naveenkumarvemula2006

Prévia do material em texto

CFD analysis of the flow disturbance 
from a lightning conductor on a Cup 
Anemometer 
 
 
 
Thesis Submitted for the degree of 
M.Sc in Wind Energy 
 
By 
 
Naveen Kumar Vemula 
 
 
 
 
Supervisors 
 
Professor: Martin O.L.Hansen 
 
 Scientist: Kurt Hansen 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
TECHNICAL UNIVERSITY OF DENMARK 
DEPARMENT OF MECHANICAL EGNINEERING 
FLUID MECHANICS –WIND ENERGY GROUP 
SEPTEMBER, 29-2006 
 
 ii
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 iii
 
Acknowledgements 
 
This thesis is submitted as partial fulfilment of the requirements for the degree of 
Master of Science in Wind Energy at Technical University of Denmark. 
 
My sincere appreciation goes to my supervisors, Professor. Martin O.L.Hansen 
and Scientist Kurt Hansen for their guidance; patience and encouragement were 
invaluable to the progress and completion of this study. 
 
My sincere thanks go to Jens Nørkær.Sørensen, the Wind Energy Coordinator for 
giving opportunity to study Wind Energy Master Programme in DTU. 
 
Thanks are extended to Mr. Arnulf Knittel, Diploma Engineer (France) and ED cup 
anemometer manufacturer (Denmark) for providing me with the required data as 
well as the equipment. 
 
Finally, I would like to thank to my parents, my family members, my friends and 
my colleagues in the Wind Energy for their help to complete my study at DTU. 
 
 
 Vemula Naveen Kumar 
 
 
 
 
 
 
 
 
 
 
 
 iv
 
Abstract 
 
The objective of the present thesis is to study CFD analysis of flow disturbance 
from a lightning conductor of Wind Mast. The field experiment indicates a 
dominant wind speed reduction behind the lightning rod despite the large 
distance L/D≥25. Therefore, it is necessary to investigate the wake behind the 
lightning rod. 
 
ANSYS CFX 10.0 is used to calculate the flow disturbance (wake) from the 
lightning conductor. The general wake behind the lightning rod is found using CFD 
calculations applied to a suitable turbulence model. The wake is calculated by 
using various turbulence models and the best result is compared to an analytical 
expression for the velocity deficit found in e.g. the book by Schlichting [7] in order 
to validate the result. 
 
Afterwards, this wake is used to determine the wind field experienced by the cup 
for various wind directions. This then can be used as input to a simple model for a 
cup anemometer to estimate the effect on the measured wind speed. Having 
done this, the estimated output is compared with the field experiment results. 
 
Furthermore, a series of curves from the different estimated wakes will be 
obtained to estimate the wake that fits the experiments best. Finally, with this 
best method investigations are made to quantify the measured error in terms of 
power density loss as a function of the distance L/D. The minimum error in the 
power density loss indicates the specific L/D distance, where the lightning 
conductor rod can be placed. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 v
Nomenclature 
 
Re-Reynolds number 
V – Air Velocity 
L - Characteristic length from lightning conductor to the cup anemometer. μ - Dynamic fluid viscosity 
ν - Kinematic fluid viscosity 
ρ - Air density 
D- Lightning conductor Diameter. 
R-Rotor arm length 
A-Cup area 
MA-Aerodynamic Torque on a rotor. ω -Angular velocity of cup anemometer. 
dvC -Drag coefficient for concave face of anemometer 
dxC -Drag coefficient of convex face of anemometer. 
αU -Free stream air velocity=8 m/s 
f = frequency occurrence of Wind speed in each bin. 
 
 
 
 
 
 
 
 
 
 
 ii
 TABLE OF CONTENT 
Acknowledgements.......................................................................................... iii 
Abstract.................................................................................................................... iv 
Nomenclature ........................................................................................................ v 
Chapter 1............................................................................................................. - 1 - 
1.1. Introduction .................................................................................................- 1 - 
1.2. Lightning ........................................................................................................- 1 - 
1.3. Objective and scope of work .................................................................- 2 - 
1.4. Thesis Organization ....................................................................................- 4 - 
1.5. Limitations to the project........................................................................- 4 - 
Chapter 2............................................................................................................. - 6 - 
2.1. Introduction to ANSYS CFX-10.0 ........................................................- 6 - 
2.1.1. Reynolds number: ................................................................................................. - 7 - 
2.1.2. Boundary layer theory:........................................................................................ - 7 - 
2.1.3. Modeling flow near the wall:............................................................................ - 10 - 
2.2. Turbulence Models.....................................................................................- 11 - 
2.2.1. ε−k Model: ........................................................................................................ - 11 - 
2.2.2. K- ω SST (Shear Stress Transport) Turbulence model:........................ - 11 - 
2.2.3. Transitional Turbulence:.................................................................................... - 12 - 
2.3. Simulations and results ..........................................................................- 14 - 
2.3.1. Model-1:.......................................................................................................- 14 - 
2.3.1.1. The modeling details:..................................................................................... - 14 - 
2.3.1.2. Create the geometry....................................................................................... - 14 - 
2.3.1.3. Mesh generation............................................................................................... - 16 - 
2.3.1.4. Boundary conditions applied to the Model. ............................................ - 18 - 
2.3.1.5. Results for ε−k Turbulence model: ................................................... - 20 - 
2.3.1.6. Results for K- ω SST (Shear Stress Transport) Turbulence model:- 22 
- 
2.3.2. Model-2:.......................................................................................................- 24 - 
2.3.2.1. Model description with respective to new grid...................................... - 24 - 
2.3.2.2. Results from Model-2 for K- ω SST (Shear Stress Turbulence 
model): ................................................................................................................................. - 27 - 
2.4. Comparison of Model-2 Velocity profiles to the Schlichting 
Analytical method: ..............................................................................................- 29 - 
2.5. Drag coefficient as a function of Reynolds number. .............- 32 - 
Chapter 3........................................................................................................... - 34 - 
3.1. Cup Anemometer model .........................................................................- 34 - 
3.1.1. Deriving the linearity expression between the angular velocity(ω ) 
and the Wind Speed ( 0V ) from the cup anemometer aerodynamics:.......... - 34 - 
3.1.2. Modeling of cup anemometer where anemometer is in wake state:- 36 - 
Chapter 4........................................................................................................... - 45 - 
4.1. Experimental results obtained from the Wind data ..............- 45 - 
 iii
4.1.1. Wind rose: .............................................................................................................. - 45 - 
4.1.2. Experimental Result: .......................................................................................... - 45 - 
4.2. Comparing the CFD simulation results to experimental 
results .........................................................................................................................- 46 - 
4.2.1. Experimental result Vs CFD Model-2 result: ............................................. - 46 - 
4.2.2. Experimental result Vs CFD Model-1 result: ............................................. - 47 - 
4.2.3. Experimental result Vs CFD Model-2& Model-1 results: ....................... - 47 - 
Chapter 5........................................................................................................... - 49 - 
5.1. Power density Calculations ..................................................................- 49 - 
5.1.1. Estimation of weibull Distribution .................................................................. - 49 - 
5.1.2. Power density calculation from Wind Readings........................................ - 50 - 
5.1.3. Error in Power density........................................................................................ - 57 - 
Chapter 6........................................................................................................... - 59 - 
6.1. Concave & Convex Velocities obtained for different L/D 
ratios............................................................................................................................- 59 - 
6.1.1. Velocity deficit profiles obtained for different L/D stations.................. - 59 - 
6.1.2. New Velocities seen by the Cup Anemometer at L/D=50 station ..... - 62 - 
6.1.3. New Velocities seen by the Cup Anemometer at L/D=75 station ..... - 63 - 
6.1.4. New Velocities seen by the Cup Anemometer at L/D=87.5 station . - 64 - 
6.1.5. New Velocities seen by the Cup Anemometer at L/D=100 station... - 65 - 
7. Conclusion .................................................................................................. - 68 - 
7. Conclusions and further work .................................................................- 68 - 
7.1. Conclusions ................................................................................................................ - 68 - 
7.2. Further work .............................................................................................................. - 70 - 
8. References .................................................................................................. - 71 - 
APPENDIX ......................................................................................................... - 73 - 
APPENDIX A......................................................................................................... - 74 - 
A.1.Model-2 inflow angle variation from CFD model for different 
L/D Ratios. ...............................................................................................................- 74 - 
APPENDIX B......................................................................................................... - 78 - 
B.1. total estimated power density from CFD simulation for 
different L/D stations ........................................................................................- 78 - 
B.1.1.POWER DENSITY CALCULATION L/D=50:................................................... - 78 - 
B.1.2.POWER DENSITY CALCULATION L/D=87.5: ............................................... - 79 - 
B.1.3.POWER DENSITY CALCULATION L/D=100 .................................................. - 80 - 
APPENDIX C......................................................................................................... - 83 - 
C.1. MAT LAB programme................................................................................- 83 - 
C.1.1. Estimation of Actual curve obtained due to the wake effect from the 
lightning conductor from Cup Model. ........................................................................ - 83 - 
C.1.2.Comparision of velocity ratio’s between Experimental wind data and 
CFD model wind data....................................................................................................... - 84 - 
C.1.3.Estimation of frequency of occurrences of wind speed in individual 
sector..................................................................................................................................... - 85 - 
APPENDIX D ........................................................................................................ - 87 - 
D.1. Cup Anemometer dimensions.............................................................- 87 - 
 iv
 
