cfd simulation of smooth and rough naca 0012 airfoils at

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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(Unpublished master's thesis).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



iv

7.1.3 Lift to drag ratio ......................................................................... 35



7.1.4 Pressure coefficient ................................................................... 36



7.1.5 Skin friction coefficient ............................................................. 45

7.2 Rough surfaces................................................................................... 46

7.2.1 Lift coefficient ........................................................................... 46



7.2.2 Drag coefficient ......................................................................... 48

7.2.2.1 Low Re number ................................................................. 48


7.2.3 Lift to drag ratio ......................................................................... 51

7.2.3.1 Low re number .................................................................. 51


7.2.4 Pressure coefficient ................................................................... 52

7.2.4.1 Low re number .................................................................. 52


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


transition-SST……………………………………………………………………………39

Figure 7.13 turbulent kinetic energy of a NACA 0012 at α = 6˚, Re = 1.5×105, Transition

SST……………………………………………………………………………………….39


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


range


Transition-SST 2.9 0.6341263 0.03% 0.26% 1.16

SA 1.9 0.618839 0.14% 0.5% 0.9569


range


Transition-SST 1.51 0.628851 0.36% 0.98% 0.96

SA 0.97 0.605138 0.25% 0.48% 0.98


range


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


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


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


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.


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


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


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


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


Figure 7.8 L/D of smooth NACA 0012 airfoil at Re = 1.5×106 between α (0˚ -10˚), compare


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


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 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


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.


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.


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


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.


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


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.


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


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].


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


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


Lift to drag ratio Low Rekw sst


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


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


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


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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