Development of a method of CFD analysis for optimization of a bicycle frame and forks for drag reduction.

Development of a method of CFDanalysis for optimization of abicycle frame and forks for dragreduction, with special mention to

UCI time trial technical regulations.

ByCraig McLennaghan

This thesis is submitted in partial fulfilmentfor the

B.Eng in Motorsport Design Engineeringunder the auspices of the University of The

West of Scotland

Advisor : David Kennedy

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May 2015

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DECLARATION

I Craig McLennaghan B00219249

hereby declare that the project entitled

Development of a method of CFD analysis for optimization of abicycle frame and forks for drag reduction, with specialmention to UCI time trial competition regulations.

Submitted by me in partial fulfilment for the B.Eng MotorsportDesign engineering is my own work and I have not contravenedUniversity regulations in submitting this project. Inparticular, I am aware of the University regulations onplagiarism, cheating and collusion, and am aware of thepotential consequences of any breach of regulations in thisregard.

Dated: 18/05/2015

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AbstractComputational Fluid Dynamics (CFD) has been developed andimplemented across a wide variety of engineering applicationsto investigate drag force reduction across a wide variety ofshapes and geometries. Thanks to the exponential developmentthrough the digital era, CFD in the 21st century finds itselfat the forefront of engineering analysis and design.

This report details the undertaking of a project developing amethod of Computational Fluid Dynamics (CFD) for analysing andoptimizing bicycle aerodynamics for the frame and forkcomponents to reduce drag. Literature readings suggest thatthis particular methodology of testing has never beenundertaken for a full-scale bicycle model before, and thisreport aims to develop a CFD method, which can be implementedwithin the cycling industry to provide full scale, fullbicycle airflow model using a basic CFD package and a desktopcomputer.

To further relate this particular piece of research to thecycling industry, this research will use the developed methodof CFD to optimize a bicycles frame and forks to internationalcompetition guidelines provided by the Union CyclisteInternationale (UCI).

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Acknowledgements

Thanks to Dave Kennedy and James Findlay for their advice bothfor the research undertaken and the writing of this report.

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ContentsAbstract.....................................................2Acknowledgements.............................................3Introduction.................................................6Bicycle optimization for drag reduction.....................6Computational Fluid dynamics Brief History..................6CFD for bicycle design......................................7

Literature Review............................................8Resistive Forces............................................8Drag optimisation...........................................8Drag reduction theory.......................................9Method of Analysis..........................................9Verifying CFD method........................................9

Experimental Research.......................................10Experimental Procedure.....................................10Model creation...........................................10ANSYS Set-up.............................................11

Basic frame and fork model analysis........................17Frame design.............................................17Importation, meshing and Fluent set-up...................18Experimentation and graphical/numerical results..........19Visual results...........................................21

Second frame...............................................26Theory for 2nd frame design from 1st frame results.........26Importation, meshing and Fluent set-up...................28Experimentation and graphical/numerical results..........29Visual Results...........................................31

Third frame creation.......................................37Applying experimental findings to the 3rd frame creation. .38Alterations made to model which lack experimental justification..........46

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Importation, Mesh and Fluent set-up........................47Experimentation and graphical/numerical results............48

Visual results...............................................49Further optimization of 3rd frame model....................54

Model creation..............................................55Experimental set up.........................................57Importation, Mesh and Fluent setup.........................57Experimentation and visual/numerical analysis..............57

Visual Results...............................................58Discussion of results from all 4 experiments................64Comparison between 1st and 2nd model........................64

Numerical Results............................................64Visual Results...............................................66

Comparison between 2nd and 3rd model experimental results. . .74Numerical Results............................................74Visual results...............................................76

Comparison between 3rd and 4th models regarding downtubealteration.................................................85

Numerical Results............................................85Visual results...............................................87

Verification of drag results through literature.............94Experimental set-up........................................95Experimental results.......................................96Numerical Results........................................96Visual Results...........................................97

Discussion of results in relation to literature findings...98Final Discussion............................................99Conclusion.................................................101References.................................................102Bibliography...............................................104

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1.0 Introduction 1.1 Bicycle optimization for drag reductionAs drag force for time trial speeds is the greatest singlefactor which determines the resistive force of a rider in atime trial (and hence greater wattage expenditure and moretime to complete the given competition), this area of bicyclephysics experiences a large proportion of research andinvestment within both the professional cycling world, and theindustry itself. A look at the history of time trial cyclingfurther suggests aerodynamics is a major influence in time

trial bicycle design. Examplessuch as Graeme Obrees’ ‘Oldfaithful’ Figure 1 and Lotus’108 Figure 2 to name but twofamous examples of a combinationof reducing Frontal area A andDrag Coefficient Cdfor thebicycle and rider combination,so much so that both of these

bikeswhere to be

banned by the UCI (governing body ofinternational cycling) shortly after competing and winning invarious competitions.

1.2 Computational Fluiddynamics Brief History

Over the last 2 decades,Computational Fluid Dynamics(CFD) has thoroughly established itself within the science andengineering industry as a tool for understanding fluidmechanics. Though the mathematical conception of theprinciples of CFD began around the 1920’s (Hunt, 1998), it was

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Figure 1, Graeme Obrees 'Old Faithful',

Source; www.4cdesign.co.uk

Figure 2, Lotus 108,

Source; www..lotusesprititworld.co.uk

only in the late 50’s and early 60’s that two-dimensional flowcharacteristics where to be defined mathematically for avariety of flows mainly to encompass drag forces occurring onbodies (Hess & Smith, 1967) (Ruppert & Saaris, 1972). By 1967these principles where to be further developed by researchersat Douglas Aircraft to model three dimensional flow andfollowing their work in this field, development ofmathematical models mainly for use in aeronautical/aerospacewere derived by a vast array of American aeronauticaldevelopers such as NASA, Boeing and Lockheed to name but afew. Outside of the nautical/aerospace industry, CFD has beenused with great effect within the automotive industry; inparticular, for vehicle body design and optimization for bothdrag and lift parameters.

1.3 CFD for bicycle designWithin the cycling industry, CFD has established itself

as an industry standard for time trial frame design andfeatures heavily in the design process within the majorbicycle manufacturing companies across the world (BoardmanBikes , 2014) (Godo, 2010) (Cervelo, 2013). Whilst a largeproportion of research has been aimed at the larger proportionof drag accumulation (the rider), there are still of courselarge reductions in drag to be made through design andoptimization of the bicycle itself. This is most obvious inobserving the most recent breed of time trial bicycles beingproduced by companies at the forefront of time trial bicyclemanufacture. Frame and fork combinations such as the PinarelloBolide ( Figure 3), Cervelos’ P5 and the Specialized Shiv( Figure 4) are all examples of bicycles that feature a CFDoptimized design being used at the World Championship /Olympic level of competition. It would be also appropriate tonote that during the design process of both the Shiv and theBolide that Aerodynamicists from Jaguar (for Pinarello) andMclaren (for Specialized) where involved heavily within theoptimization process, in Pinarellos case a 15% reduction in

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drag was achieved from their previous top end time trial frameand fork combination.

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Figure 3, Pinarello Dogma,

Source; www.pinarello.com

Figure 4, Specialized Shiv,

Source;www.roadbikeaction.com

2.0 Literature Review2.1 Resistive Forces As professional cycling moved into an era where science andengineering found its place within the sport, one such areathat was greatly considered a demeaning factor in an athlete’sperformance was the resistive forces acting against a ridersenergy input as a bicycle moves through air. The two maincomponents of resistive forces established acting upon a riderand bicycle where the rolling resistance Frolling given as:

FRolling=CrW

Where the rolling resistance factor Cr is given with W theweight of the bicycle and rider acting upon the two wheels,this was established at time trial speeds (40kph)to be in theregion of 10-20% (Pivit, 1998) (Schwalbe, 2010) of overalllosses. The larger component of resistive force experienced for anyroad cyclist and in particular, a time trial cyclist isaerodynamic drag the forces occurring as the body of the riderand the bicycle interact with the air in which the rider andbicycle are travelling through. This force is described as:

:FDrag=12ρv2CdA

Within this equation, the main components that can effectivelybe altered for time trial bicycles are Cd , the coefficient ofdrag given as a dimensionless quantity to describe the bicycleand riders’ drag resistance as it moves through thesurrounding air and A the frontal area of the bicycle which isin opposition to the direction of travel. This drag force isgiven to be around 80-90% of the resistive force experiencedby a time trial cyclist (Boardman Bikes , 2014) (Cervelo,2013). Of this total drag force, approximately 30-40% of thisis created by the bicycle itself, with the rest beingattributed to the riders body (Chowdry, Alam, & Mainwaring,2011)

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2.2 Drag optimisationFor time trial riding aerodynamic efficiency is vital in thedesign of the bicycle for performance as this is the mostdominant force of resistance in the riders’ forward motion.90% of the total resistance experienced by a cyclist at racingspeeds (±50 km/h in time trials) is caused by aerodynamicdrag, which is mainly related to the position of the cycliston the bicycle (Defraeye et al 2011) and out of the totalaerodynamic resistance, the bicycle accounts approximately 33%of the total aerodynamic resistance (Chowdhury et al 2011).This is furthered by literature suggesting that anaerodynamically shaped frame was found to provide a saving of1 minute 17 seconds over a 40km time trial stage for an elitecyclist (A.E Jeukendreup, 2001).

2.3 Drag reduction theory Reducing drag across a body for low subsonic fluid speedsmanifests itself through the control of a number of keyparameters. This mainly resides in the for an object as theshape, size , inclination to flow and velocity of the objectrelative to the airflow (NASA, 2015) (Cervelo, 2013)(Henderson, 1966). For this particular research at low fluidspeeds, the most dominant form of drag likely to occur atthese lower speeds is parasitic drag, this presides in twoforms; pressure drag and skin friction drag, both of whichrequire to be limited to reduce the overall drag coefficientof a body (Dean & Bhushan, 2010) (Lovell, 2000).

One particular area of drag reduction across a body isreduction in frontal area of the body. Literature ofrelatively comparable subsonic industries to cycling(Illumin , 2015) (Washburn, 2010) (Cervelo, 2013) (Henderson,1966), suggests that frontal area has a significant effect onthe amount of drag force that will be present throughparasitic drag across the bicycle body.

By improving the airflow separation conditions main componentsof the bicycle this too should lead to a reduction in drag.Various studies (Washburn, 2010) (Rohatgi, 2012) (Cervelo,2013) (Dean & Bhushan, 2010) (Henderson, 1966) indicate that

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by including ‘teardrop’ shaped elements on the downstreamsections of a body, this should prevent turbulence beingcreated across airflow after being disturbed by that bodymoving through the air.

2.4 Method of Analysis In determining the appropriate method of analysis, it isimportant to consider the method of analysis which is to beused through ANSYS Fluent. For this particular application, k-epsilon method was sought to be used as this has proven itselfin industry across a number of studies (CFD Online , 2011)(Keating, 2011) (Lanfrit, 2005).

The usability of this particular method, in particular therealizable method of k-epsilon has been furthered investigatedby studies (Davis, Rinehimer, & Uddin, 2012) (Cable, 2009)(Sagol, Reggio, & Ilinca, 2012) further providing evidencethat this method of analysis would be most suitable for theparticular application and also provides relevance to anindustry recognised method and set-up.

2.5 Verifying CFD method In verifying the CFD method, a number of studies have beenundertaken to verify that this particular analysis is ofrelevance to established and verified drag coefficients. Fordefining the coefficient of drag for a cylinder several CFDstudies (Mallick & Kumar, 2014) (Lavicka & Matas, 2012) havedetermined this value for a cylinder to be between 0.38 and0.7 dependant on various factors ( angle of cylinder toairflow , Strouhal number of the shape and the Reynoldsclassification of the airflow).

This is further backed up by findings undertaken physicallythrough wind tunnel and other means in several studies towhich these CFD values have been verified. From these studies(Roshko, 1960) (Anthoine, Olivari, & Portugaels, 2009)(Devenport, 2007), drag coefficient is found to be in theregion between 0.3 and 0.5 for a cylinder vertical to airflowfor these particular experiments. This approximation isfurther confirmed by literature (Sadraey, 2009) (EngineeringToolbox ) (Weisstein, 2007) suggesting that the drag

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coefficient of a cylinder is within this region determinedboth by CFD and Wind tunnel testing.