 
LIST OF FIGURES 
 
Figure 1: Mast setup and the curve showing the ratio of the wind speed measured by the cup and sonic 
anemometer for different wind directions............................................................................................ - 3 - 
Figure 2: Schematic view of the Ansys cfx. ......................................................................................... - 6 - 
Figure 3: Development of boundary layer separation with time &flow with complete boundary layer 
separation in the wake of a circular cylinder (Reproduced from Schlichting [7]) ............................... - 8 - 
Figure 4: Representation of flow in the boundary layer near a point of separation 
(Reproduced from Schlichting [7]). ...................................................................................................... - 8 - 
Figure 5: velocity deficit profile over a cylinder with distance (Reproduced from reference [4]). ...... - 9 - 
Figure 6: contour plot of distribution on the surface of the cylinder. ............................................. - 10 - 
Figure 7: Schematic view of the geometry for the model-1 ............................................................... - 15 - 
Figure 8: lightning rod cross section in model-1. ............................................................................. - 15 - 
Figure 9: generated surface mesh for the symmetrical plane & near the cylinder. .......................... - 16 - 
Figure 10: Fine mesh for cylinder in near-wall regions. .................................................................. - 17 - 
Figure 11: the cylindrical rod face with the volumetric mesh........................................................... - 17 - 
Figure 12: Boundary condition applied for the domain and circular cylinder ................................. - 18 - 
Figure 13: Solver Manager. .............................................................................................................. - 19 - 
Figure 14: velocity stream lines along the Plane 1 & 2 in model-1. ................................................. - 19 - 
Figure 15: Plane 1&2 at velocity contour plot with k-ε model ........................................................ - 20 - 
Figure 16: velocity contour plot with k-ε model ............................................................................. - 20 - 
Figure 17: Velocity distribution at cup location with k- ε model.................................................... - 21 - 
Figure 18: Comparison of Velocity distribution at two locations with k- ε model.......................... - 21 - 
Figure 19: velocity contour plot with k-w SST-Model for model-1 ...................................................- 22 - 
Figure 20: Velocity distribution at cup location with K-w SST model .............................................. - 23 - 
Figure 21: velocity distribution at two locations with k-w SST model .............................................. - 23 - 
Figure 22: Schematic view of the geometry for the model-2 ............................................................. - 24 - 
Figure 23: generated volume mesh for the symmetrical plane for model-2 ...................................... - 25 - 
Figure 24: generated surface mesh for near the cylinder for Model-2. ............................................ - 25 - 
Figure 25: Velocity contour plot with k-w SST model....................................................................... - 27 - 
Figure 26: velocity contour plot with k-w SST-Model for model-2 ................................................... - 27 - 
Figure 27: Velocity distribution at cup location with K-w SST model for Model-2 .......................... - 28 - 
Figure 28: velocity distribution at two locations with k-w SST model for Model-2 .......................... - 28 - 
Figure 29: Schematic view of the wake behind the cylinder rod from Schlichting analytical method. - 29 
- 
Figure 30: Result output for wake behind the cylinder rod from Schlichting analytical method. ..... - 30 - 
Figure 31: Wake behind the cylinder at 100mm................................................................................ - 31 - 
Figure 32: Wake behind the cylinder at 200mm................................................................................ - 31 - 
Figure 33: Wake behind the cylinder at 400mm where the cup anemometer located ....................... - 32 - 
Figure 34: Drag coefficient of circular cylinder as function of Reynolds number............................ - 33 - 
Figure 35: Cup Anemometer Aero Dynamic Effect........................................................................... - 34 - 
Figure 36: linearity curve between the angular velocity and the Wind Speed for the cup anemometer 
aerodynamics..................................................................................................................................... - 35 - 
Figure 37: Two cups velocity values chosen for cup model. ............................................................. - 37 - 
Figure 38: Actual curve obtained due to the wake effect from the lightning conductor.................... - 38 - 
Figure 39: Wind Rose for 180 to 360 sectors.................................................................................... - 45 - 
Figure 40: Velocity ratio (cup/sonic) profile from Experimental data.............................................. - 46 - 
Figure 41: Comparison between the Experimental data to the CFD simulation Velocity profile for 
Model-2 at L/D=25. .......................................................................................................................... - 47 - 
Figure 42: Comparison between the Experimental data to the CFD simulation Velocity profile for 
Model-1 at L/D=25. .......................................................................................................................... - 47 - 
Figure 43: Comparison between the Experimental data to the CFD Model-2 to the CFD Model-1 at 
L/D=25. ............................................................................................................................................. - 48 - 
Figure 44: Probability Density distribution for the Sonic & Cup anemometer Wind speed readings .- 49 
- 
 v
Figure 45: Histogram of measured wind speed data and the corresponding fitted weibull 
distribution function .......................................................................................................................... - 50 - 
Figure 46: Histogram of frequency occurrence of Wind speeds for 18 bins with respective to the Wind 
Direction............................................................................................................................................ - 51 - 
Figure 47: Histogram of frequency occurrence of Wind speeds in each bin for Cup readings for the 
direction 240 to 270........................................................................................................................... - 52 - 
Figure 48: CFD model of flow stream line obtained for different L/D ratios ................................... - 59 - 
Figure 49: Velocity deficit profiles at 00 Inflow angle to the domain for different L/D stations in CFD 
Model................................................................................................................................................. - 60 - 
Figure 50: Estimated Error in Power Density for Different L/D stations......................................... - 67 - 
 
 
 
 
 
 
 
 
LIST OF TABLES 
 
 
 
Table 1: Mesh controllers in CFX-mesh for the Model-1.................................................................. - 18 - 
Table 2: Mesh controllers in CFX-mesh for the Model-2.................................................................. - 25 - 
Table 3: mesh statistics for the Model-1 & Model-2 ......................................................................... - 26 - 
Table 4: CFD input Velocities corresponds to the Wind direction.................................................... - 39 - 
Table 5: concave and convex velocities for the different angle variation from the CFD Model-2.... - 42 - 
Table 6: concave and convex velocities for the different angle variation from the CFD Model-1.... - 44 - 
Table 7: Error in power density for different L/D stations................................................................ - 67 - 
 
 
 vi
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - 1 -
Chapter 1 
 
1.1. Introduction 
 
 
Wind speed is an important parameter in wind energy to evaluate the power 
performance, mechanical loading, power quality and acoustic emission of a wind 
turbine. The energy available in the wind varies as the cube of the wind speed 
( 3VP ∝ ). Hence, very accurate measurements of the wind speeds are essential 
to the wind energy. This is a fact for measurements of wind resources, which 
determine the overall driving economics of the wind turbines, on which 
manufactures sell their wind turbines and for which contractor agreements 
determine whether the individual wind turbines are able to perform satisfactory or 
not. So, the wind speed measurement is the most important single contribution to 
the uncertainty of the power performance measurement. The wind speed sensors 
are therefore the most important instruments to the wind energy community. 
 
