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R E G U L A R P A P E R
Jiun-Jih Miau
·
Shang-Ru Li·
Zong-Xiu Tsai·
Mai Van Phung·
San-Yi LinOn the aerodynamic flow around a cyclist model at the hoods position
Received: 16 May 2019 / Revised: 30 July 2019 / Accepted: 5 September 2019 / Published online: 9 October 2019
© The Author(s) 2019
Abstract Aerodynamic flow around an 1/5 scale cyclist model was studied experimentally and numerically.
First, measurements of drag force were performed for the model in a low-speed wind tunnel at Reynolds numbers from 5:5 104 to 1:8 105. Meanwhile, numerical computation using a large eddy simulation method was performed at three Reynolds numbers of 1:1 104, 6:5 104 and 1:5 105 to obtain the drag coefficients for comparison. Second, flow visualization was made in a water channel and the wind tunnel mentioned to examine the three-dimensional flow separation pattern on the model surface, which could also be realized from the numerical results. Finally, a wake flow survey based on the hot-wire measurements in the wind tunnel showed that in the near-wake region, the flow was featured with the formation of multiple streamwise vortices. The numerical results further indicated that these vortices were evolved from the separated flows occurred on the model surface.
Keywords Cycling aerodynamics · Flow visualization · Flow separation · Drag · Wake
1 Introduction
When cycling at reasonably high speed, the drag due to a cyclist can be much greater than that resulted from the bicycle being ridden. Evidence reported in the literature indicates that during cycling at a racing speed of 50 km/h, aerodynamic drag can contribute about 90% of the total drag (Kyle and Burke 1984), of which 70% is due to the cyclist. Therefore, it would be more effective to reduce the drag due to the cyclist than that of the bicycle.
The drag experienced by a cyclist is associated with a complicated aerodynamic flow around a three-dimensional contoured body, for which the phenomenon of flow separation plays a significant role. As noted in the literature (Lukes et al.2005; Defraeye et al.2010a,b,2011; Blocken et al.2018), the aerodyamic flow is strongly dependent upon the posture of a cyclist. Defraeye et al. (2010a) conducted a numerical and experimental study for a cyclist at the upright, dropped and time trial positions, respectively. Experiments were made in a large-scale wind tunnel that a cyclist with a racing bicycle was situated in the test section for aerodynamic drag measurements. In addition, there were 30 pressure plates (sensors) applied on the cyclist’s body to collect the instantaneous pressure measurements. Meanwhile, numerical simulations were carried out for the cases studied. Accordingly, the numerical and experimental results on the values of drag area and the pressure coefficients at different locations on the cyclist body were compared. Overall speaking, the results obtained by the two approaches were in good agreement, which inferred that the method of numerical
J.-J. Miau (&) · S.-R. Li · Z.-X. Tsai · M. V. Phung · S.-Y. Lin ·
Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan 7010, Taiwan E-mail: jjmiau@mail.ncku.edu.tw
Tel.: 886-6-2757575 J Vis (2020) 23:35–47
https://doi.org/10.1007/s12650-019-00604-2
simulation can be of use to study cycling aerodynamics. As they pointed out, using the numerical simulation method could provide the information of the flow in a more cost-effective manner, compared to using the experimental approach. Defraeye et al. (2010b) conducted the numerical simulations of flow around a cyclist with testing the turbulence models available in the literature. The numerical results of pressure distribution obtained were then compared with the experimental data of a half-sized cyclist model at 115 locations, which were obtained from wind tunnel testing. It was concluded that the RANS SSTk–ω model gave the best overall performance among the models tested. Later, Defraeye et al. (2011) extended the numerical simulation to analyze the drag and convective heat transfer corresponding to the individual segments of a cyclist model, that the cyclist model was divided into 19 segments. The numerical results of drag and convective heat transfer corresponding to each of the segments at the upright, dropped and time trial positions were examined. As found, the high drag area values were attributed to the segments of head, legs and arms. Furthermore, it was noted that the aerodynamic drag of each segment was strongly dependent upon the cyclist posture, but the convective heat transfer was less sensitive.
A group of studies were concerned with the drag of a cyclist in dynamic motions. Griffith et al. (2014) pointed out that the leg motion affected the aerodynamic drag significantly, and the transient case under consideration would represent a situation close to the reality than a steady case. Crouch et al.
(2014,2016a,b) conducted a series of studies on the effect of pedaling with regard to a cyclist at the time trial position. In the wind tunnel experiments with a full scale mannequin (Crouch et al.2014), the data of total drag measurements and pressure measurements on the body surface together with the velocity mea-surements in the wake region unveiled that the three-dimensional flow distribution around the mannequin varied with pedaling at different crank angles. As noted, the flow with significant momentum deficit in the turbulent wake behind the hip played a predominant role in the development of unsteady flow around the cyclist body.
