investigation of the drag crisis on the leg of a cycling ...mannequin used by jux et al. and terra...

15th International Conference on Fluid Control, Measurements and Visualization27-30 May, 2019, Naples, Italy

Investigation of the drag crisis on the leg of a cycling mannequin by means ofrobotic volumetric PIV

Francesco Scarano1,*, Wouter Terra2, Andrea Sciacchitano2

1Department of Industrial Engineering, University of Naples “Federico II”, Naples, Italy2Faculty of Aerospace Engineering, TU Delft, The Netherlands

*[email protected]

Abstract Reducing the aerodynamic drag of bluff bodies can have a strong impact in different engineering fields,one of the most meaningful example is the improvement in sports performances. The phenomenon of the drag crisishas been known in the literature since the 1950s: the drag coefficient decreases in a certain range of high Reynoldsnumber reaching a minimum value in correspondence of the so-called critical Reynolds number. Evaluating thepresence of the drag crisis and the critical Reynolds number is then a fundamental topic in the aerodynamics ofbluff bodies. The present work aims to investigate experimentally the drag crisis phenomenon on one leg of acycling mannequin. This has been carried out through the analysis of the topological characteristics of the wakeat various velocities. The most recent works in the literature have shown crucial progress in the field of ParticleImage Velocimetry (PIV) due to the introduction of the Helium Filled Soap Bubbles (HFSB) as tracers and thedevelopment of the Coaxial Volumetric Velocimetry (CVV) with the employment of robotic actuation. Anothercritical step has been the improvement of the Lagrangian tracking algorithm Shake The Box (STB) that has helpedto obtain a good accuracy even at high speeds. For these reasons, Large scale Robotic Volumetric PIV has beenused for the measurements at five different speeds within the range of 5 m/s to 25 m/s. The Open Jet Facility (OJF)of TU Delft has been employed to perform the experiment. The subsequent analysis demonstrates that the dragcrisis occurs at different velocities for three different parts of the leg; 10 m/s for the thigh, 15 m/s for the knee and20 m/s for the calf. This can lead to the conclusion that, in order to reduce the drag and improve the performancesin professional cycling, a new design of skin suits has to be devised.Keywords: PIV, sports aerodynamics, drag crisis, skin suits, cycling

1 Introduction

Aerodynamics plays a key role in many sports such as Formula 1, speed-skating, ski-jumping and elite-cycling.It has a strong influence in the performances improvement, in the elaboration of the regulations and in thedesign of velodromes or race tracks. Concerning cycling, the role of the aerodynamics is fundamental becauseof the complex nature of the flow field, because of the intrinsic three-dimensionality of the object and the lackof symmetry. When a cyclist rides on a flat surface, aerodynamic resistance accounts for over 90% of theresistance that a cyclist has to prevail [1].

Cycling aerodynamics is a particularly interesting subclass of bluff-body aerodynamics because a cyclistand his bicycle, even in a time-trail position, do not present a streamlined shape. This behavior is confirmedanalyzing the flow field that exhibits large regions of separation [2]. For this reason, unlike streamlined bodies,where the viscous tangential wall shear stress forces (τw) contribute the largest proportion to aerodynamic drag,the aerodynamic resistance in cycling is mainly due to pressure drag [3], Fig. 1.

It is therefore useful to summarize some important results relative to a cylinder that can help us to under-stand the aerodynamic behavior of a bluff body up to Reynolds number relative to cycling.

At very low Reynolds number there is the absence of a proper wake, we are in presence of the so-calledStokes flow. Between Reynolds number of 100 and 100,000 a Karman street is visible, which is firstly laminarand then it becomes turbulent. The wake topology does not change up to Reynolds approximately equal to105 with a symmetric behavior of the Karman vortex street [5]. Before the value of Reynolds number equal to2 ·105 the flow is in the so-called sub-critical regime, the drag coefficient (CD) measured by Roshko [6] is equalto CD = 1.2.

