Lab 8 Drag on Cylinder from an Integrated Pressure Distribution PDF

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Drag on Cylinder from an Integrated Pressure Distribution...

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Drag on Cylinder from an Integrated Pressure Distribution By Quang Nguyen, Huynh Anh, Aldo Fenalli, Kendall Shaw

School of Engineering Laboratory 8 EGR 365 – Fluid Dynamics

June 30, 2017

1. Introduction

Quang Nguyen EGR 365 Lab 8 Summary Report

The purpose of the experiment were to measure the drag on a cylinder in crossflow by integrating the surface pressure distribution, and to compare the experimental values of drag coefficient on smooth and rough cylinder. In this lab, the smooth part of the cylinder was from the angle was from the angle

180 °

0°

rad to

to 180 ° rad, and the rough part of the cylinder 36 0 °

rad. In the laboratory, the diameter of

cylinder, the width and height of test section, and the length of wind tunnel were measured. After collected the dimension, the wind tunnel was activated, and the measurement of rake pressure, and atmospheric pressure were recorded to calculating drag. The key equation, which would be derived Appendix A, to calculate the experimental drag coefficient, CD, is: 2π

CD= where

1 ∫ C cos ( θ ) dθ (1) 2 0 p

C p , pressure coefficient, was experimentally calculated using the formula (2)

and ideally calculating using formula (3): Cp=

( p− p ∞) (2) 0.5 ρ U ∞2 C p =1−4(sin (θ ) )2 ¿(3) where

p∞ is free-stream pressure, and

respectively of the following fluid, and

p

is local pressure,

ρ

is density

U ∞ is free-stream velocity.

The experimental drag coefficient in smooth cylinder was 1.792, and the experimental drag coefficient in rough cylinder was 1.675. The drag coefficient in smooth cylinder was bigger than the experimental drag coefficient in rough cylinder because of the high friction drag on rough surface and the presence of the surface roughness that would promote early transition of the separated boundary layer causing it to achieve a turbulent state and reattach to the cylinder.

2. Raw Data

Quang Nguyen EGR 365 Lab 8 Summary Report

Table 1: Measurement of 24 pipes

Pipe

Height (in)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

NA 2.4 3 4.7 6.9 8.7 8.6 8.4 7.9 7.9 7.9 7.9 7.9 7.9 7.7 7.6 7.6 7.7 8.4 11.1 11.3 9.9 7.5 4.7 3

Rake ΔHeight (in)

Manometer Tube ΔHeight

NA 0.1 -0.5 -2.2 -4.4 -6.2 -6.1 -5.9 -5.4 -5.4 -5.4 -5.4 -5.4 -5.4 -5.2 -5.1 -5.1 -5.2 -5.9 -8.6 -8.8 -7.4 -5 -2.2 -0.5

(in) NA 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3

Table 2: Experimental Parameters Atmosphere height (in) U-tube Manometer Atmosphere (in) U-tube Manometer Atmosphere (in) Cylinder Diameter (in) Total section width (in) Total section height (in)

2.5 ± 0.5 8.5 ± 0.5 10.8 ± 0.5 4.016 ± 0.002 11.5 ± 0.03125 11.375 ± 0.03125

Quang Nguyen EGR 365 Lab 8 Summary Report

3. Results and Discussion Table 3: Calculated Values in Lab �

Cp

Cp

C p cos(θ)

C p cos(θ)

U∞

Uθ

(degree)

(experimental)

0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 360

1.000 1.043 0.783 0.043 -0.913 -1.696 -1.652 -1.565 -1.348 -1.348 -1.348 -1.348 -1.348 -1.348 -1.261 -1.217 -1.217 -1.261 -1.565 -2.739 -2.826 -2.217 -1.174 0.043 0.783

(theoretical) 1.000 0.732 0.000 -1.000 -2.000 -2.732 -3.000 -2.732 -2.000 -1.000 0.000 0.732 1.000 0.732 0.000 -1.000 -2.000 -2.732 -3.000 -2.732 -2.000 -1.000 0.000 0.732 1.000

(experimental) 1.000 1.008 0.678 0.031 -0.457 -0.439 0.000 0.405 0.674 0.953 1.167 1.302 1.348 1.302 1.092 0.861 0.609 0.326 0.000 -0.709 -1.413 -1.568 -1.017 0.042 0.783

(theoretical) 1.000 0.707 0.000 -0.707 -1.000 -0.707 0.000 0.707 1.000 0.707 0.000 -0.707 -1.000 -0.707 0.000 0.707 1.000 0.707 0.000 -0.707 -1.000 -0.707 0.000 0.707 1.000

(in/s) N/A 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160 42.160

(in/s) N/A 21.823 42.160 59.623 73.023 81.446 84.319 81.446 73.023 59.623 42.160 21.823 0.000 -21.823 -42.160 -59.623 -73.023 -81.446 -84.319 -81.446 -73.023 -59.623 -42.160 -21.823 0.000

