Aerodynamic effect of bicyclewheel cladding— A CFD study

Aerodynamic drag in a bicycle can originate through the rotation of wheels, and the addition of cladding on the wheels has a pronounced impact on the same. In the present work, the effect of cladding on the wheels of a bicycle is studied in terms of the percentage cladding in order to predict the aerodynamic drag using a validated CFD model. SolidWorks Flow Simulation is used to conduct an external analysis of flow air around the bicycle and rider. The k-ε turbulence model is used to study aerodynamic drag among cladding percentages varying between nil to maximum, i.e., 100%. The aerodynamic drag force is observed to decrease with increase in cladding percentage. Analyses were carried out at velocities 6 m/s, 8 m/s and 10 m/s and there was an observed maximum decrease in drag coefficient in the range of 5.2–5.3% as compared to the bicycle without cladding. © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).


Introduction
Cyclists utilize a large amount of power to overcome the aerodynamic drag experienced by them. Aerodynamic drag may represent between 70% and 90% of the total resistance experienced by a cyclist riding a bicycle (Chowdhury et al., 2011b;Debraux et al., 2011). The power required by the cyclist to overcome this resistance is a third-order polynomial of the velocity of travel (Swain, 1994). However, the power of a cyclist may be considered limited, and as the competitiveness of sports increases, so does the need to improve the design of equipment in order to achieve better levels of performance with the same effort. Such improvements in design can be made possible by reducing the aerodynamic drag.
The rotation of wheels is a major source of drag in a bicycle. The drag created by conventional spoked wheels can be limited by reducing the number of spokes. However, strength and rigidity factors limit this ability (García-López et al., 2008;Greenwell et al., 1995). A number of studies have attempted to examine the aerodynamics of bicycle wheels, primarily through wind tunnel and field tests. Kyle and Burke (1984), Godo et al. (2009) and Wickern et al. (1997), through experimental analysis, observed a considerable difference in the aerodynamic drag observed in rotating and stationary wheels. Sunter and Sayers (2001) analyzed the differences in the aerodynamic drag and * Corresponding author.
E-mail address: iskander.tlili@tdtu.edu.vn (I. Tlili). power expended by eight different wheels, and attributed these to characteristics such as the tire diameter, width and profile. Karabelas and Markatos (2012) similarly observed that the rotation of wheels significant increased the drag and side force, and that an increase in the number of spokes also increased the axial drag and vertical force on the wheel. Jermy et al. (2008) analyzed the power dissipated by aerodynamic resistance for a range of bicycle wheels, and found that rotational drag due to wheels comprised 10-15% of the drag experience by the bicycle. Zdravkovich (1992), Crane and Morton (2018), Greenwell et al. (1995) and Tew and Sayers (1999) conducted experimental studies on a range of bicycle wheels, and concluded that aerodynamically designed wheels such as tri-spoke and disk wheels exhibited a considerable reduction in aerodynamic drag, up to 50% as compared to commercially utilized wheels. It was also observed that velocity of rotation did not have a large impact on the drag coefficient of a wheel. Dyer and Noroozi (2015) conducted field tests on nine different cycle wheels and found the power expended with the traditional spoked wheel to be over 20% higher as compared to deep section wheels, whereas the full disk wheel was observed to expend the lowest power. Monte et al. (2016) observed that non-spoked continuous wheels were aerodynamically advantageous and exhibited lower drag than discontinuous and spoked wheels. Barry