Authors: Paul Mannion1,2,4, Eoghan Clifford1,4, Bert Blocken2,3, Yasin Toparlar2, Magdalena Hajdukiewicz1,4 Affiliations: 1.) Department of Civil Engineering, National University of Ireland Galway, University Road, Galway, Ireland 2.) Department of the Built Environment, Eindhoven University of Technology, P.O. box 513, 5600 MB Eindhoven, the Netherlands 3.) Department of Civil Engineering, KU Leuven, Kasteelpark Arenberg 40 - bus 2447, 3001 Leuven, Belgium 4.) Informatics Research Unit for Sustainable Engineering (IRUSE), Ireland


Technology enhances the performance of athletes at the Olympics (Hanna, 2012), resulting in new records as the years progress, and the same can be said for the athletes competing in Paralympics (Keogh, 2011). Aerodynamics is an important factor when optimising an athlete’s performance for all high-speed sports. Para-sports are no different, with aerodynamics impacting triathlons, biathlons, skiing, athletics and cycling. Equally, reducing hydrodynamic drag is key to faster times in swimming. Prosthetics can be designed to minimise their aerodynamic drag and skin-suits worn by cyclists or swimmers can be designed to reduce the friction drag. In recent years, elite Para-cycling has started to receive attention in aerodynamics research (Belloli et al., 2014; Mannion et al., 2017). Among the research methods, computational fluid dynamics (CFD) has established itself as a suitable tool for aerodynamic analysis and optimisation within elite sports (Blocken, 2014; Crouch et al., 2017; Hanna, 2012; Hart, 2006), in conjunction with experimental methods such as wind-tunnel testing and on-site measurements. This hopefully marks the beginning of a trend which will see aerodynamic optimisation being conducted across a wider range of Para-sports, with CFD used as a valuable tool for analysis and optimisation purposes. This article discusses the application of CFD for aerodynamic analysis in Para-cycling.

Introduction to CFD and aerodynamics

CFD: A typical aerodynamic analysis with computational fluid dynamics is composed of three-steps: pre-processing, solving and post-processing. Within sports aerodynamics applications, the pre-processing step includes the formation of a representative geometry of athletes and sports equipment for the analysis. Later, the surfaces of the representative geometry and the air volume around it is discretised spatially into numerous control volumes (cells) to generate a grid (Figure 1a). This grid can contain upwards of millions of cells to accurately discretise the fluid domain and to be able to sufficiently resolve the flow field around the geometry investigated. The pre-processing step also includes the specification of target parameters, setting of appropriate boundary conditions and defining relevant computational settings, which are all essential for CFD simulations. The 'solving' step indicates the execution of the necessary simulations. Simulations can be performed by solving Reynolds-Averaged Navier-Stokes (RANS) equations in combination with a turbulence model to achieve closure. Throughout the simulations, specified target parameters (that is, pressure (Figure 1b)) can be monitored and data from these target parameters can be recorded. Alternatively, simulations can be performed by other numerical models, such as with Large Eddy Simulations (LES). LES is known to be able provide a more accurate analysis of the flow field than the RANS approach (Blocken, 2015; Fintelman et al., 2015). However, the RANS approach is commonly used because of its computational efficiency. Turbulence modelling is a key aspect of RANS simulations, and an appropriate turbulence model must be chosen for the application at hand. There are numerous turbulence models available in modern commercial and open-source CFD codes. Commonly, the choice of turbulence model is based on a dedicated sensitivity analysis. Prior studies on sports aerodynamics have typically used the two-equation standard k-ε model (Jones & Launder, 1972), and the shear stress transport (SST) k-ω model (Menter, 1994) as the turbulence model of choice in their studies. Aerodynamics Aerodynamics can be defined as the interaction of air flowing around solid bodies. Typically, in aerodynamics research, the drag coefficient (equation 1) is used as a non-dimensional indicator for comparisons, or to determine improvements between designs/scenarios. The drag coefficient equation comprises the drag force (FD) [N], fluid density (ρ) [kg/m3], flow velocity (V) [m/s], and the reference area (A) [m2]. C_D= F_D/(0.5ρAV^2 ) (1) The frontal area is typically used as the reference area in sports applications. However, the frontal area is commonly unknown and difficult to measure for cyclists. Thus, the following form of the drag coefficient equation is often used as an indicator which is termed the ‘drag area’. This term is the drag coefficient (CD) [-] multiplied by the reference area (A) [m2], and is described in equation 2 with the units of m2. The drag area is directly scalable to the drag force, and is most commonly used for the aerodynamics studies in cycling and Para-cycling events. C_D A= F_D/(0.5ρV^2 ) (2)