Quang Nguyen EGR 365 Lab 8 Summary Report

�) (�versus angle � 100.000 80.000 60.000 40.000

�) (�

20.000 0.000 -20.000

u(theta) 0

50

100

150

200

250

300

350

400

-40.000 -60.000 -80.000 -100.000

angle � (degree)

Figure 1: Graph of

U θ versus angle θ

According to Table 3 and graph of

U θ versus angle θ

maximum magnitude of tangential velocity was 84 in/s when

θ

shown in Figure 1, the was equal

270 ° , and the minimum magnitude of tangential velocity was 0 in/s when

equal

90 °

and

θ

was

180 ° .

Figure 2 shown the graph of theoretical and experimental pressure coefficient versus angle θ

equal

was equal

θ .. Experimentally, the highest pressure coefficient was 1.043 when 15 ° , and the lowest pressure coefficient was -2.826 when

300 ° . Ideally, the highest pressure coefficient was 1.00 when

0 ° , and the lowest pressure coefficient was -3.00 when

θ

θ

was

was equal

θ was equal 270 ° .

Quang Nguyen EGR 365 Lab 8 Summary Report

Cp

Cp versus theta 1.500 1.000 0.500 0.000 -0.500 0 -1.000 -1.500 -2.000 -2.500 -3.000 -3.500

50

100

150

200

250

300

350

400

Cp (experimetal) CP (theoretical)

Angle �(degree)

Figure 2: Graph of pressure coefficient versus angle

Figure 3 showed the graph of theoretical value of

C p cos(θ)

, and Figure 3 showed the graph of experimental value of

θ

versus angle θ

C p cos(θ)

versus angle

θ . Furthermore, Figure 4 provided the equation that described the relationship

between

C p cos(θ)

and angle θ , which is:

C p cos ( θ )=9 ∙ 10−14 ∙θ6 +10−10 ∙ θ5−5 ∙ 10−8 ∙θ 4 +9 ∙ 10−6 ∙θ 3−0.0004 ∙ θ2−0.0214 ∙θ+1.1755 After integrating

0.5 C p cos ( θ )

from 0 rad to

π

rads, the values of drag

coefficient, CD, on smooth side of the cylinder was found as 1.792. On the other hand, after integrating

0.5 C p cos ( θ )

from

π

rads to

2π

rads, the values of drag

coefficient, CD, on rough side of the cylinder was found as 1.675. Consequently, the drag coefficient on smooth side of the cylinder was greater than the drag coefficient on rough side of the cylinder. The possible reasons are the fact that the drag on smooth cylinder was dominated by the pressure component. However, the pressure component of the drag on rough cylinder was reduced significantly because of the friction drag from a sandroughened surface. Consequently, the drag on smooth surface was larger than drag on rough surface, which made the drag coefficient on smooth surface larger than drag coefficient of rough surface. Another reason was that the presence of the surface roughness would promote early transition of the separated boundary layer causing it to achieve a turbulent state and reattach to the cylinder.

Quang Nguyen EGR 365 Lab 8 Summary Report

Theoretcal ��cos (� ) versus theta 1.500

�� cos(�)

1.000 0.500 (Cp)(Cos(theta)) (theoretical)

0.000 -0.500

0

50

100

150

200

250

300

350

400

-1.000 -1.500 Angle (degree)

Figure 3: Graph of theoretical

C p cos(θ)

versus angle θ

Experimental ��cos (� ) versus theta 2.000 1.500 f(x) = − 0 x⁶ + 0 x⁵ − 0 x⁴ + 0 x³ − 0 x² − 0.02 x + 1.18 R² = 0.94

�� cos(�)

1.000 0.500

(Cp)(Cos(theta)) (experimental) Polynomial ((Cp)(Cos(theta)) (experimental))

0.000 -0.500

0

50

100 150 200 250 300 350 400

-1.000 -1.500 -2.000 Angle (degree)

Figure 4: Graph of experimental

C p cos(θ)

versus angle θ

4. Conclusion After integrating the experimental formula of

0.5 C p cos ( θ ) from 0 rad to

π

rads, the values of drag coefficient on smooth side of the cylinder was found as 1.792. On the other hand, after integrating the experimental formula

0.5 C p cos ( θ )

from

π

Quang Nguyen EGR 365 Lab 8 Summary Report

rads to

2 π rads, the values of drag coefficient on rough side of the cylinder was found

as 1.675. Consequently, the drag coefficient on smooth side of the cylinder was greater than the drag coefficient on rough side of the cylinder. The possible reasons were the high friction drag on rough surface, and the presence of the surface roughness that would promote early transition of the separated boundary layer causing it to achieve a turbulent state and reattach to the cylinder....