For drag coefficient of a cube, this has been defined throughliterature to be 1.05 (Sadraey, 2009) (Bengston, 2010).Studies involving various methods of CFD provide a wide rangeof drag coefficients ranging from 0.83 to 1.2 dependant on theairflow classification and the placement and geometry of thecube itself (Abohela, Hamza, & Dudek, 2012) (Lim, Thomas, &Castro, 2008) (Scanlon).

3.0 Experimental Research3.1 Experimental Procedure 3.1.1 Model creationThree frame and fork models where created separately using PTCCreo CAD software and assembled together with a front and rearwheel of standard dimensions along with a simple crank-set,pedals and saddle configuration. These where deemed to beeither close enough to the frame to create changes in airflowaround the frame and forks, or to be a factor in effecting thepath of flow acting on the frontal faces of individual piecesof the frame tubing, hence these components were added in thehope of creating a more accurate and relevant estimation offlow behaviour around the frame and forks.

Within PTC creo, an assembly was created involving the frame,fork, saddle, crank-set, legs and front and rear wheels. Thisallowed an IGES file to be created of the entire bicycleassembly for analysis in the ANSYS software. An IGES file waschosen as this provides good translation of data between Creowhich can be easily utilised by ANSYS within the geometrymodelling system.

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Four crank angles where established for each model to allowfor averaging to take place across each of the three models,averaging was used here to improve the quality of results, asan animated mesh for the cranks rotating within the analysiswhere not possible with the given computational resources.Within each model, the handlebars were removed as they weredeemed less relevant than the other components considered inanalysing the flow behaviour. This was considered in part dueto the fact that the handlebars lie above and out of the wayof the majority of the flow path over the frame and forks, butalso partly due to the cell count in meshing for ANSYS studentbeing limited to half a million cells.

3.1.2 ANSYS Set-upFor this experiment, a ‘workbench’ was used to contain all 4models of each of the 3 bicycles, the 4 models beingalterations made to the leg positions. ANSYS workbench allowssimple transfer of data between several computationalexperiments easily, in practice this allows for a duplicationof one experiment where all of the models with differentframe/fork and leg configurations can be imported. Thispractice means only 1 fluid analysis system requires to be

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Figure 5, detailing the assembly of the basic frame within Creo, Source; PTC Creo

set-up instead of 18, saving a considerable amount of time inexperiment creation.

A fluid analysis system was used predetermined by ANSYS to useits Fluent CFD operation. This allows for the geometry of thebicycle and the surrounding air domain to be modelledprimarily in a geometry modeller, which can then betransferred directly into a meshing, CFD and results steps.

3.1.2.a Geometry creationWithin the geometry editor of ANSYS, the IGES model from CreoParametric was imported using the ‘import geometry’ tool.After insertion of geometry, face groupings where createdusing the ‘merge’ function of ANSYS to allow for faces ofsimilar geometrical alignment to be grouped together, thisallows for ease in future steps. After merging all parts ofthe bicycle, a freeze function is used to ensure the bicycleremains unaltered through the set-up of the enclosure.

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Figure 6, ANSYS workbench allowed for all 4 experiments to be stored in one directory, Source; Capture from ANSYS experimental modelling

An enclosure was created to represent the air domain aroundthe body of the bicycle; this uses the ‘enclosure’ function ofANSYS to define this parameter. The dimensions of theenclosure are found are given as a box of width of 2m, lengthof 4m, height of 2m. This enclosure size was proportioned toensure that the enclosure would not inflict on themathematical meshing used to model the air, which forms its

mesh due to geometrical parameters. This air domain was alsorequired to give clearance to the bicycle to ensure that theairstream would unaltered by airflow behaving with wall-shearbehaviour, whereby airflow velocity is slowed due to theeffect of boundary layers upon that surface, this is displayedin Figure 7 detailing this phenomenon.

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Figure 7, wall shear for a fluid, Source;www.efm.leeds.ac.uk

In modelling the fluid flow within ANSYS Fluent, the method ofanalysis involves modelling only the air behaviour around thebicycle and not the bicycle body itself. This requires thebicycle body to be removed from the enclosure leaving behindthe void in which the bicycle once took, the void is defined

as a solid void within the geometrical editor, whilst theenclosure is defined as a fluid with the software’s predefinedcharacteristics of air. A Boolean function is used to subtractthe bicycle from the air domain to leave Figure 8.

3.1.2.b Meshing Due to the size of test specimen being used within theanalysis, economy of the cell count was crucial to ensureefficiency within the analysis. Within ANSYS student the cellcount cannot exceed more than 500,000 cells, whilst this leadsto a reduction in accuracy of modelling the airflow and hencereduces the accuracy of the results, a good mesh can still becreated to give adequate results.

Models where imported into ANSYS as IGES files to simulate thegeometry of the bicycle. From creating the geometry of thebicycle, meshing was then carried out on the airflow domainaround the bicycle model to be processed by Fluent. Due to thesimplicity of the model legs used in the analysis, the meshsolver was unable to process the mesh model sufficiently forthe first few attempts at meshing; this was due in part to

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Figure 8, geometry of the air domain used, Source; ANSYS Geometry set-up

poor model refinement through Creo, irregularities beingtranslated from Creo into the IGES file and also the geometryprocessing system within ANSYS.

The solution to anomalies created during meshing was to refinethe CAD model within PTC Creo to remove small surface areaswithin the legs of the model to eliminate the need for thosesurfaces to be processed by the meshing solver in ANSYS.

For meshing, 3 classifications of mesh refinement can be usedwithin ANSYS. These are Coarse, Medium and Fine. Theclassifications are used to describe the sizing of elementsused to mathematically calculate the characteristics of fluidaround the bicycle body in terms of air flow within thedomain. There are several factors which define a mesh as beingany of the 3 classifications, predominantly there are about 6parameters which can be altered to decrease/increase thenumber of elements, the accuracy of the elements and thebehaviour of the elements with regards to proximity.

These are define in ANSYS as:

Minimum Cell Face Size Maximum Cell Face Size Maximum Tetrahedral size Growth rate Smoothing Inflation

A fine mesh refinement yields the highest cell count with thehighest degree of accuracy and detail within smaller closed insections of the air domain such as frame surfaces atintersecting sections of tubing, this is due to a smallminimum cell sizing of 1 mm with a maximum size of with 8mm.On the contrary, a coarse mesh refinement uses a minimum cellsizing of 10 mm with a maximum size of 300 mm. Cell sizing isa key factor in determining the resolution of calculatingairflow as this determines the amount of averaging that cantake place, ANSYS uses an automatic system to determine whichareas of the airflow require more cells than others ( such asaround the frame , in particular at edges/corners ).

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For this particular mesh, the predefined setting of ‘coarse’was used to create the meshing, this coarse meshing is moreacceptable for larger scale models as generally flow areas arelarger in concentration ( less tight corners or small edges).However, this coarse setting still will yield poorer resultsfor airflow particularly in close in regions around the bodyof the bicycle, where wall-shear is expected along withseveral effects of air viscosity though the velocity.

Table 1

Mesh sizing setting Defined as; Smoothing HighInitial size speed Active assemblyTransition SlowCurvature normal angle 18°Proximity Accuracy 0.5Number of Cells across gap 5Minimum Face Size 1mmMaximum Face Size 300 mmMaximum Tetrahedral Size 600mmGrowth 1.2

The above settings in table 1 define the mesh parameters formodelling the airflow, due to the size of model being used itwas necessary to allow a large maximum face and tetrahedralsize for the whole domain in less relevant areas of the fluidflow. A slow transition setting is again used here to furtherensure that mesh count around the most relevant areas of air

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domain are kept at an acceptable size to improve detail inimportant sections whilst inflation settings are defined as‘smooth transition’ to ensure that the amount of calculationsis gradually decreased as proximity of the cells to thebicycle body increases. Figure 9 details an example mesh,given for the first bicycle model for a 3d detail of the meshthat was created.

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3.1.2.c Fluent analysis set-upThrough the workbench again, the ANSYS system of analysisallows for the mesh and geometry to feed into the analysis forCFD. The system used for this particular research was Fluent,this was used as Fluent is one system of CFD that is commonwithin industry and has been established to provide goodresults (Keating, 2011) (Lanfrit, 2005)

For this particular piece of research, a commonly occurringmathematical model to be used by the FLUENT system was to beimplemented that can be used on most desktop computers. Thisimproves the usability, accessibility and cost cutting of thisparticular method of analysis whilst also being established asan industry recognised method of analysis commonplace withinthe world of fluid dynamics today.

In modelling the airflow around the bicycle, a viscous modelwas required as turbulent flow was to be expected to occur onsome areas of the model. A k-epsilon Reynolds Averaged Navier-Stokes Linear eddy viscosity, two equation model was used.This model is most appropriate for this research field, whilstalso being suitable to be used on a typical desktop computer.This is thanks to the use of transported variables to defineproperties of the flow whereby initially energy is definedwith the turbulent flow of the system and is characterized asthe turbulent kinetic energy (k) defined for the realizablemodel below in figure 9:

Figure 10, turbulent kinetic energy transport equation, Source; www.cfd-online.com

Secondly, turbulent dissipation is determined as the secondtransported variable in the equation for dissipation toprovide the two equation model detailed in figure 9:

Figure 11,, turbulent energy dissipation equation used in combination with theturbulent kinetic energy equation, Source;www.cfd-online.com

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Realizable k-epsilon is utilised here as this is a more up todate and relevant version of the k-epsilon model. In usingrealizable models the accuracy of the flow characteristics aresignificantly more accurate in prediction for phenomenon suchas separation and vortices which were expected to occur on thebackside of the models, reduction in separation is also a keyfactor which needs to be addressed for drag reduction and iscrucial for improving airflow across the bicycle body.Therefore, the use of a realizable model is justified for suchresearch (Lanfrit, 2005)

This model allows for suitable modelling of the factorsaffecting the turbulent kinetic energy of the fluid flow. Thismathematical model allows for a free-shear flow to be modelledfor this application whilst providing good results despiteonly requiring a limited amount of conditions to be specifiedfor the flow. The limited number of conditions required ismost suitable for this application as only a basic model wasto be created and simulated with no prior determined flowcharacteristics other than the air velocity.

In reducing the amount of time required to calculate results,a Pressure-Based coupled solver was implemented for thissystem of calculation. This uses 100 first order upwindcalculations of the K-epsilon method to initialize thecalculations for the solution, once this has been calculated,the pressure-based derivations for characterizing the airflowcan then be set to second order upwind and a further 500iterations undertaken, 500 steps where chosen as this would bemore than enough to ensure that the coefficient of drag valuecalculated by the system had converged. This methodology hasbeen implemented in a number of industrial applications and isnow at the forefront of improving solution finalization.(Keating, 2011).

Conditions for airflow within the domain was defined bydefining the boundary conditions for specific zones. Thevelocity inlet (at the front of the air domain) definesairflow which will enter the front air domain and pass through

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the geometry of the airflow. This velocity inlet is specifiedto have a velocity of 16.67ms, this velocity is specified asthis is a typically occurring air velocity in a time trial andwere the most energy should be saved through aerodynamicoptimization.

Turbulence was specified for this airflow as 3% to replicatetypical air behaviour for a relatively calm day, whilstairflow is difficult to model for real world atmosphericconditions, an approximation of using 3% is used in the hopeof providing more relevancy to the findings in comparison toreal world conditions. (ANSYS, 2011)

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3.2 Basic frame and fork model analysis 3.2.1 Frame design The first frame and fork model (Basic Frame and ForksModel) , (figure 11), was of a basic bicycle frame ofdimensions specific to a typical 54cm road bike frame andforks. This model was created to primarily investigate thefull flow across a frame and forks and to address theparticular areas of interest for optimizing the bicycle forfrontal area and coefficient of drag. A standard frame ofknown size was also used to add a degree of legitimacy and

relevancy to the design by considering both structuralintegrity and handling of the bicycle. Figure 12 details thePTC Creo CAD model created of the standard frame and forks tobe analysed.

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3.2.2 Importation, meshing and Fluent set-upImportation was carried out through ANSYS as an IGES file,this particular model was received well by the geometrymodeller within ANSYS and was processed after smallrefinements for the model using PTC Creo to remove anyintersecting surfaces that would create anomalies within themesh system of ANSYS.

