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University of Calgary
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Graduate Studies The Vault: Electronic Theses and Dissertations
2018-12-11
CFD simulation of Smooth and Rough NACA 0012
Airfoils at low Reynolds number
Li, Yunjian
Li, Y. (2018). CFD simulation of Smooth and Rough NACA 0012 Airfoils at low Reynolds number
(Unpublished master's thesis). University of Calgary, Calgary, AB.
http://hdl.handle.net/1880/109338
master thesis
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UNIVERSITY OF CALGARY
CFD simulation of Smooth and Rough NACA 0012 Airfoils at low Reynolds number
by
YUNJIAN LI
A THESIS
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF SCIENCE
GRADUATE PROGRAM IN MECHANICAL ENGINEERING
CALGARY, ALBERTA
DECEMBER, 2018
© Yunjian Li 2018
ii
Abstract The objective of this study is to investigate the accuracy of turbulence model prediction in
the computational fluid dynamics (CFD) of airfoil aerodynamic performance with and
without roughness. It is very important to study the roughness effect on airfoil aerodynamic
characteristics for wind turbine blades and aviation. Since roughness alters the lift and drag
coefficients, it affects the aerodynamics performance directly. NACA0012 airfoil is used
in the CFD simulation. Low Reynolds number of 1.5105 is used to allow comparison to
experimental results, and high Reynolds number of 1.5106 is used to check the
aerodynamic performance at conditions more suitable to large wind turbines, but for which
there is no experimental data. The range of angle of attack (degrees) is from 0˚ - 10˚ as this
covers the range that gives maximum power extraction. The roughness is selected from a
previous experiment which is a sand grain roughness grit-36 with a 500μm thickness. The
equivalent sand roughness height is used in turbulence models for rough surface simulation.
This parameter represents the whole effect of the roughness. The simulation results of lift,
drag, pressure and skin friction coefficients as well as the lift to drag ratio between smooth
and rough surfaces are compared with the available experimental results. Three turbulence
models: low Reynolds SST k-ω, transition-SST and SA models were used for the prediction.
The results show the surface roughness can decrease the lift coefficient, lift to drag ratio
and increase the skin friction and drag coefficients. At the low Reynolds number (1.5105),
the prediction of low Reynolds SST k-ω, transition-SST on the smooth surface show a good
agreement with the experimental data than SA model. However, only the low Reynolds
SST k-ω model has a good consistency with the experimental results on the rough surface.
At high Reynolds number (1.5106), the results of transition-SST on drag coefficients are
more closed to experimental data than low Reynolds SST k-ω and SA model. Three models
have similar results with experimental data on lift coefficients.
iii
Table of Contents
1 Introduction .................................................................................................. 1
2 Surface roughness and its sources ............................................................... 7
2.1 Dust accumulation ............................................................................... 7
2.2 Insect contamination ............................................................................ 7
2.3 Ice accretion ......................................................................................... 9
2.4 Erosion ............................................................................................... 10
3 Roughness .................................................................................................. 11
3.1 Characterization of roughness ........................................................... 11
3.2 Effect of roughness on the flow field ................................................ 11
3.3 Roughness theory............................................................................... 15
3.4 Motivation of the work ...................................................................... 18
4 Turbulence models ..................................................................................... 19
4.1 Spalart Allmaras ................................................................................ 19
4.2 SST k-ω .............................................................................................. 20
4.3 Transition (γ-Reθ) SST ...................................................................... 21
5 Choice of Airfoil and Experiment ............................................................. 22
6 Mesh refinement ........................................................................................ 24
6.1 Domain detail ..................................................................................... 24
6.2 Grid Independence Check ................................................................. 25
6.3 Grid convergence index study ........................................................... 27
7 Results ........................................................................................................ 30
7.1 Smooth Airfoil ................................................................................... 30
7.1.1 Lift coefficient ........................................................................... 30
7.1.1.1 Low Reynolds number ...................................................... 30
7.1.1.2 High Reynolds number...................................................... 31
7.1.2 Drag coefficient ......................................................................... 32
7.1.2.1 Low Reynolds number ...................................................... 32
7.1.2.2 High Reynolds number...................................................... 34
iv
7.1.3 Lift to drag ratio ......................................................................... 35
7.1.3.1 Low Reynolds number ...................................................... 35
7.1.3.2 High Reynolds number...................................................... 36
7.1.4 Pressure coefficient ................................................................... 36
7.1.4.1 Low Reynolds number ...................................................... 36
7.1.4.2 High Reynolds number...................................................... 43
7.1.5 Skin friction coefficient ............................................................. 45
7.2 Rough surfaces................................................................................... 46
7.2.1 Lift coefficient ........................................................................... 46
7.2.1.1 Low Reynolds number ...................................................... 46
7.2.1.2 High Reynolds number...................................................... 47
7.2.2 Drag coefficient ......................................................................... 48
7.2.2.1 Low Re number ................................................................. 48
7.2.2.2 High Reynolds number...................................................... 50
7.2.3 Lift to drag ratio ......................................................................... 51
7.2.3.1 Low re number .................................................................. 51
7.2.3.2 High Reynolds number...................................................... 51
7.2.4 Pressure coefficient ................................................................... 52
7.2.4.1 Low re number .................................................................. 52
7.2.4.2 High Reynolds number...................................................... 55
7.2.5 Skin friction coefficient ............................................................. 57
8 Comparison of the aerodynamic performance of the smooth and rough
airfoils ........................................................................................................... 58
9 Discussion .................................................................................................. 63
10 Conclusion ............................................................................................... 64
11 Recommendation ..................................................................................... 66
Reference ...................................................................................................... 67
v
List of Figures
Figure 1.1 (a) blade leading edge affected with pits and gouges (b) blade leading edge with
delamination……………………………………………………………………………….1
Figure 1.2 Influence of airfoil L/D and number of blades on wind turbine power
coefficient…………………………………………………………………………………3
Figure 1.3 Schematic of leading edge separation bubble…………………………………5
Figure 2.1 Rough surfaces of wind turbine blades caused by insects, ice, and erosion,
respectively………………………………………………………………………………..7
Figure 2.2 Classification of ice accumulation types……………………………………….9
Figure 3.1 Transition over the surface of a NACA0012 for various Re at zero angle of
attack (degrees)………………………………………………………………….……….12
Figure 3.2 Turbulence intensity increase for a smooth and rough NACA 0012 airfoil at Re
= 1.25×10-6……………………………………………………………………………….13
Figure 3.3 Experimental Cl of S814 airfoil with varying roughness…………………….14
Figure 3.4 experimental Cd of S814 airfoil obtained at Ohio State University………….14
Figure 3.5 Downward shift of the logarithmic velocity profile………………………….16
Figure 3.6 Illustration of equivalent sand grain roughness………………..……………..17
Figure 6.1 Domain with Structured Mesh………………………………………………..24
Figure 6.2 Close view of the mesh adjacent to the airfoil………………………………..25
Figure 6.3 Dependence of Cl at stall angle of attack (degrees) against number of grid cells
from Eleni………………………………………………………………………………...26
Figure 7.1 Cl of smooth NACA 0012 airfoil at Re = 1.5×105 between α (0-10) compared
with experiment of Chakroun et al[24]and Althaus[25].………………...……………….30
Figure 7.2 Liu and Qin’s computational results: Cl of smooth NACA 0012 airfoil at Re =
vi
1.5×105 compared with experiment of Chakroun et al [24]……..………………………31
Figure 7.3 Cl of smooth NACA 0012 airfoil at Re = 1.5×106 between α (0-10), compare
with experiment data of Gregory [5]………………………….…………..…………..…32
Figure 7.4 Cd of smooth NACA 0012 airfoil at Re = 1.5×105 between α (0-10) compare
with experiment of Chakroun et al [24] and Althaus[25]..……………..………………..33
Figure 7.5 Liu and Qin’s computational results: Cd of smooth NACA 0012 airfoil at Re =
1.5×105 compare with experiment of Chakroun et al [24]…………………………….33
Figure 7.6 Cd of smooth NACA 0012 airfoil at Re = 1.5×106 between α (0-10), compare
with experiment data of Gregory [5]……………………………………………………..34
Figure 7.7 L/D of smooth NACA 0012 airfoil at Re = 1.5×105 between α (0-10) compare
with experiment of Chakroun et al [24]. and Althaus [25]…………….………………35
Figure 7.8 L/D of smooth NACA 0012 airfoil at Re = 1.5×105 between α (0-10), compare
with experiment data of Gregory [5]……………………………………………………..36
Figure 7.9 Cp on the smooth surface of a NACA 0012 at α = 6˚, Re = 1.5×105 compared
with the experiment of Chakroun et al [24]………………………………………….. 37
Figure 7.10 streamlines on the smooth surface of a NACA 0012 at α = 6˚, Re = 1.5×105,
low Re SST k-ω ………………………………………………………………………….38
Figure 7.11 turbulent kinetic energy of a NACA 0012 at α = 6˚, Re = 1.5×105, low Re SST
k-ω……………………………………………………………………………………….38
Figure 7.12 streamlines on the smooth surface of a NACA 0012 at α = 6˚, Re = 1.5×105,
transition-SST……………………………………………………………………………39
Figure 7.13 turbulent kinetic energy of a NACA 0012 at α = 6˚, Re = 1.5×105, Transition