Then, starting from a Reynolds number approximately equal to 2 ·105 the so-called critical regime occurs.This configuration of the flow is unstable and it is possible to notice the presence of the vortex sheddingphenomenon and the von Karman alternating vortices [7] that cause a quasi-periodic variation of drag and lift.

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Fig. 1 Flow field around a cyclist, reproduced from [4] (left) and drag crisis for a cylinders, reproduced from [10] (right)

An indicative value for the drag coefficient is CD ∼= 0.8. In the critical regime (Re ∼= 3 ·105) the wake is quitestable, the CD is approximately equal to 0.5 [8]. At the end of critical regime (Re between 3.5 ·105 and 5 ·105)the drag coefficient reaches a minimum of CD between 0.22 and 0.4 [9] [8] [6] [10]. In the the super-criticalregime (Re ∼= 6.5 · 105), according to Roshko [6], the drag coefficient starts to increase reaching a value ofCD = 0.7 for a Reynolds number around 106.

Considering the wake at the downstream location xd = 1, being d the cylinder diameter and x = 0 the most

downstream point of the cylinder, when the flow is in sub-critical regime the adimensionalized wake widthis dw

d > 1. When the flow enters critical regime there is a reduction of the wake width that is estimated tobe dw

d∼= 0.87 until it reaches the value of dw

d∼= 0.67 which determines the onset of the super-critical regime.

Starting from the super-critical regime the width decreases and then remains constant and approximately equalto dw

d = 0.4 [8].The separated regions appear then to be reduced in extension when the flow passes from a sub-critical

regime to the super-critical regime which corresponds to the transition from the laminar to the turbulent regimeof the separating boundary layer. This is because turbulent boundary layers are characterized by intense small-scale eddies that transfer momentum from the freestream to the viscous interface at the body walls. The in-creased momentum at body’s surface gives turbulent boundary layers a greater ability to overcome adversepressure gradients compared to laminar ones [10]. The consequence of the reduction of the separated region isthe reduction of the pressure drag causing a so-called drag crisis. A drag deficit phenomenon that appears thenin a range of Reynolds numbers between 2 · 105 and 8 · 105 is therefore appreciable. The Reynolds number atwhich the drag crisis occurs is called critical Reynolds number Rec.

Achenbach [11] showed that, for a cylinder, the CD is a function of both Reynolds number and surfacetexture, the latter depending on the surface roughness. Roshko was the first who assessed that the criticalReynolds number can be reduced introducing more turbulence in the flow and adding surface roughness [6].

Turbulence transition can then be triggered on body parts of a cyclist at lower Reynolds number by meansof the use of skin suits. The use of textured skins suits can improve the performances delaying or moving theseparation point towards the back of the body reducing the size of the wake and reducing the pressure dragcomponent of aerodynamic resistance; conversely in areas of attached flow, smooth fabrics that minimize skinfriction should be used. The potential to improve cycling performance using a range of textured fabrics to treatspecific areas of the body has been well demonstrated, assessing a decrease in drag of up to 10% [12].

Typically, measurements on isolated cylinders are the basis for a suit design. With such an approach it isvery questionable if an optimal suit can be designed because of the more complexity of the flow around thehuman geometry. The common strategy to test garments is through balance measurements on an actual athleteor on a mannequin. This technique is based on the trial and error approach, the design of the equipment thenis refined until a satisfying configuration that exhibits a low aerodynamic drag is defined [13]. If one wants toimprove the aerodynamic performances in cycling and not rely only on trial and error balance measurements,it is necessary to analyze in a topological way the flow field in order to have a better feedback on the efficiencyof garments. Investigating the wake structures along the body of the cyclist can lead to a better understanding

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of how local changes in garments can affect the pressure distribution over the body and isolate specific areas onthe body where the greatest drag savings can be achieved.