et al. (2012) compared the experimental results obtained for a range of wheels in a cycleonly configuration with those obtained when a rider was included in the analysis and observed a significant impact on the drag area trends, suggesting that the choice of wheels must not be based on the individual aerodynamic characteristics of the wheels alone, but also on biomechanic characteristics concerned with the rider. Petrone et al. (2018) similarly applied a full-scale methodology in the analysis of a cyclist riding a cycle with three different sets of spoked wheels and observed a change of 3.7% to 9% in time required in competitive time trial conditions. Computational fluid dynamics (CFD) is powerful tool the use of which has been increasing in regularity over the past decades. Increased computational power has meant that complex CFD simulations can now be conducted in formerly reclusive fields such as bioenergy (Madhania et al., 2019), microfluids (Asadollahi et al., 2018), nanofluid mechanics Mansour and Bakier, 2015;Milani Shirvan et al., 2017a,b;Rashidi et al., 2018Rashidi et al., , 2017 and acoustics (Kashyap and Bhattacharjee, 2019). Since cycling aerodynamics involves the study of the flow of air across an external body, i.e., a bicycle, computational fluid dynamics can be used for analysis (Defraeye et al., 2010a;Kashyap and Bhattacharjee, 2019). Knupe and Farmer (2009) and Godo et al. (2010) conducted an experimental and computational analysis of the flow of air across a bicycle wheel and observed the CFD results to be in good agreement with the wind tunnel results, thus validating the use of CFD in the context. Schwab et al. (2018) used computer model analysis to study the effect of crosswinds on the dynamics and control of a bicycle, and observed that crosswinds adversely affect the stability of a bicycle and increase its tendency to steer into the wind. Blocken et al. (2013) analyzed the impact of fender coverage angle on the drag experienced by a bicycle computationally, and obtained an optimum angle for reduced drag. Yu et al. (2018) analyzed various computational methods for the study of wheel rotation, and concluded moving wall and moving reference frame methods were appropriate when aerodynamic drag was of import. Mannion et al. (2018) computationally analyzed the moving wall, moving reference frame and sliding mesh approaches in the modeling of bicycle wheel rotation, and observed results to be in good concordance with CFD values. Hobeika and Sebben (2018) concluded that the moving reference frame method was appropriate for modeling wheel rotation independent of geometry. Ilea et al. (2019) studied the impact of wheels rims on the aerodynamics of wheels, and observed that alloy rims performed better. Pogni and Petrone (2016) used CFD for the analysis of five spoked wheels using the k-ε model for a range of yaw angles, and reported results of drag and side forces, observing deeper wheel rims offered greater aerodynamic advantages.
The addition of cladding on bicycle wheels plays an important role in the reduction of aerodynamic drag force and drag coefficient (Sayers and Stanley, 1994;Zdravkovich, 1992). The same can have a substantial effect on the power expended by the cyclist. On a survey of available literature, it is observed that a computational or parametric analysis of the effect of cladding on these aerodynamic parameters of a bicycle is sparsely available. The current work is an attempt in this direction.
In the present study, analyses have been carried out in order to determine the frontal area, aerodynamic drag force and drag coefficient as a function of percentage cladding, using Computational Fluid Dynamics. The diameter of the cladding varies from 0% to 100% of wheel diameter with a difference of 10% between consecutive analyses. The impact of velocity has been studied by simulating at 6 m/s, 8 m/s and 10 m/s.