SST……………………………………………………………………………………….39
Figure 7.14 streamlines on the smooth surface of a NACA 0012 at α = 6˚, Re = 1.5×105,
SA………………………………………………………………………………………..40
Figure 7.15 Liu and Qin’s results: Cp on the smooth surface of a NACA 0012 at α = 6˚, Re
= 1.5×105 compared with the experiment of Chakroun et al [24]……………………….41
Figure 7.16 Cf of three turbulence models on smooth surface at α = 6 and Re= 1.5×105…42
Figure 7.17 Liu and Qin’s results: Cf of three turbulence models on smooth surface at α =
vii
6 and Re= 1.5×105……………………………………………………………………….42
Figure 7.18 Cp of smooth surface at α = 6˚, Re = 1.5×106……………………………….43
Figure 7.19 Cf of three turbulence models on smooth surface at α = 6 and Re=
1.5×106………………………………………………………………………….….…….44
Figure 7.20 Cf comparison with experiment results on smooth surface at α = 2˚ and Re=
1.5×105…………………………………………………………………………..……….45
Figure 7.21 Cl of rough NACA 0012 airfoil at Re = 1.5×105 between α (0-10) compare
with experiment of Chakroun et al [24]…………………….…………………………46
Figure 7.22 Liu and Qin’s results: Cl of rough NACA 0012 airfoil at Re = 1.5×105 compare
with experiment of Chakroun et al [24]………………………………………….……47
Figure 7.23 Cl of rough NACA 0012 airfoil at Re = 1.5×106 between α (0-10)……..…..48
Figure 7.24 Drag coefficients of rough NACA 0012 airfoil at Re = 1.5×105 between α (0-
10) compared with experiment of Chakroun et al [24]…………….…………………..49
Figure 7.25 Liu and Qin’s results: Drag coefficients of rough NACA 0012 airfoil at Re =
1.5×105 compared with experiment of Chakroun et al [24]……………………….….49
Figure 7.26 Drag coefficients of rough NACA 0012 airfoil at Re = 1.5×106 between α (0-
10)……………………………………………………………………………….……….50
Figure 7.27 L/D of rough NACA 0012 airfoil at Re = 1.5×105 between α (0-10) compare
with experiment of Chakroun et al [24]……..…………………………….…………51
Figure 7.28 L/D of rough NACA 0012 airfoil at Re = 1.5×106 between α (0-10)………52
Figure 7.29 Cp of rough surface at α = 6˚, Re = 1.5×105 compare with experiment of
Chakroun et al [24] ……………………………………………………………………53
Figure 7.30 Liu and Qin’s results: Cp of rough surface at α = 6˚, Re = 1.5×105 compare
with experiment of Chakroun et al [24]………………………………………………..53
Figure 7.31 Cf of three turbulence models on rough surface at α = 6˚, Re =
1.5×105………………………………………………………………………………...…54
viii
Figure 7.32 Liu and Qin’s results: Cf of two models on rough surface at α = 6˚, Re =
1.5×105………………………………………………………………….…………..……54
Figure 7.33 Cp of rough surface at α = 6˚, Re = 1.5×106……………. ……………..……55
Figure 7.34 Cf of three turbulence models on rough surface at α = 6˚, Re =
1.5×106……..………………………………………………………………………….…56
Figure 7.35 Cf comparison with experiment results on rough surface at α = 2˚ Re =
1.5×105……..………………………………………………………………………….....57
Figure 8.1 Cl comparison between smooth and rough surface at Re= 1.5×105……..…...58
Figure 8.2 Cd comparison between smooth and rough surface at Re= 1.5×105……..……59
Figure 8.3 L/D comparison between smooth and rough surface at Re= 1.5×105…………60
Figure 8.4 Cp at angle of attack 6˚ comparison between smooth and rough surface at Re=
1.5×105……………………………………………………………………………...……61
Figure 8.5 Cf comparison between smooth and rough surface at angle of attack 6˚ at Re=
1.5×105……………………………………………………………………………...……62
ix
List of Tables
Table 1.1 Surface roughness experiments with airfoils……..…………………….…….....4
Table 6.1 Cd comparison for grid independency check at α = 6 using the low Reynolds
SST k- ω model……..…………………………………………………….………..….....26
Table 6.2 Cd for three grids with a refinement ratio of 2 using the low Reynolds SST k- ω
model at α=6˚ and Re number =1.5×105……..…………………………………..…….....27
Table 6.3 Results of grid convergence index ……..…………………………................28
Table 6.4 Grid convergence index of Cl on smooth surface at α=6˚ and Re number
=1.5×105………………………………………………………………………………….29
Table 6.5 Grid convergence index of Cd on smooth surface at α=6˚ and Re number
=1.5×105………………………………………………………………………………….29
Table 6.6 Grid convergence index of Cl on rough surface at α=6˚ and Re number
=1.5×105………………………………………………………………………………….29
Table 6.7 Grid convergence index of Cd on rough surface at α=6˚ and Re number
=1.5×105………………………………………………………………………………….29
x
List of Symbols
c aerofoil chord length
Cl lift coefficient
Cd drag coefficient
Cp pressure coefficient
Cf skin friction coefficient
𝐶𝑏2 constant
Cμ constant
E constant
𝑓𝑟 a roughness function that quantifies the shift of intercept due to roughness effect
h roughness height
h roughness height
hs+ non-dimensional roughness height
hs equivalent sand grain roughness
k turbulent kinetic energy
L/D lift to drag ratio
Re Reynolds number
Rek roughness Reynolds number
Rek crit critical Reynolds number
u+ dimensionless velocity
uτ friction velocity
u’ root -mean -square of velocity fluctuations
xi
uavg mean flow velocity
up velocity of centre point P of the wall adjacent cell
𝑆�̃� user defined source term
V streamwise velocity
x position along the chord from 0 to c
x/c station of chord length
y⁺ non-dimensional wall distance for a wall bounded flow (y+= 𝑦𝜌𝜇𝜏
𝜇)
yp distance from point P to the wall
Greek sympols
α angle of attack (degrees)
κ Von Karman constant
μ dynamic molecular viscosity
μt eddy viscosity
ν kinematic molecular viscosity
ρ fluid density
𝜎�̃� constant
Γω effective diffusivity of k
Γk effective diffusivity of and ω
τw wall shear stress
ΔB a downward shift of the logarithmic velocity profile
Δn distance of the first and second grid points off the wall
xii
Roman symbols
Yk dissipation of k
Yω dissipation of ω
YV destruction of turbulent viscosity
GV production of turbulent viscosity
Gω generation of turbulent kinetic energy
Gk generation of specific dissipation rate
1
1 Introduction
With the increase of human population and industrial production, the energy consumption
of world is growing. Although fossil fuels are the main energy source, the contribution to
global warming has attracted people’s attention to seek renewable energy and reduce the
pollution. Wind energy is one of the outstanding clean energies with a reasonable cost. The
operating environment of a wind turbine can have contaminants such as dust, ice and
insects [1]. These can cause damage to the surface of the wind turbine blade and the
generated irregularities can change the flow field, and reduce the power output from the
blades. In addition, the freeze and thaw cycles caused by the variation of temperature may
produce smaller cracks in the blade coating that can propagate, promote the removal of the
coating and finally delamination [28].
The leading edge is the main affected part of the blade. Particles follow the streamlines,
they tend to accumulate near the stagnation point close to the leading edge [1]. Accreted
insect debris, ice and sand or dirt on the leading edge will decrease the turbine performance
especially in the high speed tip region which is very important to energy production [2]. In
general, roughness on the leading edge of wind turbine blades begins with small pits [2].
As the time grows, the small pits formed near the leading edge will increase in density and
form gouges [2]. Gouges also can grow with time in size, density and finally cause
delamination (Fig 1.1 b) [2]. Part (a) shows the pits and gouges are formed near the leading
edge. Part (b) shows the blade after long service with delamination over the leading edge.
Figure 1.1 (a) blade leading edge affected with pits and gouges (b) blade leading edge with
delamination [2].
2
The aerodynamic behaviour of blades is affected seriously by the distributed roughness on
the surface. If the roughness is concentrated near the leading edge, the laminar to turbulence
transition will happen earlier than on a smooth blade. In addition to early transition, leading
edge roughness also modifies the aerodynamic forces. The lift is decreased by the
increasing displacement effect of a thicker turbulent boundary layer and drag is increased
by the shear stress increase at the surface [3]. This causes a reduction of lift to drag ratio
for all angles of attack [3]. In order to maximize aerodynamic performance, a blade must
operate at the angle that gives maximum lift to drag. With roughness, both the boundary
layer and displacement thickness are increased as well. Timmer [41] investigated the effect
of leading edge roughness on a thick airfoil (DU 97 aerofoil). The results showed that there
was a reduction of lift coefficient (Cl ) by 32-45% depending on the Reynolds number, Re.
Re is the Reynolds number based on the chord and velocity of freestream[39]. The
roughness used in the experiment was carborundum 60 (grain size of 0.25 mm) and
wrapped around the 8% of the airfoil on either side of the leading edge. Refs. [11] found
that leading edge roughness at Re = 106 can cause a maximum Cl decrease of 16% for the
S809 and NACA4415 airfoils. The minimum drag coefficient (Cd) is increased by 41% and
67% respectively. Cl and Cd are defined as
𝐶𝑙 =𝐿
1
2𝜌𝑉2𝑐
(1.1)
𝐶𝑑 =𝐷
1
2𝜌𝑉2𝑐
(1.2)
where L is lift, D is drag, V is velocity of freestream, c is chord length, ρ is density, ν is
kinematic viscosity [51], and the Reynolds number, Re, is
𝑅𝑒 =𝑐 𝑉
𝑣 (1.3)
The Lift to Drag ratio (L/D) is the most important aerodynamic property for an airfoil,
because it has a direct effect on the performance of a wind turbine blade using that airfoil.
Cl is up to 200 times higher than Cd for well designed modern airfoils. If the L/D is low,
the power efficiency is decreased as well. The optimum point of power efficiency shifts to
lower tip speed ratio, tip speed ratio is defined as the ratio between tangential speed of the
tip of a blade and actual speed of the wind [21]. When the L/D and tip speed ratio are high,
the number of rotor blades have little influence on the rotor power efficiency. On the
3
contrary, when the L/D and tip speed ratio are low, the number of rotor blades is very
important. In other words, low speed rotors need many blades, but the airfoil L/D is not
very important. High speed rotors need fewer blades, but the airfoil L/D is significant for
energy production.
Figure 1.2 Influence of airfoil L/D and number of blades on wind turbine power coefficient
[21].
Roughness effects on wind turbine blades are still not well understood and need to be
studied further, since it has a negative effect on the aerodynamics of wind turbine blade
and there is not much previous research work on wind turbine blade roughness. Table 1.1
shows the contamination accumulation surface roughness models used in most of the
experimental studies of airfoils [42]. Most of the research work on wind turbine blade
roughness focus on ice accumulation rather than particle and insect accumulation and
erosion cases [42].
4
Re Airfoil Surface roughness status Ref.
1 × 106 to 10 × 106 Modified DU 97-W-
300
Clean
Zigzag tape
Carborundum 60 roughness
[42]
105 to 5 × 105 E387
FX63-137
S822
S834
SD2030
SH3055
Zigzag trip type F [45]
0.43 × 106
0.65 × 106
0.85 × 106
1.15 × 106
Not mentioned zigzag tape with angle 60°
zigzag tape with angle 90
Strip tape contamination
roughness model
[46]
1.6 × 106
3 × 106
NACA 633-418 Sandblasting aluminum
Rapid prototyping roughness
Zig-zag trip tape
[47]
0.43 × 106
0.65 × 106
0.85 × 106
1.15 × 106
Airfoil near to NACA
6-series
Zigzag tape with angle 60°
Zigzag tape with angle 90°
Strip insertion contamination
roughness model
[48]
6 × 106 NACA 64-018
NACA 64-218
NACA 64-418
Wrap around roughness [49]
78 × 103
169 × 103
260 × 103
NACA 64-618
GA (W)-1
Aligned, roughness height
Staggered, roughness height
[35]
1.5 × 105 NACA0012 Sand grain roughnesss (grit 36) [24]
Table 1.1 Surface roughness experiments with airfoils [42].
