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WIND TUNNEL EXPERIMENT

Students

ALEKSEI ALEKSEEV

XU CHENG

MARTINUS PUTRA WIDJAJA

Professors

A. DUCOIN

EMSHIP

EUROPEAN MASTERS COURSE

IN INTEGRATED ADVANCED SHIP DESIGN

COLE CENTRALE DE NANTES

2015

WIND TUNNEL EXPERIMENT 2015

2 EMSHIP 5th COHORT- COLE CENTRALE DE NANTES

LIST OF CONTENTS LIST OF FIGURES .............................................................................................................. 2

LIST OF TABLES ................................................................................................................ 2

INTRODUCTION ................................................................................................................ 3

THEORETICAL BACKGROUND ....................................................................................... 4

WIND TUNNEL EXPERIMENT ......................................................................................... 7

RESULTS & DISCUSSION ................................................................................................. 9

JEAN D'ALEMBERT PARADOX ..................................................................................... 10

REFERENCE ..................................................................................................................... 12

APPENDIX ........................................................................................................................ 12

LIST OF FIGURES FIGURE 1. TOP VIEW OF THE THEORETICAL SKETCH ........................................................................................... 4

FIGURE 2. PITOT TUBE SCHEMA ......................................................................................................................... 7

FIGURE 3. CP VS SIN AT 2 DIFFERENT VELOCITY .............................................................................................. 9

FIGURE 4. CP VS ANGLE (DEG) AT DIFFERENT VELOCITIES ........................................................................... 10

FIGURE 5. PRESSURE DRAG COEFFICIENT BASED ON BOUNDARY LAYER THEORY.............................................. 11

LIST OF TABLES TABLE 1. GENERAL PARTICULARS OF THE FLUID ................................................................................................ 7

TABLE 2. VELOCITY RANGE OF THE EXPERIMENT & TABLE 3. SELECTED VELOCITY OF THE EXPERIMENT ............ 7

TABLE 4. PRESSURE DRAG COEFFICIENT RESULTS BY DIFFERENT METHOD ........................................................ 9

TABLE 5. RESULTS OF THE CALCULATED EXPERIMENTAL DATA ....................................................................... 12



INTRODUCTION In this experiment, a study of the pressure distribution around a cylinder will be conducted.

This pressure will occur due to the fluid movement around the cylinder and air will be the

fluid of the experiment. One small wind tunnel will provide a constant air flow rate on the

cylinder. Pitot and Prandtl tube will be used to calculate the wind velocity and the pressure on

the cylinder body. The differential manometers will give the information of pressure

difference from both tubes in mmCE which should be modified in order to get the correct

dimension. All of the information above is needed for calculating the drag coefficient which

depend on the flow velocity, length of the body, and the physical properties of the fluids

(density and viscosity). Finally, the total drag coefficient will be compared with the other

experimental data and the comparison between real flow motions and perfect potential flow

theory will be analyzed in order to have a deeper understanding of the fluid mechanics.

Nomenclature

g Gravity Acceleration (m/s2)

Air Density (Kg/m3)

eau Water Density (Kg/m3)

T Drag Force

S Section of the Body (m2)

V Velocity in m/s2

P Pressure in Pascal

Dynamic Viscosity (kg/ms)

Kinematic Viscosity (m2/s)

D Cylinder's Diameter (m)

Incident's Angle (0)

Cx/Cp Local Pressure Coefficient

Re Reynold's Number



THEORETICAL BACKGROUND

Figure 1. Top View of the Theoretical Sketch

Calculation of the pressure drag coefficient Cxp for a cylinder

The total force exerted by a fluid on a body can be divided in :

A component parallel to the incident flow direction

A lift component perpendicular to the incident flow direction

These forces are due to the action of pressure and viscosity. The total force due to the fluid

can be written under the following form :

Where the stress vector is with :

For a newtonian fluid

The normal unit ( ) directed to the outer of cylinder (

For an incompressible fluid, the relation between stresses and strains can be written as :

Where P is the pressure at the point M of the cylinder.



If we consider the contribution of pressure :

In a polar frame with , we have for horizontal component ( on ):

Where R is the radius of the cylinder and l is the length

We define the pressure drag coefficient as

For the cylinder, the reference surface is S = Dl, then we can write :

By using the Bernoulli theorem between the infinite upstream and the stagnation point :

With a velocity equal to zero at the stagnation (VA=0), we obtain :

Finally :

Then :

By measuring the local pressure coefficient Cp around the cylinder (on a perimeter) we can

obtain the pressure drag coefficient Cxp by doing the numerical integration or with a

planimeter.