Methodology
For the present study, the Computer-Aided Design (CAD) modeling of the geometry was first carried out. The geometry was then meshed and grid independence tests were performed in order to ascertain the appropriate grid fineness. CFD analysis was performed on the optimized mesh and the results were validated by comparison with reported data. The validated model was then used for performing the parametric study.

CAD model
The 3-dimensional CAD assembly was modeled according to a standard city bicycle containing the following parts -the bicycle frame, wheels (2 nos., 32 spokes each), cladding (2 nos.), cyclist (a female of height 5 ft 11 in.), helmet and a solid plane under the bicycle wheels, representing the road. The cladding constitutes two disks on either side of the wheel, present on both the front and back wheel of the bicycle, and the center of the cladding disks coincides with the wheel center. The various dimensions of the bicycle and cyclist are shown in Fig. 2.1. The assembly was created using Autodesk Fusion360 and SolidWorks, as shown in Fig. 2 The diameter of the cladding was varied between 0% and 100% of the diameter of the wheel, with a difference of 10% between consecutive assemblies. SolidWorks was used to compute the frontal areas of the various CAD assemblies used for the present study. Fig. 2.3 shows the frontal areas plotted as a function of the percentage cladding.

Mathematical modeling
The algorithm used for the analysis is depicted using a flow chart shown in Fig. 2.4. SolidWorks Flow Simulation was used for the CFD analysis. Flow Simulation uses a time-implicit solver for the approximation of convective/diffusive equations for low compressible flows such as those in the current study. Defraeye et al. (2010a) studied various turbulence models and concluded that the aerodynamic drag of cyclists was most accurately predicted by the k-ε model as compared to the corresponding wind tunnel result. Taking these findings as a basis, the k-ε model was used for the current study. The analysis was governed by the 3D steady Favre Averaged Navier-Stokes (FANS) (Sobachkin and Dumnov, 2013) equations solved with second-order accuracy using the kε model (Jones and Launder, 1973), which were then discretized over the domain using the finite-volume method. Favre-averaging is beneficial in the given physical conditions, since it simplifies the averaged equations significantly by suppressing terms related to density fluctuations in compressible flow. The finite-volume method ensures that spatial discretization is performed in the physical space, reducing the possibility of errors derived from transformation between the physical and computational coordinate system. The governing equations are as follows (Sobachkin and Dumnov, 2013).
where the density of the medium is represented by ρ, time is represented by t and velocity of flow in the x i direction is represented by u i .
where velocity in the x j direction is represented by u j , represents fluid pressure is represented by P, the shear stress tensor is represented by τ ij and body force is represented by S i .
A computational domain of length 32 m, height 8 m and width 8 m was chosen in accordance with best practice guidelines (Franke et al., 2007) as shown in Fig. 2.5. To simulate the travel of the bicycle on a road, the road was modeled as a nonslip moving wall with its velocity equal to the relative velocity of travel of the bicycle with respect to air. All analyses were carried out at an ambient pressure and temperature of 1 bar and 298 K respectively. Inlet velocities of 6, 8 and 10 m/s were applied as a uniform velocity profile on the upstream face of  the computational domain, while the downstream face was given an ambient pressure outlet. The wheels were given a rotational velocity corresponding to the relative velocity of travel. Table 2.1 lists the input and output parameters defined for the analysis.
The following equations were used to define the drag coefficient and lift coefficient.
The required grid fineness for the parametric study was chosen by performing a grid independence study (Arora, 2014). Solid-Works Flow Simulation implements a Cartesian meshing scheme, which carries the advantages of a robust differential scheme, minimized truncation errors and greater speed (Sobachkin and Dumnov, 2013). The fineness of the mesh is represented by the ratio factor. This ratio factor governs the relative size of the Cartesian mesh elements. A greater ratio factor represents higher fineness in the section containing the CAD model.
Further parametric study was carried out to find the effect of cladding percentage on the aerodynamic drag force and drag coefficient of a bicycle being ridden by a cyclist. The diameter of the cladding was varied between 0% and 100% of the diameter of the wheel, with a difference of 10% between consecutive analyses. The effect of velocity on the drag force and drag coefficient was also studied by varying the velocity from 6 m/s to 10 m/s. Convergence was monitored and the analysis was concluded when residuals of velocity components, continuity, k and ε reached an    order of 10 −6 , as shown in Fig. 2.6. The results were tabulated post convergence and the next model was analyzed.