5
From Table 1.1, most of the previous research work were at a high Re. Little research has
been done on low Re airfoil roughness. The low Re (100,000<Re<1,000,000) range covers
large soaring birds, remotely piloted aircraft (used for military and scientific sampling,
monitoring and surveillance), mid and high altitude UAV’s, micro air vehicles (MAV),
sailplanes, jet engine fan blades, inboard helicopter rotor blades and wind turbine rotors
are some of the aerodynamic applications [27]. The flow fields may be unstable at the low
Re numbers due to the flow separation, transition and reattachment.
At low Re, the laminar boundary layer may separate at locations on the airfoil that the
turbulent boundary layer at higher Re would not. The separated flow can form a shear layer
which is very unstable which may cause the transition to turbulence. Once transition occurs,
the shear layer is energized by the turbulent shear stresses through entraining the fluid from
the outer stream [27]. The layer is moved closer to the surface by the redistributed energy
from the higher momentum outer flow [27]. It can reattach the separated layer downstream
which is the turbulent boundary layer. The region between the separation and reattachment
is called the “laminar separation bubble” [27].
Figure 1.3 Schematic of leading edge separation bubble [56].
Surface roughness may prevent laminar separation bubble formation. It can lead to the
earlier boundary layer transition and decrease or prevent the separation bubble. In this
research work, low Re = 1.5×105 is considered, since the experiment data of NACA0012
from Chakroun et al [24] at this Re number is available to compare with the CFD results,
6
high Re = 1.5×106 is also used in the simulation to check the performance of airfoils for
large wind turbine blades. The simulation results of smooth surface at high Re number are
compared with experimental data from Gregory [5].
7
2 Surface roughness and its sources
When a wind turbine is exposed to ice and dirt, the blade could be contaminated by airborne
particles.
Figure 2.1 Rough surfaces of wind turbine blades caused by insects, ice, and erosion,
respectively [4–6].
2.1 Dust accumulation
Wind can blow small particles like dust, dirt and sand to the height of wind turbine blades.
When these particles collide with the blade, the smoothness of blade surface is affected.
Since roughness particles follow the streamlines, they tend to accumulate near the
stagnation point close to the leading edge [1]. The effect of dust contamination has not
been extensively studied [1]. A few research works have given some important results for
dust roughness effects on wind turbine blades, such as the relationship between power
generation, roughness size and the duration of dust exposure. In the experiment of
Khalfallah and Koliub [7], the dust accumulated on the blade surface of 300kW pitch
regulated wind turbine was examined after different periods of operation. It is found that
the dust accumulation is around the blade profile which has a high concentration on the
leading edge and the blade tip.
2.2 Insect contamination
Insects are one of the possible sources of blade contamination. However, the presence of
insects was not considered as the source of the power loss until recently. The California
wind farms [10] have been monitored by recording the power output of its wind turbines
8
[8,9]. Varying power outputs were detected which means that for the same wind speed. In
order to find the reason of the phenomenon, the insect hypothesis was proposed by Corten
and Veldkamp [10] that for insect accumulation, with increasing the roughness of the blade
surface may lead to power reduction. Corten and Veldkamp found a 25% energy output
reduction on a 700kW stall regulated turbine due to the insect roughness [10]. At low wind
speed, insects can contaminate the turbine blade because these are the speeds at which
insect fly. However, the power production is not affected significantly by insect accretion
at low wind speed since the flow is insensitive to the contamination, Corten and Veldkamp
[10]. They concluded that due to the flow pattern around the blade has been changed in
high wind speed, this caused a decrease in power [10]. With an increase of wind speed,
there was a loss in the power output with the increase of insect roughness [10]. Furthermore,
in their hypothesis, the contamination levels are decided by the atmospheric conditions that
are conducive for insects. The best conditions are temperatures above 10°C and no rain to
allow insect flight. In addition, very low temperature and humidity prevents insect flight.
Apart from the atmospheric conditions, another factor for insect accretion is altitude. There
is a dramatically decreased density of insects from ground level to 152 meters [8].
In order to validate the hypothesis that the power output can be affected by the insect
accumulation which increases the surface roughness of blade, two wind turbines were
monitored in the same wind farm [1]. The first turbine had blades with natural
contamination of insects and the second had artificial surface roughness. The roughness
was a zigzag tape with a maximum thickness of 1.15mm and a surface roughness of 0.8mm
[10]. The power generation of the two turbines was monitored regularly. In the beginning,
the output of first turbine was larger than the second, but with passing time, the
contamination level increases, the power production of first one decreased to be close to
the production of second one. Compared with the artificially-roughened turbine, the results
show that the contamination of insects causes a similar level of roughness on the blade
surface. It also validates the hypothesis that the insect contamination increases the surface
roughness of blade and can reduce the power generation.
It is difficult for insects to fly in high winds, so blades in high winds are not easily
contaminated [13]. The power output is steady at wind speeds above the rated speed which
9
is typically 13-15 m/s [13]. If the leading edge is already contaminated by insects, power
generation will reduce. After operation at low wind speed for a period, the level of insect
contamination may be changed and lead to a different power output in high wind [13].
2.3 Ice accretion
The accumulation of ice on turbine blades has been studied widely for the risk in the wind
turbine operation. Ice is formed in cold weather, when the water droplets are cooled in
clouds. They strike the blade surface and freeze. Typical ice shapes and classification is
shown in Fig 2.2
Figure 2.2 Classification of ice accumulation types [7].
Ice is divided into four representative types: roughness, horn ice, streamwise and spanwise
ridge ice [29]. Fig 2.2 shows the four kinds of ice with the horizontal axis representing flow
disturbance and the vertical axis representing dimensionality of the icing geometry [29].
Roughness is in the left lower corner with low to middle level of flow field disturbance.
Streamwise, horn and spanwise ridge ice have the increasing effect on the aerodynamics
in the form of reducing L/D [29]. The overlap of these circles indicates that icing can have
characteristics of more than one type.
Ice accumulation on the blade surface is either glaze (horn) ice, rime (streamwise) ice,
10
ridge ice, or ice roughness shown in Fig 2.2. Glaze ice is horn shaped, formed as a thick
ice layer is covered by a thin water layer [1]. The horn shape is formed from the water that
does not freeze on impact, but when it moves to the trailing edge, there will be an impact
on the blade [1]. Rime ice contains ice layers formed at the intersection of the water droplet
streamlines and solid surfaces [1]. Rime ice may not have a significant effect on the flow
field, but glaze ice does due to its shape. These two kinds of ice accumulation are the most
frequently occurring [1]. Ridge ice can form the single large barrier on the suction side of
a turbine blade and this can lead to a large separation region which has a greater effect on
the flow field than other kinds of ice accretion [1]. There is a negative effect on the turbine
performance due to the ice roughness, the effect is governed by the roughness height,
concentration, and location.
2.4 Erosion
Apart from accretion of dust, insects and ice roughness, erosion is another cause of poor
aerodynamics of wind turbines. Wind can carry a lot of dust, dirt, sand and water droplets
to the blade surface which may erode the leading edge and cause roughness without the
particles adhering to the surface. The impact of particulate matter on the airfoil determines
the erosion level. It also depends on the geometric shapes and the relative velocities of both
the airfoil and the particles. The impact velocity is determined by the wind speed and
rotational speed [13].
van Rooij and Timmer [14] state that the geometric design of a blade determines the
aerodynamic performance degradation due to roughness, so a blade can be adapted to have
minimum energy loss [13]. However, the roughness change in the surface with increasing
operation will cause a power output loss that is difficult to predict.
11
3 Roughness
3.1 Characterization of roughness
No matter the source like dust, ice and insects, roughness of the blade surface is represented
by the height, density, and location. Roughness height is characterized by the size of a
representative roughness element. The height from the surface can define the roughness
size for randomly distributed shapes and by the diameter for spherical elements. In order
to compare these cases accurately, the roughness height h, is non-dimensionalized by the
chord length c, and expressed as h/c [1]. The aerodynamic characteristics can be compared
by this parameter h/c for similar Re [1]. Roughness density measures how densely the
roughness is spread on the blade surface.
3.2 Effect of roughness on the flow field
[15-18] indicate that surface roughness can cause two significant effects on boundary layer
transition (the process by which a laminar flow becomes turbulent): the transition region
moves upstream which means the transition process occurs earlier and is often prolonged
[1]. In order to demonstrate the effect, Turner [13] studied flow visualizations of boundary
layers for both clean and rough surfaces. Although the experiment was to investigate
roughness effects for turbomachine blades, it provides a good explanation of the flow
behavior of rough and curved surfaces. The experimental results show that the leading edge
roughness lead to early transition of boundary layer.
Roughness height, shape and distribution are important to be taken into consideration of
the roughness effects [26]. In general, if the roughness element height is less than the height
of the laminar sublayer (the region near a no-slip boundary in which the flow is laminar).
There is little effect on the transition process due to the high level of viscous damping of
the disturbances [26]. The roughness height is described by using a roughness Reynolds
number Rek [26]:
Rek = ρUkk /μ (3.1)
12
where Uk is the velocity at height k, ρ is the density, μ is the dynamic viscosity. Even if k
is constant, Rek will change along the surface with the development of boundary layer.
Some experimental research tried to define a critical Reynolds number Rek crit, for a rough
surface, at which transition will immediately start. Due to factors such as freestream
turbulence, acoustic noise and crossflow contamination may affect the transition
characteristics, the Rek crit has some uncertainty [26].
Kerho and Bragg [16] measured the transition on a NACA0012 airfoil with different Re,
roughness locations and sizes. The results show that roughness elements lead to a slow
boundary layer transition according to the roughness location, size and Re. Figure 3.1
shows an insignificant effect on low Re flow from the size of roughness elements. From
[8-13], the flow field and performance are not affected by the roughness when Re is less
than Rek crit. Regarding the roughness effect on the flow from laminar to turbulent, [40]
indicate that transition occurs after Rek exceeds a critical value between 600 to 700 [3]. Fig
3.1 shows that the roughness effect is significant at high Re for any size and location.
Compared with the clean surface the transition flow is increased as well.
Figure 3.1 Transition over the surface of a NACA0012 for various Re at zero angle of
attack (degrees) [16], x/c is the station of chord length. (s is surface length from the
stagnation point to the leading edge of the roughness strip) [16].
13
Roughness also can modify the turbulence intensity (defined as the ratio of root-mean-
square of the velocity fluctuations to the mean flow velocity). Bragg et al [29] presented
the turbulence intensity increase for a smooth and rough NACA 0012 airfoil at Re =
1.25×106. Fig 3.2 shows roughness elements increase the turbulence intensity level.