In the last years great steps forward have been made in flow visualization techniques but a topologicalanalysis of the flow field to varying of the Reynolds number around such a complex shape is not present yet inliterature.

Thanks to the introduction of Helium Filled Soap Bubbles (HFSB) [14] that has permitted to increase themeasurable volume, Terra et al. [15] used the tomo-PIV technique for large-scale measurements analyzing aa cross-plane behind the stretched leg of a 1:1, 3D printed, static mannequin of the professional cyclist TomDumoulin. The measurements were performed at a range of speeds up to 23.3m/s by means of Lagrangian Par-ticle Tracking. A general wake narrowing has been noticed and a decrease of area of reverse flow at increasingspeed going from the sub- to the super-critical regime.

Jux et al. [16] proposed a novel approach for measuring large-scale complex aerodynamic flows: the use ofCoaxial Volumetric Velocimetry attached to a robotic arm, the so-called Robotic Volumetric PIV. This techniqueallowed to measure the entire 3D flow field at a free-stream velocity of 14m/s on the same mannequin usedby Terra et al., recording 450 time-resolved acquisitions combining a spacial resolution of 5 mm and a greatoptical accessibility that leads to investigate even the most complicated shapes, Fig. 2.

Fig. 2 Aquisition sample using Coaxial Volumetrical Velocimetry, reproduced from [16]

The objective of this thesis is then to perform measurements with Robotic Volumetric PIV on the samemannequin used by Jux et al. and Terra et al. for five different velocities (from 5m/s to 25m/s) focusing onthe left stretched leg. Then, after the measurements, the aim is therefore to investigate in a quantitative way theflow field in the wake of the cyclist model at the aforementioned different velocities, to determine whether thedrag crisis can be identified.

2 Measurement technique and experimental apparatus

The experimental campaign has been performed in the Open Jet Facilities (OJF) of High Speed Laboratories atTU Delft, which is an atmospheric closed-loop open jet wind tunnel with an octagonal exit of 2.85×2.85 m2.The contraction ratio is 3:1 (horizontal contraction of 1.88 and vertical one of 1.62). An electrical motor of500kW drives a fan that permits to accelerate the flow up to 35m/s. The test section is placed in a 13×8 m2

room equipped at the end with a cooling mesh, not used in this experiment.For this experiment a 3D-printed model made from a thermoplastic polyester has been used. The model

was obtained after a 3D-scan of Olympic silver medalist Tom Dumoulin, it is the same mannequin used in [15],[16]. The mannequin is equipped with a Giant time trial helmet and a Giant time trial bike has been chosen.

The measurement technique used during the experimental campaign is the Coaxial Volumetrical Velocime-try (CVV). The idea of this system, that can allow a handy measurement of a large-scale industrial flow field,was proposed by Schneider [17] and then realized by the company LaVision. The system consists of four cam-eras with a fixed position one to each other and mounted together in a small and extremely compact frame. Thecameras are arranged in a tomo-PIV configuration and have an angle between lines of sight or tomographicaperture small compared to a typical tomo configuration. An optical fiber is placed through the frame and endsin the middle of the four cameras providing a conical laser beam that covers almost the entire field of viewallowing coaxial illumination and imaging.

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The use of Helium Filled Soap Bubbles (HFSB) as tracers [18] overcomes the difficulties in doing large-scale measurements with PIV linked to the limits of the light scattered by standard tracer particles [19].

One of the main advantages of the CVV is that it is an extremely compact system in which the camerasare in a fixed position, it is indeed possible to move it like a probe without requiring a new calibration. Forthis reason the CVV has been mounted as a tool of a 6 DoF a Universal Robots-UR5 robotic arm: we willrefer to the Coaxial Volumetrical Velocimetry attached to a 6 DoF robotic arm as Robotic Volumetric PIV. Anacquisition computer is used to control the CVV (cameras and the laser trigger) and acquire the images forthe PIV using the software Davis 10.05 from LaVision while the robotic arm is controlled by the commercialsoftware RoboDK.

