10 Copyright © 2018 N. Rabino

models was f ound to extend roug hly 1.4 meters downst ream, or appro x-

imately 4 tim es the width of the torso, whic h agrees stron gly with Ok a-

moto’ s and Sunabashiri’s findings. T he type of vortex shedding in this

recircula tion region cannot be determined, but it is expected to nonethe-

less be asym metric , with the larg e - scale structures b eing ad vected

downstream ba sed on the findings of Edg e et al. The wake behavior

behind the leg s were also dis covered to obey the findings s ummarized

by Zhou and A lam, with the region fr om the ankles to the knees havi ng

wake structures associated with each leg , and the region from the knees

to the hips behaving as a unifie d bluff - body . The figure als o shows a

distinct vertical “jet sheet” stem ming from the gap between the legs,

with a n average magnitude app roximately 35% greater than t he free

stream velocity . A vortex pair originating from the top of the legs is also

evident . This vortex pair ca n be seen being ca used by the downwash of

the hair ; the momentum of the downw ard flow interacts with t he air

flowing p ast the t op of the thi ghs , whic h results in these promine nt

structures . Additional momentum provide d by the jet of air between the

legs further enhances the s trength of these vortices. Fur thermore , t he

effects of the downwash are evident in the way the vor tex pair assumes

a downward a ngle as the flow advects; this is indicative of the signif i-

cant amount of air being captured by the geo metry of the hair.

From what can be drawn from c omparin g Figu re 10 (a) and 10 (b) ,

the Flat model has a weaker, less organized vor tex stemming from the

legs . This observation may further explain why the Normal model h as

lower lift than the Flat model. Aider et al. [ 71 ] descr ibed the effect of

vortex pairs affecting lift and drag , and show n that inflow caused by

streamwise counter - rotating vortices res ult in a net dow nward force.

Thus, the weaker vortex pair on the Flat model contribu tes less towards

reducing lift t han the Norma l model. Following this, it is r easonable to

suggest that the beha vior of the drag curve in Figure 7 (a) can be a t-

tributed to the f ormation of these vortices; the energy being redirected

into the formation of these structures diverts a portion of the mean flow

away from the PRR, leading to drag redu ction as the velocity increases.

Figure 11 provides a clos e - up look at t he same streamlines in F igure

10 around the torso of bot h models. A s can be seen in 11 (a) and correc t-

ly determined in Section 4.1 , the breasts provide a gradual interfac e for

the air to mov e around the torso compar ed to the relatively abrupt o b-

struction the Flat m odel imposes as reflected in 11 (b). This is further

exemplified in Figure 12 , which s hows a set of horizontal strea mlines

positioned at z =1.18m. In 12 (a), the air flows smoothly atop the breasts

at a velocity approximatel y 40% to 60% of the fr ee stream velocit y ,

whereas the Flat model in 12 (b) simply forc es a r elatively larger portion

of the incoming air to stall at th e torso. It is interesting to note that a

small recirculation region develops directly a top the breasts, which most

likely is dependent on the an gle between them and the chest. From what

can be seen in 12 (a), this small re circulat ion region prevents a s mall

portion of air from surmounting the shoulders and i nstead redirects the

air downwar ds and off to t he sides of the torso. Figure 13 provides an

upwards facing view of the models along with horizontal streamlines

emanating from z=1.14m. In 13 (a), air flowing beneath the bust gains a

velocity that is approximately 20 % hig her than the mean free strea m

velocity before being diverted perpendicula r to the body and interacting

w ith the incoming air stream a nd the rest of the torso . By the action of

the breasts, the air is diverted in s uch a way that it is able to maintain

momentum w hile it moves around the rest of the chest. This is in co n-

trast to 13 (b), wh ere a portion of the air is forced to stall in front of the

chest before being r edirected around the torso, much like as was seen in

other fig ures involving streamlines with the Flat model.

Figure 14 compares the velocit y magni tude of the wake behind the

two models at five differen t z - locations . At these locations, data is sa m-

pled along a line centered at the midline (x=0 ) and span s downstream

from −1    2 meters . The z - locations are taken at heights of z =

0.1m, z = 0.5m , z = 0.9m, z = 1.18m, and z = 1.55m, all of w hich corr e-

spond to the feet, legs, h ips, chest, and head , respectively. From this

comparison, the differences in wake velociti es are sli ght, with the only

significant difference occ urring at the height of the legs. At this height,

it can be seen that the Flat mod el has a wake velocity that is co nsistently

higher than that of the Norm al model. This obs ervation can be attributed

by the lower energy present in the vortices generated by the Flat model;

these weaker formations are affe cted by the mean flow to a great er de-

gree and thus the velocity magnitude in this region is higher t han if the

vortices were to have greater stre ngth, as seen with the Normal model.

4.2.2 Tur bulence Kinetic Energy

Figure 15 shows a slice of the domain through the m edi an plane of

the models, indica ting the TKE present in the flow . At first glance, co n-

tours for bot h models presen t the same general structures as d escribed

earlier, such as the PRR behind the torso an d the smaller structures a s-

sociated with the legs. Due to the autom atic scaling of the colors, the

differences present in the P RR of the Flat model compar ed to the No r-

ma l model are slightly exagger ated. However, the differences are still

distinguishable in that the PRR for th e Flat model has a measu rably

higher level of TKE than that of the Norm al model. Indeed , 15 (b) ind i-

cates that the two appar ent bands of significa nt TKE associa ted with the

PRR are generally more intense, even after factoring the d ifferences

between the color scales . Comm on to both models is a reg ion behind

the hips where the relatively highest TKE was measured. This lower

band within the PRR was found to be more compact for the Normal

model, whereas the Flat model had a marginally less intens e and more

widespread ba nd. This eff ect may be attribut ed to the way the down-

wash from the hair interacts with the P RR.

Directly below the PRR is the TKE present in the vortex pa irs ori g-

inating from the legs. In 15 (a), the Normal model has a notably higher

level of TKE associated with these vortices, coup led with the observa-

tion that this energy is maintained as the f low advects downstream. In

contrast, 15 (b) shows that the TKE in the vort ices is lowe r and that the

energy is di ssipated sooner . This remark further s upports the inte rpret a-

tions hitherto ; that the formation of stronger vortices the Normal model

generates plays a role in reduc ing both drag and lift by diverting energy

away from the PRR.

Smaller reg ions with notable TKE present betw een both models are

those associated dir ectly behind the legs , at the ankles, and directl y

above the brim of the baseball cap . Between the two, the TKE at the

ankles rema ins unperturbed by the diff erences in the wake structures

above it . This region is related to the individual wakes associated with

each foot, beha ving much like the two cylinder a rrangeme nt as de-

scribed earlier. A dow nward “jet” of TKE origina ting from the thighs

and curling pa rallel to the mean flow dir ection at the height of the knees

shows some variability between the two models. This region is link ed to

the “jet” of air that is formed between the legs interacting with the

downwash f rom the hair . With the Norm al model in 15 (a), this “jet” of

turbulence remains both vertical and closer to the legs. In 15 (b), this

region takes on a slightly more horizontal transition and extends farther

into the wake. A small recirculation region , much like that associated

with the breas ts on the Norma l model, is found above the br im of the

baseball cap, w hich is due to the blunt t ransition the shape of th e head

imposes to the i ncoming flow .

Figure 14 . Compari son of wake velocity magnitud es at 5 z- locations centered

along x = 0 and ranging from

−1    2

meters .

Lucoa positioned and to sca le

with x - axis.