Figure 3.2 Turbulence intensity increase for a smooth and rough NACA 0012 airfoil at Re
= 1.25×106 [29].
Ferrer and Munduate [35] presented roughness effects on the S814 airfoil with a molded
insect pattern. Fig 3.3 shows the Cl and Cd at various α and Re with and without grit. At
the high angle of attack, Cl has an obvious reduction in magnitude. In Fig 3.4 the pressure
drag is affected by roughness at high angle of attack where the separation occurs [1].
14
Figure 3.3 Experimental Cl of S814 airfoil with varying roughness (re is Reynolds number,
grit is roughness) [35]
Figure 3.4 Cd of S814 airfoil obtained at Ohio State University (Cdp is pressure drag, Cdw
is wake drag) [35]
15
3.3 Roughness theory
Due to the complicated geometry of distributed roughness, the detailed geometry of the
roughness is not usually retained for simulation. This type of roughness is close to the real
life rough surfaces and the density is different with the roughness shape and location.
Huebsch [30] modeled the dynamic roughness strip through retaining the extract geometry
in the simulation. However, this lead to expensive computations that a large number of
computational cells and time are needed.
The early experiments of Nikuradse [31] used semi-spheres and packed them as densely as
possible. The rough surface was easily characterized by the semisphere height. This is the
origin idea of using single parameter to analysis the complex rough surfaces [22].
Schlichting [43] studied roughness elements of varying size, shape and density. After that
he purposed the concept of a single parameter to describe the rough surfaces: equivalent
sand grain roughness (hs). This parameter aims to generate the same effect as the real
roughness configuration no matter how complex the roughness distribution [22].
Equivalent sand roughness approach is based on the Nikuradse’s early rough pipe
experiments [31]. Equivalent sand roughness can be estimated from the correlations in the
density and shape of roughness elements from Nikuradse’s sand grains like Dirling’s
correlation [33]. The height of equivalent sand grain roughness hs is deduced from the
empirical correlations proposed by Dirling [33], he developed these equations from
experimental data of Nikuradse and Schlichting:
ℎ
ℎ𝑠= {
60.95𝛬−3.98 𝑓𝑜𝑟 𝛬 < 4.92
0.00719𝛬1.9 𝑓𝑜𝑟 𝛬 > 4.92 (3.2)
where
Λ =𝑙
ℎ(
𝐴𝑠
𝐴𝑝)
43⁄
(3.3)
and l is the average distance between roughness elements, h is their average height, As is
16
the windward surface area of the rough element and Ap is the projected area in the direction
of the freestream [33]. The parameter hs is dependent on the real rough elements size and
the covered area.
In CFD simulations, wall roughness effects are simulated through the modified law of wall.
The law of wall for mean velocity modified for rough walls is:
𝑢𝑝𝑢∗
𝜏𝑤/𝜌=
1
𝜅𝑙𝑛 (𝐸
𝜌𝑢∗𝑦𝑝
𝜇) − 𝛥𝐵 (3.4)
where 𝑢∗ = 𝐶𝜇
1
4/𝑘1
2, Cμ =0.09, k is turbulent kinetic energy, ρ is density, τw is wall shear
stress, up is velocity of centre point P of the wall adjacent cell, κ is Karman constant = 0.4,
E is constant = 9.793, yp is distance from point P to the wall, μ is dynamic viscosity, 𝛥𝐵 =
1
𝑘𝑙𝑛 𝑓𝑟. 𝑓𝑟is a roughness function that quantifies the shift of intercept due to roughness
effect [19] .ΔB is a downward shift of the logarithmic velocity profile and formulated as:
1. hs+
≤ 2.25, the hydraulically smooth, ΔB = 0
2. 2.25 ≤ hs+ ≤90, the transitional region,
ΔB = 1
𝜅𝑙𝑛 (
ℎ𝑠+−2.25
87.75+ 𝐶𝑠ℎ𝑠
+) × 𝑠𝑖𝑛[0.4258(𝑙𝑛ℎ𝑠+ − 0.811)]
3. hs+˃90, the fully rough region, ΔB =
1
𝑘𝑙𝑛 (1 + 𝐶𝑠ℎ𝑠
+)
hs+ =
𝜌ℎ𝑠𝑢∗
𝜇, where Cs is the roughness constant which is 0.5 [55].
Figure 3.5 Downward shift of the logarithmic velocity profile
17
Roughness effects are negligible in the hydrodynamic smooth regime, since the roughness
peaks were wholly immersed in the viscous sublayer [53]. Roughness effects become
increasingly important in the transitional regime, both Reynolds and roughness had an
influence on losses, because viscosity is no longer able to damp out the turbulent eddies
formed by the roughness [53]. Roughness effects take full effect in the fully rough regime,
the losses only depend on the roughness level [53].
The downward shift ΔB leads to a singularity in the logarithmic velocity profile for large
roughness heights and low values of y+ [19]. Depending on the turbulence models and near
wall treatment, two approaches are used to avoid this issue. For two equation turbulence
models based on the ω-equation (low Re SST k-ω), the first approach is called “virtually
shifting the wall” [19]. It is based on the observation that viscous sublayer is fully
established only near hydraulically smooth walls [19]. It can be assumed that the roughness
has a blockage effect, which is about 50% of its height [19]. Therefore, virtually shifting
the wall to 50% of the roughness height results in a correct y+ for the first cell: y+rough =
y++ hs+/2 [19]. This gives a correct displacement caused by roughness and the singularity
issue is avoided [19].
The second approach is called “reducing the roughness height as y+ deceases” which is
used in transition SST and SA models [19]. It redefines the roughness height based on the
mesh refinement. The mesh requirement for rough wall is y+rough ˃ hs
+ which can maintain
the full effect of roughness on the flow [19].
Fig 3.6 illustration of equivalent sand grain roughness [19]
18
3.4 Motivation of the work
Roughness effects on the aerodynamic characteristics of airfoils is very important to wind
turbine and aviation. Surface roughness not only affects the aerodynamic characteristics
but also causes early transition and decreases turbine power output. Aerodynamic
predictions of airfoil with the distributed roughness is a challenging problem. The limited
number of roughness configurations that have been thoroughly analyzed. The review given
above indicates that there are only a few simulations for airfoil with distributed surface
roughness. It is not practical to test each airfoil profile for all possible conditions of
roughness, hence developing a numerical method to study the roughness effect is a very
important. However, there are limited computational techniques available to study the
roughness effect on aerodynamic properties. For the purpose of analyzing the flow over
airfoil surface with distributed roughness, a robust computational method that the
prediction of roughness on the airfoil surface is strongly desired.
CFD prediction was carried out to study the aerodynamic behavior of airfoil with
distributed roughness on the airfoil surface. The implementation of three turbulence models:
Spalart-Allmaras (SA), low Re SST k-ω and Transition (γ-Reθ) SST models are described
in this thesis, airfoil aerodynamic forces are simulated and analyzed with the distributed
roughness over the surface. The accuracy of each model on the smooth and rough airfoil
surface was compared.
The specific aim of this project is to undertake CFD simulation of the roughness effects on
an airfoil aerodynamic performance, principally in terms of its lift and drag, and determine
which turbulent models are accurate for the prediction of roughness effects.
19
4 Turbulence models
For the low Re number range, the flow will be laminar, transitional and turbulent along the
airfoil, it is necessary to effectively capture the three types of flows. Various RANS models
are used to compute the flow over the smooth and rough airfoil surface. low Re SST k-ω
model, Transition (γ-Reθ) SST are selected to predict the onset of transition or the
formation of laminar separation bubbles. Spalart-Allmaras (SA) model was developed for
aerodynamic flows which in its original form is a low Re number model [19]. Prediction
of flow transition is very important for low Reynolds number airfoil flows, because
transition has an influence on flow separation and aerodynamic forces. The proper
simulation of transition will lead to an accurate result for these aerodynamics coefficients.
4.1 Spalart Allmaras
The Spalart-Allmaras (SA) turbulence model is a one-equation model that solves a
modeled transport equation for the kinematic eddy (turbulent) viscosity. The Spalart-
Allmaras model was designed specifically for aerospace applications involving wall-
bounded flows and has been shown to give good results for boundary layers subjected to
adverse pressure gradients. It is also gaining popularity in turbomachinery applications.
This model is very efficient and robust to model the flow on an airfoil [17-18]. The
transport equation for the modified turbulent viscosity is:
𝜕
𝜕𝑡(𝜌�̃�) +
𝜕
𝜕𝑥𝑖(𝜌�̃�𝑢𝑖) = 𝐺𝑣 +
1
𝜎�̃�[
𝜕
𝜕𝑥𝑗{(𝜇 + 𝜌�̃�)
𝜕�̃�
𝜕𝑥𝑗} + 𝐶𝑏2𝜌(
𝜕�̃�
𝜕𝑥𝑗)2] − 𝑌𝑣 + 𝑆�̃� (4.1)
ṽ is turbulent kinematic viscosity. v is molecular kinematic viscosity. GV is the production
of turbulent viscosity and YV is the destruction of turbulent viscosity. 𝜎�̃� and 𝐶𝑏2 are the
constants and ν is the molecular kinematic viscosity. 𝑆�̃� is a user-defined source term
(since turbulent kinetic energy is not calculated in SA model when estimating Reynolds
stresses, then this term is ignored) [19]. The turbulent viscosity μt is calculated as:
𝜇𝑡 = 𝜌�̃�𝑓𝑣1 (4.2)
where fv1 is the viscous damping function given by
20
𝑓𝑣1 =𝑥3
𝑥3+𝐶𝑣13 and 𝑥 ≡
�̃�
𝑣 (4.3)
4.2 SST k-ω
The Menter SST k-ω model combines the Wilcox k-ω and the standard k-ɛ model. K is the
turbulence kinetic energy and ω is the specific dissipation rate [23]. The SST k-ω blends
the robust and accurate formulation of k-ω model in the near wall region with the free
stream independence of the k- ɛ model in the far field [6]. The SST k-ω model is more
accurate and reliable for a wider class of flows (adverse pressure gradient flows, airfoils,
transonic shock waves) than the standard k-ω model [44].
The two equations of the SST k-ω model are
𝜕
𝜕𝑡(𝜌𝑘) +
𝜕
𝜕𝑥𝑖
(𝜌𝑘𝑢𝑖) =𝜕
𝜕𝑥𝑗(Γ𝑘
𝜕𝑘
𝜕𝑥𝑗) + 𝐺𝑘 − 𝑌𝑘 + 𝑆𝑘 (4.4)
and
𝜕
𝜕𝑡(𝜌𝜔) +
𝜕
𝜕𝑥𝑗(𝜌𝜔𝑢𝑗) =
𝜕
𝜕𝑥𝑗(Γ𝜔
𝜕𝜔
𝜕𝑥𝑗) + 𝐺𝜔 − 𝑌𝜔 + 𝐷𝜔 + 𝑆𝜔. (4.5)
Gω and Gk are the generation of turbulent kinetic energy and the specific dissipation rate
[44]. Γω and Γk represent the effective diffusivity of k and ω respectively, Yk and Yω are
dissipation of k and ω. Sk and Sω are source terms [44]. The extra cross diffusion term Dω
is the mixed function for the standard k-ε model and standard k-ω model.