 
The wind speed is measured by using various devices. The Cup anemometer is 
one of the most commonly used measuring devices because they tend to be cost 
attractive in comparison to other types of instrument and they can be very 
robust. When the cup anemometer effected by the turbulence it responds more 
quickly to an increase in the wind than to a decrease of the same magnitude and 
thus tends ‘to spend more time on the high side than on the low side of the 
mean’ with the consequence that the measured mean wind speed will be too 
high(Reference [11]). 
 
 
When planning a test campaign prior thought needs to be given to ensure that 
the measurement system has reliability and that the data will have good 
integrity. A specific attention needed to the possible effect of the climate 
environment, here the Key aspect is lightning. 
1.2. Lightning 
 
Wind sites by their nature are susceptible to lightning damage. As 50% of 
lightning strikes involve currents of more than 28000 amps it is obvious that a 
strike (or flashover from an adjacent structure) directly onto an anemometer will 
cause physical damage to the instrument as well as destroying any electronics 
within. Cups can be blown off rotors,pieces melted out of fins, moving parts 
welded together etc. Instruments damaged in this way are usually irreparable 
with few parts being recoverable necessitating a replacement instrument. 
Damage can be reduced by using a lightning rod, heavy duty copper tape and 
earth rods to divert the main portion of any strike away from the instruments. 
Due to the amount of energy involved in lightning strikes, it is impossible to 
devise an economic system which will guarantee total immunity, protection 
measures can only attempt to restrict the damage by trying to divert most of the 
energy in the strike to earth by-passing sensitive instruments and electronics. 
 
 
 - 2 -
For this reason, installation of the lightning conductor is essential on the top of 
the wind mast. Normally, a 600 protection umbrella can be used to protect from 
the lightning strikes. The tower is used as path to ground, when lightning occurs 
it can pass through the structure. Sometimes the probability of lightning strike 
will be very low and it may be decided not to use a lightning conductor so as not 
to disturb the mast top Cup Anemometer. 
Unfortunately, the presence of a vertical rod causes disturbance in the airflow 
which can cause additional errors in the readings obtained from an anemometer. 
It is therefore necessary to come to a compromise to maximise protection and 
minimise errors. Increasing the spacing between the instruments and the central 
vertical lightning rod will reduce disturbance effects. However it is necessary to 
increase the height of the rod to keep the instruments within the protected area. 
So it is recommended to use the thicker rod to prevent it swaying about 
excessively. A 16mm diameter type of lightning conductor is typical. (Reference 
[28]) 
1.3. Objective and scope of work 
 
In this thesis project, a field experiment in France is investigated where a 
lightning conductor was installed on a wind mast in order to protect the Mast 
from the lightning tricks. It was discovered that top cup anemometer was 
significantly affected by the large directional sector due to the wake of a lightning 
conductor that protruded to a height greater than the cup as indicated by 
measured data shown in the figure 1. Cup and the sonic anemometers are 
situated at 50m, 47m height of the Wind Mast. Mast setup and the curve showing 
the ratio of the wind speed measured by the cup and sonic anemometer for 
different wind directions is shown in figure 1.The lightning rod is 16mm in 
diameter and at a distance of 400mm from the cup anemometer, i.e. L/D=25.The 
installation of the lightning conductor rod has been made in accordance with the 
IEA recommendation: 11 for ‘Wind seed measurement and use of cup 
anemometry’. The purpose of the analysis is to evaluate refinement of the 
recommendations on how to install a cup anemometer in order to overcome wake 
of a lightning conductor. This is the reason why it is necessary to analyze flow 
around the lightning rod and distortion of this flow at the location of 400mm from 
the lightning protection where the anemometer is situated on the wind mast. 
 
 
 
 
 - 3 -
 
Figure 1: Mast setup and the curve showing the ratio of the wind speed measured by the cup and 
sonic anemometer for different wind directions 
 
 
The overall scope of this thesis project can be summarized as follows: 
 
1. In the first step, a CFD model is generated in ANSYS CFX to study the flow 
behind the lightning conductor of wind mast. 
 
 
o Model-1(section 2.3.1) is built to study the general air flow over 
the cylinder rod, then Velocity deficits at L/D=25 where the Cup 
anemometer is situated are studied. The curve showing the ratio of 
the local wind speed at the position of the cup anemometer and the 
undisturbed wind speed for different wind directions is carried out 
by changing the inflow angle to the Domain. 
 
o Model-2(section 2.3.2) is built with improved mesh near the 
cylinder wall to study the velocity deficit for different L/D stations. 
The curve showing the ratio of the wind speed for different wind 
direction is carried out by changing the inflow angle to the Domain 
for different L/D stations. 
 
o Compare the two Models with the experimental result. Finally the 
best grid is selected for further study. 
 
2. Estimate the total Wind power density available from wind data and from the 
computed CFD Wind data. 
 
 
o Wind power density can be estimated from available Sonic and cup 
anemometer wind data. The error in the power density calculated 
due to the presence of the lightning conductor against the Cup 
Anemometer is investigated. 
 
o Wind power density estimated for different L/D stations from the 
CFD model for 45 bins. Finally error in the total power density at 
each station is carried out. 
 
o Minimum distance between the lightning conductor and the Cup 
anemometer is estimated from the power density calculation. 
 - 4 -
1.4. Thesis Organization 
 
The thesis is complied as follows: 
 
Chapter 2 gives an introduction to ANSYS CFX and related theory. Furthermore, it 
explains the creation of two models and meshing of these models, in order to 
obtain the results from CFD. 
 
In chapter 3, the cup anemometer model is clearly explained in order to compute 
the curve of the velocity ratio obtained from the CFD model for different wind 
directions at L/D=25. 
 
In Chapter 4, the result from the CFD simulation (the curve showing the velocity 
ratio for different wind directions at L/D=25) is compared with experimental 
curve. 
 
Chapter 5 illustrates the total Power Density available from the Sonic & Cup 
anemometer. The error in the power density losses are compared with the CFD 
estimated Power Density. 
 
Chapter 6 describes the velocity deficit obtained for different stations. The 
available concave and convex velocities of cup anemometer for different station 
are estimated. The curve showing the velocity ratio for different wind directions 
obtained from the CFD simulation for different L/D stations is compared with 
experimental velocity ratio curve at L/D=25. Finally, the error in the power 
density is estimated, which will indicate at which particular L/D distance the 
lightning rod should be installed. 
 
In chapter 7 the conclusions are given. Finally, the accuracy of the model is 
explained based on the comparison with the available measured data. 
1.5. Limitations to the project 
 
The listed below are various limitations related to the various aspects of this 
project: 
 
1. This project is limited to a two cup anemometer instead of three cup 
anemometer. It is more convenient to look at aerodynamic effect analytically for 
two cup arrangement than the three cup anemometer. 
 
2. Applied inlet wind velocity to the CFD model is 8 m/s which is a constant in all 
wind directions, but in reality the wind varies with the time and direction. This will 
creates the turbulence affect on cup anemometer, which will influence the Wind 
speed readings. 
 
3. Limited time for the project is one of the constraints, since a lot of 
experimental work was supposed to be done as well to compare the CFD model 
data to experimental data (limitations continue….). 
 
 
 
 
 
 
 - 5 -
4. The cup anemometer has generally a lower performance compared to sonic 
(anemometer) due to the following reasons: 
 1. Rotational shear effect. 
 2. Friction. 
 3. Wake of one cup and the arm effect over other cup (3 cup anemometer). 
 4. Rotational effect disturbances to the Wind (Very low). 
 5. Over speeding. 
 
5. In this project the flow past a lightning rod is investigated for 2D-CFD 
simulation. In reality wind varies with the time and space, hence it has additional 
parameters in the third dimension (z-direction). Therefore for moreaccuracy of 
the investigation 3D-CFD simulation is needed to be performed. 
 
