A Thesis Report for
Fluid Flow Effects on Objects with a Dimpled Surface
A Thesis Submitted In Fulfilment
Of the Requirements for
The Degree of Bachelor of Mechanical Engineering
By
Sean Brown
Student No: 138378
Primary Supervisor: Micah Thorbjornsen
Secondary Supervisor: Dr. Daria Surovtseva
Thesis Coordinator: Kamal Debnath
School of Engineering and Information Technology
Faculty of Engineering, Health Science and the Environment
Charles Darwin University
Darwin
Abstract
This thesis investigates the fluid flow effects of geometries with a dimpled surface as
compared to smooth surfaces. Geometries studied include cylinders, pointed orgives and
streamlined bodies. The surfaces of the geometries studied have an array of evenly spaced
dimples with specific dimensional properties to achieve a reduction in total drag forces
exerted by fluid flow. Computational Fluid Dynamic flow simulations were conducted to
observe boundary layer initiation and development along each object profile and drag forces
experienced at speeds ranging from 5m/s to 40m/s. Along with the computed analysis, wind
tunnel testing was conducted to observe real time boundary layer formation and drag forces
resulting from wind speeds of the same range over geometry models. For visualisation in
wind tunnel testing a smoke wand was utilised to demonstrate fluid flow over each model.
Drag data was collected from surface integration calculations produced in CFD testing and
from force gauges in wind tunnel testing. All results were compared with the performance of
smooth surfaced models of the same geometry to observe the effects of the dimpled surface
application.
Predominantly the investigation of this thesis is to experimentally determine whether or not
the drag forces are either increased or diminished due to the dimpled surface texture.
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Fluid Flow Effects On Objects With A Dimpled Surface
Acknowledgements
The author would like to acknowledge with gratitude, Dr. Daria Surovtseva and Micah
Thorbjornsen for their supervision, contributions and support during the progress of this
thesis. The author would also like to thank Damien Hill and Ben Saunders for their
contributions and assistance with the development of testing models. Additional recognition
is given to Gethin Barden, Adil Salat, Alan Brown, Deborah Brown, Joyce Gleeson and
Gurveer Singh for their support. Thank you all.
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Fluid Flow Effects On Objects With A Dimpled Surface
Contents
ABSTRACT...............................................................................................................................1
ACKNOWLEDGMENTS..........................................................................................................2
LIST OF TABLES.....................................................................................................................5
LIST OF FIGURES....................................................................................................................6
1.0 -THESIS INTRODUCTION................................................................................................7
1.1 –Thesis Scope.................................................................................................8
1.2 –Thesis Objectives.........................................................................................8
1.3 –Thesis Budget...............................................................................................8
2.0 -Thesis BACKGROUND.....................................................................................................9
2.1 -Common Shapes and Reasons for this Study.........................................................9
2.2 –Golf Ball Dimple Theory.......................................................................................9
3.0 -LITERATURE REVIEW.................................................................................................11
3.1 -Fluid Flow Effects Due to Surface Roughness.....................................................11
3.2 -Effect of Boundary Layer Formation and Drag by a Dimpled Surface................15
3.2.1 -Flat Plate Investigation....................................................................................15
3.2.2 -Spherical Body Investigation...........................................................................19
3.3 -Fluid Flow Characteristics around Bluff and Sharp Surfaces...............................23
4.0 -METHODOLOGY ..........................................................................................................27
4.1 -Geometry Design..................................................................................................27
4.2 -Cylinder Design....................................................................................................28
4.3 -Orgive Design.......................................................................................................28
4.4 -Streamline body Design.......................................................................................29
4.5 -Dimple Geometry.................................................................................................29
5.0 -THESIS TESTING...........................................................................................................32
5.1 -Testing Objectives................................................................................................32
5.2 -COMSOL Flow Tests...........................................................................................33
5.3 -Wind Tunnel Flow Testing...................................................................................38
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Fluid Flow Effects On Objects With A Dimpled Surface
6.0 -RESULTS ANALYSIS AND DISCUSSION..................................................................40
6.1 -Cylinder.................................................................................................................41
6.2 –Streamline Body...................................................................................................48
6.3 -Orgive...................................................................................................................53
6.4 -Drag Coefficients..................................................................................................60
6.5 -Errors.....................................................................................................................67
7.0 -THESIS CONCLUSION......................................................................................................69
8.0 -FURTURE WORK...........................................................................................................70
REFERENCES.........................................................................................................................71
APPENDIX..............................................................................................................................73
Appendix A -Testing Data...........................................................................................73
Appendix B –Creo Parametric Models........................................................................76
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Fluid Flow Effects On Objects With A Dimpled Surface
List of Tables
Number
1
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3
4
5
Name/ Content
Thesis Budget
Dimple Design Parameters
Geometry Characteristic Lengths
Geometry Cross Sectional Areas
Sphere Calibration COMSOL Parameters
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Calibration Data for COMSOL Testing
36
7
COMSOL Parameters for Official Testing
37
8
Controller Frequencies and Velocities
38
9
Atmospheric Testing Conditions
39
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Drag and Cd Values for Smooth Cylinder, CFD
73
11
Drag and Cd Values for Dimpled Cylinder, CFD
73
12
Drag and Cd Values for Smooth Cylinder, Wind Tunnel
73
13
Drag and Cd Values for Dimpled Cylinder, Wind Tunnel
73
14
Drag and Cd Values for Smooth Orgive, CFD
74
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Drag and Cd Values for Dimpled Orgive, CFD
74
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Drag and Cd Values for Smooth Orgive, Wind Tunnel
74
17
Drag and Cd Values for Dimpled Orgive, Wind Tunnel
74
18
Drag and Cd Values for Smooth Streamline Body, CFD
75
19
Drag and Cd Values for Dimpled Streamline Body, CFD
75
20
Drag and Cd Values for Smooth Streamline Body, Wind Tunnel
75
21
Drag and Cd Values for Dimpled Streamline Body, Wind Tunnel
75
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Fluid Flow Effects On Objects With A Dimpled Surface
List of Figures
Number
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A.1-A.6
Name/ Content
Smooth and Dimpled Sphere In Laminar Flow
Skin Layer Types
Nano Surface Applications
Axial Drag vs. Channel Velocity
Wind Tunnel Dimpled Array Setup
Shear Stress vs. Location
Flow Visualisation
Wind Tunnel Experimental Setup
Measured and Predicted Data
Sectional View of Dimples
Cd vs Re # for Dimple Geometries
Spark Tracing Flow Visualisation
Geometry Configuration for Test Models
Corner Shape Effect
Vortex Shedding
Cylinder Design
Orgive Design
Streamline Body Design
Dimple Geometry Cross Section
Sphere Drag Accuracy Testing
Drag vs. Re for Smooth and Dimple Cylinder, CFD
CFD Flow Imagery Over Smooth Cylinder, 40m/s
CFD Flow Imagery Over Dimpled Cylinder, 40m/s
Drag vs. Re for Smooth and Dimple Cylinder, Wind Tunnel
Wind Tunnel Flow Imagery for Cylinders at 15m/s
Drag vs. Re for Smooth and Dimple Streamline Bodies, CFD
CFD Flow Imagery Over Smooth Streamline Body, 10m/s
CFD Flow Imagery Over Dimpled Streamline Body, 10m/s
Drag vs. Re for Smooth and Dimple Streamline Body, Wind Tunnel
Wind Tunnel Flow Imagery for Streamlined Bodies at 15m/s
Drag vs. Re for Smooth and Dimple Orgives, CFD
CFD Flow Imagery Over Smooth Orgive, 5m/s
CFD Flow Imagery Over Dimpled Orgive, 5m/s
Drag vs. Re for Smooth and Dimple Orgives, Wind Tunnel
Orgive Model Strut
Wind Tunnel Flow Imagery for Orgives at 15m/s
Cd vs. Re# for Smooth Sphere and Cylinder
Cd vs. Re# for Smooth and Dimple Cylinder, CFD
Cd vs. Re# for Smooth and Dimple Cylinder, Wind Tunnel
Cd vs. Re# for Smooth and Dimple Streamline Body, CFD
Cd vs. Re# for Smooth and Dimple Streamline Body, Wind Tunnel
Cd vs. Re# for Smooth and Dimple Orgive, CFD
Cd vs. Re# for Smooth and Dimple Orgive, Wind Tunnel
Creo Parametric Models
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Fluid Flow Effects On Objects With A Dimpled Surface
1.0 -Introduction
In fluid mechanics, boundary layers form when a fluid moves past objects that are
immersed in the fluid flow. The boundary separation causes viscous friction or a ‘drag
force’ on the immersed object (Munson et al. 2009). For many of these objects the drag
forces are unwanted which has led to streamlined designs for many modern
requirements such as vehicles, airfoils, pipes, sporting equipment, firearm projectiles
and many more fluid affected components. Reducing drag on objects produces benefits
such as smaller energy losses, better performance and flight stability. Examples of how
drag is diminished can be seen in many different variations. Some include flow
disrupting fins seen on modern cars and airfoils, special paint applications on high
performance vehicles including race cars and aircraft, sleeker helmet designs for
professional bike riders and dimpled surfaces for golf balls.
Apart from drag there are several other important fluid flow characteristics that exist
with dynamic flow on immersed objects. One characteristic is boundary layer
production along the surface of an object. The design of this layer depends on several
fluid attributes including the Reynolds Number, density, velocity, viscosity and
temperature. The shape and surface finish of the object will affect the boundary layer
also.
Another important characteristic is flight stability. The stability of an immersed object is
relied upon for predictability during performance. Fluid flow can be unpredictable in
nature for example the erratic behaviour of wind currents over objects that rely upon
constant flow performance can be affected by unexpected fluid movement. Designs for
these objects compensate for these unpredictable events. An example is the surface
design for formula one race cars; side winds are reflected at angles that produce down
force instead of lift. This effect decreases lifting forces on the vehicles that could
otherwise diminish the control that the driver has while racing.
This thesis project will investigate drag and fluid flow characteristics of dimpled surface
objects immersed in a dynamic flow.
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Fluid Flow Effects On Objects With A Dimpled Surface
1.1 –Thesis Scope:
The aim of this thesis is to investigate the drag and flow characteristics produced by the
application of dimpled surfaces on various geometrical shapes. Geometries studied will
include sharp pointed ogives, streamlined bodies and cylinders. Computational Fluid
Dynamics testing is utilised along with Wind Tunnel testing to produce results concerning
drag and fluid flow characteristics on models developed for each shape for varying velocities.
These results are compared to the smooth surfaced models of the same geometrical shapes
tested at identical flow velocities.
1.2 -Thesis Objectives
The primary objectives of this thesis include the following...
 Identify through research key characteristics of Drag and Fluid Flow over differing
geometrical objects for smooth and dimpled surfaces.
 Develop a Methodology to investigate smooth and dimpled geometries in subsonic
flow.
 Investigate Drag and Fluid Flow data for smooth and dimpled geometries utilizing
Computational Fluid Dynamics and Wind Tunnel testing.
1.3 -Thesis Budget
The following is an estimated budget of the materials needed for thesis testing...
Table One: Thesis Cost Estimate
Materials
Wind Tunnel Materials
Scale Models/ Polymers(3D
Plastics)
Final Cost
Estimated Cost
Printer $25.00
$25.00
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Fluid Flow Effects On Objects With A Dimpled Surface
2.0 -Thesis Background
2.1 -Common Shapes and Reasons for This Study
The study undertaken considers shapes of varying geometry for applications on existing
geometries used within industry including air craft (cylindrical objects, air foils),
submersibles (air foils), buildings (blunt and bluff objects) and communications towers
(cylindrical objects). The applications of this study are not exhausted by the examples
stated. The shapes studied include an ogive, streamlined body, and cylinder.
2.2 -Golf Ball Dimple Theory
As the research of the thesis is for surface dimples in flow, the traditional dimpled golf ball
was taken into account as a ‘real life’ working theoretical basis. The science for fluid
dynamics around golf balls is itself complex but on a larger and simpler scale several
important traits of the golf ball stand out that have lead to the many variants of dimple
designs. The principles for the dimples on drag reduction relate to the boundary layer
separation, pressure distribution and flow wake. Laminar flow over surfaces allows for lower
drag force imparted onto the object through lower fluid friction interaction along the surface.
