Aerodynamic drag determination of a full-scale cyclist mannequin from largescale PTV measurements

Delft University of Technology

Aerodynamic drag determination of a full-scale cyclist mannequin from largescale PTV measurements

Sciacchitano, Andrea; Terra, Wouter; Shah, Yash

Publication date 2018

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Proceedings of the 19th international symposium on application of laser and imaging techniques to fluid mechanics

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Sciacchitano, A., Terra, W., & Shah, Y. (2018). Aerodynamic drag determination of a full-scale cyclist mannequin from largescale PTV measurements. In Proceedings of the 19th international symposium on application of laser and imaging techniques to fluid mechanics

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Aerodynamic drag determination of a full-scale cyclist mannequin from

large-scale PTV measurements

A. Sciacchitano1,*_{, W. Terra}1_{, Y. H. Shah}2

1: Dept. of Aerospace Engineering, Delft University of Technology, The Netherlands 2: Dept. of Mechanical and Mechatronics Engineering, University of Waterloo, Ontario Canada

* Correspondent author: a.sciacchitano@tudelft.nl

Keywords: Aerodynamic drag, PIV wake rake, human-scale PTV, helium-filled soap bubbles, cycling aerodynamics

ABSTRACT

Large-scale Particle Tracking Velocim etry (PTV) m easu rem ents are cond u cted in the w ake of a fu ll-scale cyclist m od el in tim e-trial p osition at freestream velocities betw een 12.5 and 15 m / s, corresp ond ing to Reynold s nu m bers of the ord er of 5×105

. Lagrangian p article tracking is em p loyed to d eterm ine the velocity and static p ressu re statistics in the w ake p lane, show ing good agreem ent w ith p reviou s resu lts rep orted in literatu re. The aerod ynam ic d rag is estim ated from the large-scale PTV m easu rem ents invoking the conservation of m om entu m in a control volu m e enclosing the m od el (PIV w ake rake ap p roach). The estim ated d rag follow s the exp ected qu ad ratic increase w ith increasing freestream velocity. The accu racy of the d rag estim ate is evalu ated by com p arison to state-of-the-art force balance m easu rem ents, resu lting in a resolu tion of the PIV w ake rake ap p roach of 30 d rag cou nts. The three term s com p osing the overall d rag force, associated w ith the tim e-average stream w ise velocity, its flu ctu ations and the tim e-averaged p ressu re, resp ectively, are evalu ated sep arately, d em onstrating that the contribu tion of the p ressu re term is negligible and the resistive force is d om inated by the tim e-average stream w ise m om entu m d eficit.

1. Introduction

Determ ination of the aerod ynam ic load s is relevant in m any flu id d ynam ic ap p lications, e.g. for the fu el-efficient d esign of air and grou nd transp ortation system s, the safe stru ctu ral d esign of w ind tu rbines, and the m axim ization of p erform ances in elite sp eed sp orts su ch as cycling and skating. To qu antify the aerod ynam ic load s, w ind tu nnel m easu rem ents are typ ically cond u cted on m od els im m ersed in a hom ogeneou s stream of air, m easu ring the aerod ynam ic forces and m om ents acting on the m od el u sing a six com p onent force balance (e.g. Zd ravkovich 1998, Trop ea et al. 2007). Du e to their high resolu tion (u p to 0.0003% of the fu ll scale load , Trop ea et al. 2007), these balance system s are now ad ays consid ered as stand ard tool esp ecially for m easu rem ents in ind u strial w ind tu nnels. N evertheless, balance m easu rem ents are regard ed as “blind ”, in the sense that they d o not p rovid e any insight in the flow field and flow stru ctu res generating the aerod ynam ic load s. Alternatively, the aerod ynam ic load s can be evalu ated u sing w ake rakes, invoking the conservation of m om entu m across a control volu m e containing the m od el and m easu ring the total and static p ressu re in the w ake of the m od el (Betz 1925; Jones 1936; Goett 1938; Som ers 1997, am ong others). In contrast to balance m easu rem ents, the w ake

rake ap p roach p rovid es not only the aerod ynam ic d rag, bu t also inform ation on the p ressu re and velocity field and m om entu m d eficit in the w ake of the m od el, yield ing a d eep er insight into the generation of the total resistive force (e.g. Maskell 1973, H u cho and Sovran 1993).