6. The collected wind data for sonic and cup anemometers is at 47 m and 50 m 
heights respectively on the mast. The difference in these heights can cause the 
wind shear that will affect the wind speeds seen by anemometers. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - 6 -
 
Chapter 2 
 
2.1. Introduction to ANSYS CFX-10.0 
 
For this thesis work Computational Fluid Dynamics (CFD) is the primary means of 
analysis. For this purpose ANSYS CFX 10.0 version is used to analyse the flow 
disturbance to the cup anemometer due to the presence of lightning conductor on 
the top of the Wind Mast. ANSYS CFX is based on finite volume technique where 
the region of interest is divided into small sub-regions, called control volumes. 
The equations are discretized and solved iteratively for each control volume. As a 
result, an approximation of the value of each variable at specific points 
throughout the domain can be obtained. In this way, the full picture of the 
behaviour of the flow over a body can be analysed. In this CFD analysis the set of 
equations which describes the processes of momentum, heat and mass transfer 
are known as the Navier-Stokes equations. These partial differential equations 
were derived in the early nineteenth century and have no known general 
analytical solution but can be discretized and solved numerically. Often, an 
approximating model is used to derive these additional equations, turbulence 
models being a particularly important example. The figure below represents the 
Schematic view of the ANSYS CFX (Reference [3]). 
 
 
Figure 2: Schematic view of the Ansys cfx. 
 
In this project the flow past a lightning cylindrical rod is modelled. The cylinder is 
represented in a 2D-CFD model of the flow through the fluid domain. The 
diameter of the cylinder is specified, and the flow domain is adjusted based on 
these dimensions. A very fine grid is used near the cylinder and coarse mesh is 
applied to whole domain for minimum possible time by keeping the less memory 
space in machine. The wake is calculated by using various turbulence models like κ -ε Model and κ -ω SST (Shear Stress Turbulence) models. The best 
turbulence model is used for further problem analysis. Finally, computed curve of 
the velocity ratio for different wind directions is constructed and it is compared 
with the measurements. This kind of investigation can also be carried in Wind 
tunnel, where setup for the cup anemometer with lightning conductor at distance 
of L/D=25 can be made. The wind speed measurements can be collected for 
various inflow angles. Finally, the curve of the velocity ratio for varying wind 
directions can be constructed. 
 
 - 7 -
2.1.1. Reynolds number: 
 
The Reynolds number is the most important dimensionless number in fluid 
dynamics providing a criterion for dynamic similarity. It is named after Osbourne 
Reynolds. The Reynolds is used for determine whether a flow is laminar or 
turbulent. Laminar flow within e.g. pipes will occur when the Reynolds number is 
below the critical Reynolds number of Recrit, pipe=2300 and turbulent flow when it 
is above 2300 where the Reynolds number is based on diameter and the mean 
velocity within the pipe. The value of 2300 has been determined experimentally 
and a certain range around this value is considered the transition region between 
laminar and turbulent flow. The computed Reynolds number for this problem 
is 4101.7 × , that is relatively low, so the transition will play a big role. Typically it 
is given as follows for this problem: 
• Re = ρ v D / μ or 
• Re = v D / ν 
 = 5108.1/016.0*8 −× 
 = 4101.7 × 
Local Reynolds number and the strong gradient of variables near the wall region 
requires more attention, it could not be solved by simply following the standard 
procedure as the Reynolds number changing and becomes low when the flow 
reaches the near wall region. A fine grid is required near the wall region in order 
to calculate the flow precisely (Niels.N.Sørensen [6]1995). 
2.1.2. Boundary layer theory: 
External flows past a cylinder experiences boundary layer separation and very 
strong flow oscillations in the wake region behind the body. In certain Reynolds 
number range, a periodic flow motion will develop in the wake as a result of 
boundary layer vortices being shed alternatively from either side of the cylinder. 
This regular pattern of vortices in the wake is called a von Karman vortex street. 
One of the objectives of this project is to investigate the flow past a circular 
cylinder and study the turbulent wake flow at the cup anemometer. For that 
purpose it is necessary to study some key points related to this kind of 
phenomena and they are boundary layer flow separation, wake flow; vortex 
shedding will be discussed in the following section. 
 
The presence of the fluid viscosity slows down the fluid particles very close to the 
solid surface and forms a thin slow-moving fluid layer called a boundary layer. 
The flow velocity is zero at the surface to satisfy the no-slip boundary condition. 
Inside the boundary layer, flow momentum is quite low since it experiences a 
strong viscous flow resistance. Therefore, the boundary layer flow is sensitive to 
the external pressure gradient (as the form of a pressure force acting upon fluid 
particles). If the pressure decreases in the direction of the flow, the pressure 
gradient is said to be favorable. In this case, the pressure force can assist the 
fluid movement and there is no flow retardation. However, if the pressure is 
increasing in the direction of the flow, an adverse pressure gradient condition can 
exist. In addition to the presence of a strong viscous force, the fluid particles 
now have to move against the increasing pressure force. Therefore, the fluid 
particles could be stopped or reversed, causing the neighboring particles to move 
away from the surface. This phenomenon is called the boundary layer 
 - 8 -
separation. The deviation in the pressure distribution from an ideal is the cause of 
form drag, and its calculation is thus made possible with the boundary layer 
theory. Turbulent flow with the aid of boundary layer theory was introduced by 
Prandtl’s mixing length theory (1925) which, together with systematic 
experiments, paved the way for the theoretical treatment of turbulent flow 
(Schlichting [7]).the figure below represents the development of boundary layer 
separation with time and the flow with complete boundary layer separation in the 
wake of a circular cylinder. 
 
 
Figure 3: Development of boundary layer separation with time &flow with complete boundary 
layer separation in the wake of a circular cylinder (Reproduced from Schlichting [7]) 
 
 
2.1.3. Wake: 
 
Consider a fluid particle that flows within the boundary layer around the circular 
cylinder, the pressure is a maximum at the stagnation point and gradually 
decreases along the front half of the cylinder. The flow stays attached in this 
favorable pressure region as expected. However, the pressure starts to increase 
in the rear half of the cylinder and the particle now experiences an adverse 
pressure gradient. Consequently, the flow separates from the surface and 
creating a highly turbulent region behind the cylinder called the wake. The 
pressure inside the wake region remains low as the flow separates and a net 
pressure force (pressure drag) is produced. The figure 4 represents the flow in 
the boundary layer near a point separation. 
 
Figure 4: Representation of flow in the boundary layer near a point of separation 
(Reproduced from Schlichting [7]). 
 
 - 9 -
2.1.4. Vortex Shedding: 
 
The boundarylayer that separates from the surface forms a free shear layer and 
is highly unstable. This shear layer will eventually roll into a discrete vortex and 
detach from the surface (a phenomenon called vortex shedding). Another type of 
flow instability emerges as the shear layer vortices shed from both the top and 
bottom surfaces interact with one another. They shed alternatively from the 
cylinder and generate a regular vortex pattern (the Karaman vortex street) in the 
wake. According to the Newton's second law, time rate change of the linear 
momentum is equal to the sum of all external forces acting on a system. 
Therefore, an integration of the linear momentum inside a control volumes 
surrounding the circular cylinder can provide information of the aerodynamic 
forces (lift and drag) acting on the cylinder. 
 
2.1.5. Momentum Balance: 
 
The external force acting on an object can be determined using the momentum 
balance concept. In general, there is a momentum deficit in the wake profile 
along the stream wise direction as relative to the incoming momentum upstream 
of the object. Therefore, a simple balance of the momentum flow in and out of 
the control volume surrounding the object suggests that there is net force acting 
on the object. (Note: the pressure is considered to be relatively constant if the 
momentum flow is measured far away from the object.) This net force along the 
flow direction is called the drag. Averaged velocity profiles of the flow past a 
circular cylinder is provided as a general representation of the wake flow field. 
Immediately behind the cylinder, a recirculation region exists with a strong 
reversing flow. The region between the cylinder and the end of the recirculation 
region is called the vortex formation region. The centerline velocity becomes zero 
at the end of the vortex formation region. Further downstream, the two 
separating shear layers merge and the velocity profile presents a typical wake 
profile. It is clear that there is a deficit in the center of the wake. This deficit in 
the momentum flow is the direct result of drag force acting on the cylinder. The 
figure5 represents the velocity deficit profile over a cylinder with distance. 
 
 
Figure 5: velocity deficit profile over a cylinder with distance (Reproduced from reference [4]). 
 - 10 -
2.1.3. Modeling flow near the wall: 
 
Logarithmic profile approximates the velocity distribution near the wall which 
helps to compute the fluid shear stress as a function of the velocity at a given 
distance from the wall. The low Reynolds number methods resolves the details of 
the boundary layer profiles by using very small mesh length scales in the 
direction normal to the wall which means very thin inflation layers. The low 
Reynolds method doesn’t refer to the device Reynolds number, but to the 
turbulent Reynolds number which is low in the viscous sub layer. 
The wall conditions to the dependent variables at the near wall mesh node which 
is presumed to lie in the fully turbulent region of the boundary layer is given by 
the logarithmic relation. 
 
