Many elite cyclists therefore try to optimise their position for drag by means of field tests or wind tunnel tests. More recently, also Computational

Transcription

1 The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai, China; September 2-6, 2012 RANS and LES simulations of the interference drag of two cyclists B. Blocken a, T. Defraeye b,c, E. Koninckx d, J. Carmeliet e,f, P. Hespel g a Building Physics and Services, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands, b.j.e.blocken@tue.nl b Division of Building Physics, Katholieke Universiteit Leuven, Kasteelpark Arenberg 40, Leuven, Belgium c Division of Mechatronics, Biostatistics and Sensors, Katholieke Universiteit Leuven, Willem de Croylaan 42, Leuven, Belgium d Flemish Cycling Federation, Globelaan 49/2, 1190 Brussels, Belgium e Chair of Building Physics, Swiss Federal Institute of Technology Zurich (ETHZ), Wolfgang- Pauli-Strasse 15, 8093 Zürich, Switzerland f Laboratory for Building Science and Technology, Empa, Überlandstrasse 129, 8600 Dübendorf, Switzerland g Research Centre for Exercise and Health, Department of Biomedical Kinesiology, Katholieke Universiteit Leuven, Tervuursevest 101, 3001 Heverlee, Belgium ABSTRACT: This paper presents a numerical study of the interference drag of two cyclists in dropped position and in time-trial position. The study is based on 3D laser scanning of the cyclist geometry and on high-resolution grid generation, where the centre of the wall-adjacent cell is at about 15 micrometer from the body surface, resulting in y* values well below 5. The cell size in the wake is about 0.03 m. Both the Reynolds-averaged Navier-Stokes (RANS) approach with closure provided by the standard k-ε model and Large Eddy Simulations (LES) are performed. For LES, the time step is 3x10-4 s based on the CFL number. The interference drag is evaluated for inter-cyclist spacing varying from d = 0.01 to d = 1 m. Although the RANS and LES approach provided similarly accurate results for pressure coefficients and aerodynamic drag of a single cyclist, the results of both approaches for the interference drag are quite different. Compared to a single cyclist, the drag reduction for the dropped position with d = 0.01 m and with RANS is 2% for the first cyclist and 26% for the second one, while with LES it is 3% and 34%, respectively. For the time-trial position with d = 0.01 m, the reductions with RANS are 3% for the first cyclist and 16% for the second one, while with LES these values are 2% and 36%, respectively. Additional wind tunnel experiments with two cyclists are scheduled for further validation studies. Additional analysis of the CFD results will be performed to analyze the reasons for the large differences between RANS and LES results. KEYWORDS: Cyclist aerodynamics, drag resistance, Computational Fluid Dynamics. 1. INTRODUCTION At racing speeds (± 50 km/h in time trails), the aerodynamic resistance experienced by a cyclist, also called drag, is about 90% of his/her total resistance (Grappe et al. 1997, Kyle and Burke 1984). The major part is caused by form drag, related to the position of the cyclist on the bicycle. 1666