A mesh was created for airflow around all 4 of the modelscreated using the basic frame and forks assembly. The mesh wasthen imported into fluent where parameters where specified for

elements of the mesh, figure 13 details an example mesh forthe basic frame and fork assembly complete with legs.

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Figure 13, meshing conditions created in ANSYS Fluent, Source; Capture from experimentation

3.2.3 Experimentation and graphical/numerical resultsFluent calculated the airflow behaviour and characteristicsusing the described method within the experimental set-up,case checking verified that the mathematical procedure to becarried out was legitimate and accurate. Once the 600iterations of calculation had been carried out, various

effects could be modelled across the frame and airflowgenerated by the Fluent solver. Figure 14 details thecoefficient of drag convergence of this basic model.

Figure 14 details the value of drag coefficient which thesolver has calculated against the iterations of calculationundertaken, as can be seen for this particular result, and forthe other results included within this report, convergence wasobserved across the result for drag coefficient. Convergenceis required to ensure that an accurate and relevant quantityis defined for the air flow behaviour around the model

From this calculated coefficient of drag, ANSYS could definethe drag force occurring on this model for the relativeairspeed. Table 2 defines the results for each of the dragforces for the basic frame with respect to the 4 leg

28Figure 14, Coefficient of drag convergence history, Source; Experimental Capture

positions. These are taken using the print function within theFLUENT system text box detailed in figure 15.

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Table 2

The results for drag force conformed to expectations that ahigher drag force would be seen in positions with the pedalslevel ( pedal back, pedal forward) than that of the legs andcranks in a more upright position relative to airflow ( pedaldown, pedal up). Results are also consistent in quantity andscale across all 4 results, leading to suggest a goodconsistent and relevant result has been established for thismodel in quantifying drag.

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Figure 15, raw data taken from ANSYS Fluent text output

Basic Frame and Forks(16.67 ms)

Leg and Crank position Drag Force (N)Right pedal up 19.112Right pedal back 17.327Right pedal forward 17.571Right pedal down 19.314Average 18.331

3.2.4 Visual resultsThrough ANSYS, results can be refined and displayed using apost processing system. Example results for the Basic Frameand Forks model are detailed below for Velocity magnitude,dynamic pressure, static pressure, turbulent kinetic energyfor both the bicycle model surfaces and the airflow.

3.2.4.a Velocity MagnitudeVelocity magnitude is given from a front view of the bicycleand a side view using a plane through the centreline of thebicycle gives vector velocity on the frontal plane with figure16 and 17 giving velocity magnitude using a vector and contourdisplay.

Here, fluid dynamic theory for velocity magnitude has been

upheld.As expected,the velocity of the air travelling across the frame reducessignificantly downstream any geometry, which would act to slowthe airflow down. This reduction in velocity indicates anincrease in the dynamic pressure and hence decrease in thestatic pressure through Bernoulli’s equation and the equationfor dynamic pressure below;

Dynamicpressure=ρv2

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Figure 16, Velocity magnitude frontal plane, Source; ANSYS Experimental Results

Figure 17, Velocity magnitude side plane, Source; ANSYS Experimental Results

3.2.4.b Static pressure The reduction in velocity magnitude downstream coupled withthe increase in velocity magnitude upstream of the tubingsections will create a higher static pressure in front and alower static pressure rear of each piece of tubing that isnear not parallel to the airstream flow.

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Figure 18, surface static pressure frontal plane, Source; ANSYS Experimental Results

Figure 19, Surface static pressure side plane, Source; ANSYS experimental Results

Figure 20, surface static pressure rear plane. Source; ANSYS Experimental Results

Figure 21, static pressure on the air domain at centreline. Source; ANSYS Experimental results

3.2.4.c Dynamic pressure Dynamic pressure details the velocity at the surface of eachbicycle, detailed in figure 22 and 23.

Here, dynamic pressure is given and conforms to expectationsfor this particular analysis. Resolution for this particularanalysis yields a poorly distributed colour spectrum, this islikely due to a few cells containing anomalies which havecaused for a very high pressure (2630 pascals) to be created

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Figure 22, dynamic pressure at the surface, Source; ANSYS experimental results

Figure 23, Dynamic pressure at the rear surfaces, Source; ANSYS Experimental results.

for a few cells. This increase in the maximum pressure willhave a negative effect on adequately displaying dynamicpressure for this particular set of results.

3.2.4.d Turbulent kinetic energy Turbulent kinetic energy front and rear are detailed in figure24 and 25 respectively. Turbulent kinetic energy is used todescribe the kineticenergy per unit mass ofturbulent airflow givenby the following equation (CFD Online , 2011):

Turbulent energy is given at the surface of the bike (figure24) and for the centreline plane to represent turbulent energyof the surrounding air stream (figure25).

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Figure 24, turbulence kinetic energy at the frame surface, Source; ANSYS Experimental results

Figure 25, air domain at centreline turbulence kinetic energy dissipation, Source; ANSYS Experimentalresults

3.3 Second frame 3.3.1Theory for 2nd frame design from 1st frame resultsThe second frame and fork package (Profile Reduction Model)was created with the same tubing construction as the BasicFrame and Forks Model with the exception of the tubethickness. From the CFD results from the first frame analysis,it was made evident that particularly against the front of thehead tube, a large accumulation of high static pressure iscreated. This high pressure area is due to the acceleration ofthe airflow in changing its path around each tubing sectionand this area is directly influenced by the volume of airwhich strikes the frontal area of each tubing section. Byreducing A, the frontal area of tubing, the coefficient ofdrag and hence drag force can be reduced through the equation:

FDrag=12ρv2CdA

Thicker tubing sections are also likely to aid flow separationon the backside of each piece of tubing, separation in airflowoccurs due to an adverse pressure gradient occurring due to anincrease in the static pressure of the air as it strikes thefront of a piece of tubing and accelerates around it. Forthicker sections of tubing this is larger in comparison to

thinner tubing sections due to the increased magnitude of anadverse pressure gradient with thicker tubing as a larger voidis created in the airflow. Figure 26 details flow separation

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for a cross section of a piece of cylindrical tubing (Scott,2005).

The separated flow area detailed in figure 26 downstream ofthe cylinder can be reduced by reducing the diameter of eachpiece of cylinder tubing hence reducing the amount ofacceleration the airflow will experience, hence reducing thestatic pressure gradient and turbulent kinetic energydissipation.

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Figure 26, flow separation across a sphere or cylinder,Source; www.aerospaceweb.org

By using this identical configuration of bicycle assembly withthe same geometry specifications except tube thickness, thismodel aims to investigate the reduction in drag expected tooccur through the reduction of area, A, the frontal projectionof the bicycle frame and forks, whilst allowing a relationship

to be drawn between drag and tube thickness irrespective ofother aerodynamic features to be included in the third frame.Figure 27 gives an image taken from PTC Creo of the assemblyCAD model..

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Figure 27, Creo assembly of profile reduced frame and fork, Source; Capture from PTC Creo

3.3.2 Importation, meshing and Fluent set-upImportation was done through the same method as the basicframe and forks model. In creating the mesh, some anomaliesoccurred in attempting to mesh some areas of the frame whichhad very small edges or corners which had to be modelled,similar to the first model created, this was addressed byrounding and chamfering some of the tubing sections to improvethe surface quality in Creo, to be taken into ANSYS by an IGESfile.

Figure 28 details the mesh within the Fluent analysis, createdusing an identical method as in the first model to ensure thatresults would remain consistent and controlled.

38

Figure 28, mesh with fluent constraints, Source; Fluent experimentation

3.3.3 Experimentation and graphical/numerical resultsThrough the same procedure as the first experiment , detailedon page 18, fluent analysis was carried out. An example of thescaled residuals and coefficient of drag for this profilereduction model is given below in figure 29 and 30respectively:

Here in Figure 29 and Figure 30, it can be observed that the

CFD methodhascalculated and converged upon a value of drag coefficient forthis particular study by using the scaled residuals tocalculate the various parameters associated with dragcoefficient.

39

Figure 29, Scaled residuals given from Fluent experimentation, Source; ANSYS Fluent experimental work

Figure 30,, Cd given from Fluent experimentation, Source; ANSYS Fluent experimental work

Taken through the establishing of Cd, values for drag force oneach of the 4 models can be deduced through the plot screenFigure 31 and defined in Table 3 for each crank and legposition.

Table 3

For the drag results calculated, it can be observed again thatdrag theory has been upheld within the numbers generated, boththe upwards (larger area) models experienced higher levels ofdrag across them. Convergence in calculation was also observedthrough all the results and is evident in figure 30 detailedthe coefficient of drag calculations and the levelling of theresult.

40

Figure 31, text output from FLUENT detailing calculated forces, Source; Fluent experimentation

Profile Reduction(16.67 ms)

Leg and Crankposition

Drag Force(N)

Right pedal up 17.25721Right pedal back 15.431Right pedal forward 15.535Right pedal down 17.614Average 16.45925

3.3.4 Visual ResultsThrough solution calculation, ANSYS enables results to bedisplayed visually in terms of characteristics of the airflowaround the frame and attached to the frame surface.

3.3.4.a Velocity MagnitudeVelocity magnitude was again plotted using a centreline planeto improve ease of visualization along with being plotted withreference to the frontal section of the bicycle. Figure 33provides details of the side velocity magnitude relative tothe centre point, whilst figure 32 gives velocity vectorsacross the entire test area from the frontal plane.

3.3.4.b Static PressureStaticpressure

is given for front, side and rear surface profiles of the bikefrom figure 34 to 36 respectively. A side plane is used todisplay static pressure in the surrounding air domain infigure 37.

41

Figure 32, frontal velocity magnitude vectors, Source; ANSYS Experimental Results

Figure 33, side profile of velocity magnitude vectors; Source; ANSYS Experimental Results

Figure 34, frontal static surface pressure, Source; ANSYS Experimental Results

3.3.4.cDynamic PressureDynamic pressure on the surfaces of the frame are given for afront (figure 38), side (figure 39) and rear (figure 40)profile of the frame. This gives indication of low pressureareas occurring on the surrounding air of the frame, whereblue areas represent areas of low dynamic pressure likely dueto flow separation of air around the frame geometry.

42

Figure 35. Side surface static pressure, Source; ANSYS Experimental Results

Figure 36, rear static pressure surface, Source; Experimental results ANSYS

Figure 37, Air domain static pressure, Source’ Experimental results ANSYS

High dynamic pressure is observed around areas of the model

wherefluid velocity is at its highest, this is due to accelerationaround features of geometry particularly the legs. Consideringthe frame itself, a high dynamic pressure is observed aroundthe sides of the head tube and also is observed to an extentaround the seat tube, whilst dynamic pressure does not createproblems around the sides of the tubing, it is the reductionin dynamic pressure downstream which creates issues. Thislowered dynamic pressure is indicative of flow separationcaused by an adverse pressure gradient as the angle betweenairflow and the tubing profile is too great.

43

Figure 38, front dynamic surface pressure, Source; ANSYS Experimental Results

Figure 39, side dynamic surface pressure, Source; ANSYS Experimental Results

Figure 40, rear surface static pressure, Source; ANSYS Experimental Results

3.3.4.d Turbulent Kinetic energyTurbulent kinetic energy is given at the surface of the frame(figure 41) and at a centreline of the frame for the

surrounding airstream (figure 42).

Turbulent kinetic energy across this model surface indicatesin particular a region between the wheel and seat tube sectionwhere a large accumulation of turbulent energy is beingconverted from airflow into a detrimental effect of the framesaerodynamic performance. Furhtermore when considering figure42, a significant portion of turbulent energy is also beingcreated downstream of the head tube.

44

Figure 31, side profile of turbulent kinetic energy at the frame surface, Source; ANSYS Experimental ResultsFigure 42, turbulent kinetic energy for the air domain at a centreline point, Source; ANSYS Experimental Results

3.4 Third frame creation The following section of this report will aim to optimize theairflow with consideration of the 2nd model analysis to justifygeometry alterations. This frame is to be designed with aspecification abiding by the UCI Technical Rules forcompetition time trial bicycles , with particular reference tothe 3:1 tube thickness rule.

The 3:1 thickness rule provides restraints to particularsections of tubing on the bicycle by limiting each length of

tubing so that it does not exceed 3 times the width of thetubing, The limitations present on the frame and forks isdetailed in figure 43.