Where, 
k =von Karman's constant =0.41 
C=Constant=5.1 
Near wall velocity is given by the following way: 
*u
Uu ≡+ 
The dimensionless distance from the wall through the boundary layer to the first 
node away from the wall can be defined in the following way: ν
yuy *≡+ 
The above mentioned model (log law of the wall) is valid for high values of +y and 
high Reynolds number. According to the reference [21], the +y requirement for the 
mesh needed for the simulations should be in between 0< +y >5-7, for the low 
Reynolds number turbulence model. The figure below represents contour plot of 
+y distribution on the surface of the cylinder from the CFD simulation. The 
computed maximum +y value from the CFD simulation is 0.008, which is in 
between the valid +y range. 
 
 
Figure 6: contour plot of distribution on the surface of the cylinder. 
Cy
k
u += ++ )ln(1
 - 11 -
2.2. Turbulence Models 
Turbulence consists of fluctuations in the flow field in time and space. It is a 
complex Process, mainly because it is three dimensional, unsteady and consists of 
many scales. It can have a significant effect on the characteristics of the flow. 
Turbulence occurs when the inertia forces in the fluid become significant 
compared to viscous forces, and is characterized by a high Reynolds Number In 
principle, the Navier-Stokes equations describe turbulent flows without the need 
for any additional information. However, turbulent flows at realistic Reynolds 
numbers span a large range of turbulent length and time scales and would 
generally involve length scales much smaller than the smallest finite volume 
mesh which can be practically used numerical analysis. To enable the effects of 
turbulence to be predicted, a large amount of CFD research has concentrated on 
methods which make use of turbulence models. Turbulence models have been 
specifically developed to account for the effects of turbulence without recourse to 
a prohibitively fine mesh and Direct Numerical Simulation. The two models which 
are used here to analyze the flow over the lightning conductor rod are κ -ε 
model and κ -ω SST (Shear Stress Turbulence) model (Reference [3]). 
 
2.2.1. ε−k Model: 
 
The standard ε−k model is used in the perdition of most turbulent flow 
calculations because of its robustness, economy, and reasonable accuracy for a 
wide range of flows. However, the model performs poorly when faced with no-
equilibrium boundary layers. It tends to predict the onset of separation too late 
and to under-predict the amount of separation. Separation influences the overall 
performance of many devices, such as diffusers, turbine blades and aerodynamic 
bodies. It is the two equation model where the turbulent velocity scale is 
computed from the turbulent kinetic energy which is provided from the transport 
equation. The turbulent length is estimated from the turbulent kinetic energy and 
the rate of dissipation which is also available from the solution of its transport 
equation. This model introduces two equations for the estimation of the turbulent 
coefficients namely κ andε . 
 
 k Equation: 
 
The turbulent kinetic energy ‘κ ’ is defined as the variance of fluctuations in the 
velocity. Turbulent flow focuses on average kinetic energy per unit volume and 
the average internal energy per volume. 
 ε Equation: 
 
The rate at which the velocity fluctuation dissipates is given by epsilon ‘ε ’. 
Epsilon in turbulent flows is dependent on the viscosity affects in the small scale 
turbulent structure. The relation governing epsilon is derived from the Navier 
Stokes equations and by manipulation the standard equation is obtained. 
2.2.2. K- ω SST (Shear Stress Transport) Turbulence model: 
 
One of the main problems in turbulence modelling is the accurate prediction of 
flow Separation from a smooth surface. Standard two-equation turbulence models 
(κ - ε model) often fail to predict the onset and the amount of flow separation 
under adverse pressure gradient conditions. In general, turbulence models based 
 - 12 -
on the ε-equation predict the onset of separation too late and under-predict the 
amount of separation later on. The k-ω based Shear-Stress-Transport (SST) 
model was designed to give highly accurate predictions of the onset and the 
amount of flow separation under adverse pressure gradients by the inclusion of 
transport effects into the formulation of the eddy-viscosity. This results in a major 
improvement in terms of flow separation predictions. This model is combination of 
the k-epsilon and Baseline K-omega model (Reference [3]). 
2.2.3. Transitional Turbulence: 
 
The point where instability first occurs is always upstream of the point of 
transitionto a fully turbulent flow. The distance between the point of instability 
where the Reynolds number equals critx,Re and the point of transition trx,Re 
depends on the degree of amplification of the unstable disturbances. The 
transition to turbulence is strongly affected by factors such as pressure gradient, 
disturbance levels, wall roughness and heat transfer. The transition process 
influences a sizeable fraction of the flow is that of external wall boundary layer 
flows at intermediate Reynolds number ranging from 104 to 105 .A dramatic 
change take place when the Reynolds number is around 5102× when the 
boundary layer becomes turbulence before separation. Now the separation is 
postponed since a turbulent boundary layer is able to sustain for a longer time 
than a laminar flow (Reference [27]). 
 
The transition model is based on two transport equations, the first is an 
intermittency equation used to trigger the transition process and the second helps 
in avoiding additional non-local operations introduced by the quantities used in 
the experimental correlations. 
 
The intermittency concept can be incorporated into the computations by two 
ways, using conditioned average navier-stokes equations and other by 
multiplying the eddy viscosity ( tμ ) obtained from the turbulence model with 
intermittency factor (γ ).the first method has major difficulty in implementing as 
it requires to solve the two sets of highly coupled conditioned navier-stokes 
equations and this method is computationally expensive. For this reasons the 
second method is used. 
 
Simon and Stephens (Reference [23]) showed that by combining the two sets 
conditioned average navier-stokes equations and by making the assumption that 
the Reynolds stress in the non turbulent part are negligible. The intermittency can 
be incorporated in to the computations by using the eddy viscosity ( *tμ ), which is 
obtained by multiplying the eddy viscosity from the turbulence model ( tμ ), with 
the intermittency factor.That is *tμ (= γμ *t ) is used in the mean flow equations. 
This current intermittency approach was applied in conjunction with the 
correlation of Suzen (Reference [22]) for the onset of transition. 
 
[ ])10*3.0(4coth)150120(Re 532 tKTut −+= −θ 
 
tK Is the minimum value of the acceleration parameter in the downstream 
deceleration region and Tu is the free stream turbulence intensity at onset point 
of transition. 
 
 - 13 -
The above two concepts have been included with the SST turbulence model to 
create a new SST transition Turbulence model.Proper grid refinement and 
specification of inlet turbulence levels is crucial for accurate transition prediction. 
In general, there is some additional effort required during the grid generation 
phase because a low-Re grid with sufficient stream wise resolution is needed to 
accurately resolve the transition region. As well, in regions where laminar 
separation occurs, additional grid refinement is necessary in order to properly 
capture the rapid transition due to the separation bubble. Finally, the decay of 
turbulence from the inlet to the leading edge of the device should always be 
estimated before running a solution as this can have a large effect on the 
predicted transition location. 
 
 
 
 
 
 
 
 
 
 
 - 14 -
 
2.3. Simulations and results 
 
In this section creation of two CFD models and meshing of these models in 
accordance with the geometry is explained. Afterwards, simulated results are 
obtained for model 1 and 2 for different turbulence models. Finally the best grid, 
best turbulence model is selected to calculate the total power density available for 
diffferent L/D stations from the CFD wind data. 
 
