A numerical analysis of different approaches for rotation modelling on the aerodynamic drag of a spoked cycling wheel

Wheels account for about 10% of the total aerodynamic drag of a cyclist. While different types of wheels are commercially available, spoked wheels are commonly used in cycling races. This paper presents computational fluid dynamics (CFD) simulations of spoked wheels, and systematically evaluates different boundary conditions that are usually used for rotation modelling of wheels, namely (i) rotational moving wall, (ii) moving reference frame (MRF) and (iii) sliding mesh. Steady and unsteady Reynolds-Averaged Navier-Stokes (RANS) CFD simulations are thus performed for an isolated wheel. Moreover, the impact of the volume enclosing the wheel, where the MRF is applied, on the predicted wheel drag is evaluated. The evaluation is based on validation with wind-tunnel measurements of force coefficients. The results of this study can be used for accurate CFD simulations of cyclist aerodynamics. 1Introduction In the 2017 Tour de France, 10 different manufacturers provided the wheels for the 22 teams in the race (Arthur, 2017), while each manufacturer had several wheels in their catalogue. The wheels are selected among the large variety of commercially available options based on their performance in terms of aerodynamic drag, weight, inertia and stiffness (Kyle, 1995). The aerodynamic performance of wheels is of significant importance since the drag of both wheels is responsible for about 10% of the total cyclist resistance (Greenwell et al., 1995). It is usually evaluated using wind-tunnel tests (Greenwell et al., 1995; Kyle, 1995, 1991; Tew and Sayers, 1999) and more recently using CFD simulations (Godo et al., 2010). CFD is capable of computing forces and moments acting on each single wheel’s component (rim, tyre, spokes and hub) and providing fundamental information that can be used by designers to improve the aerodynamic performance of wheels. Nevertheless, one critical aspect in the CFD simulations of wheels is appropriate rotation modelling approaches. To the best of our knowledge, the impact of different rotation modelling approaches on the accuracy of CFD simulations of cycling wheel aerodynamics has not yet been investigated. 2Methodology In this study, CFD simulations are first validated with the wind-tunnel measurements by Tew and Sayers (1999). The Campagnolo Shamal wheel has a 19 mm rim width and a 61 mm depth, spanning from the tyre to the rim edges (Fig. 1a). The spoke’s cross section is approximated to a rectangle of 3 mm  1 mm (Fig. 1b). The computational domain has a cross-section of 8.6 m  7.8 m. The upstream and downstream length of the domain are 3.9 m and 7.4 m, respectively. The computational grid consists of about 13.2 million cells, while about 246,000 surface cells are used on the wheel (Fig. 1b). The mean velocity inlet boundary condition is a uniform profile (48 km/h), accordingly to the experiment (Tew and Sayers, 1999). The 3D RANS equations are solved in combination with the k-ω SST turbulence model. It should be noted that the good performance of the k-ω SST turbulence model has been already shown in previous studies on cycling aerodynamics, e.g. Defraeye et al. (2010). Three approaches are evaluated to model the rotation of the wheel: (i) the rotational wall approach (RW), (ii) the moving reference frame approach (MRF) and (iii) the sliding mesh approach (SM). The latter two methods are applied on a volume surrounding the wheel, as shown in Fig. 1a and Fig. 1c. Moreover, the impact of the volume enclosing the wheel, where the MRF is applied, on the predicted wheel drag is evaluated. (Fig. 1c). 3Results The CFD results show a good agreement with the wind-tunnel results in terms of the drag coefficient with a deviation of about 1.8 % at 0˚ yaw angle. Further and more detailed information about the different approaches will be provided in the full paper.