45Figure 43, areas of the frame which are required to abide by 3:1 thickness ruling Source; www.uci.ch

3.4.1 Applying experimental findings to the 3rd frame creation From the 2nd frame and fork model created, it is evident thatan improved fluid flow quality and hence reduced coefficientof drag can be induced across this frame by geometricalalteration. From analysis of the and 2nd frames, there wouldappear to be three main profile geometries for the frame whichcan be altered in to give the greatest reduction incoefficient of drag along with improving the fork by bettershaping its geometry for airflow optimisation. In regardingthe frame there are 3 main areas targeted to improve theairflow, these are;

Head tube Downtube Seat tube

Alongside altering the profile of these three tubes, furtherwork will be undertaken in an attempt to reduce separation ofminor areas regarded to be of lesser significance than thethree main problem areas, however these areas will still beoptimized in aid of further improving airflow. These points ofalteration are;

Sea tstays Seat post Fork Connections between tubing sections ( in particular

between the top tube-head tube connection, and the toptube-seat tube connection)

3.4.1.a Optimizing airflowConsidering airflow through visual results, this section ofthe report aims to justify geometry changes made to thebicycle frame in PTC Creo, to then be modelled in ANSYS withthe hope of reducing the Drag force occurring.

Optimizing airflow is carried out mainly through reducing theReynolds number of the airflow. Reynolds number is acharacteristic for flow classification, which bears nodimension and is used in fluid mechanics to aid in describingthe airflow quality parameter. Reynolds number has a directinfluence in the drag force present through the coefficient of

46

drag, this provides the coefficient of drag as a function ofthe Reynolds number, with the Reynolds number constantlychanging across a body with respect to displacement or time.

Head tubeConsidering in particular velocity magnitude results fromexperiment 2 (figure 33), it is evident that separation isoccurring once airflow has passed the thickest point oftubing, through an adverse pressure gradient, separation iscreated and causes drag to be present. Along with creating lowpressure downstream of the head tube, this tubing profile alsocreates turbulent air which will then carry itself onwardstowards the seat tube/rear wheel/top tube, creating unwanteddisturbance in the flow field of all 3 of sections. Figure 44details a focused velocity magnitude study upon the head tubeof the 2nd frame:

As

can beseen

highlighted by the blue vectors, a substantial reduction invelocity is observed. When closely considering the directionof the airflow, reversal is observed around this section,which is significant in indicating that separation, andturbulent airflow has been caused. This is also evident byconsidering figure 41 and figure 42 detailing the turbulent

47

Figure 44, focused velocity vector magnitude across the head tube, Source; ANSYS Experimental Results

kinetic energy that has been increased due to this flowseparation downstream of the head tube.

The solution for improving airflow around the head tube is toincrease the head tube length and taper the head tube,tapering is now common part of road bike design (Cervelo,2013) (Boardman Bikes , 2014) where rules allow and seeks toprevent major flow separation occurring on the backside of thedowntube. This prevention of flow separation provides two keybenefits;

Reduction in low pressure area behind the head tube Reduction in turbulent flow through reducing the Reynolds

number of the flow in this area

The head tube construction is detailed in figure 45 with a

comparison between the 2nd frames head tube and the optimizedhead tube detailed in figure 46 and47.

48

Figure 46, altered head tube configuration for aerodynamic profile, Source;Creo modelling

Figure 45, construction of head tube, Source; Creo Modelling

DowntubeIn considering the focused velocity magnitude vectorvisualization in figure 33 (page 33), a large proportion ofvelocity reduction is also occurring on the downstream sectionof the down tube. This separation is likely to have a largereffect on the magnitude of drag compared to the head tubeseparation observed. This reduction in airflow velocitydownstream of the down tube section has 3 main effects;

Increase in Reynolds number for the airflow at this pointand hence formation of turbulent airflow downstream ofthe downtube

Low pressure area downstream of the downtube Reduction in airflow quality around the rear wheel, the

seat tube, crank and seat stay area. This is addressed using a similar profile method as for thehead tube, by creating a ‘teardrop’ shape around thedownstream edge of the downtube to aid laminar flowmaintenance across this section. Tapering is again used tocreate this profile in the hope of preventing turbulence and a

49

Figure 47, standard profile head tube configuration, Source; Creo Modelling

Figure 47, downtube construction, Source; Creo Modelling

low pressure area behind the downtube section. Figure 47details the construction of the downtube, whilst figure 48details the dimensions of the downtube, which must be of a 3:1length to thickness ratio.

50

Seat tubeIn considering the seat tube, it is also important to considerthe roll that the wheel also plays in the behaviour of theairflow around this particular section. Due to the proximityof the wheel and the seat tube, the effect of turbulence issignificant not just on the seat tube itself, but also on dragforce on the leading surface of the wheel. The effect this hason airflow is evident within the first two bike results, inparticular this is very clear within the second results, alarge portion of decelerated turbulent air is present betweenthe seat tube and the rear wheel, this is detailed in figure49 for a concentrated visualization of velocity magnitude forthe seat tube and rear wheel area.

51

Figure 49, focused velocity vector study for the seat tube, Source; ANSYS ExperimentalResults

As can be observed in figure 49, airflow is made turbulent bythe seat tube section where separation occurs, this turbulentairflow is then channelled through the gap between the seattube and rear wheel, causing an increase in drag between thissection due to an increase in the static pressure on the frontside of the rear wheel, along with a reduction in staticpressure towards the top of the rear wheel and seat tubesection. This is made evident also by the increase in staticpressure ( seen in green) between the wheel and seat tube forstatic pressure taken within the same plane (figure 50),whilst contour representation for velocity magnitude indicatesa reduction in velocity occurring in light blue across theentire seat tube (figure 51).

52

Figure 50, centreline air domain static pressure, Source; ANSYS Experimental Results

Figure 51, centreline air domain for velocity magnitude, Source: ANSYS Experimental Results

Higher static pressure on any frontal area is crucial toreducing the effect of fluid flow upon a body and hence makesthis a crucial area which must be considered within thisoptimization. Furthermore, this area propagates one of thelargest areas of low velocity across the frame itself,irrespective of the main flow separation seen downstream ofthe rear wheel.

One such solution to this problem is a feature found in almostevery time trial design found at the elite level ofcompetition, this is to close over this entire sectiondownstream of the seat tube. This aids to completely removethe void in which airflow would populate after encounteringthe seat tube section, this creates several benefits:

Reduction in Reynolds number, and hence reduction incoefficient of drag for the airflow

Complete removal of the channelled area of airflowbetween the rear wheel and downtube

Complete removal of the high pressure found on theleading edge of the rear wheel

Figure 52 details the construction of the seat tube closed inwith the wheel, it can be noted that the wheel and seat tubein this model have been created as one solid surface. Thisfully enclosed wheel would be deemed by the UCI to be illegaldue to its confliction on rule stipulating that a credit cardmust be able to fit between the frame and wheel. However, thismethod of construction would aid to improve the cell meshingeconomy of the model in ANSYS, where a large proportion ofsmall cells would be required to model such a small section.

53

Whilst accepting that this model simply is a representativemodel for demonstrative purposes and that the precision ofairflow behaviour is not entirely met across this particularsection, it can also be established that this particularaspect of the model will not yield a large effect on eitherthe drag force calculated or the Reynolds flow around thisparticular section as the gap would be small enough to ensurethe majority of air would pass over this section unchanged.

54

ForkAerodynamic profiling was created across the forks, this wasdone by maintaining the thickness of the forks whilst adheringthe length of the fork to the 3:1 rule. Tapering also featureson the downstream section of the fork in an attempt to reducethe Reynolds number of the airflow after it encounters thefork tubing. In the section where the fork and wheel come intothe closest proximity, a geometry altercation has been made inan attempt to prevent a large mass of air being permittedthrough this section of the fork. An alteration is made to thefork detailed in Figure 53 for the profile of the fork withthe aerodynamic tapering.

55

Figure 53, a teardrop shaped profile was created on the fork assembly, Source; Creo Modelling

Bottom BracketA focused velocity magnitude vector study shows that aroundthe area of the bottom bracket and the wheel, a degree of flowseparation is also occurring at this point, figure 54 detailsthis phenomenon occurring across the Bottom bracket section.

This flow reversal observed in figure 54 has effect also uponthe turbulent kinetic energy as observed in figure 41 andfigure 42 (page 35). This is indicative that this is an areacausing a proportion of drag upon the bicycle body and shouldbe addressed to improve the frame optimization. By creating aflange across this section airflow is expected to be keptlower down the Reynolds number scale, by preventing flowreversal and allowing airflow to accelerate easier back to thesurrounding airstream flow. Figure 55 details the flangesection created.

56

Figure 54, flow around the bottom bracket, Source; ANSYS Experimental Results

Figure 55, detailing the flange created to improve flow quality downstream of the BB area, Source; Creo Modelling

3.4.2 Alterations made to model which lack experimental justification Due to the nature of the formatted results using a planethrough the centreline of the bicycle model, certain aspectsof the flow field have not been properly addressed. Inparticular the seat stays do not have a large proportion ofresults that are defined or clear enough to be observed. Thisis due to the thickness of the tubing created on the seatstays which is too small to be able to observe the effectsthat this section creates on the airflow. Furthermore thissection is not considered to be of large significance to frameoptimization in comparison to the previous section parameters.However, to fully optimize the airflow around the frame it isstill of benefit to alter the tubing.

Seat stay One common approach seen within many top time trial bicyclesis to alter the configuration of the seat stay from a typicalarrangement as seen in the first two models created.

This frame aims also to incorporate such an idea, by reducingthe angle of the seat stays to the relative airflow this willallow the drag force present on the seat stays to reduceaccordance with A the frontal area to be somewhat reduced inthe equation:

FDrag=12ρv2CdA

Along with aiming to reduce frontal area of the seat stays,profile alteration is undertaken to prevent a Reynolds numberincrease in airflow which would lead to an increase in dragthrough Cd, the coefficient of drag of the seat stays. By

57

rounding the leading edge of the seat stays coupled withtapering the trailing edge of the seat stays relative to theairflow , this allows the same principles used in forming thedowntube and head tube to be used for the seat stays. Figure56 details the final seat stay configuration within the framedesign whilst Figure 57 details the seat stay alteration interms of angle adjustment.

Chamfering Chamfering was created on a number of front facingintersecting sections to improve the airflow around theseparts and to prevent ‘snag points’ which would increase static

pressure on these surfaces. This was implemented on theconnection between the seat tube and the top tube figure 58

58

Figure 58, chamfering featured between the seattube and downtube sections to improve airflow, Source; Creo Modelling

3.4.3 Importation, Mesh and Fluent set-upAfter an IGES file was created of the 3rd model , it wassubsequently imported within a new fluid analysis geometry toanalyse the frame using ANSYS Fluent. Figure 59 details the

importation of the 3rd bicycle model into ANSYS geometricalfunction.

3.5 Experimentation and graphical/numericalresultsAs with the first two experimental procedures, an identicalset-up was established for the 3rd experimental procedure.ANSYS Fluent ran 600 iterations of calculation ( 100 in firstorder upwind and 500 in 2nd order upwind ) these converged forthe coefficient of drag result (example in figure 60).

59

Figure 59, importation of the fluid and bicycle model mesh in fluent, Source; Fluent experimental setup

Figure 60, converged drag results , Source; ANSYS Fluent experimental output

Numerical values for each of the 4 drag positions are given intable 4 with the average of the 4 experiments taken also inthis table. Figure 61 details an example of the text displaywithin ANSYS proving the drag force in Newtons for the modelbody at 16.67ms

Table 4

60

Figure 61, text output from fluent calculations, Source; Fluent experimentation

Aerodynamic shapedframe and fork (16.67ms)  

Leg and Crank PositionDrag Force(N)

Right pedal up 15.732Right pedal back 14.4419Right pedal forward 14.172Right pedal down 16.042Average 15.096975

Again similar to the previous 2 experiments for the individualmodels, with an increase in area ( for pedal positions up anddown) the drag force increases noticeably verifying thatairflow behaviour has been modelled correctly to an extent inabiding by the drag force equation. In terms of consistency ofresults, all the results are witness to have a difference ofapproximately 0.4 Newtons ( in comparing the right pedalback/right pedal forward and right pedal up/ right pedal downresults) This consistency leads to a rudimentary justificationthat the results appear to be of some relevance andconsistency. A higher result is seen for the right pedal downand right pedal back, likely due to the proximity of the rightleg against the frame for these particular positions.