Once turbulence is reached flow separation occurs when the pressure gradient becomes
adverse from the incoming flow. This can cause large pressure differences across the object
profile resulting in kinetic losses in the form of drag forces. In this situation large wake
regions are created.
Reducing this wake region results in lower pressure differences along an objects profile and
therefore reducing drag. In order for golf balls to lower this pressure difference dimples are
added to initiate a turbulent flow sooner across the surface. Figure one below shows a
representation of the flow pattern caused by an energised boundary layer staying in contact
with a dimpled surface longer then its smooth counterpart due to a dimpled surface.
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Fluid Flow Effects On Objects With A Dimpled Surface
Figure 1: Comparison of Smooth and Dimpled Spheres in Laminar Flow (Korry. F, Why Does A Golf Ball Have Dimples?,
2008)
This turbulent flow energises the surface fluid region by encouraging ‘mixing’ between
slower laminar flows. The surface flow therefore has a higher kinetic energy and stays in
close contact further around the ball before it eventually separates. This in turn lowers the
pressure difference and reduces drag. At lower Reynolds numbers for laminar flow drag is
slightly increased as the friction drag outweighs pressure drag, but once higher velocities are
reached the effect described above takes over to work positively for drag reduction.
From this working example, dimpled models for each geometrical shape studied have been
developed in order to identify drag force reduction or increase and drag force components
being affected in this force change. The two components of drag force include friction drag,
which is directly related to the shear stress on the object caused by the fluid movement past
the objects surface and pressure drag which is related to the pressure differential over the
object surface (Munson et al. 2009).
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Fluid Flow Effects On Objects With A Dimpled Surface
3.0 -Literature Review
In order to identify the key characteristics that contribute to the drag force experienced by an
object in immersed dynamic fluid flow, the following review of published literature has been
established. The review covers three important topics that relate to the study of dimples in
fluid flow to accurately design a methodology of experimentation to review the impacts this
surface finish has on total drag for different geometries. The first review case is based on
surface augmentation practices for the purpose of drag reduction. Similar to the surface
augmentation produced from dimpling, nano and micro extruded fibres have an impact on
drag reduction. The second case looks at the study of dimple performance in terms or drag
and boundary layer production, focusing on flat plates and spherical geometries that have
relevance to the three geometrical shapes under study in this thesis. The final case looks into
the boundary layer and wake region formation. This study helps to identify the factors of flow
directions and reactions over geometries that will be used during the analysis process of the
experimentation results.
3.1 -Fluid Flow Effects Due to Surface Roughness
Surface roughness on objects immersed in flow effects fluid energies passing over their
surfaces. In some circumstances smooth surfaces are desired greatly such as aeroplane wings
and high speed racing cars, but for other applications it is proving more effective to increase
surface roughness. The most famous use is the golf ball where dimpling was utilised to
increase surface roughness for the purpose of drag reduction and therefore greater
performance. Other applications being investigated include sports helmets (Bike Radar Uk,
26/9/12) and even water bottles for long distance cycle racing (B.R. 29/3/10). The following
review looks into surface augmentations by small micro surface protrusions for the purpose
of fluid drag reduction.
A study on surface roughness effects on drag by M. B. Martell, J. B. Perot, J. P. Rothtein,
(2008) was done to determine the changes in surface drag on flat plates with super
hydrophobic surfaces. The aim of the research was to identify the performance differences of
differing surface geometry for ridges and posts applied to the surface of a flat plate at the
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Fluid Flow Effects On Objects With A Dimpled Surface
micro meter level. The theory for these augmentations was to create a high slip surface in
turbulent flow which will reduce drag as a micro layer of static fluid pockets allowing for
faster fluid velocities near the wall surface. This in turn would help to reduce the drag. The
experimental set up included flat surfaces with two main surface types placed inside a wind
tunnel, one consisting of ridges and the other of poles. The geometry of these surface
structures can be seen in figure 2 below.
Figure 2: Representations of Skin Layer Types, a) ridges b) poles. (M. B. Martell, J. B. Perot, J. P. Rothtein, 2008).
Varying Reynolds numbers from tests were graphed against ratios of surface structure height
and surface shear force. The results showed the surfaces with lower structure height produced
lower drag results. These heights were around 15µm and performed better against 30µm
heights by around 30%. The testing showed the ability to lower drag on surfaces with micro
structures applied. In the testing completed by the authors, ridged surface structures out
performed pole structures by an average of 10%.
Another study done by C. Henoch, T. N. Krupenkin, P. Kolodner, J. A. Taylor, M. S. Hodes,
A. M. Lyons, C. Peguero , K. Breuer, (2006) looked into the performance of super
hydrophobic surfaces in fluid flow situations and the drag reduction due to this surface
roughness. The researchers developed accurate nano structured grids comprising of 400nm
diameter square poles with 7µm height and 1.25µm spacing. The structure of these grids
allows trapped air to exist between each pole giving a non wetting characteristic of the
surface. This allows fluids to ‘ball’ and slip off the surface without increased friction drag.
The structure of this surface can be seen in figure 3.
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Fluid Flow Effects On Objects With A Dimpled Surface
Figure 3: Nano Surface Application. (C. Henoch, T. N. Krupenkin, P. Kolodner, J. A. Taylor, M. S. Hodes, A. M.
Lyons, C. Peguero , K. Breuer, 2006)
Testing for varying velocities was done in a small water tunnel on a plate consisting of
several sections of the super hydrophobic nano surfaces. Sensors were attached to this
flexible testing surface to calculate drag forces acting on the plate. The test section measured
at height and width of 0.3m and length 3.1m and the test section was placed 370mm from the
leading edge of the test section. Varying velocities for laminar and turbulent conditions were
then applied within the test section and drag results were measured. Initial estimates were that
the plate would show a reduced drag effect due to the surface application. A secondary
smooth PVC surface was used to determine a comparison of results obtained. The drag data
produced for the super hydrophobic surface showed a 50% drag reduction compared with the
smooth PVC surface. This can be seen in the figure 4 below.
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Fluid Flow Effects On Objects With A Dimpled Surface
Figure 4: Axial Drag vs Channel Velocity for PVC plate and Nanograss Surface Application. (C. Henoch, T. N. Krupenkin,
P. Kolodner, J. A. Taylor, M. S. Hodes, A. M. Lyons, C. Peguero , K. Breuer, 2006)
This graph shows a transition from laminar to turbulent flow at around 1m/s. The red dot data
for the super hydrophobic surface consistently shows a greater drag performance compared to
the smooth PVC plate in both flow type regions.
The research studied here relates to the intended surface augmentation compromising of
intruding dimples with the similar approach to reduce drag. Each study compromised of
micro structures to create hydrophobic surfaces. The first study showed with results that a
shorter height of micro structures produced lower drag results. This study introduces the
importance of augmentation geometry. It highlights that smaller poles reduced drag greater
than the larger type. Considerations should be made for this fact when reviewing data for
actual dimple design. These will include dimple depth and width as well as array structure
type. Another important aspect developed from these studies is the hydrodynamic effects. By
steadying flow within the structure of the micro and nano poles a controlled surface area was
developed. This shows the similarity between the controlled surface of the golf ball and
boundary layer formation. During testing this phenomenon may be observed and will be
important for analysis.
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Fluid Flow Effects On Objects With A Dimpled Surface
3.2 -Effect of Boundary Layer Formation and Drag by a Dimpled Surface on
a Flat Plate
3.2.1 Flat Plate Investigation
Boundary layer formation and drag forces attributed to the fluid flow over an objects surface,
provides an understanding of the performance of the object itself. Research has been focussed
on reducing forces related to fluid flow in order to allow for greater performance of the object
wether it is stationary or dynamic. Surface finishes and shapes are the main focus of ongoing
research in performance areas such as ballistics and sporting. One of the techniques of this
research is the surface application of ‘dimples’. Fluid flow characteristic contributed to the
presence of dimples develop complex reaction structures. Due to this complexity research on
dimples in immersed fluid flow has been conducted in order to develop a greater
understanding of these flow structures. The following cases investigate drag effects produced
by dimpled surfaces. These studies will introduce the effects dimples have in terms of flow
characteristics and potential reduction techniques. It will also look into the dimple sizes
utilised as this is an important aspect for the thesis geometrical models. The geometrical
types studied here are flat plates and spherical surfaces.
One investigation on the boundary layer formation caused by flow over dimples
(Mitsudharmadi, H.; Tay, C. M. J. & Tsai, H. M. 2009) investigated the design of rounded
edged dimples with different depths. The purpose of the research was to identify the
differences in boundary layer formation compared to sharp edged dimples. The authors also
investigating at varying the depths of the dimples in order to locate an effective dimple
‘shape’. Figure 1, b) shows the layout of the dimpled design used. Three different depths
corresponding to d/D of 4%, 8% and 12%, where d is the depth of the dimple and D is the
diameter of the dimple were determined. Each dimple was 40mm diameter for each varying
depth and set in an array of 59 on a flat surface seen in figure 5, (a) Flow over the plate was
kept constant at 5.5m/s and tripped upstream by a wire to induce turbulent flow.
Measurements were taken across the flow field by an adjustable hot wire probe.
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Fluid Flow Effects On Objects With A Dimpled Surface
Figure 5: a) Wind Tunnel Dimple Array Setup, b) Dimple Geometry. Mitsudharmadi, H.; Tay, C. M. J. & Tsai, H.
M. (2009)
Flow visualisation was also conducted with the use of additives introduced into the flow
made of a mixture of TiO2 (Titanium Oxide) particles, WD40 lubricating oil and kerosene.
With the use of a camera inserted into the wind tunnel images of flow behaviour over the
dimples were captured. This can be seen in figure 7.
Results for the first experiment were used to determine average sheer stresses across sections
of the dimpled plate compared to the same lengths for a flat plate. These results showed the
depth percentage of 8% showed slightly reduced shear stress for each location on average
compared to the other depths of dimples. Compared to flat plate there was an observable
difference in shear stress further downstream at x/D = 3.50 seen in figure 6 with the dimpled
plate showing a lower shear stress average across this section.
Figure 6: Shear Stress vs Location. Mitsudharmadi, H.; Tay, C. M. J. & Tsai, H. M. (2009)
The results for the flow visualisation can be seen in the images in figure 7. The results
obtained did not show a clear boundary layer formation image as the pictures were not taken
in a side angle but from above. The authors did conclude the separation produced by the
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Fluid Flow Effects On Objects With A Dimpled Surface
dimples was present in a small area surrounding each dimple but effects diminished soon
after and turbulent flow similar to flat plate effects took over until the next dimple.
Figure 7: Flow Visualisation For Differing Dimple Geometries, a) d/D of 4%, b) d/D of 8%, c) d/D of 12%.
Mitsudharmadi, H.; Tay, C. M. J. & Tsai, H. M. (2009)
A second study done by H. Lienhart, M. Brueur, C. Koksoy, (2008) was conducted to
investigate the drag effects caused by shallow dimples in a channel. The objective of this
study was to determine if a dimpled surface would reduce ‘skin friction’ drag.
The experimental setup for the testing involved a wind tunnel with test section geometry of
Height 50mm, width 600mm and length 6000mm. A turbulence inducing trip wire was
located 2000mm upstream of the test section. Two sizes of dimples were tested, these
included a smaller geometry with a diameter of 15mm and depth 0.75mm (d/D of 0.05) and a
larger geometry of diameter 47mm and depth of 2mm (d/D of 0.04). With the use of pressure
taps along the length of the test section a pressure distribution was collected and shear stress
was calculated. Figure 8 below shows the technical setup used for this experimentation.
Figure 8: Wind Tunnel Experimental Setup (H. Lienhart, M. Brueur, C. Koksoy, 2008)
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Fluid Flow Effects On Objects With A Dimpled Surface
Wind speeds allowing a distribution of Reynolds numbers across the test section were
produced and a comparison of the skin friction coefficients of the smooth plate were made to
the dimpled plates. Results showed no compelling change in performance for the dimpled
section. The figure (9) below shows the results of the skin friction coefficient of both plates
vs the Reynolds numbers achieved.