Thanks to its non-intru sive natu re and w hole-field m easu rem ent cap ability, in the last tw o d ecad es Particle Im age Velocim etry (PIV) has been u sed extensively as a viable alternative to the p ressu re p robe w ake rakes, for load s d eterm ination from w ake velocity d ata. Lin and Rockw ell (1996) and su ccessively Unal et al. (1997) cond u cted PIV m easu rem ents in the w ake of a tw o-d im ensional cylino-d er to characterize its u nsteao-d y lift coefficient at Re = 3,780. Sim ilarly, Ku rtu lu s et al. (2007) m ad e u se of tim e-resolved PIV to qu antify the u nstead y aerod ynam ic forces of a squ are-section cylind er at Re = 4,890. Using PIV velocity d ata and the control volu m e app roach, van Ou d heu sd en et al. (2006) characterized the tim e-average aerod ynam ic forces (lift, d rag and p itching m om ent) of an airfoil; the au thors rep orted d iscrep ancies betw een the d rag coefficient m easu red from PIV and the conventional w ake-rake ap p roach of 1 d rag cou nt (or 'C_D=10-3

). Ragni et al. (2009) p roved the feasibility of the PIV w ake rake for d rag d eterm ination of a transonic airfoil at Mach = 0.6. In a su ccessive w ork, the au thors extend ed the u se of the PIV w ake rake to m oving objects for the d eterm ination of the aerod ynam ic load s on an aircraft p rop eller blad e (Ragni et al. 2011). A d etailed review of load s estim ation ap p roaches from PIV m easu rem ents has been recently carried ou t by Rival and van Ou d heu sd en (2017).

Desp ite the p op u larity of the PIV w ake rake for m easu ring the tim e-average and instantaneou s load s and investigation of the governing flow field s, its ap p lication has been lim ited to relatively sm all-sized w ind tu nnel m od els (typ ical characteristic length of the ord er of 10 cm ) d u e to the lim ited d om ain of conventional PIV m easu rem ents (Raffel et al. 2018). This is largely ascribed to the low scattering efficiency of conventional m icrom etric flow tracers. The introd u ction of su b-m illib-m eter H eliu b-m -filled soap bu bbles (H FSB) as flow tracers for PIV b-m easu reb-m ents (Bosbach et al. 2009; Scarano et al. 2015) allow ed an increase in m easu rem ent volu m e, w hich has m ainly been exp loited for volu m etric PIV m easu rem ents. Carid i et al. (2016) m ad e u se of large-scale tom ograp hic PIV over a volu m e of 12 liters to investigate the flow field at the tip of a vertical axis w ind tu rbine blad e. By cond u cting large-scale PTV m easu rem ents and solving the Poisson equ ation for p ressu re, Schneid ers et al. (2016) m easu red the instantaneou s volu m etric p ressu re in the w ake of a tru ncated cylind er over a volu m e of abou t 6 liters. Load s d eterm ination from large-scale PIV has been attem p ted for the first tim e by Terra et al. (2017), estim ating the d rag coefficient of a transiting sp here at Re = 10,000. H ow ever, load d eterm ination from large-scale PIV in w ind tu nnels has been ham p ered , firstly, by the lim ited H FSB tracers concentration achieved so far, w hich has been below 1 bu bble/ cm3 (Carid i et al. 2016) and , second ly, by the lim ited size of the seed ed stream tu be cross-section (~0.1 m2, Carid i et al. 2016; Ju x et al. 2018).

The p resent w ork aim s at assessing the feasibility of u sing a large-scale PIV w ake rake for the d eterm ination of the aerod ynam ic d rag on a three-d im ensional hu m an-scale w ind tu nnel m od el. For this p u rp ose, Lagrangian p article tracking is em p loyed to obtain the velocity field in a p lane of ap p roxim ately 1.6 m2 in the w ake of a fu ll-scale cyclist m annequ in, d em onstrating the PIV w ake rake ap p roach over a hu m an-scale m od el on a fu lly three-d im ensional, u nstead y and highly com p lex flow. The obtained tim e-average flow top ology is p resented and valid ated against literatu re. Furtherm ore, for the first tim e the d istribu tion of stream w ise velocity flu ctu ations and p ressu re coefficient in the w ake of a cyclist m od el are p resented and d iscu ssed . Finally, the accu racy of the PIV w ake rake ap p roach for d rag estim ation is evalu ated by varying freestream velocity and by com p arison w ith state-of-the-art balance m easu rem ents.