This setup, Fig. 3, guarantees a great optical access as it is underlined in the work of Jux [16] where thesuitability of this system for measuring the full velocity vector around large-scale complex shape is assessedeven in the presence of reverse flow and in proximity of solid surfaces, concave or enclosed regions.

Fig. 3 Sketch and photo of the experimental setup, in blue is represented the Global reference frame

After the acquisition process a 5×5 Gaussian Smoothing filter and a Butterworth filter, proposed by Sciac-chitano and Scarano [20], are applied on the raw images. Then the Shake The Box with Double Pulse-DoubleFrame algorithm (STB DP-DF) [21], implemented in Davis 10.05, is used to process the images, this leads toobtain the particle tracks for each acquisition in a Lagrangian reference frame. Then a transformation to anEulerian velocity field is necessary, obtaining in the Global reference frame a grid of 15 mm spacial resolution.

3 Methodology

Evaluating the drag crisis can be a complicated procedure, especially if the test object has a particular shape andan intrinsic three-dimensionality as the human body. In fact, for this kind of object, obtaining a local estimationof the drag coefficient is extremely difficult.

A good indication of the presence of drag crisis may be provided by the behavior of the wake downstreamof the test object. As well discussed by Rodriguez et al. [8] for a cylinder, the wake tends to narrow to thebody when the flow passes from the sub-critical to super-critical regime: a decrease in the extension of therecirculation region and of the wake width can be noticed.

According to the data of Rodriguez it is indeed possible to notice a crisis in both wake width and dragcoefficient. This result can be extended finding a correlation between CD data for cylinders related to drag crisispresented in the literature and non-dimensional wake width. In other terms it is possible to assess that in therange of Reynolds number related to the drag crisis CD = f (Re) and dw

d = g(Re) with g and f generic functionsthat are linearly dependent. For this reason, in this investigation, assuming that the aerodynamic behavior ofthe leg is similar to that of a cylinder, the wake width will be used as an indicator of the drag crisis.

Considering the stream-wise velocity component u profile at a certain downstream location, it is possible to

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evaluate the wake width computing the distance between the points of the maximum gradient of u, Eq.1, Fig. 4.

dw =∣∣∣y|min( du

dy )− y|max( du

dy )

∣∣∣ (1)

Fig. 4 Estimate of the wake width, sample of 5 m/s acquisition

This criterion will be chosen considering a downstream location of xd = 0.50. This choice seems to be a

good compromise given that it is desirable to stay quite close to the object but the quality of the flow fieldnear the leg can be lower: this depends on the noise due to the reflection of the light on the model during theacquisition process.

4 Results

Firstly it is possible to compare a cross-plane YZ (with respect to the Global reference frame) of the flow fieldat 5 m/s and 25 m/s, Fig. 5, computed just behind the bottom of the model.

Fig. 5 Non-dimensional streamwise velocity contour uu∞

, comparison between 5 m/s (left) and 25 m/s (right)

It is possible to notice an overall narrowing of the wake when passing from 5 to 25 m/s. Going more intodetails, the hip and the upper part of the leg do not seem to be affected by drag crisis or one should considerthat the crisis happens at a very low velocity and then the wake returns larger at 25 m/s. The lower part of theleg, instead, presents a different behavior: a truly narrowing of the wake is assessable starting from the middleof the thigh.

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The topological analysis on the wake behind the mannequin is done on discrete sections (plane XY withrespect to the Global reference frame chosen). The region of our analysis will be the part of the leg thatshould provide an improvement in the performances if dressed with texture fabrics. In the lower part of the leg,below the calf, rapid changes from vertical to near horizontal orientation during a pedal stroke combined withthe initial turbulence created by the spinning front wheel reduce the effectiveness of surface roughness. Ouranalysis covers a region of 500 mm of extension between the upper part of the leg (before the connection withthe hip) and the lower part of the calf.