Figure 9: Measured and Predicted Data of Cf for Different Reynolds Numbers. (H. Lienhart, M. Brueur, C. Koksoy,
2008)
Figure 9 shows only the results of the smaller dimples tested. The larger dimples were
reported to produce larger shear stresses and a greater drag force but were not published in
the findings.
The authors concluded from their analysis that the dimpled section tested did not reduce drag.
Further CFD simulations conducted on a smaller test section with the same geometry
provided evidence for this conclusion. The author did note that the performance of the
shallow ‘smaller’ dimples did perform without a large drop of pressure across the testing
surface compared to the larger dimples. Further recommended by the author were within the
realm of heat transfer applications. Heat transfer augmentation techniques may be provided
with the use of shallow dimples without significant losses in pressure gradients across a
surface.
The research reviewed here shows some similarities with each case mainly being the
performance of differing dimple depths. In the first article the authors defined three different
dimples with depths 4%, 8% and 12% of the dimple diameter of 40mm. The dimple
producing the greatest performance for these test showed to be the 8% of diameter structure
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Fluid Flow Effects On Objects With A Dimpled Surface
with a depth/diameter 0.08 ratio. The second study looked at the performance of two differing
dimple sizes with the smaller dimple d = 0.75mm, D = 15mm and the larger with d = 2mm
and D = 47mm. From testing it was reported the smaller dimple produced better results with a
depth/ diameter ratio of 0.05.
In both cases the larger dimples produced larger shear forces which can be related to higher
friction drag. It should also be noted that the d/D of the smaller and larger dimples in the first
study are 0.04 and 0.12 respectively and the larger dimple in the second study has a d/D of
0.042. From the analyses of these ratios in these two studies there appears to be an effective
range where drag is lower due to dimple depth and dimple diameter. This will be taken into
account when designing dimples to be tested in this study. It should also be noted that both
articles reviewed showed no discernible decrease of drag force due to dimples but as testing
was done on a flat surface in both cases this result may be different for curved and bluff
geometries.
3.2.2 Spherical Body Investigation
A study conducted by K. Aoki1, K. Muto, H. Okanaga, Y. Nakayama (2009) determined drag
forces on spheres of diameter 42.6mm with differing dimple depth and height ratios. Spheres
of dimple ratios in terms of dimple height and depth and ratios of dimple depth to spherical
diameter were designed and tested by three methods.
Figure 10: Sectional View of Dimples and Specifications of Test Spheres. (K. Aoki1, K. Muto, H. Okanaga, Y.
Nakayama, 2009)
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Fluid Flow Effects On Objects With A Dimpled Surface
The first method was by a blow down wind tunnel with a testing section of 400x400mm with
each model suspended by a piano wire attached to a force load cell. Drag force measurements
for each sphere model were tested at Reynolds numbers ranging from
to
. The second test was for flow visualisation using spark tracing methods. Each electrode
was set at 30mm from away from the test spheres and powered by pulse generator. For the
third experiment CFD testing was conducted using the software FLUENT using large eddy
simulation methods (LES). This testing allowed for another flow visualisation method.
For the wind tunnel testing of various dimpled spheres, the following graph for drag
coefficient vs. Reynolds number was produced.
Figure 11: Cd vs. Re # for differing dimple geometry. (K. Aoki1, K. Muto, H. Okanaga, Y. Nakayama, 2009)
From testing the graph shows that arc type dimple ratios overall produced greater
performance then the smooth sphere. For the varying dimple ratios performance changed
with type E producing the lower drag coefficients at a k/d ratio of 0.0079 and k/c of 0.0958.
From spark tracing methods visual flow patterns were produced for the same dimple ratio
spheres in the graph above. This visualisation helps to see the flow patterns produced by the
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Fluid Flow Effects On Objects With A Dimpled Surface
varying dimple ratios. CFD testing was also introduced into this visualisation with surface
pressure coefficients represented by colour intensities applied of spark tracing imagery.
Figure 12: Spark Tracing Flow Visualisation with pressure distribution colour intensity display. (K. Aoki1, K. Muto,
H. Okanaga, Y. Nakayama, 2009)
The figure above shows flow intensity at Reynolds value of
. From this flow
visualisation it can be seen the Type E dimpled sphere producing a boundary layer separation
point further downstream then the other types. Each dimpled type out performs the smooth
sphere which has a larger wake region and the earliest boundary layer separation point.
Relating back to figure 12 above along with the flow imagery it can be understood the form
drag characteristic has the greatest effect on overall total drag. Note the smaller wake region
produced by each dimpled sphere. This represents a smaller pressure differential between
both front and rear side of each dimpled sphere compared to the smoother sphere which
would experience a larger form drag resulting in a larger overall total drag.
However as the dimple ratio changes it was found that after a k/d ratio of around 0.003 the
dimple depth has adverse effects of drag reduction and begins to retreat the separation point
towards the front of the sphere.
From this study, ratios of dimple depth to spherical diameter and dimple depth to dimple
diameter were established as the changing variable. Differing ratios produced results showing
greater pressure drag reduction then the smooth sphere. The information from this study also
encourages the application of dimples on different geometries as the sphere can be seen as a
uniform bluff geometrical shape. Dimple ratio data, drag coefficient data and spark tracing
flow patterns help to understand potential outcomes in testing for this thesis. Further
21
Fluid Flow Effects On Objects With A Dimpled Surface
investigation for dimple geometry design will be utilised from the reviewed literature in this
section in order to produce dimples with drag reducing potential for the geometries studied. It
appears a relationship with the geometry size to the dimple size should be established in order
to control variables between the two with consistency and clarity.
22
Fluid Flow Effects On Objects With A Dimpled Surface
2.4 -Fluid Flow Effects Around Bluff and Sharp Surfaces
The flow effects around bodies of varying geometries is an important field of study as it helps
to identify the effective shapes for aerodynamics, structural integrity, structural vibration,
drag reduction and other important features of performance for objects that exist in dynamic
flow situations. The following review covers studies in the areas of boundary layer
development and drag forces experienced by common shapes and geometries in fluid flow
applications. Due to the use of semi blunt and bluff geometries studied in this thesis it is
important to develop an understanding of differing flow patterns over similar objects. In the
following studies fluid flow behaviour is investigated when flow is subjected to sharp
directional changes developing boundary layers and wakes.
A study done by T. Tamura, T. Miyagi, (1999) looked into the effects of drag and the drag
coefficient on square cylinders in a cross flow with varying corner geometry. The aim of the
study was to identify the characteristics of performance with varying edge types, including
straight corners, chamfered corners and rounded corners. The designed study can be seen in
figure 13.
Figure 13: Geometry Configuration for Test Models. (T. Tamura, T. Miyagi, 1999)
The experimental setup included an Eiffel type wind tunnel with a testing section of
1000mmx800mmx800mm. Turbulence was introduced into the testing chamber by the use of
a wire grid up stream of the test section. All models were located 1000mm downstream of the
23
Fluid Flow Effects On Objects With A Dimpled Surface
turbulence grid. Wind tunnel parameters allowed for a controlled velocity between 0.2 and
25m/s. A Reynolds number of 3.0x104 was used for the testing and angles of corner geometry
were varied instead of wind speeds. This was done to test the geometry performance at a set
wind speed. All models were 300mmx300mm with a 50mm bore. Load cells located beneath
each model were arranged to indicate values of lift and drag. From these readings results of
the drag and lift coefficients were determined and graphed against the varying corner
geometry. This can be seen in figure 14 below.
Figure 14: Corner Shape Effect on Cf and Cd at Differing Corner Angles. (T. Tamura, T. Miyagi, 1999)
These results showed the increase of drag coefficient as angles of the corner geometry for
each shape were increased positively. This figure shows the performance of the chamfered
and rounded corners increase to the standard flat surface of the sharp corner shape before its
own change in corner angle witch once again increased the drag coefficient. The authors
concluded this is due to the detachment of the turbulent boundary layer at the start of the
object and reattachment further down the object length which ultimately increased the
following wake. This is true for positive corner angle changes but for negative changes a drag
reduction was observed with a smaller wake behind the structure.
24
Fluid Flow Effects On Objects With A Dimpled Surface
Another flow study done by S. Becker et al. J. Wind Eng. Ind. Aerodyn. 90 (2002), looked
into differing flows around ground based structures. The purpose of the study was to simulate
effects of building type structures up to 100m with small models and equivalent Reynolds
numbers for turbulent flow types. The researchers visually observed the flow patterns from
wind tunnel testing and computer simulations. Testing points at differing times and model
orientations were captured with high speed cameras to observe the boundary layer
development before the object and the flow change around and after the object. In figure 15
below vortex shedding can be seen after the structure under Reynolds number conditions
around 2–7x104.
Figure 15: Vortex Shedding for Uniform Flow Conditions. (S. Becker, H. Lienhart, F. Durst, 2002)
The authors identified the vortex shedding acting similar to Karmen vortexes and due to the
nature of the analysis verified the effect to be similar to large buildings in domestic areas.
The purpose of these experiments was to create a visualisation of the flow structures as they
appear on buildings. The authors identified the importance of these studies as they can relate
to safe building techniques. Several other similar studies completed by the authors also
looked into the models suspended in flow at differing angles of attack and observation for
flow separation features such as ‘stalling’ were reconstructed. The study is also important due
to the concentration of vortex shedding wind flutter that is experienced by both static and
dynamic structures.
The articles studied here helped to identify some of the flow patterns that may be produced
during testing. From the articles studied here and additional resources on flow characteristics
identification of fluid flows before, around and after the geometries with both smooth and
dimpled surfaces can be better estimated, understood and analysed.
25
Fluid Flow Effects On Objects With A Dimpled Surface
The first article looks at differing trailing and leading edge angles. As angles increased to a
sharper degree greater drag forces were experienced. Detachments of boundary layers
gradually existed closer to the leading edge. This helped to show that smother edged objects
usually perform better in flow situations. Therefore an expectation for the performance of
some of the studied geometries boundary layer characteristics can be made and observations
may be made clearer for any difference in these boundary layer when different surface
finished are compared. The cylindrical geometry is expected to have similar properties from
the T. Tamura, T. Miyagi, (1999) study as the cross section is circular and may have effects
to those of traditional golf balls. The ogive has a smoother frontal section but blunt rear
tailing section. This is expected to produce the Karmen like vortexes as seen in the S. Becker
et al. J. Wind Eng. Ind. Aerodyn. 90 (2002) study where large eddy’s appear within the
trailing wake region. Wake sizes observed may help indicate the controlling factor of total
drag in terms of the friction and pressure drag components. For the streamline body wake
regions are expected to be small but fractionally larger for the dimpled model. This is due to
the increased surface friction which traditionally is avoided in situations where slim long
components are used in flow operations (Airfoils). Due to this increased friction for the
streamline body, boundary layer initiation may be forced to start earlier along the surface
resulting in a larger total drag.
26
Fluid Flow Effects On Objects With A Dimpled Surface
4.0 –Methodology
The following sections (4.0 and 5.0) are developed to establish techniques for building the
models for testing and the experimental procedures used to produce data for the analysis of
dimpled surface geometries. Section 4.0 will cover design details for each of the three
geometries studied and the dimple geometry surface application applied to each shape.
Section 5.0 will cover processes of experimentation for both Computational Fluid Dynamics
and Wind Tunnel Testing of the smooth and dimpled model geometries.
4.1 –Geometry Design
The three geometries studied are designed to be used for both simulation testing and wind
tunnel testing with models developed via the use of a 3D printer for the latter. Geometry sizes
are for testing purposes and are not modelled on any specific engineering components.