𝐷𝜔 = 2(1 − 𝐹1)𝜌𝜎𝜔 , 21
𝜔
𝜕𝑘
𝜕𝑥𝑗
𝜕𝜔
𝜕𝑥𝑗 (4.6)
The turbulent viscosity is modeled through:
𝜇𝑡 =𝜌𝑘
𝜔
1
max [1
𝛼∗,𝑆𝐹2𝛼1𝜔
] (4.7)
S is the strain rate magnitude and F2 is the blending function defined in Menter [37]. α1 is
one of the model constants which value is 0.31.
Low Reynolds SST k-ω is the expansion of the original SST model [23]. The idea of the
Low Re correction is to damp the turbulent viscosity by a coefficient α*. α* is calculated
21
from [19] as
𝛼∗ = 𝛼∞∗ (
𝛼0∗ +𝑅𝑒𝑡/𝑅𝑘
1+𝑅𝑒𝑡/𝑅𝑘) (4.8)
with Ret = ρk/μω, Rk=6, α*0 = 0.024 and α*∞ = 1.
4.3 Transition (γ-Reθ) SST
The model was developed to include the simulation of transitional flow as well as the
turbulence. Four transportation equations are solved for the transitional flow in this model
[44]. The transition SST model is based on the coupling of the SST k-ω transport equations
with two other transport equations, which are the equation of intermittency 𝛾 (the fraction
of time at a fixed location for which the flow is turbulent [20]) and transition momentum
thickness Re are
𝜕(𝜌𝛾)
𝜕𝑡+
𝜕𝜌𝑈𝑗𝛾
𝜕𝑥𝑗= 𝑃𝑥𝛾1 − 𝐸𝛾1 + 𝑃𝛾2 − 𝐸𝛾2 +
𝜕
𝜕𝑥𝑗[(𝜇 +
𝜇𝑡
𝜎𝛾)
𝜕𝛾
𝜕𝑥𝑗] (4.9)
𝜕(𝜌𝑅𝑒̅𝜃𝑡)
𝜕𝑡+
𝜕(𝜌𝑈𝑗𝑅𝑒̅𝜃𝑡)
𝜕𝑥𝑗= 𝑃𝜃𝑡 +
𝜕
𝜕𝑥𝑗[𝜎𝜃𝑡(𝜇 + 𝜇𝑡)
𝜕𝑅𝑒̅𝜃𝑡
𝜕𝑥𝑗] (4.10)
Py1 and Ey1 are transition sources. The association of transition model with SST k-ω is
through the modification of the k equation.
𝜕
𝜕𝑡(𝜌𝑘) +
𝜕
𝜕𝑥𝑖(𝜌𝑘𝑢𝑖) =
𝜕
𝜕𝑥𝑗(Γ𝑘
𝜕𝑘
𝜕𝑥𝑗) + 𝐺𝐾
∗ − 𝑌𝑘∗ + 𝑆𝑘 (4.11)
𝐺𝑘∗ = 𝛾𝑒𝑓𝑓�̅�𝑘 (4.12)
𝑌𝑘∗ = min(max(𝛾𝑒𝑓𝑓 , 0.1) , 1.0) 𝑌𝑘 (4.13)
�̅�𝑘 and Yk are the original production and destruction terms for the SST model.
22
5 Choice of Airfoil and Experiment
The NACA0012 airfoil is used in this research work since it is widely used in different
kinds of research and the research of roughness effect on the airfoil is few. McCroskey [32]
analysed NACA0012 experimental results obtained from more than 40 wind tunnels. He
correlated these data for Re > 106. The experimental results [5] used in this work is from
the group of experiments that McCroskey considered were reliable. The roughness effect
on this airfoil at a low Re (1.5×105) which can be studied and compared with the experiment
data. The roughness effect was modeled as the sand grain roughness grit-36 from the
experiment of Chakroun et al [24]. The turbulence models were tested on the smooth
NACA0012 by validating using the experiment data from Chakroun et al [24] and Althaus
[25] at Re = 1.5×105. The results of turbulence models used on the rough airfoil are
compared with Charkroun experimental results [24]. For the roughness at high Re of
1.5×106, the simulation results of smooth surface are compared with Gregory [5], the
experimental data of rough surface is not available. The turbulence intensity of in the wind
tunnels of Chakroun et al [24] and Gregory [5] were 0.4% [59] and 0.2 % [58] respectively.
The Cl, Cd, Cp and Cf coefficients were collected from their papers as the reference data.
Cl and Cd are defined by equations 1.1 and 1.2. The remaining coefficients are defined by
Cp=𝑝−𝑝
∞1
2ρ𝑉2
(5.1)
Cf=𝜏
1
2ρ𝑉2
(5.2)
where p is static pressure at the wall, p∞ is static pressure of freestream, V is the freestream
velocity,τ is the surface shear stress [52].
The generated airfoil points were imported to ICEM model in the Ansys package for
meshing. The Grit-36 (500μm roughness) is selected as the roughness element from
Chakroun et al [24] research. The roughness was obtained through sticking sand papers of
Grit-36 on the airfoil surface using double sided adhesive tape [24]. The roughness height
of equivalent sand grain is not easy to obtain. Ferrer and Munduate’s [35] estimated a
relationship of hs/h = 2.043 for a Grit-40. Pailhas et al. [36] stated that the average value of
23
hs/h for a 3MP40 rough surface was 2 in their experiment. Due to the Grit-36 similarity
with the Grit-40 in height, hs/h =2 is assumed in the simulation.
Liu and Qin [55] simulated clean and rough NACA0012 for Grit 36 roughness at the
Reynolds number 1.5×105. They used low Reynolds SST k-ω and transition SST models
in their research. A C-type mesh is used and the iterations were taken to be converged when
the variation of lift and drag coefficient drops below 10-4. Their results are used as the
reference to compare with the results of this work.
In comparing the simulations to the experiments, it should be mentioned here the
experimental data collection may also have an error in the accuracy of value when compare
with the origin data, since all the data collected is from the graphs of the papers. These data
were not tabulated. They were read using the getdata graphic digitizer from the figures in
the papers cited. This may lead to an error in the accuracy of experimental data.
24
6 Mesh refinement
6.1 Domain detail
A H-Grid domain was created around the airfoil of the chord length c unit. The front, top
and bottom walls were set as the inlet and the outlet is located behind the trailing edge. The
inlet boundary was set 15c upstream to minimize inlet disturbances. The outlet boundary
was located 20c which is far enough from the trailing edge to minimize any disturbances
caused by the outlet boundary condition of no development in the flow direction. ICEM
was used to generate the mesh. The domain was discretized into various zones by a
blocking approach. The mesh consists of 50 grid lines along the airfoil surface and 160
grid lines normal to it. The total number of nodes for all the results was 134066 in fig 6.1.
Figure 6.1 Domain with Structured Mesh.
25
The boundary conditions set of the domain are velocity inlet for the top, bottom and left.
The angle of attack is changed by changing the direction of free stream, and the geometry
does not rotate. The right is set as pressure outlet.
Fig 6.2 shows the mesh close to the airfoil surface has a very high grid density, generated
by enclosing a layer of very fine mesh. The mesh density is coarsened from surface to inlet
and outlet. The y+ is fixed ≤ 1 to resolve the viscous sublayer properly. Wall y+ is the
non-dimensional wall distance [21-22]. It is often used to describe how coarse or fine a
mesh is.
Figure 6.2 Close view of the mesh adjacent to the airfoil
6.2 Grid Independence Check
The first step of simulation is to create the geometry and meshes, before that the effect of
mesh size has to be investigated. In general, a numerical solution becomes more accurate
when more nodes are used. However, the use of additional nodes will increase the
calculation time and the required computer memory. The choice of node number should be
determined by increasing the number of nodes to achieve an adequately fine mesh and the
further mesh refinement does not change the results significantly [38].
26
Figure 6.3 Dependence of Cl at stall angle of attack (degrees) against number of grid cells
from Eleni et al [38].
For this project, the grid independence was also assessed by the varying the number of
nodes of the mesh. The iterative convergence is reached when the residuals in Cl and Cd
changed by less than 1 × 10-6 between successive iterations. The nodes number was varied
from 8324 to 134066. Cd is used as the criterion to check the mesh independency. At the
angle of attack of 6˚, Cd = 0.016935 which is very close to the experimental result
(0.016984) from Chakroun et al [24] with 134066 nodes. The Cd comparison is in table 6.2.
The mesh with 134066 nodes was selected for all further simulations.
Number of nodes Cd
8324 0.016225
33036 0.016741
134066 0.016935
Table 6.1 Cd comparison for grid independency check at α = 6 using the low Reynolds
SST k- ω model.
27
The number of nodes of geometry is also important to the simulation results. The first
airfoil geometry had 101 nodes along the chord. However, the results of Cf shows
oscillation near the leading edge. The second new geometry with 1053 nodes was used to
build a mesh with same size (nodes of edges and expansion ratio) of previous one. The
comparison after the computation shows the oscillation was removed. This is due to a finer
geometry than the previous one, hence the computation results are improved as well. For
Cl at α = 6˚ and Re = 1.5×105, the first geometry gave a Cl = 0.63103, the value for the finer
geometry is 0.62051 (1% difference). Cd for the first geometry and finer geometry are
0.016881 and 0.016935 (0.5% difference) respectively. This indicates only a little bit
change to the lift and drag.
6.3 Grid convergence index study
The grid convergence index (GCI) is used to measure the difference between computed
value percentage to the asymptotic numerical value (i.e. true numerical solution). It
indicates an error band on how far the solution is from the asymptotic value. It also
indicates how much the solution would change with a further refinement of the grid. A
small value of GCI means the computation results is with the asymptotic range [54].
Three grids are generated which are coarse mesh, medium mesh and fine mesh with a
number of nodes: 8324, 33036 and 134066 respectively. A refinement ratio of 2 is used for
the three grids.