2. Theoretical background

Consid er a bod y in relative m otion w ith resp ect to a flu id . In the incom p ressible flow regim e, the instantaneou s d rag of the object can be d eterm ined invoking the conservation of m om entu m in a control volu m e enclosing the bod y (Rival and van Ou d heu sd en 2017):

U

³³³

³³

³³

w here V is the control volu m e, S_wake is the d ow nstream bou nd ary of the control volu m e, U, p’ and

U_’ are the air d ensity, freestream velocity and freestream static p ressu re, resp ectively; p and u are the static p ressu re and stream w ise velocity at the location S_wake, as illu strated in Fig. 1.



Fig. 1 Schem atic of the control volu m e ap p roach to d eterm ine the aerod ynam ic d rag of an object.

Ap p lying Reynold s d ecom p osition to velocity and p ressu re and averaging both sid es of equ ation (1), the tim e-averaged d rag is obtained (Terra et al. 2017):

'

wake wake wake

S S S

w here u is the tim e-average stream w ise velocity com p onent, X¶ the fluctuating streamwise velocity com p onent and p the tim e-average static p ressu re. In the rem ind er of this w ork, the first, second and third term at the right hand sid e of equ ation (2) are referred to as the m om entu m term , the Reynold s stress term and the p ressu re term , resp ectively. Equ ation (2) allow s evalu ating the tim e-average aerod ynam ic d rag from velocity and p ressu re statistics in the w ake of the w ind tu nnel m od el. The tim e-averaged static p ressu re is com p u ted from the PIV d ata by solving the Poisson equ ation w ith ap p rop riate bou nd ary cond itions (van Ou d heu sd en 2013).

The accu racy of the d rag estim ation via the PIV w ake rake ap p roach is assessed via d irect com p arison w ith state-of-the-art balance m easu rem ents. The m easu rem ents are rep eated in a narrow range of Reynold s nu m bers, w here the d rag coefficient is assu m ed to be constant. The d rag resolu tion of the PIV w ake rake is evalu ated as:

, , 2 1 1 ( ) i PIV i bal N D D D i C C C N '

¦

C are the tim e-average d rag coefficients from PIV w ake rake and balance system , resp ectively, and N is the nu m ber of rep eated m easu rem ents at d ifferent freestream velocities.

3. Experimental apparatus and procedure 3.1 Wind tunnel model

The exp erim ents are cond u cted in the Op en Jet Facility (OJF) of the Aerod ynam ics Laboratories at the Delft University of Technology. This atm osp heric closed -loop , op en-jet w ind tu nnel has an octagonal cross-section of 2.85×2.85 m2 w ith a contraction ratio of 3:1, that allow s the generation of a hom ogeneou s jet at sp eed s betw een 4 to 35 m / s w ith 0.5% tu rbu lence intensity (Lignarolo et al. 2014). The w ind tu nnel m od el consists of a rigid -bod y fu ll-scale cyclist m annequ in seated on a tim e-trial bike. The latter is su p p orted at the front and rear axis, as illu strated in Fig. 2, w ith the front w heel centerline located 1 m d ow nstream of the OJF contraction exit. The m annequ in, w earing a long-sleeve Etxeond o tim e-trial su it along w ith a Giant tim e trial helm et (season 2016), is m anu factu red from therm op lastic p olyester by ad d itive m anu factu ring after three-d im ensional scanning of an elite cyclist in tim e-trial p osition (Van Tu bergen et al. 2017). The legs of the m annequ in are in asym m etric p osition (left leg stretched and right leg bend ed ) relating to a 75o crank angle (Fig. 2). The hip w id th W, torso length T and frontal area A of the m od el are 0.365 m , 0.600 m and 0.32 m2, resp ectively. More d etails of the m annequ in d im ensions are

p rovid ed in the w ork of Ju x et al. (2018). A 4.9 m long and 3.0 m w id e w ood en table, elevated 20cm above the wind tunnel contraction exit, reduces the boundary layer thickness interacting w ith the m od el.