2.3.1. Model-1: 
The purpose of designing model-1 is to analyse the general flow disturbance from 
the lightning conductor at a distance of L/D=25. Suitable mesh controllers are 
applied to see wake deficit from the lightning conductor. Finally the results are 
compared with the model-2 results for selection of fine grid. 
2.3.1.1. The modeling details: 
The flow field around the cylindrical rod is modelled in two dimensions with the 
axis of the lightning rod perpendicular to the direction of flow. The lightning rod is 
modelled as a circle and domain is created around the cylinder. A steady state 
velocity is applied to the fluid domain. The procedure for solving the CFD model is 
shown below: 
1. Create the geometry (cylinder and the flow domain). 
2. Mesh generation. 
3. Applying the boundary conditions. 
4. CFX Solver 
5. Post-processor. 
2.3.1.2. Create the geometry 
Sketching surface (the low-x surface) as a rectangle of domain size of 960Χ640 
mm is drawn. A circle of diameter of 16mm is drawn over the rectangle 
(Rectangle and circle will both be part of sketch 1). Afterwards, extrude in the z 
direction by 1.6mm.The 3D body formed by the box with the cylinder cut out, 
sometimes confusingly referred to as the “solid”, is where the fluid will flow. 
Schematic view of the geometry for the model-1 is shown in figure 7. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - 15 -
 
 
 
 
 
 
 
 
 
 
 
 Figure 7: Schematic view of the geometry for the model-1 
The figures below represent the extruded model-1 with the scale factor of 1.6mm 
depth along the z-direction. Rectangle with the cylinder cut can be observed at 
the centre of the rectangle. 
 
 
Figure 8: lightning rod cross section in model-1. 
 
Diameter of the 
cylinder 16 mm 
Default 2D Regions. 
960 mm 
X
Y
 
400 mm 
Domain Width =1.6 mm 
Inlet Outlet 
Z
L/D=25.Cup anemometer position 
 - 16 -
2.3.1.3. Mesh generation. 
 
CFX-Mesh is a mesh generator aimed at producing high quality meshes for use in 
computational fluid dynamics (CFD) simulations. CFX-Mesh produces meshes 
containing tetrahedral, prisms and pyramids in standard 2D, 3D meshing mode, 
and additionally can be include hexahedra in extruded 2D meshing mode. It 
produces output in the form of a CFX –Pre mesh file suitable for importing directly 
into CFX-Pre, the CFX-5 pre-processor. A fine mesh is used in CFX-mesh for the 
better results. The grid used for this purpose is 2D mesh. Delaunay surface and 
volume mesh generation controls are used for accurate results in a solver. The 
figures below represent the generated surface mesh in whole domain and at the 
location of the cylinder walls. 
 
Figure 9: generated surface mesh for the symmetrical plane & near the cylinder. 
In near-wall regions, boundary layer effects give rise to velocity gradients which 
are greatest normal to the face. Computationally-efficient meshes in these 
regions (cylinder wall regions) require that the elements have high aspect ratios. 
If tetrahedral are used, then a prohibitively fine surface mesh may be required to 
avoid generating highly distorted tetrahedral elements at the face. CFX-Mesh 
overcomes this problem by using prisms to create a mesh that is finely resolved 
normal to the wall, but coarse parallel to it. The figure below represents the 
prismatic mesh layers that are created near the wall region of cylinder. The mesh 
is used in the local face element normal to 'inflate' 2D triangular face elements 
into 3D prism elements at selected walls or boundaries. We can control the 
creation of these elements and determine their size and distribution in near-wall 
regions. Delaunay surface meshing is characterized by its speed and its ability to 
mesh closed faces (Reference [3]). 
 - 17 -
 
Figure 10: Fine mesh for cylinder in near-wall regions. 
 
The applied number of inflation layers for this model is 30. And the relative 
thickness of adjacent inflation layers is determined by a geometric expansion 
factor. Expansion Factors used for this modelis 1.2. Each successive layer, as we 
move away from the face to which the Inflation is applied, is approximately 1.2 
Expansion Factor thicker than the previous one. Minimum Internal Angle governs 
the minimum angle that is allowed in the triangular face of a prism nearer to the 
surface before it is deemed to be of unacceptable quality and marked for deletion. 
The given Minimum Internal Angle to the model is one. First Layer Thickness 
option is used to specify the height for the first prism. This option does not 
control the overall height of the inflation layers, but creates prisms based upon 
the First Prism Height (0.00001). The creation of an Inflated Boundary is used to 
specify which faces we want inflation to apply. For this purpose we specify the 
cylindrical circle rod face. The figure below represents the cylindrical rod face 
after having the volumetric mesh. 
 
Figure 11: the cylindrical rod face with the volumetric mesh 
 
 - 18 -
The table below shows the given input values for the mesh controller in the CFX- 
mesh generation for model-1: 
 
2.3.1.4. Boundary conditions applied to the Model. 
The output file from the CFX mesh (*.gtm) is used to specify the boundary 
condition for model in CFX-5 pre-processor. In order to apply the boundary 
conditions to the model it is necessary to create fluid domain for initialization of 
boundary conditions. And then it is needed to specify the physical properties like 
specifying flow type and domain model and the fluid models (turbulence model). 
The time dependence of the flow characteristics for this problem is specified as 
steady state simulation type. Steady state simulations, by definition, are those 
whose characteristics do not change with time and whose steady conditions are 
assumed to have been reached after a relatively long time interval. They 
therefore require no real time information to describe them. 
The flow velocity is zero at the default 2D regions (up and down side walls) to 
satisfy the free-slip boundary condition. Inside the boundary layer, flow 
momentum is quite low since it experiences a strong viscous flow resistance. 
Therefore, the boundary layer flow is sensitive to the external pressure gradient. 
The Figure below shows the applied boundary conditions for different regions of 
the fluid domain in CFX-5 pre-processor. 
 
 
 
 
Figure 12: Boundary condition applied for the domain and circular cylinder 
 
 Spacing Inflation 
Simulation Default Body 
Spacing 
Default Face 
Spacing 
No of 
Inflation 
Layers 
Expansion 
Factor 
Minimum 
Internal 
Angles 
First 
Prism 
Height 
1.6mm 
Element Thick 
50 20 30 1.2 1 0.00001 
Table 1: Mesh controllers in CFX-mesh for the Model-1. 
 - 19 -
CFX solver control parameters like time scale control, the convergence criteria 
which represent the maximum number of iterations are defined in the CFX-Pre. 
The maximum number of iterations used here are 100 and the residual target is 
1e-6 .The CFX file written as solver file (*.def), which is called as definition file. 
The CFD solver gives the CFD calculation with the graphical user interface. Figure 
below represents the solver manager which provides feed back on convergence 
progress through run definition and control. The main area of the graphical 
window shows the value of each plotted variable i.e. the RMS residual at each 
time step and the text window displays the simulation information and how the 
solution is proceeding. 
 
 
Figure 13: Solver Manager. 
CFX –solver generates two files a result file (*.res) and an output file (*.out) for 
the CFD calculation. Finally, post-processor will give the result output from the 
CFD analysis. The data generated by the result file from the solver is used here to 
analyze the result from the post-processor. The Plane 1 & 2 is drawn at cylinder 
and at the 400mm from the cylinder where the cup anemometer is situated. The 
velocity deficit from the different turbulence models are taken at Plane 1 & 2. 
Figure below represent the velocity stream lines in domain by presenting the 
Plane 1 & 2. 
 
 
Figure 14: velocity stream lines along the Plane 1 & 2 in model-1. 
 - 20 -
2.3.1.5. Results for ε−k Turbulence model: 
The results obtained for model-1 from the CFX –post processor are presented 
below. These results are calculated for the Reynolds number 7e+04.The contour 
plots of velocity stream lines obtained in domain is shown below. Two planes are 
created at the lightning rod, L/D=25 in order to get velocity deficit plots at these 
specific locations. Here wind flow is normal to the domain which is equal to 2600 
wind direction sector where the Cup readings are fully influenced by the lightning 
conductor. 
 
Figure 15: Plane 1&2 at velocity contour plot with k-ε model 
 
 
Figure 16: velocity contour plot with k-ε model 
 
 
 - 21 -
As it can be observed from the above velocity stream lines flow past the circular 
cylinder, it experiences boundary layer separation and steady state velocity 
streamlines can be observed over the body. At a certain Reynolds number, a 
periodic flow motion will develop in the wake as a result of boundary layer 
vortices being shed alternatively from either side of the cylinder. This regular 
pattern of vortices in the wake is called a Karman vortex street. The figure: 
17represents velocity deficit at L/D=25 (at Cup anemometer) and the figure: 
18represents the combined plot of velocity distribution near the lightning rod and 
at L/D=25 from the lightning rod where the cup anemometer is located. 
 