3.5.1 Visual resultsVisual results are displayed created by the RANS equations todefine characteristics of the airflow and surface pressurewitnessed within the 3rd model design.

3.5.1.a Velocity MagnitudeVelocity magnitude vectors are given across the model at a

centreline plane in figure 62 and for the domain in figure 63.

61

62

Figure 62, centreline velocity magnitude vectors, Source; ANSYS Experimental Results

Figure 63, domain velocity vectors at a frontal plane, Source; ANSYS Experimental Results

3.5.1.b Static pressureStatic pressure is given for the front (figure 64), side(figure 65) and rear (figure 66) for the 3rd model experiments.A plane contoured view of the surrounding air at thecentreline of the bicycle is also given in figure 67.

Here for static pressure at the surface, a significant lack of

low staticpressure accumulation can be observed on the downstream tubeprofiles. This is thanks primarily to the improvement inairflow behaviour across each downstream tube section bypreventing a significant increase in dynamic pressure throughseparation of fluid flow.An accumulation of low pressure is found on the air gapbetween the main tube sections (figure 66) this indicates that

63

Figure 64, front surface static pressure, Source; ANSYS Experimental Results

Figure 65, side profile of surface static pressure, Source; ANSYS Experimental Results.

Figure 66, rear view of surface static pressure, Source;ANSYS Experimental Results

Figure 67, air domain static pressure, Source; ANSYS Experimental Results

some form of turbulent airflow is present here which may yielda negative effect however, due to the proximity of this lowpressure air being away from the downtube and head tubesection, it is likely to have limited effect on the drag forceobserved.

64

3.5.1.c Dynamic PressureDynamic pressure is displayed also for the model on the samebasis as the previous 2 frames, provided are 3 surface contourvisualizations for the front (figure 68), side (figure 69).

65

Figure 68, frontal dynamic surface pressure, Source; ANSYS Experimental Results

Figure 69, side dynamic surface pressure, Source; ANSYS Experimental Results.

3.5.1.d Turbulent kinetic energyTurbulent kinetic energy is a key indicator in the areas inwhich turbulent flow is being created across the bicycle modebody. Figure 70 details surface turbulent kinetic energy with

Figure 71 detailing this turbulent propagation for acentreline in the surrounding air.

66

Figure 70, surface turbulent kinetic energy propagation, Source; ANSYS Experimental Results

4.0 Further optimization of 3rd framemodel From the results obtained for the 3rd frame model, it wasobserved that there was still some degree of alteration thatcould be carried out to further improve the aerodynamicefficiency of the frame.

In observing the static pressure contour graph for the 3rd

model, an accumulation of high static pressure can be observedon the upstream face of the downtube at this on thisparticular plane, indicating that a large reduction invelocity is observed at this point. Figure 72 details thishigh pressure accumulation between the wheel and the downtubesection. (UCI , 2014)

In

aiming to reduce this pressure through air velocitydeceleration, a dual downtube system was sought to improveairflow around this region. This dual down tube complies withUCI regulation in that ruling (UCI , 2014) stipulates that asplit down tube section is permitted. This section of frameaimed to maintain the beneficial long tapered tubing with areduction in frontal area of the tubing.

67

Figure 72, high pressure accumulation between the down tube and wheel. Source; ANSYS Experimental Results

4.1 Model creationThe split in the downtube was created in PTC Creo and isdetailed in Figure 73 and 74, theoretically this would allowair to be channelled through in between the frame sectionsremaining relatively unchanged in terms of its velocity. The

geometry of the down tube alteration was made so that aminimum cell sizing of 10mm would be sufficient and noanomalies would be created across this section when meshingwas undertaken.

This section was created within the aerodynamic frame and wasthen created as an STL file for an assembly featuring only theframe, forks and a set of wheels. Figure 75 details thisassembly within Creo.

68

Figure 73, sketch used for down tube profile, Source; Creo Modelling

Figure 74, down tube detail in Creo, Source; Creo Modelling

A replication of the 3rd model used in analysis was alsocreated with removed legs and crank set (figure 76), this wasused to provide relevancy and a measurable comparison to fully

investigate if drag could be reduced using this method.

Both frames are included in this experiment without legs and acrank set to simplify the meshing and aid in reducing the cellcount across the fluid domain in an attempt to improveresolution across this section. Furthermore it was establishedthat due to the legs and cranks being of a position bothdownstream and at a large enough proximity to the downtube, itwould not be necessary to model those features in theanalysis.

69

Figure 76. 4th model with down tube split, Source; Creo modelling

4.2 Experimental set upIn further analysing this section of frame, an alternatemethod of procedure was created to adequately investigate thenew downtube configuration across a variety of speeds, to aidin justifying this feature within the frame optimization.

4.2.1 Importation, Mesh and Fluent setupThe method of importation and meshing remained identical tothe other models created

Three Fluent solutions where to be obtained for 3 differentinlet velocities. 3 inputs where used for the inlet velocityto measure model the air across each model, this was done toprovide average readings, but also to investigate if thedowntube gap would yield a reduction in drag even at lowerspeeds as this would further justify using this method in timetrial frame construction. The three speeds used where:

10.5ms 12.5ms 16.67ms ( as used and established in previous results)

A speed above 16.67ms could have been used to establish amagnitude of air velocity to which the downtube gap yielded anegative effect (increase in drag), this was not done asspeeds above 16.67ms are not commonly found to occur withintime trials($).

4.2.2 Experimentation and visual/numerical analysisExperimental results where carried out at 3 separate inletvelocities, an example of convergence for the coefficient ofdrag is given in figure 77.

70

71

Figure 77, detailing the coefficient of grad convergence

4.3.3 Visual Results Visual results here are displayed purely for static pressure,dynamic pressure, velocity magnitude and turbulence kineticenergy.

4.3.3.a Static PressureStatic pressure is given for the frame surface and for acentreline plane to establish accumulations of static pressureon and around the frame. Figure 78 gives static pressure for

the surrounding air domain with figure 79 detailing thesurface pressure at a side view of the frame surface.

72

Figure 78, air domain static pressure, Source; ANSYS Exerpimental Setup

73

Figure 79, side static pressure at surface, Source; ANSYS Experimental setup

Considering static pressure across the air domain, it can beobserved an accumulation of higher static pressure isoccurring at the bottom edge of the downtube gap where itconnects to the bottom bracket, this is caused by the abruptwall section that is at 90 degrees to the fluid flow, causinga large amount of deceleration of airflow at this particularpoint. Both figure 78 and 79 lead to suggest that a highstatic pressure is occurring on the seat tube frontal sectiondue to airflow across this area, this will be furtherunderstood when analysing velocity magnitude around thissection.

4.3.3.b Dynamic PressureDynamic pressure indicates the fluid pressure across thesurface of the bicycle, this was done in particular to analysewhether airflow velocity had been reduced or increased acrossthe downtube outer surface in creating a gap. Front, side andrear dynamic surface pressures are displayed for the framewith a downtube gap in figure 80, 81 and 82 respectively.

In

considering inparticular the

downtube section, a noticeably low dynamic pressure can beobserved in figure 82 (rear) within the downtube gap itself.This can be seen to verify expectations that a Venturi effect

74

Figure 80, front surface dynamic pressure, Source; ANSYS Experimental Results

Figure 81, side surface dynamic pressure, Source; ANSYS Experimental Results.

Figure 82, rear surface dynamic pressure, Source; ANSYS Experimental Results

has taken place, where air has been forced through a narrowercross section ( the downtube gap) causing an acceleration inthe fluid which creates a reduction in the dynamic pressure inthe fluid through the equation:

p1−p2=ρ2

(v22−v1

1)

This describes the difference in fluid pressure being directlyinfluenced by the difference in air velocity, for a constantdensity. This reduction in dynamic fluid pressure is somewhatnegative in that this will increase the static pressurethrough this downtube gap section, however an increase influid velocity is likely to be observed to some extent betweenentrance and exit through the downtube gap.

75

4.3.3.c Velocity MagnitudeVelocity magnitude allows conclusions drawn from the staticand dynamic pressure results to be further addressed, alongwith aiding in characterising the airflow in vector form forair across the downtube gap. Figure 83 details a side profileof the air domain and velocity vectors occurring across thecentreline of the frame, figure 84 details a frontal profileof the same centreline plane.

In

figure 83, some detail can be seen upon the air behaviourentering the downtube section, resolution is somewhat limiteddue to the mesh cell sizing within this section along with alack of appropriate accuracy. Regardless of lack ofresolution, airflow can still be observed to followexpectations to an extent in that velocity vectors indicatethat airflow is being sent through this section of tube gap.

On the downstream edge of the downtube, it can be observedthat a relatively good Reynolds classification of laminar flowis still being created on this section, despite the increasedlikelihood of separation and turbulence across the downtubegap. This is most probably prevented due to the acceleratedairflow through this section allowing separated air to

76

Figure 83, side profile of velocity magnitude through the centreline, Source; ANSYS Experimental Results

Figure 84, Front/side mixed view of centreline velocity pathlines, Source; ANSYS Experimental results.

accelerate relative to the airflow stream exiting thedowntube.

77

4.3.3.d Turbulence Kinetic EnergyTurbulence kinetic energy is the final indication to beconsidered for the downtube alteration. Turbulence kineticenergy will aid in addressing expectations in that turbulenceacross the frame should decrease with the addition of thedowntube gap. Figure 84 details this turbulence kinetic energyat the model surface with figure 85 detailing for a centrelineplane.

78

Figure 84, detailing turbulent kinetic energy at the surface of the model, Source; ANSYS Experimental results

Figure 85, turbulent kinetic energy for the air domain at a centreline point, Source; ANSYS Experimental Results

Turbulence is still observed being generated across the sideof the downtube in figure 84 indicating that some degree ofseparation is being induced due to the profile of thedowntube, this could be possibly addressed by reducing theoverall width of the downtube section in a trade off forreducing the length of the downtube profile also. Inconsidering figure 85, turbulent flow is present on thedownstream air from the wheel which appears to then be reducedas it passes the downtube section, this indicates that animproved case of turbulence behaviour can be witnessed, thisis further discussed through the comparison between bothaerodynamic models on page 81-83.

5.0 Discussion of results from all 4experiments5.1 Comparison between 1st and 2nd model In comparing results both visually and numerically between thefirst and second model. It is evident that a difference influid behaviour has been created between the two modelcreations and analysis. A reduction overall in drag waswitnessed on the 2nd frame which is most likely attributed tothe reduction in the frontal area of the model throughreducing tubing profile thicknesses.

5.1.1 Numerical ResultsTable 5 details the difference in numerical results for dragforce between the 1st and 2nd models.

Table 5

 1st model DragForce (N)

2nd model DragForce (N)

Percentagereduction

Right pedal up 19.112 17.257 9.70594391Right pedalback 17.327 15.431 10.94245974Right pedalforward 17.571 15.535 11.58727449Right pedaldown 19.314 17.614 8.801905354Average 18.331 16.45925 10.21084502

79

From table 5, the reduction in drag observed from the visualresults can be quantified. This average drag force can then beused to establish the average coefficient of drag across eachbicycle:

A total average reduction in drag of 10% has been observed inreducing the tube thickness across the 2nd model. This can befurther used to define average wattage for each bicycle over10km at steady state to further aid quantifying the dragreduction. In establishing the wattage difference throughaerodynamic changes, restive forces due to rolling andmechanical effort are to be presumed as constant and thereforecan be removed from the wattage determination:

80

Power=FDrag∗D

t

This equation can be used to find the power for each modelacross a 10km and 40km distance at an average speed.

For the first model, power loss through drag for a 10km timetrial is given

Poweracross10kmtimetrial=203.677Watts

And the second model;

Poweracross10kmtimetrial=182.88Watts

Giving overall an approximate 10.34% reduction in wattageconsumption across a 10km race.

In providing the same wattage expenditure of 200 watts acrossthe time trial, a time reduction can be estimated for theamount of time saved in using the second bicycle:

Timetakenusingfirstmodel=916seconds

Timetakenusingsecondmodel=822seconds

Giving therefore overall a very significant reduction in timetaken.