Calculation of local pressure coefficient Cp of a cylinder with perfect fluid flow theory

We assume that the studied flow is a 2D flow. In perfect fluid flow theory, the flow around a

cylinder can be modelized by using kinematics of :

An uniform flow :

A dipole located at the origin of the frame :

Total velocity of the flow can be written as:

Boundary conditions must be verified :

At infinity ( r =), we must have: that always verified

On the cylinder ( r = R ), velocity must be tangential to the body

That implies

Finally :

Or :

By using Bernouli on a streamline between infinity and stagnation point A :

By using Bernouli on a streamline between infinity and stagnation point M :

The local pressure coefficient becomes :



WIND TUNNEL EXPERIMENT Inside the wind tunnel there is a one cylinder that could be rotated around its vertical axis

with the diameter as 30 mm. This cylinder has a pressure probe at point M which will define

the pressure difference for each angle of rotation on its vertical axis. In order to calculate this

pressure difference, two differential manometers is being used to read the air velocity and the

pressure difference on the cylinder surface, in terms of the height of the fluid inside the

manometer which is in this case is the water (in mmCE).

The figure 2 below will allow us to understand the relation between pressure and the velocity

by using the pitot-static tube. The stagnation pressure is the summation between static and

dynamic pressure, it could be explained as the equation below,

The relation for the static fluid will be,

By knowing this relation above, the height of

manometer which represent the air velocity between 20 and 27 m/s could be determined.

While the water and air density could be determined by referring to the table inside the

laboratory by reading the lab. temperature.

Table 1. General Particulars of the Fluid

Air Density (kg/m3) Gravity (m/s

2) Kin. Viscosity (m

2/s)

1.2005 9.81 8.930E-07

Water Density (kg/m3) Diameter (m) Dynamic Viscosity (kg/m s)

997.1 0.03 8.900E-04

Table 2. Velocity Range of the Experiment Table 3. Selected Velocity of the Experiment

Velocity

(m/s)

Manometer

Height (mm CE)

20 24.576

27 44.789

Velocity

(m/s)

Manometer

Height (mm CE)

22.462 31

25.515 40

Figure 2. Pitot Tube Schema



EXPERIMENTAL FLOW CHART

Calculate the max. and min. h (mmCE)

Turn the cylinder until the hollow part (M) is

located at the upstream side of the flow

Rotate the cylinder as per counter

from 0 to 360 with increment of 10

Draw Cp vs and Cp vs Sin graph and adjust

the until the graph looks symmetrical

Read and write down the height of lower manometer

START

END

Lower

Manometer

Height

Change the flow between the

connection of the lower manometer

POSITIVE NEGATIVE

Turn on the power and adjust the speed until

reach the height of upper manometer as calculated

Calculate the Cp Experimental and

Theoretical by using Numerical Integration

Calculate the Cp by using planimeter on Cp vs

Sin graph and compare the results



RESULTS & DISCUSSION

After writing all the data from the manometer, the relation between Cp and Sin could be

shown as in figure 3. As we know that the integration of local pressure coefficient (Cp) value

on Sin will give the information of the pressure drag coefficient. This integration shall be

done in two method by using the numerical integration and by using a planimeter tool as can

be seen beside figure 3. When using this tool, we need to print out the corresponding graph

and check how much 1 by 1 area on the graph represent. Afterwards, we just need to follow

the shape of the graph by using the tip of the needle on the tool and check the results. Do not

forget to add 0.1 to the experiment calculation of Cxp in order to represent the contribution of

the viscosity. The result of the calculation could be seen in table 4 below.

Table 4. Pressure Drag Coefficient Results by Different Method

Item Numerical Planimeter B.L Theory I.F Theory

Cxp (22.462m/s) 1.16 1.16 1.2 0

Cxp (25.515m/s) 1.14 1.187 1.2

As can be seen that the results from numerical and planimeter method has the same order of

magnitude. And after the results being added with 0.1 value, it will gives a correct relation

with the reference which had been done by Schlichting as can be seen in figure 5. While on

the other hand, the theoretical integration resulting a zero value which will be discussed in the

following parts.

Figure 3. Cp vs Sin at 2 Different Velocity



JEAN D'ALEMBERT PARADOX

" With the irrotational flow approximation, the aerodynamic drag force on any nonlifting

body of any shape immersed in a uniform stream is zero"

This statement above was expressed by Jean-le-Rond d'Alembert (1717-1783) in 1752. This

conducted experiment being done in order to have a better understanding of the effect on the

fluid assumption to solve the physical problems. As can be seen in figure 4 below, the

theoretical result is symmetrical between the front and the rear part of the cylinder, which

means that there will be no net pressure drag on the cylinder. By using the irrotational flow

approximation, the pressure fully recovers at the rear stagnation point to become the same as

in front stagnation point. The net aerodynamic drag on the cylinder by using irrotational flow

assumption will become zero, since the no slip condition on the cylinder body could not be

satisfied when applying the irrotational flow assumption

Figure 4. Cp vs Angle (Deg) at Different Velocities

The speed of the flow will decelerated to zero speed at the stagnation point and will become

twice of the free-stream velocity at the very top of the cylinder (900). Zero pressure point

could be seen when Cp=0 (210 & 131

0), at this point the pressure acting normal to the body

surface is the same, even though the body moves faster through the fluid. The theoretical

approximation seems to have a same shape below 750 but afterwards it does not work at all.