Fig. 2 Wind tu nnel m od el and PIV seed ing system . 3.2 PTV system

The flow field in the w ake of the cyclist m od el is m easu red by Lagrangian p article tracking w ith neu trally bu oyant heliu m -filled soap bu bbles (H FSB) as flow tracers. The latter have a d iam eter of ap p roxim ately 300 Pm (Scarano et al. 2015) and are introduced into the flow by an in-house d evelop ed seed ing rake installed on a tw o-axis traversing system at the w ind tu nnel contraction’s exit (Fig. 2). 80 H FSB generators are integrated into the fou r-w ing seed ing rake w ith a vertical and horizontal p itch of 25 m m and 50 m m , resp ectively. The rake is installed 85 cm u p stream of the front w heel’s axis and releases ap p roxim ately 2×106 bu bbles p er second seed ing a stream tu be of 20×50 cm2 cross-section in the freestream . The resu lting seed ing concentration at a freestream velocity of 14 m / s is estim ated at 1.4 tracer/ cm3

(Carid i et al. 2016). The flow rates of heliu m , air and bu bble flu id solu tion are regu lated via a Flu id Su p p ly Unit from LaVision Gm bH . In ord er to seed the entire w ake of the m od el, m easu rem ents are rep eated at 15 d ifferent p ositions of the seed ing rake, 5 along the horizontal d irection and 3 along the vertical d irection. Tw o m eters d ow nstream of the fou r-w ing seed ing rake, the tu rbu lence intensity of the OJF freestream jet is increased from 0.5% to 1.9%, w hile the m ean flow rem ains u naltered (Ju x et al. 2018).



Fig. 3 Schem atic rep resentation of the exp erim ental setu p .

Collim ated light is p rovid ed by a Continu u m Mesa PIV 532-120-M laser (N d :YAG d iod e p u m p ed laser, p u lse energy of 18 m J at 1 kH z) illu m inating a 5 cm thick p lane, 80 cm d ow nstream of the trailing ed ge of the sad d le of the bike (see Fig. 3). Tim e-resolved im ages are acqu ired by three Photron FastCAM SA1 cam eras (CMOS sensor, 12 bit, 20 Pm pixel pitch, 1,024×1,024 p ixels at fu ll resolu tion) over a region of ap p roxim ately 1.0×1.6 m2. The cam eras are located abou t fou r m eter d ow nstream of the m od el, tw o m eters from the op en jet’s central axis (Fig. 3). The cam eras are equ ip p ed w ith 50 m m N ikkor objectives w ith an ap ertu re set to f/ 4 and tilt ad ap ters to satisfy the Scheim p flu g cond ition. The op tical m agnification is equ al to 0.0125, resu lting in a d igital im age resolu tion of 1.6 m m / p x. For the geom etrical cam era calibration, an in-hou se d evelop ed d ou ble-p lane calibration target of 1.2 m × 1.2 m is p laced vertically at tw o locations, 5 cm u p stream and 5 cm d ow nstream of the m easu rem ent p lane. The target contains a total of 156 circu lar d ots of 8 m m d iam eter p er p lane, d istribu ted over 12 row s and 13 colu m ns w ith a p itch of 9 cm in both vertical and horizontal d irection. The offset betw een the tw o p lanes is 2 cm ; the d ots of the tw o p lanes are staggered by 4.5 cm in both the vertical and horizontal d irections.

3.3 PTV measurement procedure

The im ages are record ed in short bu rsts of 11 im ages at 4 kH z acqu isition frequ ency resu lting in a m ean track length of five sam p les w hich is ap p roxim ately ind ep end ent of the transverse location on the w ake p lane. Particle streaks, obtained as the m axim u m im age intensity over the 11 su bsequ ent im ages of a bu rst, in the center of the m od el’s w ake and the freestream are d ep icted in Fig. 4-left and right, resp ectively. The nu m ber of p articles p er p ixel (p p p ) varies

betw een 0.04 and 0.1 d ep end ing on the seed er p osition, being the highest in the freestream (w here the seed ed stream tu be is m ainly u naffected by the w ake of the m od el) and the low est in the cyclist’s w ake d u e to the m ixing of the seed ed flow w ith u n-seed ed air. The average particle intensity is rather ind ep end ent of the seed er p osition and is equ al to 200 cou nts over a backgrou nd intensity of abou t 20 cou nts, resu lting in an im age signal-to-noise ratio of 10. For each p osition of the seed ing generator, 480 bu rsts are acqu ired w ith 0.1 s sep aration betw een tw o su ccessive bu rsts to obtain a statistical ensem ble of u ncorrelated p article tracks. Im age acqu isition and p rocessing is cond u cted w ith DaVis 8.4 from LaVision Gm bH .



Fig. 4 H FSB seed ing in the w ake of the m od el. Particle streaks in the central w ake w ithou t im age p re-p rocessing (left) and in the freestream area after im age p re-p rocessing by tim e-average intensity su btraction (right).