The flow phenomenon around multi-cyclists has been concerned greatly in the competition of team pursuit cycling. Blocken et al. (2013) conducted numerical analysis of flow around two drafting cyclists with different separation distance. Based on the numerical findings, discussion on the strategy of reducing the total drag was carried out. Defraeye et al. (2014) performed numerical simulations for four cyclists in a pace line with different postures and variable separation distances. Based on the results of the cases studied, the drag forces resulted from different segments of the bodies of the cyclists were examined. The aim of the work was to evaluate the reduction in the total drag subjected to the flow conditions specified.
In discussing the cyclist drag, a quantity called the drag area (Defraeye et al. 2010a) or the effective frontal area (Debraux et al. 2011) as the product of the drag coefficient and the frontal area is frequently referred. An obvious reason of using this quantity is that it can be obtained directly from the drag force measured and subsequently divided by the dynamic pressure based on the characteristic velocity. Never-theless, as far as the strategy of reducing the drag is concerned, it would be better to examine the two quantities separately, since each of which has its own physical significance. The frontal area is realized to be critically dependent upon the posture of the cyclist. To determine the frontal area of a cyclist in laboratory or actual racing situations is not trivial. For instance, Debraux et al. (2011) reviewed the methods for the determination of the frontal area of a cyclist. On the other hand, the drag coefficient is a non-dimensional quantity representing the aerodynamic characteristics of concern. In general, it can be referred to as an indicator concerning the bluffness of an aerodynamic body. A cyclist is regarded as a blunt body since a large portion of the drag produced is associated with the form drag. For a cyclist at a fixed posture, the drag coefficient may vary with the Reynolds number (Defraeye et al. 2010a, 2011) as well as the surface roughness as introduced by the sportware (Oggiano et al.2007,2009; Chowdhury and Alam2014; Hsu et al.
2019).
This study is focused on the aerodynamic flow around a cyclist model at the hoods position, a posture applying to a wide range of speed (4.2–12.5 m/s) in cycling. An 1/5 scale cyclist model was employed for experiment with using the methods of flow visualization, force measurement and wake flow survey.
Moreover, the numerical simulation was made to obtain the flow distribution around the cyclist model. The numerical results were of use to complement the experimental findings and to assist in explaining the complicated flow phenomenon around the cyclist model.
36 J.-J. Miau et al.
2 Methodology 2.1 The cyclist model
The cyclist model at the hoods position for experiment is shown in Fig.1a. It is an 1=5 scale model made by a 3D printer, whose surface data were provided by GIANT Inc., Taiwan. The dimension of the model is further given in Fig.1b. Notably, the inclination angle of the upper body of the model,a, is 32. The torso length, C, is 110 mm; C is denoted as the reference length in this study. The crank angle, h ¼ 195, is associated with the foot positions of the model. The frontal area of the model called AC is 0:0122 m2, excluding that of the sting support.
The Cartesian coordinate system employed in this study is shown in Fig.1b with the origin located at the root of the sting support;x, y and z denote the streamwise, lateral and vertical directions, respectively. In this study, the instantaneous, time mean, fluctuating and root-mean-square velocities in thex, y and z directions are denoted as (u, u, u0,u0rms), (v, v, v0,v0rms) and (w, w, w0,w0rms), respectively.
2.2 Water channel experiments
In this work, a water channel facility was employed for the experiments of flow visualization and PIV velocity measurements. The test section of the water channel was 0:6 m in width, 0:6 m in height and 2:5 m in length. The cyclist model was situated 1 m downstream from the inlet of the test section, where the freestream turbulent intensity was about 1%. The blockage ratio of the model was 5:9%. Experiments were made at the Reynolds number,ReC, about 1:1 104, whereReC is based onC, and the incoming velocity, U1.
An arrangement for PIV system is shown in Fig. 2a, where the cyclist model was positioned upside down. The PIV system employed was capable of measuring two components of the flow velocity, with an Argon ion laser as the light source. A sketch of the model included in this figure provides an indication of the central plane,y=C ¼ 0, where the PIV velocity measurements were performed. The measurements were made by taking 2000 images continuously at a rate of 200 fps. In addition, flow visualization in the water channel was conducted with the ink dots and dye-injection methods.
2.3 Wind tunnel experiments
An open-jet low-speed wind tunnel employed for the present study is shown in Fig.2b. The cyclist model was situated in an extended test section of 0.5 m in diameter, that the area blockage ratio of the model was 6:8%. The flow speed in the test section could reach 35 m/s, at which the freestream turbulence intensity measured was less than 0:7%. The incoming velocity U1was monitored by a Pitot tube located immediately downstream of the inlet. Further, this figure provides a schematic view depicting an X-type hot-wire probe situated on a 3-D traversing mechanism for conducting the velocity measurements in the wake behind the cyclist model.