This happened due to the real flow which has a significantly less pressure on the back surface



than that on the front. This will induced a pressure drag and also the flow separation and as

can be seen from the graph that the separation angle for this cylinder is around 910.

Figure 5. Pressure Drag Coefficient based on Boundary Layer Theory



REFERENCE [1] Study of pressure Distribution on a cylinder Guidance. ECN,2015

[2] Cengel, Yunus A. ,Cimbala John M. Fluid Mechanics : Fundamental and Applications,

McGraw-Hill Companies. 2006

APPENDIX

Table 5. Results of the Calculated Experimental Data

-0.156 351.000 28.500 36.000 0.919 0.900 1.000 -0.146 -0.133 -0.163

-0.326 341.000 23.550 25.200 0.760 0.630 0.879 -0.095 -0.071 -0.119

-0.485 331.000 11.500 -8.400 0.371 0.210 0.532 -0.018 0.005 -0.042

-0.629 321.000 -4.500 -11.100 -0.145 -0.278 0.000 0.053 0.072 0.047

-0.755 311.000 -18.500 -29.000 -0.597 -0.725 -0.653 0.097 0.109 0.123

-0.857 301.000 -30.500 -41.500 -0.984 -1.038 -1.347 0.106 0.107 0.167

-0.934 291.000 -35.500 -44.200 -1.145 -1.105 -2.000 0.081 0.076 0.167

-0.982 281.000 -33.000 -38.000 -1.065 -0.950 -2.532 0.045 0.042 0.122

-1.000 271.000 -29.500 -37.300 -0.952 -0.933 -2.879 0.014 0.014 0.045

-0.988 261.000 -29.500 -38.800 -0.952 -0.970 -3.000 -0.015 -0.015 -0.045

-0.946 251.000 -30.000 -38.100 -0.968 -0.953 -2.879 -0.044 -0.044 -0.122

-0.875 241.000 -30.500 -39.300 -0.984 -0.983 -2.532 -0.074 -0.073 -0.167

-0.777 231.000 -31.500 -40.000 -1.016 -1.000 -2.000 -0.103 -0.103 -0.167

-0.656 221.000 -32.500 -42.700 -1.048 -1.068 -1.347 -0.132 -0.131 -0.123

-0.515 211.000 -34.000 -42.200 -1.097 -1.055 -0.653 -0.157 -0.152 -0.047

-0.358 201.000 -34.000 -43.000 -1.097 -1.075 0.000 -0.175 -0.170 0.042

-0.191 191.000 -34.500 -43.000 -1.113 -1.075 0.532 -0.189 -0.181 0.119

-0.017 181.000 -35.000 -42.900 -1.129 -1.073 0.879 -0.196 -0.185 0.163

0.156 171.000 -35.000 -42.500 -1.129 -1.063 1.000 -0.196 -0.184 0.163

0.326 161.000 -35.000 -42.200 -1.129 -1.055 0.879 -0.187 -0.176 0.119

0.485 151.000 -34.000 -41.500 -1.097 -1.038 0.532 -0.171 -0.162 0.042

0.629 141.000 -33.000 -40.300 -1.065 -1.008 0.000 -0.150 -0.142 -0.047

0.755 131.000 -32.000 -39.300 -1.032 -0.983 -0.653 -0.125 -0.119 -0.123

0.857 121.000 -31.000 -38.200 -1.000 -0.955 -1.347 -0.099 -0.095 -0.167

0.934 111.000 -30.500 -37.700 -0.984 -0.943 -2.000 -0.072 -0.069 -0.167

0.982 101.000 -30.000 -36.900 -0.968 -0.923 -2.532 -0.043 -0.042 -0.122

1.000 91.000 -29.500 -36.800 -0.952 -0.920 -2.879 -0.015 -0.015 -0.045

0.988 81.000 -31.000 -41.500 -1.000 -1.038 -3.000 0.016 0.016 0.045

0.946 71.000 -35.000 -44.300 -1.129 -1.108 -2.879 0.049 0.046 0.122

0.875 61.000 -33.000 -36.800 -1.065 -0.920 -2.532 0.067 0.053 0.167

0.777 51.000 -23.500 -21.200 -0.758 -0.530 -2.000 0.054 0.030 0.167

0.656 41.000 -10.000 2.500 -0.323 -0.063 -1.347 0.009 -0.021 0.123

0.515 31.000 5.500 16.000 0.177 0.400 -0.653 -0.058 -0.083 0.047

0.358 21.000 19.500 30.700 0.629 0.768 0.000 -0.122 -0.138 -0.042

0.191 11.000 28.500 39.300 0.919 0.983 0.532 -0.164 -0.168 -0.119

0.017 1.000 32.000 40.600 1.032 1.015 0.879 -0.175 -0.172 -0.163

-0.156 -9.000 30.500 38.600 0.984 0.965 1.000 0.000 0.000 0.000

Cp

(25.515 m/s)

Cp

(Theory)

Integration

Cp 31

Integration

Cp 40

Integration

Theoreticalsin(_modif) modif

h manometer

(22.462 m/s)

h manometer

(25.515 m/s)

Cp

(22.462 m/s)