3.4 Force balance measurements

Force m easu rem ents are carried ou t w ith a six-com p onent balance d esigned , m anu factu red and calibrated by the Du tch Aerosp ace Laboratory (N LR). Und er sim u ltaneou s load ing of all six com p onents (three forces and three m om ents), the balance is cap able of m easu ring load s u p to 250 N in the stream w ise d irection w ith a m axim u m u ncertainty of 0.06% (Alons 2008). The balance is m ou nted d irectly u nd er the grou nd p late, shield ed from the air below the p late, and connected to the bike su p p orts. The balance m easu rem ents are cond u cted at each p osition of the seed ing rake; the acqu isition frequ ency is set to 2 kH z and the observation tim e is 30 second s. Finally, the PIV and force balance m easu rem ents are rep eated at five d ifferent freestream velocities betw een 12.5 m / s and 15 m / s, corresp ond ing to Re = 5×105 to 6×105 based on the torso length.

3.5 PTV data reduction

The acqu ired im ages are p re-p rocessed by su btraction of the tim e-averaged intensity of each bu rst to rem ove backgrou nd noise (see Fig. 4-right) and are then p rocessed w ith the

Shake-The-Box algorithm (STB; Schanz et al. 2016) yield ing Lagrangian p article tracks. Particle tracks of single im age bu rsts obtained at the 15 d ifferent locations of the seed ing rake are d ep icted in Fig. 5 by sep arate color illustrating the extent of overlap of tracks from d ifferent seed er p ositions.



Fig. 5 Lagrangian p article tracks in the w ake of the m od el from a single im age bu rst (d ifferent colors rep resent the d ifferent seed er locations).

Velocity statistics (tim e-average and flu ctu ations root-m ean-squ are) is com p u ted from the Lagrangian velocity ensem ble w ithin bins of size 5×4×4 cm3 w ith 75% overlap in all d irections (Agü era et al. 2016). The resu lting velocity field is d efined on a Cartesian grid w ith a vector p itch of 1 cm along y and z d irections. The bin size w as d eterm ined requ iring a m inim u m nu m ber of 25 tracks p er bin. A u niversal ou tlier d etection filter (Westerw eel and Scarano, 2005) w as ap p lied to the p article velocity d ata in each bin, to red u ce sp u riou s tracks, resu lting in an average nu m ber of u sed tracks p er bin of ap p roxim ately 2000. The u ncertainty of the obtained velocity d ata is estim ated from the tim e-average stream w ise velocity in the overlap p ing regions betw een seed er p osition. Discrep ancies in the ord er of 5% are 2% are obtained in the w ake and the freestream , resp ectively.

For the com p u tation of the aerod ynam ic d rag accord ing to Eq. (2), ap art from the velocity statistics in the w ake p lane, the freestream velocity U_’ and static p ressu re p_’ are requ ired . The m easu red freestream velocity U’,m eas is obtained as the m ean stream w ise velocity over the three free bou nd aries of the w ake p lane, exclu d ing a region in relative p roxim ity to the floor (y > 50 cm ). A correction for the jet exp ansion, İ_S, and the nozzle blockage, İ_N, is ap p lied accord ing to Mercker and Wied em ann (1996):

, 1 S N meas U U H H f f         (4)

w ith İ_S = 0.0018 and İ_N = 0.0132. The static p ressu re is obtained solving the Poisson equ ation for p ressu re p rescribing N eu m ann cond itions on the bottom bou nd ary and Dirichlet cond itions w ith freestream p ressu re on the three free bou nd aries. The stream w ise grad ients of the tim e-average velocity and its flu ctu ations are neglected in the p ressu re reconstru ction after estim ating that these are tw o ord ers of m agnitu d e sm aller than the corresp ond ing in-p lane grad ients.