The hot-wire velocity measurements were carried out at six streamwise locations indicated in a sketch included in Fig.2b. Specifically, in the cross-sectional planes ofx/C=0.8, 1.2, 1.6, 2.0 and 2.4, the hot-wire
Fig. 1 aAn 1/5 scale cyclist model employed for experiment, b the model marked with the dimension and the Cartesian coordinate system employed
On the aerodynamic flow around a cyclist model at the hoods position 37
velocity measurements were made at the grid points spaced by 10 mm; at each of the grid points, the hot-wire output signals of each channel were sampled at 1 kHz for 8192 samples. In addition, atx=C ¼ 1:0, the velocity measurements were made with a finer grid spacing of 5 mm for a detailed survey of the wake flow.
In this case, the hot-wire signals of each channel were sampled at 2 kHz for 16,384 samples. All of the measurements mentioned above were made at ReC¼ 6:5 104. Note that in order to obtain the flow quantities of the three-dimensional flow, the hot-wire velocity measurements at each grid point were actually made twice. The second time was made after the hot-wire probe rotated 90°.
The statistical quantities reduced from the velocity measurements are described below. The non-di-mensional time mean streamwise velocity (u) is defined as u=U1. The total turbulence intensity (TIxyz) is defined as u0rms2þ v0rms2þ w0rms2
=3
0:5=U1 100%. In addition, the non-dimensional shearing Rey-nolds stresses associated with the xy and xz terms (Rxy, Rxz) are defined as u0v0=U12 and u0w0=U12, respectively, which have the physical implications of transporting the momentum and kinetic energy through the respective components of turbulent fluctuations. The non-dimensional time mean streamwise vorticity (xx) is defined byxxC=U1, wherexx¼ o w=oy ov=oz.
In order to identify the presence of streamwise coherent vortices in the wake region, the k2-criterion (Jeong and Hussain1995; Chen et al. 2015) was adopted in this study, whereas a different method was adopted by Crouch et al. (2014) for vortex identification in their study. One may refer to Li (2017) for more details about the discussion on the methods of vortex identification. To describe the strength of a vortex identified, a non-dimensional streamwise circulation (C) is defined asPN
n¼1xx
nDyDz=AC, whereΔy and Δz denote the spacing of the measurement grid points in the y and z directions, respectively, within the vortex region defined.
To measure the drag force experienced by the cyclist model, a self-made one-component external force balance of a platform type was employed, which is shown in Fig.3a. The drag force of the testing model was sensed by the strain gauges on the flexure plate. More details regarding the balance design can be found in Tsai et al. (2016).
The balance was calibrated using a single-vector force calibration method (Parker et al.2001). The 95%
confidence interval (abbreviated as 95% CI) with regard to the measurement uncertainty of the balance is shown in Fig.3b. The 95% CI was reduced according to a formula ofk ffiffiffiffiffiffiffi
ps=n
=fm 100%, where fm ands y/C=0
(a)
(b)
Fig. 2 a The experimental setup of the PIV system in a water channel, and b the experimental setup of the hot-wire velocimetry in a wind tunnel
38 J.-J. Miau et al.
represent the average and standard deviation values corresponding ton times of the applied forces measured, respectively;k ¼ 2 is assumed as n was greater than 21 (Bandet and Perisol1991). As seen in Fig.3b, for the applied forces above 0:6 N, the corresponding uncertainties of the balance were no more than 0.8%, indicated by a dashed line in the figure, which is comparable to that of a commercial grade balance. On the other hand, if the applied forces lower than 0:6 N, the uncertainties were increased substantially due to the impact of the background noise on the accuracy.
In this study, the balance output was sampled at 1 kHz for 120 s. The measured results were expressed in terms of the drag coefficient, CD; CD¼ FD=ð0:5qU12ACÞ, where FD and ρ denote the drag force and the density of the working fluid, respectively. Apart from the self-made balance, a commercial balance of JR3, Inc., was available for the present study. Therefore, a comparison on the data obtained by the two balances was made in this study.
Flow visualization experiment using an oil film technique was conducted in the wind tunnel for revealing the limiting streamline patterns on the model surface. Details regarding this technique can be found in Li et al. (2017).
2.4 Numerical simulation
Numerical simulation of flow around the cyclist model was carried out by a large eddy simulation (LES) method using the Fluent/ANSYS software. The parameters of the simulation were defined according to the experiments made in the water channel and the wind tunnel, respectively.