 
Figure 17: Velocity distribution at cup location with k- ε model 
 
 
Figure 18: Comparison of Velocity distribution at two locations with k- ε model 
 
 - 22 -
 
2.3.1.6. Results for K- ω SST (Shear Stress Transport) 
Turbulence model: 
 
The figure below represents the contour plot of stream lines at cylinder for k-ω 
Shear-Stress-Transport (SST) model. As it can be observed from this contour plot 
behind the cylinder there is more flow separation in comparison to the k-epsilon 
model. In the Reynolds number range 104 to 105 one sees a laminar boundary 
layer to the left of the vertical centreline of the cylinder. The flow separation point 
makes an angle of about 800 with the centre line of the cylinder. A wide wake is 
seen at down stream. 
 
 
 
Figure 19: velocity contour plot with k-w SST-Model for model-1 
 
 
The figure20 represents velocity deficit for k-ω based Shear-Stress-Transport 
(SST) model, at L/D=25 from the lightning rod. The combined plot for the 
velocity distribution at lightning rod & at the Cup anemometer is shown in figure 
21. This turbulence model is designed to give highly accurate predictions of the 
onset and the amount of flow separation under adverse pressure gradients by the 
inclusion of transport effects into the formulation of the eddy-viscosity. 
 - 23 -
 
Figure 20: Velocity distribution at cup location with K-w SST model 
 
 
Figure 21: velocity distribution at two locations with k-w SST model 
 - 24 -
2.3.2. Model-2: 
 
2.3.2.1. Model description with respective to new grid 
 
 
The purpose of model-2 design is to analyse the flow disturbance from the 
lightning conductor at different L/D station. A very refined mesh at cylinder wall is 
used to predict the accurate velocity deficit from the lightning conductor. The 
computed new velocity seen by cup anemometer is used to quantify the 
measured error in terms of power density loss as for instance as a function of the 
distance L/D. For this investigation the domain is size of 2000 Χ 1000 mm is 
created with circle diameter of 16mm is drawn. Figure below shows the 
Schematic view of the geometry creation for model-2.Figure 22: Schematic view of the geometry for the model-2 
 
The left figure in figure23 represents the extruded model-2 with the scale factor 
of 1.6mm depth along the z-direction. The right figure represents the generated 
surface mesh for whole of the domain. 
 
 
 
Diameter of the 
cylinder 16 mm 
Default 2D Regions. 
2000 mm 
 (0,0,0) 
XYZ
400 mm
Domain Width=1.6 mm 
Inlet Outlet 
1000 mm 
L/D=25.Cup anemometer position 
 - 25 -
 
Figure 23: generated volume mesh for the symmetrical plane for model-2 
 
The figures below represent the generated surface mesh near the cylinder wall 
regions. The surface mesh looks fine as it can compare with the Model-1. 
 
 Figure 24: generated surface mesh for near the cylinder for Model-2. 
The table below represents the given input values for the mesh controller with 
improved mesh near the wall region of the cylinder. 
 
 Spacing Inflation 
Simulation Default 
Body 
Spacing 
Default 
Face 
Spacing 
No of 
Inflation 
Layers 
Expansion 
Factor 
Minimum 
Internal 
Angles 
Minimum 
external 
angle 
First 
Prism 
Height 
1.6mm 
Element 
Thick 
50 20 40 1.3 1 10 0.00011 
Table 2: Mesh controllers in CFX-mesh for the Model-2 
 - 26 -
A very refined mesh near the cylinder wall region is having a great influence over 
the final results. The numbers of Inflated Layers which control boundary layer 
effects give rise to velocity gradients which are greatest normal to the face. With 
the improved number of inflation layers at this region which will produce fine grid. 
The number of inflation layer applied to the model is 40. 
 
If First Layer Thickness is used to specify the thickness of the inflation layer, then 
this is a maximum number of inflation layers. Otherwise, it will be the actual 
number of inflation layers, except in places where layers are removed locally for 
reasons of improving mesh quality (e.g. where inflation layers would otherwise 
collide with each other). The Number of Inflated Layers is restricted to be no 
more than 50.the applied thickness of the inflation layer is 0.00011 where in case 
of model-1 is 0.00001. And the relative thickness of adjacent inflation layers is 
determined by a geometric expansion factor. Each successive layer, as we move 
away from the face to which the Inflation is applied, is approximately 1.3 
Expansion Factor is thicker than the previous one. This value improves the quality 
of the mesh at cylinder wall region. 
 
Table: 3 represent the mesh statistics for the Model-1 & Model-2, where a fine 
grid is selected for the better agreement with the experimental result. The fine 
grid from the model-2 result is used to calculate the error in power density for 
different stations. For the Model-2 the number of elements and total number of 
hexahedrons are higher than the Model-1. Hence, the outcome result from the 
Model-2 will produce the better result than that of Model-1. 
 
Model Number of 
Elements 
 Domain 
size 
Total 
number of 
Nodes 
Off Wall 
Spacing 
Expansion 
Factor 
Total Number 
of Wedges 
Total Number of 
hexahedrons 
Model-1 4404 640 Χ 960 5464 0.00001 1.2 960 960
Model-2 6764 2000 Χ 1000 9580 0.00011 1.3 4204 2560
 Table 3: mesh statistics for the Model-1 & Model-2 
 - 27 -
2.3.2.2. Results from Model-2 for K- ω SST (Shear Stress 
Turbulence model): 
 
The results obtained for model-2 from the CFX –post processor are presented 
below. The below figures show refined mesh generation near cylinder wall region 
which can produce a better accuracy for the velocity deficit. 
 
 
Figure 25: Velocity contour plot with k-w SST model 
 
 
Figure 26: velocity contour plot with k-w SST-Model for model-2 
 
 - 28 -
The outcome of velocity deficit for model-2 at zero degree inflow angle to the 
domain at L/D=25 is shown below (figure 25). As it can be observed from this 
velocity deficit plot it can produce accurate predictions of flow separation as 
compared with the Model-1. At this location we can see that there is a speed 
reduction from the cup model (Chapter: 3) about 11% from the initial given inlet 
velocity of 8 m/s. This is due to the wake effect from the lightning rod. But it can 
also be seen that there is raise in the velocity of 0.06 m/s, this could be because 
of the restriction of the fluid domain. The velocity deficit is high compared with 
the model-1 result at the centre of the domain where the cup anemometer is 
situated. 
 
 
 
Figure 27: Velocity distribution at cup location with K-w SST model for Model-2 
 
 
Figure 28: velocity distribution at two locations with k-w SST model for Model-2 
 
 - 29 -
2.4. Comparison of Model-2 Velocity profiles to the 
Schlichting Analytical method: 
 
The fully developed turbulent eddy street is subjected to the action of viscosity as 
it is carried down stream along the wake. The viscous action causes a continuous 
reduction in the mean velocity deficit, diffusion of vorticity and dissipation of 
turbulent fluctuations. Schlichting(Reference [7]) was the first who developed a 
mathematical model for far wake, based on momentum transfer, Prandtl’s 
concept’s of ‘mixing length’ and the coefficient of apparent turbulent diffusion. In 
the case of a wake, the velocity profiles become similar only at large distances 
downstream from the body, there being no similarity at smaller distances. Hence 
there is a restriction to the consideration of large distances ‘X’ so that the velocity 
difference 1UUU −= α .The initial experiments by Schlichting and by the 
subsequent researchers were in excellent agreement with the theory providing 
that the downstream station is at least 50/ ≥DX . 
 
The ratio of the wake deficit (U1) to free stream velocity ( αU ), at ‘X’ distance 
from the cylinder is given from the Schlichting analytical method The equation 
below represents the velocity ratio of free stream velocity to the wake velocity. 
 
⎟⎠
⎞⎜⎝
⎛−⎟⎟⎠
⎞
⎜⎜⎝
⎛=
−
2
2
1
0
1
4
1
4
1 ηεπ
α
α
EXP
DC
XDCU
U
U
d
d 
Where 0ε is the virtual kinematics Viscosity. 
DCU dαε 0222.00 ≈ (From the measurements) 
 
⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎟⎟⎠
⎞
⎜⎜⎝
⎛−⎟⎠
⎞⎜⎝
⎛≈
2
2
1
1 26.26.1195.0
DXC
yEXP
X
DC
U
U
d
d
α
 
 
Figure 29: Schematic view of the wake behind the cylinder rod from Schlichting analytical 
method. 
 