4. Results

4.1 Wake flow topology

The tim e-average w ake flow top ology of the cyclist m annequ in is d iscu ssed consid ering the sp atial d istribu tion of the stream w ise velocity (Fig. 6-left) and vorticity w ith in-p lane vectors (Fig. 6-right). The stream w ise velocity contou r exhibits tw o m ain regions of significant velocity d eficit. The first one is located behind the low er back of the m annequ in (y ~ 100 cm ) slightly tow ard s the left, and featu res a m inim u m velocity of u/U_’~0.6. The lateral asym m etry of this velocity d eficit originates from the asym m etric leg p osition (left leg extend ed d ow nw ard s and right leg bent u p w ard s), and is in good agreem ent w ith w hat rep orted in literatu re e.g. by Crou ch et al. (2014) and Ju x et al. (2018). The m inim u m valu e of the stream w ise velocity is com p aratively higher than that m easu red by Crou ch et al. (2014, u/U_’~ .5) and Ju x et al. (2018,

u/U_’~0.35), w hich in the latter case is attribu ted to the fu rther u p stream location of the m easu rem ent p lane (x = 30 cm instead of 80 cm ), w here larger velocity d eficits are exp ected . In the com p arison w ith Crou ch et al. (2014), the sm aller velocity d eficit can be attribu ted to the com bined effect of the sm aller angle of attack of tru nk of the m annequ in (Į~5o

for the present m od el and Į =12.5o for the m od el u sed by Crou ch et al.), the m ore aerod ynam ic p osition of the head (the head and helm et in the p resent case d o not contribu te to the frontal area of the m od el, w hile they d o in the case of the m annequ in u sed by Crou ch et al. 2014), and the higher cu rvatu re of the u p p er back of the p resent m od el. The second region of high velocity d eficit, w ith a m inim u m velocity of abou t u/U’~0.45, is observed d ow nstream of the w heel axis and the d rivetrain configu ration (y~40 cm ), and m atches w ell the w ork of Crou ch et al. (2016) in term s of location and m agnitu d e.



Fig. 6 Tim e-averaged stream w ise velocity com p onent (left) and stream w ise vorticity com p onent w ith in -p lane velocity vectors (right). Free-stream velocity equ al to 14.5 m / s (Re = 5.8×105

).

Fig. 6-right also show s a region of strong d ow nw ash behind the cu rved back of the m annequ in (y~120 cm ), w ith a p eak vertical velocity of v/U_’~-0.17 that agrees w ell w ith literatu re (Crou ch et al. 2016; Griffith et al. 2014, am ong others). Tw o strong cou nter-rotating vortices (m arked T1/ T2) originate from the cyclist’s thighs and are fed by the d ow nw ash behind the m od el’s back, as also d ocu m ented in p reviou s literatu re (Crou ch et al., 2014). Besid es the vortex p air T1/ T2, other cou nter-rotating vortex p airs originate from the left foot (m arked F1/ F2), p rod u cing an u p -w ash in the foot w ake (v/U_’~-0.12), and from the right foot (m arked F3/ F4), w hich agree w ell w ith the robotic-PIV m easu rem ents of Ju x et al. (2018). The regions of stream w ise vorticity em anating from the hip s (H 1/ H 2) are shearing regions rather than vortex regions stem m ing from the interaction betw een the d ow nw ash m otion, d iscu ssed before, and the su rrou nd ing stream w ise m otions.

The stream w ise velocity flu ctu ations are illu strated in Fig. 7. The tw o sep arated u nstead y shear layers behind the left low er leg can be observed (m arked S3/ S4), yield ing a flu ctu ation p eak of abou t ~0.1U_’. These shear layers bend inw ard s ju st below the knee d u e to the strong inw ard velocity com p onent in this region (y~50; z~-20, Fig. 6-right), p ossibly resu lting from a cou nter-clockw ise stream w ise vortex originating from the left knee/ low er leg. Also the ou ter shear layer originating from the up p er p art of the extend ed leg exhibits m axim u m flu ctu ations of sim ilar m agnitu d e (y~90 cm and z~-15 cm ). Conversely, the stream w ise velocity flu ctu ations behind the

bent leg are com p aratively low er, w ith p eaks of abou t ~0.06 U_’. The location of cou nter-rotating stream w ise vortex p airs originating from the thighs (T1/ T2 in Fig. 6-right) and the shearing regions (H 1/ H 2) coincid es w ith tw o regions of high stream w ise velocity flu ctu ations (T1/ T2 and H 1/ H 2 in Fig. 7) ind icating that these flow stru ctu res are u nstead y in natu re. H ence, the p resented tim e-average stream w ise vorticity levels in Fig. 6-right are below the p eak valu es rep resentative for the instantaneou s vortex top ology. Finally, other local m axim a of the stream w ise velocity flu ctu ations ap p ear in the w ake of the d rivetrain and behind the low er p art of the w heel (V-shap e area). To the best know led ge of the au thors, the sp atial d istribu tion of the stream w ise flu ctu ating velocity at the cu rrent freestream velocities has not been rep orted in literatu re. Crou ch et al. (2014) p resent the sp atial d istribu tion of the p rincip le tu rbu lence intensity for the u p p er p art of the w ake (y > 70 cm ) rep orting m axim u m valu es arou nd 0.2, w hich m atch reasonably w ell the p resent find ings.

