Masters project atmoshperic turbulence

1. NEW YORK CITY COLLEGE, MECHANICAL ENGINEERING
Atmospheric Turbulence
For Master’s Project with Dr. Goushcha
Johnaton McAdam
Spring 2017

2. 1
Contents
1. Abstract.................................................................................................................................................2
A. Problem Statement............................................................................................................................2
B. Objective...........................................................................................................................................2
2. Introduction...........................................................................................................................................2
C. Atmospheric Turbulence...................................................................................................................2
D. Governing Equations ........................................................................................................................3
3. Geometry...............................................................................................................................................4
A. Setup .................................................................................................................................................4
B. Materials .......................................................................................................................................6
4. Procedure ..............................................................................................................................................6
5. Results...................................................................................................................................................7
6. Discussion.............................................................................................................................................8
7. Conclusion ............................................................................................................................................9
8. Acknowledgements...............................................................................................................................9
9. References...........................................................................................................................................10
10. Appendix.........................................................................................................................................10

3. 2
1. Abstract
A. Problem Statement
This experiment will measure the turbulence boundary layer that is created from the turbulent
geometries inside a wind tunnel. The velocity profile, Turbulence intensity and Kinetic energy
dissipation will also be studied to improve upon the experiment.
B. Objective
The purpose of this research paper is to generate a working experiment model of atmospheric
turbulence in a wind tunnel to study its effects. The methodology that will be used to tackle this
problem will include the use of three main components, turbulent fins, step barriers and the
turbulence grid. The goal is to create the boundary layer as seen below and to validate the results;
the data computed will be compared to those found in literature.
2. Introduction
C. Atmospheric Turbulence
In many engineering and physics research the study of the turbulent spectrum and its
influence of the atmospheric are important for many applications such as wind turbine, air craft
design and even weather phenomenon. The term Atmospheric turbulence is used to describe the
dynamic irregular motion of winds that varies in velocities and directions, this occurrence causes
the water vapor, smoke and as well as the energies to become distributed horizontally and
vertically in 3D. The boundary layers created at the lowest part of the atmospheric are created
from the effects of earth surface roughness, temperature and other turbulent movements.
Scientist has always wanted to replicate this phenomenon to study its effect on aerodynamic
bodies such as rockets because it has been argue that the upper atmosphere wind conditions is a
contributing factor to rocket crashes or to simply harvest this natural energy with the use of wind
turbines.
Figure 1:
Atmospheric
Turbulent Boundary
Layer illustration