Considerations had to be made in terms of size for the integration in a wind tunnel with a test
chamber dimension of 500mm x 500mm x 1000mm. Geometry sizes were also limited to the
3D printer used (Prusa-Mendel Iteration 2) which had a printing area of 200mm x 200mm x
100mm although the orgive and cylinder each where made in two separate parts allowing
larger models. The measurements for the studied geometries are shown below. Due to the
limited flow velocity of the wind tunnel Reynolds Numbers for each model fell within the
laminar flow range with some velocities producing turbulent Reynolds Numbers. The
following figures (16, 17, 18, and 19) show the measurements for each geometry studied
along with the design process for dimples applied to each object. Both smooth and dimpled
geometries have identical measurements.
27
Fluid Flow Effects On Objects With A Dimpled Surface
4.2 –Cylinder Design
Figure 16: Cylinder design for analysis and testing for the comparison of Smooth vs. Dimpled surface texture.
4.3 – Orgive Design
Figure 17: Orgive design for analysis and testing for the comparison of Smooth vs. Dimpled surface texture.
28
Fluid Flow Effects On Objects With A Dimpled Surface
4.4 –Slimline Body Design
Figure 18: Slimline Body design for analysis and testing for the comparison of Smooth vs. Dimpled surface texture.
4.5 –Dimple Geometry
Figure 19: Dimple geometry cross section.
29
Fluid Flow Effects On Objects With A Dimpled Surface
The designs for the dimples were produced from analysis of reviewed literature in which flow
tests were conducted along dimpled surfaces. There contained three main characteristics for
dimple design. The first is the ratio of the dimple depth ‘k’ over the diameter of the dimple
‘C’. In flow test conducted by Katsumi. A, Koji. M, Hiroo and Yasuki testing on spherical
bodies several ratios were designed and flow test conducted to investigate boundary layer
separation. From these tests the minimal point that produced later boundary layer detachment
was around a ratio of 0.03 to 0.05. Similarly tests by Mitsudharmad, Tay, C. M. J and Tsai,
H. M found results that showed smaller k/C ratios performed better than larger k/C ratios
with the greatest performance ratio of around 0.08. Studies done by H. Lienhart, M. Brueur,
C. Koksoy found greater performance of smaller ratios again with the greatest performance of
their dimple designs to be around 0.05.
Taking into account the previously documented research it was decided to use the minimal
value of 0.03 for the slimline body and up to 0.05 for both the orgive and the cylinder. This
would allow for analysis on differing k/C ratios.
The second design parameter was the ratio of dimple depth ‘k’ over main geometry diameter
‘d’. Once again from research it was found in the flow studies by Katsumi. A, Koji. M, Hiroo
and Yasuki (2009) that certain ratios produced later boundary layer separation over spherical
surfaces. The study found that ratios smaller and larger than that of k/d of 0.003 started to
produce boundary layer separation closer to the frontal surface. It was decided to apply these
results to the dimple design on each geometry studied.
Each geometry utilised the main circular axis for the value of ‘d’. With both the cylinder and
orgive having d = 50mm and the slimline body of d = 25mm. By applying the ratio of k/d =
0.003, k values for each where evaluated. Thus from this known k value dimple diameters ‘C’
for each geometry where calculated. The following is the dimple design layout for each
geometry.
Table Two: Dimple Design Parameters.
k/d
k/C
K
d
C
Cylinder
0.003
0.05
0.15mm
50mm
3mm
Orgive
0.003
0.05
0.15mm
50mm
3mm
Slimline Body
0.003
0.03
0.075mm
25mm
2.5mm
30
Fluid Flow Effects On Objects With A Dimpled Surface
The third parameter for dimple design was the surface interaction shape. There are two
potential shapes. The first is flat edged where the dimple meets the surface and becomes
instantly flat following the normal surface direction. The second is a slopping rounded edge
where the dimple edges are curved towards the surface. As the design for dimple diameter
and shape would be changed from the latter the flat edged surface shape was chosen. This is
not a greatly important aspect with the dimple parameters chosen but for deeper dimples
where surface shape can tend towards 90◦ then a sloped edge would be potentially less
aggressive in interaction with fluid flow.
Another feature taken into account when designing each model was the dimple surface
layout. Two potential designs exist, these are staggered and aligned. The aligned array is a
simpler design but only covers over the surface in strait perpendicular lines. The aligned
array covers the surface in sloped lines allowing for a more even coverage. For each
geometry the aligned pattern was utilised for simplicity and would still perform as a flow
manipulator to affect drag.
The layout for each geometry dimple array was measured with dimples beginning from edges
at a distance of half the dimple diameter and spacing of half the dimple diameter in both
directional axes. The exception is the cone section for the orgive for which tappers dimples
closer in the direction of the frontal tip.
The main surface area of each geometry was covered with these dimple layouts leaving the
left and right sides blank of both the cylinder and slimline body and the front and rear
sections of the orgive.
31
Fluid Flow Effects On Objects With A Dimpled Surface
5.0 –Thesis Testing
5.1 -Testing Objectives
The objectives for this Thesis concerning obtaining results include the following:
 Establishing complete models (ogive, cylinder and slim line body) for simulation
testing and wind tunnel testing in Creo Parametric/Pro Engineer.
 Correctly enabling model interaction with COMSOL CFD module.
 Correct instillation of Models into the wind tunnel.
 Complete Meshing of test area and models in COMSOL.
 Correctly adjusting fluid attributes including air densities and viscosities.
 Successful simulations with varying flow velocities over models.
 Observable differences in boundary layer development for varying flows.
 Results for drag on models for varying flow velocities using COMSOL and wind
tunnel testing.
32
Fluid Flow Effects On Objects With A Dimpled Surface
5.2 –COMSOL Flow Test
For simulations on the objects undergoing studies for this thesis COMSOL Multiphysics was
employed as the primary software for this purpose. COMSOL uses finite element analysis for
studies across multiple fields of physics including Fluid Dynamics.
For the COMSOL flow test each model geometry with both smooth and dimpled variations
where tested using the parameters in table 7 below. Each model was tested from 5m/s to
40m/s in 5m/s increments. This equated to 48 flow tests with 8 tests per model type. Drag
force on each model was collected from each test along with maximum pressures at the front
and rear section. From this data two graphs where produced for each geometry comparing the
smooth models with the dimpled models. The first graph is the drag coefficient vs. Reynolds
number. The second graph is pressure differential vs. Reynolds number. From these graphs a
comparison is made. See results and discussion section bellow for data and graphs produced.
For calculation of Reynolds number over each model the following equation was used...
Equation One
Where is the density of the fluid. In each test standard Air is used with a density of 1.165
kg/m3.
is the fluid velocity from 5m/s to 40m/s in 5m/s increments.
is the Dynamic Viscosity of Air at 0.00001568 kg/ms.
is the characteristic length for each model. The characteristic lengths are shown in table
three below.
Table Three: Geometry Characteristic Lengths
Geometry
Cylinder
Orgive
Slimline Body
Characteristic
Section
Diameter
Full Length
Full Length
Length
50mm
170mm
150mm
For calculation of the Drag Coefficient produced from the drag for each fluid velocity the
following equation was used.
Equation Two
33
Fluid Flow Effects On Objects With A Dimpled Surface
Where
is the density of the fluid. In each test standard Air is used with a density of 1.165
kg/m3.
is the fluid velocity from 5m/s to 40m/s in 5m/s increments.
is the cross sectional area normal to the fluid flow. The cross sectional areas for each model
are shown in table four bellow.
Table Four: Geometrical Cross Sectional Areas
Geometry
Cylinder
Orgive
Slimline Body
Cross Sectional Area
0.19
0.19
0.12
Before flow tests are conducted a process for mesh accuracy determination is necessary. The
CFD module in COMSOL supplies preset meshing densities that apply to both the fluid
environment and the model surface. These mesh densities involve varying CFD computations
and in order to determine the correct mesh density a test model with known theoretical drag is
used to compare with drag calculated from COMSOL.
This test sphere was modelled using Creo Parametric software with a 50mm diameter. The
testing flow velocity is 10m/s. The theoretical drag coefficient was determined and from this
a theoretical drag was calculated. The following table shows all set fluid attributes used for
sphere calibration tests along with the calculated drag coefficient and drag.
34
Fluid Flow Effects On Objects With A Dimpled Surface
Table Five: Sphere Calibration COMSOL Parameters
Model Type
Model Material
Flow Material
Flow Type
Fluid Density
Dynamic Viscosity
Pressure
Flow Velocities
Test Section Dimensions
Sphere Diameter
Frontal Area
Reynolds Number
Cd
Drag Force
3D, Stationary
Polyethylene
Air
Laminar Flow, k1.165 kg/m3
0.00001568 kg/ms
101.325 kPa
11m/s
200x200x500mm
0.05m
0.001963495m2
40864.15816
0.464412894
0.06427106 Newtons
The Reynolds number was calculated through the following process...
For the drag coefficient the following equation was used...
Equation Three
This is a simplified equation developed by Clift, Grace, and Weber (Bubbles, Drops, and
Particles, Academic Press, 1978) for the study of drag coefficients on spheres and terminal
velocities in fluids.
The drag coefficient matches other calculated drag coefficients for spheres. For the drag force
the following equation was used.
35
Fluid Flow Effects On Objects With A Dimpled Surface
Equation Four
For the testing of the sphere each mesh density was applied to both the test section and the
model sphere. Drag force was calculated for each mesh density test and the following graph
was produced to determine at which mesh density the drag forced matched that of the
theoretical drag force.
Table Six: Calibration Data for COMSOL Testing
Mesh Density
Extremely Coarse
Extra Coarse
Coarser
Coarse
Normal
Fine
Finer
Extra Fine
Extremely Fine
Simulated Drag (Newtons)
0.40318
0.34642
0.27443
0.17865
0.06757
0.06230
0.04579
0.04153
0.03089
Theoretical Drag (Newtons)
0.064271060
0.064271060
0.064271060
0.064271060
0.064271060
0.064271060
0.064271060
0.064271060
0.064271060
36
Fluid Flow Effects On Objects With A Dimpled Surface
Figure 20: Sphere Drag Accuracy Testing with ‘Normal’ Mesh Density Application, COMSOL.
It was determined that the mesh size classed ‘Normal’ would be sufficient for testing all
geometry models in COMSOL. The minimum element size at this mesh density is 0.018mm
and the maximum is 0.1mm. This mesh density was suitable for each model when testing was
conducted.
From the testing of the sphere in COMSOL, the following parameters were set for the testing
of each model.
Table Seven: COMSOL Parameters for Official Testing
Final COMSOL Testing Parameters
Model Type
Model Material
Flow Material
Flow Type
Fluid Density
Dynamic Viscosity
Pressure
Flow Velocities
Test Section Dimensions
Test Section Mesh Type
Model Mesh Type
Values/ Attributes
3D, Stationary
Polyethylene
Air
Laminar Flow, k1.165 kg/m3
0.00001568 kg/ms
101.325 kPa
5m/s to 40m/s in 5m/s increments
200x200x500mm
Normal, max size-0.1mm, min size-0.018mm
Normal, max size-0.1mm, min size-0.018mm
37
Fluid Flow Effects On Objects With A Dimpled Surface
5.3 –Wind Tunnel Flow Test
For the wind tunnel flow tests a wind tunnel on the Charles Darwin University Campus was
utilised. This wind tunnel has a nine to one reducer section into a 500mmx500mmx1000mm
test section where a drag and lift force measuring apparatus was set up. The wind tunnel
controller sets fan frequencies to control wind speed with the fan situated near the exhaust
section of the wind tunnel.
Each 3D printed model was connected to the drag/ lift reading load cell which sent force data
to a Lab View software programme designed by Gethin Barden and measurements were read
directly from a laptop.
Each model was attached in the same direction to flow as its counterpart in COMSOL. All
drag force data was collected to the third decimal place. To prevent additional drag due to
incorrect instillation of the models lift data was monitored to assure a zero angle of attack
was achieved.
The frequency controller for the fan set the wind speeds. To determine the correct wind speed
each frequency was manipulated by the following equation produced by Gethin Barden.
Equation Five
Frequencies were set to produce wind speeds the same as those during COMSOL testing for
better comparison during results analysis. Table eight shows frequencies set and wind speeds
produced. Due to limitations for the output of the controller, a maximum wind speed for the
wind tunnel was 38m/s instead of 40m/s.