Application of CFD in Para-cycling aerodynamics

The difficulty with geometry acquisition of athletes has been a factor in the later adoption of CFD for elite cycling and Para-cycling by comparison to the automotive or other industries. However, advances in 3D scanning technology allow for athletes and equipment to be accurately scanned using handheld devices (Artec Europe, 2017) within a matter of minutes. The geometries of the athletes and equipment are imported into a virtual wind tunnel, where the air flow can be simulated using CFD. In wind tunnel experiments, information can be attained for velocities through point measurements with anemometers, or on a plane using Particle Image Velocimetry (PIV). On the other hand, CFD holds an advantage over wind tunnel experiments and track testing methods by providing whole flow-field data for any target parameter, thus, eliminating the limitations of measurement equipment. In addition, CFD can provide drag information on specific components within the simulation, such as the bicycle frame, wheels, helmets, and specific locations on the athlete such as the arms or legs. In the case for tandem paracycling, CFD has been used effectively to determine the drag experienced by both tandem athletes (pilot and stoker) individually by Mannion et al. (2017). The wealth of information yielded through CFD simulations can aid in understanding the fundamental mechanics behind the formation of drag. Furthermore, this allows for new and innovative measures to be developed to decrease aerodynamic drag. Typical applications of CFD within Para-cycling include investigating athletes' postures to refine their position on the bicycle to reduce their drag. Through the use of Computer Aided Design (CAD) software, systematic studies can be conducted on equipment variations for a particular athlete. Helmets, bicycle frames and equipment can be changed using CAD to determine the best match for each athlete tested. Figure 2 illustrates this concept being applied to a hand-cyclist, with different wheel types and combinations. [caption id="attachment_44399" align="alignright" width="300"] Figure 2. CAD models of a hand-cyclist with different wheel selections for CFD analysis[/caption]

Best practice guidelines for CFD simulations of Para-cycling aerodynamics

Turbulence modelling is a key aspect of RANS simulations and sensitivity studies have been published outlining suitable models for use in specific applications. In the case of cycling aerodynamics, Defraeye et al., (2010) determined that the standard k-ε turbulence model (Jones & Launder, 1972) provided good predictions by comparison to experimental results. However, for tandem Para-cycling, the SST k-ω model (Menter, 1994) was found to yield the most accurate results (Mannion et al., 2017). It is advisable that turbulence model sensitivity studies are conducted for new studies within the sphere of sports aerodynamics if there is no relevant information available in the literature. Grid generation is another critical aspect for aerodynamics simulations. There are various cell types that can comprise a grid, including tetrahedral, polyhedral, hexahedral and prismatic shapes (Figure 3a). The appropriate resolution of the grid is essential for obtaining accurate results. An important aspect of aerodynamics modelling is capturing the near wall flows termed the ‘boundary layer’ close to the surfaces of athletes and equipment/apparel. There are three regions in a boundary layer (from close to the wall surface to further): the laminar sublayer, the buffer layer and the outer turbulent layer. Viscous effects are important in the laminar sublayer and in the buffer layer.

Primary methods for simulating boundary layers

There are two primary methods for simulating boundary layers: the wall functions approach and the Low Reynolds Number Modelling (LRNM) approach. Wall functions use the logarithmic law for velocity to model boundary layers and typically utilise hexahedral or tetrahedral grids (Figure 3) where the height yP to the centre point P of the first cell is not always within the laminar sub layer of a boundary layer. LRNM uses a low-Reynolds number turbulence model to solve the flow all the way to the wall with an appropriate grid. The LRNM approach requires prism layers (Figure 3) to create thin, high aspect ratio cells that grow from wall surfaces. The height of the centre point of the first cell in the prism layers can be within the laminar sublayer of the boundary layer. [caption id="attachment_44400" align="alignright" width="300"] Figure 3. Cell types and their application for resolving boundary layer flows using wall functions and LRNM methods[/caption] Wall functions are commonly used in CFD simulations (Blocken, 2015). The impact that different approaches for resolving near-wall flows can have on the CFD drag predictions for Para-cycling has been highlighted by Mannion et al. (2017). A tetrahedral-only grid (combined with the wall-functions approach) and a tetrahedral-prismatic grid (combined with the LRNM approach) were created for a tandem para-cycling case study (Figure 4) by Mannion et al. (2017). Both grids predicted a CD within 8.8 per cent of each other; a presumably small difference between the simulations. However, the tetrahedral-only grid incorrectly predicted that the stoker (the rear tandem athlete) experienced a larger drag force than the pilot (the front tandem athlete) (Figure 4). The tetrahedral-prismatic grid correctly predicted the aerodynamic drag distribution for the pilot and stoker athletes. Thus, for para-cycling aerodynamics, the LRNM approach is recommended for solving near-wall flows. Additional best practice guidelines relevant to modelling sports and cycling aerodynamics with CFD include those by Tominaga et al., (2008), Franke et al. (2007) and (Blocken, 2015). These provide best practice guidelines for appropriate domain dimensions, boundary conditions and numerical schemes. [caption id="attachment_44401" align="alignright" width="300"] Figure 4. A summary of results from Mannion et al. (2017). The aerodynamic drag simulated using two different grids is presented[/caption]