 
D
X 
Y
2
1b 
U1,Wake Deficit 
αU 
U
 - 30 -
The half of the wake width can be represented mathematically as 
 
( )21
2
1 4
1 DXCb d= 
From these expressions it can be concluded that the width of the two dimensional 
wake increases as x and the velocity decreases as
x
1
. 
The figure below represents the Wake behind the cylinder at 400mm 
obtained by using the Schlichting analytical method. 
 
Figure 30: Result output for wake behind the cylinder rod from Schlichting analytical method. 
 
The plots obtained from the Schlichting analytical method and the CFD models for 
different distances from the lightning conductor are compared to check the 
validity. 
 
The plot below shows the comparison of velocity wake profile obtained from the 
Schlichting analytical method to the CFD model at the distance of 100 mm. It can 
be observed from this plot that there is a good agreement between the 
Schlichting analytical method and CFD model. From the CFD graph we can see 
peaks in velocity wake profile when the wind leaves the cylindrical conductor. This 
is due to the turbulence models that they produce high pressure gradients near 
the cylinder walls. 
 - 31 -
. 
Figure 31: Wake behind the cylinder at 100mm.Plot below shows the velocity deficit profile from the Schlichting analytical method 
at the distance of 200 mm (figure 32) and 400mm (figure 34).From these plots it 
can be seen that the width of the wake increases more than the formula from 
Schlichting when the distance increases from the lightning conductor. This is due 
to the numerical diffusion from the CFD model. In CFD mesh generation there are 
unstructured hexahedrons. When the flow moves from one element to the other 
element in a domain, there recirculation occurs which tends to increase the width 
of the wake. 
 
Figure 32: Wake behind the cylinder at 200mm. 
 - 32 -
 
Figure 33: Wake behind the cylinder at 400mm where the cup anemometer located 
As finally the plots from the CFD model and from the Schlichting analytical 
method model do not agree in the wake depth at the same L/D location. Here it 
has to be admitted that, there is a great mismatch to such an extent with regard 
to the depth of the wake, since both of them matched in the region outside the 
wake. The depth of the wake matches to a great extent in the zone of L/D =100, 
but starts to mismatch afterwards. This explanation could be summarized by 
stating that this problem might have arisen because of the chosen Grid in CFD 
and also by the numerical diffusion as we go away from the rod. 
 
2.5. Drag coefficient as a function of Reynolds 
number. 
 
The force acting on the body is the surface integral of all normal and shearing 
stresses acting on it. If F denotes the component of the resultant force in any 
given direction ,it is possible to write the dimensionless force coefficient of the 
form F / 22 Vd ρ .the dimensional analysis leads to conclude that for geometrically 
similar systems this coefficient can depend only on the dimensionless group 
formed with V, d, ρ , and μ ,i.e. on the Reynolds number. The component of the 
resultant force parallel to the undisturbed initial velocity is referred to as the 
drag F . Hence the dimensionless coefficient for drag calculated by using given 
formula below. 
 
 
AV
FCF
2
2
1 ρ
= 
 Where, A is the projected frontal area. 
 
The computed drag coefficient from the CFD model is 1.01, which is equals to 
unity. From the book of Schlichting [7] page number: 17 which graphs a curve of 
drag coefficient of circular cylinders as function of the Reynolds number, which is 
shown in the figure below. The experimental points for the drag of circular 
cylinders of widely differing diameter fall on a single curve. The sudden decrease 
 - 33 -
in the value of the drag coefficient, which occurs at 5105Re ×= is shown in the 
figure. 
 
 
 
 Figure 34: Drag coefficient of circular cylinder as function of Reynolds number. 
 
 
 
 
 
 
The extrapolated drag coefficient from the above plot for specific Reynolds 
number (7.0 e+04) and the diameter of 16mm is unity, which is the same 
calculated above from the CFD model. 
 
Finally, we conclude that the simulated results are in good agreement with the 
experimental findings, as to validate the analytical and theoretical findings found 
from CFD model and from the model of Schlichting analytical method. And as we 
found that they are in good match. 
 - 34 -
 
Chapter 3 
 
This chapter explains the cup anemometer aerodynamics effect when the cup is in 
the undisturbed wind speed and in the wake of the lightning conductor. The 
measured wind speed readings are collected from the ED three cup anemometer, 
where as this work is carried out for two cup anemometer. This is because it is 
more convenient to look at analytically by using the two cup anemometer. 
3.1. Cup Anemometer model 
The objective of this project is to investigate velocity deficit (distortion in the 
velocity distribution) caused by the presence of the lightning rod on wind mast. 
This analysis enables us to determine the influences on the cup anemometer 
measurements made in real time which is dependent upon the location of the 
lightning protection rod. For that purpose the obtained velocities of concave and 
convex from the CFD model are used as an input to the cup model. 
 
As the cup anemometer is placed inside the flow stream, the concave surfaces of 
the cups have higher wind resistance than their convex counter parts. 
Consequently, this produces an unbalanced moment with respect to the centre 
axis and forces the cups to rotate. Under steady flow condition, the rotational 
speed of the anemometer is directly proportional to the wind speed, that is: V=f 
(ω ).it is necessary to investigate theoretical expression when the two cups 
experience the same wind speed. 
 
Figure 35: Cup Anemometer Aero Dynamic Effect 
3.1.1. Deriving the linearity expression between the angular 
velocity (ω ) and the Wind Speed ( 0V ) from the cup 
anemometer aerodynamics: 
 
This model explains the theoretical expression between the how the constant 
angular velocity varies with the wind speed when the two cups feels the same 
wind speed( 0V ) when the wind direction is normal to the Cups. 
The instantaneous aerodynamic torque on the rotor of the cup AM is given by 
expression. 
 20
2
0 )(2
1)(
2
1 ωρωρ rVACrrVACrM dxdvA +−−= 
 - 35 -
Where A is the frontal area of the anemometer, ρ is the air density and dvC and 
dxC are the drag coefficients for the concave and convex faces of the anemometer 
cup. In the study state, there is perfect torque balance (MA=0), and the equation 
reduces to: 
 20
2
0 )(2
1)(
2
1 ωρωρ rVACrrVACr dxdv +=− 
 There fore 20
2
0 )()( ωω rVCrVC dvdx +=− 
 
 ω
ω
rV
rV
C
C
dv
dx
−
+=
0
0 
 ωω RVCrCV +=− 00 Where 
dv
dx
C
C
=C 
 ωrCVC )1()1( 0 +=− 
 Therefore 
rC
VC
)1(
)1( 0
+
−=ω 
 
 i.e.: 0KV=ω ------------------------ (1) 
 
 Where 
rC
CK
)1(
)1(
+
−= 
The above equation represents linearity between the angular velocity and the 
Wind Speed for the cup anemometer. It means the angular velocity of the cup 
anemometer is proportional to the Wind Speed. Using MATLAB the linearity curve 
for this modelling phenomenon is plotted as shown below. 
 
Figure 36: linearity curve between the angular velocity and the Wind Speed for the cup 
anemometer aerodynamics 
 
 - 36 -
 
 
3.1.2. Modeling of cup anemometer where anemometer is in 
wake state: 
 
In the flow regime which a uniform shear across the face of the anemometer 
resulting in the ‘left hand cup position’ seeing a flow surplus of 0.2% and the 
‘right hand cup position seeing a flow deficit of 0.2%, the anemometer will 
indicate a wind speed which will either be in error by +0.7% or-0.7%, depending 
on whether it is convex or concave cup face which sees the flow deficit. The 
anemometer does not average out the sheared flow to indicate the correct mean 
value. It might be thought in the presence of a uniformly sheared flow across the 
face of the anemometer, that the anemometer should indicate the mean flow 
speed (Reference [1]). Below theoretical expression derived when the two cups are 
in full wake state 
The instantaneous aerodynamic torque on the rotor of the cup anemometer AM , 
is given by 
 20
2
0 )(2
1)(
2
1 ωρωρ rVACrrVACrM dxdvA +−−= 
 
In the study state, there is perfect torque balance (MA=0), and the equation 
reduces to: 
 20
2
0 )(2
1)(
2
1 ωρωρ rVACrrVACr dxdv +=− 
 
 
When the cup anemometer is in the wake state the convex or concave cup