Ou tsid e of the w ake of the m annequ in, the root-m ean-squ are of the stream w ise velocity flu ctu ations red u ces significantly, reaching a level of abou t 4% of the free-stream velocity. With an estim ated freestream tu rbu lence level in the w ake of the seed ing system of 1.9% (Ju x et al., 2018), it is argu ed that abou t half of the m easu red free-stream flu ctu ations valu e stem s from m easu rem ent errors of the large-scale PTV system . As a consequ ence, the contribu tion of the Reynold s stress term in the exp ression for the d rag (second term in Eq. (2)) is overestim ated , thu s yield ing an u nd erestim ation of the aerod ynam ic d rag by ap p roxim ately 0.15 N .

Fig. 8 d ep icts the sp atial d istribu tion of the p ressu re coefficient show ing the p resence of a large high p ressu re (H P1) region behind the u p p er back of the cyclist. This overpressu re is attribu ted to the exp ansion of the flow after p assing the cu rved back of the cyclist. Below this, at arou nd y = 90 cm , the flow has sep arated over the low er back of the cyclist, resu lting in a sep arated region w here the local static p ressu re is below the free-stream p ressu re (LP1). Fu rtherm ore, a second low p ressu re region takes p lace becau se of the flow sep aration betw een the left foot and the rear w heel (LP2). The overall d istribu tion m atches w ell to that obtained by Blocken et al. (2013) solving the stead y Reynold s-averaged N avier–Stokes equ ations, d esp ite the sm all d ifferences in m od el geom etry and crank angle (sym m etric leg p osition instead of the p resent asym m etric case). Desp ite the d istingu ished contou rs, the sp atial variations of the pressu re coefficient are sm all (u p to 0.03 betw een m inim u m and m axim u m Cp in the w ake p lane) and the p ressu re in m ost of the d om ain equ als the freestream p ressu re, su ggesting that the contribu tion of the p ressu re term to the aerod ynam ic d rag evalu ated by Equ ation (2) is sm all, w hich is d iscu ssed in m ore d etail in the next section.



Fig. 7 Stream w ise velocity flu ctu ations in the w ake p lane at free-stream velocity of 14.5 m / s (Re = 5.8×105

).

Fig. 8 Tim e-averaged p ressu re coefficient in the w ake p lane at free-stream velocity of 14.5 m / s (Re = 5.8×105

).

The flow top ology at d ifferent freestream velocities is ad d ressed in Fig. 9. The present exp erim ent is rep eated w ithin a narrow range of freestream velocities (12.5 m / s < U_’ < 15 m / s) w here the d rag coefficient is constant (Grap p e 2009) and , hence, the flow top ology is exp ected to rem ain u naltered . The contou rs of 90% of u/U_’ at five freestream sp eed s coincid e w ell and d iscrep ancies of abou t 5% in non-d im ensional stream w ise velocity are observed betw een the d ifferent freestream cond itions, ind icating a good level of rep eatability of the exp erim ent.



Fig. 9 Contou rs of 90% u/U_’ at the d ifferent freestream velocities.

4.2 Drag estimation

Consid ering the u naltered flow top ology at the d ifferent freestream velocities, the d rag coefficient of the cyclist can be assu m ed constant and the aerod ynam ic d rag is exp ected to scale qu ad ratically w ith increasing velocity. Therefore, d esp ite the narrow range of freestream velocities, the d rag force is exp ected to increase by alm ost 50%. This exp ected increase is clearly observed in Fig. 10 d ep icting the resistive force at five freestream velocities. A qu ad ratic fit (D = 0.14U_’2) throu gh the five d ata p oints and (0,0) is also inclu d ed . The accu racy of the obtained d rag is estim ated from the root-m ean-squ are of the resid u als betw een the m easu red d ata and the qu ad ratic fit, and is equ al to ¨D = 1.2 N.



Fig. 10 Tim e-averaged aerod ynam ic d rag at five freestream velocities inclu d ing a qu ad ratic fit to the five d ata p oints.