4. 3
D. Governing Equations
Continuity
1.
𝜕𝑈𝑖
𝜕𝑥 𝑖
= 0
Momentum
2. 𝜌 (
𝜕𝑈𝑖
𝜕𝑡
+
𝜕(𝑈𝑖 𝑈 𝑗)
𝜕𝑥 𝑗
) = −
𝜕𝑃 𝑖
𝜕𝑥 𝑖
+ 𝜇 (
𝜕2 𝑈𝑖
𝜕𝑥 𝑗
2) + 𝜌𝑔𝑖
Reynolds-averaged Naiver–Stokes equations
Let: 𝑈𝑖
′̅̅̅̅ = 0 𝑈𝑖
′′̅̅̅̅ ≠ 0 = 𝑈𝑖
′ 2̅̅̅̅̅ 𝑈𝑖=𝑈̅𝑖 + 𝑈𝑖
′
𝑈̅𝑖
̅ = 𝑈̅𝑖
Plug in appropriates values
𝜕(𝑈̅𝑖 + 𝑈𝑖
′
)
𝜕𝑥𝑖
= 0
𝜌 (
𝜕(𝑈̅𝑖 + 𝑈𝑖
′
)
𝜕𝑡
+
𝜕(𝑈̅𝑖 + 𝑈𝑖
′
)(𝑈̅𝑗 + 𝑈𝑗
′
)
𝜕𝑥𝑗
) = −
𝜕(𝑃̅𝑖 + 𝑃𝑖
′
)
𝜕𝑥𝑖
+ 𝜇 (
𝜕2(𝑈̅𝑖 + 𝑈𝑖
′
)
𝜕𝑥𝑗
2 ) + 𝜌𝑔𝑖
Take the Average of both equations
𝜕(𝑈̅𝑖 + 𝑈𝑖
′̅̅̅̅̅̅̅̅̅̅)
𝜕𝑥𝑖
= 0
3.
𝜕(𝑈̅𝑖)
𝜕𝑥 𝑖
= 0
𝜌 (
𝜕(𝑈̅𝑖 + 𝑈𝑖
′)
𝜕𝑡
+
𝜕(𝑈̅𝑖 + 𝑈𝑖
′)(𝑈̅𝑗 + 𝑈𝑗
′)
𝜕𝑥𝑗
̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
) = −
𝜕(𝑃̅𝑖 + 𝑃𝑖
′̅̅̅̅̅̅̅̅̅)
𝜕𝑥𝑖
+ 𝜇 (
𝜕2
(𝑈̅𝑖 + 𝑈𝑖
′̅̅̅̅̅̅̅̅̅̅)
𝜕𝑥𝑗
2 ) + 𝜌𝑔𝑖
4. 𝜌 (
𝜕(𝑈̅ 𝑖)
𝜕𝑡
+
𝜕(𝑈̅ 𝑖 𝑈̅ 𝑗)
𝜕𝑥 𝑗
) = −
𝜕(𝑃̅ 𝑖)
𝜕𝑥 𝑖
+ 𝜇 (
𝜕2(𝑈̅ 𝑖)
𝜕𝑥 𝑗
2 ) − 𝜌
𝜕(𝑈𝑖
′ 𝑈𝑗
′̅̅̅̅̅̅̅)
𝜕𝑥 𝑗
+ 𝜌𝑔𝑖
Κ − 𝜖 𝑀𝑜𝑑𝑒𝑙
5.
𝐷 𝑘
𝐷𝑡
=
𝜕
𝜕𝑥 𝑖
(
𝜇 𝑒𝑓𝑓
𝜎 𝑘
𝜕 𝑘
𝜕𝑥 𝑖
) + [𝜇 𝑇 (
𝜕(𝑈̅𝑖)
𝜕𝑥 𝑗
+
𝜕(𝑈̅ 𝑗)
𝜕𝑥 𝑖
) −
2
3
𝜌 𝛿𝑖𝑗𝑘]
𝜕(𝑈̅ 𝑗)
𝜕𝑥 𝑖
− 𝐶 𝐷
𝜌𝜅3/2
𝑙 𝑚
6.
𝐷ϵ
𝐷𝑡
=
𝜕
𝜕𝑥 𝑖
(
𝜇 𝑒𝑓𝑓
𝜎ϵ
𝜕ϵ
𝜕𝑥 𝑖
) + 𝐶1 [𝜇 𝑇 (
𝜕(𝑈̅𝑖)
𝜕𝑥 𝑗
+
𝜕(𝑈̅ 𝑗)
𝜕𝑥 𝑖
) −
2
3
𝜌 𝛿𝑖𝑗𝑘]
𝜕(𝑈̅ 𝑗)
𝜕𝑥 𝑖
− 𝐶2
𝜌ϵ2
𝜅

5. 4
Turbulence Log Wall Law
𝑢 =
𝑢 𝑟
𝑘
ln
𝑦
𝑦𝑜
3. Geometry
A. Setup
The basic turbulence geometry to simulate atmospheric turbulence includes the use of an
elliptical vortex generation, roughness element and a barrier wall. For this experiment the
geometries were replaced, for example the turbulence grid and barrier steps were taken instead of
the roughness element and barrier wall. The elliptical vortex generators were implemented from
the Counihan design with is use in various wind tunnel experiments as seen in figure 5; they
were design to be this way to reduce the effects of wakes which may skew with the data.
Figure 2: Initial Geometry Representation

6. 5
Figure 3: Modify Geometry Representation
Figure 4: Final Geometry Representation