Table Eight: Wind Tunnel Controller Frequencies and Velocities
Frequency
6.57
13.15
19.73
26.31
32.89
39.57
46.05
50.00
Hertz
Wind Speed m/s
5.00
10.00
15.00
20.00
25.00
30.00
35.00
38.00
Atmospheric conditions were also taken into account for data analysis with weather data
gathered from the Darwin Bureau of Meteorology for the testing days. The following average
38
Fluid Flow Effects On Objects With A Dimpled Surface
conditions are shown in the following table. These values were used for calculating the
coefficient of drag for each test.
Table Nine: Atmospheric Wind Tunnel Testing Conditions
Weather Condition
Atmospheric Temperature ◦C
Atmospheric Air Density
kg/m3
Atmospheric Air Dynamic Viscosity
kg/m.s
Value
28
1.1726
0.000018586
Initial conditions were also considered for correct drag calculation. This took into account
drag readings by the load cell when fan speed is at zero. These readings needed to be
subtracted or included to drag data after testing was complete in order to determine correct
drag forces on each model.
All data and graphs produced by COMSOL and wind tunnel testing can be seen in appendix
A and results.
Due to the construction method used for each model used in the wind tunnel test a final
surface finish was done by hand. Each model was created through the use of 3D printing and
left a moderately smooth surface. The surfaces still had some rough defects due to the
printing construction so a smoothing process for the ‘smooth’ and ‘dimpled’ models was
necessary. The models were made from Acrylonitrile Butadiene Styrene (ABS), this plastic
has properties that allows for easy deformation when exposed to Acetone vapour or liquid.
Testing Acetone vapour with a sample model showed some smoothing improvements on the
surface but from observation caused slightly deformed dimple geometry. Therefore a simpler
smoothing process using fine sand paper was done carefully to increase surface finish but not
so much as to deform model and dimple geometry.
39
Fluid Flow Effects On Objects With A Dimpled Surface
6.0 –Results and Discussion
The aim of the thesis is to identify the effects surface dimpling has on fluid flow over
differing geometrical 3D shapes. With the use of computational fluid dynamic software and
wind tunnel model testing, data and observations were collected and made. The following
discussion is focused on the results for both CFD and wind tunnel tests conducted for the
thesis. The discussion will be structured to look at results for all three geometries studied with
the aid of graphs for Drag vs. Reynolds Number and Drag Coefficient vs. Reynolds Number
along with visual flow imagery from CFD and Wind tunnel testing. This discussion will also
look into unexpected data results and observations, and the reasoning behind these
phenomena. All raw data gathered can be seen in appendix A along with values calculated for
Reynolds Numbers and Drag Coefficients.
40
Fluid Flow Effects On Objects With A Dimpled Surface
6.1 –Cylinder
The cylinder geometry studied had measurements of 100mm long with a 50mm diameter.
This was a set geometrical size for both CFD and wind tunnel testing for the smooth surfaced
model and dimpled surfaced model. The flow range tested for in both experimental
procedures covered laminar and turbulent flow types with turbulent flow starting around 105.
Most flow velocities produced flow types under this Re# but were likely exhibiting
transitional type behaviour as true laminar flow exists for very low Reynolds numbers in the
magnitude of 102. Due to similarities to the circular cross section of a sphere which presents a
somewhat correlative cross section to that of the cylinder, comparable traits in the dimple
application in terms of flow behaviour were expected pre testing. From the resulting data for
both experimental techniques it was established within the testing flow range that the dimpled
surface application affected the flow in the expected manner.
These results were the same in both experimental cases for CFD and wind tunnel testing. For
each flow velocity test conducted the dimpled surfaced cylinder produced lower drag
readings. It was observed when comparing collected data that as flow velocities increased the
differences in drag forces grew. For the CFD testing results, drag data gathered vs. Reynolds
number representations of flow velocities are graphed to compare the smooth and dimpled
cylinders in figure 21.
Drag vs. Re # for Smooth and Dimpled Cylinder
by CFD Testing
Drag Force Newtons
Smooth Cylinder
Dimpled Cylinder
4.50000
4.00000
3.50000
3.00000
2.50000
2.00000
1.50000
1.00000
0.50000
0.00000
0
20000
40000
60000
80000
100000
120000
140000
160000
Reynolds Number
Figure 21: Drag vs. Re# for smooth and dimpled cylinder by CFD testing.
41
Fluid Flow Effects On Objects With A Dimpled Surface
As the flow velocities increase it can be seen in this graph that the drag forces are
diminishing for the dimpled cylinder compared to the smooth cylinder. Percentage decrease
in drag force for the dimpled cylinder at a velocity of 5m/s is 89.05% and narrows to a
56.98% difference at 40m/s. At around 15m/s this percentage difference levels out at the 56%
mark. As velocities increase the percentage difference between the two drag forces get larger
until at 15m/s where the difference between the two stays around the same point.
For the flow region tested by CFD experimentation, overall results show a lower resulting
drag force experienced by the dimpled surfaced cylinder. As the cylinder cross section can be
compared to a limited extent with the axis cross section of a sphere it is apparent the
controlling drag force component on the cylinder is the pressure drag. To determine if this is
true, visual flow imagery can be used to compare flow characteristics. The following figures
22 and 23 show comparable flow imagery for smooth and dimpled cylinder tests produced by
CFD experimentation for a flow velocity of 40m/s. Figure 22 represents flow over the smooth
model at 40m/s and figure 23 for flow over the dimpled model at 40m/s.
42
Fluid Flow Effects On Objects With A Dimpled Surface
Figure 22: CFD Flow imagery over smooth cylinder at 40m/s.
Figure 23: CFD Flow imagery over dimpled cylinder at 40m/s.
The first thing to point out for the comparison of these two flow image results is the colour
flow representation. Although both induced flows are at 40m/s COMSOL has produced flow
intensity colour representation differences. However important flow characteristics are still
visibly present. Before further analysis it should also be stated that imagery for all flow
velocities were gathered for each surface type cylinder, but differences in flow patterns are
43
Fluid Flow Effects On Objects With A Dimpled Surface
visibly very small. The representation at 40m/s shown above is almost the same for each
velocity tested. Imagery for this flow velocity is considered a competent representation for all
flow velocities tested. In addition it should be noted the smooth cylinder appears to be a
multisided polygon but during testing all meshing densities were consistent therefore both
cylinders were tested with the same accuracy.
From observations of the flow imagery three key characteristics stand out. The first is the
boundary layer separation points along the two model types. Similar to the application of
dimples on a sphere resulting in a later boundary separation point to that of a smooth sphere,
the dimpled cylinder has comparable properties. The separation point for the boundary layer
over the dimpled cylinder is further to the rear section of the cylinder with respect to the flow
direction from left to right when compared to the smooth cylinder. This effectively produces
a smaller wake area. The wake can be seen behind each cylinder. This leads to the second
observation, the wake size and intensity. Once again similar to the wake differences for a
sphere, the dimpled cylinder is producing a considerably smaller wake region then the
smooth model. This is tied to the point of separation of the boundary layer. As the separation
point for the smooth cylinder is further forward towards flow, the lower velocity flow within
the boundary layer region is larger. From the study presented by K. Aoki1, K. Muto, H.
Okanaga, Y. Nakayama (2009) similar observations for the cross section of smooth and
dimpled spheres were made shown in figure 12. This forward separation point prevents flow
converging around the cylinder profile earlier as compared to the dimpled cylinder. The
larger wake region developed traditionally produces a larger adverse pressure gradient along
the geometry profile ultimately resulting in a larger pressure drag force.
This observation leads to the third flow characteristic presented in the figures above. The
immediate flow regions at the front and rear surface of the cylinders show a slower moving
fluid region. The frontal regions experience stagnation flow points where velocities tend
towards zero. At the rear sections turbulent ‘eddy’s’ exist with low flow velocities. These
slower velocity regions represented in darker blue intensities also experience a pressure
differential. For the smooth cylinder a larger region of slow velocity fluid flow exists as the
boundary layer takes a longer time to converge. This produces a low pressure region of flow
causing a vacuum area relative to surrounding pressures resulting in an increased pressure
drag on the smoother cylinder. The dimpled cylinder experiences this effect also but at a
smaller intensity effectively producing a lower overall drag force.
44
Fluid Flow Effects On Objects With A Dimpled Surface
Friction drag forces are present also but seem to be negligible by the controlling factor of the
pressure drag. Evidence of friction drag can be seen in the forward region of the dimpled
cylinder. It can be seen at this point a lower intensity flow region compared to the smooth
model, likely produced by the increased surface friction developed by the incoming fluid
flow.
From these three observations complemented with the drag force data collected over the flow
velocities tested by CFD, the dimpled cylinder performs better in regards to lowered drag
forces.
The second form of testing was done by the use of a load cell producing drag force data for
cylinder models mounted into a wind tunnel. These models where developed by a 3D printing
method and where built to the same dimensions as the models tested by CFD. In order to
produce similar data as CFD, surfaces were smoothed to an extent that wouldn’t change the
overall geometrical shape. Each model was mounted into the wind tunnel test section on a
narrow aluminium arm connected to a drag force load cell. Connection to the arm was done
by running internal threaded rods through the cylinder models and bolted to the cylinder
sides. The addition of surface areas caused by the model holder arm and exposed bolts is
minimal and care was taken to prevent these components from disturbing flow over the main
surface section.
Test runs were conducted from 5m/s to 35m/s by five 5m/s increments with a final maximum
reading at 38m/s. This was done in order to produce comparable data to CFD testing. Care
was also taken to keep each model level during testing and all data readings were made by
Gethin Barden who developed the hardware and software program and had prior experience
with this operating system. It was decided to keep the data reading persons to one to prevent
additional errors as drag fluctuations may have been read differently between different
observers.
The results for the drag forces vs. the Reynolds number representations of velocity for wind
tunnel cylinder tests can be seen in figure 24 below. Once again the results showed that for
each velocity tested the dimpled cylinder produced lower drag readings. At 5m/s the dimpled
cylinder experienced a drag force of 34.37% the magnitude the smooth cylinder. Similar to
the testing by CFD the results around 35 to 38m/s were at a magnitude of 42% and 47%. As
the testing range was limited to 5 to 38m/s it isn’t possible to tell if results for drag forces are
45
Fluid Flow Effects On Objects With A Dimpled Surface
converging for the dimpled cylinder towards to results of the smooth cylinder at higher
velocities, but within the range tested the dimpled cylinder experiences lower drag forces.
Drag vs. Re # for Smooth and Dimpled Cylinder
by Wind Tunnel Testing
Smooth Cylinder
Dimpled Cylinder
Drag Force Newtons
6
5
4
3
2
1
0
-1 0
20000
40000
60000
80000
Reynolds Number
100000
120000
140000
Figure 24: Drag vs. Re# for smooth and dimpled cylinder by wind Tunnel testing.
From figure 25 below, imagery for the wind tunnel test was produced with the help of a
smoke wand to show fluid flow profiles of the smooth and dimpled cylinders.
Figure 25: Wind Tunnel Flow imagery over smooth and dimpled cylinder at 15m/s.
46
Fluid Flow Effects On Objects With A Dimpled Surface
Although the smoke flow over the dimpled cylinder is more transparent the separation point
can still be observed. The results show similar characteristics to the CFD images. The
dimpled cylinder retards the boundary layer initiation and ultimately results in a smaller wake
and pressure differential across the cylinder profile and therefore lower drag forces.
47
Fluid Flow Effects On Objects With A Dimpled Surface
6.2 -Streamline Body
The streamline body was subjected to the same testing procedures as for the cylinder and
orgive. This was the ‘most elongated’ geometry in terms of its shorter height and width to the
longer length, it was chosen as a comparable model to define potential differences in drag
force components to the other two geometries. For testing between the velocity range of 5m/s
to 40m/s and 38m/s for CFD and wind tunnel experimentation respectively the streamline
body experienced flow types mainly within a turbulent flow region. This is due to the
elongated surface for which the Reynolds equation defined flow types to be over the expected
fully turbulent point of 105.