Grid Normalized grid spacing h Drag coefficient
Coarse (3) 4 0.016225
Medium (2) 2 0.016741
Fine (1) 1 0.016935
Table 6.2 Cd for three grids with a refinement ratio of 2 using the low Reynolds SST k- ω
model at α=6˚ and Re number =1.5×105
28
P 1.82
Pr h=0 0.016944
GCI12 0.4%
GCI23 1.5%
Asymptotic range of convergence check 1.00657
Table 6.3 Grid convergence index of Cd for low Reynolds SST k- ω model at α=6˚ and Re
number =1.5×105
P is the order of convergence
𝑝 = ln ((𝑓3−𝑓2)
(𝑓2−𝑓1)) /ln (𝑟) (6.1)
r is the refinement ratio, f is the result from grid. Pr h=0 is the value of richardson
extrapolation prediction at h=0, h is normalized grid spacing. GCI12 is grid convergence
index for the medium and fine refinement levels. GCI23 is grid convergence index for the
coarse and medium refinement levels.
𝐺𝐶𝐼 =𝐹𝑠|𝑒|
𝑟𝑝−1 (6.2)
Fs is an optional safety factor (1.25), e is the error between the two grids.
Asymptotic range of convergence is
𝐺𝐶𝐼2,3
𝑟𝑝×𝐺𝐶𝐼1,2 1 (6.3)
From [54] the value of asymptotic range of convergence check should be 1, the result of
1.00657 is sufficiently close to it which indicates that the solutions are well within the
asymptotic range of convergence.
29
Table 6.4 Grid convergence index of Cl on smooth surface at α=6˚ and Re number =1.5×105
Table 6.5 Grid convergence index of Cd on smooth surface at α=6˚ and Re number =1.5×105
Table 6.6 Grid convergence index of Cl on rough surface at α=6˚ and Re number =1.5×105
Table 6.7 Grid convergence index of Cd on rough surface at α=6˚ and Re number =1.5×105
Through the grid convergence index study, the asymptotic range results for Cl and Cd on
smooth and rough surfaces are around 1. This indicates the results are converged and grid
independent. GCI12 of all the results showed a very low error band (the maximum value
is 1.1%) which means the uncertainty of simulation results of each turbulence model is
very small. The error bar is not used in plotting the results, since the value is too small to
be seen against the symbols and lines used in drawing the figures.
Grid of three models P Pr h=0 GCI12 GCI23 Asymptotic
range
low Reynolds SST k-ω 0.46 0.6251451 1.17% 1.59% 0.9879
Transition-SST 2.9 0.6341263 0.03% 0.26% 1.16
SA 1.9 0.618839 0.14% 0.5% 0.9569
Grid of three models P Pr h=0 GCI12 GCI23 Asymptotic
range
low Reynolds SST k-ω 0.46 0.6251451 1.17% 1.59% 0.9879
Transition-SST 2.9 0.6341263 0.03% 0.26% 1.16
SA 1.9 0.618839 0.14% 0.5% 0.9569
Grid of three models P Pr h=0 GCI12 GCI23 Asymptotic
range
low Reynolds SST k-ω 1.6 0.547726 0.47% 1.4% 0.98
Transition-SST 1.51 0.628851 0.36% 0.98% 0.96
SA 0.97 0.605138 0.25% 0.48% 0.98
Grid of three models P Pr h=0 GCI12 GCI23 Asymptotic
range
low Reynolds SST k-ω 2.5 0.033243 0.36% 1.97% 0.97
Transition-SST 0.5 0.016617 1.1% 1.5% 0.96
SA 2.9 0.020227 0.11% 0.98% 1.19
30
7 Results
7.1 Smooth Airfoil
7.1.1 Lift coefficient
7.1.1.1 Low Reynolds number
Fig 7.1 shows that three turbulence models are consistent with experimental results in
predicting Cl. However, the results of Low Re SST k-ω and transition SST are more
accurate than SA model from angle of attack 0˚-6˚, After α=6˚, the results of SA is more
close to experimental data than other two models. For 0˚ α 4˚, the results of transition
SST are not as accurate as the Low Re SST k-ω. For 0˚ α 10˚, the Low Re SST k-ω
showed a good agreement with the experiment results.
Figure 7.1 Cl of smooth NACA 0012 airfoil at Re = 1.5×105 between α (0˚ -10˚) compared
with experiment of Chakroun et al [24] and Althaus [25].
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 2 4 6 8 10
CL
ANGLE OF ATTACK (DEGREES)
Low Re k-w SST
Transition SST
SA
Lift Chakroun expt
Lift Althaus expt
31
Figure 7.2 Liu and Qin’s [55] computational Cl for a smooth NACA 0012 airfoil at Re =
1.5×105 compared with experiment of Chakroun et al [24]
From Fig 7.2, when α is from 0-5˚, their results are in the agreement with the experimental
data. However, after 5˚ the results are under-predicted than the experiment’s. The results
of current work have the same trend.
7.1.1.2 High Reynolds number
At the high Re number 1.5×106, three turbulence models predicted similar results for 0˚
α 10˚. There is no obvious difference between each model’s result. Compare with the
experiment result of Gregory [5], all three models have a good agreement with it, except
the alpha = 10˚ which is lower than experiment data.
32
Figure 7.3 Cl of smooth NACA 0012 airfoil at Re = 1.5×106 between α (0˚ -10˚), compared
with experiment data of Gregory [5].
The value of Cl of three models at α =0˚ is zero, since NACA0012 is a symmetrical airfoil.
With the increase of the angle of attack (degrees), the value of Cl increases as well, the
simulations reproduce the linear range of Cl.
7.1.2 Drag coefficient
7.1.2.1 Low Reynolds number
Compared with the experimental results, Cd from the SA model is high for 0˚ α 6˚.
Both Low Re SST k-ω and transition SST have a good agreement with the experiment data
for 0˚ α 10˚.
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7 8 9 1 0
CL
ANGLE OF ATTACK (DEGREES)
SA
Transition SST
Low Re k-w SST
lift Gregory expt
33
Figure 7.4 Cd of smooth NACA 0012 airfoil at Re = 1.5×105 between α (0˚ -10˚) compare
with experiment of Chakroun et al [24] and Althaus [25]
Figure 7.5 Liu and Qin’s [55] computational results: Cd of smooth NACA 0012 airfoil at
Re = 1.5×105 compared with experiment of Chakroun et al [24]
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0 2 4 6 8 10
CD
ANGLE OF ATTACK (DEGREES)
Drag Chakroun
Drag Althaus
Low Re k-w SST
Transition SST
SA
34
From Fig 7.5, when α=0-8˚, the results of Liu and Qin’s [55] are consistent with the
experimental data. However, at α=10˚, there is an obvious difference between them. This
difference also exists in the current simulation results in fig 7.4. From fig 7.6, the
simulation results agree with the experimental data [5] at high Re (1.5×106) in the range α
= 0˚-10˚. This indicates the simulation is in a reasonable agreement with experiment [5].
However, both simulation results in fig 7.4 and 7.5 have much lower drag than the
experimental results at α = 10˚ which probably indicates stall of the airfoil. Also the
experimental results from [57] (these results are in the collection of McCroskey [32] which
are high reliable experimental data) at Re = 2×106 show that in the range α = 0˚-15˚, Cd
does not increase unlike Chakroun et al [24] at α =10˚. [57] indicated a stall angle of 17˚.
Therefore, the increase in Chakroun et al [24] at α=10˚ is not consistent with the high
quality higher Re experiments [57], [5] and the two simulation results fig 7.4 and 7.5.
7.1.2.2 High Reynolds number
Unlike Cl, three turbulence models predicted different values of the Cd. Low Reynolds SST
k-ω and SA models over-predicted the results at α = 0˚-10˚. Compare with the two models,
the results of transition SST and has a good agreement with the experiment results.
However, transition SST under-predicted Cd from α = 0˚- 4˚. The Cd at alpha = 0˚ is the
minimum, since the airfoil is a symmetrical one.
Figure 7.6 Cd of smooth NACA 0012 airfoil at Re = 1.5×106 between α (0˚ -10˚), compare
with experiment data of Gregory [5].
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0 1 2 3 4 5 6 7 8 9 1 0
CD
ANGEL OF ATTACK
Low Re k-w SST
SA
Transition SST
drag Gregory expt
35
7.1.3 Lift to drag ratio
7.1.3.1 Low Reynolds number
The L/D of Low Re SST k-ω and transition SST shows good agreement with the experiment
data. SA model under-predicted the results. The L/D shows an optimum value (the highest
number) for the three models. From the experimental data from Chakroun et al [24], the
optimum alpha = 4˚. The value in the experiment of Althaus [25] is between 6˚-8˚. Low Re
SST k-ω and transition SST models have the similar optimum value between angle of
attack 4˚- 5˚. However, the value of SA model is at angle of attack 8˚.
Figure 7.7 L/D of smooth NACA 0012 airfoil at Re = 1.5×105 between α (0˚ -10˚) compare
with experiment of Chakroun et al [24] and Althaus [25]
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4 5 6 7 8 9 10
L/D
ANGLE OF ATTACK (DEGREES)
Lift to drag ratio SA
Lift to drag ratio Low Re kw sst
Lift to drag ratio Transsition SST
Lift to drag ratio Althaus
Lift to drag ratio chakroun
36
7.1.3.2 High Reynolds number
Figure 7.8 L/D of smooth NACA 0012 airfoil at Re = 1.5×106 between α (0˚ -10˚), compare
with experiment data of Gregory [5].
The L/D of transition SST shows the most accuracy with the experiment data. The
prediction of low Reynolds SST k-ω and SA models are lower than experiment results. The
maximum value of L/D of transition SST and low Reynolds SST k-ω is at alpha = 8˚ and
10˚ for SA models.
7.1.4 Pressure coefficient
7.1.4.1 Low Reynolds number
The distribution of the airfoil Cp at the angle of attack of 6˚ from the experiment of
Chakroun et al [24] is compared with the simulation results. The Cp of three models on the
upper surface from 0-30% of chord length is in a good agreement with experimental data.
After 30% of chord length, the results are lower than experiment data. On the lower surface,
the prediction is a little higher than experiment results.
-10
0
10
20
30
40
50
60
70
80
0 1 2 3 4 5 6 7 8 9 1 0
L/D
ANGLE OF ATTACK
Lift to drag ratio Low Re kw sst
Lift to drag ratio SA
Lift to drag ratio transition sst
Lift to drag ratio Gregory expt
37
In fig 7.9 the maximum Cp is at the x/c = 0. The maximum Cp between the upper and lower
surfaces is near the leading edge. With the flow moves to the downstream, the pressure
decreases until a point then starts to increase again.
For the smooth surface, the plateau in Cp at x/c ~ 0.2 indicates that the low Re SST k-ω and
transition SST predicted a transitional leading edge separation bubble on the upper surface.
The prediction of the two models is similar. The location of transitional region is similar
in the two models between 0.05c to 0.23c.