2 Many elite cyclists therefore try to optimise their position for drag by means of field tests or wind tunnel tests. More recently, also Computational Fluid Dynamics (CFD) has been applied in cycling (Hanna 2002, Lukes et al. 2004, Defraeye et al. 2010a, 2010b). Most studies were performed by solving the steady Reynolds-averaged Navier-Stokes (RANS) equations. Most studies have also employed wall-function modelling for the near-wall region. Recent studies however have explicitly resolved the boundary layer by low-reynolds number modelling (LRNM) (Defraeye et al. 2010a, 2010b). These CFD simulations were validated with detailed wind tunnel measurements on a full-scale (real) cyclist (Defraeye et al. 2010a) and a ½ scale model (Defraeye et al. 2010b). The study by Defraeye et al. (2010a) compared CFD simulations with drag measurements on a full-scale cyclist and indicated that, for the dropped position, Large Eddy Simulation (LES) yields a deviation in the drag area of 3%, while steady RANS with the standard k-ε model yields a deviation of 7% compared to the measurements. However, for the reduced-scale (1:2) model (upright position), steady RANS with the standard k-ε model provided a deviation in the drag area of only 4% compared to 6% with LES (Defraeye et al. 2010b). These results indicate that the RANS and LES results for the aerodynamic drag are very close. Therefore, they might suggest that further studies in cyclist aerodynamics can be conducted with steady RANS and the standard k-ε model, and that more time-consuming and intrinsically more accurate simulations with LES would not be necessary. To analyze the validity of this hypothesis, this paper provides results of a numerical study with both RANS and LES of the interference drag of two cyclists, riding one behind the other, in still air (zero wind speed). 2. CFD SIMULATIONS: COMPUTATIONAL PARAMETERS AND SETTINGS A digital model of the cyclist was obtained for the dropped position and the time-trial position using a high-resolution 3D laser scanning system (K-Scan, Nikon Metrology, Belgium), capturing the specific body characteristics of the cyclist. For meshing purposes, surface details were smoothed out to some extent and the bicycle was not included in the computational model. Two of these virtual cyclists were placed in a computational domain, one behind the other, with a spacing d varying from d = 0.01 m to 1m, including: 0.01 m, 0.25 m, 0.5 m and 1 m (Figs. 1 and 2). The size of the computational domain, for the two cyclists with d = 0.01 m, is L x W x H = 21 m x 6 m x 7 m. For the other distances, the length of the domain is increased with the spacing d. The grid is a hybrid grid, consisting of very small prismatic cells in the boundary-layer region near the cyclist s surface, with the first computational cell at only 15 m from the body surface. This high resolution is needed because low-reynolds number modelling requires the y * values of the wall-adjacent cells to be about 1 and certainly lower than 5 (Casey and Wintergerste 2000). Further away from the surface, tetrahedral cells have been used, with an average cell size in the wake region of about 0.03 m. The resulting grids for a single cyclist contain about 7.7x10 6 cells, while the grids for the two cyclists contain about 12.0x10 6 cells. The grids are based on gridsensitivity analysis according to best practice guidelines in CFD (Casey and Wintergerste 2000, Franke et al. 2007, Tominaga et al. 2008). The grid discretisation error was estimated by means of Richardson extrapolation and was about 3% for the drag force of the single cyclist. At the inlet, a uniform inlet velocity of 15 m/s is imposed, with zero turbulence intensity, which represents the relative air movement around the cyclists due to the cycling speed in still air 1667

3 The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai, China; September 2-6, 2012 (zero wind speed). For the side and top boundaries, a slip-wall boundary (symmetry) was used. Slip walls assume that the normal velocity component and the normal gradients at the boundary are zero, resulting in flow parallel to the boundary. At the outlet of the computational domain, ambient static pressure was imposed. Two approaches are used: (1) 3D steady RANS with the standard k- turbulence model (Launder and Spalding 1972) and with low-reynolds number modelling (LRNM), for which the one-equation Wolfshtein model (Wolfshtein 1969) is used in this study. Second-order discretisation schemes are used throughout. The SIMPLE algorithm is used for pressure-velocity coupling. Pressure interpolation is second order. (2) 3D LES simulations with the dynamic Smagorinsky subgrid-scale model (Kim 2004) with LRNM. Second-order discretisation schemes are used except for momentum, for which a central differencing scheme is used. Second-order implicit time stepping is used, and 20 iterations per time step were found to be sufficient to have convergence within a time step. The temporal discretisation is related to the spatial discretisation by the CFL (Courant-Friedrichs-Lewy) number: CFL = uδt/d, where u is the characteristic velocity in the cell, t is the time step and d is the characteristic cell dimension. Time steps resulting in CFL numbers of 1 are suggested in the wake region (Spalart 2001). For the simulations, the choice of the time step and averaging period was also based on a sensitivity analysis. A time step of 3x10-4 s was chosen, resulting in CFL numbers below about 5 in the majority of the domain, with maximal values that do not exceed 10, and values of about 0.5 in the wake. A dimensionless simulation time of about 2 flow-through-times was found to be sufficient to obtain stationary, i.e. stable averaged, values for drag and surface pressures, where the flowthrough-time is defined as: t FT = UT/L D, where U is the free-stream (approach flow) wind speed (15 m/s), T is the averaging period (2.8 s) and L D is the length of the computational domain (21 m). The simulations were performed with the commercial CFD code Fluent 6.3, which uses the control volume method. Figure 1. Two cyclists in dropped position at a variable spacing d. 1668