81

5.1.2 Visual ResultsVisual results between the two frames are compared from thedata given through the experimental set-up previouslydescribed. Key components of drag and air behaviour arecompared for the 1st and 2nd frames to establish and assessairflow behaviour between the 1st and 2nd models.

5.1.2.a Static PressureStatic pressure is given for using two variations of themodels with the right pedal up position for the 1st model(figure 86) and the 2nd model (figure 87). Figure 88 and 89

below provide static pressure through a centreline plane.

82

Figure 86, frontal static pressure for the 1st model, Source; ANSYS Experimental results.

Figure 88, static pressure for the air domain at centreline, Source; ANSYS Experimental Results

Figure 87, frontal surface static pressure for the 2nd model, Source; ANSYS Experimental results.

83

As can be noted in comparing figure 86 to 89, there is asignificant reduction in static pressure in comparing the 2nd

frame models ( figure 87 and 89) to the 1st models (figure 86and 88). This reduction in magnitude of static pressureparticular on the front side of the head tube can beattributed most to the reduction in surface area, whereby lessairflow is being accelerated around this feature to create theincrease in static pressure. A maximum pressure reduction of0.73 Pa is witnessed, this gives a reduction of 4.9% inpressure occurring on this frontal head tube area.

Outside of the frontal area however, an increase in staticpressure accumulation can be seen in areas for the 2nd modelthat are not present in the first. In particular theaccumulation between the wheel and seat post, this increase instatic pressure at this area is unbeneficial as it indicatesthat there is a degree of drag being induced across thissection. This drag creation is likely due to the increasedsize of area behind the seat tube which allows more turbulentair to enter into this area and react with the wheel section.

Downtube pressure on the 2nd model can be observed to berelatively similar, other than at the top of the downtubewhere a reduction in the high pressure area (in orange) can beobserved, again this is down to the reduction in profileallowing airflow to have a smoother less altered path.Relative downtube static pressure was expected to decreaseacross the frame, however it can be observed that a largerrelative static pressure area is observed on the front of thissection, this can be likely attributed to the fact that a moresubstantial reduction in maximum static pressure is witnessedin the head tube, which reduces the colour scale in ANSYS

Overall, between the 1st model and 2nd model a reduction instatic pressure is witnessed across all frontal sections oftubing between both frame and fork experiments. A reduction indrag therefore can be deduced from findings through fluiddynamic theory in that static pressure has aided a reductionin drag across a body through the reduction in frontal area.

84

5.1.2.b Velocity MagnitudeVelocity magnitude is given to aid comparison between thefirst model (figure 90) and the second model (figure 91).Velocity magnitude is a key indicator in air behaviour aroundthe frame and within CFD is one of the greatest assets to beused in establishing and optimizing a body within a dynamicfluid. Although there are multiple areas within this

85

Figure 90, velocity magnitude across the 1st model, Source; ANSYS Experimental results

Figure 91, Velocity magnitude for the 2nd model, Source; ANSYS Experimental Results.

particular fluid flow that should be considered whenaddressing the optimization of the frame in reducing drag,this comparative section aims to focus primarily on the areaswhich would have the greatest effect on the drag across thebody of the frame and fork.

Between figure 90 and figure 91, a noticeable difference invelocity behaviour can observed in several sections for theframe and fork area. Overall a reduction in maximum velocityis witnessed which verifies findings from a reduction instatic pressure through Bernoullis equation for dynamicpressure.

The more important determination in drag reduction across abody however, is the decelerated air flow in a flow streamcaused by the body disrupting airflow and altering the energybalance and pressure balance within the fluid flow. It isevident that a larger accumulation of lower velocity air isobserved across figure 90 in comparison to figure 91. Thisincrease in the amount of vectors which have been reducedsignifies that a greater mass of air has been decelerated fromthe inlet velocity of 16.67ms and has been reduced tosomewhere in the region of around 6ms for both models.

Considering the head tube, a reduction in low velocity air canbe observed in terms of both of the quantity of air that hasbeen slowed and also to what degree the airflow has been made

86Figure 92, focused velocity vectors around the headtube area for the 1st model, Source; ANSYS Experimental results.

turbulent. This is evident in figure 92 and figure 93 showinga focused comparison between airflow on the 1st model and 2nd

models.

Whilst a reduction in velocity takes place across both frames,as is expected to uphold basic fluid dynamic theory, anoticeable effect on airflow behaviour is more apparent inconsidering figure 92 for the 1st model with a thicker headtube profile. Flow reversal can be witnessed in this sectionof the fluid flow for a number of vectors directly behind thesection between the down tube and top tube. This flow reversalis due to the size of area that has an adverse pressuregradient along with the magnitude of that adverse pressuregradient, this causes such a change in pressure that airflowis actually pulled back in towards the frame surface throughthe force created by the low pressure area. In the 2nd frameflow reversal is significantly less apparent when compared tothe 1st frame, this is due to the reduction in area of thesecond frame creating a smaller adverse pressure gradientrelative to the 1st frame section furthermore, a reduction inthe magnitude of the adverse pressure gradient is also likelyto be observed due to the volume of air which has actuallybeen disrupted, again thanks to area reduction.

A focused study across the seat tube section is also includebetween both models in figure 94 and figure 95.

87

Figure 94, velocity vectors around the seattube section for the 1st model, Source; ANSYS Experimental Results

For the 1st model (figure 94) a larger volume of reducedvelocity air can be observed behind the seat tube sectionaround the area above the rear wheel. The effect of this willagain reduce the static pressure at this point due to anincrease in the dynamic pressure through Bernoulli’s equationfor total pressure.

Flow reversal is again witnessed around the bottom bracketarea in both bicycles however, in this case it can be observedthat a larger volume of air has been decelerated around thebottom bracket area in the reduced profile construction. Thisis due to the reduced downtube profile allowing a greateramount of air to enter this section compared to the 1st framemodel, thus the profile reduction frame in fact has somedownfalls in reducing the area of certain sections of frame.

Across the air gap between the seat tube and the rear wheel, alarger volume of air can be observed to have experienced agreater reduction in velocity for the 2nd frame than the 1st

frame. This is due to the increase in the size of the air gapfrom reducing the size of the tubing filling the air gap (theseat tube), this allows air that has become attached from theseat tube to behave in a turbulent manor and reduces theinfluence that the rear wheel has in organising the flow linesof the fluid as seen more commonly in the 1st model. Thisindicates again that whilst there are many benefits toreducing tubing thickness, some negative side effects can bewitnessed through reducing the control of airflow.

5.1.2.c Turbulence Kinetic Energy Comparing turbulent energy between the 1st and 2nd bicyclemodels, a difference in turbulence formation can be found.

88

This is evident in figure 96 and figure 97 detailing turbulentkinetic energy accumulation across the fluid flow for eachmodel configuration. Turbulent kinetic energy is described onpage 14.

Around the middle triangular section of air gap between thetop tube, head tube, down tube and seat tube, a largerpresence of turbulent air can be witnessed for the 1st framemodel in comparison to the 2nd. This verifies findings forvelocity magnitude vectors that eluded to a greater presenceof low velocity, high dynamic pressure turbulent air beingpresent on the 1st frame than the 2nd. A larger presence ofturbulence kinetic energy is also witnessed downstream of theseat tube for the 1st model than the 2nd, again denoting areduced drag force being obtained through the reduction in theseat tubes profile thickness.

Magnitude of turbulence kinetic energy can also be found whencomparing the variable colour contour at the left of eachfigure. For 1st modelled a turbulence kinetic energy maximum of41.4J Kg/1 is witnessed compared to 36.5 J Kg/1 this gives a

89

Figure 97, turbulence kinetic energy for the air domain around the 2nd model. Source; ANSYS Experimental Results

reduction in maximum turbulence kinetic energy of 11.84%whilst comparing the most predominant accumulation of lightblue colour across both fluid domains, a reduction of around11.5% is witnessed.

90

5.2 Comparison between 2nd and 3rd model experimental resultsA comparison can be drawn between the 2nd bicycle model and the3rd bicycle model. This aims to investigate the implementationof aerodynamic profiling across several sections of thebicycle deemed to be key in reducing the resistive effects ofdrag from air passing across the bicycle. As both bicycleshave kept very similar thickness of tubing, effects that areahave on the drag force can be effectively discounted to allowchanges established to be solely attributed to the coefficientof drag of the bicycle model.

5.2.1 Numerical ResultsResults for calculated drag force are displayed across boththe 2nd and 3rd models created in table 6.

Table 6

o2nd model DragForce (N)

3rd model DragForce (N)

Percentagereduction

Right pedal up 17.257 15.732 8.837Right pedalback 15.431 14.442 6.410Right pedalforward 15.535 14.172 8.774Right pedaldown 17.614 16.042 8.925Average 16.459 15.097 8.277

Here it can be noted an overall reduction in drag has beenachieved of 8.277% force reduction through aerodynamicprofiling of the frame and forks. This drag force can then beused to summate the coefficient of drag.

A total average reduction in drag of 10% has been observed inreducing the tube thickness across the 2nd model. This can befurther used to define average wattage for each bicycle over10km at steady state to further aid quantifying the dragreduction.

91

In establishing the wattage difference through aerodynamicchanges, restive forces due to rolling and mechanical effortare to be presumed as constant and therefore can be removedfrom the wattage determination:

Power=FDrag∗D

t

Again quantifying this for a 10km time trial for each model;

For the second model, power loss through drag force;

Poweracross10kmtimetrial=182.88Watts

For the third model, power loss through drag force;

Poweracross10kmtimetrial=167.744Watts

Giving overall an approximate 8.276 % reduction in wattageconsumption across a 10km race.

In providing the same wattage expenditure of 182 watts acrossthe time trial, a time reduction can be estimated for theamount of time saved in using the second bicycle:

Timetakenusingsecondmodel=914.166seconds

Timetakenusingthirdmodel=838seconds

Therefore providing a significant advantage in using the thirdmodel in compared to the second.

92

5.2.2 Visual results Visual results between the two frames are compared from thedata given through the experimental set-up previouslydescribed. Key components of drag and air behaviour arecompared for the 2nd and 3rd frames to establish and assessairflow behaviour between the 2nd and 3rd models.

5.2.2.a Static PressureStatic pressure is given for using two variations of themodels with the right pedal up position for the 2nd model(figure 98) and the 3rd model (figure 99), these figuresprovide information on the static pressure from a side onview. Frontal surface pressure is not considered for thissection of discussion as frontal surface pressure is expectedto be nearly identical between both frames due to no changesmade in frontal area of sections, surface pressure ondownstream sections of tubing is to be considered in figure100 and figure 101, whilst a surface plane for air pressuresurrounding each model is also be considered in figure 102 and103.

93

Figure 98, side surface static pressure on the 2nd model, Source; ANSYS Experimental Results

A larger maximum static pressure can be observed in figure 98compared to figure 99, this is likely caused a section of legacting inconsistently, or that the maximum pressure area infigure 99 around the fork has been reduced due to thealteration in fork profile.

Considering static pressure on the side surfaces of bothmodels enables judgement to be made for the behaviour of theairflow around these surfaces. A noticeable difference inparticular can be made in comparing the relative pressure onthe 2nd model (figure 98) and the 3rd model (figure 99). For the3rd model the side static pressure has been kept higher thanthe 2nd model thanks to an improvement in the airflow thanks toa preservation of energy preventing the air entering aturbulent state.

This improvement in airflow is also evident to an extent onthe downtube, headtube and seat tube post. This increase inside static pressure leads to a presumption that the Reynoldsnumber of air flow around these components has been improved

94

Figure 99, side surface static pressure for the 3rd model, Source; ANSYS Experimental Results

through the aerodynamic changes installed into the 3rd framedetailed on page 37.

More important to relating the static pressure to drag forcebetween these models is to consider the rear static pressureat the surface of both models (figure 100) and (figure 101) ,along with considering the static pressure on the surroundingair (figure 102) and (figure 103).