Figure 7.9 Cp on the smooth surface of a NACA 0012 at α = 6˚, Re = 1.5×105 compared
with the experiment of Chakroun et al [24].
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cp
X/C
low re kw SST
SA
Transition SST
EXP
lower surface
upper surface
38
Figure 7.10 Streamlines above the smooth surface of a NACA 0012 at α = 6˚, Re = 1.5×105,
low Re SST k-ω, separation bubble is on the upper surface.
Figure 7.11 turbulent kinetic energy k (m2/s2) of a NACA 0012 at α = 6˚, Re = 1.5×105,
low Re SST k-ω.
-0.001
0
0.001
0.002
0.003
0.004
0.005
0.006
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
k
x/c
low Re kω SST
Separation bubble
Airfoil surface
39
Figure 7.12 streamlines on the smooth surface of a NACA 0012 at α = 6˚, Re = 1.5×105,
transition-SST, separation bubble is on the upper surface.
Figure 7.13 turbulent kinetic energy k (m2/s2) of a NACA 0012 at α = 6˚, Re = 1.5×105,
Transition SST.
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
k
x/c
Transition SST
Separation bubble
Airfoil surface
40
From figs 7.10 and 7.12, the separation bubble began at x/c = 0.2. In fig 7.11 and 7.13,
there is a sharp increase in k at same location after x/c =0.17, then it decreases gradually.
This indicates the existence of separation bubble.
Figure 7.14 streamlines on the smooth surface of a NACA 0012 at α = 6˚, Re = 1.5×105,
SA
Fig 7.10 and 7.12 shows both low Re k-ω SST and transition SST models predicted a
laminar separation bubble at x/c =0.2. However, fig 7.14 shows SA model cannot predict
the laminar separation bubble. Results are consistent with Cp in fig 7.9. Fig 7.11 and 7.13
shows the turbulent kinetic energy variation over the airfoil surface. It is seen that there is
no turbulence before the laminar separation bubble, but a sharp increase at x/c=0.2 then it
decreases gradually.
41
Figure 7.15 Liu and Qin’s [55] results: Cp on the smooth surface of a NACA 0012 at α =
6˚, Re = 1.5×105 compared with the experiment of Chakroun et al [24].
From Fig 7.15, both models predicted the separation bubble at x/c= 0.2 which is same to
the Fig 7.9 of current work.
42
Figure 7.16 x wall shear stress of three turbulence models on smooth surface at α = 6 and
Re= 1.5×105
Figure 7.17 Liu and Qin’s results: Cf of three turbulence models on smooth surface at α =
6 and Re= 1.5×105
-3
-2
-1
0
1
2
3
4
5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
X w
all s
hea
r st
ress
x/c
low Re kω sst
SA
transition SST
lower surface
upper surface
43
Fig 7.16 shows the x-component of wall shear stress is negative at x/c=0.2 for both models
which indicates the flow direction is reversed and a separation bubble has formed. The
results are similar to those of Liu and Qin [55] in figure 7.17.
7.1.4.2 High Reynolds number
In fig 7.18 Three turbulence models did not predict a separation bubble on the upper surface.
The Cp results of all models are very similar. Fig 7.19 shows transition SST and low Re
SST k-ω models predict the transition process, transition onset location of transition SST
model is at 0.1 x/c on the upper surface and no transition on the lower surface, as the Cf is
the minimum. For low Re SST k-ω model, the location is at 0.02 x/c and 0.2 x/c on the
upper and lower surfaces. The transition SST model predicted the later transition on the
upper surface and lack of transition on the lower surface result in a lower Cf than low Re
SST k-ω model. This is confirmed in fig 7.6, the Cd of transition SST is lower than low Re
SST k-ω model.
Figure 7.18 Cp of smooth surface at α = 6˚, Re = 1.5×106
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cp
x/c
low Re kw sst
SA
transition SST
upper surface
lower surface
44
Figure 7.19 Cf of three turbulence models on smooth surface at α = 6 ˚ and Re= 1.5×106
0
0.005
0.01
0.015
0.02
0.025
0.03
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cf
x/c
low Re kω sst
SA
transition SST
upper surface
lower surface
45
7.1.5 Skin friction coefficient
In Fig 7.20 with increasing x/c, Cf decreases on the smooth surface. Both low Re SST k-
ω and transition SST models showed a good agreement with experiment data at the location
of x/c at 0.4, 0.6 and 0.8, but the value of both models at 0.2 is lower than experiment data.
SA model over-predicted the Cf between 0.4 ≤ x/c ≤ 0.8. Low Re SST k-ω predicted a
short separation bubble between 0.8 - 0.85c and transition SST predicted a transition which
begun at 0.92c.
Figure 7.20 Cf comparison with experiment results on smooth surface at α = 0˚ and Re=
1.5×105.
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cf
X/C
EXP smooth
Low Re kω SST
Transition SST
SA
46
7.2 Rough surfaces
7.2.1 Lift coefficient
7.2.1.1 Low Reynolds number
On the rough surface, the Cl of low Re SST k-ω model and SA model from angle of attack
0˚-6˚ are close to the experiment results, the results of transition SST are higher. After
angle of attack 6˚, both SA and transition SST models over-predict Cl, only low Re SST k-
ω model predicted results well with the experiment data.
Figure 7.21 Cl of rough NACA 0012 airfoil at Re = 1.5×105 between α (0˚ -10˚) compare
with experiment of Chakroun et al [24]
-0.2
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7 8 9 10
CL
ANGLE OF ATTACK(DEGREE)
Lift exp
Low Re k-w SST
SA
Transition SST
47
Figure 7.22 Liu and Qin’s [55] results: Cl of rough NACA 0012 airfoil at Re = 1.5×105
compare with experiment of Chakroun et al [24]
From Fig 7.22, low Re SST k-ω model agrees well with experimental results from a=0-10˚.
After a=6˚, transition SST model over-predicted the results. The results of current work
have the similar trend.
7.2.1.2 High Reynolds number
Due to the lack of experiment data, the results of three turbulent models are used to
compare with each other. From angle of attack 0˚-2˚, the results of three models are very
close. However, after α=2 ˚, the results difference between SA and other two models
increases gradually. SA model shows the highest results followed by transition SST and
low Re SST k-ω models. The results of both transition SST and low Re SST k-ω models
are very similar.
48
Figure 7.23 Cl of rough NACA 0012 airfoil at Re = 1.5×106 between α (0˚ -10˚).
7.2.2 Drag coefficient
7.2.2.1 Low Reynolds Number
From figure 7.24, all the three turbulence models under-predicted Cd. For the rough surface,
Cd is higher than smooth surface, this means roughness causes higher Cd. However,
compare with SA and transition SST models, the prediction of low Re SST k-ω is more
closed to the experimental data.
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7 8 9 1 0
CL
ANGLE OF ATTACK (DEGREE)
Low Re k-w SST
SA
Transition SST
49
Figure 7.24 Drag coefficients of rough NACA 0012 airfoil at Re = 1.5×105 between α (0˚
-10) compared with experiment of Chakroun et al [24].
Figure 7.25 Liu and Qin’s [55] results: Drag coefficients of rough NACA 0012 airfoil at
Re = 1.5×105 compared with experiment of Chakroun et al [24].
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 1 2 3 4 5 6 7 8 9 10
CD
ANGLE OF ATTACK(DEGREE)
Drag exp
Low Re k-w SST
SA
Transition SST
50
From Fig 7.25 both models under-predicted the Cd in all α. However, Low Re SST k-ω
model is more closed to the experimental data. The results of current work also have the
same trend.
7.2.2.2 High Reynolds number
In fig 7.26 the increasing trend of three models is similar. SA shows the lowest values
among the three turbulent models, followed by transition SST model and low Re SST k-ω
model. The latter two models have the similar results and higher than SA model. The results
of low Re k-ω SST are lower than transition SST.
Figure 7.26 Drag coefficients of rough NACA 0012 airfoil at Re = 1.5×106 between α (0˚
-10˚).
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 1 2 3 4 5 6 7 8 9 1 0
CD
ANGLE OF ATTACK (DEGREE)
Low Re k-w SST
SA
Transition SST
51
7.2.3 Lift to drag ratio
7.2.3.1 Low Reynolds Number
The L/D of low Re SST k-ω model has the best agreement with experiment results in the
three models. SA and transition SST models do not have a good prediction in the L/D, both
models over-predicted the results.
Figure 7.27 L/D of rough NACA 0012 airfoil at Re = 1.5×105 between α (0˚ -10˚) compare
with experiment of Chakroun et al [24].
7.2.3.2 High Reynolds number
SA model shows the highest L/D in the three turbulence models and other two models have
the very close results. The SA model gives the best aerodynamics performance from α =
10˚. α = 8˚ is the highest value for other two models.
-5
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4 5 6 7 8 9 1 0
L/D
ANGLE OF ATTACK(DEGREE)
Lift to Drag ratioEXP
Lift to drag ratioLow Re k-w SST
Lift to drag ratioSA
Lift to drag ratiotransition SST
52
Figure 7.28 L/D of rough NACA 0012 airfoil at Re = 1.5×106 between α (0˚ -10˚).
7.2.4 Pressure coefficient
7.2.4.1 Low Re number
The three turbulence models have the similar results in the Cp at the angle of α = 6˚.
Compare with the experiment data, the Cp of lower surface is a little higher. For the upper
surface, the prediction of three models is very good from 0-50% of chord length, it is in a
consistency with experiment data. After 50% of chord, the result is a little lower than the
experiment data. Both low Re SST k-ω and transition SST models predict no separation
bubbles on the upper surface. In fig 7.29, the Cp results of transition SST model are higher
than the low Re SST k-ω and SA models. This indicates in fig 7.21 that the Cl of transition
SST model is highest.
Fig 7.31 shows that the low Re SST k-ω model predicts turbulent boundary layer starting
from the leading edge as confirmed by the x wall shear stress results with a rapid increase.
Transition SST model predict the later transition on the upper surface and no transition on
the lower surface cause a lower Cf than low Re SST k-ω. That is why the cd predicted by
transition SST in fig 24 is lower.
-10
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9 1 0
L/D
ANGLE OF ATTACK (DEGREE)
Lift to drag ratio Low Rekw sst
Lift to drag ratio SA
Lift to drag ratiotransition sst
53
Figure 7.29 Cp of rough surface at α = 6˚, Re = 1.5×105 compare with experiment of
Chakroun et al [24]
Figure 7.30 Liu and Qin’s results: Cp of rough surface at α = 6˚, Re = 1.5×105 compare
with experiment of Chakroun et al [24]
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-0.1 0.1 0.3 0.5 0.7 0.9 1.1
Cp
X/C
EXP
low Re kw SST
Transition SST
SA
upper surface
lower surface
54
From figure 7.30, there is no separation bubble on the rough airfoil surface, both models
did not predict that. The results of current work have the same trend. These results indicate
roughness can prevent the formation of separation bubble on the airfoil surface.