4 Figure 2. Two cyclists in time-trial position at a variable spacing d. 3. CFD SIMULATIONS: RESULTS Figure 3 shows an instantaneous image of the velocity contours in a vertical centreplane for the two cyclists in dropped position and with spacing d = 0.01 m. The low-velocity stagnation regions directly upstream of every cyclist can be observed, as well as the turbulent low-velocity wake of the first cyclist that partly engulfs the second cyclist. In this vertical centreplane and in this dropped cyclist position, flow separation is observed at the top of the helmets. The figure also shows the very dense grid resolution on the cyclist bodies and helmets. Figure 3. Instantaneous velocity contours in vertical centreplane for two cyclists in dropped position at distance d = 0.01 m. 1669

5 The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai, China; September 2-6, 2012 The results of the simulations are reported in Figures 4 and 5, in terms of drag reduction (DR) for the two cyclists, with respect to a single cyclist, and as a function of the inter-cyclist spacing d. Figure 4 shows the drag reduction for the first and for the second cyclist in dropped position, as obtained with RANS and with LES. It is noteworthy that there is also a drag reduction for the first cyclist due to the proximity of the second cyclist behind him/her, although this drag reduction is limited and it rapidly disappears with increasing inter-cyclist spacing. The intrinsically more accurate LES simulations indicate a larger drag reduction for both cyclists compared to RANS. For d = 0.01 m, LES indicates a reduction of 3% for the first cyclist and 34% for the second cyclist, while RANS indicates 2% for the first cyclist and 26% for the second one. Both approaches indicate a near-linear decrease of the drag reduction with increasing inter-cyclist spacing, although this decrease is more pronounced according to the LES results. At a distance of 1 m, the drag reduction for the second cyclist is still 28% (LES), while that for the first cyclist has become negligible. Figure 4. Drag reduction of two cyclists, with respect to a single cyclist, in dropped position at a variable spacing d, as obtained by RANS and LES simulations. 1670

6 Figure 5 shows the drag reduction for the first and for the second cyclist in time-trial position, as obtained with RANS and with LES. Also here, the drag reduction for the first cyclist due to the proximity of the second cyclist is clearly present. As opposed to the results for the dropped position, the results for the time-trial position show a very large difference between RANS and LES results for the second cyclist, more than a factor 2, while the differences in results for the first cyclist are negligible. For d = 0.01 m, LES indicates a reduction of 2% for the first cyclist and 36% for the second cyclist, while RANS indicates 3% for the first cyclist and 16% for the second one. Both approaches indicate a near-linear decrease of the drag reduction with increasing intercyclist spacing, which is most pronounced for the second cyclist with LES. At a distance of 1 m, the drag reduction for the second cyclist is still 30% (LES), while that for the first cyclist has become negligible. Figure 5. Drag reduction of two cyclists, with respect to a single cyclist, in time-trial position at a variable spacing d, as obtained by RANS and LES simulations. 1671