Grid independence study
In order to determine the grid size for the analysis, a grid independence study was performed. The values of drag coefficient were compared at various ratio factors at mesh level 7. The mesh level of the mesh quantifies the number of times the mesh has been refined, i.e. the maximum number of times the elements of the mesh have been divided in regions of greater complexity in geometry. A mesh level of 1 hence means a uniform mesh with elements of equal dimensions, while increasing refinement increases the fineness of the mesh. It may be noted from Fig. 2.10 that the Cartesian mesh is significantly finer in regions close to the model. The ratio factor of the mesh is the proportion between the aspect ratios of elements of consecutive levels of refinement. A high ratio factor hence leads to finer and better quality elements close to the model, and lower quality elements in regions farther away. This contributes to savings in computational time without compromising on accuracy. The study was conducted on the bicycle without cladding, at a velocity of 6 m/s with the kε model. It was observed that beyond a ratio factor of 8.5, the observed drag coefficient was minimally variant (<1%), as evident from Fig. 2.7.
For further analysis of grid independence, 9 different line segments on the rotating region of the front bicycle wheel were analyzed. One-line segment passed through the center of the wheel and 4 each were present on either side of it, at equal intervals. Each line segment contained 11 points, geometrically distributed, as shown in Fig. 2.8. Grids of mesh level 7 and ratio factor 8.5, 9, 9.5 and 10 were studied. The number of cells in the meshes studied ranged from 4 × 10 6 to 5 × 10 6 , with an average element characteristic length between 0.7 mm and 0.8 mm.
The velocity in the direction of travel (v) was plotted as a function of non-dimensional y-coordinate Y/Y max , where the Y-coordinate of the point under consideration from the origin (assumed at the center of the wheel) is represented by Y and the maximum Y-coordinate for the line segment under study is represented by Y max . All 4 meshes showed considerable mutual agreement. The results of two of the grid independence studies are shown in Fig. 2.9 for brevity. Trends of computational time are provided in Fig. 2.9; from which it is evident that an increase in ratio factor leads to a corresponding increase in computational time. Taking into account the results of the grid independence study, further analysis was carried out with a ratio factor of 8.5, using the mesh shown in Fig. 2.10.

Validation
The drag area (AC D ) values obtained from the study were considered for validation. Drag area is a coefficient introduced by (A brief introduction to fluid mechanics, 1997; Barratt, 1965;Pedley, 1997) as the ratio between the aerodynamic force and the dynamic pressure, and is considered useful in cases where the area of reference is not obvious, or the geometry consists of various parts (Zdravkovich, 1992). The drag area is regularly used as a parameter in both computational and experimental studies of bicycles (Blocken et al., 2013;Chowdhury et al., 2011a;Defraeye et al., 2010a;Zdravkovich, 1992).
The drag area values obtained through the current CFD analysis were validated against data reported by Zdravkovich et al. (1996)