95

Figure 101, rear surface static pressure for the 2nd model, Source; ANSYS Experimental Results

Figure 102, rear surface static pressure for the 3rd model, Source; ANSYS Experimental Results

Despite a lack of clarity visually in establishing thisparticular result, it is still visible to an extent that anincrease in static pressure on the downstream sections offrame have been achieved on the 3rd frame design. Increase instatic pressure is directly linked to the reduction inturbulent fluid flow through dynamic pressure and Bernoulli’stheory, for the 3rd model a prevention in separation has beenachieved downstream of several tubing sections thanks toaerodynamic profiling significantly reducing the adversepressure gradient that could be observed in the 2nd model. Thisreduction in negative pressure can also be observed for acentreline plane for each model in figure 103 and figure 104.

96

Figure 103, air domain static pressure through centreline, Source; ANSYS Experimental Results

Figure 5Figure 104, air domain static pressure through centreline, Source; ANSYS Experimental Results

In considering the static pressure within the surroundingfluid, it is evident that a larger presence of static pressureof higher magnitude on both the downtube and head tubesections is for the 3rd model in compared to the 2nd. This islikely caused by the alterations made to closing the forksections within the 3rd model compared to the 2nd model. Thiswould not drastically alter the reference area but create alarger volume of air which is having to be redirected aroundthe frame, whilst this has a negative impact upon the frontalstatic pressure, this is beneficial for flow around the entireframe as specified on page 76.

Considering the static pressure downstream of the head tubeand down tube, a smaller accumulation of negative pressure canbe observed across the 3rd model in compared to the 2nd model.This static pressure increase denotes an improvement in theReynolds number classification around this section of bike asthe gradient that reduces static pressure and increase dynamicpressure has been reduced to some effect. This is thanks tothe reduced angle between the air stream and the framegeometry downstream of the down tube and top tube, this allowsair to remain attached to the surface geometry and remain as alaminar flow.

5.2.2.b Velocity MagnitudeVelocity magnitude is given for both the 2nd model (figure 105)and the 3rd model (figure 106) to aid in describing the airflow

97Figure 105, air velocity at centreline for the 2nd model, Source; ANSYS Experimental Results

between both frame configurations. This is taken at acentreline point to assess the flow at this particular region.

Here velocity magnitude relative to the plane is detailed,whilst a relatively similar magnitude of maximum velocity isdetailed between both frames, it is the decelerated vectors(shown in blue) which really represent the energy lost betweenthe air and the bicycle travelling through the air.

Across the 3rd frame, a significant reduction in the volume ofair which has been decelerated can be observed on thedownstream sections, particularly the head tube and downtube.Laminar flow has been effectively maintained for the most partfor this frame, this has been done by preventing separation ofairflow on the backside of these tubes using tapering toremove the low pressure area behind this tubing. Thismaintenance of laminar flow is most evident when observing the

98

Figure 107, focused velocity vectors across the head tube of the 2nd model, Source; ANSYS Experimental Results.

uniform vector path lines created on the backside of thedowntube and head tube merge whilst the area around the seattube and rear wheel, which once hosted a very large proportionof turbulent air, has been completely removed. Thisimprovement is made more apparent by visualizing a focusedstudy on each head tube/down tube connection Figure 107 and108 respectively.

For the 3rd model (figure 108), fluid reversal has beenpractically eliminated for the scale of vectors considered.The area of high dynamic pressure drag inducing air on theback side of each tubing section has been almost completelyremoved, slower air is still observed across this section

99

Figure 109, focused seattube velocity vectors across the 2nd model, Source; ANSYS Experimental Results

Figure 110, velocity vectors across the 3rd model at centreline, Source; ANSYS Experimental Results.

(represented in dark blue) however in the case of the 3rd

model, this air accelerates easily into the air stream onceagain in a laminar fashion hence reducing the amount of energythat is lost from this fluid flow.

Again here a reduction in improvement in air velocitydeceleration is achieved, this is done by removing the adversepressure gradient occurring downstream of the seat tubeentire. This also reduces the channelling effect that the rearwheel creates for airflow moving upwards towards the top ofthe wheel in figure 109, this channelling of air will furtherdisrupt airflow in this region and create an even greateradverse pressure gradient behind this section of frame, butalso the rider of the bicycle.

5.2.2.c Turbulence Kinetic EnergyFigure 111 and 112 gives a planar view along the centrelinefor the 2nd model and the 3rd model respectively.

100

Figure 111, Turbulence Kinetic Energy for the 2nd model air domain, Source; ANSYS Experimental Results

Whilst maximum turbulence kinetic energy is greater on the 3rd

model than the 2nd for this experimental comparison, it is theabundance of energy that is being lost to turbulence in figure112 that is most significant to drag reduction across thebicycle. In figure 112 it is evident that a large proportionof turbulent energy across the frame has been removeddownstream of all of sections of tubing. This signifies adrastic drop in the amount of energy that the fluid hasconverted from velocity into dynamic pressure which hence hasa negative impact on the aerodynamic efficiency of thebicycle. This lack of turbulence indicates a significant lackof flow separation is occurring thanks to the inclusion ofprofiled parts.

5.3 Comparison between 3rd and 4th models fordowntube alteration

This final comparison aims to address the effect that analtered downtube section has between the 3rd and 4th aerodynamicmodels. Both models experienced identical analysis conditionsto understand what differences could be made to airflowbehaviour through downtube alteration.

5.3.1 Numerical Results Finally, numerical results aim to fully justify the use of thedowntube alteration in this particular frame geometry. Table 7gives numerically the values for drag between both models.

Table 7

Speed(ms)

3rd model DragForce (N)

4th model DragForce (N)

Percentagereduction

10.5 1.92 1.827 4.84412.5 2.759 2.622 4.96616.67 4.795 4.621 3.629Average 3.158 3.023 4.264

An overall reduction in drag has been deduced across the 4th

model in comparison with the 3rd. This reduction as apercentage is higher at lower speeds which was as expected due

101

to the larger accumulation of static pressure within thedowntube gap section through venturi’s theory for crosssectional fluid flow reduction. This would most probably reacha point at some velocity where the drag reduction would be anegative reduction (increase in drag) however; this speed islikely to far surpass the speed that a time trial cyclist islikely to experience.

A total average reduction in drag of 4.26% has been observedin the addition of the downtube gap.This can be further usedto define average wattage for each bicycle over 10km at steadystate to further aid quantifying the drag reduction. Inestablishing the wattage difference through aerodynamicchanges, restive forces due to rolling and mechanical effortare to be presumed as constant and therefore can be removedfrom the wattage determination:

Power=FDrag∗D

t

Specifically considering the downtube gap in comparing wattageconsumption through drag force:

For the third model, power loss through drag for a 10km timetrial is given

Poweracross10kmtimetrial=35.089Watts

And the fourth model;

Poweracross10kmtimetrial=33.589Watts

Giving overall an approximate 4.275% reduction in wattageconsumption across a 10km race.

In providing an expenditure in wattage taken as 200 watts(approximately similair to wattage expenditure in the 1st modelfor 10km), a time reduction comparison can be created for theamount of time saved in using the 4th bicycle:

Timetakenusing3rdmodel=157.2seconds

102

Timetakenusing4thmodel=151.15seconds

Here , whilst the actual time taken is a misrepresentation dueto the drag force only being estimated for the bicycle with norider, a conclusion can still be made for this alteration.Across a 10km time trial, this slit in the down tube profilewould likely provide a saving of around 6 seconds in competingagainst the 3rd model.

103

5.3.2 Visual results 5.3.2.a Static PressureStatic pressure is considered for both model air domains infigure 113 (normal downtube) and figure 114 (downtube with

gap).

104

Figure 113, static pressure for the air domain for the 3rd model; Source; ANSYS Experimental Results

Figure 114, static pressure for the air domain for the 4th model, Source; ANSYS Experimental Results.

Between the two models, a higher static pressure maximum isobserved in figure 114 for the 4th model in comparing to the3rd. A relatively similar accumulation of higher staticpressure can still be observed on the upstream section ofdowntube, however this is not observed to as much of an extentin figure 114 (gap downtube) as figure 113 ( no gap).

This reduction in frontal static pressure will aid in reducingdrag force but perhaps is countered by the large presence ofstatic pressure on the frontal face of the bottom bracket areain figure 114, this will lead to a significant amount of dragforce creation. In comparing the static pressure across bothseat tube sections, a slight decrease in frontal staticpressure can be observed in figure 114 compared to figure 113.

This reduction in static pressure accumulation can be found tobe down to either the role that the gap in the downtube playsin altering the air speed, or that airflow is altered to suchan extent that the bottom bracket flow upwards interrupts theair flow towards this seat tube section. This will be furtherverified in considering the velocity magnitude.

105

5.3.2.b Dynamic pressureDynamic pressure is considered at a side profile for eachmodel, this will allow visualization of airflow effect at the

surface of the downtube section.

106

Figure 114, Dynamic surface pressure for the 4th model, Source; ANSYS Experimental Results

Figure 113, Dynamic surface pressure for the 3rd model, Source; ANSYS Experimental Results.

In considering the downtube section, a slight reduction in thepresence of a higher dynamic pressure on the side edge of thedowntube can be observed. This may indicate that less air hasbeen forced around the side section of the downtube in figure114 thanks to the gap introduced into the downtube sectionwhich would reduce the volume of air that will deviate fromthe fluid flow path.

Further considering the difference in pressure across the headtube section , a lower dynamic pressure is present around thejoining section between head tube and down tube for thestandard downtube model (figure 113) in comparison to themodified downtube (figure 114). This is likely due to animproved airflow upstream of the head tube and down tubeconnecting section, where the wheel and fork are creating asmall air gap section. Again this is likely due to thelimitation on the amount of airflow which will deviate fromthe fluid flow path.

107

5.3.2.c Velocity MagnitudeVelocity magnitude is displayed for both models of bicycle and

downtube configuration.

Thanks to the gap in the downtube, a larger presence volume ofhigher velocity is observed across figure 116 than figure 115within the air gap between the downtube and seat tube, this isdue to more air being sent into this section of air gap at ahigher speed. Airflow can also be observed to be entering thedowntube gap in figure 116 which allows for less turbulence tobe created through air deviating around the downtube rather

108

Figure 115, velocity magnitude vectors at centreline for the 3rd model , Source; ANSYS Experimental Results

Figure 116, velocity magnitude vectors at centreline for the 4th model, Source; ANSYS Experimental Results

than passing straight through in the case of figure 115( gap).

The accumulation of lower speed air can be observed for figure116 than figure 115, this may appear to be of no benefit butthis lower air velocity replaces what was left of the reducedadverse pressure gradient present from flow separation at thispoint.

5.3.2.d Turbulence Kinetic EnergyTurbulence kinetic energy is considered at the surface (figure119 and 120) and for surrounding air at centreline (figure 117

and 118) for the two frame models. This set of visual resultsaims to further determine drag creation through turbulence foreach model.

109

Figure 117, air domain turbulence kinetic energy across the 3rd model, Source; ANSYS Experimental Results.

In considering maximal turbulence kinetic energy created, asignificant reduction of 7.9% can be observed between bothmodels. This indicates the drag reduction has been achievedacross the 4th model in reducing the maximum amount ofturbulence kinetic energy created. Focusing on turbulenceapparent across the downtube, a slight reduction in turbulencecan be observed across the 4th model (figure 120) compared tothe third (figure 119).

110

Figure 119, turbulence kinetic energy at surface for the 3rd model, Source; ANSYS Experimental Results

Figure 120, turbulence kinetic energy at surface for the 4th model, Source; ANSYS Experimental Results

The most key area in establishing the benefit of the downtubegap is considering the plane views for both figure 117 and118. This indicates the dispersal of turbulent kinetic energythanks to the addition of the downtube gap likely acceleratingthe air back into a laminar state by increasing the Reynoldsnumber of the airflow. For the 3rd frame this air would notexperience such simple acceleration and would first have tonegotiate the rounded section of downtube to re-join airflowat the rear of the downtube.

111

6.0 Verification of drag resultsthrough literature

Whilst fluid dynamic theory has been observed to be upheld(verifying the four models and experimental work), a furthersmall scale study is undertaken to use this method of analysisto define known drag coefficients of simple three dimensionalobjects. For this particular study , three shapes will betested which have a known drag coefficient taken fromliterature (Sadraey, 2009) (Bengston, 2010) (Weisstein, 2007)and experimentally (Mallick & Kumar, 2014) (Lavicka & Matas,2012) (Anthoine, Olivari, & Portugaels, 2009) (Devenport,2007) both for CFD and wind tunnel testing.