Figure 7.31 Cf of three turbulence models on rough surface at α = 6˚, Re = 1.5×105
Figure 7.32 Liu and Qin’s results: Cf of two models on rough surface at α = 6˚, Re = 1.5×105
-3
-2
-1
0
1
2
3
4
5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1X w
all s
hea
r st
ress
X/C
low Re kω SST
Transition SST
SA
upper surface
lower surface
55
Fig 7.32 shows low Re SST k-ω model predicted the turbulent boundary layer in the leading
edge and transition SST predicted transition happened at x/c = 0.52 (the minimum value of
Cf ) on upper surface. The value of transition SST is lower than low Re SST k-ω. Figure
7.31 captured the same trend with figure 7.32.
7.2.4.2 High Reynolds Number
Three turbulence models have the similar results on the Cp. In fig 7.33, the results of SA
are a little higher than other two models, this indicates the Cl of SA model has the higher
value in fig 7.23.
Fig 7.34 shows, low Re SST k-ω and transition SST models predicted the turbulent
boundary layer in the leading edge respectively. The results of both models are higher than
SA model, this explained the higher Cd than SA in fig 7.26.
Figure 7.33 Cp of rough surface at α = 6˚, Re = 1.5×106
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cp
x/c
low Re kω sst
transition
SA
56
Figure 7.34 Cf of three turbulence models on rough surface at α = 6˚, Re = 1.5×106
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cf
x/c
low re kω SST
Transition SST
SA
upper surface
lower surface
57
7.2.5 Skin friction coefficient
For the Cf on the rough surface, the trend of skin friction is going down in the location of
x/c from 0.2-0.6 from experimental data. However, after x/c=0.6 it increases again. Both
SA and transition SST models under-predicted the Cf. Low Re SST k-ω model has the best
consistency with the experiment data, but at the location of x/c = 0.8, the prediction is lower
than the experiment result.
Figure 7.35 Cf comparison with experiment results on rough surface at α = 0˚ Re = 1.5×105.
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
cf
x/c
EXP rough
Low re kω SST
Transition SST
SA
58
8 Comparison of the aerodynamic performance of the
smooth and rough airfoils
Since low Re SST k-ω model has better agreement with the experimental results than
transition SST and SA models on rough surface, the simulation results of this model are
used to compare the Cl , Cd, L/D, Cp and Cf between smooth and rough surfaces. The
comparison of aerodynamic characteristics of NACA0012 at a low Re of 1.5×105 on the
smooth and rough surfaces will be presented below:
In Fig 8.1 the Cl is 0 at the angle of attack 0˚, since NACA0012 is a symmetrical airfoil.
With the increase of angle of attack the Cl of rough surface is slightly lower than the smooth
surface. The maximum difference is about 0.1 at the angle of attack 4˚, the decrease is
nearly 20%.
Figure 8.1 Cl comparison between smooth and rough surface at Re= 1.5×105.
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 1 2 3 4 5 6 7 8 9 10
CL
ANGLE OF ATTACK (DEGREES)
Low Re k-w SST smooth
Low Re k-w SST rough
59
Fig 8.2 shows the Cd of NACA0012 on the smooth and rough surfaces. From angle of
attack 0˚-10˚, the Cd increases with a similar trend in the two surfaces. At angle of attack
0˚, the Cd are roughly 0.01 and 0.03 for smooth and rough surfaces. There is about a 200%
increase.
Figure 8.2 Cd comparison between smooth and rough surface at Re= 1.5×105.
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0 1 2 3 4 5 6 7 8 9 10
CD
ANGLE OF ATTACK (DEGREES)
Low Re k-w SST smooth
Low Re k-w SST rough
60
In fig 8.3 the smooth airfoil shows a significantly higher L/D than the rough airfoil. The
highest L/D of smooth airfoil in this case is at α = 4˚. However, maximum L/D occurs at 8˚
for rough airfoil. The largest difference is at α = 4˚. The values are 37.8 and 11.5 for smooth
and rough surfaces. The decrease of L/D at this angle of attack is about 70%.
Figure 8.3 L/D comparison between smooth and rough surface at Re= 1.5×105.
-5
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4 5 6 7 8 9 10
L/D
ANGLE OF ATTACK (DEGREES)
Lift to drag ratio Low Re kwsst smooth
Lift to drag ratio Low Re k-wSST rough
61
In fig 8.4 the maximum difference in the Cp of smooth and rough surfaces is at the leading
edge upper surface. For the lower surface, Cp of both smooth and rough surface is similar.
The effect of roughness on the Cp is obvious at the leading edge, since the Cp is higher in
this region. Except this region, the effect of roughness on Cp is very small.
In fig 8.4 on the other hand, roughness reduces the separation bubble formation. The benefit
of surface roughness usually can be attributed to the reduction or elimination of separation
bubble.
Figure 8.4 Cp at angle of attack 6˚ comparison between smooth and rough surface at Re =
1.5×105.
In fig 8.5, the Cf of rough surface is larger than smooth surface at all stations. This is the
due to the existence of the turbulent boundary layer. The rough surface has higher Cf than
smooth surface explained why the Cd of rough surface is higher than smooth surface as
well. From fig 8.5 the turbulent boundary layer in the leading edge of rough surface shows
roughness causes the transition occurs earlier than smooth surface.
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 1.2
Cp
x/c
low Re kω sst smooth
low Re kω sst rough
upper surface
lower surface
62
Figure 8.5 Cf comparison between smooth and rough surface at angle of attack 6˚ at Re =
1.5×105.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cf
x/c
low Re kω sst smooth
low Re kω sst rough
upper surface
63
9 Discussion
For the simulation of the smooth airfoil at low Re, the low Re SST k-ω, transition SST and
SA models were compared with the experiment results for Cl , Cd , L/D, Cp and Cf. The first
two models agreed well with experiment data in Cl , Cd and L/D. However, some L/D results
of SA model are lower than the experiment data, and Cf results are higher than experiment
results as well. Since SA model can not predict transition. Low Re SST k-ω and transition
SST models have the similar trend and values with the experiment for the Cf at α = 0˚. Both
models predicted the transition at x/c =0.2 at α=6˚in fig 7.19. At high Re, three models
predict the Cl very well, but transition SST is more close to experimental data for Cd and
L/D. SA model over-predicted the Cd. Due to the lack of experiment data in Cp and Cf, the
comparison between simulation data and experiment data is not available.
For the rough surface prediction at low Re, the low Re SST k-ω model showed a better
consistency with the experiment data than the transition SST and SA models. The latter
two models over-predicted Cl and L/D, and under-predicted Cd and Cf. The L/D, Cl, Cp and
Cf results of the low Re SST k-ω model are very close to the experiment data. At high Re,
due to the lack of experiment data on rough surface, the simulation results cannot be
assessed.
In summary: the low Re SST k-ω model shows the better accuracy than transition SST and
SA models for the airfoils studied here.
In comparing the aerodynamic performance between the smooth and roughness surface,
the maximum reduction of Cl can be up to 80% of the smooth airfoil at α = 4˚and Re =
1.5×105, and the maximum increase of Cd can reach up to 200% of the smooth airfoil at α
= 0˚and Re = 1.5×105. Therefore, there is a direct effect on the L/D with a maximum 70%
loss. The increase of skin friction on the rough surface lead to Cd of rough airfoil to be
higher than the smooth airfoil. However, the benefit of roughness is that the formation of
separation bubble could be reduced which is showed in fig 8.4.
64
10 Conclusion
The roughness on an airfoil surface can affect aerodynamic performance parameters such
as Cl, Cd, Cp, L/D, and Cf. The transition process can occur earlier than smooth surface. The
experiment results at low Re=1.5×105 on smooth and rough surface also high Re=1.5×106
on smooth surface are used to verify the simulation results. Cl, Cd, Cp, Cf as well as L/D are
presented to show the turbulence models results between experiment data and simulation
data also aerodynamic performance between smooth and rough surfaces. After the
comparison, the simulation results have a good consistent with the experiment results. As
the exception, some results of high Re are more accurate than low Re since the separation
bubble and transition issues.
In comparing simulation results with the experiment data on smooth surface, the low Re
SST k-ω, transition SST and SA models simulate the Cl, Cd and Cp results well, the former
two models are more accuracy than SA model in Cf and L/D results. For the rough surface,
only the low Re SST k-ω model shows the best accuracy in Cl, Cd , Cp, Cf and L/D results
with experiment data.
Comparing the L/D, Cl, Cd, Cp and Cf between smooth and rough airfoil, the results show
the roughness has a negative effect on the aerodynamic performance of the NACA 0012
airfoil. With the roughness effect, Cd and Cf increase higher also Cl and L/D decreases lower
than these of the smooth surface. The skin friction on rough surface has a larger increase
compare with the smooth surface which leads to a higher drag than the smooth surface.
Therefore, the smooth airfoil has the better aerodynamic characteristic than the rough
airfoil.
Overall, low Re SST k-ω model shows the best agreement with the experimental results
than the SA and transition SST models in the research work. It is validated that the low Re
SST k-ω model has the best prediction for the low Re of a NACA0012 airfoil on the smooth
and rough surfaces. On the other hand, the smooth airfoil has the better aerodynamics
characteristics than rough airfoil in Cl, Cd, Cp, Cf as well as L/D. The benefit of roughness
is that the separation bubble can be prevented. In order to avoid the detrimental effect of
roughness, the airfoil surface should be kept without roughness to reach a good
65
aerodynamic performance. Roughness mitigation strategies are needed to prevent the
losses from the blade performance degradation.
66
11 Recommendation
The current research work of the meshing type used is “H” grid, another two popular
meshing types “C” and “O” grids could be chosen in the further research to check the grid
accuracy (result) and efficiency (calculation time), cost effective approach should be
considered.
Three turbulence models: low Re SST k-ω, transition SST and SA are used to do the
simulation. The future work could consider the different turbulence models such as k-ɛ and
Reynolds stress models etc to check each accuracy for the NACA0012 aerodynamic
performance simulation.
Chakroun et al [24] used another two kinds of roughness on the NACA0012 airfoil which
are P80(200μm roughness) and wire roughness (2mm) in his research. The further research
can consider the two kinds roughness in the simulation and compare with the experiment
results.
The experimental results of roughness on the NACA0012 airfoil at high Reynolds number
are rare, and further studies would be valuable, especially at high Reynolds number. Also,
the effect caused by different location of roughness on the airfoil surface is also an
important issue to study, such as roughness is localized to the leading edge to simulate
blade erosion. The experiments are needed to carry out and relevant numerical simulation
should be used for the validation.
67
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