As the streamline body has a greater elongated area to cross sectional area roughly 0.009m2
to 0.0007m2 (a 92% larger surface area) it was expected to act similarly to that of a flat plate
with differing surface roughness’s. As surface friction for flat plates is increased friction drag
is directly affected and shear stresses attributed to fluid movement past the plate’s surface are
increased. As the dimpling on the streamline body can be considered to act as increased
surface roughness it was expected to produce higher drag forces for the dimpled model. From
the studies produced by H. Lienhart, M. Brueur, C. Koksoy, (2008) it was seen in figure 9
that a flat dimpled plate consistently produced slightly higher drag results. Although the
streamline body is not a perfect flat plate it can still be considered relatively flat in
comparison to the more bluff geometries of the cylinder and orgive.
Testing by Computational Fluid Dynamics yielded results relative to those of the H. Lienhart,
M. Brueur, C. Koksoy, (2008) study with higher drag readings experienced by the dimpled
streamline body compared to the smooth model. From figure 26 it can be seen the
comparison of the smooth and dimpled streamline bodies resulting drag forces over the tested
velocity range represented by Reynolds numbers. For all velocities from 10m/s to 40m/s there
was an increase in drag force on the dimpled model compared to the smooth model. The
exception was for the lowest velocity at 5m/s where the dimpled streamline body experienced
a drag force at 60.29% the magnitude of the smooth streamline body. For the remaining
velocities the dimpled model drag forces exceed those of the smooth model from a 2.14%
drag force increase at 10m/s to a 17.90% increase at 40m/s and velocities in between
produced consistently greater percentage increases.
48
Fluid Flow Effects On Objects With A Dimpled Surface
Drag vs. Re # for Smooth and Dimpled
Streamline Body by CFD Testing
Smooth Streamline Body
Dimpled Streamline Body
0.45000
DragForce Newtons
0.40000
0.35000
0.30000
0.25000
0.20000
0.15000
0.10000
0.05000
0.00000
0
50000 100000 150000 200000 250000 300000 350000 400000 450000 500000
Reynolds Number
Figure 26: Drag vs. Re# for smooth and dimpled streamline body by CFD testing.
As flow velocity increases it is seen also that the drag forces experienced on the dimpled
model are increasing faster than for the smooth model. From the 2.14% increase at 10m/s to
the 17.90% increase at 40m/s the drag force difference appears to increase over the velocity
range investigated.
The results produced from CFD testing were expected in terms of the dimpled model
experiencing greater drag due to previously documented research on flat plates. In order to
confirm the controlling drag component acting on the total drag, analysis of the imagery
produced can be made to define flow characteristics. In figure 27 and 28 below a velocity
representation produced by COMSOL is seen for the smooth and dimpled models at 10m/s.
Similar to the cylinder and orgive imagery, 10m/s is an accurate representation of the flow
silhouette for all other velocities for the streamline body model types. Also the main flow
velocity colour intensity representation is different between each figure. Consideration is
made for analysis.
49
Fluid Flow Effects On Objects With A Dimpled Surface
Figure 27: CFD Flow imagery over smooth streamline body at 10m/s.
Figure 28: CFD Flow imagery over dimpled streamline body at 10m/s.
From the flow imagery for the 10m/s flow velocity over the smooth and dimpled models two
key characteristics stand out. The first is the visible production of a boundary layer on the top
and bottom sides of the dimpled model. Although the smooth model shows slightly reduced
velocity flow near the same surface region the dimpled model has a more intense boundary
layer. This represents increased surface friction and an increase of shear stresses. The
initiation point for the dimpled model boundary layer is close to the top and bottom apex of
50
Fluid Flow Effects On Objects With A Dimpled Surface
the forward curved section. Here velocity is increased and represented in both figures as a
dark intense red immediately before an observable reduction in fluid velocity. For the
dimpled model the boundary layer does not grow quickly but gradually increases. This is
both due to the faster moving fluid outside the boundary layer and the angle of the incline of
the geometry.
The second characteristic is the wake region size. Both models have a comparatively similar
sized wake tail and intensity immediate slow moving flow regions at the front and rear
sections. By judgment of the boundary layer on the dimpled model however there is a slightly
larger pressure differential due to the enlarged size of the boundary layer at the model trailing
edge. Comparing data and observations it is clear that for this geometry the main controlling
factor of the overall total drag is the friction drag. There also is a potentially larger pressure
drag but without pressure data this cannot be assured. Interestingly though due to the obvious
development of the boundary layer on the dimpled model the drag force percentage
difference initially is very small. Without further testing it is not possible to determine the
flow and drag effects at higher velocities.
For the secondary experimentation using the 3D printed models and wind tunnel load cell the
streamline body was tested within the same flow range minus the final 40m/s velocity, using
38m/s instead. This produced data for drag forces and visual flow profiles. The following
graph in figure 29 shows the resulting drag forces vs. the Reynolds Number range tested.
Drag vs. Re # for Smooth and Dimpled
Streamline Body by Wind Tunnel Testing
Smooth Streamline Body
Dimpled Streamline Body
Drag Force Newtons
0.60000
0.50000
0.40000
0.30000
0.20000
0.10000
0.00000
-0.10000
0
50000
100000
150000 200000 250000
Reynolds Number
300000
350000
400000
Figure 29: Drag vs. Re# for smooth and dimpled streamline body by Wind Tunnel testing.
51
Fluid Flow Effects On Objects With A Dimpled Surface
From observation of data for wind tunnel testing it was found that once again drag forces
experienced by the dimpled model were at a marginally higher magnitude then for the smooth
model. For the wind tunnel data every velocity tested produced higher drag forces.
For the 5m/s velocity the dimpled model exceeds the drag force of the smooth model by 68%.
The results differ more for percentage increased then for CFD as is expected due to additional
variables present during live testing but for the final three results studied, 30, 35 and 38m/s
the is a percentage increase from 2.19% to 3.23% and 5.77%. This is similar to the expanding
nature of the drag forces produced by CFD for these points and may point to a further
expanding section past the 38 and 40m/s velocities.
From flow visualisation for the models placed within the wind tunnel in figure 30 below
additional observations were produced. Similar to the orgive and cylinder wind tunnel
observations, the smoke is hard to accurately observe due to the reflexions off the wind
tunnel test section. But one flow characteristic can be seen encircled in red within the tail
wake flow regions. The top image is of the dimpled model and appears to have a wider and
‘thicker’ smoke tail then the smooth model below. This may indicate flow behaviour
influence produced by the dimpled surface in the form of a boundary layer. Similar boundary
layer production over the dimpled model for CFD in figure 28 was not observed during
testing though drag data does agree with the dimpling having an effect to increase overall
total drag.
Figure 30: Wind Tunnel Flow imagery over smooth and dimpled streamline body at 15m/s.
52
Fluid Flow Effects On Objects With A Dimpled Surface
6.3 –Orgive
The orgive was tested under the same conditions as the cylinder and streamline body.
Integration into the CFD program COMSOL proved to be troublesome and slight adjustment
of the models had to be made. The only adjustment was altering the frontal tip geometry.
Instead of a flat tip it was changed to be pointed. This change was made in order to have
correct interaction within the CFD software. This is the only change in geometry from the
CFD models from the wind tunnel models whose geometry stays the same seen in figure 17.
By developing a slightly reduced bluff frontal tip, potential drag forces may be reduced. This
only affects comparison between the CFD and wind tunnel data but not for comparisons of
model types in each experimental process.
The data for the CFD testing for the orgive can be seen below in figure 31. Although the
geometry needed to be slightly altered it was still expected that if any difference in the results
for each model type was evident, then the dimpled orgive may experience lower drag force.
From CFD testing this proved to be true. In all velocity tests the dimpled orgive experienced
slightly reduced drag from that of the smooth orgive. The velocity range indicates Reynolds
values within the turbulent range. This is likely due to the characteristic length being the full
orgive length of 0.17m which is 70.60 % longer then the orgive width and height.
Drag vs. Re # for Smooth and Dimpled Orgive
by CFD Testing
Smooth Orgive
Dimpled Orgive
Drag Force Newtons
0.70000
0.60000
0.50000
0.40000
0.30000
0.20000
0.10000
0.00000
0
100000
200000
300000
400000
500000
600000
Reynolds Number
Figure 31: Drag vs. Re# for smooth and dimpled orgive by CFD testing.
53
Fluid Flow Effects On Objects With A Dimpled Surface
The orgive experienced a 15.95% lower drag force at 5m/s and a smaller difference of 5.14%
at 40m/s. For each velocity in between the percentage differences are diminishing within this
tested range. Therefore as velocity is increased the drag forces on the dimpled orgive
approach those experienced by the smooth surfaced orgive, although it cannot be estimated
what interactions the drag forces for each cylinder have outside of the range of 5m/s to
40m/s.
As it was expected that the orgive may experience reduced drag forces, the reasoning behind
this estimation can be accompanied with COMSOL flow imagery. For the ogives, flow
imagery was produced and can be seen in figures 32 and 33. These images show flow
visualisation over the orgive models at a 5m/s velocity flow. Once again this flow
visualisation is considered an accurate representation for all imagery produced from orgive
CFD testing.
54
Fluid Flow Effects On Objects With A Dimpled Surface
Figure 32: CFD Flow imagery over smooth orgive at 5m/s.
Figure 33: CFD Flow imagery over dimpled orgive at 5m/s.
The orgive for both models has a flat rear section that has a 90 degree angle change from its
cylindrical section. As the change is so abrupt the geometry was considered bluff with a
smooth front section (the cone). It was expected to be influenced by both firction and
pressure drag components more then the other two geoemtries studied due to its length and
closed end. The length was expected to experience a greater friction drag but due to the
55
Fluid Flow Effects On Objects With A Dimpled Surface
effected boundary layer the wake region may be reduced. From figures 32 and 33 there are
two characteristic flow observations.
The first is seen on the dimpled orgive where the drimpled surface effects the fluid flow. A
thin boundary layer is produced here which doesnt exist on the smooth orgive. This boundary
layer expereinces a lower velocity as the kenetic fluid energy of the main flow is converted to
shear stresses in the form of friction drag. As the fluid velocity is lowered it has a greater
tendancy to change direction. The abrupt surface change at the rear section of the dimpled
orgive creates a lower pressure zone which pulls fluid flowing past inwards. As the boundary
layer fluid passes the orgive end, it is pulled inwards to the low pressure zone. This is the
second observation. As this occurs constantly the rear low pressure area of the dimpled
orgive experiences higher pressures then the smooth orgive due to the slower moving
boundary layer. This can be seen as a higher velocity flow shown as a lighter blue around
2m/s then for the smooth orgive which shows flow velocities around 1m/s and lower. This
effectively careates a smaller pressure drag on the dimpled orgive.
Both orgives are influenced by friction and pressure drag but the dimpled model appears to
have a smaller pressure drag and increased friction drag. The resulting friction drag does not
exceed the overall pressure drag reduction produced by the smaller presure differential across
the dimpled orgive.
Wind tunnel tests were also conducted to observe drag and flow charateristics on the dimpled
and smooth orgive. The results for these tests can be seen in figure 34 below.
56
Fluid Flow Effects On Objects With A Dimpled Surface
Drag vs. Re # for Smooth and Dimpled Orgive
by Wind Tunnel Testing
Smooth Orgive
Dimpled Orgive
Poly. (Smooth Orgive)
Poly. (Dimpled Orgive)
0.80000
Drag Force Newtons
0.70000
0.60000
0.50000
0.40000
0.30000
0.20000
0.10000
0.00000
-0.10000 0
50000
100000 150000 200000 250000 300000 350000 400000 450000
Reynolds Number
Figure 34: Drag vs. Re# for smooth and dimpled orgive by wind tunnel testing.
The results for the wind tunnel tests show a different set of data for the dimpled orgive. For
velocity values 20 to 35m/s the dimpled orgive experiences greater drag forces. The
percentage increases for 20, 25, 30 and 35 are 14.01%, 20.27%, 9.69% and 2.29%
respectively. From observing these percentages it appears the dimpled drag forces are
reducing compared to the smooth orgive. For all other velocities the dimpled orgive
experiences smaller drag forces then the smooth model. From additional testing results, the
dimpled orgive only experienced greater drag forces at 20 and 25m/s but by much greater
percentage of 98.31% and 23.17%. From the secondary data it appears there are inaccuracies
within the wind tunnel data.