The accu racy of the d rag estim ation, or d rag resolu tion, is evalu ated com p aring the d rag coefficients obtained w ith the PIV w ake rake w ith those obtained w ith the force balance. The

balance m easu rem ents d ep icted in Fig. 11-left (d ashed -red ) show that the d rag coefficient is ap p roxim ately constant in the narrow range of free-stream velocities, w ith variations of abou t 1.5%. The error bars on the tim e-average d rag coefficient ind icate the u ncertainty of the m ean valu e at 95% confid ence level. In contrast to the m easu rem ents by force balance, the variations observed in the d rag coefficient obtained from the PIV w ake rake are significantly larger (Fig. 11-left solid -blu e), illu strating the higher m easu rem ent u ncertainty of this techniqu e. Fig. 11-right (d ashed -red ) show s the error in the d rag coefficient m easu red by PIV w ake-rake app roach relative to that obtained by balance m easu rem ents, w hich varies betw een 0.75 and 6.5%. Using Eq. (3), a d rag resolu tion of the PIV w ake rake of ¨CD = 0.03 or 30 d rag cou nts, is estim ated (Fig. 11-right solid -blu e line).



Fig. 11 Aerod ynam ic d rag coefficient from the PIV w ake rake vs force balance (left) and the relative error of the PIV w ake rake valu e as a p ercentage of the balance d ata (right).

Finally, the sep arate contribu tions of the m om entu m term , Reynold s stress term and p ressu re term (Eq. (2)) to the overall aerod ynam ic d rag are d ep icted in Fig. 12. The contribu tion of the latter is ap p roxim ately zero at all freestream cond itions, w hich w as exp ected from the sm all valu es of the p ressu re coefficient in the w ake p lane (Fig. 8). H ence, the p ressu re reconstru ction can be om itted in fu tu re cyclist d rag estim ations w ith a w ake p lane d ow nstream p osition x/ L•2.2, w here L=W (being W the hip w id th) is the characteristic length scale rep resentative for the w ake top ology, thu s significantly sim p lifying the evalu ation of the aerod ynam ic d rag. The Reynold s stress term consistently contribu tes to ap p roxim ately 5% of the d rag and cannot be neglected . Finally, the m om entu m term d om inates the air resistance accou nting for the rem aining 95%.



Fig. 12 Tim e-average aerod ynam ic d rag from the PIV w ake rake at five freestream velocities inclu d ing the ind ivid u al m om entu m , p ressu re and Reynold s stress term .

5. Conclusions

Large-scale PTV m easu rem ents are achieved at Reynold s nu m bers of ap p roxim ately 5×105 in a thin volu m e of 5×100×160 cm3, sp anning the entire w ake of a cyclist m annequ in, u sing H FSB flow tracers. The obtained tim e-average flow top ology m atches w ell to literatu re, and resu lts obtained at d ifferent freestream sp eed s exhibit the sam e flow top ology, confirm ing the rep eatability of the exp erim ent. Du ring the exp erim ent, the in-hou se bu ilt seed er w as traversed into d ifferent p ositions to obtain flow tracers in the fu ll d om ain. The cam eras and laser, instead , alw ays im aged and illu m inated the entire m easu rem ent region. By invoking the conservation of m om entu m in a control volu m e containing the m od el, the tim e-average aerod ynam ic d rag acting on the w ind tu nnel m od el is exp ressed as the su m m ation of the m om entu m , Reynold s stress and p ressu re term s, resp ectively. It is fou nd that the latter term is negligible; hence, the p ressu re reconstru ction can be om itted for d rag evaluation at a d ow nstream d istance of x/ L•2.2, being L the characteristic length of the m od el, in this case selected as the hip w id th. Conversely, the m om entu m term d om inates the overall d rag force, contribu ting to abou t 95% of the d rag valu e. The d rag accu racy of the techniqu e is valid ated against force balance d ata, from m easu rem ents at five freestream velocities. The resu lting d rag resolu tion of the PIV w ake rake ap p roach is 30 d rag cou nts or ¨CD = 0.03. Althou gh this qu alifies the PIV w ake rake as a rather coarse instru m ent for d rag d eterm ination, increased accu racy can be exp ected u sing a seed ing system p laced insid e the settling cham ber of the w ind tu nnel, w hich w ou ld red u ce the ind u ced velocity flu ctu ations. Ad d itionally, increasing the cross-section of the seed ed stream tu be w ou ld allow a m ore hom ogenou s seed ing concentration and red uce the u ncertainty stem m ing from the d isp lacem ent of the seed ing system .

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