As example, the behavior of a knee section is reported. In the Fig. 6 the non-dimensional wake contour uu∞

is showed for 5, 15 and 25 m/s. It is possible to notice how the free-stream condition of 15 m/s is the one atwhich the wake is narrower.

Fig. 6 Comparison of the contour of uu∞

on the wake behind a knee section for 5 m/s (left) 15 m/s (middle) and 25 m/s(right)

For the same section it is possible to obtain the velocity profiles as illustrated in the Methodology. In Fig. 7it is possible to see the velocity profiles for each of the five free-stream velocity. Starting from the velocityprofiles it is finally possible to compute the wake width.

Fig. 7 Non-dimensional velocity profile of u component at different free-stream velocities, section on the knee

Assumed the analogy between CD value and wake width, it is possible to assess a series of consideration onthe drag crisis along the leg based on the calculations of the wake width. We will not refer to critical values ofthe Reynolds number but directly to critical velocities uc that correspond to u∞.

The analysis assesses that it is possible to divide the leg in three different regions that exhibit differentbehaviors. The first part that we can call thigh region exhibits a critical velocity of uc =10 m/s, the second thatis related to the zone around the knee, called knee region, where uc =15 m/s, and finally the third one to whichwe can refer as calf region where the critical velocity is uc =20 m/s.

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Considering then a typical time-trial velocity of 14 m/s, it is clear how at this velocity on the upper part ofthe leg, the thigh region, the drag crisis has already occurred. At the same time the other two parts of the legare still in a sub-critical regime.

Fig. 8 Different wake width behaviors for thigh, knee and calf regions

As assessed by Brownlie [22] the skin suits are used to force the transition to turbulent regime and gain alower level of pressure drag; it is therefore fundamental the use of segmented suits where each part of the bodyof an athlete is covered with a different kind of fabrics.

Applying a suit with surface roughness at the thigh region, according to this research, should cause anincreased value of drag due to the friction but no advantage in terms of decreasing of pressure drag. In the caseof the knee region it is possible to anticipate the drag crisis at the time-trial velocity if this part of the leg isdressed with a suit made of a texture with a certain surface roughness while for the calf region a larger value ofsurface roughness is needed. With this kind of approach it would be possible to have the entire leg working ina close range of the critical regime.

Finally, according to the different kinds of races, and by consequence of the different values of typicalvelocities, a different kind of suit will be then necessary.

5 Conclusions

In world-class athletic competitions, extremely small performance differences between competitors can pro-foundly affect race outcomes, it is often a matter of a few seconds that can lead to victory or a defeat. For thisreason even a small improvement of the performances can be fundamental. To this purpose the drag crisis hasbeen identified as a crucial phenomenon for improving the performances. In fact, triggering the drag crisis withgarments and skin suits can improve dramatically the performances, reducing the drag even up to 10%. Usually,the investigation and test methods used for the design of skin suits are based on trial and error approach and areperformed through simple balance measurements.

This work presents a topological analysis of the flow field around a cyclist mannequin focusing on thestretched leg in order to find on which parts of the leg the drag crisis occurs and at which velocity. RoboticVolumetric PIV has been used as measurement technique. A correlation between drag coefficient and wakewidth has been proven and this topological parameter has been chosen as an index of drag crisis.

Based on this work it is possible to assess that on the upper part of the leg, the thigh, the crisis occursearlier than in the other regions, the critical velocity is 10 m/s. For this reason, contrarily to what is the currentdesign of skin suits, in time-trial conditions the upper part of the leg would need to be covered with a fabrichaving a smooth texture. On the other hand, using two different kinds of rough textured fabric would prove

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valuable in the knee and calf regions, where it could force the drag crisis to time-trial velocity from the valuesof respectively 15 and 20 m/s.

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investigation of the drag crisis on the leg of a cycling ...mannequin used by jux et al. and terra...

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