The innacuracy is likely to be from the connecting strut for the orgive models. This strut was
designed to connect to the rear surface of each orgive model. Unfortunately as the rear
section appears to produce smaller pressure drag forces as seen in the CFD flow imigery
(figures 32 and 33), the strut has potentially caused increased drag forces. The strut can be
seen in firgure 35 below attached to the rear smooth orgive. The strut is extended out from
the surface to connect to the load cell arm. The design of this strut effects the flow at the rear
surface by causing an extended geometry from the orgive models. Although both models
utilised this strut the boundary layer effects produced from the dimpled model have possibly
been altered from those seen in the CFD images. This is most likely a drag increasing
component which altered results during testing.
57
Fluid Flow Effects On Objects With A Dimpled Surface
Figure 35: Orgive Model Strut used during wind tunnel testing.
It can be seen here the strut extents around 30mm from the rear of the orgive. The load cell
arm attaches to the two holes on the extended fin in the left hand picture and the strut is
attached to the rear of the orgive through the two holes on the right hand picture.
In figure 36 for flow test visualisation the braket for the model holder can be seen at the rear
of the orgive models to the right of each picture. Due to the colour of the ABS polomer used
for construction of the orgive, indetification of the ‘white’ smoke is harder to make out.
During testing it was difficult to determine the expected flow effects talked about earlier
including the smaller wake and boundary layer production over the dimpled orgive. Another
factor impeding the visual results in figure 36 is the reflective test chamber walls. This caused
a large amount of reflection due to sunlight entering the experimental laboratory. For these
reasons a correct anlysis for the orgive cannot be made for the visual imagery produced from
the wind tunnel tests. During the testing ten second videos captured the smoke flow over the
orgive at 15m/s but from reveiwing the footage no discenible flow characteristics could be
made. Further testing with isolation from reflections would be neccesary in order to produce
a productive visualisation analysis.
58
Fluid Flow Effects On Objects With A Dimpled Surface
Figure 36: Wind Tunnel Flow imagery over smooth and dimpled orgive at 15m/s.
59
Fluid Flow Effects On Objects With A Dimpled Surface
6.4 –Drag Coefficients
Another form of drag performance data is the drag coefficient. This is a value directly related
to drag force and Reynolds number used to graph an object’s drag performance in a fluid
medium at differing velocities. The drag coefficients for all tests were determined using
equation two and graphed against Reynolds numbers calculated.
Figure 37 shows an
example for drag coefficient vs. Re for a smooth surfaced sphere and cylinder. The data
shows performance characteristics for each geometry and the flow types from laminar (0 to
103 Re#), to transitional (103 to 5x105 Re#) and finally turbulent (Re#>5x105) . The following
graphs produced help to show possible fluid flow behaviour for the CFD and wind tunnel
tests for each geometry.
Figure 37: Drag Coefficient vs. Reynolds Number for Smooth Sphere and Cylinder. (Munson et al. 2009)
60
Fluid Flow Effects On Objects With A Dimpled Surface
Cylinder
For the cylinder the drag coefficient from CFD and wind tunnel test was graphed and can be
seen in Figure 38 and 39. For the cylinder a comparison for the graphs produced can be made
against the graph in Figure 37.
Cd vs. Re # for Smooth and Dimpled Cylinder
by CFD Testing
Smooth Cylinder
Dimpled Cylinder
4.00000
Drag Coefficent Cd
3.50000
3.00000
2.50000
2.00000
1.50000
1.00000
0.50000
0.00000
0
20000
40000
60000
80000
100000
120000
140000
160000
Reynolds Number
Figure 38: Drag Coefficient vs. Reynolds Number for Smooth and Dimpled Cylinder, CFD Data.
Cd vs. Re # for Smooth and Dimpled Cylinder
by Wind Tunnel Testing
Smooth Cylinder
Dimpled Cylinder
1.4
Drag Coefficient Cd
1.2
1
0.8
0.6
0.4
0.2
0
0
20000
40000
60000
80000
100000
120000
140000
Reynolds Number
Figure 39: Drag Coefficient vs. Reynolds Number for Smooth and Dimpled Cylinder, Wind Tunnel Data.
61
Fluid Flow Effects On Objects With A Dimpled Surface
It was previously stated that turbulent condition start around 105 Reynolds number, from the
figure 38 and 39 at this point starting at 10000 Re# there appears to be no significant change
in Cd (Drag Coefficient) over the following velocity changes. Figure 38 does show similar
results as seen in Figure 37 for laminar to transitional flow types from 0 to 4x104 and 4x104 to
1.6x105. These results are comparable to the published results by Munson et al. 2009.
For the graph in figure 39 the results show similar properties to those seen in the turbulent
range in figure 37 with an ascending transition for Cd values. This happens across the entire
range of results with some settling near 105. It may be considered from these observations
that the values determined in the CFD testing fit the curve for the cylinder in figure 37. It
may be also considered that the results for the wind tunnel tests show a turbulent flow type
produced over the cylinder. While figures 21 and 24 show similar drag data it cannot be
confirmed the state of the flow type was the same without a larger range of testing velocities
within the wind tunnel.
62
Fluid Flow Effects On Objects With A Dimpled Surface
Streamline Body
For the streamline body the following figures 40 and 41 show the drag coefficient data vs.
Reynolds number for the velocity range tested with both CFD and wind tunnel.
Cd vs. Re # for Smooth and Dimpled Streamline
Body by CFD Testing
Smooth Streamline Body
Dimpled Streamline Body
0.00230
Drag Coefficient Cd
0.00225
0.00220
0.00215
0.00210
0.00205
0.00200
0.00195
0.00190
0
50000 100000 150000 200000 250000 300000 350000 400000 450000 500000
Reynolds Number
Figure 40: Drag Coefficient vs. Reynolds Number for Smooth and Dimpled Streamline Body, CFD Data.
Cd vs. Re # for Smooth and Dimpled Streamline
Body by Wind Tunnel Testing
Smooth Streamline Body
Dimpled Streamline Body
0.004
Drag Coefficient Cd
0.0035
0.003
0.0025
0.002
0.0015
0.001
0.0005
0
0
50000
100000
150000
200000
250000
300000
350000
400000
Reynolds Number
Figure 41: Drag Coefficient vs. Reynolds Number for Smooth and Dimpled Streamline Body, Wind Tunnel Data.
63
Fluid Flow Effects On Objects With A Dimpled Surface
The first observation from these two graphs is the path of the dimpled Cd values in figure 40
and both data sets for smooth and dimpled models in figure 41. It was know from
observations of the CFD imagery that the dimpled model developed a turbulent boundary
layer. The comparison of the Cd data sets in figure 40 shows there is a clear difference for the
dimpled model with higher Cd values of the Re# range. Knowing the turbulent effects the
dimpled model produced and looking at the data set in figure 41, a turbulent flow pattern
emerges. If the dimpled data for CFD tests shows turbulent effects and increased drag then by
comparison with wind tunnel data there appears to be turbulence present for both smooth and
dimpled models. Looking at figures 26 and 29 for drag data there is an apparent increase in
drag forces at all velocity points for the wind tunnel data compared to CFD. This along with
the Cd data graphs shows there is potentially an influence of turbulent flow within the wind
tunnel test chamber.
Data produced for Cd values still showed the increase of drag force performance for the
dimpled model in CFD and wind tunnel tests. With further velocity tests it would be possible
to determine the initiation points of all three flow types from laminar to transitional and
turbulent, but from the data range tested for in this thesis a confirmation for these point
cannot be suitably made.
64
Fluid Flow Effects On Objects With A Dimpled Surface
Orgive
The following figures 42 and 43 show the Drag coefficient data produced from orgive testing
vs. Reynolds numbers.
Cd vs. Re # for Smooth and Dimpled Orgive by
CFD Testing
Smooth Orgive
Dimpled Orgive
0.00400
Drag Coefficient Cd
0.00350
0.00300
0.00250
0.00200
0.00150
0.00100
0.00050
0.00000
0
100000
200000
300000
400000
500000
600000
Reynolds Number
Figure 42: Drag Coefficient vs. Reynolds Number for Smooth and Dimpled Orgive, CFD Data.
Cd vs. Re # for Smooth and Dimpled Orgive by
Wind Tunnel Testing
Drag Coefficient Cd
Smooth Orgive
Dimpled Orgive
0.005
0.0045
0.004
0.0035
0.003
0.0025
0.002
0.0015
0.001
0.0005
0
0
50000
100000 150000 200000 250000 300000 350000 400000 450000
Reynolds Number
Figure 43: Drag Coefficient vs. Reynolds Number for Smooth and Dimpled Orgive, Wind Tunnel Data.
65
Fluid Flow Effects On Objects With A Dimpled Surface
Ogive data appears to produce similar results as the streamline body results where there
appears to be increased turbulence for the wind tunnel data. Figures 31 and 34 show the
majority of drag forces for the dimpled model are lower than those experienced by the
smooth orgive model. In figure 42 the Cd values for the dimpled model appear to follow a
similar pattern to both data sets in figure 43. As it is know from observation of CFD imagery
the dimpled model experienced a slightly more energetic surface interaction and developed a
thin turbulent boundary layer. As the results for Cd values for CFD data represent the
presence of an increased turbulent flow the data from the wind tunnel test appear to
experience the same influence. Both graphs it can be seen that these variations occur at
around 105 Reynolds Number. This is around the predicted point of turbulent initiation.
Although the wind tunnel data shows higher drag results which is potentially due to slightly
increased turbulent flow as seen in other Cd data plots, the potential initiation point for
turbulent flow is within a close range to the Cd data in the CFD plot. Further testing over a
wider and denser velocity range would be additional proof of this observation.
66
Fluid Flow Effects On Objects With A Dimpled Surface
6.5 –Errors
Throughout the experimental procedures, all potential variables were identified and
controlled to provide data with the smallest possible error. Variables for both testing
procedures were identified based on environmental conditions of the testing mediums. CFD
testing and wind tunnel testing had differing potentials for inaccurate data production. In
section 5.0 these testing procedures were designed with intention of providing accurate
experimental practises. The following is a short discussion on potentially unforseen variables
that may have caused error within data produced from both experimentation processes.
For the Computational Fluid Dynamics testing, environmental flow conditions were taken
into account before experimentation began. These included fluid density for the main fluid
medium of atmospheric air at sea level, fluid viscosity and flow type physics. Additional pre
testing was produced to identify accurate meshing densities. The errors potentially existent
within the official testing lay mainly with meshing densities and accurate convergence within
the flow simulations. In CFD experimentation, converged tests can sometimes include
unreasonable oscillations within flows leading to unrealistic results. While this influence was
accounted for during the process of comparing mesh density tests with theoretical spherical
analysis to a satisfactory accuracy. There is not 100% certainty that inaccuracies within
testing of the thesis geometries do not exist. For this reason wind tunnel test were also
conducted.
Since the CFD testing was produced in an environment with limited potential variables it was
understood the wind tunnel ‘real world’ testing would be susceptible to a greater number of
potential errors. Errors for wind tunnel tests taken into account included, inaccurate model
construction, incorrect fan frequency to wind speed relationship, additional turbulence in
testing chamber, inaccurate drag force results, incorrect model set up, additional drag from
model brackets and human errors. The aim was to take into account largely manipulating
variables such as those stated here and eliminate them by correct experimentation procedures.
Results do show what is believed to be errors existing with some data collected. An example
is the drag results produced for the orgive testing. In this case it was believed to have been
the model holding rear bracket witch potentially disrupted important wake conditions and
may also have offset the orgive from the direction of fluid flow.
67
Fluid Flow Effects On Objects With A Dimpled Surface
For each model, re-testing produced drag forces with minimal variations of original data.