The future of CFD in Para-sports?

CFD is establishing itself as an important tool for Para-cycling aerodynamics optimisation, complementing traditional wind-tunnel testing. Advances in CFD software, computer hardware, and the dissemination of knowledge are aiding in making CFD accessible to all athletes and sport institutions. CFD and aerodynamics analysis may become an integral component of an athlete’s preparation for competitive events in not just Para-cycling, but in all high-speed Paralympic sports. NUI Galway and Eindhoven University of Technology research project: This article is from a research collaboration between the College of Engineering & Informatics at NUI Galway and Eindhoven University of Technology. This research is also in collaboration with the University of Liège, Cycling Ireland, Sport Ireland Institute, and Paralympics Ireland. The authors would also like to acknowledge the partnership with the ANSYS Inc. References 1.) Artec Europe. (2017). Artec Eva, 3D Scanners. Retrieved May 22, 2017, from 2.) Belloli, M., Cheli, F., Bayati, I., Giappino, S., & Robustelli, F. (2014). Handbike aerodynamics: wind tunnel versus track tests. In The 2014 conference of the International Sports Engineering Association, Procedia Eng. (Vol. 72, pp. 750–755). Elsevier B.V. 3.) Blocken, B. (2014). 50 years of Computational Wind Engineering: Past, present and future. Journal of Wind Engineering and Industrial Aerodynamics, 129, 69–102. 4.) Blocken, B. (2015). Computational Fluid Dynamics for urban physics: Importance, scales, possibilities, limitations and ten tips and tricks towards accurate and reliable simulations. Building and Environment, 91, 219–245. 5.) Crouch, T. N., Burton, D., LaBry, Z. A., & Blair, K. B. (2017). Riding against the wind: a review of competition cycling aerodynamics. Sports Engineering, 20(2), 81–110. 6.) Defraeye, T., Blocken, B., Koninckx, E., Hespel, P., & Carmeliet, J. (2010). Computational fluid dynamics analysis of cyclist aerodynamics: Performance of different turbulence-modelling and boundary-layer modelling approaches. Journal of Biomechanics, 43(12), 2281–2287. 7.) Fintelman, D. M., Hemida, H., Sterling, M., & Li, F.-X. (2015). CFD simulations of the flow around a cyclist subjected to crosswinds. Journal of Wind Engineering and Industrial Aerodynamics, 144, 31–41. 8.) Franke, J., Hellsten, A., Schlünzen, H., & Carissimo, B. (2007). Best practice guideline for the CFD simulation of flows in the urban environment. COST Action 732: Quality Assurance and Improvement of Microscale Meteorological Models. Hamburg Germany. 9.) Hanna, R. K. (2012). CFD in Sport - a Retrospective; 1992 - 2012. Procedia Engineering, 34, 622–627. 10.) Hart, J. H. (2006). The use of CFD in the chase of Olympic gold . Sports Engineering, 1–11. 11.) Jones, W. P., & Launder, B. E. (1972). The prediction of laminarization with a two-equation model of turbulence. International Journal of Heat and Mass Transfer, 15(2), 301–314. 12.) Keogh, J. W. L. (2011). Paralympic sport: An emerging area for research and consultancy in sports biomechanics. Sports Biomechanics, 10(3), 234–253. 13.) Mannion, P., Toparlar, Y., Blocken, B., Hajdukiewicz, M., Andrianne, T., & Clifford, E. (2017). Improving CFD prediction of drag on Paralympic tandem athletes: Influence of grid resolution and turbulence model. Sports Engineering. 14.) Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32(8), 1598–1605. 15.) Tominaga, Y., Mochida, A., Yoshie, R., Kataoka, H., Nozu, T., Yoshikawa, M., & Shirasawa, T. (2008). AIJ guidelines for practical applications of CFD to pedestrian wind environment around buildings. Journal of Wind Engineering and Industrial Aerodynamics, 96(10–11), 1749–1761.