7. 6
B. Materials
Initial Setup
Features Materials Dimension Quantity
Turbulent Fins Plywood Minor Radius 6in,
Major Radius 24in
3
Trip Wire Plywood 1 in x 0.5in x 48in 1
Surface Roughness Plywood 2in x 2in x 0.5 in
4in x 4in x 2in
12
Modify Setup
Features Materials Dimension Quantity
Turbulent Fins Cardboard Minor Radius 6in,
Major Radius 24in
4
Surface Roughness Plywood 2in x 2in x 0.5 in
4in x 4in x 2in
12
Trip Wire Plywood 1 in x 0.5in x 48in 1
Rectangular Cut outs Cardboard 6in x 3in 3
Final Setup
Features Materials Dimension Quantity
Turbulent Fins Cardboard Minor Radius 14in,
Major Radius 32in
4
Surface Roughness Plywood 1in x 1in x 48in 8
4. Procedure
1. Remove any devices that may be inside of the wind tunnel, and then mount the probe to
begin the calibration process. After this is complete remove the probe from the wind
tunnel.
2. Place the turbulence grid into the wind tunnel to create the distortion in the wind velocity
downstream.
3. Calculate the minor and major radii from various research papers and sketch those
dimensions on to the working material, then cut the quarter ellipses from the material and
place in the wind tunnel with equal distance distances apart.
4. Create the surface roughness according to the specify dimensions and place them in the
wind tunnel with its required distance downstream.
5. Check the experiment, to make sure everything is secured and there are no loose objects.
6. Cautiously start the wind tunnel, while maintaining a finger over the stop button in the
event of loose objects during the experiment.
7. If the initial test was successful, carefully install the test probe.
8. Record the data of the wind velocity at various heights of the input velocity.
9. Repeat until steps 3-9 until the desired velocity profile is achieved.

8. 7
5. Results
Figure 5: Mean Velocity Profile
Figure 6: Turbulence Kinetic Energy

9. 8
Figure 7: Turbulence Intensity
6. Discussion
The results obtain from the first experimental setup failed to achieve the desired
atmospheric boundary layer due to its crude structure. The design was poorly structured from a
number of reasons such as limited number fins, limited roughness element and lack of fin lengths
in the downstream direction. To address this issue an extension of rectangular cut outs of
cardboard were placed in the downstream direction to increase its length; however this created a
new scope of concerns. One of them being the creation of wakes downstream, the wakes were
created from the rectangular cutouts due to the nature of the geometry to create recirculation
zones behind the turbulence fins. The final setup included four turbulence fins; the height was
created to roughly be half of the vertical distance of the wind tunnel and its width to be two-
thirds of its own height. The data measured from the final setup was desirable for the input wind
velocity of 5 m/s and unfortunately due the nature of this experiment being incomplete, the data
was not able to be plotted against the turbulence log wall at this time.

10. 9
7. Conclusion
In conclusion, the experimental study of atmospheric turbulence was a very tedious process;
however the knowledge and experience acquired was very rewarding. I was able to apply my
creativity and problem solving skills to solve a real world problem which I was able to learn
fundamentally from the classroom. This is still a project in progress; therefore there is still room
for improvement in the future.
8. Acknowledgements
I would like to thank the various scientist and engineers who made their research available so
that many young aspiring students may learn and implement our ideas to that field of research. I
would also like to thank my Professor Dr. Goushcha for providing guidance for me when I
needed it the most.

11. 10
9. References
[1] Adrián Roberto Wittwer, Guilherme Sausen Welter and Acir M. Loredo-Souza (2013). ,
Wind Tunnel Designs and Their Diverse Engineering Applications, Dr. Noor Ahmed (Ed.),
Intech, DOI: 10.5772/54088. Available from: http://www..com/books/wind-tunnel-designs-and-
their-diverse-engineering-applications/statistical-analysis-of-wind-tunnel-and-atmospheric-
boundary-layer-turbulent-flows
10.Appendix
Nomenclature
𝑈̅𝑖 − 𝑚𝑒𝑎𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 (𝑚 𝑠⁄ )
𝑈𝑖
′
− 𝑓𝑙𝑢𝑥𝑎𝑡𝑖𝑛𝑔 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 (𝑚 𝑠⁄ )
𝜌 − 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 (Kg/L)
𝑃𝑖 − 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 (𝑃𝑎)
𝜇 − 𝑣𝑖𝑠𝑐𝑜𝑖𝑠𝑡𝑦 (𝑃𝑎 − 𝑠)
𝑢 𝑟 − 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 (𝑚 𝑠⁄ )
𝑧 𝑟 − 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 ℎ𝑒𝑖𝑔ℎ𝑡 (𝑚)
𝑧 − ℎ𝑒𝑖𝑔ℎ𝑡 (m)
𝛼 − 𝑝𝑜𝑤𝑒𝑟 𝑖𝑛𝑑𝑒𝑥
𝐶𝜀1 𝐶𝜀2 𝐶𝜇 𝜎𝑘 𝜎𝜀 − 𝑘 𝑒𝑝𝑖𝑙𝑠𝑜𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑠
𝑔𝑖 − 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 (𝑁)
Κ − 𝑡𝑢𝑟𝑏𝑢𝑙𝑒𝑛𝑡 𝑘𝑖𝑛𝑒𝑡𝑖𝑐 𝑒𝑛𝑒𝑟𝑔𝑦 (𝑚2
/𝑠2
)
𝜖 − 𝑑𝑖𝑠𝑠𝑝𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 (𝑚2
/𝑠^3)