The three objects tested were a cube, cylinder and teardropshaped cylinder. The most important coefficient of drag todetermine is the cylinder shape, as this is the most easilyspecified and is also the most commonly occurring profileshape on a bicycle. This is the easiest to specify as the onlyfactor which will affect the magnitude of drag coefficient isthe frontal area of the cylinder, which is factored out of thecoefficient of drag equation. The most difficult to find arelevant quantity for is the teardrop shaped cylinder; this isdue to variations in the studies used, as many studies usedifferent configurations of teardrop angle.

These particular shapes where used as they represent the mostcommon fluid behaviour that will be witnessed across thebicycle frame and fork. These behaviours are;

Flow separation downstream Flow reversal downstream Flow reversal upstream Vortex shedding downstream Eddy formation downstream Maintenance of laminar flow downstream High/Low turbulent kinetic energy

112

Particular to each shape, each of these airflow behaviours canbe attributed to certain shape profiles, this allows for avery obvious relationship between drag coefficient and dragforce to be observed across each experiment. Each object wasexpected to display the following behaviours detailed in table8 over page :

Shape Behaviour Cube Flow separation , Flow reversal (both

upstream and downstream, Eddy Formation,Highest turbulent kinetic energy

Cylinder Flow separation, flow reversal(downstream), vortex shedding, Eddyformation , lower turbulent kinetic energythan the cube but higher than the teardropprofiled cylinder.

Cylinder withteardrop

Maintenance of laminar flow downstream,lowest turbulent kinetic energy, lack ofseparation/reversal/vortex shedding andeddy formation

113

Because coefficient of drag is a dimensionless quantity whichis used to describe the effect that the object will have onthe Reynolds number of the fluid flow, each object could beinvestigated irrespective of particular parameters such as airspeed velocity and frontal area. This is due to therelationship between velocity, area and drag force allnegating each other’s effects to allow for a pure factor fordrag coefficient to be achieved regardless of sizing andvelocity. Regardless of this each object was given a standardsize of 50mm in width (and height for the cube) with a heightof 180mm for the two cylinders to emulate the head tubeprofile for some of the models tested.

114

Table 8

6.1 Experimental set-upExperiments were undertaken for the 3 shapes using anidentical process to the previous 4 studies undertaken tomodel airflow around the bicycle models. IGES files wherecreated of each shape and imported into ANSYS. Figure 122

gives an example of the 3D mesh creation for one of the

objects (cube) whilst Figure 123 details the mesh within ANSYSFluent for the cube. Figure 124 details the geometry of theteardrop cylinder within its air domain.

115

Figure 122, 3D mesh for the cube, Source; ANSYS Meshing

Figure 123, mesh within fluent for the cube shape tested, Source; ANSYS Fluent

Due to the simplicity and number of geometries which were tobe meshed, a significantly lower cell count was witnessedacross every one of the three experiments undertaken in thisparticular experimental work. This means that a higher meshsetting could have been used for these particular shapes toimprove the resolution and accuracy. However, to investigatethe effectiveness of the course meshing modelling, this waskept as standard to the previous experiments for the bicyclemodels.

116

Figure 124, teardrop shaped cylinder within air domain , Source ; ANSYS Geometry editor

6.2 Experimental results 6.2.1 Numerical Results Coefficient of drag was calculated across each of the 3

objects. This is presented in table 9 for each object:

Shape Coefficient of Drag Cube 0.9853Cylinder 0.42743Teardrop cylinder 0.26737

Here it can be observed that a reduction in drag coefficientis obtained through streamlining the airflow across eachobjects body, this improves the airflow quality around theshape in terms of Reynolds number and hence reduces thecoefficient of drag.

Particularly in comparing the cylinder and teardrop cylinder,both of same frontal area, a direct comparison can be madebetween the two in investigating the direct influence onpreventing separation back side of the cylinder and thecoefficient of drag can be derived. In this particular case, areduction in the coefficient of drag of 62.553% is witnessedbetween both cylinder profiles.

6.2.2 Visual Results Visual results will be considered solely for the basiccylinder shape analysed. This is due to this particular shapebeing the most easily comparable to studies undertaken for a

117

Table 9

cylinder shape through CFD (Devenport, 2007) (Weisstein,2007). Figure 124, 125 and 126 detail results for the cylinderexperimentation.

118

Figure 125, velocity vectors for magnitude across the cylinder. Source; ANSYS Results

Figure 126, turbulence kinetic energy across the cylinder. Source; ANSYS Results.

6.3 Discussion of results in relation toliterature findingsTable 10 compares values of Coefficient of Drag between thegiven shapes experimented and literature results forcomparative geometries. From literature, these coefficientshave been determined through a number of CFD methods alongwith wind tunnel testing.

Shape CD ( experimental) CD ( Literature)Cube 0.9853 0.83-1.2Cylinder 0.42743 0.38-0.7Teardropcylinder

0.26737 N/A

Table 10

Here in table 10, it can be observed that the two defined dragcoefficients lie within the region expected from citingvarious studies. Whilst no literature is available to confirmthe drag coefficient of the teardrop shaped cylinder, thisparticular result is expected as previously discussed acrossthe various sections of bicycle frame and fork tested.

Variation across the literature derived CD is likely due tothe methodology of determining each drag coefficient for eachbody. Depending on the values of Reynolds number of airflowthis can have an effect on the results particular to eachobject and air speed velocity. For the particular case of theexperimental findings, a turbulent factor of 3% was set withinthe air domain in an attempt to emulate real world conditionsfor a typical calm day. This turbulent factor will play asmall part perhaps in affecting the value of CD calculatedacross each object but as can be observed, overall this methodof analysis has been justified as expected values for CD havebeen upheld.

These upheld values indicate that this analysis is mostsuitable for modelling cylindrical and square objects whereflow separation and pressure drag are most likely to occur.These airflow phenomenon are similar to behaviours witnessed

119

across the bike and therefore provide validation to theexperimental results both numerically and visually.

120

7.0 Final DiscussionConsidering the overall effectiveness across the 4 sets ofexperimentation, it can be observed that results are primarilyconsistent and of the same order of magnitude for each varietyof results.

Visually, the majority of results displayed a similar patternof behaviour between each model. However, due to ANSYSautomatically creating the colour scale for each set ofresults this created issues mostly consisting of;

Results for the 4th set of experimental results forvelocity magnitude

Dynamic pressure across different model surfaces Turbulent kinetic energy appearing much more incoherent

This problem of scaling could be addressed by standardizingthe display across all 4 experimental procedures in displayingminimum and maximum contour colourings for all the variousairflow speeds, leg positions and frame and fork combinationsused.

Numerically results may have inaccuracies through a few keyareas;

Cell anomalies Mesh skewedness

Whilst these are likely to be eliminated in comparing all ofthe models due to averaging and using the same system ofanalysis, there may still be an element of inaccuracy fromreal world values.

However overall, visual results confirm to fluid dynamictheory in that modifying various parameters a number offindings can be derived, which all have conformed toexperimental expectations and also fluid dynamic theory in thedrag equation;

FDrag=12ρv2CdA

121

Regarding this specific equation, visual findings have proventhis equation and proven the effectiveness of this researchthrough indicating that;

A reduction in A, frontal area (tubing thickness),reduces the magnitude and quantity of high pressure onfront facing surfaces of the model ( reduction in drag)

A reduction in A, the frontal area (tubing thickness),reduces the amount of separation and hence turbulencekinetic energy that the bicycle model produces( reduction in drag)

A reduction in Cd of the model body, reduces the amountof separation that occurs ( reduction in drag)

An increase in air velocity increases the amount of dragpresent

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Numerical results for all 4 experiments also suggest thatfindings are further abiding by fluid mechanic laws for drag.Considering the 3 sets of experimentation that included legsand a crank-set, it can be observed that across all resultsmaximum drag force is observed where the leg positions areeither up or down. This verifies that airflow has beensuccessfully modelled in terms of drag force, as leg positionsin the up/down position would create a greater amount offrontal surface area and hence drag force. along with the legsections being at an angle closer to normal to the fluid flow,as previously discussed surfaces normal to fluid flow willlikely see the highest accumulation of static pressure throughdeceleration of airflow.

In considering the percentage reductions observed across eachframe, it is evident that the most effective method forreducing drag force across each model is reducing the frontalarea of the bicycle. A reduction of 10% is observed inreducing the tube thickness of the 1st frame compared to the2nd, whereas the improvement of airflow by adding profiles toreduce separation yield an 8% average reduction in drag.

Further improving visual results could also be achieved byincreasing the cell count and hence improving the mesh qualityaround the model to analyse the airflow behaviour to a higherdegree of accuracy. By increasing the amount of calculationsundertaken within the same amount of domain area, a greateramount of averaging can be undertaken by the software usingthe k-epsilon realizable mathematical model, this greateramount of averaging across smaller cell sizes would improvethe resolution of results visually, along with improving theaccuracy of numerical drag force results obtained.

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8.0 Conclusion8.1 Concluding for cycling industry In considering this method of analysis in establishing fluidflow across a bicycle frame and fork, it is evident that basicfluid dynamic principles have been observed and upheld acrossthe vast majority of results obtained visually andnumerically. Theoretical principles utilised in theoptimization of the frame yielded positive results which wereexpected. This method has a number of key benefits in itsimplementation, these are;

Relevant results Suitability for assessing simple geometries Full scale results can be modelled Changes can be investigated numerically and visually Can be undertaken on a desktop computer

This has a number of benefits, relating this to bicyclemanufacturers which can occasionally be on small scale / lowbudget type of operations, this particular of method could bean affordable and viable option for smaller companies tofeature computer optimization within the design of theirbicycles.

Furthermore in considering this particular method across manysporting applications, it has also a degree if usage withinlower budget sports where drag reduction is key to improvingperformance (bobsleigh, downhill skiing , low budget motorracing).

As confirmed by analysing this method using simple shapes andcomparing these to literature, a good estimation of drag forceand geometry effect on air flow behaviour for low speed fluidflows can be established.

8.2 Issues to be addressed through findings ofthis method The shortcomings of this method of simulation are;

Poor resolution compared to high end industry modelling

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Irregularity in colouring display Limited cell count Difficulty in meshing certain bicycle geometries using a

lower cell count Lengthy calculation run time ( between1.5 and 2 hours)

Shortcomings can be addressed through a number of methods,these are;

Upgrading to full ANSYS software to increase the cellcount to increase resolution and air flow modelling

Using a more powerful computer resource to speed upcalculation, prevent crashing the software and increasethe cell count which can be used

Using a dynamic mesh to create spinning legs to moreaccurately represent the bicycle and rider combination

Using a more detailed model ( for both bicycle andrider ), inclusion of all components and a full rider

8.3 Future work and Overall conclusion Considering future work for this particular field of research,a number of evolutions of this particular piece of work can besought. The main aspects of future work leading from thisreport are;

Investigating the effects of more geometry alterations ondrag force

Investigating the effects of geometry alterations onstructural integrity of a bicycle

Using this method of analysis for investigating othersporting applications

Using this method of analysis for investigating other lowspeed fluid flow applications

Investigate relevancy of this method of analysis ( windtunnel/ real world comparison)

Along with the future work which could be done for thisparticular method, as established within this report, accuracycould be greatly improved with the use of an improvedmathematical model and mesh resolution. Currently at the

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forefront of CFD technology is techniques such as Large EddySimulation (LES) and Direct Numerical Simulation (DNS) whichhave currently proven to yield for more accurateapproximations of airflow across a domain. In implementingsuch computationally intense methods of analysis, a far largerand more powerful computing resource would be necessary tomodel the airflow.

To conclude the findings of the experimental work and thisreport;

Reduction in the parameters involved in the drag forceequation leads to a reduction in drag force across thebicycle model

ANSYS Fluent is capable of modelling full scale bicyclemodels to an acceptable degree of relevancy andresolution for a low speed fluid flow

A desktop computer can yield results which are of use inindustry for frame and fork optimization.

A method of averaging for the leg positions eludes tosome degree of relevancy for results

From this particular research, it is evident that the use ofCFD within time trial bicycle design is vital to theinvestigation of airflow quality across the bicycle and thatthe method detailed within this report can be utilised toreduce drag reduction across a bicycle frame and forkspackage.

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