Therefore testing was regarded as accurate for the conditions set. Re-calibration of the drag
load cell was conducted on several occasions to ensure the load setup was accurate. It was
also understood wind tunnel tests would experience additional drag forces due to the model
holding load cell arm and exposed connecting nut and threaded rods. As comparison was
mainly with smooth and dimpled models for each testing process and less with a comparison
between the two processes the additional drag forces were considered acceptable as both
models would experience the same amount of additional drag.
Human error was also considered for data collection from wind tunnel tests. Collection of all
data was done by one person to prevent biased data reading as drag results fluctuated. Correct
reading of these fluctuations was important to gather accurate data.
Along with reduced errors, final analysis processes and observations would have benefitted
from additional data. It was intended to produce surface pressure distributions for each model
and testing procedure but due to unforseen errors with software interaction with CREO
Parametric and COMSOL CFD additional pressure distributions were not able to be
produced. However, it is understood with the production of surface pressure distributions,
analysis of drag force components would have been supported but not necessarily changed.
During analysis care was taking in identifying potential pressure differentials across each
model surface from data and imagery produced.
Overall the aim was to produce data with the highest accuracy. Although testing was done
thoroughly, some errors were not accounted for until an analysis of results identified
inaccuracies within the data collected. It is believed data produced holds a high enough level
of accuracy to make various observations from the testing of the dimpled surface applications
on the geometries studied.
68
Fluid Flow Effects On Objects With A Dimpled Surface
7.0 –Thesis Conclusion
The purpose of this thesis was to observe drag and fluid flow effects produced by the
application of a dimpled surface on differing geometrical shapes. Testing using
Computational Fluid Dynamics software and Wind Tunnel Experimentation produced data
showing the effects of the dimpling application. Three geometries were tested to observe
different drag component influences on the overall drag forces experienced by the tested
geometries. It was seen that the application of dimples on a cylinder lowered drag forces over
a range of 5 to 40m/s primarily due to the reduction of pressure drag compared to the drag
forces experienced by a smooth cylinder with the same measurements. The outcome for the
dimpled orgive was the same from CFD results with some drag forces exceeding those
experienced by the smooth orgive model seen during wind tunnel tests. While the ogive
experienced an apparent increase in friction drag, the pressure drag component had the largest
influence with overall drag reduction compared to the smooth model. The streamline body
geometry had the opposite effects with an increase in the drag forces experienced over the
velocity testing range for the dimpled model. This was comparable in ways to a flat plate as
the streamline body had a larger influence by friction drag then pressure drag due to its
increased surface area parallel to flow compared to the perpendicular cross section. The
streamline body was not considered a bluff geometry unlike the cylinder and orgive therefore
the increased drag force due to an increased friction drag was an understandable outcome.
In summation the designed dimpling pattern geometry effectively reduced drag forces on the
dimpled cylinder compared to the smooth model. A majority reduction of drag forces over
the range of velocity tests was experienced by the dimpled orgive compared to its smooth
counterpart. And finally the dimpled streamline body experienced an increase in drag force
for all flow velocities applied compared to the smooth surfaced streamline body.
The thesis successfully produced observable data and the aim was reached through the
gathering of data from the various experimentation and results analysis.
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Fluid Flow Effects On Objects With A Dimpled Surface
8.0 -Future Work
Additional study and research may be produced in the future within the fluid physics field
regarding the impact of dimpled surfaces on varying geometries. The following is a brief list
of future research and work intended to be produced from the outcomes of this thesis.
 Varying the Dimple Geometry. As the thesis provided results for one set of dimple
sizes for each of the three geometries further research into the effects of changing
dimple size characteristic can be made. This may include altering dimple depths,
dimple radiuses and altering the relationship with the larger geometry.
 Experimenting With Different Patterns. The thesis was limited to the study of an
aligned dimpled array for each geometry. Testing with different dimpling patterns
may produce much different outcomes for drag forces and fluid performance. With
the addition of different dimple sizes an almost infinite set of dimple surface patterns
can be produced.
 Study Using Different Geometries. The study can increase to include additional
geometrical shapes. These may include replication of vehicle bodies for studying
effects of dimples on real world applications. Geometry sizes can increase and
account for very large objects with dimpled applications, the same can be done with
reduced geometrical sizes.
 Applying Dimpled Surface At Different Areas. The three geometries studied had
nearly an entire coverage of dimpled surface areas. Further testing can investigate
positions of dimpled areas at different locations across the surfaces of the testing
geometries. Further anaylsis can be a combination of the other points stated here.
As there is potential for an infinite study field with the investigation of dimpled surfaces,
there lies a feasible influence with real world applications.
70
Fluid Flow Effects On Objects With A Dimpled Surface
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Wiley, R.R. Donnelly, Jefferson City, 2009.
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Fluid Flow Effects On Objects With A Dimpled Surface
Appendix A
Cylinder Testing Data
Appendix A
Table A.1 Drag and Cd Values for Smooth Cylinder, CFD
Flow Velocity m/s
Reynolds Number Simulated Drag Newtons
5
18574.61735
0.24939
10
37149.23469
0.35930
15
55723.85204
0.56052
20
74298.46939
0.99607
25
92873.08673
1.55591
30
111447.7041
2.24004
35
130022.3214
3.04844
40
148596.9388
3.98111
Table A.2 Drag and Cd Values for Dimpled Cylinder, CFD
Drag Coefficient Cd
0.09013
0.03246
0.02251
0.02250
0.02249
0.02249
0.02248
0.02248
Flow Velocity m/s
Reynolds Number Simulated Drag Newtons
5
18574.61735
0.02731
10
37149.23469
0.10818
15
55723.85204
0.24249
20
74298.46939
0.43010
25
92873.08673
0.67097
30
111447.7041
0.96511
35
130022.3214
1.31239
40
148596.9388
1.71275
Table A.3 Drag and Cd Values for Smooth Cylinder, Wind Tunnel
Drag Coefficient Cd
0.00987
0.00977
0.00974
0.00972
0.00970
0.00969
0.00968
0.00967
Flow Velocity m/s
Reynolds Number Drag Newtons
5
14983.9933
0.01100
10
29967.9867
0.18300
15
44951.9800
0.46700
20
59935.9733
0.84600
25
74919.9666
1.38100
30
89903.9600
1.97600
35
104887.953
2.57200
38
119871.947
3.15200
Table A.4 Drag and Cd Values for Dimpled Cylinder, Wind Tunnel
Drag Coefficient Cd
0.004376551
0.018202473
0.020644942
0.021037284
0.021978242
0.021838546
0.020884023
0.019595011
Flow Velocity m/s
5
10
15
20
25
30
35
38
Drag Coefficient Cd
0.001989341
0.002188275
0.013571728
0.016660733
0.018890785
0.019749738
0.019950251
0.018631424
Reynolds Number
14983.9933
29967.9867
44951.9800
59935.9733
74919.9666
89903.9600
104887.953
119871.947
Drag Newtons
0.00500
0.02200
0.30700
0.67000
1.18700
1.78700
2.45700
2.99700
73
Fluid Flow Effects On Objects With A Dimpled Surface
Orgive Testing Data
Appendix A
Table A.5 Drag and Cd Values for SmoothOrgive, CFD
Flow Velocity m/s
5
10
15
20
25
30
35
40
Reynolds Number
63153.69898
126307.3980
189461.0969
252614.7959
315768.4949
378922.1939
442075.8929
505229.5918
Simulated Drag Newtons
0.00965
0.03837
0.08615
0.15298
0.23884
0.34373
0.46766
0.61060
Drag Coefficient Cd
0.00349
0.00347
0.00346
0.00346
0.00345
0.00345
0.00345
0.00345
Table A.6 Drag and Cd Values for Dimpled Orgive, CFD
Flow Velocity m/s
5
10
15
20
25
30
35
40
Reynolds Number
63153.69898
126307.3980
189461.0969
252614.7959
315768.4949
378922.1939
442075.8929
505229.5918
Simulated Drag Newtons
0.00811
0.02640
0.07215
0.13750
0.21677
0.31539
0.43931
0.57918
Drag Coefficient Cd
0.00293
0.00239
0.00290
0.00311
0.00313
0.00317
0.00324
0.00327
Table A.7 Drag and Cd Values for Smooth Orgive, Wind Tunnel
Flow Velocity m/s
5
10
15
20
25
30
35
38
Reynolds Number
50945.5773
101891.155
152836.732
203782.309
254727.887
305673.464
356619.041
407564.619
Drag Newtons
0.01200
0.02500
0.07600
0.13500
0.23600
0.38200
0.55400
0.74100
Drag Coefficient Cd
0.004774419
0.002486677
0.003359776
0.003357013
0.003755876
0.004221824
0.004498347
0.004606568
Table A.8 Drag and Cd Values for Dimpled Orgive, Wind Tunnel
Flow Velocity m/s
5
10
15
20
25
30
35
38
Reynolds Number
50945.5773
101891.155
152836.732
203782.309
254727.887
305673.464
356619.041
407564.619
Drag Newtons
0.00900
0.01600
0.07100
0.15700
0.29600
0.42300
0.56700
0.73000
Drag Coefficient Cd
0.003580814
0.001591473
0.003138738
0.003904082
0.004710760
0.004674952
0.004603904
0.004538185
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Fluid Flow Effects On Objects With A Dimpled Surface
Streamline Body Testing Data
Appendix A
Table A.9 Drag and Cd Values for Smooth Streamline Body, CFD
Flow Velocity m/s
5
10
15
20
25
30
35
40
Reynolds Number
55723.85204
111447.7041
167171.5561
222895.4082
278619.2602
334343.1122
390066.9643
445790.8163
Simulated Drag Newtons
0.00539
0.02141
0.04800
0.08518
0.13292
0.19123
0.26010
0.33953
Drag Coefficient Cd
0.00193
0.00193
0.00193
0.00192
0.00192
0.00192
0.00192
0.00192
Table A.10 Drag and Cd Values for Dimpled Streamline, CFD
Flow Velocity m/s
5
10
15
20
25
30
35
40
Reynolds Number
55723.85204
111447.7041
167171.5561
222895.4082
278619.2602
334343.1122
390066.9643
445790.8163
Simulated Drag Newtons
0.00325
0.02187
0.05251
0.08909
0.14130
0.22137
0.30391
0.40032
Drag Coefficient Cd
0.00117
0.00198
0.00211
0.00201
0.00204
0.00222
0.00224
0.00226
Table A.11 Drag and Cd Values for Smoot Streamline Body, Wind Tunnel
Flow Velocity m/s
5
10
15
20
25
30
35
38
Reynolds Number
44951.97998
89903.95997
134855.9400
179807.9199
224759.8799
269711.8799
314663.8599
359615.8399
Drag Newtons
0.00160
0.02420
0.05320
0.10520
0.17520
0.25820
0.35320
0.47020
Drag Coefficient Cd
0.000636589
0.002407103
0.002351843
0.002615984
0.002788261
0.002853600
0.002867899
0.002923088
Table A.12 Drag and Cd Values for Dimple Streamline Body, Wind Tunnel
Flow Velocity m/s
5
10
15
20
25
30
35
38
Reynolds Number
44951.97998
89903.95997
134855.9400
179807.9199
224759.8799
269711.8799
314663.8599
359615.8399
Drag Newtons
0.00300
0.03200
0.08500
0.11000
0.15300
0.22600
0.36300
0.49700
Drag Coefficient Cd
0.001193605
0.003182946
0.003757645
0.002735344
0.002434954
0.002497728
0.002947473
0.003089696
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Fluid Flow Effects On Objects With A Dimpled Surface
Appendix B
Creo Parametric Models: Cylinder
Appendix B
Figure A.1: Smooth Cylinder.
Figure A.2: Dimpled Cylinder.
76
Fluid Flow Effects On Objects With A Dimpled Surface
Creo Parametric Models: Streamline Body
Appendix B
Figure A.3: Smooth Streamline Body.
Figure A.3: Dimpled Streamline Body.
77
Fluid Flow Effects On Objects With A Dimpled Surface
Creo Parametric Models: Orgive
Appendix B
Figure A.4: Smooth Orgive.
Figure A.5: Dimpled Orgive.
78
Fluid Flow Effects On Objects With A Dimpled Surface