In the water channel case (ReC ¼ 1:1 104), the sub-grid scale (SGS) eddy viscosity model suggested by Smagorinsky (1963) was adopted. The Smagorinsky constant chosen was 0.16 to make the best corre-lation between numerical simucorre-lation and experiment (McMillan and Ferziger1979). On the other hand, in simulating the cases of the wind tunnel experiments at higher Reynolds numbers, ReC¼ 6:5 104 and 1:5 105, the Wall Adapting Local Eddy (WALE) viscosity model (Nicoud and Ducros1999) was adopted, and the WALE coefficient was set to be 0.5. In addition, a much finer grid system was implemented in the viscous boundary-layer region. Referring to Blocken et al. (2013), the height of the first cell from the model Fig. 3 aThe self-made force balance, and b variations of the 95% CI (the confidence of interval) versus the applied forces
On the aerodynamic flow around a cyclist model at the hoods position 39
surface, namely the distance from the wall normalized by the viscous length scale of the turbulent boundary layer, yþ, was kept around 0.6 for all the cases studied. More details of the present numerical simulation method can be found in Phung (2017).
3 Results and discussion
3.1 Drag force measurements compared with the numerical results
TheCDvalues of the cyclist model reduced from the wind tunnel experiment for the Reynolds numbers in a range of ReC¼ 5:5 104 to 1:8 105, together with the results of numerical simulation obtained at ReC¼ 1:1 104, 6:5 104, and 1:5 105, are presented in Fig.4. In this figure, two sets of theCDvalues obtained by the self-made balance and the commercial balance, JR3, are provided for comparison. At ReC¼ 6:5 104, both of theCDvalues reduced from the measurements of the two balances are around 0.8, and theCDvalue obtained by the numerical simulation is around 0.76. Thus, the difference is about 4:3%.
However, at ReC ¼ 1:5 105, the discrepancy between the data of the self-made balance and the JR3 balance is quite substantial, 14:9%, while the numerical result and the data obtained by JR3 are quite close.
The trend that theCD values obtained by the self-made balance appear to be higher at higher Reynolds numbers could be due to the side force generated by the cyclist model, which would introduce additional moment to the slide. However, this speculation requires further clarification. It should be mentioned that none of theCD data in the plot have been corrected with the blockage effect of the model.
According to the data presented in Fig. 4, one can say that the CD values are rather insensitive to the Reynolds number range studied. This observation is noted in line with the findings reported by Crouch et al.
(2016b) that for the major flow structures observed in the low Reynolds number case were comparable to those at the relatively higher Reynolds numbers in the order of 105. This viewpoint was also mentioned by Spohn and Gillieron (2002) with regard to a configuration of the Ahmed body that the flow structures revealed by flow visualization in a water channel at Reynolds number of 103were similar to those seen at the Reynolds number of 106.
The aerodynamic bluffness of the present model can be discussed with reference to the two generic models of circular cylinder and sphere. It is known from the literature that the CD values of a smooth circular cylinder (Roshko 1993) and a smooth sphere (Schlichting 1979) for Reynolds numbers in the subcritical range of 104–105are 1.2 and 0.47, respectively, Thus, theCDvalues of the present model found fall between these two reference categories. Furthermore, referring to the drag coefficients of several types of the transportation vehicles (Hucho and Sovran1993), mostly are in the range of 0.2–0.5. Apparently, the present model is bluffer than these transportation vehicles aerodynamically speaking.
3.2 Flow visualization on the model surface
Detailed features concerning the flow structures near the surface of the cyclist model can be learned from the results of flow visualization. Figure 5 presents the limiting streamline patterns revealed by the oil film method made in the wind tunnel (Fig.5a) and the ink dots method made in the water channel (Fig. 5b),
Self-made balance, FSSL Commercial balance, JR3 CFD result
( )
Fig. 4 Comparison of theCDvalues obtained by the two balances in the wind tunnel and the numerical simulation
40 J.-J. Miau et al.
which consistently indicate that there exists a pair of counter-rotating vortices around the cyclist’s shoulder, which persist downstream over the back of the model. Based on these observations, a sketch of limiting streamlines depicting the formation of the recirculation regions, called RC, is given in Fig.5c. The sketch further explains that the fluid in RC would be trapped and spinning in a three-dimensional manner, which would result in gathering the oil film materials on the surface. Figure 5d further provides the results of
which consistently indicate that there exists a pair of counter-rotating vortices around the cyclist’s shoulder, which persist downstream over the back of the model. Based on these observations, a sketch of limiting streamlines depicting the formation of the recirculation regions, called RC, is given in Fig.5c. The sketch further explains that the fluid in RC would be trapped and spinning in a three-dimensional manner, which would result in gathering the oil film materials on the surface. Figure 5d further provides the results of