distance of 20 mm from eading Edge

      Distance from surface (mm)	Velocity u (m/s)	u/U
      0.0	00.00	0.00
      0.5	37.62	0.99
      1.0	37.62	0.99
      1.5	37.62	0.99
      2.0	37.69	0.99
      2.5	37.69	0.99
      3.0	37.80	1.00
      3.5	37.80	1.00
      4.0	37.80	1.00
      4.5	37.80	1.00
      5.0	37.96	1.00

      Distance from surface (mm)	Velocity u (m/s)	u/U
      0.0	00.00	0.00
      0.5	37.62	0.99
      1.0	37.62	0.99
      1.5	37.62	0.99
      2.0	37.69	0.99
      2.5	37.69	0.99
      3.0	37.80	1.00
      3.5	37.80	1.00
      4.0	37.80	1.00
      4.5	37.80	1.00
      5.0	37.96	1.00

      = 2

6. Reynolds number can be calculated by following formula:

   =

   µ

7. Boundary Layer Thickness is calculated by following formula:

= 5

1. Assumptions and Nomenclature

   1. Assumptions

The basic assumptions used in the following calculations are:

6

Depth (mm)

Depth (mm)

5

4

3

2

1

0

0 5 10 15 20 25 30 35 40

5

Boundary Layer Thickness (mm)

Boundary Layer Thickness (mm)

4.5

4

3.5

3

2.5

2

1.5

1

0.5

Velocity (m/s) 0

Graph 1. Depth v/s Velocity at 20 mm from Leading Edge

0 20 40 60 80 100 120 140 160 180 200

Distance from Leading Edge (mm)

Parameters Calculated:

Boundary layer thickness () = 0.5 mm Reynolds number (Re) = 51491.06

Similarly the test was repeated adjusting the pitot tube at 40, 60, 80, 100, 120, 140, 160, 180, 200 mm

from the leading edge of the flat plate and graphs were plotted.

1. Nature of Boundary Layer

   The following table shows the parameters calculated for all the positions of pitot tube from the leading edge of the flat plate.

   Table 5. Reynolds Number, Flow Type and Boundary Layer Thickness as Function of x

   Sr. No.	x (mm)	Reynolds Number	Flow Type	Boundary Layer Thickness (mm)
   1	0	0	Laminar	0.0
   2	20	51491.06	Laminar	0.5
   3	40	102379.81	Laminar	1.0
   4	60	153569.71	Laminar	1.0
   5	80	205745.09	Laminar	1.0
   6	100	258139.46	Laminar	1.0
   7	120	310752.83	Transition	1.5
   8	140	362928.20	Transition	1.5
   9	160	413680.12	Transition	1.5
   10	180	464281.47	Transition	2.0
   11	200	514910.20	Turbulent	2.0

2. Boundary Layer over Flat Plate

The following graph shows the nature of boundary layer over the flat plate for the above observations made.

Graph 2. Boundary Layer Growth along the Distance from Leading Edge

1. Simulation

   We have simulated the test environment conditions in MATLAB to verify the experimental results.

   1. Simulation Results

      For x = 20 mm

      Figure 8. Simulation Result of Distance of 20 mm from Leading Edge

      Parameters Calculated:

      Boundary layer thickness () = 0.4 mm Reynolds number (Re) = 52011.17

      Similarly the simulation was repeated for x = 40, 60, 80, 100, 120, 140, 160, 180, 200 mm.

   2. Nature of Boundary Layer

      The following table shows the simulation results for all the positions of pitot tube from the leading edge of the flat plate.

      Table 6. Nature of Boundary Layer

      Boundary Layer Thickness (mm)

      Boundary Layer Thickness (mm)

      Sr. No.	x (mm)	Reynolds Number	Flow Type	Boundary Layer Thickness (mm)
      1	0	0	Laminar	0.0
      2	20	52011.17	Laminar	0.4
      3	40	104022.35	Laminar	0.6
      4	60	156033.52	Laminar	0.7
      5	80	208044.69	Laminar	0.8
      6	100	260055.87	Laminar	0.9
      7	120	312067.04	Transition	1.0
      8	140	364078.21	Transition	1.1
      9	160	416089.39	Transition	1.2
      10	180	468100.56	Transition	1.3
      11	200	520111.73	Turbulent	1.3

      Sr. No.	x (mm)	Reynolds Number	Flow Type	Boundary Layer Thickness (mm)
      1	0	0	Laminar	0.0
      2	20	52011.7	Laminar	0.4
      3	40	104022.35	Laminar	0.6
      4	60	156033.52	Laminar	0.7
      5	80	208044.69	Laminar	0.8
      6	100	260055.87	Laminar	0.9
      7	120	312067.04	Transition	1.0
      8	140	364078.21	Transition	1.1
      9	160	416089.39	Transition	1.2
      10	180	468100.56	Transition	1.3
      11	200	520111.73	Turbulent	1.3

      5

      4.5

      4

      3.5

      3

      2.5

      2

      1.5

      1

      0.5

      0

      0 50 100 150 200

      Distance from Leading Edge (mm)

      Experimental Results Simulation Results

      Graph 3. Boundary Layer Growth along Distance from Leading Edge

   3. Boundary Layer over Flat Plate

      The following graph shows the nature of boundary layer over the flat plate for the simulation results obtained.

      Figure 9. Boundary Layer Growth along the Distance from Leading Edge

2. Validation

   Table 7. Validation

   X (mm)	Simulation Results			Experimental Results			Error
   	Re	BL	Flow	Re	BL	Flow	Re	BL
   0	0	0.0	Laminar	0	0.0	Laminar	0.0	0.0
   20	52011.17	0.4	Laminar	51491.06	0.5	Laminar	520.1	0.1
   40	104022.35	0.6	Laminar	102379.81	1.0	Laminar	1642.5	0.4
   60	156033.52	0.7	Laminar	153569.71	1.0	Laminar	2463.8	0.3
   80	208044.69	0.8	Laminar	205745.09	1.0	Laminar	2299.6	0.2
   100	260055.87	0.9	Laminar	258139.46	1.0	Laminar	1916.4	0.1
   120	312067.04	1.0	Transition	310752.83	1.5	Transition	1314.2	0.5
   140	364078.21	1.1	Transition	362928.20	1.5	Transition	1150.0	0.4
   160	416089.39	1.2	Transition	413680.12	1.5	Transition	2409.3	0.3
   180	468100.56	1.3	Transition	464281.47	2.0	Transition	3819.1	0.7
   200	520111.73	1.3	Turbulent	514910.20	2.0	Turbulent	5201.5	0.7

   The following graph shows the nature of boundary layer over the flat plate both experimentally and by simulation.

   1. Error

      Error is calculated by using following formula: Error = Simulation value Experimental value

3. Conclusion

The project was to design, develop and validate a specialized fixture for wind tunnel. The objective behind the project was to develop a fixture that would enable us to study boundary layer over a flat plate for different velocities.

The project was split in two phases. The first phase consisted of design and fabrication of a fixture. Later phase involved the validation part.

The nature of boundary layer over a flat plate for different points is studied experimentally as well as by computation. The computation results show that the experimental results are adequate.

References

1. Dr. R.K. Bansal, Fluid Mechanics

2. Ronald B. Stull, Introduction to Boundary Layer

3. MATLAB help