7 The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai, China; September 2-6, DISCUSSION AND CONCLUSIONS The interference drag (drag reduction) experienced by a second cyclist due to a cyclist in front of him/her is well-known. The fact that the first cyclist also experiences a drag reduction by the presence of the second one however, is less known, although there are some previous studies that suggest drag reduction of an upstream body by its downstream counterpart (e.g. Iniguez-de-la Torre and Iniguez 2009). The reason for the drag reduction of the first cyclist by the second one is the overpressure region in front of this second cyclist. This overpressure region merges with the underpressure region (wake) behind the first cyclist, thereby reducing the underpressure in this region and reducing the drag force. This effect is more pronounced as the cyclists ride closer behind each other. Previous numerical studies on the aerodynamics of a single cyclist riding in still air (Defraeye et al. 2010a, 2010b) have shown that the RANS and LES approach provided similarly accurate results for pressure coefficients and aerodynamic drag. In particular, the study by Defraeye et al. (2010a) compared CFD simulations with drag measurements on a full-scale cyclist and indicated that, for the dropped position, Large Eddy Simulation (LES) yields a deviation in the drag area of 3%, while steady RANS with the standard k-ε model yields a deviation of 7%. However, for the reduced-scale (1:2) model (upright position), steady RANS with the standard k-ε model provided a deviation in the drag area of only 4% compared to 6% with LES (Defraeye et al. 2010b). These results might suggest that further studies can be conducted with steady RANS and the standard k- ε model, and that more time-consuming and intrinsically more accurate simulations with LES would not be necessary. However, the comparison of RANS and LES simulations of the interference drag of two cyclists show large to very large differences between both approaches. Compared to a single cyclist, the drag reduction for the dropped position with d = 0.01 m and with RANS is 2% for the first cyclist and 26% for the second one, while with LES it is 3% and 34%, respectively. For the time-trial position with d = 0.01 m, the reductions with RANS are 3% for the first cyclist and 16% for the second one, while with LES these values are 2% and 36%, respectively. Hereby not only the differences between RANS and LES is remarkable, but also the fact that this difference is much larger for the time-trial position than for the dropped position. Additional wind tunnel experiments with two cyclists are scheduled for further validation studies. Also, additional analysis of the CFD results will be performed to analyze the reasons for these large differences between RANS and LES results. 5. REFERENCES Casey, M., Wintergerste, T., Best Practice Guidelines. ERCOFTAC Special Interest Group on Quality and Trust in Industrial CFD, ERCOFTAC. Defraeye, T., Blocken, B., Koninckx, E., Hespel, P., Carmeliet J., 2010a. Aerodynamic study of different cyclist positions: CFD analysis and full-scale wind-tunnel tests. Journal of Biomechanics 43(7): Defraeye, T., Blocken, B., Koninckx, E., Hespel, P., Carmeliet J., 2010b. Computational Fluid Dynamics analysis of cyclist aerodynamics: Performance of different turbulence-modelling and boundary-layer modelling approaches. Journal of Biomechanics 43(12): Franke, J., Hellsten, A., Schlünzen H., Carissimo, B., Best practice guideline for the CFD simulation of flows in the urban environment, COST Action 732. Grappe, G., Candau, R., Belli, A., Rouillon, J.D., Aerodynamic drag in field cycling with special reference to the Obree s position. Ergonomics 40 (12),

8 Hanna, R.K., Can CFD make a performance difference in sport?. In: Ujihashi, S., Haake, S.J. (Eds.), The Engineering of Sport 4. Blackwell Science, Oxford, pp Iniguez-de-la Torre, A., Iniguez, J., Aerodynamics of a cycling team in a time trial: does the cyclist at the front benefit? European Journal of Physics 30, Kim, S.-E., Large eddy simulation using unstructured meshes and dynamic subgrid-scale turbulence models. In: Proceedings of the 34th AIAA Fluid Dynamics Conference and Exhibit, Technical Report AIAA Port- land, Oregon. Kyle, C.R., Burke, E.R., Improving the racing bicycle. Mechanical Engineering 106 (9), Launder, B.E., Spalding, D.B., Lectures in Mathematical Models of Turbulence, Academic Press, London, England. Lukes, R.A., Hart, J.H., Chin, S.B., Haake, S.J., The aerodynamics of mountain bicycles: The role of computational fluid dynamics. In: Hubbard, M., Mehta, R.D., Pallis, J.M. (Eds.), The Engineering of Sport 5. International Sports Engineering Association, Sheffield. Spalart, P.R., Young person s guide to Detached-Eddy Simulation grids. NASA Contractor Report CR NASA, Virginia. Tominaga, Y., Mochida A., Yoshie, R., Kataoka, H., Nozu, T., Yoshikawa, M., Shirasawa, T., AIJ guidelines for practical applications of CFD to pedestrian wind environment around buildings, Journal of Wind Engineering and Industrial Aerodynamics 96(10-11), Wolfshtein, M., The velocity and temperature distribution in one-dimensional flow with turbulence augmentation and pressure gradient. International Journal of Heat and Mass Transfer 12 (3),