12. 11
Matlab Code
clear all
close all
clc
load('Calibration.mat')
load('Calibration2.mat')
cd('2017Jan10-Velprofile')
list_files1=ls;
for j= 3:18
y=[35:36:600];
fid=fopen(list_files1(j, :));
C = textscan(fid, '%f %f', 'HeaderLines', 8);
data=[C{1} C{2}];
fclose(fid);
velocityi=polyval(p,data(:, 2));
TKE(j-2,:) = 0.5*(mean((velocityi - mean(velocityi)).^2));
Vm(j-2,:) = mean(velocityi);
TKEP(j-2,:) = (mean(sqrt( (velocityi - Vm(j-2,:)).^2))./ Vm(j-2,:));
end
cd('..')
cd('2017Feb17-Velprofile')
list_files3=ls;
for i= 3:17
fid3=fopen(list_files3(i, :));
C3 = textscan(fid3, '%f %f', 'HeaderLines', 8);
data3=[C3{1} C3{2}];
fclose(fid3);
velocity3i=polyval(p2,data3(:, 2));
TKE3(i-2,:) = 0.5*(mean((velocity3i - mean(velocity3i)).^2));
Vm3(i-2,:) = mean(velocity3i);
TKEP3(i-2,:) = (mean(sqrt( (velocity3i - Vm3(i-2,:)).^2))./ Vm3(i-2,:));
end
cd('..')
cd('2017Apr25-Velprofile')
list_files4=ls;
for i= 3:29
fid5=fopen(list_files4(i, :));
C3 = textscan(fid5, '%f %f', 'HeaderLines', 8);
data4=[C3{1} C3{2}];
fclose(fid5);
velocity5i=polyval(p2,data4(:, 2));
TKE5(i-2,:) = 0.5*(mean((velocity5i - mean(velocity5i)).^2));
Vm5(i-2,:) = mean(velocity5i);
TKEP5(i-2,:) = (mean(sqrt( (velocity5i - Vm5(i-2,:)).^2))./ Vm5(i-2,:));
height(i-2) = str2num(list_files4(i, 25:27));
end

13. 12
cd('..')
% y4 = 600e-3/exp(3.5/5);
y3=[0:300];
yo = 0.300;
Uo =5;
nu = 1.5e-05;
K=0.41;
% U = (Uo/K)* log(y3./y4)+ 5.1 ;
% plot(Vm5, height, U, y3)
y1=[40:40:600];
figure(1)
hold on
plot(TKE,y,'-o', TKE3,y1,'-*', TKE5, height,'k')
xlabel('Turbulence Kinetic Energy, m^2/s^2')
ylabel('Height, mm')
title('Turbulence Kinetic Energy vs. Height')
legend('Initial Setup','Modify Setup','Final Setup')
%legend('Jan 10 Data','Jan 19 Data', 'Feb 2 Data','Feb 17 Data','April 21
Data')
axis([0 0.3 0 600 ])
figure(2)
hold on
plot(Vm,y,'-o',Vm3,y1,'-*',Vm5 ,height,'k')
xlabel('Velocity, m/s')
ylabel('Height, mm')
title('Mean Velocity')
legend('Initial Setup','Modify Setup','Final Setup')
axis([2 6 0 600 ])
figure(3)
hold on
plot(TKEP,y,'-o',TKEP3,y1,'-*', TKEP5, height,'k')
xlabel('Percent Turbulence')
ylabel('Height, mm')
title('Percent Turbulence')
%legend('Jan 10 Data','Jan 19 Data', 'Feb 2 Data','Feb 17 Data','April 21
Data')
legend('Initial Setup','Modify Setup','Final Setup')
axis([0 0.2 0 600 ])