Results and discussion
CFD analyses were conducted in order to predict drag force and drag coefficient as a function of percentage cladding on the    Fig. 4.1 depicts the velocity contours of the analysis conducted at a velocity of 10 m/s with 0% cladding. The drag experienced by the cyclist of primarily profile drag, which is created due to the presence of a pressure differential. The complex geometry of the cycle and cyclist makes the occurrence of adverse angles of attack for the air flow inevitable. This leads to adverse pressure gradients, which further cause separation of the flow from the body. This separation of flow leads to the development of a wake behind the cycle. It is observed that a considerable wake is generated behind the cyclist, which leads to the creation of vortices. In the region of the wake, significant losses in pressure take place due to eddy formation, which contributes to the creation of a low pressure region. This further increases the drag force experienced by the cycle and cyclist.  Fig. 4.2 depicts the turbulence intensity in the region of the bicycle and rider at 0% and 100% cladding. It is evident from the figure that there is a marked difference between the turbulence intensities observed in the cycle with and without cladding, with the cycle with cladding possessing a considerably lower turbulence intensity in the region behind the wheels. This leads to a decrease in the low pressure region created at the wheel rear, leading to a decrease in the drag experienced by the cycle. In turbulent flows, a considerably large amount of energy is dissipated in the formation of eddies, leading to pressure losses. Hence, in comparison to laminar flow, turbulence has a greater contribution to drag. As turbulence increases, the region of low pressures exhibits greater efficacy in the development of drag force, which leads to an increase in drag. Fig. 4.3 depicts the velocity streamlines for the analysis of the cycle at 5 m/s, with and without cladding. A significant reduction in turbulence, rotational velocity of air and irregularity of the vectors is observed in the cycle with cladding, alongside the presence of a smaller wake region. The presence of a cladding on the wheels of the bicycle provides the air with significantly lower exposure to adverse geometries such as wheels spokes, which exhibit a greater proclivity towards the separation of flow. Through this reduction in flow separation, the formation of eddies and regions of low pressure is also reduced. This leads to a reduction in turbulence and vorticity behind the wheels of the cycle, which lead to a reduction in the drag force. Fig. 4.4 represents the drag force as a function of the percentage cladding on the bicycle wheels. From the graph, it is evident that the drag force shows a similar decreasing trend for all velocities under consideration. Fig. 4.5 represents the percentage change in drag force as compared to the model without cladding. All 3 velocities show a similar decrease for all models considered. This decrease is seen to proceed at a greater rate as the percentage increases. In experimental studies of a rotating cycle wheel conducted by Sayers and Stanley (1994), it was observed that wheels with cladding over the wheels exhibited  a considerably lower drag coefficient than wheels with spokes.
This was attributed to the division of flow around the wheels.
This division prevents the creation of eddies due to the rotation of the wheel, reducing drag. A change in velocity is found to have a negligible impact on the reduction in drag force. Fig. 4.6 represents the drag coefficient as a function of cladding percentage at air velocities of 6 m/s, 8 m/s and 10 m/s. The drag coefficient at all 3 velocities shows similar trends of decrease. As in case of drag force, drag coefficient is observed to decrease steadily with increase in cladding. However, the rate of reduction increases with increasing percentage cladding. For any particular cladding percentage, the drag coefficient is found to increase with decrease in velocity. This follows research conducted by Grappe (2009) as reported by Debraux et al. (2011), where drag area (AC D ) was observed to decrease with increase in velocity, when velocities were within the range of the current study. Fig. 4.7 represents the percentage change in drag coefficient as compared to the model without cladding. As observed in case of drag force, the change in drag coefficient is similar in case of all 3 velocities. The minimum drag coefficient is observed at 100% cladding for all 3 velocities. The maximum reduction in drag coefficient is calculated as 5.3%, 5.3% and 5.2% for the 6 m/s, 8 m/s and 10 m/s case respectively.
The study conducted points toward the importance of a reduction in turbulence to improve the aerodynamics of a cycle. Introducing an accessory such as a cladding on the wheels of a bicycle can go a long way in reducing the aerodynamic drag of the bicycle, which is of much interest for both city and competitive cycling, as reduction in the drag produced by the cyclist can further lead to a reduction in the time taken to ride the same distance, as well as conservation of the energy consumed in doing so (Blocken et al., 2013;Swain, 1994).
In order to determine the physical effects of the change in drag force, the virtual gain in travel time is plotted as a function of cladding percentage in Fig. 4.8. This gain is calculated for a travel distance of 10 000 m at the velocities simulated. It is evident from the figure that the virtual travel time gained increases with increase in cladding percentage. The maximum gain varies from 23 s for a travel velocity of 10 m/s to 40 s for a velocity of 6 m/s. These gains are significant, especially considering that the decisions of competitive races hinge on margins of less than a second. It must however, be mentioned that these are only virtual gains; velocities during the race are often non-uniform, and factors such as drafting, track length and geometry and air flow can greatly change the actual times of travel.

Conclusion
• 3-dimensional CFD simulations were conducted using Solid-Works Flow Simulation in order to assess the impact of cladding on the aerodynamic drag force and drag coefficient of a cyclist riding a bicycle.    • Analyses were performed from a cladding percentage of 0% to 100% at velocities of 6 m/s, 8 m/s and 10 m/s, and the drag force and drag coefficient were seen to decrease with increase in cladding percentage. A maximum reduction in drag coefficient of 5.3%, 5.3% and 5.2% respectively in the 6 m/s, 8 m/s and 10 m/s case was computed.
• It is implied through all cases studied that the addition of cladding over the wheels of a bicycle is associated with a considerable change in drag force as well as drag coefficient. It is also observed that partial cladding of wheels has a lower effect on the drag coefficient than full cladding.
• While the increase in frontal area with addition of cladding is marginal, the aerodynamic impact is comparatively large.
• Drag force and drag coefficient both showcase a greater decrease in value for higher cladding percentages, while the decrease is marginal for lower cladding percentages. This reaffirms the positive aerodynamic impact of cladding on the wheels of a bicycle. A reduction in drag force and drag coefficient further implies a reduction in the effort required on part of the cyclist, as well as a reduction in time required to travel long distances.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.